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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。
The shape and size of the plastic zone of type Ⅰ crack tip were solved by geometric center line (GM) yield criterion, and the results based on Mises and Tresca criteria were compared. It is shown that under the plane strain condition, the plastic zone area solved by the GM criterion is between the Tresca and Mises results. The Tresca plastic zone has the largest area, the Mises area is the smallest, the GM plastic zone and the Mises plastic zone are very close, and the plastic zone of the three are dumbbells shape. Under the plane stress, the plastic zone of GM and Mises are still the closest and sprouts-like, and the plastic zone of Tresca is the largest. Regardless of plane stress or plane strain, the GM criterion results have the best approximation to the Mises result.