Análise da influência do fator de escala na superfície biaxial e obtenção da superfície tridimensional de falha de materiais quase frágeis com o método dos elementos discretos

Abstract

The study of fractures in brittle materials always was one of the main problems faced in computer simulation because of the complexity of the subject in the branch of engineering. The main goal of this work is check the influence of the scale effect and built the three-dimensional failure surface for brittle materials using Discrete Element Method formed by bars. The DEM, differently throw the Finite Element Method, represents the solid by a cubic arrangement of truss bars that becomes much advantageous to study fractures, where the method has autonomy to remove some of these bars and give continuity to the simulation across explicit numeric simulation. It is used as base material a specimen with brittle characteristics like a rock. The boundary condition that is used to check the scale effect is the contour of prescribed displacements, while to obtain three-dimensional failure surface it is used the contour of prescribed forces. The scale effect uses to be phenomenom that is not relate to the maximum tensile strength of the body but to the rate of cracking propagation of the same, happening only in traction cases proportionally to the size of the cubic elements until the size equals to 40 modules, when we realize that there is not anymore changes of the characteristics. After, the three-dimensional failure surface presents itself similarly to the theoretical proposal from William e Warnke, where the surface presents resistance tending to infinite on the cases of hydrostatic compression. Lastly it is noted that the phenomenom of scale effect affects the rate of cracking propagation for some cases of traction loads, and the three-dimensional failure surface for brittle materials in DEM shows the behaviour proposed by the criterion of William e Warnke.