Properties of MetalsDOE-HDBK-1017/1-93STRESS-STRAIN RELATIONSHIPA graph of the results is made from the tabulated data. Some testing machines are equipped withan autographic attachment that draws the graph during the test. (The operator need not recordany load or elongation readings except the maximum for each.) The coordinate axes of the graphare strain for the x-axis or scale of abscissae, and stress for the y-axis or scale of ordinates. Theordinate for each point plotted on the graph is found by dividing each of the tabulated loads bythe original cross-sectional area of the sample; the corresponding abscissa of each point is foundby dividing the increase in gage length by the original gage length. These two calculations aremade as follows.Stress = = psi or lb/in.^{2}(2-9)loadarea of original cross sectionPA_{o}Strain =(2-10)instantaneous gage length originaloriginal gage lengthelongationoriginal gage length= = inches per inch x 100 = percent elongation(2-11)L L_{o}L_{o}Stress and strain, as computed here, are sometimes called "engineering stress and strain." Theyare not true stress and strain, which can be computed on the basis of the area and the gage lengththat exist for each increment of load and deformation. For example, true strain is the natural logof the elongation (ln (L/L_{o)}), and true stress is P/A, where A is area. The latter values are usuallyused for scientific investigations, but the engineering values are useful for determining the load-carrying values of a material. Below the elastic limit, engineering stress and true stress arealmost identical.Figure 3 Typical Ductile Material Stress-Strain CurveThe graphic results, or stress-strain diagram, ofa typical tension test for structural steel isshown in Figure 3. The ratio of stress to strain,or the gradient of the stress-strain graph, iscalled the Modulus of Elasticity or ElasticModulus. The slope of the portion of the curvewhere stress is proportional to strain (betweenPoints 1 and 2) is referred to as Young'sModulus and Hooke's Law applies.The following observations are illustrated inFigure 3:Hooke's Law applies betweenPoints 1 and 2.Hooke's Law becomes questionable between Points 2 and 3 and strain increasesmore rapidly.Rev. 0Page 17MS-02