Convergence properties of a continuum damage mechanics model for fatigue of adhesive joints

Abstract: The effect of the element length is examined in modelling crack growth in fatigue loading of an adhesive joint. This is done for a cohesive element using an expression for the damage evolution developed at the University of Skövde which is implemented using the UMAT subroutine in the FE-solver Abaqus. These analyses are done for pure mode I loading by analysing a DCB-specimen loaded by a pure moment. An expression is developed in which the critical element length is dependent on the geometry of the specimen (in the form of the wave number of the adhesive joint), the element length, the material properties of the adhesive (in form of the material parameters , , ), the load applied (in form of the stress in the crack tip), the time step used in the analysis and the crack growth rate. It is shown that the results converge by decreasing the element length and the time step used. Therefore an expression for the crack growth rate as a function of the remaining parameters can be determined. Another expression is thereafter developed for the element length needed in order to get a crack growth rate within a certain range of the critical element length. The results show a regular pattern but are not monotone. Therefor two different definitions of the critical element length are tested, either by defining the critical element length as the point where the error is greater than an arbitrary boundary of 1 % of a converged result or where a least square approximation of the error is within 1 % of the converged results. The first method shows a highly irregular result which makes it difficult to develop an expression out of these results. The second method on the other hand gives results that are predictable enough to develop a function out of them. This is done using a regression analysis with all parameters of a third order expression in order to get an expression.