A stiffness independent Interfacial Thick Level Set method

Abstract

Crack growth is an important failure mechanism in many engineering materials. Numerical models for crack growth have been developed within the framework of damage mechanics. All these models aim for the same goal, obtaining accurate results for crack growth under various loading conditions. Many damage models are based upon the cohesive crack approach. However, level set based models provide advantages compared to the cohesive crack models with regard to fatigue analysis. An alternative method to the existing thick level set (TLS) method was proposed, the interfacial thick level set (ITLS) model. The use of interface elements made the model more suitable to simulate several failure processes. In this thesis it is demonstrated that this method suffers from a dependency on the initial interfacial stiffness for the global response of a system by conducting a parameter study under quasi-static loading conditions. This parameter study proves that for a varying value of the initial interfacial stiffness parameter K the global response varies as well. This gives motivation to conduct further research on the removal of the initial interfacial stiffness from the current ITLS model. Two methods are developed to overcome the initial interfacial stiffness dependency. The first method assumes that the initial interfacial stiffness dependency is caused by the current formulation of the constitutive
law of the interface. A new expression for the interfacial stiffness is adapted after which all constitutive relations are updated. The new method shows a
perfect agreement with the current ITLS model, which validates the method as an accurate alternative. Compared to the current ITLS model, method 1 allows for the control of the initial stiffness of the undamaged part of the interface by changing the lower bound damage without affecting the global response. However, when executing simulations for a varying initial interfacial stiffness K the same problem as for the current ITLS is observed. It can be concluded that in a way this method removes the dependency on the initial interfacial stiffness but the initial interfacial stiffness parameter K should then remain constant. Furthermore, the calibration process is not simplified compared to the current ITLS model. For this reason method 1 is rejected as the final solution to the problem and a second method is proposed. The second method assumes a direct relation between the damage parameter c1 and the initial interfacial stiffness parameter K. This damage parameter is responsible for the steepness of the damage profile. The results from the parameter study showed that an increase of one of these parameters results in opposite behaviour for the initial stiffness of the global response. The leading hypothesis becomes that an increase in the stiffness parameter K can be neutralized by an increase in the damage parameter c1. Proportionality between both parameters is assumed. By trial and error the proportionality is found to be one to one. When using this proportionality condition, simulations with different values for the initial interfacial stiffness showed a perfect agreement for the load-displacement and the crack growth responses. Moreover, the proportionality condition is accurate for both a linear elastic (LE) material and an elastic-plastic (EP) material. The proportionality condition is proven by elaborating the interfacial stiffness over the damaged zone. This elaboration is done both numerically and analytically and proves that there is a one to one proportionality between c1 and K, which validates the replacement of c1 by a constant c multiplied with K. Lastly, the method should be compared to a response obtained through a different type of analysis. The method is compared with the solution of an analytical analysis resulting in a very good agreement for both a LE and an EP material. Therefore, method 2 can be approved as a solution to the initial interfacial stiffness dependency problem.