微小特征尺度塑性变形的二阶功理论研究

Many recent experimental studies show that peculiar strain burst events are universal in plastic deformation of single crystal metals of small feature sizes. This Research Proposal considers this strain burst phenomenon as a kind of instability behavior inside material system, starts from the classical Hill stability condition, to investigate the applicability and universality of second order work criterion as a criterion for strain burst judgment. First, theoretical analysis will be performed for the strain burst periods, including their energy balance equations, second order work variables and its relation to Drucker stability’s postulate. Then, mechanical tests under combined loads such as compression and torsion, bending and torsion, will be done using small-sized specimens, and the aim is to examine the validity of second order work criterion under general loading conditions. Based on these, initial yielding condition and hardening condition will be proposed for the single crystal metals with feature sizes between 100 nm and 20 micrometer. All these may help us to develop a new constitutive theory for small-sized metal plasticity, considering the second order work as a basis. These issues are scientifically important in describing the plastic deformation of small metals and making certain predictions related, and also practically beneficial for designing, fabricating, deformation and strength analysis of small-sized metals and the related components and structures.

近年来许多实验测试表明，微纳米特征尺寸金属塑性变形过程中普遍存在着十分特殊的应变突变现象。本项目将应变突变看作材料内部的一种失稳行为，从经典Hill稳定性条件的二阶功准则出发，探讨二阶功准则用于判别应变突变的一般性和合理性。首先对应变突变过程中能量守恒情况、二阶功参量、与Drucker公设关系等问题进行理论分析，然后开展微小金属试样在压缩和扭转、弯曲和扭转等联合作用下的加载实验测试，考察微尺度金属在复杂加载条件下应变突变二阶功准则的有效性。在此基础上，针对100纳米至20微米范围内特征尺寸的单晶金属，提出应变突变情形下的初始屈服条件和强化条件，进一步尝试构建以二阶功参量为基本要素的微尺度塑性本构新理论。这些工作对于合理描述和理论预测微尺度金属塑性变形十分重要，同时也关系到微纳米金属材料及其结构的设计、加工、变形分析和强度计算，能够支撑相关微小器件和系统的高性能设计、制备与安全使用。

本项目旨在构建微小特征尺寸金属塑性变形的应变突变理论。研究的出发点是将应变突变现象看作材料内部的一种失稳行为，基于经典Hill稳定性条件的二阶功准则，考察微尺度金属在复杂加载条件下应变突变二阶功准则的有效性。工作中针对微纳米特征尺度金属塑性变形行为，提出了基于二阶功参量、动能变化的应变突变一般性判据，该准则能够适用于复杂加载情形；建立了基于平均应力-应变曲线的1%初始屈服条件，发现了该平均屈服应力服从类韦伯随机分布；提出了基于位错源物理机制的应变强化模型、尺寸相关的应变强化模型、单滑移和多滑移情形下的特殊应变强化模型。由此，初步建立了基于上述要素的二阶功微小尺度金属塑性变形新理论。该塑性本构新理论以二阶功量W2为核心要素，是对经典J2塑性流动理论的一种新发展。这些工作有助于合理描述和理论预测微尺度金属塑性变形，相信能够用于微纳米金属材料及其结构的设计、加工、变形分析和强度计算，支撑相关微小器件和系统的高性能制备与安全使用。