1st lectuer mechanical properties of material.pdf

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Port Said UniversityFaculty of Engineering

Naval Architecture and Marine Engineering Department

1st lecture

Mechanical properties of material

Post Graduate Course:

Structure design (2)

Course Code:

Supervisor:

Dr. Heba Elkilani

31th Dec. 2012

Prepared By:Mohamed Elmaadawy Design engineer N.A.M.E. B.Sc. Port Said Shipyard Suez Canal Authori ty



Mechanical properties of materialtructure design (2) Code: 606

2

Contents

1. Introduction 3

2. Load 4

3. Stress 4

4. Strain 4

5. Young's Modulus or Modulus of Elasticity 4

6. Shear Stress and Strain. 5

7. Shear Modulus or Modulus of Rigidity 5

8. Stress-strain Diagram 6

9. Linear and Lateral Strain 7

10. Poisson's Ratio 7

Prepared by: M.Elmaadawy




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1. Introduction.

The mechanical properties of a material are those properties that involve a reaction to an applied load. Themechanical properties of metals determine the range of usefulness of a material and establish the service lifethat can be expected. Mechanical properties are also used to help classify and identify material. The mostcommon properties considered are strength, stiffness, elasticity, plasticity, ductility, brittleness, malleability,toughness, resilience, creep and hardness. We shall now discuss these properties as follows:

1. Strength. It is the ability of a material to resist the externally applied forces without breaking or yielding. Theinternal resistance offered by a body to an externally applied force is called *stress.2. Stiffness. It is the ability of a material to resist deformation under stress. The modulus of elasticity is themeasure of stiffness.3. Elasticity. It is the property of a material to regain its original shape after deformation when the externalforces are removed. This property is desirable for materials used in tools and machines.4. Plasticity. It is property of a material which retains the deformation produced under load permanently. Thisproperty of the material is necessary for forgings, in stamping images on coins5. Ductility. It is the property of a material enabling it to be drawn into wire with the application of a tensile force.

A ductile material must be both strong and plastic. The ductility is usually measured by the terms, percentageelongation and percentage reduction in area.6. Brittleness. It is the property of a material opposite to ductility. It is the property of breaking of a material withlittle permanent distortion. Brittle materials when subjected to tensile loads, snap off without giving any sensibleelongation. Cast iron is a brittle material.7. Malleability. It is a special case of ductility which permits materials to be rolled or hammered into thin sheets.

A malleable material should be plastic but it is not essential to be so strong.8. Toughness. It is the property of a material to resist fracture due to high impact loads like hammer blows.9. Machinability. It is the property of a material which refers to a relative case with which a material can be cut.

10. Resilience. It is the property of a material to absorb energy and to resist shock and impact loads. It ismeasured by the amount of energy absorbed per unit volume within elastic limit.11. Creep. When a part is subjected to a constant stress at high temperature for a long period of time, it willundergo a slow and permanent deformation called creep. This property is considered in designing internalcombustion engines, boilers and turbines.12. Fatigue. When a material is subjected to repeated stresses, it fails at stresses below the yield pointstresses. Such type of failure of a material is known as *fatigue. The failure is caused by means of a progressivecrack formation which are usually fine and of microscopic size. This property is considered in designing shafts,connecting rods, springs, gears, etc.13. Hardness. It is a very important property of the metals and has a wide variety of meanings. It embracesmany different properties such as resistance to wear, scratching, deformation and machinability etc. It also

means the ability of a metal to cut another metal. The hardness is usually expressed in numbers which aredependent on the method of making the test. The hardness of a metal may be determined by the following tests:(a) Brinell hardness test,(b) Rockwell hardness test,(c) Vickers hardness (also called Diamond Pyramid) test, and(d) Shore scleroscope.





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2. Load

It is defined as any external force acting upon a body.The following four types of the load are important from the subject point of view 1.1 Dead or steady load 1.2. Live or variable load. 1.3. Suddenly applied or shock loads 1.4. Impact load.

3. Stress sigma When some external system of forces or loads acts on a body, the internal force per unit area resisting theexternal forces at any section of the body is known as unit stress or simply a stress .

Stress, = P/ AWhere P = Force or load acting on a body,

A = Cross-sectional area of the body.

Stress is usually expressed in megapascal (MPa) and gigapascal (GPa), such that1 MPa = 1 × 106 N/m2 = 1 N/mm2

4. Strain epsilonWhen a system of forces or loads acts on a body, it undergoes some deformation. This deformation per unitlength is known as unit strain or simply a strain.

Tensile / Compressive Stress and StrainWhen a body is subjected to two equal and opposite axial P as shown in Fig, then the stress induced at anysection of the body is known as tensile / compressive stress as shown in Fig.

