脆性固体中内聚断裂点阵列的扩张行为及间隔影响

建立一个一维模型, 分析脆性材料中多个等间距虚拟断裂点在均匀应变率拉伸作用下的扩张断裂过程. 采用线弹性波动方程组描述材料内部动力学关系, 采用线性内聚力断裂模型(linear cohesive fracture model)描述虚拟断裂点的扩张行为, 根据初始均匀拉伸条件和虚拟裂纹等间距假设给出定解条件, 形成一个初边值问题. 采用Laplace变换方法求解控制方程组, 得到虚拟断裂点扩张过程中内聚应力随时间变化曲线, 以及发生完全断裂的临界时间和单位裂纹体(碎片)的临界膨胀位移. 在此基础上分析应变率和裂纹间距对碎裂发生时间及单元裂纹体临界膨胀位移的影响. 在假设脆性材料在自然碎裂过程中单元裂纹体临界膨胀位移最小的基础上,进一步研究应变率对碎片尺度的影响. 

GROWTH OF AN ARRAY OF COHESIVE CRACK POINTS IN BRITTLE SOLIDS AND THE INFLUENCE OF CRACK SPACING

In this paper, an analytical model is established forinvestigating the dynamic fragmentation process of a brittle material thatcontains an array of fictitious cohesive cracks. The material expands atuniform strain rate, and the crack points are equally-spaced. Using theelastodynamic equations for the undamaged material and a linear cohesivefracture model for the separation of the cracks, the governing equations forthe stress and velocity in the material are deduced, which turned to be aninitial-boundary value problem (IBVP). By using Laplace transform technique,the IBVP is solved to obtain an exact expression for the cohesive stresshistory at the crack point. The material's fracture process is then studiedto determine the critical time when full fracture occurs, and the criticalexpansion of a unit crack body at this time. The influences of the crackspacing and the applied strain rate on the fracture and fragmentationprocess are investigated. Furthermore, by assuming that the critical crackbody expansion has the minimum value during a natural fragmentation process,the fragment size is estimated for different applied strain rates in thepresent study.