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Nanoscale multiphase phase field approach for stress- and temperature-induced martensitic phase transformations with interfacial stresses at finite strains

机译:纳米多相相场法在有限应变下具有界面应力的应力和温度引起的马氏体相变

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A thermodynamically consistent, novel multiphase phase field approach for stress- and temperature-induced martensitic phase transformations at finite strains and with interfacial stresses has been developed. The model considers a single order parameter to describe the austenite↔martensitic transformations, and anotherNorder parameters describingNvariants and constrained to a plane in anN-dimensional order parameter space. In the free energy model coexistence of three or more phases at a single material point (multiphase junction), and deviation of each variant-variant transformation path from a straight line have been penalized. Some shortcomings of the existing models are resolved. Three different kinematic models (KMs) for the transformation deformation gradient tensors are assumed: (i) In KM-I the transformation deformation gradient tensor is a linear function of the Bain tensors for the variants. (ii) In KM-II the natural logarithms of the transformation deformation gradient is taken as a linear combination of the natural logarithm of the Bain tensors multiplied with the interpolation functions. (iii) In KM-III it is derived using the twinning equation from the crystallographic theory. The instability criteria for all the phase transformations have been derived for all the kinematic models, and their comparative study is presented. A large strain finite element procedure has been developed and used for studying the evolution of some complex microstructures in nanoscale samples under various loading conditions. Also, the stresses within variant-variant boundaries, the sample size effect, effect of penalizing the triple junctions, and twinned microstructures have been studied. The present approach can be extended for studying grain growth, solidifications, para↔ferro electric transformations, and diffusive phase transformations.
机译:已经开发出一种热力学一致的新颖多相相场方法,用于在有限应变和界面应力下由应力和温度引起的马氏体相变。该模型考虑了一个用于描述奥氏体-马氏体相变的单阶参数,以及一个用于描述N变量并约束在N维阶数参数空间中的平面上的另一个N阶参数。在自由能模型中,单个材料点(多相结)处三相或更多相的共存以及每个变量-变数转换路径与直线的偏离都受到了惩罚。解决了现有模型的一些缺点。假定变换变形梯度张量的三个不同的运动学模型(KMs):(i)在KM-1中,变换变形梯度张量是贝恩张量对变量的线性函数。 (ii)在KM-II中,变换变形梯度的自然对数取为贝恩张量自然对数乘以插值函数的线性组合。 (iii)在KM-III中,它是使用孪晶方程从晶体学理论推导得到的。已经为所有运动学模型导出了所有相变的不稳定性判据,并进行了比较研究。已经开发了大应变有限元程序,并用于研究在各种加载条件下纳米尺度样品中某些复杂的微观结构的演变。此外,还研究了变体-变体边界内的应力,样本大小效应,惩罚三重连接的效应以及孪生微结构。本方法可以扩展到研究晶粒的生长,凝固,超铁电转变和扩散相转变。

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