Explain why the three broken lines (simple tension, plane strain, and equal biaxial stretching) in Fig. 7.63a have those particular slopes.

Explain why the three broken lines (simple tension, plane strain, and equal biaxial stretching) in Fig. 7.63a have those particular slopes. Recall that the major and minor strains shown in Fig. 7.63 on p. 399 are both in the plane of the sheet. Thus, the simple tension curve has a negative slope of 2:1, reflecting the Poisson’s ratio effect in plastic deformation. In other words, the minor strain is one-half the major strain in simple tension, but is opposite in sign. The

plane-strain line is vertical because the minor strain is zero in plane-strain stretching. The

equal (balanced) biaxial curve has to have a 45_ slope because the tensile strains are equal

to each other. The curve at the farthest left is for pure shear because, in this state of strain,

the tensile and compressive strains are equal in magnitude (see also Fig. 2.20 on p. 49).

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