Mechanical Test Instruments Among the large number of
Let us examine these test devices in some detail:
Sigma = P / Ao And the engineering strain is given as: e = (l – lo) / lo In the linear elastic region, the specimen elongates proportionately to the load up to the proportional limit. Beyond this limit, even though not linearly, the specimen will continue to deform elastically up to the yield point Y. In this elastic region, the material will return to its original length if we remove the load. Hooke’s Law applies in this region and gives us the Young’s Modulus: E = Sigma / e If we increase the load and move beyond the yield point Y, the material begins to yield. In other words, the specimen begins to undergo plastic deformation. Plastic deformation means permanent deformation. The cross-sectional area of the specimen decreases permanently and uniformly. If specimen is unloaded at this point, the curve follows a straight line downward and parallel to the original line in the elastic region. If the load is further increased, the curve reaches a maximum and begins to decrease. The maximum stress point is called the tensile strength or ultimate tensile strength and is denoted as UTS. The UTS can be interpreted as the overall strength of materials. When load is greater than the UTS, necking occurs on the specimen and the elongation between gage marks is no longer uniform. In other words, the specimen becomes really thin at the location where necking occurs. During necking, the elastic stress drops. If the test is continued, the engineering stress drops further and the specimen fractures at the necking region. The stress level at fracture is the fracture stress. The strain at point of fracture is an indicator of ductility. The strain up to the UTS is referred to as uniform strain, and the elongation at fracture is referred to as total elongation. Elongation = ((lf – lo) / lo) x 100 Reduction of Area = ((Ao – Af) / Ao) x 100 Elongation and reduction of area are good indicators of ductility.
de / dt = - v / ho, where v is die speed, ho original specimen height. True strain rate on the other hand is: de = dt = - v/ h, with h being the instantaneous specimen height. To keep the true strain rate constant during the test, a cam plastometer thru a cam action reduces the magnitude of v proportionally as the specimen height h decreases during the test. Using the compression test ductilities of materials are determined by observing cracks formed on barreled cylindrical surfaces. Another test with some differences in the die and workpiece geometries is the Y’ = 1.15 Y
Here, T is the applied torque, r is the mean radius and t is the thickness of the reduced section in the middle of the tube. Shear strain on the other hand is given by: ß = r Ø / l Here l is the length of the reduced section and Ø is the twist angle in radians. Within the elastic range, the shear modulus (modulus of rigidity) is expressed as: G = The relation between shear modulus and the modulus of elasticity is: G = E / 2( 1 + The torsion test is applied to solid round bars at elevated temperatures to estimate the forgeability of metals. The more twists the material can withstand prior to failure, the more forgeable it is.
Sigma = M c / I Here, M is the bending moment, c is one-half of the specimen depth and I is the moment of inertia of the cross-section. The magnitude of stress is the same in both three and four-point bending when all other parameters are kept constant. The four-point test is likely to result in a lower modulus of rupture as compared to the three-point test. Another superiority of the four-point bending test over the three point bending test is that its results are more consistent with less statistical scattering of values.
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