Department of Aeronautical engineering

School of Mechanical engineering

Vel Tech Dr RR & SR Technical University

Course Material

U6AEA24 Experimental Stress Analysis

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U6AEA24 EXPERIMENTAL STRESS ANALYSIS L T P C3 0 0 3

OBJECTIVETo bring awareness on experimental method of finding the response of the structure to different types of load.

UNIT I Measurements 9Principles of measurements, Accuracy, Sensitivity and range of measurements.

UNIT II Extensometers 9Mechanical, Optical Acoustical and Electrical extensometers and their uses, Advantages and disadvantages.

UNIT III Electrical Resistance Strain Gauges 9Principle of operation and requirements, Types and their uses, Materials for strain gauge. Calibration and temperature compensation, cross sensitivity, Rosette analysis, Wheastone bridge and potentiometer circuits for static and dynamic strain measurements, strain indicators.

UNIT IV Photoelasticity 9Two dimensional photo elasticity, Concept of light – photoelastic effects, stress optic law, Interpretation of fringe pattern, Compensation and separation techniques, Photo elastic materials. Introduction to three dimensional photo elasticity.

UNIT V Non – Destructive Testing 9Fundamentals of NDT, Radiography, ultrasonic, magnetic particle inspection, Fluorescent penetrant technique, Eddy current testing, Acoustic Emission Technique, Fundamentals of brittle coating methods.

TOTAL: 45 periods

TEXT BOOKS1. Srinath, L.S., Raghava, M.R., Lingaiah, K., Garagesha, G., Pant B., and Ramachan-

dra, K., “Experimental Stress Analysis”, Tata McGraw-Hill, New Delhi, 1984.

REFERENCE BOOKS1. Dally, J.W., and Riley, W.F., “Experimental Stress Analysis”, McGraw-Hill Inc., New York,

1998.

2. Hetyenyi, M., “Hand book of Experimental Stress Analysis”, John Wiley and Sons Inc., New York, 1972.

3. Pollock A.A., “Acoustic Emission in Acoustics and Vibration Progress”, Ed. Stephens R.W.B., Chapman and Hall, 1993.

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UNIT I Measurements

Principles of measurementsAccuracySensitivity Range of measurements.

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UNIT – I

MEASUREMENTSExperiment:

The special observation mode to confirm or disomething doubt 801.

Stress analysis:

It is an Engineering discipline that determines the stress in materials & structures subjected to static or dynamic forces (or) loads.

Aim of the analysis: To determine whether the [element or collection of elements] “STRUCTURE” can safely with stand the specified forces.

Normally the safety load can be measured using F.O.S [factor of safety]

This FO.S. given to design engineering for the purpose of design. From the F.O.S the design Analyst calculate design

“Design factor “

Types of load acting on a structure:

TensionCompression Shear Design factor is got by use of these variablesTorsionBending

Software Used By Design Engg

Pro - Mechanica Analysis Misc software Nastron Rohrz [analysis software] Caesar II

1. What is measurement?

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The process of obtaining the magnitude of a quantity such as length or mass relative to a unit of measurement such as meters or kilogram.

The act of measuring or the process of being measured [used] The system of measuring

System & unit is:

International System of units Imperial system Metric system

TYPES OF MEASUREMENT:

Generally two measurements

1) VECTOR’S : have an magnitude [an amount] & a direction2) SCALAR’S : have an magnitude but have no direction.

On the basis of S.I units the measure divided & classified into following,

Linear [length or distance] Mass [weight] Volume Temperature

All measuring instruments have calibrations. These are markings or division in measuring tool.

Linear:Linear measurements are made using a Metric stick or Metric Ruler.

Measured in meter centimeter millimeter m cm mmMass:

Mass measurements are made using a balance

There are several kinds of balance,o Triple beam balanceo Dial – a gram balanceo Electric / digital balanceo Analytical balance

Measured in gram, kilograms, centigrams, milligrams.

Volume:

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The volume of any solid, liquid, gas, plasma or vacuum is how much 3-D space it occupies Measured in cubic meters, cubic centimeter liters, milliliters.

Temperature:

Temperature measurement using modern scientific thermometers & temperature scales. Measured in Fahrenheit, Kelvin, celcius.

Principles of measurement:

The techniques of measurement are of immense importance in most facets of scientific research & human civilization.

Computation with decimals frequently involves the addition or subtraction of numbers do not have the same number of decimal places.

Estimation:

Estimation is the calculated approximation of a result which is usable even if input data may be incomplete or uncertain. It can be computed precisely.

Precision:

The Measurement of a precision depends upon how precisely the instrument is marked. It is important to realize that precision refers to the size of the smallest division on the scale.

Simply we can say, that one instrument is more precise than another does not imply that the less precise instrument is poorly manufactured.

The precision of measurement system also called reproducibility or repeatability

It is degree to which repeated measurement under unchanged conditions show the

same result’s.

Reproducibility:

It is one of the main principles of the scientific method & refers to the ability of a test or experiment to be accurately reproduced.Repeatability:

It is the variation in measurement taken by a single, person or instrument on the same item & under the same conditions.

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Accuracy:

The accuracy of measurement depends upon the relative size of the probable error.

The Accuracy of a measurement system is the degree of closeness of measurements of a quantity to its actual [true] value.

The measurement system is valid if it is both accurate & precise.

Accuracy = (Sensitivity ) (prevalence) + specificity [1-prevalency]

Accuracy may be determined from sensitivity & specificity provided prevalence.

Sensitivity:

Specificity:

specificity= Example:

True positives (TP) – sick people correctly diagno as sickFalse positives (FP) _ Healthy as sickTrue Negatives (TN) _ Healthy correctly indentified as healthyFalse negatives (FN)_ Sick people incorrectly identified as healthyFalse positives & False negatives also called as Type –I & Type II errorTP condition present + positive resultFP condition absent + positive resultFN condition present + Negative resultTN condition absent + Negative result

Example:

1) 3.72 inches or 2417 feet

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o We can say 3.72 inches is more preciseo 2417 feet is more accurate

2) 30 seconds or 28 second’s 30 second is more accurate & Precise.

Error:It is classified into two types

Systematic error impacts the accuracy of measurement results

1) Factory instrument2) Faculty measuring3) Personal bias

Errors to avoided systematic error:

1) Instrument error2) Procedural error3) Personal bias

Random error’s:

1) Least count error2) Mean value of measurement

Percent of Error =

UNIT II Extensometers

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Mechanical Extensometers.Optical Acoustical Extensometers.Electrical Extensometers. Extensometers uses.Advantages and disadvantages.

UNIT – II

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EXTENSOMETERS

Strain Measurement

Introduction

Strain gauges are mostly used to measure strains on the free surface of a body. The state of strain at any point on the free surface of a body can be characterized in terms of three Cartesian strain components xx, y y and x y as

x x =

XY =

Where u and v are the displacement components in x and y directions respectively. These equations suggest that if the two displacements u and v can be measured at all points on the surface of a body, strains at any point on the surface can be determined.

It is seen from Eq. (16.1) that the Cartesian strains are actually the slopes of the displacement surfaces u and v. For precision in the estimation of the slopes of the displacement surfaces, the in-plane displacements u and v should be determined quite accurately. However, particularly for small elastic strains, the in-plane displacements are exceedingly small. No versatile and easy method is yet available for the direct measurement of these displacements over the entire surface of a body. This difficulty is overcome partially by using a strain gauge to measure the change in the distance between two points on the surface of the body due to straining. This change in length is converted to axial strain by the following relationship:

xx

Here u is the change in length over a distance or the gauge length, x. It is to be noted that the strain measured in this manner represents only the average strain over the gauge length, x. The magnitude of error in the strain measured this way depends on the strain gradient along the gauge length x and the length x. This aspect is discussed further in Sec.

Strain gauges of all types are essentially devices that sense the change in length, magnify it and indicate it in some form. They can be classified into broadly five groups on the basis of the physical employed for the magnification of change in length.

(i) Mechanical(ii) Optical(iii) Electrical(iv) Pneumatic, and

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(v) Acoustical.

Strain gauges of these types are discussed briefly in the following sections.

Mechanical Strain Gauges:

(a) Huggenberger and CEJ Extensometers

These mechanical devices are generally known as extensometers and are used to mea-sure strain under static or gradually varying loading conditions. An extensometer is usually provided with two knife edges which are clamped firmly in contact with the test component at a specific distance or gauge length apart. When the test component is strained, the two knife edges undergo a small relative displacement. This is amplified through a mechanical linkage and the magnified displacement or strain is displayed on a calibrated scale.

The Berry strain gauge (Fig. 16.1) uses a system of a lever and dial gauge to magnify the small displacement between the knife edges. It can Measure strains down to 10 microstrain over a 50 mm gauge length. The mechanical amplifying element in the CEJ extensometer is a twisted metal strip or torsion tape stretched between the knife edges.

Figure: Berry Strain Gauge

Figure: Johansson extensometer

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Half the length of this strip is twisted in one direction while the other half is twisted in the opposite direction. A pointer is attached at the centre. The displacement of the knife edges, i.e. starching of the torsion

Figure: Huggenberger extensometer

tape is converted into a highly amplified rotational movement of the pointer. The CEJ exten-someter can measure strain with a sensitivity of 5 micro strain over a gauge length of 50 mm.

In the Huggenberger extensometer (Fig. 16.3) a set of compound levers is used to magnify the displacement of the knife edges. The extensometer is highly accurate, reliable, light-weight and self-contained. The movable knife edge (f) rotates the lever c about the lower pivot. The lever c in turn rotates the pointer through the link d. The magnification ra-tio is given by 1112/a1a2. Extensometers with this ratio varying between 300 and 2000 and with gauge lengths in the range 6.5 to 100 mm are available. The sensitivity of these exten-someters could be as high as 10 micro strain. It is well suited for applications where its un-usually large height does not pose problems of instability in mounting.

(b) Scratch Gauge

The scratch gauge is a self-contained compact device providing a permanent record of displacement over a period of time. In this gauge

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Figure: Scratch gauge (Prewitt Associates, USA)

the relative displacement between two stainless steel base planets L and S secured to the test component causes a scriber D to scratch sharply the actual component deformation on a small brass (targer, T). The target is held in position by two tiny rollers and two stainless steel brushes. The free end of the long driver brush B engages a peripheral groove of the tar-get. It is also guided in a bent tube BT. When a tensile deformation is removed or a com-pressive deformation is produced, the plates L and S move towards each other. This causes the driver brush B to rotate the circular target by a small amount. However during a tensile deformation the driver brush B just slides back in the target groove without rotating it. Thus tensile movements scribe a line parallel to the gauge axis (Fig. 16.5). Compressive move-ments and removal of tensile strain scribe a line at approximately 45o to the gauge axis. The height h of the recorded data is the product of the strain and gauge length. The traces on the target are evaluated by viewing them with a microscope having a calibrated eye-piece scale. The minimum strain that a scratch gauge can sense is about 100 micro strain. The gauge lengths of these gauges are rather large.

Figure: Scratch gauge record

The scratch gauge is compact in size and weighs less than 30 g. It can be attached to almost any surface with clamps or screws or adhesive bonding. It can measure stresses un-der all types of loading-static, fatigue or shock. It can be used to record stresses in all types of environments- room and elevated temperatures, under water, under radiation, etc.

Optical Gauges

(a) Mechanical-Optical Gauges

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In mechanical-optical gauges a combination of mechanical and optical levers are used to amplify the relative displacement between the knife edges. The moving knife is pivoted.

So that it rotates while undergoing displacement.

The principle of the signal mirror system is illustrated in Fig. 16.6. The pivoting knife edge carries a mirror A. The reflection of an illuminated scale B in this mirror is viewed through the observing telescope. Any deformation of the structure to which this gauge is fixed, rotates the mirror A and thereby brings different portion of the scale into view.

Figure: Martens optical gauge

Thus the change in the reading on the scale is directly proportional to the deformation being measured.

A schematic diagram of the Tuckerman optical gauge and the autocollimator used with it is given in Fig. 16.7. The autocollimator carries both the source of a parallel beam of light and an optical system with reticle to measure the deflection of the reflected ray. A tungsten-carbide.

Figure: Tuckerman optical gauge (American Instrument Co., Inc)

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Rocker (lozenge) functions as the moving knife edge. One face of this lozenge is pol-ished to function as a mirror. The rotation of the lozenge resulting from a deformation of the structure deflects the incident parallel light beam back to the measuring reticle. Actually, three images are visible on the reticle- one giving the measured displacement or strain and the other two helping the alignment of the gauge. In this system, any relative motion between the component and the autocollimator will not affect the measurement. Also, errors due to rota-tion of the extensometer are eliminated in this system.

The sensitivity of the Tuckerman gauge is 2 micro strain. The gauge is available with a wide range of gauge lengths, starting from 6 mm. It can reliably measure both static and dy-namic strains. With the gauge, cyclic strains up to a frequency of 180 c/s have been success-fully measured.

(b) Photoelastic Strain Ganges

A Photoelastic Strain Gauges (Fig. 10.8) essentially consists of: (i) a strip of plastic with a reflective backing containing a “frozen-in” fringe pattern of equally spaced fringes, (ii) a sandwich sheet of a Polaroid and a quarter-wave plate covering the plastic strip, and (iii) a graduated scale for measurement. This gauge when bonded to a test component will indicate visually and quantitatively the presence of strain through the movement of the resid-ual fringe pattern. Usually a principle strain difference of 1000 microstrain causes one fringe to move a distance equal to the fringe spacing. If one can read the fringe position to one-twentieth of the fringe spacing, a sensitivity of 50 microstrain can be obtained.

Figure: Photoelastic strain gauge

In an electrical strain gauge a change in length or strain produces a change in some electrical property. The greatest advantage common to all electrical gauges is the ease with which the electrical signal can be displayed, recorder or conditioned as required. Three types of electrical gauges are in use: (i) inductance gauges, (ii) capacitance gauges and (iii) electrical resistance gauges. Well over 90 per cent of the strain gauges used in practice are of the electrical-resistance type and a large proportion of these are foil gauges. The electri-cal-resistance gauge, in view of its importance, will be covered in detail in subsequent chap-ters.

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(a) Inductance Strain Gauges

Of the various types of variable inductance gauges, the linear variable differential transformer (LVDT) is well known for the measurement of displacement. A variety of transducers for measurements of strain, displacement, pressure, acceleration and force have been built with LVDT as the sensing element. In a transducer with LVDT as the strain-sens -ing element, the base carrying the primary and secondary coils is attached to one knife edge while the movable magnetic core is connected to the order (Fig.16.9). The centre primary coil is fed from an at supply. The two balanced secondary windings on either side of the pri-mary coil, connected together in phase opposition function as pick-up coils. The output from the LVDT is theoretically zero when the sliding magnetic core is placed midway

(a) Gauge

(b) Output voltage vs. core position

Figure: Linear variable differential transformer gauge

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Between the secondary coils. Movement of the core in one direction away from the null po-sition produces an output alternating voltage proportional to the displacement from the cen-tre. Displacement of the core in the opposite direction will produce an output 180 0 out of phase with the first output. The phase angle has to be determined for finding out the direction of displacement of the core.

