基于应变梯度理论的微尺度循环塑性本构模型研究

The cyclic elasto-plastic deformations in the metal components of micro-instruments like micro-electro-mechanical-systems (MEMS) have many remarkable characteristics, including size effects in elastic limit and plastic hardening, anomalous Bauschinger effect, plastic softening and so on, which play an important role in properties of MEMS components. To date a constitutive model which is capable of predicting all these micron-scale effects is still missing. Thus, in this project we will establish a micron-scale cyclic plastic constitutive model based on the Fleck-Hutchinson strain gradient plasticity theory (FH SGP), by the following two strategies: 1. An elasto-plastic multiplicative decomposition method for strain gradients according to the orthogonal flow rule is proposed in order to guarantee the thermodynamical consistency, and the higher-order stress is calculated based on the strain gradient elasticity theory to ensure the continuous change in higher order stress. This way the theoretical issues of FH SGP arising when dealing with cyclic plastic deformations have been eliminated. 2. Multiple physical mechanisms which lead to the aforementioned micron-scale effects, including geometrically necessary dislocations, micro-plasticity, reversibility of dislocations and influences of surface/interface, are taken into account according to the Taylor dislocation theory when establishing the constitutive model. We will then develop the numerical simulation procedure accordingly and validate the newly proposed constitutive model by both simulations via discrete dislocation dynamics and experiments. If this project is conducted successfully, the proposed model is very promising to achieve a broader application range of SGP theories, and it is very significant for analyses of materials’ micron-scale mechanical properties and for optimizing design and manufacturing of MEMS.

MEMS等微型仪器仪表中的金属构件在循环载荷下的弹塑性变形，呈现出显著的微尺度效应：弹性极限和塑性强化尺度效应、超强包辛格效应和塑性软化等，对MEMS器件性能具有重要影响。目前仍缺少能够全面描述以上微尺度效应的本构模型。项目拟建立基于Fleck-Hutchinson应变梯度塑性理论(FH SGP)的微尺度循环本构模型：1.根据正交流动法则进行应变梯度分解以保证热力学自洽，采用应变梯度弹性本构关系计算高阶应力以确保高阶应力连续性，改进现有FH SGP理论处理循环塑性问题时的理论缺陷；2. 基于Taylor位错理论，综合考虑产生微尺度效应的多种物理机制：几何必需位错、微塑性、位错可逆性和表/界面的影响等。项目拟开发本构模型的数值程序，并利用位错动力学模拟和实验等手段验证模型有效性。该课题有望促进SGP理论的发展与应用，对微尺度材料力学行为的研究以及MEMS优化设计与制造具有重要意义。

微尺度金属器件在弹塑性变形中表现出显著的尺寸效应。该项目建立了一种应变梯度弹塑性模型（SGEP），能够对该尺度上的弹性极限和应变强化尺寸效应、超强包辛格效应和塑性软化等现象进行全面的预测。系统分析了弹、塑性特征尺寸的量级和物理意义，发现弹性尺寸比塑性尺寸小至少两个量级，并由该事实得到推论：1）高阶弹性应力对材料本构行为影响甚微，这与微尺度金属纯弹性变形并无可观尺寸效应的事实相符；2）基于正交流动法则而进行应变梯度分解，发现应变梯度的塑性部分远小于弹性部分，与有关文献报道相符。因此，进一步建立了简化的应变梯度弹塑性模型，即令弹性特征尺寸为零，发现简化理论的预测能力仍然相当可靠。基于所建SGEP理论，研究了如下问题：a）微金属丝扭转。模型计算结果与文献实验相符，并且拟合所得特征尺寸都在微米量级。b）微尺度镍梁弯曲。Hutchinson与Evans曾经指出现行的梯度塑性理论较难用于该实验，塑性特征尺寸甚至要设置为几十厘米才能接近实验结果。本理论却以微米量级的特征尺寸取得了吻合。c）微尺度孔洞动态生长。主要发现有：孔洞的临界失稳载荷强烈依赖于孔洞尺寸；惯性最初抑制孔洞变形，但跨过临界载荷后转为促进孔洞快速生长；应变梯度附加强化和热软化之间的竞争机制，是影响材料强度的重要因素。d）微铜丝拉扭组合。此为典型非比例加载问题，结论如下：初始预拉伸变形削弱了应变梯度附加强化的效果；即使预拉伸作用下已经达到屈服极限，在后继扭转伊始仍可呈现一定纯弹性阶段。模型处理复杂加载的能力得以体现。 e）镁合金中的孪晶-位错系统相互作用和孪晶所致晶格重取向。建立了位错、孪晶等微观塑性机制自身及相互间的强化法则，预测了物质点孪晶的积累将导致晶格重取向。f) 钝化。研究了表面钝化对位错运动的影响。项目发表国内外学术期刊论文13篇，待发表2篇。培养博士2名，硕士10名，已毕业硕士5名。投入经费60万元，已支出44.56万元，剩余经费将用于后继研究。