【作者】 梁文彦；

【导师】 王振清；

【作者基本信息】 哈尔滨工程大学 ， 固体力学， 2006， 博士

【摘要】 裂纹尖端场的研究是断裂力学研究的重要课题之一，它一直被力学工作者所关注。在所有的应力分析问题中，没有哪个问题像裂纹问题那样，受到众多的力学工作者如此持久的关切和进行详尽的分析，也没有哪个问题像裂纹那样，愈分析愈感到问题的复杂和困难。究其原因，裂纹问题与工程结构的破坏紧密相连，强大的工程实际的需要是推动裂纹问题研究的主要动力。 工程中许多材料，如聚合物、土壤、金属和岩石等，在某些条件，如高应变率或高温度下，往往同时出现弹性、粘性和塑性的特征，单凭粘弹性力学或塑性理论来讨论裂纹尖端应力、应变和其它物理量并来确定材料参数对裂纹尖端场的影响及材料破坏断裂准则会引起较大的误差。为了能够较好地解决这些实际问题，需要考虑与时间和荷载历程同时相关，具有弹性、粘性和塑性特征的弹粘塑性模型。 在扩展裂纹尖端，无论是准静态扩展还是动态扩展，都存在着一些难以解决的矛盾，如裂纹尖端场存在应力或应变的间断线，动态解不能退化为准静态解等，其原因在于以前的研究中忽略了材料的粘性效应这一影响。由于裂纹尖端在扩展过程中会出现较高的应变速率并产生大量不可逆的变形能，一部分变形能会以热的形式释放出来，导致裂纹尖端局部温度升高，此时材料具有粘性特征，因而材料的粘性性质对材料断裂性能影响的研究受到越来越大的重视。 本文考虑材料的粘性效应，采用一种比较简单然而实用的弹粘塑性模型来描述扩展裂纹尖端附近材料的应力应变关系。通过对材料的粘性系数做出合理的假设，即认为其与塑性应变率的幂次成反比，经过渐近分析确定了奇异性的阶次，推导出了该模型下的率敏感型本构方程。通过进一步的分析，材料的弹性、粘性和塑性三者可以在量级上得到合理的匹配。 采用这种率敏感型本构关系，本文对不可压缩条件下平面应变Ⅰ型、Ⅱ型和压剪混合型扩展裂纹的尖端场进行了渐近分析，分别求得了其裂纹尖端应力和应变场的动力学控制方程。对各个特征参数选取适当的数值，并结合不同问题的边界条件，对控制方程进行了数值计算，求得了完全连续的裂纹尖端应力和应变场。分析了不同问题中渐近解的性质，并讨论了解随各参数的变化规律。更多还原

【Abstract】 The research of crack-tip fields is one of the most important task of fracture mechanics. It has been attracting the attentions of mechanics researchers. In all stress analysis’s problem, there is no problem just like crack’s problem that get perpetual attention and elaborate analysis. In crack analysis, we will feel more and more complicate and difficult. Discuss its reason, we will find crack’s problem is tightly contact with the engineer’s problem, the main motive to drive crack’s problem is the mighty and practical need on the engineer.Many engineering materials such as polymer, soil, metal and rock et. al., often exhibit the features of elasticity, viscosity and plasticity at the same time under certain circumstances, for example, high strain-rate or high temperature. More error may arise if the theory of viscoelasticity or plasticity is employed solely to discuss the stress ,strain and other physical quantum and be used to confirm material parameter bring influence to crack-tip field and material fracture principle. The elastic-viscoplastic model should be considered in order to solve them better which possesses the features of elasticity, viscosity and plasticity as well as correlations to time and loading history.At the tip of a growing crack, some unresolved contradictions is existed whether quasi-static or dynamic growth, e.g. the existence of discontinuity of stress or strain at the crack-tip field, the unability of transformation from dynamic solution to quasi-static solution, et al. The reason is the influence on the viscosity of material is ignored. In propagating process, due to high strain rate will occur and a great amount of energy of irreversible deformation will be caused at the tip of crack, a part of energy will be released by form of heat, which will cause local temperature rise at the tip of crack, material possess the features of viscosity, Thus, the study of influence of material’s viscosity property on fracture performance of material has aroused more and more recognition.The viscosity is considered in the dissertation, with the adoption of a rather simple but practicable elastic-viscoplastic model to describe the stress-strain relation of the material at the crack-tip. With a rational assumption of the viscosity coefficient of the material, namely it has a inverse ration to the plastic strain rate raised to some power, the exponent of singularity is determined through asymptotic analyses, and the rate-sensitive constitutive equations is derived under the model. With the aid of further analyses, the elasticity, viscosity and plasticity of material can be logically matched on magnitude.With the adoption of the rate-sensitive constitutive relationship, it is asymptotically investigated the propagating tip fields of plane strain mode I,II and compress-shear mixed mode propagating crack under the condition of incompressibility, and the dynamics equations are obtained separately governing the stress and strain fields at the crack-tip. Numerical calculations of governing更多还原