. The ratio of the increase /decrease in length to the original length is known as tensile / compressive strain P = Axial tensile / compressive force acting on the body,

A = Cross-sectional area of the body,l = Original length, and

= Increase / Decrease in length.∴ Tensile / Compressive stress , / = P/ A∴ Tensile / compressive strain /Note: Incase of tension or compression, the area involved is at right angles to the external force applied.

5. Young's Modulus or Modulus of ElasticityHooke's law* states that when a material is loaded within elastic limit, the stress is directly proportional to strain,

Where E is a constant of proportionality known as Young's modulus or modulus of elasticity.





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Table 4.1. Values of E for the commonly used engineering materials.

6. Shear Stress and Strain tau & phi

When a body is subjected to two equal and opposite forces acting tangentially across the resisting section, as aresult of which the body tends to shear off the section, then the stress induced is called shear stress. The corresponding strain is known as shear strain and it is measured by the angular deformationaccompanying the shear stress.

7. Shear Modulus or Modulus of Rigidity

It has been found experimentally that within the elastic limit, the shear stress is directly proportional to shear

strain.Mathematically

C = Constant of proportionality, known as shear modulus or modulus of rigidity. It is also denoted by N or G. The following table shows the values of modulus of rigidity ( C) for the materials in everyday use:

Table 4.2. Values of C for the commonly used materials.





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8. Stress-strain DiagramIn design process it is necessary to know how the material will function in service. For this, certaincharacteristics or properties of the material should be known. The mechanical properties mostly used inmechanical engineering practice are commonly determined from a standard tensile test.The values of the stress and corresponding strain are used to draw the stress-strain diagram of the materialtested.

A stress-strain diagram for mild steel under tensile test is shown in Fig.

1. Proportional limit. From point O to AIt is defined as that stress at which the stress-strain curve begins toDeviate from the straight line.Hooke's law holds good up to point A2. Elastic limit From A upto the point B This point is known as elastic limit. It is defined as the stressdeveloped in the material without any permanent set. Note: Since the above two limits are very close to each other,therefore, for all practical purposes these are taken to be equal.3. Yield point .If the material is stressed beyond point B, the plastic stage will reach i.e. on the removal of the load; the materialwill not be able to recover its original size and shape. A little consideration will show that beyond point B, thestrain increases at a faster rate with any increase in the stress until the point C is reached. At this point, thematerial yields before the load and there is an appreciable strain without any increase in stress. In case of mildsteel, it will be seen that a small load drops to D, immediately after yielding commences. Hence there are twoyield points C and D. The points C and D are called the upper and lower yield points respectively. The stresscorresponding to yield point is known as yield point stress. 4. Ultimate stress .

AtD,

the specimen regains some strength and higher values of stresses required for higher strains, than thosebetween A and D. The stress (or load) goes on increasing till the point E is reached. The gradual increase in thestrain (or length) of the specimen is followed with the uniform reduction of its cross-sectional area. The workdone, during stretching the specimen, is transformed largely into heat and the specimen becomes hot. At E, thestress, which attains its maximum value known as ultimate stress . It is defined as the largest stress obtainedby dividing the largest value of the load reached in a test to the original cross-sectional area of the test piece.11. Breaking stress .The stress (or load) necessary to break away the specimen, is less than the maximum stress.The stress corresponding to point F is known a s breaking stress .

Note: The breaking stress ( i.e. stress at F which is less than at E) appears to be somewhat misleading. As the

formation of a neck takes place at E which reduces the cross-sectional area, it causes the specimen suddenly tofail at F. If for each value of the strain between E and F, the tensile load is divided by the reduced crosssectionalarea at the narrowest part of the neck, then the true stress-strain curve will follow the dotted line EG.However, it is an established practice, to calculate strains on the basis of original cross-sectional area of thespecimen using nominal stress.Strain hardening.When yielding has ended, an increase in load can be supported by the specimen, resulting in a curve that risescontinuously but becomes flatter until it reaches a maximum referred to as the ultimate stress . The rise in thecurve in this manner is called strain hardening .





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9. Linear and Lateral StrainConsider a circular bar of diameter d and length l, subjected to a tensile force P as shown in Fig.a

A little consideration will show that due to tensile force, the length of the bar increases by an amount and thediameter decreases by an amount as shown in Fig.(b). Similarly, if the bar is subjected to a compressiveforce, the length of bar will decrease which will be followed by increase in diameter.It is thus obvious, that every direct stress is accompanied by a strain in its own direction which is known aslinear strain and an opposite kind of strain in every direction, at right angles to it, is known as lateral strain.

10. Poisson's RatioIt has been found experimentally that when a body is stressed within elastic limit, the lateral strain bears aconstant ratio to the linear strain,

Mathematically,

This constant is known as Poisson's ratio and is denoted byTable 4.4. Values of Poisson’s ratio for commonly used materials.


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