MATERIALS SCIENCE

Week 4MECHANICAL

PROPERTIES AND TESTS

Stress

Stress is a measure of the intensity of the internal forces acting within a deformable body.

Mathematically, it is a measure of the average force per unit area of a surface within a the body on which internal forces act

The SI unit for stress is Pascal (symbol Pa), which is equivalent to one Newton (force) per square meter (unit area).

Three types of stresses -> Tensile; Compressive; Shear

Mechanism of Stress (Tensile)

Strain

Strain is deformation of a physical body under the action of applied forces

It is the geometrical measure of deformation representing the relative displacement between particles in the material body

Strain is a dimensionless quantityStrain accounts for elongation, shortening, or

volume changes, or angular distortionNormal stress causes normal strain (tensile or

compressive)Shear strain is defined as the change in angle

between two originally orthogonal material lines

Types of Strains

tensile load producesan elongation andpositive linearstrain.

compressive loadproduces contractionand a negative linearstrain.

torsionaldeformation

TENSILE TEST AND STRESS-STRAIN RELATIONSHIP

Tensile Test

Used for determining UTS, yield strength, %age elongation, and Young’s Modulus of Elasticity

The ends of a test piece are fixed into grips. The specimen is elongated by the moving crosshead; load cell and extensometer measure, respectively, the magnitude of the applied load and the elongation

Stress-Strain Relationship

Important Terms (Stress-Strain Rel.)

Elastic Limit -> Maximum amount of stress up to which the deformation is absolutely temporary

Proportionality Limit -> Maximum stress up to which the relationship between stress & strain is linear.

Hooke’s Law -> Within elastic limit, the strain produced in a body is directly proportional to the stress applied.

σ = E ε

Important Terms (Stress-Strain Rel.)

Young’s Modulus of elasticity -> the ratio of the uniaxial stress over the uniaxial strain in the range of stress in which Hooke's Law holds

Elasticity -> the tendency of a body to return to its original shape after it has been stretched or compressed

Yield Point -> the stress at which a material begins to deform plastically

Important Terms (Stress-Strain Rel.)

Plasticity -> the deformation of a material undergoing non-reversible changes of shape in response to applied forces

Ultimate Strength -> It is the maxima of the stress-strain curve. It is the point at which necking will start.

Necking -> A mode of tensile deformation where relatively large amounts of strain localize disproportionately in a small region of the material

Important Terms (Stress-Strain Rel.)

Fracture Point -> The stress calculated immediately before the fracture.

Ductility -> The amount of strain a material can endure before failure.

Ductility is measured by percentage elongation or area reduction

Important Terms (Stress-Strain Rel.)

A knowledge of ductility is important for two reasons:

1.It indicates to a designer the degree to which a structure will deform plastically before fracture.

2.It specifies the degree of allowable deformation during fabrication

Engineering stress– strain behavior for Iron at three temperatures

Resilience

Resilience is the capacity of a material to absorb energy when it is deformed elastically and then, upon unloading, to have this energy recovered

Modulus of Resilience (Ur) is the strain energy per unit volume required to stress a material from an unloaded state up to the point of yielding.

Resilience

Assuming a linear elastic region

For SI units, this is joules per cubic meter (J/m3, equivalent to Pa)

Thus, resilient materials are those having high yield strengths and low moduli of elasticity; such alloys would be used in spring applications

Shear and Torsional Tests

Shear Stress:

The shear strain γ is defined as the tangent of the strain angle θTorsion is a variation of pure shear, wherein a structural member is twisted in the manner of the figureTorsional stress -> The shear stress on a transverse cross section resulting from a twisting actionTorsional forces produce a rotational motion about the longitudinal axis of one end of the member relative to the other end

ANELASTICITY

In most engineering materials, there also exists a time-dependent elastic strain component.

This time-dependent elastic behavior is known as anelasticity

For metals the anelastic component is normally small and is often neglected

For some polymeric materials its magnitude is significant; in this case it is termed viscoelastic behavior

EXAMPLE PROBLEM 6.1

A piece of copper originally 305mm (12 in.) long is pulled in tension with a stress of 276MPa (40,000psi). If the deformation is entirely elastic, what will be the resultant elongation?

Magnitude of E for copper from Table 6.1 is 110GPa

Poisson’s Ratio

Poisson’s ratio is defined as the ratio of the lateral and axial strains

Theoretically, Poisson’s ratio for isotropic materials should be 1/4; furthermore, the maximum value for ν is 0.50

EXAMPLE PROBLEM 6.2

A tensile stress is to be applied along the long axis of a cylindrical brass rod that has a diameter of 10mm. Determine the magnitude of the load required to produce a 0.0025mm change in diameter if the deformation is entirely elastic.

For the strain in the x direction:

EXAMPLE PROBLEM 6.2

True Stress and Strain

The decline in the stress necessary to continue deformation past the point M, indicates that the metal is becoming weaker.

