脆性损伤材料Ⅲ型裂纹尖端的渐近场  

The Asymptotic Field of Mode Ⅲ Crack Tip in Brittle Damage Material

作　　者：王秀红[1,2] 刘波[1] 唐立强 

机构地区：[1]河北工业大学机械工程学院,天津300130 [2]天津商业大学理学院,天津300134 [3]哈尔滨工程大学航天与建筑学院,哈尔滨150001

出　　处：《力学季刊》2011年第4期577-583,共7页Chinese Quarterly of Mechanics

基　　金：国家自然科学基金资助项目(10172032);河北省自然科学基金资助项目(E2011202011;A200900005)

摘　　要：裂纹尖端应力、应变损伤场的研究是一个十分复杂的问题,其核心问题是如何给出描述材料的损伤本构方程和裂纹尖端中物理量奇异量级的判定。考虑到损伤过程是能量(应变)累积的过程,初始损伤门槛值存在,在Lemaitre研究的基础上,给出带有初始损伤量并与应变成幂次关系的脆性材料损伤本构方程;在应力(应变)为有限值的假设条件下,研究了Ⅲ型裂纹尖端损伤场的构造,给出了裂纹尖端应力(应变)渐近场解,讨论了裂纹尖端初始损伤区和完全损伤破坏区的尺度与材料参数的关系。这些工作为材料的工程设计和评估结构的可靠性提供了理论依据。The research of crack-tip field in damage materials is a very complex problem. The key question is how to give the damage constitutive equation and determine the crack tip singularity order of the physical quantities magnitude. Since the damage process is a process which the energy （strain） accumulates and the initial damage threshold value exists, the brittle material damage constitutive equation that has the initial damage quantity and the power order relationship with strain is given on the Lemaitre＇s re- search foundation. Under the assumption that stress （strain） is finite, the construction of Mode HI crack tip damage fields is studied and the solution of crack-tip stress （strain） asymptotic field is given. Finally, the relationship of the initial crack tip damage zone and full damage zone scale and material parameters are discussed. These works provide theoretical basis for the material engineering design and the appraisal structure reliability.

关 键 词：非线性脆性损伤材料的本构方程 Ⅲ型裂纹尖端场 损伤场的构造 

分 类 号：O34[理学—固体力学]