Consider a material composed of equal volumes having different yield strengths, YB = 1.5YA, but the same elastic moduli, EA = EB. Assume that during strain- ing both regions undergo the same strains (εA = εB ) and that there is no strain- hardening in either region.
A. Let the material be subjected to a tensile strain εA = εB = 2YB/E. Sketch the individual and overall stress strain curves, σ A, σ B, and σ av = (σ A + σ B)/2. What is the overall yield strength of the material (i.e., the value of σav corresponding to the ?rst deviation from linearity)?
B. Now consider the behavior on unloading to σ av = 0. Add plots of σ A, σ B, and o av to your sketch. What is the level of residual stress in each region?
C. After loading in tension and unloading, consider the behavior on loading un- der compression until the entire material yields. Assume that the tensile and compressive yield strength of each region is the same (|YAcomp|=YAtens and |YBcomp|= YBtens). Add the compressive behaviors to your plot. What is the new overall yield strength in compression and how does this compare with what the overall yield strength would be if it had not been ?rst loaded in tension?