A comparative and parametric study of dynamic cohesive and linear elastic fracture mechanics models

In cohesive fracture mechanics (CFM), fundamental nondimensional parameters are the ratios of spacetime domain geometries and loadings to corresponding intrinsic scales implied by the cohesive fracture traction-separation relations (TSRs). One of these parameters is the nondimensional load-to-strength parameter which is the ratio of the applied loads, expressed in stress form, to an intrinsic strength scale implied by a TSR. Herein the radii of stress singularity from asymptotic Linear Elastic Fracture Mechanics (LEFM) solutions are derived to normalize cohesive process zone (CPZ) sizes from CFM. By approximating these nondimensional CPZ sizes, a simple small-scale yielding (SSY) indicator is derived for dynamic fracture which in turn is shown to be proportional to the square of the load-to-strength parameter. Thus, the load-to-strength parameter serves two purposes. First, increasing this ratio is shown to correspond to more ductile response for families of cohesive fracture self-similar solutions. Second being related to SSY condition, it is used to evaluate the validity of an LEFM model. Numerical results compare characteristic differences between these groups of CFM solutions, investigate the accuracy of the proposed SSY indicator, demonstrate LEFM solutions underestimate crack length and speed even when the SSY condition is satisfied, and study the evolution of the CPZ size.