The frequency of the applied ac voltage, i.e. the carrier frequency, limits the dynamic response of the LVDT. The frequency of the signal being measured should be less than about one – tenth of the carrier frequency. Further, the dynamic response of the LVDT is restricted by the mass of the core and the supporting mechanical components.

The LVDT requires a driving force of the order of a fraction of a gram to move the core in the coils. It can be used over a wide range of temperature – below zero to elevated temperatures. It provides a high – level output. The sensitivity of LVDT usually lies in the range 0.02 to 0.15 V/mm displacement per volt of excitation applied to the primary coil. A point to be noted is that the performance of the LVDT can be severely affected by the pres-ence of metal masses and stray magnetic fields in its vicinity. The size and mass of the LVDT and the problem of mounting through knife edges rather restricts its use in strain gauge work.

(b) Capacitance Strain Gauges:

The capacitance of a condenser can be varied by either varying the distance between the condenser plates or by varying the area. In a capacitance strain gauge the displacement. Resulting from the strain in the test

(a) Cross – section view

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(b) Gauge in a alignment frameFigure: Hitec capacitance gauge (Hitec Corporation, USA)

Component varies its capacitance either by varying the distance between the con-denser plates or by varying the area between the plates. In the capacitance gauge shown schematically in figure, capacitance changes occur due to axial sliding of an outer cylinder relative to two concentric inner cylinders. Temperature compensation is achieved by using a compensating rod fabricated from a material with the same thermal characteristics as the test component. It functions satisfactorily at temperatures up to about 8000C. With a refined measurement technique, it can measure 20, 000 with a sensitivity of 1 .

Pneumatic Strain Gauges

Figure shows the basic arrangement in a pneumatic strain gauge. Air at constant pressure flows through two orifices of cross – sectional areas A1 and A2. The area A2 of the variable area orifice is a function of the gap d which varies as the distance between the knife edge changes. The pressure p built up in the chamber is approximately given by

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Figure: Pneumatic strain gauge – Single pressure output

Thus the relationship between p and the displacement of the extensometer d is nonlinear. However, with proper design this non linear characteristics of the gauge can be minimized and a nearly linear characteristic can be obtained over a narrow range of displacement.

Better linearity can be obtained in the arrangement shown in figure. Magnifications up to 100,000 and gauge lengths as small as 1 mm are possible to achieve in these gauges.

Figure: Pneumatic strain gauge – Differential pressure output

Pneumatic gauges are sensitive, robust and reliable. They are suitable for both static and dynamic strain measurements.

Acoustical Strain Gauge:

The vibrating wire or acoustical gauge consists essentially of a steel wire tensioned between two supports a predetermined distance apart. Variation of the distance alters the natural frequency of vibration of the wire and this change in frequency may be correlated with the change in strains causing it. An electro-magnet adjacent to the wire may be used to set the wire in vibration and this wire movement will then generate an oscillating electrical signal. The signal may be compared with the pitch of an adjustable standard wire, the degree of adjustment necessary to match the two signal frequencies being provided by a tensioning screw on the standard wire. Calibration of this screw allows a direct determination of the change of length of a measuring gauge to be made once the standard gauge has been tuned to match the frequency of the measuring wire.

The visual display produced or a CRO renders adjustment easier. Tuning is now more usually accomplished by feeding the two signals into the two pairs of plates of an

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oscillograph and making use of the Lissajous figure formation to balance the frequencies. Matching of the tones is simplified and made more accurate by tuning out the beats which results when the vibration frequencies of two wires are nearly the same, which can be compared by using earphones.

The fundamental frequency of a stretched wire may be estimated from the expression.

Figure: Acoustical Strain Gauge

Where A = cross – sectional area of vibrating wireE = Young’s modulus of wire materialL = length of vibrating wirem = mass per unit length of the wireP = tensioning force in the wireL = increment in length of the vibrating wire.

Figure: Shows an acoustical gauge developed by Dr. O. Schaefer about 1933. The sensitivity of this gauge is very high, with possible determinations of displacement of the order of 0.25 µ cm. The range is limited to about 1/1000 of the wire length. The gauge is temperature sensitive unless the thermal coefficients of expansion of the base and wire are closely matched over the temperature range encountered during a test.

Pneumatic Strain Gauge:

The principle of operation of an air or pneumatic gauge depends upon the relative discharge of air between a fixed orifice and a variable orifice. Fig. shows a pneumatic gauge. Air under constant pressure H, flows through two orifices placed in series. The pressure h which

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Figure: Pneumatic

strain gauge

Prevails between these two orifices is a function of the ratio of their areas. The fixed orifice G is called the nozzle and the second orifice S, which is smaller, is called the exhaust orifice and is of variable area of cross-section. As a result of it, the pressure h serves to measure the dimension of S. Air after passing through the orifice G, strikes the top plate and is vented to the atmosphere. The flow of air through the two orifices in series must be equal if incompressibility is assumed. This assumption is practically valid as the pressures are quite low. Let,

AG = cross – sectional are of nozzle orifice GAS = cross – sectional area of discharge orifice S

CG, CS = coefficients of contraction for the orifices = density of air g = acceleration due to gravity

Since the flow through each orifice is the same, hence

When CS = CG = C, then

When the specimen is leaded, the distance between the two gauge points changes. This elongation is transmitted through the level’s system to the pneumatic gauge, where it changes the gap between orifice S and the top plate, this changing the area As in direct proportion to the strain. From Eq. it is obvious that the manometer reading varies as a quadratic function of the strain. However, it has an inflection point when h/H = ¾ or AS/AG = 0.58. Hence, for values in this neighbor- hood, the relation is very nearly linear.

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Multiplication factors of 100.000 are possible with this type of pneumatic amplification.

Scratch Gauge:

Of all the gauges available, perhaps the most ingenious because of its simplicity, is the scratch gauge. The instrument consists of two parts; a target, and a scratch arm. These parts may be secured to the test piece by screw, solder, or clamp applied at g and e. The target is a small plate with a chromium – plated surface and includes a raised clip arm ‘a’. The scratch arm b is pivoted at the elastic hinge C and carries, at f, several grit particles embedded in cured rubber. Motion between e and g is recorded as scratches made by the grit particles f on the chromium plated target. Propulsion of the scratch arm across the target is accomplished by the spring action of the elastic hinge C.

(a) Scratch recording system

(b) Magnified strain recordFigure: Scratch gauge

The cross motion is regulated by the pressure of clip a on arm b. This pressure develops sufficient static friction to restrain the arm, but cross motion is permitted by the smaller sliding friction, which results from relative motion of the target and arm and the test piece is strained. The rate of the scratch arm cross travel is a function of the sliding motion occurring, rather than of time. It can be controlled by variation of the clip pressure and the thickness of the spring hinge. The several grit particles scratch patterns of varying depth, depending on the alignment of target and arm. Of course, the most clearly defined pattern is used for interpreting the record. T he base line is established by moving the arm across the target while the test piece is in an unloaded condition. The measurements of deformation indicated by the scratches on the target, is accomplished by means of a microscope. Figure (b) shows the strain record.

This gauge is used for measuring deformation of rail – road rails because of the load caused by a passing train. Strain measurements can be made inside pressure vessels, inside moving mechanisms, under water etc. Dynamic strains pattern on analysis can be separated

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into various harmonics of a vibratory deformation. However, this gauge cannot be applied to small structures or finished surfaces, and extreme care has to exercised in measuring the scratch record to obtain any degree of precision. The gauge is also little affected by its own inertia forces. Readings may be estimated to 0.0025 mm.

Electrical Strain Gauges:

Introduction:

An electrical stain gauge is a device in which a change in length produces a change in some electrical characteristics of the gauge.

The electrical strain gauges may be classified as follows:(a) The inductance or magnetic strain gauges.(b) The capacitance strain gauges.(c) The electrical resistance strain gauges.

Out of these three types of gauges, the resistance strain gauges (RSG) have become more popular and reliable. Hence, in this chapter, we shall study the first two types of gauges briefly and lay more emphasis on the resistance gauges.

The inductance type of strain gauges in which the strain is measured as a change in the magnetic field, was developed as a strain gauge about 1930 by Shamberger. Since then this gauge has been used for various applications, particularly in motion measurements. An important application of inductance type of gauge is the linear variable differential transformer, developed by Schaevitz about 1947.

The capacitance type of gauges have found very little use as strain gauges and are not commercially available. However, these type of gauges have found applications as transducers to measure pressure, force and displacement.

In 1856 Lord Kelvin reported that the electrical resistance of certain wires varied with the tension to which the wires were subjected. Bridgeman in 1923 confirmed Kelvin’s results in a series of tests involving wires under hydrostatic pressure. Little use was made of this knowledge until after 1930, when attempts were made to apply the phenomenon of strain sensitivity in wires to the actual measurement of strain in other bodies. The first use of this principle for strain measurements was made by Carlson and Eaton about 1931. A non metallic, unbounded resistance gauge was however developed and used by Mc – Collum and Peters in 1924. A non – metallic, bonded resistance gauge was developed by Bloach in 1935.

The bonded wire metallic strain gauge was developed independently and almost simultaneously in 1938 by Simmons at the California Institute of Technology and Ruge at the Massachusetts Institute of Technology, now commercially known as the SR 4 gauges, and marketed by Baldwin – Lima – Hamilton Corporation of U.S.A. Since then the activity in this field has been on the increase and a lot of improvements has been made in these gauges. During the 1950’s considerable attention was given to the foil – type strain gauges. Much of the credit for development and acceptance of this type of gauge goes to Bean, Saunders and Roe. Currently the foil gauges have largely displacement the wire gauges.

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A uniquely constructed weld able wire filament strain gauge has been developed recently for application in may hostile environments and installation by Ailtech (U.S.A)

Inductance Strain Gauges:

An electric inductance gauge is a device in which the mechanical quantity to be measurement produces a change in the magnetic field, and hence in the impedance, of a current – carrying coil. The impedance of a coil depends on its inductance and on its effective resistance, and either or both of these quantities can be made sensitive to the mechanical quantity being measured. The inductance which is changed can be either the self inductance eof the coil or its mutual inductance with respect to another coil. Depending upon the method of varying the impedance, electric – inductance gauges may be classified as follows:

1. Variable – air – gap gauges. In which the reluctance of the magnetic field is varied by changing the air gap.

2. Movable – core solenoid gauges. In which the reluctance of the magnetic circuit is varied by changing the position of the iron core in the coil.

3. Eddy current gauges. In which the losses in the magnetic circuit are varied by changing the thickness or position of the high – loss element inserted in the magnetic field.

4. Magnetostriction gauges. In which the reluctance of the magnetic circuit is varied by changing the stress in the magnetic core of the coil.

The impedance of a coil to the passage of alternating current is given by the expression:

Where Z = impedance in ohmsf = frequency in hertzsL = inductance of the coil in henrysR = resistance component in ohms.

In general, R is negligible as compared to L and the impedance varies almost in proportion to the inductance. The inductance of a variable – air – gap gauge is given by

Where N = number of turns.li = length of iron magnetic circuit, cmla = length of air gap, cm = permeability of magnetic material at the maximum alternating flux

densityai = cross – section of iron, cm2

aa = cross – section of air gap, cm2

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If the valve of is sufficiently large, then is negligible as compared to and we find that

The relationship between the voltage applied across a coil and the flux density in its core is

E = 0.10667 BaNf 10-8

Where E = voltageB = flux density in lines per square cma = cross section of core, cm2.

Thus, we find that under ideal conditions, the impedance of an iron – core coil varies inversely with the length of the air gap in the magnetic circuit. If the motion to be measured is a large percentage of the initial air gap, very large change in impedance can be produced and large amounts of electric energy become available. Therefore, the variable – air – gap gauge is one of the best – known methods of converting small motions into high energy electric signals. For large motions, it is more advisable to use the moving – core solenoid. Eddy – current gauges find applications in special fields, such as the measurement of motion and of the thickness of non ferrous sheets Magnetostriction effect is small in most commercial magnetic irons but is large in nickel and some nickel – iron and cobalt – iron alloys. Figure shows circuits for some of thee gauges. These gauges are placed in one arm of an inductance bridge with either a voltmeter or CRO to indicate the out – of – balance potential to the bridge. The bridge is supplied with an alternating current of about 1000 hertzs for static strain measurements. For dynamic strains, the frequency of current source must be 20 to 30 times the frequency of the strain being measured. One serious difficulty is that magnetic forces set up across the air gap frequently give rise to serious vibrations in the structure. These gauge cannot be applied to light structures. Large strains cannot be measured as the strain – inductance relationship is linear only over a small range of strain. These gauges are weighty, bulky and susceptible to magneto – mechanical resonance.

(a) Variable air gap gauge

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(b) Moving coil solenoid gauge

(c) Eddy current gaugeFigure: Inductance strain gauges

Figure shows the basic impedance bridge circuit. E1 and E2 are the laminated iron cores and A is the armature. When the armature A moves the air gap between A and E 1

increases and that between A and E2 decreases or vice versa. This changes the reluctance of the magnetic paths in E1 and E2 and consequently changes the impedance of the two coils which are wound on them. Let Z1, Z2, Z3 and Z4 be the impedance of the gauge coils and balancing elements. Z5 is the impedance of the instrument circuit. In order to reduce the voltage across Z5 to zero, both the resistive and the reactive components of the bridge legs must be balanced. Both of the following conditions must be fulfilled.

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Figure: Basic impedance bridge circuit

And

Electromagnetic Strain Gauge:

If a magnetic bar is loaded by a torsional moment, a voltage is recorded by a galvanometer connected to a coil through which the bar is put. An electromotive force is induced in the coil of the electromagnet which depends on the torsional moment acting on the core of the electromagnet which is twisted. This is known as Wiedemann’s effect. The factors which influence the magnitude and linearity of the induced electromotive force are: the degree of saturation of magnetic field, the geometry of the attachment to the structure, the frequency of power supply, the size of the tube, the number of turns of the wire wound round the tube, the material of the pipes and its condition. The electromagnetic strain – gauge is shown in figure. The pick up unit, measuring the longitudinal component of the magnetic flow, consists of a pick up coil and a low drain a.c. voltmeter. The influence of the pick up unit depends on the non – inductive resistance Rm of the measurement device, on the inductive resistance wl of the coil, on the non – inductive resistance Rc of the coil and on the slenderness ratio r = lD of the tube. The mathematical formula expressing the influence of the measurement unit on the variation of the induced electromotive force or the actual, i.e., measured slope of the characteristics Km’ is

Figure: Electromagnetic strain gauge (Wiedemann’s effect)

Where K0 = ideal slope of the characteristic, for r = 0.8.x = ratio of induced electromotive force for general r to the voltage Em for r =

0.8.

