Tensile Test
Introduction:-
Tensile tests are conducted on test specimens of the material to be tested. Test pieces are standardized in order that results are reproducible and comparable. Figure 11 indicates standardized test specimens.
Gauge length is the length of the parallel portion of the test piece over which elongations are measured. For a cylindrical test piece, the gauge length used for calculation of percentage elongation is a function of the cross-section area or the diameter of the test bar.
Standard shapes of tensile specimens
The specimen is held between grips fixed to platens on the two crossheads of the tensile test machine. The specimen is subjected to a pulling load by gradually moving one grip away from the other by moving of the cross head of the machine (Figure 12). As the grips move apart the tensile load on the test specimen increases and the specimen elongate. The load is increased till the specimen breaks.
Tensile Test Machine
The longitudinal stress based on the original cross sectional area of the specimen and the corresponding strain in the specimen are plotted to give a stress-strain diagram for the material of the specimen. With increasing load and elongation, the cross sectional area of the specimen reduces. Therefore, the true stresses on the specimen for large loads are higher than the stresses shown in the diagram.
Figure shows the stress -strain relationship for a specimen of ductile mild steel.
Stress – Strain Diagram
Stress Vs Strain for Mild Steel
The strain is directly proportional to the corresponding stress from O to A. Beyond A, the strain is not directly proportional to the stress. The line O A is called the line of proportionality. Hook’s law is valid in this range. The stress at A is known as the Proportionality Limit. If the load is increased beyond this, elongation increases more rapidly as indicated in the diagram from A to C. At a point B, between A and C, the elastic limit for the material is reached and thereafter a permanent set or deformation takes place. C is the point of sudden large elongation, known as the Yield Point. Beyond the Yield point, the piece elongates further — the strain increasing at a higher rate as shown in the diagram from C to D. In this range, owing to plastic deformation of the material the stress may initially drop with further increase in stress. From D to E, the specimen elongates further and, the point E of maximum load or ultimate strength is reached.
With further increase in stress, plastic flow of the material begins. A local reduction in cross-section (necking) of the specimen takes place. With plastic flow a drop in stress and increased elongation takes place till the specimen fractures. The breaking load, if divided by the actual cross section area of the necked specimen, is the actual stress at rupture, and is greater than the stress at F in the stress- strain diagram. The actual stress at rupture is greater than the ultimate stress (at E). The actual values are different because the calculated stresses are based on original area of cross section.
Limit of Proportionality:-
Limit of proportionality is the maximum stress beyond which the longitudinal strain is not proportional to the longitudinal stress causing the longitudinal strain. It is the stress beyond which the stress-strain diagram ceases to be a straight line. In figure 13, stress corresponding to point A is the limit of proportionality
Elastic Limit:-
The elastic limit of an engineering material is the maximum stress that a tensile test specimen of the material can be subjected to, so that there is no permanent or residual deformation. If loaded below the elastic limit, upon removal of the load the deformed body recovers its original condition.
For many materials, the values of the elastic limit and the proportionality limit are very close, and the terms aresometimes used interchangeably. The elastic limit – point B in Figure 13, is however, greater than the proportionality limit.
Yield Point:-
Yield point is the stress on a tensile test specimen, at which there is an appreciable elongation or yielding of the material without an increase in load. (C in Figure 13).
This type of yielding is more specific to structural steel, and is seen only under tensile load. Other materials do not posses well-defined yield points. For more ductile materials like annealed low carbon steel on the yielding of the material, the stress at C decreases to D. For such cases, the point C is the higher yield point and point D is the lower yield point.
A brittle material does not have a well-defined yield point.
Yield Strength:-
Yield strength of a material is the maximum stress to which tensile test specimen can be loaded without causing plastic deformation. It is the stress at which a material exhibits a permanent deformation. The stress at which deformation of a material continues without further increase in load is called the yield strength. It is measured on the tensile testing machine. A permanent increase in gauge length is confirmed by checking the gauge length with dividers. The corresponding stress is the yield strength. This is an inaccurate measurement process.
Therefore, yield strength is determined by an offset method. A line offset by an arbitrary amount of 0.2% of strain is drawn parallel to the straight- line portion of the original stress-strain diagram, as illustrated in figure
Yield strength for 0.002 strain
The stress corresponding to the point of intersection of this projected line with the stress- strain curve is the yield strength of the material.
Elastic range is the range on the stress-strain curve from the origin to a point on the stress-strain curve between the proportionality limit and the yield point.
Ultimate Stress :-
The maximum stress that a material can withstand without breaking is called its ultimate stress. On the stress-strain curve, the stress corresponding to the point E is the ultimate stress of the material of the specimen.
