Viscoplastic Solution to the Field at Steadily Propagating Crack Tip in Linear-Hardening Materials
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摘要: 采用弹粘塑性力学模型，对线性硬化材料中平面应变扩展裂纹尖端场进行了渐近分析．假设人工粘性系数与等效塑性应变率的幂次成反比，通过量级匹配表明应力和应变均具有幂奇异性，奇异性指数由粘性系数中等效塑性应变率的幂指数唯一确定．通过数值计算讨论了Ⅱ型动态扩展裂纹尖端场的分区构造随各材料参数的变化规律．结果表明裂尖场构造由硬化系数所控制而与粘性系数基本无关．弱硬化材料的二次塑性区可以忽略，而较强硬化材料的二次塑性区和二次弹性区对裂尖场均有重要影响．当裂纹扩展速度趋于零时，动态解趋于相应的准静态解；当硬化系数为零时便退化为HR(Hui-Riedel)解．Abstract: An elastic-viscoplastic constitutive model was adopted to analyze asymptotically the tipfield of moving crack in linear-hardening materials under plane strain condition.Under the assumption that the artificial viscosity coefficient was in inverse proportion to power law of the rate of effective plastic strain,it is obtained that stress and strain both possess power law singularity and the singularity exponent is uniquely determined by the power lawexponent of the rate of effective plastic strain.Variations of zoning structure according to each material parameter were discussed by means of numerical computation for the tip-field of modeòdynamic propagating crack,which show that the structure of crack tip field is dominated by hardening coefficient rather than viscosity coefficient.The secondary plastic zone can be ignored for weak hardening materials while the secondary plastic zone and the secondary elastic zone both have important influence on crack tip field for strong hardening materials.The dynamic solution approaches to the corresponding quasi-static solution when the crack moving speed goes to zero,and further approaches to the HR (Hui-Riedel) solution when the hardening coefficient is equal to zero.
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