Two dimensional numerical simulation of crack kinking from an interface under dynamic loading by time domain boundary element method

Abstract

The hybrid time-domain boundary element method, together with the multi-region technique, is applied to simulate the dynamic process of propagation and/or kinking of an interface crack in a two-dimensional bi-material. The whole bi-material is divided into two regions along the interface. The traditional displacement boundary integral equations are employed with respect to each region. However, when the crack kinks into the matrix material, the non-hypersingular traction boundary integral equations are used with respect to the part of the crack in the matrix. Crack propagation along the interface is numerically modelled by releasing the nodes in the front of the moving crack-tip controlled by the fracture criterion. Kinking of the interface crack is controlled by a criterion developed from the quasi-static one. Once the crack kinks into the matrix, its propagation is modeled by adding new elements of constant length to the moving crack-tip controlled by a criterion extended from the quasi-static maximum circumferential stress. The numerical results of the crack growth trajectory for different material combinations are computed and compared with the corresponding experimental results. Good agreement between numerical and experimental results implies that the present boundary element numerical method can provide an excellent simulation for the dynamic propagation and deflection of an interface crack.

Numerical simulation of crack deflection and penetration at an interface in a bi-material under dynamic loading by time-domain boundary element method

“…The dynamic crack deflection/penetration criterion is extended from the quasi-static case (He and Hutchinson 1989b). If the crack deflects to the interface, the propagation of the deflected interfacial crack will be governed by the dynamic HH-criterion proposed in Lei et al (2007). Numerical results are presented for different interface strength and compared with the corresponding experimental results by Xu et al (2003) to validate the numerical method and the criteria developed in this paper.…”

“…Because these have been described in details in our previous work (Lei et al 2007), next we will give a brief introduction.…”

“…When the crack deflects to the interface, its propagation will be firstly controlled by dynamic HH criterion (He and Hutchinson 1989a) as proposed by Lei et al (2007) to judge whether the deflecting interfacial crack will tend to propagate along the interface or advance by kinking out off the interface. Briefly, the criterion states that the crack will stay at the interface if…”

“…But in fact, an interfacial crack under dynamic loading may have another growing tendency to kink out off the interface and run into the matrix governed by a fracture criterion. This has been studied by experiments (Kimberley and Lambros 2004) and numerical methods in our previous work (Lei et al 2007). Additionally, most cracks in the matrix under certain loading conditions will approach the interfaces and meet them at last.…”

Нейросетевой Метод Прогнозирования Образования Дефектов На Поверхности Тонких Пленок ITO При Механических Нагрузках

“…Значения напряжений, возникающих в каждом эле-менте, рассчитываются на основании механических характеристик и размеров системы пленка−подложка, а также смещения относительно недеформированного положения. При деформациях сжатия и растяже-ния дефекты на поверхности пленки имеют распределение с периодом λ [9][10][11] Аппроксимация r(h f ) была получена на основе экспериментально измеренных четырехзондовым методом поверхностных сопротивлений образцов ITO-пленок на PET-подложке.…”