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构建耦合材料微介观结构信息的物理模型是损伤力学的发展趋势, 同时也能不断促进数值计算方法、实验技术以及理论研究的发展. 因缺乏微介观尺度孔洞分布特征的演化信息, 目前的层裂损伤模型不仅在极端加载条件下的应用受到制约, 同时也无法有效提供一些工程中十分关注的材料损伤与最后材料破碎颗粒度之间的关联信息, 因而迫切需要发展反映损伤材料内部微介观孔洞分布特征变化规律的层裂损伤模型. 通过对孔洞成核过程中各种影响因素的分析, 结合孔洞早期增长的特点, 同时考虑到解析求解方便, 本文给出了基于余弦函数形式的孔洞成核概率分布函数, 采用新的孔洞成核概率函数的解析计算结果不仅与分子动力学计算的孔洞数随时间变化结果相符, 而且与损伤发展早期的金属钽层裂实验结果也符合很好, 也就是说, 采用新的孔洞成核概率函数可以在一定程度上反映层裂损伤早期微孔洞分布特征的变化规律.The development trend of spallation damage mechanics is to construct a physical model that couples information with micro-mesoscale structure of materials, which also promotes the development of numerical calculation methods, experimental techniques and theoretical research. The mechanism responsible for plastic deformation and failure of structural metal materials at high strain rates is complex and ainfluenced by heterogeneities in the micro-mesoscale structure that comprises the distribution of grain boundaries, interfaces, and pre-existing densities voids. The distribution of these mesoscale heterogeneities can provide either strengthening behavior or void nucleation sites and influence spall failure behavior. Due to the lack of evolutionary information of micro-mesoscopic void distribution characteristics, the current spallation damage model is not only restricted in its application in extreme environments with high strain rates, high pressures, and shock, but also does not effectively provide some information about the correlation between material damage and final material fragmentation particle size, which is of very concern in engineering. Therefore, it is urgent to develop a spallation damage model that can reflect the variation law of micro-mesoscopic void distribution characteristics in damaged materials. The probability distribution function of void nucleation based on cosine function is given in this work by analyzing various influencing factors in the process of void nucleation, combining the characteristics of early void growth, and considering the convenience of analytical solution. The analytical calculation results of the new probability function of void nucleation are consistent not only with the results of the variation of void number with time calculated by molecular dynamics, but also with the experimental results of tantalum spallation in the early stage of damage development, that is to say, the new probability function of void nucleation can reflect the variation law of micro-void distribution characteristics in the early stage of spallation damage to a certain extent.
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图 2 孤立孔洞数随时间的变化
Fig. 2. Number of independent voids as a function of time from MD data and our work.
图 3 所有的孔洞数随时间的变化
Fig. 3. Number of sum of independent voids and void cluster as a function of time from MD data and our work.
图 4 孔洞体积份额(损伤度)随时间的变化
Fig. 4. Void volume fraction as a function of time from MD data and our work.
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