Mode I elastic-plastic fracture theory from the perspective of fracture process zone
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摘要: 以飞机金属薄壁结构失效为典型代表的等温或常温环境下弹塑性裂纹扩展问题, 因涉及大范围屈服与稳态扩展特征, 对线弹性断裂力学及J积分理论的适用性构成了严峻挑战. 尽管学术界相继提出了断裂应变、裂纹尖端张开角/位移、断裂本征功及增量裂纹尖端积分等多种参量, 但因其物理内涵差异显著、内在关联模糊且“可迁移性”存疑, 严重阻碍了统一理论的构建与工程应用. 针对上述困境, 本文作者以断裂过程区 (FPZ) 为核心视角, 在忽略热源效应及体积力的简化假设下, 构建了一套统一的弹塑性断裂理论框架. 该框架不仅对Rice悖论等历史难题提供了统一且自洽的解释, 更系统论证了增量积分、裂纹尖端张开角/位移、断裂应变与断裂本征功等主流参数在本质上均等价于“定常FPZ”的驱动力, 从而揭示了现有弹塑性断裂参数的内在统一性. 在此基础上, 通过阐释含扩展裂纹体功率平衡定律的热力学意义, 该框架证明了FPZ可视为具有“自治性”的独立热力学系统, 为断裂参数的“可迁移性”提供了坚实的理论支撑. 本文系统阐述了该理论框架的构建过程、核心论点及其学术价值.Abstract: The problem of elastoplastic crack propagation in isothermal or room temperature environments, typified by the failure of thin-walled aircraft metallic structures, poses a severe challenge to the applicability of Linear Elastic Fracture Mechanics (LEFM) and J-integral theory due to characteristics such as large-scale yielding and stable crack growth. Despite the successive proposal of various parameters—including fracture strain, Crack Tip Opening Angle/Displacement (CTOA/D), Essential Work of Fracture (EWF), and incremental crack-tip integrals—the distinct physical interpretations, ambiguous interrelationships, and questionable “transferability” of these parameters have severely hindered the development of a unified theory and its engineering applications. To address this dilemma, this paper constructs a unified theoretical framework for elastoplastic fracture, adopting the Fracture Process Zone (FPZ) as the core perspective under the simplifying assumptions of neglecting thermal source effects and body forces. This framework not only offers a unified and self-consistent explanation for historical conundrums such as the Rice paradox but also systematically demonstrates that mainstream parameters, including incremental integrals, CTOA/D, fracture strain, and EWF, are intrinsically equivalent to the driving force on “steady FPZ”, thereby revealing the inherent unity among existing elastoplastic fracture parameters. Furthermore, by elucidating the thermodynamic significance of the power balance laws for a body with an extending crack, the framework establishes the FPZ as an independent thermodynamic system possessing “autonomy”, providing a solid theoretical foundation for the “transferability” of fracture parameters. This paper aims to systematically elaborate on the construction process, core arguments, and academic significance of this theoretical framework.
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图 12 弹塑性裂纹扩展过程中不同围线的能量耗散率(Brust et al. 1985; Okada et al. 1999)
图 16 CTOA的工程定义与裂纹面的三角形等效 (右图为A710高强度低合金钢韧性裂纹扩展的光学显微照片, 引自McMeeking & Parks 1979)
表 1 基于DENT试样的“临界CTOA与EWF关系式”验证
文献 材料 B/mm $ {w}_{\mathrm{e}} $/(N/mm) $ {\sigma }_{\mathrm{u}} $/MPa $ {l}_{\text{FPZ}} $/mm $ {\psi }_{\mathrm{c}} $ $ \psi _{\mathrm{c}}^{\text{es}} $ Chandra et al. 2018 IF 1 210.1 324 2 0.316 0.282 Sarkara et al. 2019 DP780 1 233 840 2 0.132 0.121 Mohammed 2017 AL-C* 1.55 51.5 93.2 2 0.254 0.24 Marchal & Delanny 1996 Zn* 0.6 78.2 140 3 0.142 0.161 Marchal & Delanny 1996 Zn* 1 102.8 140 4 0.160 0.160 Marchal & Delanny 1996 Zn* 1.3 128.7 140 4 0.213 0.200 Knockaert et al. 1996 LC* 0.7 206 360 3 0.22 0.169 Knockaert et al. 1996 LC* 1 247 360 3 0.216 0.203 Knockaert et al. 1996 LC* 1.5 400.5 360 4 0.222 0.247 Knockaert et al. 1996 LC* 2 442 360 4 0.237 0.272 Cotterell & Reddel 1977 LA* 1.6 234 510 3 0.1 0.125 Chaitanya et al. 2018 PC* 1 28.5 56 2 0.215 0.221 
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