Abstract In this work, a phase-field approach (PFA) is presented to study crack nucleation and propagation in martensitic micro-structures resulted from multi-variant martensitic phase transformations (MPT) within the framework of a finite element method (FEM). To this end, first, a coupled system of the time-dependent Ginzburg-Landau (TDGL) equation and the equilibrium equation is established based on the micro-elasticity theory, which reveals the nucleation and growth of diffusionless martensitic multi-variants forming a twinned martensitic micro-structure. The Helmholtz free energy used in this work consists of a second-degree polynomial of the phase variable, which leads to a nonlinear dependence on the order parameter in the TGDL equation. Thereafter, the nucleation and propagation of a crack is scrutinized in the obtained martensitic specimen, with and without pre-existing crack, according to three types of martensitic embryos. To do so, a damage variable is introduced to the multi-variant MPT model to study the interactions between the martensitic transformation and fracture. The key contributions of this study are not only to shed light on the evolution of the martensitic variants in the micro-structure with three types of pre-existing martensitic embryos, but also to investigate onset and growth of a crack in the martensitic specimen.

中文翻译：

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马氏体显微组织的裂纹萌生和扩展；相场法

摘要 在这项工作中，提出了一种相场方法 (PFA)，以在有限元方法 (FEM) 的框架内研究由多变量马氏体相变 (MPT) 产生的马氏体微观结构中的裂纹形核和扩展。为此，首先，基于微弹性理论建立了时变Ginzburg-Landau(TDGL)方程与平衡方程的耦合系统，揭示了无扩散马氏体多元变体的形核和生长形成孪晶。马氏体显微组织。这项工作中使用的亥姆霍兹自由能由相位变量的二阶多项式组成，这导致对 TGDL 方程中阶参数的非线性依赖性。此后，根据三种类型的马氏体胚胎，在获得的马氏体试样中仔细检查裂纹的形核和扩展，有或没有预先存在的裂纹。为此，将损伤变量引入多变量 MPT 模型以研究马氏体转变与断裂之间的相互作用。这项研究的主要贡献不仅在于揭示了具有三种类型的预先存在的马氏体胚胎的微观结构中马氏体变体的演变，而且还研究了马氏体试样中裂纹的发生和发展。