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Capacitance Strain Gauge:

The electrical capacity between parallel plates is given by:

WhereC = capacitance in pico farads.K = dielectric constant of the medium between the two plates.N = number of platesh = distance between plates, mm.

Now

Strain

Hence

Where l0 is the gauge length

Figure: Simplified diagram of a capacitance transducer circuit

Thus the capacitance of a condenser may be changed either by changing the spacing between the condenser plates or the condenser plate area may be changed. The variation in the capacitance because of a change in the plate spacing while the change in capacitance resulting from a change in area is linear for large changes in the plate area. Two types of circuits may be used to measure the change in capacitance of a gauge. In the first methods, a

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capacitance bridge is supplied with an a.c., the out – of – balance of the bridge, because of a change in the capacitance of the gauge, is measured by either a voltmeter or CRO. In the second method, the capacitance gauge may be placed in a circuit, oscillating at resonance. As the capacitance of the condenser changes as a result of strain the frequency of oscillation of the circuit changes. The output of this resonant circuit is passed through a discriminator, the variation in frequency is indicated on the screen of CRO. The first method employs an amplitude – modulated signal, while the second method uses a frequency – modulated signal. A simplified diagram of a capacitance transducer circuit is shown in figure.

Capacitance gauges are small in size and they have excellent high – frequency response and high temperature resistance, as well as good linearity resolution and ability to measure both static and dynamic quantities. These gauges are sensitive to temperature, vibrations, have high impedance output and complexity of associated electronic equipment. Dielectric, mounting and clamping difficulties make this gauge not too desirable.

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UNIT III Electrical Resistance Strain Gauges

Principle Of Operation And RequirementsTypes and Their Uses Materials For Strain Gauge. Calibration and Temperature CompensationCross SensitivityRosette AnalysisWheastone Bridge Potentiometer Circuits For Static and Dynamic Strain Measurements. Strain Indicators.

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UNIT – III

Electrical Resistance Strain Gauges

In the electrical resistance strain gauges the displacement or strain is measured as a function of the resistance change produced by the displacement in the gauging circuit. An ideal strain gauge should have the following basic characteristics:

1. The gauge should be of extremely small size (gauge length and width) so as to adequately estimate strain at a point.

2. The gauge should be of significant mass to permit the recording of dynamic strains.3. The gauge should be easy to attach to the member being analysed and easy to handle.4. The strain sensitivity and accuracy of the gauge should be sufficiently high.5. The gauge should be unaffected by temperature, vibration, humidity or other ambient

conditions.6. The calibration constant for the gauge should be stable over a wide range of

temperature and time.7. The gauge should be capable of indicating both static and dynamic strains.8. It should be possible to read the gauge either on location or remotely.9. The gauge should exhibit linear response to strain.10. The gauge and the associated equipment should be available at a reasonable cost.11. The gauge should be suitable for use as a sensing element or other transducer systems.

Types of Resistance Strain Gauges

There are basically four types of electrical resistance strain gauges as classified below:

1. Unbonded gauges:

(a) Non-metallic(b) Metallic

2. Bonded gauges

(a) Non-metallic(b) Metallic(i) Wire type(ii) Foil type.

3. Weldable gauges.4. Piezoresistive gauges.

1. (b) Unbonded-Metallic Gauges.

The unbonded nonmetallic gauge is a mechanically actuated gauge that contains a resistance element so arranged that when one part of the gauge is displaced with respect to another there is developed a change in pressure on the measuring element of the gauge. This change in pressure changes the resistance of the element which may be recorded by electrical means. A gauge of this type was developed in 1923 and 1924 by McCollum and Peters and

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is shown in Fig. This gauge is composed of a series of carbon plates arranged in a stack. The stack is so adjusted that a displacement of one part of the gauge relative to another changes the pressure, on the stack of plates. When the strain is applied in the structure to which the gauge is attached, the change in length is communicated to the carbon-plate stack. This change in length requires a change in pressure in the stack, and the resistance of the stack changes.

Figure: Unbonded non-metallic strain gauge.

With an increase in pressure, the areas of contact between the plates are enlarged and new areas come into contact, thus decreasing the resistance of the element. If the pressure is released, the areas of contact are reduced, and some of the areas lose contact, thus increasing the resistance of the element. If the pressure becomes excessive, so that the elastic limit of the carbon in the gauges is exceeded or the carbon is even crushed, or if the plates are allowed to shift in the lateral direction with respect to each other, the results become erratic. Besides these difficulties, there is a further defect of mechanical friction and hystertsis in the mechanical parts of the gauge.

Gauge of this kind have been used to determine displacements, loads and strains in flexible cables, airplanes, bridges, vibrating members, dynamometers and pressure gauges. However, with the advancement of metallic gauges the usefulness of these type of gauges has reduced materially.

1. (b). Unbonded-Metallic Gauges.

The principle of the unbonded-metallic gauges is based on the change in electrical resistance of a metallic wire due to the change in tension of the wire. The first device of this kind was designed by Carlson and Eaton in 1930. This type of gauge is constructed by winding wire in three coils, the first providing a coil unaffected by the gauge motion, and the other two having tensions altered by the gauge motion, each in an opposite manner. The whole is mounted in a sleeve that allows only longitudinal movement. The coils are placed under initial tension into a four arm Wheatstone bridge. As the compressive strain is applied, the prestrain would simply be relieved and the unbonded element would remain taut. For the gauge to register compressive strains, the initial assembly must include a built-in tensile prestrain in the coils greater than the maximum compressive strain to be measured. A gauge of this type is shown in Fig. These type of gauges are rarely used for experimental stress analysis. However, these type of gauges have been incorporated into accelerometers and pressure pickups.

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Figure: Unbonded metallic strain gauge.

2.(a) Bonded Non-Metallic Gauges.

A strain gauge using direct bonding of a non-metallic resistor element to a material in which the strain is so to be measured was reported by Bloach in 1935. In this gauge a carbon coating is applied directly to the surface of the structure in which strain is to be measured. For metallic structures the surface is first coated with a non-conducting material. If the underlying surface of such a coating is stretched, the carbon particle would move apart, and the under-coating is compressed, the particles would move closer together, and the resistance will change. This resistance change can be interpreted in terms of strain.

Generally these type of gauges are made by impregnating carbon particles in plastic sheets. These sheets are then cut into strips about 6 mm wide and 25 mm long. On each end of the strip a silver band is plated so that lead wires may be attached (fig). The gauge is bonded directly to the surface to be strained with a common glue.

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Figure: Bonded non-metallic strain gauge.

These sensitivity and resistance of the gauge are affected by temperature and humidity. This gauge is of rugged construction and can withstand rough handling. However, the cross-sensitivity of the gauge is quite high.

2. (b) Bonded Metallic Gauges.

The bonded metallic type of strain gauge consists of a length of a strain-sensitive conductor mounted on a small piece of paper or plastic backing. In use this gauge is cemented to the surface of the structural member to be tested. These gauges may be either of the wire or foil type. In the case of wire strain gauges, the filament consists of a long length of wire in the form of a grid fixed in place with a suitable cement. The wire grid may be either of the flat type (fig. a) or wrap-around type (Fig. b). After attaching the lead wires to the two ends of the grid, a second piece of paper is cemented over the wire as a cover. In the wrap around type of wire gauges, the strain-sensitive wire is wound around a cylindrical core in the form of a close-wound helix. This core is then flattened and cemented between layers of paper for purpose of protection and insulation. Fig.(c) shows a flat wire grid free filament construction.

Figure (a): Bonded wire flat grid gauge.

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Figure (b): Bonded wire wrap-around gauge.

Flat wire grid free filament construction. Bonded flat foil grid gauge.

Figure: Types of bonded metallic gauges.

The foil type of stain gauge has a grid made from a very thin strain-sensitive foil (fig d). The width of foil is very large as compared to the thickness so that the gauge provide a much larger area for cementing the gauge. The gauge configuration is obtained by printing the desired pattern on a sheet of foil with acid resistant ink and subsequently etching away the unprotected metal. Another method of manufacture involves precision punching of the gauges from a foil sheet. The foil type of gauges have the following advantages over the wire type gauges.

1. The width of the foil at the end of each loop can be greatly increased to reduce the sensitivity of the sensitivity of the gauge to transverse strains.

2. The cross-section of the gauge conductor is rectangular, resulting in the high ratio of

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surface area to cross-section area. This increases heat dissipation and avoids adhesion between the grid and the backing material.

3. The gauge factor is higher by 4 to 10 per cent that other gauges.4. These gauges are easier to manufacture.5. These gauges can be used to measure strain on curved surfaces.6. These gauges are suitable for static and dynamic strain measurements.7. They have very good fatigue properties.8. Stress relaxation and hysterisis is very less in these gauges.

3. Weldable Strain gauges.

Some of the limitations of the bonded type of metallic gauges are their comparatively costly, time consuming and complicated method of bonding. This realization led to the development of the weldable wire resistance strain gauge-a strain gauge capable of being installed in minutes and in any environment. This unique technique, utilizing capacitive discharge spot welding equipment eliminates the need for all bonding materials.

The weldable strain gauge consists of a strain sensitive element, the Nickel Chrome or Platinum Tungsten, housed within a small diameter stainless steel tube. The strain element is insulated from the tube with highly compacted ceramic insulation or metallic oxide powder, normally high purity magnesium oxide, which also serves as a strain transfer medium from the housing to strain element. This weldable gauges are equipped with a thin flange spot welded to the strain tube. This flange is subsequently spotwelded to the structure under test and provides the bond required to transfer strain.

Integral leads are attached to the basic gauge by welding. When the gauge is welded to a specimen and the test specimen put into tension or compression, the stress is transmitted through the weld to the mounting flange, into the strain tube, and through the magnesium oxide powder.

The basic construction of a quarter-bridge or half-bridge, self-temperature compensated gauge is shown in Fig. and includes integral metal sheathed or flexible lead wire configurations. This gauge construction provides inherent mechanical and environmental protection for both the main filament and lead wires and is used over a broad temperature range from cryogenic to 65oC. Weldable strain gauges can be used for a wide range of static and dynamic measurement applications. Their rugged construction and positive attachment make it possible to measure strain at higher or low temperatures and in server environments, including shock and vibration, steam, salt water, chemicals, and other corrosive atmospheres.

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(a) Quarter bridge gauge. (b) Half bridge gauge.

Figure: Weldable strain gauges

4. Piezo-resistive strain gauges.

Crystals of silicon, germanium, quarts and Rochelle salt show a change in resistance when deformed by applying pressure. This effect can be utilized to measure strain. Such like gauges are called piezo-resistance strain gauges. We shall discuss these gauges in details.

Materials for Gauges

A good gauge material should have the following qualities:

1. High gauge factor2. High resistance3. Low temperature sensitivity4. High electrical stability5. High yield point stability6. High endurance limit7. Good workability8. Good solderability and workability9. Low hysteresis10. Good corrosion resistance11. Low thermal e.m.f. when joined with other metals.

The important properties of the most commonly used materials for strain gauges are given in Table.

Carrier Materials

A strain-gauge grid is normally supported on some form of carrier material. This provides the necessary electrical insulation between the grid and the material to be tested, dimensional stability, and also provides some degree of mechanical protection for the delicate sensing element. A good carrier material should have the following desirable characteristics:

1. Minimum thickness

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2. High mechanical strength3. High dielectric strength4. Minimum temperature restrictions5. Good adherence to cement used6. Non-hygroscopic.

Temperature Compensation

The ideal strain gauge would change resistance in accordance with stress-producing deformations in the structural surface to which it was bonded and for no other reason. Unfortunately, gauge resistance is affected by many other factors, out of which temperature is very important.

The total indicated strain occurring at a point in a structure is made up of mechanical strain and apparent strain. The mechanical strain is that produced by external forces. The apparent strain is the portion of the total indicated strain induced by thermal effects including expansion of the base metal, expansion of the gauge metal and change in electrical resistance of the gauge. Thus, when the ambient temperature increases (say), then

1. The gauge grid will elongate so that

2. The base material on which the gauge is mounted will elongate so that 3. The resistance of the gauge metal will increase because of the influence of the

temperature coefficient of resistivity of the gauge material so that

The combined effect of these three factors will produce a temperature induced change

in resistance of the gauge, with may be expressed as:

Where = thermal coefficient of expansion of the gauge material = thermal coefficient of expansion of the base material = temperature coefficient of resistivity of the gauge material F = gauge factor R = resistance of gauge = rise in temperature.

Equation holds only for small values of , where , and can be considered constant. For large values of , average values of these factors might be used without introducing large errors.

If , then the gauge will be subjected to a mechanical strain, , which

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does not occur in the specimen.

If = , then this component of apparent strain vanishes. However, the gauge will still register a change of resistance with temperature if is not zero. In order to prevent significant errors due to this effect, some form of “temperature compensation” is usually employed when strain gauges are used in applications where the steady state or static component of strain must be measured. Currently available methods of compensation for the apparent strain include the use of a dummy or compensating strain gauge, self-temperature compensating (STC) gauge, compensation by dissimilar or similar gauges in the Wheatstone bridges and compensation by computation.

1. Compensating Dummy Gauge:

The earliest form of temperature compensation makes use of the electrical bridge circuit in which the active gauge is connected to balance out unwanted temperature induced resistance change. This is usually called the “compensating dummy” arrangement. The “dummy gauge” identical to the active gauge in type and lot number, is mounted on an unstressed piece of the specimen material and placed in the same thermal environment as the active gauge. The active and compensating gauges are then connected as adjacent arms of the bridge circuit in the readout instrument. Effects common to both gauges will preserve bridge – balance conditions, and no output signal results. Since only the active gauge is exposed on mechanical or thermal strain caused by specimen stress, bridge unbalance is proportional to the magnitude of specimen stress producing strain. The method fails entirely if the temperature does not vary in an identical fashion at both gauge locations.

2. Self-temperature Compensated Gauge:

The terms ”temperature compensated” is applied to strain gauges in which the resistance change due to temperature is equal to zero. Self-temperature compensated gauges will perform properly only when used on materials having the specific value of thermal expansion coefficient for which they are designed. STC gauges can be obtained for use on materials having thermal expansion coefficients from zero to 25 ppm/oC.

Two method are used for obtaining self-temperature compensation. In the first method, self-temperature compensation is created by altering the temperature coefficient of resistance of the grid material so that, when mounted on materials having a certain thermal expansion coefficient, the apparent strain will be a suitably low value. This is done, in most cases, by special selection or thermal processing of the grid alloy. The two principal classes of strain-gauge alloys susceptible to such treatment are Constantan and Karma. The second method includes forming a grid with two lengths of gauge wires joined suitably in series so that the resultant apparent strain is zero.

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Dual-element self temperature Compensation by dissimilar gauges.

