两类应变梯度塑性理论的热力学基础与实验验证

In this proposal, we intend to study the thermodynamic basis of two frameworks of strain gradient plasticity – MSG flow theory and Gudmundson theory – by combining the basic thermodynamical principles under isothermal conditions and the virtual-work principles of Fleck-Hutchinson and Gurtin-Anand. We will study the physical nature of plastic flow rules for the MSG theory and the Gudmundson theory, and give a rigorous discussion on the issue of whether the plastic-strain gradient terms involved in the theories are energetic or dissipative. In order to demonstrate the influences of the loading conditions and the plastic-strain gradients on the mechanical behaviour of materials at small scales, we plan to apply the two frameworks of strain gradient plasticity to two typical examples having non-proportional loading, i.e. the cyclic torsion of thin metal wires and the bending of thin films with surface passivation. The cyclic torsion tests on thin metal wires will be performed to determine the material length scales involved in the two theories of strain gradient plasticity, and to answer the question of whether geometrically necessary dislocations mainly lead to energetic strengthening or dissipative strengthening. In addition, an improved micro-bending technique will be developed. By using this technique, the bending tests on thin passivated films will be performed to verify the existence of the phenomenon of stress gaps, which will be used to evaluate the validity of the incremental theory (e.g. MSG flow theory) and the non-incremental theory (e.g. Gudmundson theory). This research is significant to the development of a thermodynamically consistent theory of plasticity for accurately describing the plastic behaviour of materials at small scales.

通过连续介质热力学框架和Fleck-Hutchinson、Gurtin-Anand广义虚功原理，研究MSG和Gudmundson两类应变梯度塑性理论的热力学基础。探讨两类理论中塑性流动法则的物理特性，证明理论中所引入的塑性应变梯度项是储能的还是耗散的。基于MSG流动理论和Gudmundson理论，分析金属丝循环扭转和钝化薄膜弯曲两种典型非比例加载问题，揭示加载条件和塑性应变梯度对材料变形行为的影响。采用金属丝循环扭转实验，确定两类理论中材料长度参量的大小，澄清几何必需位错主要引起储能强化还是耗散强化这一问题。发展微弯曲实验技术，利用钝化薄膜弯曲实验，验证“应力跳跃”现象的存在性，讨论以MSG流动理论为代表的“增量”理论和以Gudmundson理论为代表的“非增量”理论的合理性。本项研究对建立热力学自洽的、能够准确描述微尺度材料塑性变形行为的连续介质力学理论具有重要意义。

应变梯度塑性理论在微尺度材料力学行为问题的研究中发挥了巨大作用。本项目针对典型高阶应变梯度塑性理论的热力学基础和实验验证问题开展了深入研究。主要成果包括：1. 基于Fleck-Hutchinson虚功原理和Gurtin-Anand自由能不等式，研究了MSG应变梯度塑性理论流动法则的热力学相容性，严格证明了该理论中引入的应变梯度项是储能的；2. 采用连续位错理论分析了单晶丝扭转问题，揭示了单晶微丝扭转尺度效应的物理机理和位错分布规律；3. 基于非接触式表面轮廓仪，发展了一种微梁弯曲测试技术，通过钝化薄膜弯曲实验，验证了“钝化致强”现象的存在，为发展合理的应变梯度塑性理论提供了重要实验支撑；4. 发展一种测量材料尺度常数的非接触式实验方法，基于修正的偶应力理论获得了铜和钛两种材料的尺度常数，发现镍微悬臂梁的高阶模态振动和非线性振动存有尺度效应；5. 搭建了可控温纤维拉伸试验平台，在不同温度场下对金属丝进行了应力释放实验，获得了温度对应力释放特性的影响规律，揭示了位错与晶界间的相互作用是变形的主导机制；6. 对金属丝进行了扭转应力释放实验，观测到扭转应力释放特性具有尺度效应，且初始应力在弹性极限附近时应力释放出现峰值；7. 对Gudmundson和Fleck-Hutchinson高阶应变梯度塑性理论进行了有限元实现，并分析了细丝扭转、薄膜弯曲、钝化薄膜拉伸、受限薄板剪切等问题，揭示了加载条件和应变梯度对材料变形行为的影响。在项目执行期间，在国际权威期刊上发表SCI论文16篇，获国家发明专利1项；参加学术会议18人次。培养研究生9名，其中博士生3名。