Many engineering structures are exposed to low-velocity impact loading. A typical aerospace-related example is that of an airplane wing impacted by a bird or by runway debris. Unlike metallic structures which can absorb the impact energy by deforming plastically in the region of contact, composite laminates can only dissipate the impact energy by creating large internal damage surfaces, especially along the weaker interfaces between the plies, in a process called delamination. The ability to predict the location and extent of this damage is essential to determine the post-delamination properties of the composite laminate. The objective of this research project is to develop and implement a finite element scheme specially designed to study the onset and propagation of impact-induced delamination in polymeric-matrix fiber-reinforced composite structures.
The method, called the Cohesive/Volumetric Finite Element (CVFE) scheme, is a special form of the conventional finite element method specially deformed for dynamic fracture problems. In addition to the conventional "volumetric" finite elements, the method uses a series of "cohesive" elements placed along the boundaries between the volumetric elements. The cohesive elements act like nonlinear springs connecting the volumetric elements, and allow for the generation anywhere within the finite element domain of free surfaces (or cracks). To account of possible large deformations and/or rotations, nonlinear kinematics relations are incorporated. The time stepping scheme is explicit, since a very small time steps is required to capture the failure process taking place in the vicinity of the crack tips.
To illustrate the capabilities of the method, consider the following figure which presents the result of a CVFE simulation of the complex branching in a pre-notched plexiglas (PMMA) plate loaded dynamically in mode I.
CVFE
simulation
of crack branching in a PMMA plate
subjected to
tensile
loading
The pre-existing crack, of length equal approximately to 1/20 of
the
plate width, starts by propagating downward following a straight
path.
After reaching a critical wave speed (equivalent to approximately 50%
of
the Rayleigh wave speed, the crack branches to dissipate more
energy.
The colors correspond to the stress level, showing the stress
concentration
(in red) present in the vicinity of the
crack
tips and unloading (green) behind the
crack
tips.