Compensated gauge.Figure:

3. Compensation by Dissimilar Gauges:

Compensation of the temperature effect in a bridge network is accomplished by putting dissimilar gauges into adjacent bridge arms as shown in Figure. The gauge in the first arm should have a relatively small temperature effect in the same direction. With proper, fixed series and shunt resistances for the gauge in the second arm, it is possible to obtain an overall temperature effect for the second arm, that is equal to that of the first arm. Hence, the temperature effects of the two arms will cancel each other with a relatively small loss in the strain sensitivity of the network.

This method would appear to have a better chance of success than the self-temperature compensated gauge because the relative resistance of the filament is not critical. If will always be possible after a gauge has been made, to select the fixed resistance for proper compensation. Furthermore, compensation over a greater temperature increases. in this case, temperature would not have to be known very accurately.

4. Compensation by Similar Gauges:

Best possible temperature compensation is obtained for unpredictable effects as for predictable effects with two similar gauges in adjacent arms of a Wheatstone bridge. However, this circuit arrangement eliminates the hydrostatic component of stress from the reading and only the shear component of stress is reflected. Hence, the gauges should be arranged so as to pick up the greatest signal from the shear component of stress. This means that one gauge should be positioned in the direction of the maximum principal strain, the other in the direction of minimum principal strain. This method is likely to give best results when the direction of the principal strains is known.

5. Compensation by Computation:

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By knowing the temperature characteristics of a strain gauge and the base metal, and if the temperature can be observed separately, a correction can be calculated theoretically from Equation and applied to the observed strain.

Figure: Compensation by similar gauges.

The Transverse Sensitivity:

The strain sensitivity SA of a single, uniform length of a conductor is given by

Where is the uniform strain along the conductor and in the direction of the conductor. Whenever the conductor is wound into a strain-gauge grid, certain effects take place which alter to a certain degree this value of sensitivity of the gauge. The change is introduced by the end loops, which are transverse to the straight portion of the grid. Thus the gauge in addition to measuring the strain along its axis also measures the strain transverse to it. This affect is reflected as an error in the strain gauge reading. This is known as the transverse or cross-sensitivity of the gauge. Now

Axial (parallel) strain sensitivity

Normal (perpendicular) strain sensitivity

Transverse sensitivity factor K is defined as

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Gauge factor F as specified by the manufacturer is

Assuming that the gauge has been calibrated on steel whose Poisson’s ratio is 0.285.

Introduction:

When the state of strain at a point and the direction of principal strains is known, then the strain gauges can be oriented along these directions, and strain measurements may be made. However, when the state of strain is not known, then three or more gauges may be used at the point to determine the state of strain at the point. The resulting configuration is termed a strain rosette. Strain-rosette analysis is the art of arranging strain gauges as rosettes at a number of points on the object to be investigated, taking the measurements, and computing the state of stress at these points.

Strain rosette analysis is based on the assumptions of isotropic, homogeneous and linear material and of strain gradients so small that the strains can be considered as substantially uniform over the area covered by the rosette gauges. In this chapter, we shall study strain rosettes of various configurations currently in use.

Delta rosette Three gauge rectangular rosette

Figure:

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In one form of the rectangular rosette the gauges are in one plane and in the other on top of one another. The rosette in the first case will cover smaller area than that of the latter and hence will give more accurate results in a region in which the strains are varying. However, if this rosette is mounted on a thin member subjected to severe bending, a considerable error will be introduced since each gauge is at a different distance from the neutral axis. In this case the use of the rosette having all the gauges in one plane and of the foil type would give better results. In delta and T-delta rosettes, all the gauges are generally arranged in one plane and not on top of another.

1. Some simplifications in rosette Analysis:

The strain rosette analysis has the following advantages:

i. Extreme simplicity and speed of application.ii. Possibility of allowing for transverse effects.

iii. No requirements for additional equipment. iv. The possibility of training relatively unskilled persons to use the method.

Basic Circuits (Constant Voltage Type)

There are two types of circuits used for strain measurements.

i. The Wheatstone bridge(a) Null balance type(b) Out-of-balance type.

ii. Potentiometer.

The Wheatstone Bridge circuit

(a) Balanced bridge. Figure shows the basic circuit for the Wheatstone bridge. For a balanced bridge the current IG through the galvanometer is zero.

Hence I1 = I2, I4 = I3

The potential drops across the individual elements are:

Hence

If EBD = 0, the potential at B must equal that at D, hence the drop from A to B must

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equal that from A to D and the drop from B to C must be equal to D to C, i.e.

which is the condition for a balanced bridge.

Let R1 be the change in R1 due to straining, then

To measure the unknown strain, R4 can be calibrated directly in terms of strain or instead of balancing the bridge after straining the galvanometer deflection itself might be taken as a measure of the strain.

(b) Unbalanced bridge. For the unbalanced bridge as shown in figure, at the point B.I2 = I1 + IG

At the point D

I4 – IG = I2

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Figure: Null balance Wheatstone bridge

Null-Balanced Bridges

In static applications it is possible to employ a null balance bridge where the resistance of one or more arms in the bridge is changed to match the effect of the change in resistance of the active gauge. The null balance system is usually more accurate than the direction-readout bridge and requires less expensive equipment for its operation. A relatively simple null-balance type of Wheatstone bridge is shown in Figure. A slide wire resistance potentiometer is placed across the bridge from B to D and the point C is connected to a point C’ on the balance resistor. Assume that initially the bridge is balanced with active gauge in arm 1 so that R1R3 = R2R4 and R5 = R6. The meter G is at null or zero voltage. Now consider a resistance change in R1, which upsets this balance, causing a voltage indication on meter G. The slide wire on the potentiometer is adjusted, making R5 R6, until the bridge is again balanced. The potentiometer adjustment, which is calibrated, is proportional to the resistance change in the active gauge. Thus the mechanical movement of the potentiometer serves as the readout means, and the voltage is measured only to establish a zero or null point.

Now the equivalent resistances are

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(a) Parallel balancing circuit. (b) Equivalent circuit.

An adjustment of the potentiometer will produce a change in the resistances of R5 and R6

equal to R5 and R6, so that R5 = -R6, since the total resistance of potentiometer remains constant.

The change in equivalent resistances become,

Hence by using an active gauge in arm 1 and a dummy gauge in arm 4, the change in voltage output becomes,

For an initially balanced bridge,

When R5 = R6, R2 = R3

and R5 = -R6, we get

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Equation indicates that the strain reading obtained by using a parallel-balance circuit is nonlinear in terms of the adjustment of R5.

represents the combined effect of temperature on actual gauge installation.

Calibration Methods

Necessity of calibration

1. By knowing the output of a constant voltage or constant gauge current bridge circuit and sensitivity (units of deflection/mV or/A) of the indicator, the indicator deflection can be related to strain. This is the method generally used for designing strain gauge circuits and selecting recording or indicating equipment. However, it is not suitable for final calibration of system, since with this method the final accuracy of the system would depend upon the accuracy with which all of the parameters involved could be measure and held constant during the period of test. Hence a handy, reliable, and direct calibrations is extremely important.

2. Since the final output of the strain amplifiers is an electrical signal whose magnitude depends on the strain to which the gauge is subjected, the strain appears as nothing more than a wave or series of waves on an oscilloscope screen, and some means of judging its absolute magnitude must be provided. The following methods may be used for calibrating a strain gauge.

1. Electrical calibration. (a) Static Strain Calibration

First Method : Shunt resistor. The strain-gauge resistance in one leg of the Wheatstone bridge circuit is shunted by an open-circuited resistor of considerably high value as shown in Figure.

Constant-Current circuits:

Upto now we have discussed the wheatstone and Pot circuits driven by a constant voltage source which ideally remains constant with change in resistance of the circuit. The output of these circuits is non-linear and the non-linearity factor increases as R/R increases. To improve upon the circuit performance a constant current source instead of the constant voltage source may be used. A constant-current power supply is a high impedance

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device (of the order of 1 to 10 M) which changes output voltage with changing resistive load to maintain a constant current.

Wheatstone bridge circuit:

Consider the constant-current source Wheatstone bridge circuit as shown in Figure At point A

Also

The output voltage E from the bridge can be expressed as

For the balanced bridge under no-load conditions,

E = 0

Figure: Constant current Wheatstone bridge circuit.

Hence

Now

Hence

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Or

Thus the output voltage becomes

When the bridge is balanced, E = 0 we get

If the resistances. change by the amounts

, the output voltage measured with a very high impedance meter is

For an initially balanced bridge, we get

The output given by Eq. is nonlinear with respect to R because of the term in the denominator and the last two terms in the bracketed quantity. However, this non-linearity is

much smaller than the constant voltage source circuit. Let

i.e. is an active gauge and is temperature-compensating dummy

gauge, then Eq. then reduces to

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Where the non-linear term , is

The nonlinear term can be minimised by increasing r as is obvious from Equation . Generally r is taken to be equal to 9.

Potentiometer circuit:

Consider the constant-current potentiometer circuit shown in Figure. When a very

high impedance meter is placed across resistance , the output is

E =

When resistance and change by , then output voltage becomes

Thus

When then Equation becomes

Therefore, the output voltage is linear with respect to resistance change and strain .

Circuit sensitivity

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Figure: Constant current potentiometer circuit.

It can be easily seen that the circuit sensitivity of the constant current is higher than that of the constant-voltage circuit.

Associated Instrumentation:

Static strains:

For most analysis work, static strains may be measured by a wheatstone bridge. The bridge may be either operated on D.C. or A.C. When A.C is employed then a carrier system has to be used. Generally null balance system is preferred over the out-of-balance method because the null balance system is more accurate than the direct readout and is less expensive. The earlier commercial strain indicators use a reference bridge circuit to provide the null-balance system as shown in Figure. With commercial strain indicators, the adjustment resistance gives a direct readout in strain. A commercial null-balance system is shown in Figure(a) and (b). These models can operated either on A.C. or battery. Figure shows a direct readout amplifier and junction box. Switching and balancing units are available for multiple gauge installations.

Figure: Direct readout amplifier and junction box.

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In the manual null-balance strain indicators the output from each gauge is recorded manually on a data sheet. The data are usually processed by hand or with a simple programmable calculator. Figure shows a typical strain indicator system. Figure shows the D.C. operation of the Wheatstone bridge and Figure shows the A.C. operation. Figure shows an automatically balanced bridge, it is necessary to build a phase-sensitive detector into the rectifying circuit.

The manual direct reading strain indicator is shown in Figure. With this instrument, the Wheatstone bridge is initially balanced and then the voltage output due to stain is amplified and read out on a digital voltmeter.

Figure: Switching and balancing unit.

Figure: Direct digital readout strain indicator.

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Figure: A typical strain indicating system.

When relatively large strain-gauge installations are used to analyse a problem then automatic data-acquisition systems should be employed. The automatic data-acquisition system consists of four basic sub-system which include the controller, the signal conditioner-scanner, the analog-to-digital converter and the readout devices. The signal conditioner-scanner consists of the power supply, the Wheatstone bridges and the switches used to connect a large number of gauges in turn to the single voltage recording instrument. Each bridge has a small control panel with a balance adjustment, a span adjustment and a calibration switch. The output from the wheatstone bridge is switched into a high quality digital voltmeter, which measures the average of the input voltage over a fixed measuring period.

Figure: D.C. operation of Wheatstone bridge.

Dynamic Strains:

While recoding dynamic strains, the frequency of the strain signal is an important consideration in selecting the recording system. The help of the following table may be taken in selecting the recording system depending upon the strain frequency.

Frequency Range Recording SystemVery low (0-3 Hz) Integrating digital voltmeter, potentiometer

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recorder and xy-recorder.Intermediate (0-10 kHz) Oscillograph with a pen (0-100 Hz) and a light

writing (0-10 kHz) galvanometer.High (0-20 kHz) FM instrument tape recorder.Very high (above 20 kHz) Cathode ray oscillosope.

For very low frequencies, instruments such as potentiometer (or strip chart) recorders

and xy-recorders, which employ servo-motors together with feedback control and null-balance positioning can be used to measure the output voltage from the strain gauge bridge. The operating principle of such an instrument is shown in Figure.

Figure: Operating principle of a servo-driven null-balance circuit (potentiometer) for voltage measurement.

Potentiometer recorders can be used to measure voltages from 1 V to 100 v. The chart speeds can be varied over a wide range of 25 mm/h to 50 mm/s. Because of their low frequency response, the potentiometer cannot be used in strain gauge applications where the strain signal has frequency components greater than 1 Hz. Figure shows a double beam oscilloscope.

For recording strains at high frequencies magnetic-tape analog data recording systems are used. Data recorded and strode on magnetic tape are usually played back and displayed on an oscillograph. By varying the tape speed during playback, the time base can be extended or compressed. Information stored on magnetic tape can be reliably retrieved any number of times and different analysis made. Figure shows the schematic sketch for a magnetic tape recorder. In a magnetic tape recorder, the tape (1.27 to 25.4 mm wide) is driven at a constant speed by a served d.c. capstan motor over either the record or reproduce heads. The speed of the capstan motor is monitored with a photocell and compared with the frequency from a crystal oscillator to provide the feedback signal in a closed loop servo system designed to maintain constant tape speeds. The signal written on the tape by the record magnetic head assemblies is in the form of variations in the level of magnetism imposed on the magnetic coating of the tape. The reproduce head converts these variations in magnetism back into electrical signals.

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Figure: X-Y Recorder.

(Courtesy: Hewlett Packard, Palo Alto, California, USA)

Figure: Magnetic tape recorder.

Most instrument tape systems can be used in either direct recording or frequency modulation (FM) modes. With direct recording, the intensity of magnetization on the tape is proportional to the instantaneous amplitude of the input signal. Direct recording is usually limited to audio recording where the human ear, on playback, can average the amplitude errors or to recordings where the signal frequency and not the signal amplitude is of primary impotence.

With FM recording, a carrier oscillator is frequency modulated by the input signal. The oscillator has a centre frequency which corresponds to a zero input signal. Deviations from the centre frequency are proportional to the input signal. The polarity of the input signal determines the direction of deviation FM recording preserves the d.c. component in the signal and is much more accurate than direct recording. Figure shows a basic FM system.

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Figure: Basic F.M. systemVery high frequency recording can be accomplished with cathode ray oscilloscopes

which have bandwidths upto 500 MHz. The CRO is, in effect, a voltmeter which can be employed to measure transient voltage signals. The heart of the CRO is the cathode ray tube (CRT). The stream of electrons permits the CRT to be employed as a dynamic voltmeter with an inertialess indicating system. Now-a-days, storage oscilloscopes are available which retain the display the image of an electrical wave-form on the tube face after the waveform ceases to exist. The stored display can be instantaneously erased to ready the tube for display of the next waveform.

For dynamic strain-gauge applications, the CRO is an ideal voltage-measuring equipment. The input impedance of the instrument is quite high (about 1 M); thus, there is no appreciable interaction between THE Wheatstone bridge and the measuring instrument. The frequency response of an oscilloscope is usually quite high, and even a relatively low-frequency model (800 kHz bandpass) greatly exceeds the requirements for mechanical strain measurements, which are rarely more than 50 kHz. The sensitivity of the CRT is normally quite low and it often requires 100 V to produce 25 mm of deflection on the face of the tube. This difficulty is generally overcome by providing a built in amplifier in the CRO.

