Mixed mode partitioning of beam-like geometries: A damage dependent solution

Investigation of the mixed-mode fracture in delamination tests: numerical simulations using cohesive zone and partitioning methods

“…Dependency of the mode partitioning on cohesive zone properties is observed, confirming the findings reported in [1,15]. The dependency is more pronounced in asymmetric beam geometries (h 1 /h 2 ≠1), while for the symmetric case (h 1 /h 2 =1) mode-mixity is nearly independent on cohesive properties, as suggested by both analytical solutions.…”

“…9 shows the mode I contribution for all simulation configurations together with two analytical solutions. As the global and the local numerical approach give very close results, only the global results are plotted.The mode-mixity curve for the considered case ( Fig.1) It really seems that the two analytical solutions form the upper and lower bound for the mixed mode partitioning, confirming conclusions given in [1,15]. As already said, exceptions are the symmetrical configurations for which the contribution of mode I is nearly independent on cohesive properties.…”

“…Two pioneering theories, namely, Williams analytical solution [4], obtained by global approach using beam theory, and Hutchinson and Suo semi-analytical solution [5], based on linear elastic fracture mechanics (LEFM) and local approach, are selected here for the analysis because they can be defined as two possible extremes [6,15]. Here, the term 'global' refers to the entire region mechanically affected by the crack, and 'local' to the crack tip.…”

“…Since nominal strains are defined as separations in two directions ( , ) n t δ δ divided by the nominal thickness that is equal to 1 by default, nominal strains are equal to the separations. Uncoupled elasticity matrix is defined with arbitraly high set value of penalty stiffness with K nn = K tt = 10 15 MPa. Element damage initiation is defined using the quadratic nominal stress criterion [10]:…”

“…every cohesive element will have the same loading history; hence, in the FPZ there will be cohesive elements from all stages of a fracture process (loading history). The following integrations can then be performed along the cohesive surfaces in order to obtain the global mode I and mode II energy release rates [7,15]:…”