Ultimate Strength:-
If a test specimen is stressed more than the stress corresponding to point E, due to plastic flow, necking of the specimen takes place. Further elongation without increase in stress takes place, leading to fracture of the specimen.
The stress corresponding to the point E is the ultimate stress of the material of the test specimen.
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Factor of Safety:
Factor of safety is defined as the ratio of ultimate stress to the working stress. For a material to function without failure, we need to ensure that it is stressed well below the ultimate stress. This working stress is also called the permissible stress.
Mathematically,
Factor of safety = 
Modulus of Rigidity:-
The ratio of the shear stress τ to the shear strain φ is called the modulus of rigidity or shear modulus or modulus of transverse elasticity and is denoted by G or C. The unit for Modulus of rigidity is N/mm2.
Mathematically, G
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Table shows Typical values of shear modulus for different engineering materials
| Material, | Modulus,of Rigidity In GN/mm2 |
|---|---|
| Aluminium | 26 |
| Brass | 35 |
| Cast Iron | 35 |
| Copper | 39 |
| Lead | 7.6 |
| Steel C15 | 79 |
| Steel C35 | 79 |
| Steel C60 | 89 |
| Tungsten | 177 |
Fracture Load :-
The load at which a material breaks or fractures is called the fracture load. The fracture load is also called the breaking load.
Percentage Reduction in Area:-
When an axial pull is applied to a rod, the rod elongates. When the rod elongates, there is a reduction in its cross sectional area. When the pull is gradually increased, the area of cross section also reduces and the rod fractures or breaks at the maximum pull that the rod can withstand. When the fracture happens, the cross sectional area is considerably decreased. This decrease in the area of cross section of the rod upon fracture to its original cross sectional area, expressed in percentage, is called percentage reduction in area. It is to be noted that when tensile force acts upon a bar, the normal stress is calculated on the basis of the original area and not based on the reduced cross sectional area due to elongation.
Fracture or Breaking Stress:-
The stress at the breaking point, calculated as the ultimate load divided by the original cross sectional area is called the breaking stress.
Rupture Strength:-
The rupture strength is the stress applied at the point of failure of the test piece. In ductile materials, the rupture strength (represented by point F) is lower than the ultimate strength. This is because, the rupture strength is calculated by load at failure divided by the original area of cross-section. Actually, due to neck formation, the cross-sectional area of the test piece reduces considerably and the actual rupture strength (obtained by dividing the breaking load by the cross-sectional area at the time of rupture) is much higher than the actual ultimate strength. In figure 13, point ‘F’ corresponds to the actual rupture strength that is higher than the ultimate strength. However, the ultimate strength (corresponding to the point E) is commonly taken as the maximum stress of the test piece. No neck formation takes place upto point E and the value of the ultimate strength and the rupture strength are taken as same for practical purposes.
Modulus of Resilience:-
Let us consider a volume of a material which is subjected to a tensile load. When the tensile load is gradually increased, at a specific value of this load, the limit of proportionality between stress and strain is reached. The stress per unit volume for this load at the proportionality limit is known as modulus of resilience of the test material. This value can be calculated as the area under the stress – strain curve from the origin upto the limit of proportionality.
Modulus of Toughness:-
Let us consider a volume of a material which is subjected to a tensile load. When the tensile load is gradually increased, at a specific value of this load, the test piece ruptures after proportionality limit between stress and strain is reached. The stress per unit volume for this load at rupture is known as modulus of toughness of the test material. This value can be calculated as the area under the stress – strain curve from the origin up to the point of rupture.
Strain Hardening:-
If a ductile material can be stressed considerably beyond the yield point without failure, its hardness increases. This phenomenon is called strain hardening. Structural materials can be strain hardened.
Beating of copper and aluminum vessels to harden them is a common practical application of the strain- hardening of ductile materials.
Work out examples:- [Click Here ##eye##]
Compression Test:-
Microscopic cracks are present in all metals. In brittle materials, tensile stresses tend to widen these microscopic cracks, oriented perpendicular to the axis of tension, leading to fracture at lower stresses. Under compressive loads, microscopic cracks tend to close up, allowing the brittle material to withstand higher compressive stresses than tensile stresses.
Hence, brittle materials are mainly used in applications to withstand compressive loads.
Figure 15 shows a comparison of the stress-strain properties of brittle cast iron, under tensile and compressive loads.
Figure Comparison of the compressive and tensile strengths
Compression Test for Ductile Materials
When a ductile material is subjected to a compressive load, the area of cross-section increases. The necking does not occur. If a material is extremely ductile, we cannot test its compression properties by the compression test. The platen of the compression test apparatus, which contact the ductile material, is constricted by friction and the ductile material flows around the points of contact. The stress distribution, therefore, becomes complicated. Hence only approximate values for properties of highly ductile materials under compression can be measured.
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