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Creep crack analysis of viscoelastic material by numerical manifold method

机译：数值流形方法分析粘弹性材料的蠕变裂纹

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摘要

In order to gain an insight into creep induced cracking in viscoelastic materials, the creep crack phenomenon in viscoelastic materials are numerically investigated in this paper based on the numerical manifold method (NMM). To more realistically capture the mechanical behaviour in the vicinity of crack tips, the local displacements around crack tips are enriched with the viscoelastic crack-tip asymptotic displacement field. To better represent the viscoelastic materials, an incremental viscoelastic constitutive law based on the generalized Kelvin-Voigt model is incorporated into the NMM. To achieve these treatments in the NMM, an incremental viscoelastic NMM formulation is derived. In addition, an incremental formulation of the mixed mode viscoelastic energy release rate (ERR), which can be tackled in the same process with the incremental viscoelastic constitutive law, is derived and incorporated into the NMM for investigating the variations of the ERR in viscoelastic materials. Based on the developed method, three creep crack problems with different loading conditions and pre-existing crack configurations are simulated, and the crack opening and sliding displacements as well as corresponding mixed mode ERR are analysed. Simulation results show good agreement with the theoretical solutions, which indicate that the proposed NMM is suitable for complex creep crack problems.
机译：为了深入了解粘弹性材料中的蠕变裂纹，本文基于数值流形方法（NMM）对粘弹性材料中的蠕变裂纹现象进行了数值研究。为了更真实地捕捉裂纹尖端附近的力学行为，裂纹尖端周围的局部位移被粘弹性裂纹尖端渐近位移场所丰富。为了更好地表示粘弹性材料，将基于广义Kelvin-Voigt模型的增量粘弹性本构律并入NMM。为了在NMM中实现这些处理，需要增加粘弹性NMM配方。此外，还导出了混合模态粘弹性能释放率（ERR）的增量公式，该公式可以用增量粘弹性本构法在同一过程中解决，并将其纳入NMM中，以研究粘弹性材料中ERR的变化。在此基础上，模拟了三种不同载荷条件和既有裂纹形态的蠕变裂纹问题，并分析了裂纹的开，滑位移以及相应的混合模态ERR。仿真结果与理论解吻合良好，表明所提出的NMM算法适用于复杂的蠕变裂纹问题。

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