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Note for Testing of Materials by VSSUT Ranger

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Testing of Materials (MM 15 025) B. Tech, 6th Semester Prepared by Dr. Sushant Kumar BadJena Department of Metallurgy & Materials Engineering VEER SURENDRA SAI UNIVERSITY OF TECHNOL BURLA - 768018 1

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THE TENSION TEST 8-1 ENGINEERING STRESS-STRAIN CURVE  The engineering tension test is widely used to provide basic design information on the strength of materials and as an acceptance test for the specification of materials.  In the tension test a specimen is subjected to a continually increasing uniaxial tensile force while simultaneous observations are made of the elongation of the specimen.  An engineering stress-strain curve is constructed from the load-elongation measurements (Fig. 8-1).  The stress used in this stress-strain curve is the average longitudinal stress in the tensile specimen. It is obtained by dividing the load by the original area of the cross section of the specimen. (8.1) Figure 8-1 The engineering stress-strain curve.  The strain used for the engineering stress-strain curve is the average linear strain, which is obtained by dividing the elongation of the gage length of the specimen, δ, by its original length. 2

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(8.2)  Since both the stress and the strain are obtained by dividing the load and elongation by constant factors, the load-elongation curve will have the same shape as the engineering stress-strain curve. The two curves are frequently used interchangeably.  The shape and magnitude of the stress-strain curve of a metal will depend on its composition, heat treatment, prior history of plastic deformation, and the strain rate, temperature, and state of stress imposed during the testing.  The parameters which are used to describe the stress-strain curve of a metal are the tensile strength, yield strength or yield point, percent elongation, and reduction of area. The first two are strength parameters; the last two indicate ductility.  The general shape of the engineering stress-strain curve (Fig. 8-1) requires further explanation.  In the elastic region stress is linearly proportional to strain. When the load exceeds a value corresponding to the yield strength, the specimen undergoes gross plastic deformation.  It is permanently deformed if the load is released to zero. The stress to produce continued plastic deformation increases with increasing plastic strain, i.e., the metal strain-hardens.  The volume of the specimen remains constant during plastic deformation, AL = A0L0, and as the specimen elongates, it decreases uniformly along the gage length in crosssectional area.  Initially the strain hardening more than compensates for this decrease in area and the engineering stress (proportional to load P) continues to rise with increasing strain.  Eventually a point is reached where the decrease in specimen cross-sectional area is greater than the increase in deformation load arising from strain hardening.  This condition will be reached first at some point in the specimen that is slightly weaker than the rest.  All further plastic deformation is concentrated in this region, and the specimen begins to neck or thin down locally.  Because the cross-sectional area now is decreasing far more rapidly than the deformation load is increased by strain hardening, the actual load required to deform 3

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the specimen falls off and the engineering stress by Eq. (8-1) likewise continues to decrease until fracture occurs. Figure 8-2 Loading and unloading curves showing elastic recoverable strain and plastic deformation.  Consider a tensile specimen that has been loaded to a value in excess of the yield stress and then the load is removed (Fig. 8-2).  The loading follows the path O-A-A'. Note that the slope of the unloading curve A-A' is parallel to the elastic modulus on loading.  The recoverable elastic strain on unloading is 𝑏 = 𝜎⁄𝐸 = (𝑃1⁄𝐴 )/𝐸. 0  The permanent plastic deformation is the offset “a” in Fig. 8-2. Note that elastic deformation is always present in the tension specimen when it is under load.  If the specimen were loaded and unloaded along the path 0-A-B-B’ the elastic strain would be greater than on loading to P1, since P2 > P1 but the elastic deformation (d) would be less than the plastic deformation (c). Tensile Strength  The tensile strength, or ultimate tensile strength (UTS), is the maximum load divided by the original cross-sectional area of the specimen. 4

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