The strain gauge record showing strain as a function of time is obtained by photographing the face of the CRT as the Spot of light traverses the fluorescent screen. A still camera or a movie camera may be used to obtain a permanent strain signal record.

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UNIT IV Photoelasticity

Two dimensional photo elasticity

Concept of light – photoelastic effects

Stress optic law

Interpretation of fringe pattern

Compensation and separation techniques

Photo elastic materials.

Introduction to three dimensional photo elasticity.

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UNIT – IV

TWO –DIMENSIONAL PHOTOELASTICITY

Introduction

The photoelastic method depends upon the property of certain transparent solids by which they become doubly refractive under the action of stress, the magnitude of the optical effect bearing a definite relation to that of the stress. The optical phenomenon, known as the “photo-elastic effect” was first discovered by Sir David Brewster in 1816 in sheets of stressed glass. Brewster, however, did not succeed in obtaining a uniform stress in his model and was not able to make any quantitative estimate of the relation between the stress and the optical effect produced. In 1820 Biot demonstrated that a strip of glass became doubly reflecting when set into a state of longitudinal vibrations and Fresnel attempted to measure the changes in the velocities of the two oppositely polarized rays in glass without any decisive results. Neumann presented the first theory of the photoelastic effect in 1841 and expressed the velocities of the two waves in terms of the three principal strains in the medium. In 1853, Maxwell presented a theory in which the velocities were related to the principal stresses. Both these theories produced relations of precisely similar form and were equally applicable to an isotropic linear and elastic material under any system of combined stress.

The first numerical determinations of the stress-optical coefficients of several materials were made by Wertheim in 1854, followed by Mach in 1872 and Kerr in 1888. More accurate determinations were made by Pockets in 1902 and between 1902 and 1912 by Filon. Mesnager in 1912 carried out the most successful of the attempts to determine the stresses in an actual engineering structure by using the photoelastic effect in a glass model of a bridge. In 1911, Coker discovered xylonite an alternative photoelastic material to glass and began an extensive series of investigations into the stress-distribution in various engineering components. During the first quarter of the twentieth century, Coker and Filon met together and while working at the Cambridge University, made a break through by using the recently developed transparent plastic, for photoelasticity. By 1935, the photoelastic method has reached within the range of ordinary stress analysis laboratories. During this period various investigations on similar lines were being carried out by Baud and Heymans in U.S.A., Mesnager in France, Schultz in Germany and Tuzi in Japan.

Natural Double Refraction

When a ray of light is incident on certain crystals like Calcite or Iceland spar, it is split at entry into two components which in general are transmitted through the crystal in different directions with different velocities. This phenomenon is known as natural double refraction or birefringence. One of the rays is called the ordinary ray, which is not deviated and the other the extraordinary ray, which deviated from the original path. If the emergent rays are observed through an analyzer, it is found that they are plane-polarized in mutually perpendicular planes.

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Any line which is equally inclined to the concurring edges at the two obtuse corners of the crystal is defined as the optic axis of the crystal. A plane normal to the optic axis is called the equatorial plane. Crystals having only one optic axis are called uniaxial crystals. Many crystals have two optic axes and as such are known as biaxial crystals.

Now refractive index

where i = angle of incidence R = angle of refraction

According to Brewster’s law of polarization

n = tan iHence i + R = 90

which is the necessary condition for polarization by refraction.

The angle of incidence i corresponding to an angle of refraction R = 90 is defined as the critical angle. It is the limiting angle of incidence for which refraction will occur. Hence, the critical angle,

ic = sin-1 n

Production of Plane-Polarised Light

The following methods may be used to produce plane-polarized light:

1. Blackened glass plate. By reflecting a ray of light from a blackened glass plate upon its rear surface, plane polarized light may be produced. The angle of incidence i for glass is 57 for polarization.

2. Pile of plates. If ordinary light is made to pass through a pack of eight or ten thin plates of glass, it will emerge nearly completely polarized and the intensities of refracted and reflected beams will be nearly equal.

3. Calcite Crystal. Iceland spar or Calcite is a rhombohedral crystal bounded by six parallelograms, the angles of which are 101 - 55’ and 78 - 5’ respectively (Fig). Solid angles at A and C are all obtuse and remaining six angles are bounded by one obtuse and two acute angle. The critical angle for Iceland is 69-57’.

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Figure: Iceland spar crystal4. The Nicol Prism. This is also made out of Iceland spar crystal whose natural angle

of 19 is increased to 22 by grinding. Then the crystal is cut along a diagonal plane AC and cemented by Canada balsam after polishing (Figure).For ordinary ray,

1.65 = or sin = 0.227or 13-8’ hence R0 = 90 - (13 - 8’)

= (76 - 52’) > (ic = 69 - 57’)

Therefore, the ordinary ray is totally reflected and is absorbed by black paint on the long surface of Nicol. Extraordinary ray however passes through Canada balsam and is transmitted with no loss in intensity.

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Figure: Nicol Prism

5. The Glan Thompson Polarizer. It is made of calcite and its transparent faces are perpendicular to its axis (Fig). It is free from lateral displacement of the rays. The transmitted waves are parallel to the plane of the interface and the transmissibility is 40 percent

Figure: Glan-Thompson polarizer

6. Ahrens Polarizer. This is essentially a double Glan-Thompson prism in which, however, the ordinary ray is not stopped but emerges from the prism and is eliminated by being diverted out of the regular cone of polarized rays. It has no lateral displacement.

Temporary Double Refraction

Many transparent non-crystalline materials that are optically isotropic when free stress become optically anisotropic and display characteristic similar to crystals when they are stressed. These characteristics persist while loads on the material are maintained but disappear when the loads are removed. This behavior is known as temporary or artificial double refraction. This phenomenon was observed by Sir David Brewster in 1816 and the method of photoelasticity is based on this physical characteristic of transparent noncrystalline materials.

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Since the state of stress at a point can be represented by a stress ellipsoid or the ellipsoid of Lame, likewise, the optical anisotropy (temporary double refraction) which develops in a material as a result of stress can also be represented by an ellipsoid, known as the index ellipsoid. The similarity between these two ellipsoids suggests the presence of a relationship between stresses and indices of refraction, known as the stress-optic law.

Stress-Optic Law

Maxwell reported in 1853 that the changes in the indices of refraction were linearly proportional to the loads (thus to the stresses or strains for a linearly elastic material) and followed the relationship:

where 1, 2, 3 = principal stresses at the point

n0 = index of refraction of material in the unstressed state. n1, n2, n3= principal refractive indices of the material in the stressed state associated with the

principal stresses, 1, 2 and 3 respectively. C1, C2 = stress-optic coefficients, which depend on the material.

Equations are the fundamental relationships between stress and optical effect and are known as the stress-optic law.

Eliminating n0 from equations, we get

where C = C2 – C1 is the relative or differential stress-optic coefficient expressed in terms of Brewster’s (1 Brewster = 10-12 cm2/dyn = 10-12 m2/N).

Now the wave equation is,

Angular phase shift between two waves,

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= 2 - 1

Since the stressed photoelastic models behaves like temporary wave plate, hence

Therefore, if a beam of plane-polarized light is passed through a slice of thickness h at normal incidence, the relative retardation accumulated along each of the principal stress directions becomes

where 12, 23, 31 is the magnitude of the relative retardation developed between components of light beam propagating in the 3, 1, 2 directions respectively.

For two-dimensional or plane-stress problems (3 = 0) and we get

=

or 1 - 2 =

where N =

is the relative retardation in terms of a complete cycle of retardation and is termed the fringe order.

is a property of the model material for a given wavelength of light and is called the material fringe value in terms of normal stress and h is the model thickness.

Equation may be written as

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where f is the material fringe value in terms of shear and is equal to one-half of f.

For a perfectly linear photoelastic material,

Thus

Equation becomes

or

where

is called the material fringe value in terms of strain equation can also be written as

1 - 2 = NF

where is the model fringe value in terms of strain.

Equation states that in a transparent and isotropic model in which the stresses are two-dimensional, the angular phase difference between the two rectangular wave components travelling through the model is directly proportional to the difference of the principal stresses.

At those points in a stressed model where 1 = 2, the fringe order is zero and permanent black dots appear at these points. Such points are called isotropic points. If 1 = 2 = 0 then also the fringe order is zero at these points and permanent black dots appear. Such points are called singular points.

Basic Elements of a Polariscope

The polariscope is an optical instrument containing polaroids that utilizes the properties of polarized light in its operation. For photoelastic investigations two types of

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polariscopes are used:

1. Plane polariscope2. Circular polariscope.

In the plane polariscope, plane-polarized light is used and in the circular polariscope, circularly polarized light is used. When the light is transmitted through the model then the polariscope is called of the transmission type. The polariscope may also be either of the lens type or diffused light type.

Plane polariscope

The basic arrangement of a lens type plane polariscope is shown in figure shows the set up for a diffused light polariscope.

Figure: Lens type plane polariscope.

Figure: Diffused light plane polariscope.

The light source may be a mercury or a sodium vapour lamp, an incandescent filament lamp or a bank of bulbs. Mercury or sodium vapour lamps are used as monochromatic light sources and incandescent filament lamp is used as a white light source, for the lens type in an opaque box with a ground glass on one side to give diffused light. The

filter F is generally a Wratten filter No. 77 to give a particular wavelength of 5461 (green)

or 5893 (yellow).

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The first field lens (FL1) gives a parallel beam of light in the field of view.

The function of the polarizer (P) is to produce plane-polarized light. Polarizers are now-a-days made from thin sheets of Polaroid.

The model M made out of a photoelastic material is loaded in a loading frame by which various types of loads can be applied. The load is applied either by means of dead weight through a level or by means of a screw and measured by a spring balance.

The analyzer (A) is similar to the polarizer and is used to combine the two beams coming from the model. The polarizer and analyzer are generally coupled together by a flexible coupling to achieve their simultaneous rotation.

The second field lens (FL2) is used to make the parallel beam of light converse on the projection lens (PL), which finally projects the interference fringes onto the screen or camera (C). The aperture of the projection lens may be controlled to obtain a part or full view of the model.

Two types of set up are possible with the plane polariscope, i.e. bright, when polarizer and analyzer are parallel and dark when polarizer and analyzer are crossed.

Circular polariscope

In addition to all the elements of a plane polariscope, the circular polariscope has two more quarter wave plates (QWP), the first between the polarizer and model and the second between the model and the analyzer as shown in figure. The fast and slow axes of the QWP’s are inclined at 45 with the polarizer or the analyzer. The QWP’s are made of Polaroid film and produces a path difference of /4 or a phase difference of 90 in the two light vectors passing through them. Four different set ups are possible with the circular polariscope as depicted below:

Set up Polarizer-Analyzer Quarter-wave plates Field

1 Crossed Parallel Bright2 Crossed Crossed Dark3 Parallel Crossed Bright4 Parallel Parallel Dark

The crossed-crossed set up is called the standard set up of the circular polariscope. The first QWP converts plane polarized light into circularly polarized light and the second QWP converts circularly polarized light into plane polarized light.

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Figure:

Figure:(B) Circular Polariscope

The diffused light plane polariscope can be easily converted into a circular polariscope by interposing two QWP’s as done for the lens polariscope. Diffused light polariscope is generally used for preliminary or rough work and lens type polariscope is used for more accurate work.

Effect of a Stressed Model in a Plane Polariscope

Dark-Field set up

Consider the dark-field set up of the plane polariscope (Fig) when the polarizer and analyzer are crossed. The plane polarized light beam emerging from the polarizer can be represented by

E = cos wt

The light vector on entering the two dimensional stressed model will be decomposed into two vectors along the two principal directions, one along the fast (or 1) axis and the other along the slow (or 2) axis. Light vector (electric) along the fast axis on entering the model

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E1e = cos wt cos ,

and along the slow axis

E2e = cos wt sin

where is the angle between the axis of polarizer and maximum principal stress 1 and the subscript ‘e’ stands for entering.

Figure: Effects of a stressed model in a plane polariscope

Since the light vector E1e travels faster than E2e, therefore, on emerging out from the model they develop a phase difference. Hence the light vector leaving along the fast axis of the model E1l and falling on the analyzer becomes,

Whereas the light vector leaving along the slow axis of the model and falling on the analyzer will be given by

where the subscript l stands for leaving.

Since the axis of the analyzer is oriented at right angles to that of the polarizer, the light vector transmitted through the analyzer is

Intensity of light I is proportional to the square of the amplitude Et. Hence

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where I0 = maximum transmitted light intensity.

Light intensity I will be zero or extinction can be obtained in the following three ways:

(a) Effect of frequency

When

Then sin2 = 0 and I = 0.

However, the circular frequency for light in the visible spectrum is approximately 1015 rad/s and neither the eye nor any type of existing high speed photographic film can detect the periodic extinction associated with the t term and thus this factor can be ignored.

Hence we are left with

(b) Effect of principal stress directions.

When 2 = n, n = 0, 1, 2, …… sin2 2 = 0 and I = 0

Therefore, when one of the principal stress directions coincides with the axis of the polarizer, extinction occurs. When the entire model is viewed in the polariscope, a fringe pattern is observed; the fringes are loci of points were the principal stress directions coincide with the axis of the polarizer. The fringe pattern formed by the sin2 2 term is known as the isoclinic fringe pattern. These are the loci of points having constant stress directions. The isoclinic fringe patterns are employed to determine the principal stress directions in the in photoelastic model.

(c) Effect of principal stress difference.

When = 0

and extinction occurs. Therefore, when the principal stress difference is either zero (n = 0) or sufficient to produce an integral number of wavelengths of retardation (n = 1, 2, 3….), extinction occurs. When a complete model is viewed in the polariscope a fringe pattern is observed which are the loci of points exhibiting the same order of extinction (n = 0, 1, 2, 3,

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…). The fringe pattern produced by the sin2 term is known as the isochromatic (same colour) fringe pattern.

Now

Hence

or n = N =

when a model is viewed with white light the isochromatic fringe pattern appears as a series of coloured bands. Thus we find that in a plane polariscope the isoclinic and isochromatic fringe pattern are obtained, superimposed on each other.

Bright-Field set up

In the bright-field set up the axis of the analyzer is parallel to that of the polarizer. Hence

I = 0 when sin2 /2 sin2 2 = 1 or the intensity I is maximum when sin2 /2 sin2 2 = 0. Therefore, the conditions for maximum intensity of the transmitted light are now the same as those for extinction for the dark field set up.

