Load (N) 4000 3500 3000 X (fracture) 2500 2000 1500 1000 500 0 0 4 6 8 10 12 Extension (mm) Fig. 2 Load versus extension for Aluminum 6061-T6 during a tensile test 162 Chapter 6 / Mechanical Properties of Metals true strain Furthermore, it is occasionally more convenient to represent strain as true strain ET, defined by Definition of true strain &r=In- (6.16) If no volume change occurs during deformation-that is, if A=Aolo (6.17) then true and engineering stress and strain are related according to Conversion of engineering stress =(1+c) to true stress (6.18a) ET=In (1+ c) (6.18b) Conversion of engineering strain to true strain True stress-true strain relationship in the plastic region of deformation (to the point of necking) Equations 6.18a and 6.18b are valid only to the onset of necking; beyond this point, true stress and strain should be computed from actual load, cross-sectional area, and gauge length measurements. A schematic comparison of engineering and true stress-strain behaviors is made in Figure 6.16. It is worth noting that the true stress necessary to sustain increasing strain continues to rise past the tensile point M. Coincident with the formation of a neck is the introduction of a complex stress state within the neck region (ie., the existence of other stress components in addition to the axial stress). As a consequence, the correct stress (axial) within the neck is slightly lower than the stress computed from the applied load and neck cross-sectional area. This leads to the "corrected" curve in Figure 6.16. For some metals and alloys the region of the true stress-strain curve from the onset of plastic deformation to the point at which necking begins may be approxi- mated by Key (6.19) In this expression, K and n are constants; these values vary from alloy to alloy and also depend on the condition of the material (whether it has been plastically de- formed, heat-treated, etc.). The parameter n is often termed the strain-hardening exponent and has a value less than unity. Values of n and K for several alloys are given in Table 6.4. Stress True M M Corrected Engineering Figure 6.16 A comparison of typical tensile engineering stress-strain and true stress-strain behaviors. Necking begins at point M on the engineering curve, which corresponds to M' on the true curve. The "corrected" true stress-strain curve takes into account the complex stress state within the neck region. Strain