Abstract
Dynamic crack propagation in an unidirectional Carbon/Epoxy composite is studied through finite element analyses in total Lagrangian co-ordinates. A finite deformation anisotropic visco-plastic model is used to describe the constitutive response of the composite. Crack initiation and propagation is simulated by embedding zero thickness interface element along the possible crack path. An irreversible cohesive law is used to describe the evolution of normal and shear tractions as a function of displacement jumps. The compressive response prior to interface failure is analyzed using contact impenetrability conditions. The failure of the first interface element at the pre-notch tip models crack initiation. Crack propagation is modeled through consecutive failure of interface elements. Dynamic crack propagation phenomena are 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′. Analyses are first carried out for the dynamic crack propagation along bi-material interfaces. The results obtained from present analyses agree well with literature data. Detailed analyses are carried out for a pre-notched unidirectional Carbon/Epoxy composite material. The impact velocity in the analyses is an imposed velocity over an assumed impact region and remains constant throughout the analysis. 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 along the crack surfaces. The analyses established intersonic crack speed in the fiber reinforced composite material. Intersonic crack propagation for the impact velocities of 40 m/s is 400% of the shear wave speed and 87% of the longitudinal wave speed. Detailed discussion is given on the features of sub-sonic and intersonic crack propagation in Carbon/Epoxy composite materials. It is shown that the friction coefficient along the crack surface plays an important role by smearing the discontinuous field that develops behind the crack tip and by reducing crack speed in the intersonic regime. The analyses show that the contour integral J′ computed at near field contours are path independent and can serve as a parameter for characterizing intersonic crack propagation.
Analysis of Dynamic Fracture Parameters in Functionally Graded Material Plates with Cracks by Graded Finite Element Method and Virtual Crack Closure Technique