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Effect of a Stressed Model in a Circular Polariscope

Dark-field set up

Consider the standard set up (crossed-crossed) of the circular polariscope as shown in figure. The light vector leaving the polarizer can be written as

E = cos t

Components of light vector on entering the first QWP become

The first QWP produces a phase deference of /2 and converts plane polarized light into circularly polarized light. Components of light vector on leaving the first QWP become

If the principal axes of the model are inclined at angle with the axis of the first QWP, the components of light vector along the principal axis of the model on entering are

The model introduces a phase difference of. Therefore, the components of light vector on leaving the model and entering the second QWP become,

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The second QWP also produces a phase difference of /2. Therefore, the components of light vector on leaving the second QWP and entering the analyzer become

Figure: Effect of a stressed model in a standard circular polariscope

The resultant light vector transmitted through the crossed analyzer become,

Intensity of light I E2. Hence

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I = 0, i.e., extinction can be obtained in two ways.

(a) Effect of frequency

When

then

Hence I = 0.

But the frequency is very high and any extinction produced by it cannot be detected by eye or any photographic equipment. Hence the isoclinics are automatically eliminated. Thus

(b) Effect of stress difference.

When = n, n = 0, , 2,….

Then sin2 = 0

and I = 0

This type of extinction is identical with that for the plane polariscope and referred to as isochromatic fringe pattern.

Fractional Fringe Order Determination

We can determine the isochromatic fringe order to the nearest order by using both the dark and bright-field arrangements of a polariscope. Further improvements on the

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accuracy of the fringe order determination can be achieved either by using the mixed-field patterns or by using Post’s fringe multiplication method. In order to achieve higher accuracy, as is desirable in many applications, the following methods may be used:

1. Compensation techniques2. Colour matching techniques3. Equidensometry method

Compensation Techniques

Compensation is a technique in which partial modification of relative retardation either by addition or subtraction is brought about so that the fractional fringe order at a point become integral. Then by knowing the amount of relative retardation added or substracted the actual fringe order at that point can be ascertained. The following methods for compensation techniques are most commonly used:

1. The Babinet compensation method.2. The Babinet Soleil compensation method.3. Tension or compression strip method.4. Tardy method of compensation.5. Senarmont method of compensation6. Photometric method.

1. The Babinet Compensation Method. The Babinet compensator uses two wedges of quarts, which is a naturally double refracting material. As shown in Figure, one of the wedges is fixed in the instrument, while the other can be displaced relative to the first so as to alter combined thickness by means of a fine micrometer screw with graduated drum head. With micrometer screw at zero, the compensator is said to be in the neutral position. The compensator is placed in the polariscope in between the model and second quarter wave plate. The optic axis of the two wedges are orthogonal to each other. The polarized light beam in one and retarded in the other wedge.

The relative retardation R produced when the two wedges have been displaced from their neutral position is given by,

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Figure: The Babinet Compensator

where K = n1 – n2

= angle of wedge 2.5x = horizontal displacement, which is equal to the micrometer reading

or R = = C. x

where C =

thus R =

The Babinet compensator allows fringe orders, to be determined to within 0.01 fringe.

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2. The Babinet Soleil Compensation Method. The Babinet-Soleil compensator shown in figure is an improvement upon the Babinet compensator. This instrument consists of a quartz plate of uniform thickness and two quartz wedges. The optical axes of the quartz crystals employed in the plate and the wedges are mutually orthogonal. The birefringence exhibited by the compensator can be controlled by adjusting the thickness of the two wedges by turning a calibrated micrometer screw. When t1 = t2, no relative retardation takes place, however for

, both positive and negative retardation can be produced over the whole area of the compensator plate. This compensator is very useful for measuring boundary stresses.

Figure: The Babinet-Soleil Compensator.

In practice, a point is selected on the model where the fringe order is to be established precisely. Then isoclinic parameters are established for this point to give the direction to either 1 or 2. The compensator is then aligned with the principal stress direction and adjusted to cancel out the model retardation. The reading of the screw micrometer is proportional to the fringe order at that point. Like this fringe order at a point can be ascertained to within 0.001 fringe.

3. Tension or Compression Strip Method. In a standard circular polariscope, at an isotropic point the fringe order is always zero. Based upon this fact a method for the determination of (1 - 2) has been suggested by Wetheim and developed by Coker. In this method a pure tensile or compressive stress is superimposed over an arbitrary system of 1

and 2 in such a way as to convert the given stress system into one which is optically equivalent to an isotropic point. White light is exclusively used in this method.

Figure shows how the plane stress system at a point can be converted to an isotropic system plus a tension of (1 - 2). A tension compensator may be placed parallel to the minimum stress 2 and the compression compensator must be placed parallel to the maximum stress 1. The value of (1 - 3) equals numerically the stress in the compensator at extinction. If the fringe order at a point by placing a tension compensator increases, then

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that point is having tensile stress.

Figure: Superposition of retardation exhibited by model and compensator

4. The Tardy Method of Compensation. The Tardy method of compensator is generally preferred over the Babinet-Soleil method since no auxiliary equipment is required and the analyzer of the polariscope serves as the compensator. In this method the polarizer of the polariscope is aligned with the direction of the principal stress 1 at the point of interest and all other elements of the polariscope are rotated relative to the polarizer so that a standard dark-field polariscope exists. Then the analyzer alone is rotated to obtain extinction. The rotation of the analyzer gives the fractional fringe order.

As shown in Figure, here = -/4 and the light vector emerging out from the second QWP becomes (see Art).

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Figure: The Tardy compensation method.

Let be the angle through which analyzer should be rotated to obtain extinction, i.e. E t = 0, then

Simplifying, we get

Hence

or

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or

or

If the analyzer is rotated in the opposite direction then

N = (n + 1) -

Thus the Tardy method of compensation can be accomplished in the following way:

1. Using a plane-polariscope set up, determine the principal stress directions at the point of interest by rotating the crossed polarizer and analyzer until an isoclinic passes through that point.

2. Now rotate only the quarter wave plates of a circular polariscope to obtain a standard dark-field arrangement.

3. Rotate only the analyzer then until an isochromatic fringe coincides with the point. Determine the angle that the analyzer has rotated.

4. If the Nth order fringe moves to the point as the analyzer rotates through the angle , the fringe order N0 at the point is

If the (N + 1)st order fringe moves to the point as the analyzer rotates through the angle , the fringe order N0 at the point is

To account for the finite fringe width, the following procedure, as illustrated in fig, may be followed:

1. The angle of analyzed ra = 0 [Fig (a)].2. Rotate the analyzer until the fringe N just touches the boundary at the point of

interest. This is angle rb. [Fig (b)].

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Figure: Illustration of Tardy method of fringe order determination.

3. Continue to rotate the analyzer until N vanishes from the field of view. This is angle rc [Fig.]

Then the fringe order at the point of interest of the free boundary is

This method is commonly referred to as the Tardy in-out method.

5. The Senarmont Method of Compensation.

(Friedel’s Method)

The following steps are involved for this method:

1. Remove first quarter wave plate.2. Rotate system of polarizer and analyzer so that their axes make angles of 45 with the

principal directions in the modal at the point of interest.3. Rotate second quarter-wave plate until one axis is parallel to the axis of the polarizer.4. Rotate the analyzer until extinction is obtained at the point of interest.

The arrangements of the elements of the polariscope are shown in Fig.

Let the light vector from the polarizer be given by

E = a cos t

Since the polarizer is set as 45 to the principal directions in the model hence on entering the model the light vector is resolved into two components, given by

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The model introduces a phase different of . Therefore, on leaving the model, the components of light vector become,

The fast axis of the QWP is set at 90 to the polarizer axis. Hence on entering the QWP, the light components become

Figure: Senarmont compensation method

The QWP introduces a phase difference of /2. Hence on leaving the QWP , the light vectors become,

Now the analyzer is rotated through an angle to obtain extinction at the point of interest.

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Light transmitted through the analyzer is

Hence sin cos + cos sin = 0

or f

Tardy and Senarmont compensation methods are called the ‘goniometric’ or ‘null location’ methods.

Three-dimensional Photoelasticity

Introduction

Many stress analysis problems are three-dimensional in nature for which the two-dimensional photoelastic method cannot be employed. These problems, however, can be solved either by locking in the stresses in the model or a multilayer reflection technique may be used to determine the stresses at the inner layers of the body. Three-dimensional stress distribution in the body can also be determined by the scattered light method. In this chapter we shall discuss the locking-in method the stresses in three-dimensional models in detail and the multilayer reflection technique in brief.

The stresses in a three-dimensional model can be locked-in either by stress-freezing, by curing method, by creep method or by gamma-ray irradiation method. Out of these methods, the stress-freezing method is most widely used. This method consists in loading the model at room temperature (at which the primary secondary bonds break down), keeping at that temperature for few hours and then cooling to room temperature at a slow rate. The stresses thus frozen in the model can be analyzed by slicing and viewing in a polariscope.

Maxwell in 1853, and Filon and Harris in 1923 had both obtained the stress-frozen effect accidentally, while Tuzi in 1927 and Solakian in 1935 both attempted to calculate the residual stresses and to relate them to the applied loads. None of these, however, fully

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appreciated the significance of the phenomenon, and it was Solakian who in 1935 and Oppel in 1936 first produced a quantitative solution of a three dimensional problem, followed by He’tenyi, who in 1938 first established the strict proportionality of stresses. This discovery opened the way to the complete solution of the three-dimensional problems and resulted in a very sharp increases in activity in photoelastic research. Hetenyi, O’ Rourke, Drucker and Mindlin, Drucker and Woodward, Frocht and Mindlin developed methods of measurement of the frozen stresses and Jessop in 1949 devised integration methods for determining the separate stresses. Jessop and Stableford in 1953 published an extension to three dimensions of the Lame-Maxwell equations, which made it possible to determine the principal stresses along a stress trajectory in a plane of symmetry. The stress-freezing method of three-dimensional photoelasticity today is a practical instrument of stress analysis, particularly in complex structures.

UNIT V Non – Destructive Testing

Fundamentals of NDTRadiographyUltrasonicMagnetic particle inspectionFluorescent penetrant techniqueEddy current testingAcoustic Emission TechniqueFundamentals of brittle coating methods.

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UNIT – V

NON-DESTRUCTIVE TESTING (NDT)

Introduction

The non-Destructive Testing (NDT) techniques include inspection, detection and measurement of the parameters of any material, component of an assembly, without altering any of its property of affecting its serviceability. In other words, the NDT techniques indicate directly the ‘State of health’ of the system without interfering, in any way, with the working of he system i.e., without causing any damage or destruction of the object under test. Consequently, the awareness and the use of the NDT instrumentation is continually increasing because of its ability to demonstrate the integrity and reliability of the components and the operating systems. This thereby enhances the safety of the personnel involved int eh use of materials and products and also ensures efficient operations of plants and machinery. A lot of progress has been made in the recent years in their NDT techniques by application of microelectronics, signal processing methods and computer processing of data. In addition, the use of Artifical Intelligence (AI) techniques have resulted into implementation of smart and automated types of NDT procedures. The following are some of the salient features of the NDT techniques:

1. These techniques are quite simple and generally, do not require very skilled opera-tions.

2. They are economical, both in time as well as money spent.3. They ensure efficient material manufacturing, improved quality assurance, enhanced

safety in plane operations and increased reliability and availability of products and services.

4. These techniques are suitable for both on-site and in-service testing of large number of industrial systems/ components. Common examples are detection of flaws in oil and gas pipelines, bridges and tall structures, pressure vessels of power plants and nu-clear plants, aircraft and refinery installation, etc.

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5. These techniques can detect the onset of deterioration in the working of a plant or a system and this way they provide sufficient advance warning for the repair or replace-ment of the failure-prone components/ systems

However, non-destructive techniques the following limitations that must be taken into account whenever these methods are used for the inspection/testing of the equipment.

1. Tests often involve indirect measurement of properties with no dire3ct significance in serviceability. Consequently, correlation between these measurements and serviceability sometimes may result in somewhat sub-optimal plant operations.

2. Tests are often qualitative in nature rather than quantitative. They do not usually mea-sure life to failure. Therefore, they usually reveal only the type of damage or expose the mechanism of failure.

3. Tests usually require skilled judgment and service experience to interpret the NDT data correctly. Hence, where correlations have not been proved or where experience happens to be limited, observers may quite often disagree in evaluating the significance of the test results.

Types of Defects Detected by NDT Techniques

The types of defects detected by the various NDT techniques can be categorized into the following three categories:

(a) Inherent defects: These defects generally get introduce during the various production stages of the raw materials. The commonly observed defects of the is type are for ex-ample, segregations inclusion, porosity , cavities, voids, surface and sub-surface cracks.

(b) Processing defects: These defects creep in during the various processing stages of the components/systems. Common examples are:

Surface and sub-surface cracks may be developed during the mechanical, ther-mal/heat treatment processes.

Lack of penetration of weld materials may result in improper weldment. Porosity may be caused by a poor plating procedure. Shrinkage and porosity defects may be introduced due to poor quality of cast-

ing. Laps and folds may be formed in a typical forging process.

(c) Service defects: These defects get produced during the operating life of the compo-nents/ systems. Some common examples re defects such as surface and sub-surface cracks caused due to fatigue, stress corrosion, hydrogen imbrittlement, intergranular corrosion, pitting etc.

Types of Non-Destructive Techniques

A number of NDT techniques are available and the selection of a particular test method depends on its suitability for a given situation and the experience of the test personnel. Generally, these test techniques are classified in two broad categories. The first types are surface inspection/test techniques, which are primarily suitable for the examination

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of the flaws on the surface of the internal features of the materials. Visual inspection, physical inspection, dye penetration, magnetic flux and eddy current techniques belongs to the first category, where ultrasonic and radiographic techniques fall in the second category.

Visual (Microscopic) Examination Technique

This technique is very widely used in the industry. Almost all the manufactured/ assembled components/assemblies are initially visually inspected for ensuring good surface finish, uniformity in texture and freedom from surface defects. In many cases, defects are visible to the naked eye on the surface of the components. Sometimes visual optical methods may be employed to facilitate convenient viewing of the surface defects by providing high-resolution type of illuminated optical magnifiers. i.e., an optical microscope. Herein, the magnification ranging from 1X to about 100x is employed. This technique enables to observe the gross features of fracture, the presence or absence of cracks and the presence of any gross defect or any corrosion or oxidation defects. During visual examination of failures, we sometimes come across a fracture which is heavily corroded and oxidized type. This indicates that a crack existed for a longtime, finally propagating to failure.

For the periodic or troubleshooting inspections of the difficult and inaccessible areas in boilers, heat exchangers, turbines and for hazardous locations like nuclear or offshore locatins, devices like light pipes which are known as optical fibers are commonly used. Optical fibers are flexible type of fine strands of glass, fused silica, or plastic that are capable of transmitting light radiation at considerable distances (several hundreds of meters or more). The diameter of optical fibers ranges from 0.05 m to as large as 0.6 cm. for the transmission of images, bundles of fibers fused at the ends are employed with a provision of focus control. Such a device is known as high resolution type ‘Flexible Fibroscope’ (FF). The other major application of NDT technique using FF is in the area of medical diagnosis where the flexibility of the fiber permits transmission of images of organs through tortuous pathways to the physician. Light pipes are used only for observation but also for illumination of objects. Herein, the ability to illuminate the objects under study without heating is often of considerable importance. Sometimes the miniature television cameras that are coupled with video recorders can be used for recording of inspection results after the test.

