幂硬化材料圆锥压入完整塑性区的应力分布模型  

Stress distribution model for the entire plastic zone of conical indentation with power-law hardening materials

作　　者：陈辉 蔡力勋[2] 彭晖[1] 毛卫国 李微[4] 傅作华 孟铮 CHEN Hui;CAI LiXun;PENG Hui;MAO WeiGuo;LI Wei;FU ZuoHua;MENG Zheng(Key Laboratory of Safety Control of Bridge Engineering,Ministry of Education,Changsha University of Science&Technology,Changsha 410114,China;School of Mechanics and Aerospace Engineering,Southwest Jiaotong University,Chengdu 610031,China;School of Materials Science and Engineering,Changsha University of Science&Technology,Changsha 410114,China;School of Energy and Power Engineering,Changsha University of Science&Technology,Changsha 410114,China)

机构地区：[1]长沙理工大学桥梁工程安全控制教育部重点实验室,长沙410114 [2]西南交通大学力学与航空航天学院,成都610031 [3]长沙理工大学材料科学与工程学院,长沙410114 [4]长沙理工大学能源与动力工程学院,长沙410114

出　　处：《中国科学：物理学、力学、天文学》2023年第1期91-100,共10页Scientia Sinica Physica,Mechanica & Astronomica

基　　金：国家自然科学基金(编号:52178186);湖南省自然科学基金(编号:2021JJ40553);湖南省教育厅优秀青年基金(编号:20B028);教育部重点实验室开放基金(编号:19KB04)资助项目。

摘　　要：经典接触力学提供了圆锥压入载荷-深度关系及应力分布的弹性解,也指明了任意钝形压头弹塑性压入的应变场近似符合膨胀空腔模型.本文回顾了前人基于膨胀空腔模型与弹塑性力学理论导出的幂硬化材料圆锥压入弹性区的应力解,并进一步借助受内压厚壁球壳应力解给出了圆锥压入塑性区内von-Mises等效应力表达式.通过数值验证发现有限元计算的等效应力与压入理论解在弹性区内较为一致,而在幂硬化材料的塑性区内仍存在较明显偏差.为进一步精准描述幂硬化材料圆锥压入完整塑性区的等效应力,结合量纲分析方法和有限元模拟建立了圆锥压入应力分布的新模型.最终在较大延性材料范围内验证了该模型,结果显示所有计算应力在完整塑性区范围内均与模型预测结果较为一致.The classical contact mechanics provides an elastic conical indentation solution,and verifies that the strain field of elastic-plastic indentation with an arbitrary blunt indenter mostly satisfies the expanding cavity model.This study reviews the stress solution of the elastic zone for conical indentation using power-law hardening materials derived from predecessors based on the expanding cavity model and elastic-plastic mechanics.Furthermore,the expression of vonMises equivalent stress in the plastic zone of conical indentation is determined according to the plastic stress solution of an internally pressurized thick spherical shell.The numerical verification revealed that the calculated equivalent stresses via finite element analysis are consistent with the theoretical solution of the elastic zone for conical indentation.However,a clear deviation in the entire plastic zone for the power-law hardening materials is still observed.Furthermore,to accurately describe the equivalent stress in the entire plastic zone of conical indentation for power-law hardening materials,a novel model for the indented stress distribution is established by combining the dimensional analysis method and finite element simulation.Finally,the stress model was verified using a wide range of ductile materials.The comparison results revealed that all of the calculated equivalent stresses are consistent with the model predictions for the entire plastic zone.

关 键 词：压入 膨胀空腔模型 量纲分析 有限元方法 

分 类 号：O344[理学—固体力学]