摘要
脆性固体在高应变率拉伸过程中常破碎为多块碎片.论文通过一个一维理论模型,研究动态脆性碎裂过程中固体内部载荷卸载规律,以及碎片尺度的计算方法.假设一维固体中裂纹等间距分布、同时起裂,研究均匀应变率拉伸作用下裂纹阵列的扩张过程.采用线弹性波动方程组描述未断裂固体的动力学关系,采用粘滞断裂模型(cohesive fracture model)描述裂纹的扩张行为,形成完整的初边值问题.采用沿特征线的有限差分计算格式求解控制方程组,得到固体在碎裂过程不同时刻下单位裂纹体内部的应力分布曲线,以及单位裂纹体平均应力随时间的变化规律,确定单位裂纹体达到完全断裂所需要的时间.在给定应变率下,分析不同裂纹间距下的碎裂卸载时间,以及使单位裂纹体以最快速度完全卸载所对应的最佳裂纹间距,并以此间距估算脆性固体在自然动态碎裂过程中的平均碎片尺度.进一步研究了具有不同粘滞性断裂特性的脆性固体的碎片尺度计算数值的差异.
Brittle solids usually break into many pieces（fragmentizes） during a uniform high strain rate expansion process.This paper established a 1-D theoretical model to study the inner unloading of a 1-D brittle solid during a fragmentation process,and developed a method to calculate the average fragment size.Assuming that there exists an array of equally-spaced cracks in the 1-D solid,and the cracks open and grow simultaneously under a rapidly expanding rate.By symmetry,a unit crack body containing a crack is analyzed,with the separation behavior described by a cohesive law,and the dynamic response of the undamaged solid described by the elastodynamic equations.The problem is numerically solved using a differential scheme along the characteristic lines.Stress distributions in the crack body at different times and the average stress across the crack body are gained.The critical time at which the average stress is unloaded to zero is determined.It is found that for a prescribed strain rate,there exists an optimum crack spacing corresponding to the rapidest unloading process.Assuming that in a natural fragmentation process the brittle solid is unloaded in the fastest way,the average fragment size can be estimated.The calculation results show that this fragment size estimation agrees fairly well with the numerical results obtained previously allowing random crack nucleation.Effect of the cohesive fracture law on the average fragment size is also investigated with this ＂rapidest unloading property＂.
出处
《固体力学学报》
CAS
CSCD
北大核心
2010年第3期286-295,共10页
Chinese Journal of Solid Mechanics
基金
国家自然科学基金(10572066
10972108)
浙江省科技项目(2006E10027)
宁波大学王宽诚幸福基金资助
关键词
脆性固体
碎裂
裂纹阵列
特征线计算
最快卸载
碎片尺度
brittle solids
fragmentation
crack array
characteristics method
the rapidest unloading
fragment size
