Properties of Metals DOE-HDBK-1017/1-93 STRESS-STRAIN RELATIONSHIP A graph of the results is made from the tabulated data.  Some testing machines are equipped with an autographic attachment that draws the graph during the test.   (The operator need not record any load or elongation readings except the maximum for each.)  The coordinate axes of the graph are strain for the x-axis or scale of abscissae, and stress for the y-axis or scale of ordinates.  The ordinate for each point plotted on the graph is found by dividing each of the tabulated loads by the original cross-sectional area of the sample; the corresponding abscissa of each point is found by dividing the increase in gage length by the original gage length.   These two calculations are made as follows. Stress   = = psi or lb/in.² (2-9)                                                 load area  of  original  cross  section      P A_o Strain   = (2-10)                                                           instantaneous  gage  length      original original  gage  length                                  elongation original  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."  They are not true stress and strain, which can be computed on the basis of the area and the gage length that exist for each increment of load and deformation.  For example, true strain is the natural log of the elongation (ln (L/L_o)), and true stress is P/A, where A is area.  The latter values are usually used 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  are almost identical. Figure 3   Typical Ductile Material Stress-Strain Curve The graphic results, or stress-strain diagram, of a   typical   tension   test   for   structural   steel   is shown in Figure 3.  The ratio of stress to strain, or  the  gradient  of  the  stress-strain  graph,  is called   the   Modulus   of   Elasticity   or   Elastic Modulus.  The slope of the portion of the curve where  stress  is  proportional  to strain  (between Points   1   and   2)   is   referred   to   as   Young's Modulus and Hooke's Law applies. The  following  observations  are  illustrated  in Figure 3: Hooke's   Law   applies   between Points 1 and 2. Hooke's Law becomes questionable between Points 2 and 3 and strain increases more rapidly. Rev. 0 Page 17 MS-02