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arXiv 1010.1871cond-mat.mtrl-sci
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热载荷作用下位移与扩散耦合微结构过程的相场模型

Phase field model for coupled displacive and diffusive microstructural processes under thermal loading

Mirko Maraldi, Garth N. Wells, Luisa Molari

摘要:

本文提出了一个非等温相场模型,它在一个统一的框架内同时描述了位移相变和扩散相变。该模型是在一个正式的热力学设置,它提供了指导,允许的本构关系和耦合的许多物理过程是活跃的。相变是由温度依赖的自由能函数驱动的,该自由能函数在转变温度以下变得非凸。高阶空间梯度存在于模型中,以考虑相边界能量,这些条款需要在能量平衡方程中引入非标准项,以满足经典的熵不等式逐点。为了解决由此产生的平衡方程,Galerkin有限元方案阐述。为了严格地处理高阶空间导数的存在与表面能在相边界的动量和质量平衡方程,一些新的数值方法被使用。数值例子,考虑边界冷却域在不同的速率,这些结果表明,该模型可以定性地再现在一些合金,特别是钢中观察到的微观结构特征的演变。所提出的模型打开了一些有趣的可能性,模拟和控制下的热和机械载荷的组合的微观结构图案的发展。

英文摘要:

A non-isothermal phase field model that captures both displacive and diffusive phase transformations in a unified framework is presented. The model is developed in a formal thermodynamic setting, which provides guidance on admissible constitutive relationships and on the coupling of the numerous physical processes that are active. Phase changes are driven by temperature-dependent free-energy functions that become non-convex below a transition temperature. Higher-order spatial gradients are present in the model to account for phase boundary energy, and these terms necessitate the introduction of non-standard terms in the energy balance equation in order to satisfy the classical entropy inequality point-wise. To solve the resulting balance equations, a Galerkin finite element scheme is elaborated. To deal rigorously with the presence of high-order spatial derivatives associated with surface energies at phase boundaries in both the momentum and mass balance equations, some novel numerical approaches are used. Numerical examples are presented that consider boundary cooling of a domain at different rates, and these results demonstrate that the model can qualitatively reproduce the evolution of microstructural features that are observed in some alloys, especially steels. The proposed model opens a number of interesting possibilities for simulating and controlling microstructure pattern development under combinations of thermal and mechanical loading.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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