GM屈服准则求解Ⅰ型裂尖塑性区

用几何中线(GM)屈服准则求解了Ⅰ型裂尖塑性区的形状与尺寸,对比了基于Mises和Tresca准则的求解结果。表明在平面应变条件下,GM准则求解的塑性区面积在Tresca和Mises结果之间,Tresca塑性区面积最大,Mises面积最小,GM塑性区与Mises塑性区非常接近,三者的塑性区均成哑铃状。在平面应力下,GM和Mises塑性区二者仍最接近并为豆芽状,Tresca的塑性区最大。无论平面应力还是平面应变,GM准则计算结果与Mises结果均有最佳接近度。

ANALYSIS OF PLASTIC ZONE OF MODE Ⅰ CRACK TIP BY GM YIELD CRITERION

Based on GM(geometrical midline) yield criterion,the analytical solutions for the shape and size of a mode I crack tip plastic zone are derived.Comparing the solutions with those based on Mises and Tresca criteria shows that under a plain strain condition the area of a plastic zone on GM is between both on Tresca and Mises criteria,and very close to Mises one.Among the areas,Tresca's is the largest and Mises is the smallest and all three zones are dumbbell shaped.However,for plane stress,the plastic zones based on GM and on Mises criteria are also proximal but with a bean-spout shape,while the area on Tresca is still the largest.Whenever plane stress or plane strain conditions the result calculated by GM criterion is always an optimal approximation to that calculated by Mises criterion.