Modeling dynamic crack propagation in fiber reinforced composites including frictional effects

Dynamic crack propagation in a unidirectional carbon/epoxy composite is studied through finite element analyses of asymmetric impact (shear loading) of a rod against a rectangular plate. A finite deformation anisotropic visco-plastic model is used to describe the constitutive response of the composite. Crack propagation is simulated by embedding zero thickness interface element along the crack path. An irreversible mixed-mode cohesive law is used to describe the evolution of interface tractions as a function of displacement jumps. Contact and friction behind the crack tip are accounted for in the simulations. The failure of the first interface element at the pre-notch tip models onset of crack extension. Crack propagation is modeled through consecutive failure of interface elements. The dynamic crack propagation phenomenon is studied in terms of crack initiation time, crack speed, mode I and mode II displacement jumps and tractions associated with the failure of interface elements, effective plastic strain at the crack tip and path independent integral J 0. Analyses are carried out at impact velocities of 5, 10, 20, 30 and 40 m/s, assuming the crack wake is frictionless. Moreover, analyses at impact velocities of 30 and 40 m/s are also carried out with a friction coefficient of 0.5, 1, 5 and 10 along the crack surfaces. The analyses show that steady-state intersonic crack propagation in fiber reinforced composite materials occurs when the impact velocity exceeds a given threshold. A steady-state crack speed of 3.9 times the shear wave speed and 83% of the longitudinal wave speed is predicted in the cases in which the impact velocity is above 10 m/s. Detailed discussion is given on the features of sub-sonic and intersonic crack propagation. It is shown that friction effects, behind the crack tip, do not have a significant effect on maximum crack speed; however, they do on characteristics of the shock wave trailing the crack tip. The analyses also show that the contour integral J 0, computed at contours near the crack tip, is indeed path independent and can serve as a parameter for characterizing intersonic crack propagation. 2002 Elsevier Science Ltd. All rights reserved. This article is based on presentations given at the ASME International Congress and Exposition, November 1998, Los Angeles, CA, and an ARO-MURI review meeting. The research here reported was then published in the second author s web page but otherwise remained unpublished. The reader will find the status of the subject, reported analyses and conclusions as given in the original presentations. Since then, several contributions have been made by various research groups. For completeness these contributions are cited and discussed in the context of the reported numerical simulations. * Corresponding author. Tel.: +1-847-467-5989; fax: +1-847-491-3915. E-mail address: [email protected] (H.D. Espinosa). URL: http://clifton.mech.northwestern.edu/ espinosa. 1 Currently at Institute of Shock Physics, Washington State University, Pullman, WA 99164-2816, USA. 0167-6636/03/$ see front matter 2002 Elsevier Science Ltd. All rights reserved. PII: S0167-6636 (02 )00266-1 Mechanics of Materials 35 (2003) 481–509 www.elsevier.com/locate/mechmat