Dynamic interaction between a sub-interface crack and the interface in a bi-material: time-domain BEM analysis

Abstract

Transient response of a sub-interface crack in a bi-material is studied with emphasis on the dynamic interaction between the crack and the interface, by combining the traditional time-domain displacement boundary element method (BEM) and the non-hypersingular traction BEM. Computations are performed for an unbounded bi-material with a crack subjected to impact tensile loading on its faces or incident impact waves and a bounded rectangular bi-material plate under remote impact tensile loading. Numerical results of the dynamic stress intensity factors (DSIFs) and dynamic interface tractions are presented for various material combinations and crack locations. It is shown that pronounced increases in DSIFs and the interface tractions may be caused in some cases because of the dynamic interaction between the crack and the interface. IntroductionWith the increased use of composite materials in engineering applications in recent decades, understanding the mechanism of dynamic fracture in multiphase materials becomes more and more important. Many problems of crack-interface interaction need deeper exploration.Most publications concerning dynamic fracture in multiphase materials are focused on the dynamic behavior of interfacial cracks [1-9]. However, it is known that flaws can appear not only on the interface but also in the component materials. Therefore, it is equally important to study the dynamic response of sub-interface cracks with consideration of the crack-interface interaction. Up to now, only few publications have considered this problem: among them, paper [10] studied the dynamic response of a layered composite under normal and shear impact in which the crack is parallel to the interface, and Ref.[11] studied the situation of a crack normal to the interface.The present paper studies the transient response of an arbitrary sub-interface crack in an unbounded or bounded bi-material under in-plane impact loading and discusses the effects of the material mismatch and crack location on the dynamic stress intensity factors (DSIFs) and interface tractions. Time-domain boundary element method (BEM), which has been successfully applied in homogeneous medium, [12][13][14][15][16][17][18], is introduced into the bi-material system.

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

“…The non-hypersingular time-domain traction BIEs developed by Zhang and Gross (1993) and traditional time-domain displacement BIEs in conjunction with the multi-region technique as used by Lei et al (2003), Lei et al (2004Lei et al ( , 2005) are adopted to treat this problem. For the external boundaries, ∂ B 1 ex and ∂ B 2 ex , the traditional displacement BIEs are written as (7) and for the matrix cracks, 1 (t) and 2 (t), the non-hypersingular time-domain traction BIE is written as…”

“…7, 8 are in the sense of Cauchy principal values. The tensor e εδ is the 2-D permutation tensor and its definition can be found in Lei et al (2003). …”

“…Their results show the excellent agreement in direct one-to-one comparisons of the experimental and the simulated records of the selected relevant metrics: crack tip position history, crack velocity history and crack initiation time. In this paper, the more complex fracture phenomena-crack deflection/penetration in a bi-material under dynamic loading will be studied by a time-domain boundary element method (BEM) which combines non-hypersingular time-domain traction boundary integral equations (BIEs) and traditional time-domain displacement BIEs (Lei et al 2003). The crack growth along the interface is controlled by a dynamic fracture criterion developed by Lo et al (1994) while crack growth in the homogeneous matrix is governed by a dynamic fracture criterion which has been used in our previous studies (Lei et al 2004(Lei et al , 2005 for a fast running crack in a bi-material.…”

3-D dynamic interaction between a penny-shaped crack and a thin interlayer joining two elastic half-spaces

“…Two-dimensional (2-D) elastodynamic analyses of layered solids with a sub-interface crack have been presented by Sih and Chen (1980a) and Lei et al (2003). The axisymmetric elastodynamic solution for layered elastic solids with a penny-shaped crack parallel to the interfaces has been given by Sih and Chen (1980b).…”

A boundary integral equation method in the frequency domain for cracks under transient loading

“…Sih and Chen [25] developed a method for the solution of normal and radial impact of layered composites with embedded penny-shaped cracks. Transient response of a sub-interface crack in a bimaterial was studied in [26]. The study was focused on the dynamic interaction between the crack and the interface.…”