Material is increasing in strength.True stress σT is defined as the

load F divided by the instantaneous cross-sectional area Ai over which deformation is occurring

True strain ЄT is defined as:

True Stress and Strain

If no volume change occurs during deformation—that is, if Aili = A0l0

Then true and engineering stress and strain are related according to

The equations are valid only to the onset of necking; beyond this point true stress and strain should be computed from actual load, cross-sectional area, and gauge length measurements

Assignment

(a) Completely describe “Compression Test”. (b) How is it different from Tensile test? (c) What are the effects of Friction and Workpiece’s height-to-diameter ratio on the test? (d) Derive relationship between true stress/strain and engineering stress/strain for compression test (also show by stress-strain curve)

Submission on or before 18-Oct-2012

EXAMPLE PROBLEM 6.4

A cylindrical specimen of steel having an original diameter of 12.8mm is tensile tested to fracture and found to have an engineering fracture strength σf of 460MPa. If its cross-sectional diameter at fracture is 10.7mm, determine:

(a) The ductility in terms of percent reduction in area(b) The true stress at fractureDuctility is computed as

EXAMPLE PROBLEM 6.4

True stress is defined by Equationwhere the area is taken as the fracture area Af

However, the load at fracture must first be computed from the fracture strength as

And the true stress is calculated as

Elastic Recovery after Plastic Deformation

Upon release of the load during the course of a stress–strain test, some fraction of the total deformation is recovered as elastic strain

During the unloading cycle, the curve traces a near straight-line path from the point of unloading (point D), and its slope is virtually parallel to the initial elastic portion of the curve

The magnitude of this elastic strain, which is regained during unloading, corresponds to the strain recovery

Hardness

Hardness is the property of material by virtue of which it resists against surface indentation and scratches.

Macroscopic hardness is generally characterized by strong intermolecular bonds

Hardness is dependent upon strength and ductility

Common examples of hard matter are diamond, ceramics, concrete, certain metals, and superhard materials (PcBN, PcD, etc)

Hardness Tests (BRINELL HARDNESS TEST)

Used for testing metals and nonmetals of low to medium hardness

The Brinell scale characterizes the indentation hardness of materials through the scale of penetration of an indenter, loaded on a material test-piece

A hardened steel (or cemented carbide) ball of 10mm diameter is pressed into the surface of a specimen using load of 500, 1500, or 3000 kg.

BRINELL HARDNESS TEST

where:P = applied force (kgf) D = diameter of indenter

(mm) d = diameter of indentation

(mm)The resulting BHN has

units of kg/mm2, but the units are usually omitted in expressing the numbers

Rockwell Hardness Test

Rockwell test determines the hardness by measuring the depth of penetration of an indenter under a large load compared to the penetration made by a preload

A cone shaped indenter or small diameter ball (D = 1.6 or 3.2mm) is pressed into a specimen using a minor load of 10kg

Then, a major load of 150kg is appliedThe additional penetration distance d is

converted to a Rockwell hardness reading by the testing machine.

Rockwell Hardness Test

Vickers Hardness Test

Uses a pyramid shaped indenter made of diamond.It is based on the principle that impressions made

by this indenter are geometrically similar regardless of load.

The basic principle, as with all common measures of hardness, is to observe the questioned material's ability to resist plastic deformation from a standard source.

Accordingly, loads of various sizes are applied, depending on the hardness of the material to be measured

Vickers Hardness Test

Where:F = applied load (kg)D = Diagonal of the impression

made the indenter (mm)The hardness number is

determined by the load over the surface area of the indentation and not the area normal to the force

Knoop Hardness Test

It is a microhardness test - a test for mechanical hardness used particularly for very brittle materials or thin sheets

A pyramidal diamond point is pressed into the polished surface of the test material with a known force, for a specified dwell time, and the resulting indentation is measured using a microscope

Length-to-width ratio of the pyramid is 7:1

Knoop Hardness Test (contd…)

The indenter shape facilitates reading the impressions at lighter loads

HK = Knoop hardness value; F = load (kg); D = long diagonal of the impression (mm)

Hardness of Metals and Ceramics

Hardness of Polymers

TOUGHNESS

It is a property of material by virtue of which it resists against impact loads.

Toughness is the resistance to fracture of a material when stressed

Mathematically, it is defined as the amount of energy per volume that a material can absorb before rupturing

Toughness can be determined by measuring the area (i.e., by taking the integral) underneath the stress-strain curve

Toughness (contd…)

Toughness =

Whereε is strainεf is the strain upon failureσ is stressThe Area covered under

stress strain curve is called toughness

Toughness (contd…)

Toughness is measured in units of joules per cubic meter (J/m3) in the SI system

Toughness and Strength -> A material may be strong and tough if it ruptures under high forces, exhibiting high strains

Brittle materials may be strong but with limited strain values, so that they are not tough

Generally, strength indicates how much force the material can support, while toughness indicates how much energy a material can absorb before rupture

Effect of Temperature on Properties

Generally speaking, materials are lower in strength and higher in ductility, at elevated temperatures

Hot Hardness

A property used to characterize strength and hardness at elevated temperatures is Hot Hardness

It is the ability of a material to retain its hardness at elevated temperatures

Numerical Problems

Problems 6.3 to 6.9; 6.14 to 6.23; 6.25 to 6.33; 6.46 to 6.48