The main advantages of the visual examination techniques are:

1. Low cost and economic in operation2. Its suitability while the work is in progress, 3. Capability of early detection/correction of the system detects.4. Timely indication of the incorrect procedures5. Early warning about the faults when the system in use

However, this method has a limitation that it can be applied only to detect the defects on the surfaces of the objects or through the surface openings or in the transparent materials.

Physical Inspection Techniques

‘Hammer Testing’ and ‘Fluid Pressure Testing’ are the ‘Physical Inspection Techniques’.

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Hammer Testing is an old technique in which the inspector often determines the integrity of pipes and vessels by the quality of he metallic ringing sound obtained when struck with a light-Weight hammer. Basically this technique is used to provide quick indications of the areas that require more thorough inspection by a more accurate technique.

On the other hand, in the ‘Fluid Pressure Testing’ technique, the defects are revealed by the flow of a gas or a liquid into or through the defects. Herein, the simplest and most commonly used procedure is a ‘Hydrostatic Pressure Test’. In this case, a liquid, usually water, is used to build up the pressure within a system. The presence of leaks due to defects is indicated by a drop in the pressure or seepage/weeping of the liquid. This traditional NDT method is suitable for revealing only larger defects, such as centerline cracks in welds or pinholes, etc. further, it may be noted that ‘Hydrostatic Pressure Testing’ is quite often mandatory for very high-pressure pipe lines, seamless type of high-pressure gas cylinders, high pressure boiler components, etc.

Gas (usually air) pressure testing is often used on welded vessels or welded transfer lines. The system is pressurized and leaks due to defects are indicates by changes in pressure. Sometimes the leaks are located by means of soap solutions applied to the outside of welds. Techniques based on pressuring with helium, halogens or radioactive materials are commonly used in refinery inspection work for leak detection of hydrocarbons and other inflammable gases. However, caution must be employed in pneumatic testing since failures resulting from such tests are usually more catastrophic than those that occur hydrostatic tests due to the compressible nature of the gases.

Dye Penetrant Method

Sometimes the surface defects are not immediately apparent during the visual inspection. Their presence can be enhanced by the use of colored or fluorescent type of dye penetrants. The test surface is first cleaned and dried and then a liquid containing penetrating dye is applied on the material surface. The dye is generally either bright red type, which is observable in white light, or fluorescent type, which is visible under ultraviolet light. Due to the wetting and surface tension properties of the liquids, the liquid penetrates into the find openings like cavities, cracks and discontinuities’, due to the capillary action. The liquid is allowed to penetrate for sometimes, say 10-15 min or so, which is known as the “Dwell” time of the dye penetrant. After that the excess penetrant is removed by washing and a developing agent is applied over the surface. The penetrant remaining in the discontinuities is drawn by the blotting action of the developer. This will cause a stain on the developer to form a visible indication on the edges of the discontinuity/crack. This way it highlights the apparent width of the crack. The steps followed in the dye penetrant technique are shown in figure.

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Procedure in dye penetrant technique for the surface crack inspections.

After the dye penetrant surface has been developed, it is examined visually for detection of the flaw under good white light. Further, the dye penetrants of the fluorescent type are examined in ultraviolent light.

The main advantages of the dye penetrant examination technique are:

1. It is simple technique , which is fast as well as economical.2. It is sensitive to small surface flaws.3. It is applicable to components of all size.4. It is applicable to all types of materials i.e. metallic or non-metallic

The major limitation of this technique is that it can detect flaws that are open to the surface and further, the depth of the defect cannot be determined. In addition, it is not helpful in case of the porous type of materials.

This technique finds wide application in the testing of turbine blades for cracks and porosity.

Magnetic Flux Method

When the material under test is of ferromagnetic type, then the test piece can be magnetized conveniently by means of an electric coil. Below the magnetic saturation level, the magnetic flux lines tend to confine within the material surface. A discontinuity, surface or near-surface crack or non-metallic inclusion in the test sample causes distortion in the magnetic flux lines due to the difference in the permeability between the map and the ferromagnetic material surrounding it. If the discontinutity is at or on the surface of the test piece, the field distortion produces a leakage of flux directly above the discontinuity. The flaw (for example, a crack) becomes visible by sprinkling of finely divided magnetic particles (generally ferric oxide, either dry or suspended in liquid) which concentrate on the site around which the flux leakage has occurred. Further, the addition of the fluorescent dye enables the indication of the crack to be easily seen under ultraviolet light. Further, the orientation of the discontinuity in a magnetized object is a major factor in the strength of the leakage field that is formed. This applies to both the surface and the internal discontinuities. The strongest leakage field is formed when the discontinuity is perpendicular to the magnetic flux flow. If the discontinuity is not perpendicular, the strength of the leakage field is

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reduced to a large extent when the discontinuity is parallel to the magnetic flux lines. Figure illustrates the effects of the orientation of discontinuities on the strength of the magnetic leakage field.

The main advantages of this technique are its low cost, simplicity and reliability in finding the surface or near-surface cracks in ferromagnetic materials of any size and shape. The indication of the defect is produced directly on the object and non auxillary read-out devices are required. In fact, this technique can be learned easily without lengthy or highly technical instructions. This technique is usually adapted to production line usage as it is capable of detecting on-line the discontinuities, which are filled with non-permeable foreign materials.

The main disadvantages of this technique is that it is applicable only to ferromagnetic materials. Further sometimes excessively high currents may be required for inspecting large or heavy sections, and in such cases, extreme care is necessary to avoid heating and/or burning of highly finished surfaces. Lastly, post-inspection demagnetization of the test sample may be required. In addition, surface irregularities and scratches can also give misleading indication. Therefore, it is necessary to ensure careful preparation of the surface before magnetic particle testing is undertaken.

The applications of this technique are inspection of incoming materials, during process and at final stage as well as during the maintenance period. In addition, this technique is also used in the inspection of castings, forgings, rolled products and welded joints.

(a) Surface defect perpendicular to the magnetic flux lines

(b) Surface defect inclined to the magnetic flux lines

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(c) Surface defect parallel to the magnetic flux lines

Eddy Current Method:

This technique employs electromagnetism principle for accessing the material properties as well as the presence of defects in the materials, which are electrically conducting in nature. In this technique, a time-varying magnetic field is produced in the probe, which consists of a coil. Herein, a probe consisting of an energized coil with a high excitation frequency, usually in the range of 100 kHz to 10 MH, is brought near the surface of the component under test. The probe induces weak electrical currents in the test sample which are sensitive to the test material conductivity and permeability. The changes in the conductivity of the material are caused by the changes in the material composition as well as the structural changes like crystal imperfection caused by voids, stress conditions or work hardening, etc. Further presence of any discontinuity in the form of crack, etc, would disturb the eddy current flow patterns and would in turn cause changes in the permeability of the test sample.

The eddy current probe, which has an ac current excitation, produces an ac magnetic field within the materials. This is turn produces eddy currents in the material, which have its own magnetic field. This eddy current generated magnetic field cuts across the coil of the probe and induces a small current to flow through the coil in a direction opposite to that of the applied current, thus weakening the applied current. This weakening in current is caused by the change n the inductive component (due to the change in the permeability produced due to the presence of a crack, etc.) as well as in the resistive component (due to changes in the composition/ structural changes, etc). of the coil. This in turn is related to the eddy current loses. It may be emphasized again that the conductivity changes are reflected in the changes of coil resistance where the permeability changes affect the coil inductance. We normally begin flaw detection by calibration the equipment. This simply means that we make our instrument insensitive to conductivity by setting a Wheatstone bridge circuit output as zero on its meter, using a known sound specimen made of the same material as the piece to be tested. The variation of the current in the test coil due to the change in its impedance caused by the presence of cracks. Etc. as well as changes in the composition/structure generates a deflection in the Wheatstone bridge circuit as shown in figure.

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Figure: A schematic diagram of the eddy current flaw detection method

The major advantages of this technique are that it is fast and it involves moderate cost. Further, it has the feasibility of very high rates of inspection. The inspection can be automated so that defective parts are identified by the test equipment. It is portable or semi-portable type. Lastly, it is free from the use of consumable material, personnel danger or hazard and contamination of parts.

The main disadvantage of this technique is that it is applicable only to electrically conductive materials and has limited penetration depth.

The applications of this technique are sorting of the components to ensure proper composition, heat treatment and hardness or dimensions, and the detection of surface or near surface defects during high-speed inspection of rods, bars, extruded tubing and welded tubing or pipes (especially, the heat exchanger tubes). This technique is also very useful in the measuring of the thickness of non-conducting coatings on metallic substrates and metallic sheet materials. In addition, this technique is used for the inspection of rods, bars, extruded tubes and spherical ball bearings for the detection of laps, seams, radial cracks, alloy and dimensional variations as well as non-uniformity of heat treatment,etc.

Ultrasonic Method

The ultrasonic method makes use of low-energy sound waves of short wavelengths(which are associated with high frequencies to measure wall thickness and also to detect defects in the materials. Ultrasonic waves are beamed into the test material and these are reflected back from the geometric boundaries as well as from the detect boundaries. Based on the time of reutnr of these echoes, metal thickness can be measured and also the location of the defects can be identified.

This NDT method employs the piezo-electric crystal type of transducer for the generation of sound signals of high frequency that is far in excess of the upper limit of audibility of the human ear, i.e. more than 20 kHz. The testing frequencies in this technique lie in the range of 0.5-2.5 MHz. When an oscillating voltage is applied to a piezo-electric crystal, it vibrates with the same frequency and vice versa. An ultrasonic flaw detector is shown in figure. The transmitter has a built-in pulse generator, which emits ultrasonic pulsed wave and this simultaneously triggers the transmitter transducer and the time base generator. Generally both the transmitter and the receiver are housed in a single probe. The pulse of the ultrasound generated from the transducer travels through the test specimen. When a flaw is encountered, a part of the ultrasound is reflected. The reflected sound travels back and reaches the receiver crystal, which converts it into electrical voltage. The voltage passing through the amplifier is fed to the CRT and a signal is observed on its screen. The CRT screen would display three

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echo signals, which are shown in the figure. These signals are namely, one from the top of the surface of the specimen, another from its bottom, and the third in between two which is known as the defect echo signal.

Fig(a) Schematic diagram of pulse-echo system (Transmitter- Receiver method) for detecting depth of flaw

(b) Typical display on CRT

Figure: A schematic diagram of ultrasonic flaw detection method

Ultrasonic technique is very widely used in the areas of detection, location and measurement of surface and internal voids such as cracks, slag inclusion, lamination, lack of fusion, lack of weld penetration, inclusions in welded and brazed structure, etc. In addition, it is employed in the determination of bond integrity of adhesive assemblies such as honeycomb and composite structures. The main advantages of this method are high sensitivity, fast response and its capability of automation. Further, very small defects and their sizes can be detected and their location can be determined accurately. In addition, this technique has great penetration power and defects up to 10 m thickness in steel can be inspected.

The limitation of this technique is that it requires coupling of the test material either by contact to the surface or immersion in a fluid such as water. Further, the micro-level defects of the order of half the wavelength of the ultrasonic beam cannot be detected by this method.

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The technique has been successfully employed in the studies of stress corrosion cracking and fatigue failure in aircraft structures, monitoring of flaws in the weldments, pressure vessels, railway rolling stock, gas turbine blades, etc.

X-ray/Radiographic Technique

In this technique, the objet is exposed to X –rays on one side and a sensitive photographic plate or film is placed on the other side of it. The intensity of the –rays is reduced by the passage through the material and also by the defects/ imperferctions that may be present in the material thickness and chemical composition of the X-rays is dependent on the change in density, material thickness and chemical composition of the material. More radiation would pass through the voids than through the surrounding area. The photographic film measures the amount of radiations absorbed by , or conversely, passed through the material under test. Darker spots due to increased radiation reaching the film would indicate voids or thinner section of materials. Thus the radiograph is really a shadowgraph. The darker areas on the film represent more penetrable and less denser areas of the sample. The radiograph is often used for the interpretation of the results.

The advantages of this technique are that it can be used for a wide range of materials and the exact nature of the defects can be determined from the visual images. Further, a permanent film is obtained which shown the defects in relation to significant features of the component. For example, defects in a weld such as cracks, porosity and lack of penetration have their distinct images and therefore, are easily recognizable. Furthermore, it is the best and the most reliable method for determining the extent of internal porosity in that part.

Figure: A schematic diagram of radiography techniqueThe main limitations of this technique are the need to incorporate safety measures as well

as to take proper precautions in respect of harmful radiations to the operating personnel. More over high investment in equipment and facilities are involved. Lastly radiography is inaccessible to detect small, tight, randomly oriented cracks.

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The radiography technique is applied for the inspection of the incoming material, manufactured components, final products and maintenance. Further, it is widely used for the inspection of castings for shrinkage, micro-shrinkage, gas pockets, inclusions and blowholes. In addition, it is also used in forging for tear, bursts, internal cracking, welded and brazed joints for porosity, lack of fusion and / or lack of penetration and the detection of the presence of the inclusions.

Acoustic Emission (AE) Monitoring Technique

The acoustic Emission (AE) monitoring technique is a highly sensitive type of Non-Destructive Technique for detecting a variety of defects and even the dynamic movement of defects like, for example, a typical initiation about the “State of Health” of the system on-line i.e., in the real time. This technique basically involves the analysis of sound signals emitted by the materials, structures or machines which are in use in the fully loaded working conditions. Further, these sound signals are typically in the range of 0.1-0.4 MHz and are beyond the range of human hearing.

Acoustic emissions are generated by high-frequency stress waves in solids which are caused by sudden defect-related movements in the stressed materials. For example, the initiation and growth of crack in a stressed material brings about rapid released of strain energy giving rise to stress induced acoustic waves. In the loaded materials, structures or machines. These waves radiate into the structures and are conveniently picked by a piezo-electric type of transducer in the form of acoustic emissions. If may be noted that the source of acoustic emission energy is the energy is the elastic stress field in the loaded machines/components. In other words, without stress in the material, there are no acoustic emissions. Hence, the acoustic emission inspection technique can be used only in the loaded structure, so structure, so that we have a stress field for the generation of stress waves caused due to the defect-related deformations.

The common sources of acoustic emissions due to system defects in the stressed fields are as follows:

Initiation and propagation of crack growth caused due to fatigue, creep or fatigue, creep or complex loading. Such a defect causes slippage/sudden changes in the orientation of grain boundaries leading to large plastic deformations.

Large plastic deformation caused by impact loads, shock waves caused by explosions or sudden loading on fluid flow structures due to water hammer phenomenon caused by the sudden closure of calves.

Turbulence noise caused in fluid flow leakages past gaskets, valves, screwed fittings or hogh-pressure vessels developing cracks.

