多価条件と塑性不安定の関連

概要

論文の詳細を見る
The condition necessary for the multiplicity in deformation rate was give by Hill. The condition is Δε_uΔs_u=0,where s_u denotes the nominal stress rate, and Δ shows the difference between any two multiple solutions. However, many proposed criteria of plastic instability in published literature did not take into consideration this necessary condition. They were based on phenomenological aspects, for example, simultaneous stationarity of loads, that is, s_i=0,which corresponds to the special case of the necessary condition. We discovered that the necessary condition can make the equivalent strain rate difference Δε_g indefinite at the critical deformation. The sufficient condition for the multiplicity is deduced from the requirement which makes the equivalent strain rate ε_g indefinite. This is given by ε_us_u=0. In the plane stress state, the sequential onset of diffuse necking (by Swift) and localized necking (by Hill) is observed, and they have been thought to be phenomena based on plastic instability. Detailed examination of their occurrences reveals that the former satisfies the instability condition but the latter does not. Therefore, in localized necking, multiplicity does not arise, and localized necking is merely the plastic deformation confined into a thin layer with a rigid region on its both sides.
一般社団法人日本機械学会の論文
1998-01-25