Simulation of delaminations induced by low velocity impacts in composites: a sensitivity study to guide an effective use of cohesive elements

Low-velocity impacts (LVIs) can seriously harm composite laminates by causing both intralaminar (fiber failure and matrix cracking) and interlaminar damage (delaminations). Extensive delaminations, although hardly detectable by visual inspections, may reduce the strength of the structure and can lead to its premature failure under compressive loads. In aeronautics, extensive experimental campaigns are used to investigate the effects of low-velocity impacts on composite structures; such experimental effort might be significantly reduced if numerical simulations were used smartly. Even though numerical simulations of LVI events require both intralaminar and interlaminar damage models, most of the impact energy is spent to produce delaminations, hence particular care must be exerted to define and tune the interlaminar damage model. The cohesive zone model (CZM) is the most used approach to simulate both onset and propagation of delaminations. Nonetheless, recent studies simulating standard interlaminar fracture toughness tests showed that the simulation results are affected by both the constitutive parameters and the size of the cohesive elements. The authors propose to investigate the influence of the constitutive law parameters and of the dimensions of cohesive elements on LVI simulations results; the study focuses on the variation of delamination shape, depth and extension and compares the related computational costs. A first reference analysis is performed in order to verify the implemented intralaminar and interlaminar damage models. Experimental results of impactor force and displacement time histories, extension and depth of delaminations (obtained by means of ultrasonic inspections) are used as a term of reference for the sensitivity study. In order to perform LVI simulations in ABAQUS two distinct user-defined material routines (UMAT) are developed; UMATs model the intralaminar behavior in solid elements (C3D8) and the constitutive behavior of the cohesive elements (COH3D8). The intralaminar routine implements a continuum-damagemechanics- based model with a smeared crack formulation for both fiber failure and matrix cracking; given the aim of the present study, the intralaminar constitutive parameters are kept constant throughout the sensitivity analyses. The interlaminar damage model uses a traction-separation bi-linear constitutive law to describe the initial elastic behavior and the subsequent progressive softening. The proposed sensitivity analysis wants to point out the relative importance of the intralaminar phenomena compared to the interlaminar ones in lowvelocity impact simulations on a carbon/epoxy material system. At the same time the authors aim at defining guidelines for the effective use of cohesive elements for such analyses through a systematic comparison between the numerical results and experimental ones. The study also evaluates the effects of different cohesive parameters on the computational costs of the simulations.