Modified J-integral Calculation Method and Program Development for Cracks in Multiphase Sandwich Materials

YOU Zhiyu; SUN Xiedong; LI Weipeng; ZHAO Xin; DING Jun; ZHANG Haicheng

doi:10.7643/issn.1672-9242.2026.10.001

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Equipment Environmental Engineering ›› 2026, Vol. 23 ›› Issue (10) : 1-14. DOI: 10.7643/issn.1672-9242.2026.10.001

Special Topic——Theoretical Analysis and Design Methods for Ships and Ocean Engineering Equipment

Modified J-integral Calculation Method and Program Development for Cracks in Multiphase Sandwich Materials

YOU Zhiyu¹, SUN Xiedong^1,*, LI Weipeng^1,2, ZHAO Xin³, DING Jun³, ZHANG Haicheng¹

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Abstract

For multiphase sandwich materials, abrupt changes in material properties across interfaces can lead to pronounced path dependence of the conventional J-integral formulated under the assumption of material homogeneity, making it difficult to isolate the contribution of material interfaces. Based on the conventional domain-integral formulation, a material-inhomogeneity correction term was introduced to establish a modified J-integral framework accounting for phase-boundary effects. An automated computational procedure was further implemented through Abaqus secondary development, enabling automatic identification of the crack front, construction of integration domains, detection of phase interfaces, and extraction of fracture parameters. By consistently evaluating the conventional domain-integral term together with the phase-interface correction term, the proposed framework enabled accurate calculation of the energy release rate at the crack tip in multiphase sandwich materials. Finite element simulations were performed on compact tension specimens of bimaterial systems containing material interfaces. The results demonstrated that the proposed modified J-integral method effectively reduced the sensitivity of the calculated fracture parameters to the selection of integration contours. The modified J-integral exhibited good contour stability, with a maximum relative deviation of less than 7% among different integration contours. In addition, the evolution of the stress field in the interfacial region under elastic-modulus mismatch and its influence on the crack-driving force were systematically investigated. The proposed modified J-integral method accounting for phase-boundary effects improves the reliability of fracture-parameter evaluation for multiphase sandwich materials and provides an effective numerical methodology and computational tool for damage assessment and structural integrity design of coating systems, laminated composites, and heterogeneous sandwich structures.

Key words

multiphase sandwich materials / phase boundary effect / modified J-integral / Abaqus secondary development / crack driving force / fracture parameter

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YOU Zhiyu, SUN Xiedong, LI Weipeng, ZHAO Xin, DING Jun, ZHANG Haicheng. Modified J-integral Calculation Method and Program Development for Cracks in Multiphase Sandwich Materials[J]. Equipment Environmental Engineering. 2026, 23(10): 1-14 https://doi.org/10.7643/issn.1672-9242.2026.10.001

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Funding

National Science and Technology Major Project (2025ZD1600600); The Development and Application Project of Ship CAE Software; Guangdong Basic and Applied Basic Research Foundation (2025A1515011471)