A study of frictional contact in dynamic fracture along bimaterial interfacesby Fabian Barras, David S. Kammer, Philippe H. Geubelle, Jean-François Molinari

Int J Fract


Mechanics of Materials / Modelling and Simulation / Computational Mechanics


Int J Fract (2014) 189:149–162

DOI 10.1007/s10704-014-9967-z


A study of frictional contact in dynamic fracture along bimaterial interfaces

Fabian Barras · David S. Kammer ·

Philippe H. Geubelle · Jean-François Molinari

Received: 24 March 2014 / Accepted: 11 August 2014 / Published online: 29 August 2014 © Springer Science+Business Media Dordrecht 2014

Abstract We investigate numerically the dynamic inplane propagation of a centered crack along bimaterial interfaces using a spectral formulation of the elastodynamic boundary integral equations. Particular attention is given to the effect of contact zones at the subsonic/intersonic transition. In a single set-up, we simulate and describe the different phenomenon observed experimentally (distinct natures of contact zones, unfavorable velocity range, asymmetric crack propagation).

We show that different behaviors are observed as function of the crack propagation direction, i.e., with respect to the particle displacements of the compliant material.

When the crack propagates in the same direction, the propagation velocities between cR and cs are forbidden and the subsonic/intersonic transition occurs with the nucleation of a daughter crack in front of the main rupture. The intersonic stress field at the crack front is compressive due to the material mismatch and a contact zone appears behind the tip. In the opposite direction, a smooth subsonic/intersonic transition occurs although crack face closure (in normal direction) is observed for

F. Barras · D. S. Kammer · J.-F. Molinari (B)

IIC-ENAC, IMX-STI, Computational Solid Mechanics

Laboratory (LSMS), Ecole Polytechnique Fédérale de

Lausanne (EPFL), Station 18, 1015 Lausanne, Switzerland e-mail: jean-francois.molinari@epfl.ch

F. Barras · P. H. Geubelle

Department of Aerospace Engineering, University of Illinois at

Urbana-Champaign, 306 Talbot Laboratory, 104 South Wright

Street, Urbana, IL 61801, USA speeds between cs and √ 2cs. In this regime, a Rayleigh disturbance is generated at the crack surface causing a contact zone which detaches from the tip. Using a contact model governed by a regularized Coulomb law, we provide a quantitative evaluation of the influence of friction on the effective fracture toughness. Finally, we show the applicability of our analysis to the description of different bimaterial situations as well as the singlematerial set-up.

Keywords Dynamic fracture · Intersonic crack propagation · Friction · Bimaterial interface ·

Boundary integral method 1 Introduction

Intersonic debonding, for which the speed of the front exceeds the shear wave speed of the material, has received increasing attention over the past two decades.

Although intersonic crack growth was thought to be unattainable for a while, it is now acknowledged that it plays an important role in interface failure of multiphase materials, composites or geophysical layers.

Experiments of crack propagation in homogeneous brittle solids measured crack propagations always slower than 65 % of the material’s Rayleigh wave speed cR (Rosakis 2002). Observed cracks were purely mode-I and their propagation speeds were often limited by branching. Singular dynamic fracture models (i.e., in which there is a stress singularity at the 123 150 F. Barras et al. sharp crack tip) also showed that super-Rayleigh crack growth is unreachable in homogeneous elastic solids.

For instance, Freund (1990) showed that the energy flux into the tip of a remotely loaded crack decreases as the crack accelerates, and vanishes at a velocity equal to cR.

However, these limitations are removed when crack branching and kinking is prevented by the existence of a weak plane of propagation where the fracture toughness is lower than in the surrounding solids. When the crack is trapped into a plane of propagation, it is usually mixed mode, which allows for a higher propagation speed. Freund (1979) studied the dynamic propagation of sharp mode-II cracks at weak interfaces. His analytical work demonstrated that the energy release rate is nonzero only at speed √ 2cs or sub-Rayleigh regimes for which the stress field is square root singular at the crack tip. Other intersonic speeds present a zero energy release rate which was not a sufficient proof of their existence. However when the rupture is not considered to be singular but smeared out in space and time within a cohesive zone, both analytical (Broberg 1989) and numerical (Andrews 1976) models showed that every intersonic mode-II crack speed is physically admissible.

The first experimental evidence of an intersonic crack propagation in a homogeneous material was provided by Rosakis et al. (1999). To avoid energetic dissipation by branching or micro-cracking, a weak plane of propagation was created by bonding two plates of

Homalite together. A pre-notch crack at the edge of the interface was loaded by a lateral impact, while crack propagation was monitored using high speed photoelasticity. Coker and Rosakis (2001) also studied crack propagation in unidirectional graphite–epoxy composite plates. If under mode-I loading the recorded speeds were bounded at cR, the authors observed intersonic crack propagations for mode-II loading conditions. The role of crack velocity on the cohesive failure along a single-material interface was studied by

Kubair et al. (2002). Their analytical work showed that the cohesive damage is purely shear when the crack is intersonic, even for mixed mode loadings.

In parallel to steady-state models, numerical simulations provided the opportunity to study the transition from subsonic to intersonic speeds. Needleman (1999) observed that the crack speed jumps from values close to cR up to a regime between √ 2cs and the P-wave speed cp.

Before these observations at single-material interfaces, it was already known that between dissimilar materials, crack can propagate intersonically with respect to the compliant medium. Lambros and Rosakis (1995) showed the first experimental proof of an intersonic crack propagation along a straight-line weak interface between PMMA and steel plates. Moreover, between two dissimilar materials, the presence of large scale contact zones after failure is a new feature of intersonic crack growth. Liu et al. (1995) derived the asymptotic solution for intersonic crack growth at the interface between an elastic solid and a rigid substrate.