Finite strain phase-field microelasticity theory for modeling microstructural evolution
Finite strain phase-field microelasticity theory for modeling microstructural evolution
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DOI：
10.1016/j.actamat.2020.03.033
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发表时间：
2020-06
期刊：
影响因子：
9.4
通讯作者：
P. Zhao;T. Low;Yunzhi Wang;S. Niezgoda
中科院分区：
文献类型：
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作者：
P. Zhao;T. Low;Yunzhi Wang;S. Niezgoda
通常认为通过谱方法无法实现有限应变下的相场模型，这主要是因为变换引起的微弹性的非线性。在这里，我们提出了有限应变下的相场微弹性（PFM）理论，并在参考配置中进行了表示，从而可以轻松地合并光谱方法。遵循哈恰图良 (Khachaturyan) 小应变 PFM 理论的精神，弹性能被公式化为仅微观结构（有序参数）的函数，它应自动满足机械平衡。严格地显示了当前理论在总变形梯度乘法分解（弹性和非弹性部分）下以及与超弹性和瞬态 Ginzburg-Landau 方程相结合的热力学一致性。新理论首先应用于经典的Eshelby包含问题，显示了几何非线性引起的剪切膨胀耦合，并进行了小应变和有限应变理论之间的收敛研究。通过模拟镁中{1 0 1¯ 2}< 1¯ 0 1 1>形变孪晶的生长，进一步研究了几何非线性对微观力学和微观结构协同演化的影响。模拟结果表明变形孪晶的形状和周围应力场存在显着差异。特别是，当前的有限应变PFM理论预测孪晶边界面与理论K 1 平面的偏差，这在小应变理论和晶体学理论中都没有捕获。参数研究进一步表明，当长宽比相对较小时，观察到的偏差是由有限尺寸双板的尖端效应引起的。还发现基于小应变和基于有限应变的相场建模之间双尖端周围应力场分布的对称性存在显着差异。实验中观察到的尖锐孪晶尖端也被证明可能与孪晶/基体界面迁移率的各向异性有关。
Implementing the phase-field model at finite strains is usually considered unattainable through the spectral method, largely because of the nonlinearity in the transformation-induced microelasticity. Here we present a phase-field microelasticity (PFM) theory at finite strains with a representation in the reference configuration, allowing the spectral method to be readily incorporated. Following the spirit of Khachaturyan’s PFM theory at small strains, the elastic energy is formulated as a functional of microstructure (order parameters) solely, which should automatically satisfy the mechanical equilibrium. Thermodynamic consistency of the current theory under multiplicative decomposition of the total deformation gradient (into elastic and inelastic parts) and in conjunction with hyperelasticity and the time-dependent Ginzburg-Landau equation is shown rigorously. The new theory is first applied to the classical Eshelby’s inclusion problem, where shear-dilation coupling due to geometric nonlinearity is shown and a convergence study between small strain and finite strain theories is also carried out. The effects of geometric nonlinearity on the co-evolution of micromechanics and microstructure is further studied through modeling the growth of {1 0 1¯ 2}< 1¯ 0 1 1> deformation twins in magnesium. The simulation results suggest significant differences in terms of the shape of and the stress field around the deformation twin. In particular, the current finite strain PFM theory predicts a deviation of the twin boundary plane from the theoretical K 1 plane, which is not captured in the small strain theory nor in the crystallographic theory. A parametric study further reveals that the observed deviation is caused by the tip effect of the finite-sized twin plate when the aspect ratio is relatively small. The symmetry of the stress field distribution around the twin tip is also found to be drastically different between the small strain and finite strain based phase-field modeling. The sharp twin tip observed in experiments is also shown to be likely related to the anisotropy in twin/matrix interface mobility.