Strain hardening and instability in biaxially streched sheets

Abstract

This work is concerned with the origins of the two different patterns of failure limits in biaxially stretched sheets which were recently described in Ref. 1: the brass-type in which the limit strain is insensitive to strain state, and that of ferritic steel in which the limit strain increases as the imposed strain-ratio, ρ = e2/e1, changes from zero (plane-strain tension) toward unity (balanced biaxial tension). An earlier proposal that different slip modes,i.e. wavy in ferrite vs planar in brass, might have contributed to these failurelimit differences was found not to be valid. There were two parts to the main experimental program: the prestraining of small sheets by proportional loading on different paths betweenρ = 0 andρ = 1, followed by tension testing, and a more direct measurement of strain hardening and instability between ρ ≅ — 1/2 (uniaxial tension) andρ = 0. The principal finding was that the overall hardening rate, essentially as it appeared in the material’s effective stress-strain curve, changed with the loading path. Inα brass it decayed as p was increased from ∼—1/2 to 1; in ferritic steel it increased; and in aluminum it was affected very little. Such changes in hardening rate cause similar changes in the material’s capacity for stable flow. The stable flow, in turn, is the base to which a quasistable-flow increment (whenρ is >0) is added in reaching the observed failure limit. Thus a base ofρ-dependent height can account for the failure-limit patterns. There is still no explanation for the ρ dependence of the hardening rate.