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力致裂尖微结构演化的晶体塑性相场模型

CRYSTAL-PLASTICITY PHASE-FIELD MODEL FOR MECHANICALLY INDUCED MICROSTRUCTURE EVOLUTION AROUND CRACK TIP

  • 摘要: 裂尖区域在循环载荷作用下的微结构演化是影响疲劳损伤与断裂行为的关键因素, 然而针对裂尖应力集中与非均匀变形如何驱动晶界迁移及晶粒尺寸演化这一问题, 目前仍缺乏有效的模拟手段. 本文融合基于位错密度的晶体塑性模型与描述晶粒尺度微结构演化的相场模型, 发展了模拟循环载荷下裂尖微结构演化的晶体塑性相场模型, 揭示了应力集中驱动的晶粒组织演化规律及其对裂尖应力场的调控机制. 在方法上, 本文采用基于位错密度的晶体塑性本构模型描述各向异性塑性变形, 相场模型则通过多序参量描述多晶结构, 以存储变形能(弹性应变能和位错累积产生的缺陷能之和)作为微结构演化驱动力, 模拟力致晶界迁移与晶粒生长过程. 通过设计无初始裂纹、单初始裂纹和对称初始裂纹的对比算例, 系统分析了裂尖晶粒尺度应力集中对微结构演化的影响. 研究结果表明: 裂纹尖端高度的应力集中可诱导晶界定向迁移, 在单初始裂纹影响下形成朝向裂尖伸长的晶粒形貌, 在对称初始裂纹影响下形成大范围的晶粒细化区, 而无初始裂纹试样中晶粒形貌保持相对均匀; 含初始裂纹试样的裂尖附近出现晶粒细化区, 形成了细晶与粗晶共存的微观组织形貌, 并出现了晶粒反常生长的现象; 随着微结构持续演化, 晶界迁移通过改变裂尖应力场使得裂尖峰值应力发生显著松弛. 本文提出的晶体塑性相场模型, 为刻画裂尖应力场与微结构演化交互作用提供了有效的模拟工具.

     

    Abstract: Microstructure evolution in the crack-tip region under cyclic loading is a critical factor influencing fatigue damage behavior. However, effective simulation approaches to address how crack-tip stress concentration and non-uniform deformation drive grain boundary migration and grain size evolution remain lacking. In this paper, a dislocation-density-based crystal plasticity model and a phase-field model describing grain-scale microstructure evolution are integrated to develop a crystal-plasticity phase-field model for simulating crack-tip microstructure evolution under cyclic loading, revealing the grain structure evolution driven by stress concentration and its regulatory mechanism on the crack-tip stress field. Methodologically, a dislocation-density-based crystal plasticity constitutive model is employed to describe anisotropic plastic deformation, while the phase-field model uses multiple order parameters to represent the polycrystalline structure. The elastic strain energy and the stored energy arising from dislocation accumulation serve as the driving forces for microstructure evolution, enabling the simulation of strain-energy-driven grain boundary migration and grain growth. Through comparative simulations of specimens without initial crack, with single initial crack and with symmetrical initial cracks, the influence of stress concentration on microstructure evolution is systematically analyzed. The results show that the high stress concentration at the crack tip induces directional grain boundary migration. Under the influence of single initial crack, a grain morphology extending towards the crack tip is formed. Under the influence of symmetrical initial cracks, a large area of grain refinement zone is formed. In the specimen without an initial crack, the grain morphology remains relatively uniform. A grain refinement zone appears near the crack tip in the specimen with initial crack, resulting in a microstructure morphology featuring coexisting fine and coarse grains, and a phenomenon of abnormal grain growth occurs. As the microstructure evolves continuously, grain boundary migration significantly relaxes the peak stress at the crack tip by altering the local stress field. The proposed crystal-plasticity phase-field model in this paper provides an effective simulation tool for characterizing the interaction between the crack-tip stress field and microstructure evolution.

     

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