相场断裂方法发展概况

张豪; 于继东; 裴晓阳; 彭辉; 李平; 蔡灵仓; 汤铁钢

doi:10.11858/gywlxb.20190777

相场断裂方法发展概况

doi: 10.11858/gywlxb.20190777

中国工程物理研究院流体物理研究所，四川绵阳　621999

基金项目: 国家自然科学基金面上项目（11772067）；国家自然科学基金青年科学基金（11702277）；国家自然科学基金重点项目（11532012）

详细信息

作者简介:
张　豪（1988－），男，博士研究生，助理研究员，主要从事高压物理与力学研究. E-mail：zhanghao17@gscaep.ac.cn

通讯作者:
蔡灵仓（1964－），男，博士生导师，研究员，主要从事凝聚态物理研究. E-mail：cai_lingcang@aliyun.com

中图分类号: O347.3
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出版历程
- 收稿日期: 2019-05-15
- 修回日期: 2019-05-22
- 发布日期: 2019-05-25

An Overview of Phase Field Approach to Fracture

Institute of Fluid Physics, CAEP, Mianyang 621999, China

摘要

摘要: 相场断裂方法自21世纪初开始发展以来，一直备受关注，在裂纹扩展模拟方面表现出了一定的特点，取得了一定的研究成果。本文分析了相场断裂方法较其他断裂模拟方法的优势，简单介绍了相场断裂方法的发展现状和发展趋势：目前脆性断裂相场方法已较为成熟，能够模拟诸多脆性断裂中的经典问题，在此基础上正在朝着解决多场耦合情况下的断裂问题发展，且也取得了一定的研究成果。最后，简单介绍了延性断裂相场方法的发展现状，提出在该方向进行深入研究的展望。
- 相场断裂方法 /
- 数值模拟 /
- 脆性断裂 /
- 延性断裂
Abstract: Phase field modeling to fracture has received much attention since the beginning of this century, which exhibits an advantage in fracture propagation simulation. In this work, we compare the phase field approach to fracture with other simulation methods, and show an overview and development of phase field approach to fracture. Up to now, the phase field method has been successfully applied to the brittle fracture and could simulate some classical crack problems. Based on this, the multi-fields problem coupled with the fracture is currently pursued. Furthermore, we introduce the study situation of the phase field simulation to the ductile fracture and put forward its development in the future.
- phase field approach to fracture /
- simulation /
- brittle fracture /
- ductile fracture

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图 1 I、III型混合模式下锯齿状裂纹的实验结果（a）和相场模拟结果（b）（c）^[21]

Figure 1. Experimental result (a) and phase field simulation (b), (c) of jag fracture under mixed condition of type I & III^[21]

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图 2 静态/准静态脆性断裂的相场模拟：（a）I、II型裂纹^[27]，（b）L形薄板中的裂纹^[29]

Figure 2. Phase field simulation of static/quasi-static brittle fracture: (a) type I & II fracture^[27], (b) fracture in L-shape sheet^[29]

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图 3 动态脆性断裂的相场模拟：（a）（b）动态裂纹经典问题^[12]，（c）三维形式的KW试验模拟结果^[32]

Figure 3. Phase field simulation of dynamic brittle fracture: (a), (b) classical problems in dynamic fracture^[12]; (c) 3D KW test^[32]

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图 4 相场断裂方法的基本框架

Figure 4. Framework of phase field approach to fracture

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图 5 带裂纹的电场分布^[37]

Figure 5. Electronic field with fracture^[37]

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图 6 带裂纹场的极化矢量场^[38]

Figure 6. Polarization field with fracture^[38]

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图 7 水坝（Koyna dam）的水力压裂^[41]

Figure 7. Phase field simulation of hydraulic fracture in Koyna dam^[41]

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图 8 Ambati等延性断裂相场模拟结果^[44]

Figure 8. Ductile fracture simulated by Ambati et al.^[44]

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图 9 脆性-延性断裂模型的能量释放率：（a）应变率决定的临界能量释放率转变^[36]，（b）应力三轴度决定的临界能量释放率转变^[46]

Figure 9. Energy release rate in fracture mode for brittle-ductile fracture transition: (a) strain rate induced energy release rate transition^[36], (b) stress triaxiality induced energy release rate transition^[46]

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图 10 KW试验相场模拟结果^[36]：（a）冲击速度20 m/s产生的脆性断裂，（b）冲击速度39 m/s产生的绝热剪切失效

Figure 10. Phase field simulation to KW test^[36]: (a) brittle fracture induced by impact velocity of 20 m/s, (b) ductile fracture induced by impact velocity of 39 m/s

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表 1 裂纹扩展的数值模拟方法对比

Table 1. Comparison of methods in fracture propagation simulation

Methods Type I tensile fracture KW test

Experimental result

Element deletion

Inter element

XFEM

Phase field

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表 2 扩展有限元及相场方法处理三维及多裂纹的对比

Table 2. Comparison of 3D and multi-fracture simulation of XFEM and phase field approach

Crack XFEM Phase field

Level sets Fast marching No need crack tracking

3D crack

Multi-crack

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