泊松比对静止平面应变裂纹尖端的理想塑性应力场的影响
Effect of the Poisson Ratio on the Perfectly Plastic Stress Field at a Stationary Plane-Strain Crack Tip
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摘要: 在裂纹尖端的理想塑性应力分量都只是θ的函数的条件下,利用平衡方程和含有泊松比的Mises屈服条件,本文导出了静止平面应变裂纹尖端的理想塑性应力场的一般解析表达式.将这些一般解析表达式用于具体裂纹,我们就可以得到静止平面应变Ⅰ型、Ⅱ型及Ⅰ-Ⅱ复合型裂纹尖端的理想塑性应力场的解析表达式,这些表达式含有泊松比.Abstract: Under the condition that all the perfectly plastic stress components at a crack tip are the functions of θ only, making use of equilibrium equations and Von-Mises yield condition containing Poisson ratio, in this paper, we derive the generally analytical expressions of perfectly plastic stress field at a stationary plane-strain crack tip. Applying these generally analytical expressions to the concrete cracks, the analytical expressions of perfectly plastic stress fields at the stationary tips of Mode Ⅰ, Mode Ⅱ and Mixed-Mode Ⅰ-Ⅱ plane-strain cracks are obtained. These analytical expressions contain Poisson ratio.
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[1] 林拜松,静止裂纹尖端的理想塑性应力场,应用数学和力学,6(5)(1985), 475-421, [2] 林拜松,平面问题奇点附近的理想塑性应力场的一般解析表达式,应用数学和力学(待发表). [3] 林拜松,平面应变和反平面应变复合型裂纹尖端的理想塑性应力场,应用数学和力学,6 (9)845-852,(1985). [4] 曾国平、黄文彬,需要考虑材料泊松比的某些塑性力学问题,力学与实践,11(3)(1989),35-39. -
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