用各向同性硬化和半径返回法建立韧性断裂的相场模型

IF 1.9 4区 材料科学 Q3 MATERIALS SCIENCE, MULTIDISCIPLINARY Modelling and Simulation in Materials Science and Engineering Pub Date : 2024-06-06 DOI:10.1088/1361-651X/ad54e2
Li Meng, A. Tabiei
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引用次数: 0

摘要

相场模型已在许多静态和动态场景中针对脆性断裂进行了研究,但其在韧性断裂中的应用并不像脆性断裂那样普遍,尤其是在采用显式方案的软件 LS-DYNA 中的应用。本研究介绍了韧性断裂相场建模的高效 LS-DYNA 实现方法,并考虑了损伤演化过程中弹性应变能的分割和不分割。详细而言,首先简要介绍了具有各向同性硬化的韧性材料的塑性公式,然后推导出经典相场模型的控制方程,从而给出位移-相位耦合问题。在对弹性应变能进行拆分时,考虑了弹性应变能的剪切分量对损伤演化的影响。还通过使用三种函数(多项式函数、代数分数函数和 sigmoid 函数)研究了退化函数对应力应变曲线的影响,从而得出了相场模型的线性和非线性有限元法(FEM)公式,并使用牛顿-拉夫逊法求解了相场模型的非线性有限元法公式。拉伸棒试验显示了临界能量释放率和降解函数对应力应变曲线的影响。三点弯曲试验的模式Ⅰ破坏、单边缺口板的模式Ⅱ破坏和非对称双缺口板的混合模式破坏验证了本研究提出的模型。从这些模拟结果来看,与未分割弹性应变能的情况相比,分割弹性应变能的情况在塑性变形方面有所改善。
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Phase field modeling of ductile fracture with isotropic hardening and radius return method
Phase field model has been investigated for brittle fracture in many static and dynamic scenarios, but its applications to ductile fracture is not as common as brittle fracture, especially implementing in software LS-DYNA with explicit scheme. In this study, an efficient LS-DYNA implementation of the phase field modeling of ductile fracture is presented and both with and without the split of elastic strain energy have been considered for the damage evolution. In more detail, plasticity formulation of ductile material with isotropic hardening is briefly presented first and then the governing equations of the classical phase field model are derived, which gives the displacement-phase coupled problem. For with the split of elastic strain energy, the shear component of elastic strain energy is considered for the damage evolution. The influence of degradation function on stress–strain curve is also investigated by using three kinds of function (polynomial function, algebraic fraction function and sigmoid function), which leads to linear and nonlinear finite element method (FEM) formulation of the phase field model and Newton–Raphson method is used to solve the nonlinear FEM formulation of the phase field model. A tensile bar test shows the influence of critical energy release rate and degradation function on stress–strain curve. Mode Ⅰ failure of three-point bending test, Mode Ⅱ failure of single-edge notched plate and mixed-mode failure of asymmetrical double-notched plate verify the proposed model in this study. From these simulations, with the split of elastic strain energy shows improvements on plastic deformation than without the split of elastic strain energy.
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来源期刊
CiteScore
3.30
自引率
5.60%
发文量
96
审稿时长
1.7 months
期刊介绍: Serving the multidisciplinary materials community, the journal aims to publish new research work that advances the understanding and prediction of material behaviour at scales from atomistic to macroscopic through modelling and simulation. Subject coverage: Modelling and/or simulation across materials science that emphasizes fundamental materials issues advancing the understanding and prediction of material behaviour. Interdisciplinary research that tackles challenging and complex materials problems where the governing phenomena may span different scales of materials behaviour, with an emphasis on the development of quantitative approaches to explain and predict experimental observations. Material processing that advances the fundamental materials science and engineering underpinning the connection between processing and properties. Covering all classes of materials, and mechanical, microstructural, electronic, chemical, biological, and optical properties.
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