Key role of boundary conditions for the 2D modeling of crack propagation in linear elastic Compact Tension tests

Abstract

In fracture mechanics, the use of experimental tests are fundamental to characterize the material properties in terms of crack initiation and propagation behavior. When modeled in boundary value problems, simplifications need to be made. Notably, the loading has to be reduced to a set of boundary conditions and the choice between plane stress and plane strain has to be done in the 2D case. Here we focus on the Compact Tension (CT) test which is a fracture setup commonly used to measure the fracture toughness at crack propagation onset and we question the possibility to use it to study crack propagation. For this, the tests are monitored by digital image correlation and compared to finite element method simulations. Three ways to guide the choice between plane stress and plane strain hypotheses are proposed. They lead to the same conclusion that the plane stress conditions are the most relevant for the geometry of the samples used here. The key role of boundary conditions is highlighted by testing several models, with imposed force or displacement boundary conditions, against the experimental data. Imposed force boundary conditions on the pin are shown to be able to reproduce the experiments before crack propagation and to be insensitive to the way this force is applied, in line with Saint Venant principle. The results with imposed displacement are in contrary very sensitive to their distribution along the pin. While the stage before propagation is accurately predicted by imposed forces, we show that for the propagation phase, Saint Venant is put in default and accurate results can only be obtained by imposing the displacement fields issued from the digital image correlation. These results can be extended to other fracture experiments, involving pin loading, like the Compact Tension Shear (CTS) or the (Tappered) Double Cantilever Beam ((T)DCB) tests.