Three-dimensional fracture modes decoupling by means of invariant integrals in wood under mixed mode loading

IF 5 2区工程技术 Q1 ENGINEERING, MECHANICAL Theoretical and Applied Fracture Mechanics Pub Date : 2024-10-05 DOI:10.1016/j.tafmec.2024.104708

Jérôme S. Afoutou, Frédéric Dubois

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Abstract

This paper addresses the determination of the energy release rate in an orthotropic elastic material such as wood with a three-dimensional view of the problem. The mixed mode loading associated with the anisotropy of the material required mode decoupling by isolating the energy release rates in mode I, mode II and in mode III. These energy release rates are calculated using the invariant integral M of Linear Elastic Fracture Mechanics (LEFM). This decoupling has necessitated the introduction of kinetically and statically admissible three-dimensional virtual displacement and stress fields in the vicinity of the crack front. The fracture mode decoupling strategy is presented and implemented through finite element modelling of a Mixed Mode Crack Growth (MMCG) specimen. Different thicknesses are investigated to highlight the 3D effects. The modelling highlighted the effect of Mode II at the edges of free surfaces for mixed loadings including mode III (mode III, mode (II+III) and mode (I+II+III)), while mode III was the predominant at the middle of the specimen. In cases of mixed mode (I+II), the energy release rate GI was highest at the middle of the specimen and lowest at the edges of the free surfaces, regardless of the degree of mixing for a given thickness. The correlation between the results obtained using the proposed approach and the non-dependence of the integration domain, as well as with the usual approaches employed in the literature, is demonstrated.

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通过混合模式加载下木材的不变积分实现三维断裂模式解耦

本文从三维角度探讨了如何确定木材等正交弹性材料的能量释放率。与材料各向异性相关的混合模式加载要求通过隔离模式 I、模式 II 和模式 III 中的能量释放率来进行模式解耦。这些能量释放率是通过线性弹性断裂力学（LEFM）的不变积分 M 计算得出的。这种解耦需要在裂缝前沿附近引入动力学和静力学上可接受的三维虚拟位移和应力场。通过对混合模式裂纹生长（MMCG）试样进行有限元建模，介绍并实施了断裂模式解耦策略。研究了不同厚度的试样，以突出三维效应。建模突出了混合载荷（包括模式 III、模式 (II+III) 和模式 (I+II+III)）下自由表面边缘的模式 II 的影响，而模式 III 在试样中部占主导地位。在混合模式（I+II）情况下，无论给定厚度的混合程度如何，试样中部的能量释放率 GI 最高，自由表面边缘最低。使用所提出的方法获得的结果与积分域的非依赖性以及文献中采用的通常方法之间的相关性得到了证明。

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来源期刊

Theoretical and Applied Fracture Mechanics 工程技术-工程：机械

CiteScore

8.40

自引率

18.90%

发文量

435

审稿时长

37 days

期刊介绍： Theoretical and Applied Fracture Mechanics'' aims & scopes have been re-designed to cover both the theoretical, applied, and numerical aspects associated with those cracking related phenomena taking place, at a micro-, meso-, and macroscopic level, in materials/components/structures of any kind. The journal aims to cover the cracking/mechanical behaviour of materials/components/structures in those situations involving both time-independent and time-dependent system of external forces/moments (such as, for instance, quasi-static, impulsive, impact, blasting, creep, contact, and fatigue loading). Since, under the above circumstances, the mechanical behaviour of cracked materials/components/structures is also affected by the environmental conditions, the journal would consider also those theoretical/experimental research works investigating the effect of external variables such as, for instance, the effect of corrosive environments as well as of high/low-temperature.