Puck’s action plane fracture criteria

Abstract

This chapter is the core part of the whole book. Here the Puck criteria are derived and presented in all detail. Puck's criteria are based on the concept of intrinsically brittle materials. As an introduction Mohr's fracture hypotheses, the concept of principal stresses and the visualization in the Mohr circles are recalled and extended to orthotropic materials. The fiber fracture criteria are presented prior to the IFF-criteria, because their explanation takes less space and the derivation of the criteria is simpler. Puck has developed FF-criteria which take all possible influences of shear and transverse normal stresses into account. However, for most cases the most simple maximum stress criterion is still valid for FF-analysis. The main focus of Puck's work has always been on Inter Fiber Fracture. Puck's criteria offer not only a perfect calculation of the fracture limit and the stress exposure. In addition the fracture angle is calculated. With this additional information the differentiation between tolerable and non-tolerable IFF becomes possible. The IFF-criteria are first explained in their general 3D-formulation. The mathematical derivation is made step by step and easy to follow. From the general formulation the equations for plane 2D-states of stress are derived. These 2D-formulations are of interest because they do not need the numerical search of the fracture plane. Puck's criteria are based on knowledge the idea that fracture is caused by the stresses on the fracture plane. Therefore in the original formulation of Puck's criteria no influence of fiber parallel stress on IFF is reflected. However, as a matter of fact high σ1 stress leads to microdamage and reduces the strength of the material against IFF. Puck has developed a way to incorporate this into his criteria. In the same way he has incorporated probabilistic effects. These later developments are discussed under the headline "Extensions to the IFF-criteria". Another chapter is dedicated to the visualization of (IFF-) criteria. This visualization is a very good means to illustrate the characteristics of a creation and to compare different criteria. This comparison is done here for the classical Tsai/Wu-criterion, the Hashin-criterion and the Puck criteria.