10-2四个强度理论及其相当应力 Theory of Strength and its equivalent stresses Ⅱ塑性流动准则 The strength theories about yielding problems (4)最大形状改变比能理论( The maximum distortion energy theory) 认为最大形状改变比能u是引起材料屈服的主要因素 破坏条件: D u Dix a 强度条件=1(- 3 (104) |ox-∞n)+(2-oy+(-y1+:+0+ 1+ 6E 6E (单向拉伸屈服时:σ1=a,O2=a3=0 土 0 +4τ O1-62)+(02- 2 (O2-0 3 +3 t§10-2 四个强度理论及其相当应力 Theory of Strength and its equivalent stresses Ⅱ.塑性流动准则The strength theories about yielding problems ( ) ( ) ( )    ( : , 0 0 6 1 6 1 1 2 3 2 2 2 3 1 2 2 3 2 1 2 = = = + + + − + − + − = + s s s s s s  s s s s s s  s s s E E 单向拉伸屈服时  (4)最大形状改变比能理论(The maximum distortion energy theory) 认为:最大形状改变比能uD是引起材料屈服的主要因素 破坏条件: uD = uDjx (a) 强度条件: ( ) ( ) ( )  [ ] 2 1 2 3 1 2 2 3 2 s r4 = s1 −s 2 + s −s + s −s  s --(10-4) 适用范围: 与(3)相同,但比其更精确(对塑性材料而言) t t’ s 例题:求图示微元体的相当应力sr3和sr4 s   2 2 2 3 1 2 2 3 2 4 1 2 2 2 2 3 1 3 2 2 3 1 ( ) ( ) ( ) 3 2 1 , 0 4 2 2 s s s s s s s s t t s s s s s t s s s s = − + − + − = +  + = = − = +      =      r  r