Cavitation phenomenon in hydraulic machines or stalling and surge phenomenon in aero-compressors.

Chatter phenomenon caused by loose parts like mismatched gears or loose particles in the loaded machines like a broken ball debris in the ball bearings.

Material property changes due to corrosion, chemical reactions, liquid-solid transformations or phase transformations.

The following ate the advantages of the AE inspection technique:

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1. The whole structure can be monitoring on-line (even at high temperatures) form few locations both reliably and economically and without taking it out of service. Further, continuous monitoring with suitable alarms I possible.

2. Microscopic changes in the defects can be detected as sufficient energy in the form of stress waves is released form the defect source.

3. The exact location of the defect can be location by using multiple sensors and employing triangulation technique.

4. The signature analysis of signal is employed to identify the nature and type of defects in the initial stages before they become serious. Thus appropriate corrective action can be taken at that stages, to reduces the growth of the that particular defect.

5. The evaluation of the nature, type and quantum of defect in AE inspection technique is based on the objective type of criteria based on the signature analysis of the defect signal. There-fore, it is less prone to subjectivity or operator’s interpretation as is common in the other NDT methods.

6. Acoustic emissions is a non-intrusive method and its piezo-electric transducer is also self-generation type i.e., it requires no external power supply as is the case in ultrasonics and radiography.

The following are the limitations of the AE inspection method:

1. Non-stressed areas in a test sample do not emit any AE signal. Therefore, acoustic emission test require an increase in stress during a test. Further, the test stresses must reach the maximum operating values and preferably stresses should be exceeding the maximum operating values so that stronger AE signals are generated by the defect-related stress waves in the test materials.

2. The AE signal for detecting a particular type of defects has cross-sensitivity to other defects simultaneously present in the stressed test sample, which constitute unwanted noise. For example AE monitoring technique when used for detecting cracks or corrosion would simultaneously pick up unwanted AE signals due to the presence of friction in some bearings as well as defects of loose parts like mismatched gears, etc. Therefore, precise discrimination of the information of the desired defects becomes feasible only after accounting for accounting for the effects of noise signals.

3. Background noise caused due to steam trap, flow in pumps, rain and wind blown cables striking the structures tend to obscure the genuine AE signals. In addition, radio and electro magnetic interferences may also introduce errors in the acoustic emissions.

AE signal processing parameters: The following arte the AE are the AE signal processing parameters of the signals of the test sample which are shown figure. These may be either of continuous type or may be in the form of discrete pluses or bursts.

(a) Peak Amplitude It is the highest value of the AE signal and is directly related to the magnitude of the source event.

(b) Ring Down Count (RDC) It is the number of times the AE signal crosses the threshold value. The threshold value is set t account for the

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background noise in the signal. RDC is obtained by incorporation a comparator circuit and pulse counter circuit in the AE signal. The value of this parameter is an indicator of the magnitude of the source event and the acoustical properties of the test sample.

(c) Integrated Event Energy Integrated energy is the area under the curve in the rectified signal envelope i. e. the energy associated with the ring down count. This parameter is dependent on the amplitude and duration of the defect in the test sample and is less dependent on the threshold settings.

(d) Event Duration It is the time elapsed form the first threshold crossing to the last. It is measured in micro-seconds. This parameter depends on the source magnitude, structural acoustics, etc.

(e) Rise Time: It represents the time duration from the first peak crossing to the signal peak. This depends on the dynamic characteristics between the source and the sensor

(f) Spectral Amplitude Analysis The frequency and amplitude count of the AE signal in the ultrasonic range i. e. between 0.1 and 0.4 MHz when considered along with other AE parameters identifies the type of defect and its severity/magnitude.

Fig:A typical acoustic emission signal showing the signal processing Parameters

Results of a study on the application of acoustic emission (A.E.) technique to new and old ball bearing of same size, are shown in figure. The plots in each case give distribution of A. E. event counts against peak amplitudes and A.E. even counts against ring down counts. It is seen that both peak amplitudes and ring down counts are in higher ranges for the old used bearings,

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(a) Plats of AE events against peak amplitude distribution

(b) Plots of AE events against ring down-count distribution

Acoustic emission studies on rolling bearings

Compared to those for new ones, even though the event counts are in the lower ranges for the formers cases of bearing viz. the old ones.

Applications of AE Monitoring Technique

The following are some of the proven applications where AE method is routinely used: Periodic and continuous monitoring of pressure vessels, oil pipelines and storage

vessels (both above and below the ground) to detect and locate active discontinuities. In service and on-line detection of initiation and propagation of fatigue cracks in the

rotating machinery, aerospace and engineering structures. Evaluation of material behaviour with respect to different types of failure

mechanisms. Monitoring of fusion or resistance weldments during welding and during the cooling

period. Detection of stress corrosion cracking and hydrogen embrittlement susceptibility of

test samples. Condition monitoring of machinery to detect faults like loss of lubrication, presence

of cavitation, bearing failure, seal failure, gear discontinuities etc. Detection of loose particles impact noise generated in the integrated circuits used for

critical applications. Detection of defects like cracking of fibers/matrix or delaminations between the fibre

and matrix in real time for providing indications of structural problems before a critical damage occurs.

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CONCLUDING REMARKS

The main purpose of non-destructive testing is to determine whether a material or a piece of equipment will satisfactorily perform its intended function. There, the driving force for the improvements and developments in the area of non-destructive testing techniques is continually increasing on order to ensure the integrity of the engineering materials, products and plants. Efficient material manufacture, the assurance of product quality and re-assurance of plant operation at regular intervals represents the salient contributions the non-destructive testing.

There is no universal non-destructive test applicable to all situations. Only through the under standing of the basic principles of each technique, one can specify the correct test. Hence, by carful consideration of the inspection problem and careful application of the correct non-destructive technique, it should be possible to determine the fitness of component/system to provide the desired service.

BRITTLE COATINGS

The brittle-coating or stress coat method is a qualitative whole-field technique where a brittle-lacquer is sprayed on the part to be analysed, dried overnight, then loaded in static, dynamic or impact mode. The brittle lacquer will crack perpendicular to the direction of maximum principal stress first, in the most highly stressed area. As the load increases the crack pattern enlarges as the coating the area of high stress becomes larger. By knowing the stresses in the coating the stresses in the coating the stresses is the specimen can be ascertained. Stresses to an accuracy of we shall study this method in detail.

The first brittle coatings to be employed were those coatings which naturally formed on structural members, such as mill scale on hot-rolled steel and oxides on heated surfaces. These brittle coatings failed by flaking or cracking when the base material yielded under load and excessive strains were produced. To improve the visibility of the crack patterns, the structural member were often coated coated with whitewash. The cracking and flaking of hr coating produced dark dark lines which were readily visible against the white back ground.

Brittle coatings have been used on plastics, wood, paper, rubber, glass, bones and metals to investigate stresses under static dynamic and impact loads. They have been used to test parts in the laboratory as well as out-of-doors under field conditions. Stresses around weldments, on pressure vessels, gas turbine blades, reactor head closure, and turbo-super charger impeller have been successfully analysed.

Types of Brittle Coatings

The following types of coating are available:

1. Resin based coating – ‘Stress Coat’. This consist of about one-third zine resinate as a base dissolved in about two-third carbon disulphide with a small amount of plasticizer. Dibutyl phthalate is used as a plasticizer to vary the degree of brittleness of brittleness of

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the coating, which increase with its increase. The strain sensitivity of this coating varies from 0.0003 to 0.0030. It can be applied to the test specimen by a spraying method. This coating can be used upto 60oC and absorbs water and oil. The thickness of this coating can be made varying from 0.10 to 0.15 mm and can be used for macro and micro applications. Stresscoat has been employed in trichloroethylene or benzene and phenolic resin mixed with titanic white and dissolved in a mixture of benzene, toluene and xylene have also been used as brittle lacquers.

2. Ceramic based coating – ‘All Temp’. It consist of finely ground ceramic particles suspended in a solvent. It can be sprayed by conventional means onto the specimen. Upon drying at room temperature the coating presents a chalklike appearance and is not suitable for use. In order to make the coating effective, it must be fired at about 540oC until the ceramic particles melt and coalesce. When fired, the coating is glasslike in appearance and brown in colour. These coatings are relatively insensitive to minor changes in temperature. They can be used upto 370oC and are not influenced by the presence of oil and water. Their disadvantage include the high temperature of 537.7oC required to fire the coating which produces detrimental effect on components fabricated from aluminum, magnesium, plastic and highly heat-treated steels. Their visual inspection for cracks is not possible and statiflux method must be resorted to. Strain sensitivity of these coating range from 0.0002 to 0.0020. Porcelain enamel coatings are also available, whose properties are similar to ceramic based coatings, but can be used at all temperatures.

3. Tens-Lac Brittle Lacquer. This is a new, high sensitivity, non-flammable, odorless and of low toxicity brittle lacquer. This lacquer can be applied by spraying on test specimens. The nominal threshold strain for Tens-Lac is 500 cm/cm. This lacquer requires a reflective under coating if the test surface is dark. Tens-Lac is available in eleven grades from TL-500-40 to TL-500-100, were 500 indicates the strain sensitivity and the last number (e.g. 40 and 100) indicates the temperature of use in F o

to obtain the strain sensitivity of 500 cm/cm. The best thickness of the coating is 0.075 mm.

Table 10.1 gives the relative comparison of these lacquers.

S. No

Property Stress-coat All-Temp Tens-Lac

1.Minor changes in

temperatureVery sensitive Insensitive Sensitive

2. Limiting temperature37.7oC (100oF)

-45oC to 370oC(- 50oF to 700oF)

37.7oC (100oF)

3.Effect of oil and

waterInfluenced Not influenced Influenced

4. Firing of coating Not required Very high Not required

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temperature of 537.7oC (1000oF) is

required for 15 minutes

5. Visual observation Possible Not possible Possible

6. Strain sensitivity300 to 3000

cm/cm200 to 2000 m/m

500 m/m at the specified temperature

7. Suitable for All materialsExcept those having melting point less

than 537.7oCAll materials

Evaluation of the Coating

The following characteristics are used to evaluate the coating1. Strain sensitivity. This is the threshold strain which is defined as the minimum

strain necessary to crack the coating in a uniaxial state of stress. Coating sensitivity is the inverse of strain sensitivity. Strain sensitivity of a coating can be determined by a calibration technique.

2. Continuous crack. This is defined as the first crack extending from one boundary of the calibration beam to the other boundary.

3. Crazing or failure by shrinkage and by thermal and humidity effects, without loading the specimen.

4. Closing of cracks after unloading5. Crack density.6. Flaking.

Basic Brittle Lacquer Technique

The following basic steps are involved in the brittle lacquer method:

1. Preparation of the test specimen surface by cleaning and spraying with a reflective coating like aluminum.

2. Selection of appropriate lacquer for the expected test conditions.3. Application of the lacquer to the test specimen and calibration strip.4. Curing the lacquer.5. Loading the test specimen and observing the cracks.6. Loading the calibration strip to determine the strain corresponding to incipient

cracking, i.e threshold strain.7. Treating with dye etchants or statiflux for improved crack visibility when desired.

Variables Influencing the Coating Behaviour

There are many variables which influence the behaviour of the coating. For stress coat, Durelli, Phillips and Tsao have listed 37 of these variables. However, the influence of these variables can be minimized if proper precautions are taken as per the manufacture’s instructions. Some of the important variables are discussed below:

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1. Number and type of coating. For stress coat and All-Temp brittle lacquers, the strain sensitivity increases as the coating code number increase. However, the strain-sensitivity of Tens-Lac is 500 cm/cm at the specified temperature. If the quantity of plasticizer is increased in stress coat then the threshold strain increases. Coatings made from old liquid are more sensitive.

2. Effect of spraying unit. Water vapours in the spraying in the spraying air causes large bubbles in the coating, which should be avoided by using a filter. The pressure of the spraying unit should also be specified by the manufacturer. Greater the pressure, the ‘dustier’ is the appearance of the coating because there is more air to evaporate the solvent in the liquid and consequently some of the lacquer reaches the surfaces of specimen in solid form.

3. Effect of coating application method. The distance of the gun from the test specimen should 75 to 100mm. The speed of spraying traverse should be applied by spraying uniform thickness in a number of passes until the specified thickness is obtained. The coating strain sensitivity decrease with coating thickness. It has been found that cross- spraying gives a more uniform coating thickness that parallel spraying. The spraying passes should be made after at least 5 seconds, and should not be more that about 40 seconds.

4. Influence of heat treatment. To improve the strain-sensitivity of the coating by a heat-treatment technique, the time between spraying and heating should be at least 5 minutes. Strain sensitivity of stresscoat at approximately 107oF is higher that that for the same coating thickness at 75oF. At any given temperature over approximately 90oF, strain sensitivity increases with decreasing thickness. At higher rate of cooling, crazing occurs. Higher humidity during curing increases the strain sensitivity. As outer layers of the coating dry first they have a higher modulus of elasticity that the inner layers.

5. Testing conditions. The strain sensitivity of all coatings increase with the increase in testing temperature and decrease with the increase in relative humidity. The coating should be tested within 48 hours after spraying. Virgin coatings have higher threshold strain than coatings that have been loaded once or twice previously upto the same load. Loads should be applied slowly enough. Static loads should be applied for 2 seconds or more and dynamic loads for about 3 or 4 milliseconds. After 15 seconds the changes in sensitivity are negligible. Therefore calibration and loading time for static tests should be standardized at 15 seconds. Waiting time between successive applications of load should be four times the loading time to eliminate the influence of creep.

6. Effect of stress conditions. If the strain gradients perpendicular to the cracks in the test specimen are appreciably different from that of the calibration strip, then the corrected strain sensitivity is given by,

where x = strain gradient at the investigated point, cm/cm/2.54 cm.

The coating behavior is also influenced by the biaxiality of stress and hydrostatic pressure. Near free boundaries the coating is thicker than inside the field. Residual stresses may be produced by shrinkage in the coating, when it passes from the liquid to the solid state

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or by change in temperature.

7. Effect of refrigeration and dye-etchant. The strain sensitivity of the coating decreases with a sudden drop in temperature. The coating sensitivity increases with the application of dye-ctchant.

Advantages of Brittle Coatings

1. It provides whole field data for both magnitude and direction of principal stresses and does not require a tedious point-by-point method.

2. It does not require the construction of a model and can usually be applied to a prototype of the actual machine component being studied.

3. There is no load simulation problem.4. The data analysis is simple.

However the accuracy of variables as discussed in the previous article, whose knowledge is very essential.

Brittle Coating Applications

Brittle coating technique may be employed in the following applications:

1. Determination of residual stresses in conjunction with the hole-drilling method.2. Determination of compressive strains by using relaxation technique.3. Determination of dynamic strains.4. Determination of strains at high temperature upto 370oC.5. Determination of yield and plastic strains.6. For outdoor operations.7. For operations under water and hydrostatic pressure.8. Determination of strains on very thin components.

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