Mechanical Properties of Materials The strength of a material is not only the only criterion that must be considered in designing structures. Mechanical properties such as hardness, toughness, ductility determine the selection of a material. These properties are determined by making tests on the materials and comparing the results with established standards. Stress strain diagrams Test results generally depend upon the size of the specimen being tested. Since it is unlikely that we will be designing a structure having parts that are the same size as the test specimen, we need to express the test results in a form that can be applied to members of any size. A simple way to achieve this objective is to convert the test results to stresses and strains. Calculation of stress: The axial stress б in a test specimen is calculated by dividing the axial load P by the cross sectional area. When the initial area of the specimen is used in calculation, the stress is called nominal stress (also named as engineering stress or conventional stress) When the actual area of the bar at the cross section where failure occurs is taken for stress calculation then this stress is called true stress. Calculation of strain: If the initial gage length is used, then nominal strain is obtained. Since the distance between the gages marks increases as the tensile load is applied, we can calculate the true strain (also named natural strain) at any value of the load by using the actual distance between the gage marks. Characteristics features of a typical stress strain diagram: Sample Description Test Name : : M.S Rod Tensile test Figure-1: Typical stress-strain diagram of MS Rod Description: The stress strain diagram of a MS Rod is shown in the Figure-1. Strains are plotted on the horizontal axis and stresses on the vertical axis. The diagrams begin with a straight line from the origin O to point A, which means that the relationship between stress and strain in this initial region is not only linear but also proportional. Beyond point A, the proportionality between stress and strain no longer exists; hence the stress at A is called the Proportional limit. The slope of the straight line from O to A is called modulus of elasticity. With an increase in stress beyond the proportional limit, the strain begins to increase more rapidly for each increment in stress. Consequently, the stressstrain curve has a smaller and smaller slope, until, at point B, the curves becomes horizontal. Beginning at this point, considerable elongation of the test specimen occurs with no noticeable increase in the tensile force (from B to C). This phenomenon is known as yielding of the material and point B is called yield point. The corresponding stress is called yield stress. In the region from B to C, the material becomes perfectly plastic, which means that it deforms without an increase in the applied load. After undergoing the large strains that occur during yielding in the region BC, the steel begins to strain harden. During strain hardening, the material undergoes changes in the crystalline structure, resulting increased resistance of the material to further deformation. Elongation of the test specimen in this region requires an increase in the tensile load, and therefore stress-strain diagram has a positive slope from C to D. the load eventually reaches its maximum value and the corresponding stress at D is called ultimate stress. Further stretching of bar is actually accompanied by a reduction in the load and fracture finally occurs at a point such as E. When a test specimen is stretched, lateral contraction occurs. The resulting decrease in cross sectional area is too small to have a noticeable effect on the calculated value of stresses up to about point C, but beyond that point the reduction in area begins to alter the shape of the curve. In the vicinity of ultimate stress, the reduction in area of the bar becomes clearly visible and a pronounced necking of the bar occurs. If the cross sectional area at the narrow part of the neck is used to calculate the stress, the true stress-strain curve is obtained To define a clear yield point When a material does not have definite yield point, an arbitrary yield stress may be determined by the offset method. A straight line is drawn on the stress-strain diagram parallel to the initial linear part of the curve but offset by some standard strain, such as 0.002. The intersection of the offset line and the stress-strain curve defines the yield point. Some important parameter Percent elongation = (L1 – L0)/L0 * 100 Where, L1 = Distance between gage marks at fracture L0 = Original gage length Percent reduction in area = (A0 – A1)/A0 * 100 Where, A0 = Original cross sectional area A1 = Final area Mechanical properties •Elasticity: Elasticity is that property which enables a body deformed by stress to regain its original dimensions when the stress is removed. •Plasticity: A perfectly plastic body is one which does not make any recovery of its original dimensions upon the removal of a stress. •Stiffness: Stiffness is the property that enables a material to withstand high unit stress without great unit deformation. Stiffness is associate with resistance to bending. •Ductility: Ductility is the property that enables a material to undergo plastic deformation under tensile stress. •Malleability: Malleability is the property which enables a material to undergo plastic deformation under compressive stress. •Brittleness: Brittleness is the absence of plasticity. A brittle material is neither ductile nor malleable. •Toughness: Toughness is the property of a material that enables it to endure shock or blows. Typical stress-strain diagram for brittle materials Figure-2: Stress-strain diagram of brittle material Assignment – 01 The following data were obtained during a tension test of an aluminum alloy. The initial diameter of the test specimen was 0.505 inch and the gage length was 2.0 inch. Load (lb) 0 2310 4640 6950 9290 11600 12600 14000 14400 14500 14600 14800 14600 13600 Elongation (inch) 0 0.00220 0.00440 0.00660 0.00880 0.0110 0.0150 0.0200 0.0250 0.0600 0.0800 0.100 0.120 Fracture Plot the stress-strain diagram and determine the following mechanical properties: a) proportional limit b) modulus of elasticity c) yield point d) yield strength at 0.2% offset e) ultimate strength f) rupture strength Problems on Simple strain Problem-01 An aluminum bar having a cross sectional area of 0.5sqinch carries the axial loads applied at the position shown in the following figure. Compute the total change in length of the bar if E = 10 x 106 psi. Assume the bar is suitably braced to prevent lateral buckling. Problem-02 A bronze bar is fastened between a steel bar and an aluminum bar as shown in the figure. Axial loads are applied at the positions indicated. Find the largest value of P that will not exceed an overall deformation of 3.0mm, or the following stresses: 140 Mpa in the steel, 120 Mpa in the bronze, and 80 Mpa in the aluminum. Assume that the assembly is suitably braced to prevent buckling. Problem-03 The rigid bar AB attached to two vertical rods as shown in the figure, is horizontal before the load P is applied. Determine the vertical movement of P if its magnitude is 50 KN. Problem-04 A uniform concrete slab of total weight W is to be attached shown in figure, to two rods whose lower ends are on the same level. Determine the ratio of the areas of the rods so that the slab will remain level.