残余应力及尺寸效应对纳米压痕力学性能的影响研究  

Effect of residual stress and size effect on the mechanical properties of nanoindentation

作　　者：卜家贺 冯露[1] 张静[1] Bu Jiahe;Feng Lu;Zhang Jing(Department of Mechanics,Tianjin University,300354,Tianjin,China)

机构地区：[1]天津大学力学系,天津300354

出　　处：《应用力学学报》2020年第6期2325-2331,I0002,共8页Chinese Journal of Applied Mechanics

基　　金：国家自然科学基金(11272231,11890682,61727810)。

摘　　要：为研究残余应力对材料纳米压痕力学性能存在的影响,本文基于低阶应变梯度塑性理论(CMSG),提出了一个采用位错密度描述残余应力的理论模型。根据该理论模型构造了相应的数值积分方案,并结合有限元模型数值分析了尺寸效应和初始残余应力对纳米压痕力学性能的影响。模拟结果发现,残余应力对材料硬度和纳米压痕载荷-位移曲线有显著影响。残余压应力几乎不影响塑性影响区的大小,但由于压痕产生的压应力场和残余压应力场叠加,使得产生压痕后的应力值更大,而残余拉应力对塑性影响区有较大影响。残余应力的存在会导致样品内位错快速增殖,位错密度几乎是无残余应力的10倍。此外,该模型成功地预测了压痕尺寸效应(ISE),即随着压痕深度减小,硬度增加。模型预测结果与已有实验结果的误差在16%以内,从而验证了模型的有效性。During the preparation,forming and heat treatment of materials,residual stress is inevitably generated,which has a significant influence on the mechanical properties of materials.Based on the low-order strain gradient plasticity theory(CMSG),a theoretical model for describing residual stress using dislocation density is proposed.Based on this theoretical model,the numerical integration scheme is constructed,and effects of size effect and initial residual stress on the mechanical properties of nanoindentation are analyzed by finite element model.Simulation results obtained show that residual stress has a significant effect on material hardness and nanoindentation load-displacement curve.The compressive residual stress hardly affects the size of the plastic affected region.However,the superposition of compressive stress field and compressive residual stress field caused by indentation makes the stress value larger,while the tensile residual stress has a great influence on the plastic affected region.The existence of residual stress will lead to the rapid dislocation multiplication in the sample,and the dislocation density is almost 10 times than that of no residual stress case.In addition,the model successfully predicted the indentation size effect(ISE),in which the hardness increases as the indentation depth decreases.The validity of the model is verified by comparison with experimental data.

关 键 词：残余应力 几何必须位错 低阶应变梯度塑性理论 纳米压痕 尺寸效应 

分 类 号：O344[理学—固体力学]