材料裂纹扩展分叉机理的晶体相场法研究

Phase-Field-Crystal Modeling for Crack Propagation and Branch of Materials

关键词:  晶体相场模型  临界应变  弹性应变能  裂纹扩展

Key words:  phase-field-crystal model  critical strain  elastic strain energy  crack propagation

摘要:

[目的]进一步探索材料裂纹扩展分叉的机理。[方法]采用晶体相场模型研究平面应力作用下材料裂纹扩展的动态演化过程,分析裂纹扩展过程体系自由能G、裂纹面积分数S、裂口周长L的变化特征;分别从G、S、L的变化阐述裂纹扩展以及三者与裂纹扩展临界应变ε_c的对应关系;探讨裂口扩展和主裂纹分叉与体系能量G的内在关联。[结果]无应力施加时期,裂纹面积分数S和裂口周长L没有变化;施加拉伸应力后,当系统应变达到一定程度时,S和L开始同时增加,此时的应变大小对应于裂纹启裂临界应变ε_c值。[结论]应力施加导致材料中心裂口处应力集中,体系能量上升,系统能量曲线一阶导数的拐点对应于中心裂纹启裂时刻或临界应变。自由能曲线一阶导数拐点处能量上升速率变缓,表明此时弹性应变能得到释放。

Abstract:

[Objective] The dynamic process of crack propagation under the biaxial tensile deformation is simulated by using the phase-field-crystal model.[Methods] The variation characteristics of the factors, such as the free energy G, crack area fraction S, crack circumference L, on crack propagation were analyzed. The crack propagation dynamic process and the corresponding relation of the critical strain for crack propagation were illustrated based on the changes of G, S, L in crack propagation. Both the crack propagation and the main crack bifurcation were investigated with their relationship to system energy G.[Results] The crack area S scores and fissure perimeter L did not change without applying stress.When the strain of system reached a certain extent, S and L began to increase at the same time.At this point the strain magnitude corresponds to the crack critical strain ε_c.[Conclusion] Application of stress to the center of the crack induces the stress concentration.The inflection point of first derivative for the free energy curve is corresponding to the crack propagation time.The first derivative of the free energy curve can be slowed down at the inflection point, which indicates that the elastic strain energy can be released at this time.