Modelling the failure behaviour of brittle or quasi-brittle materials by analysing the growth of micro-cracks

In order to better understand the failure behaviour of brittle or quasi-brittle materials, we developed a numerical model to analyse the creation of a main macro-crack from a large number of micro-cracks. The boundary element method is used to simulate numerically the formation of a main macro-crack by the growth and the coalescence of the micro-cracks. Different two-dimensional panels in PMMA with initial micro-cracks are studied. The macroscopic responses of the panels are observed by simulating the damage process induced by the growth of micro-cracks. The ultimate tensile stress of the material can be then determined. The material toughness heterogeneity is taken into account in the developed model. The toughness heterogeneity is considered as existence of different energy barriers for the growth of micro-cracks. The influences of different parameters such as the level of local stress concentration, the density and the initial length of micro-cracks and the toughness heterogeneity on the failure behaviour of the materials are also studied. The numerical results show that the present model is realistic and efficient. It can be used to describe brittle or quasi-brittle material failure due to the creation of a main macro-crack from micro-cracks.