Efficient 3D and 2D failure conditions for UD laminae and their application within the verification of the laminate design

Abstract The paper presents a set of three-dimensional (3D) and 2D strength failure conditions for unidirectional (UD) laminae made from fibre-reinforced plastics (FRP). The conditions are based on a concept termed the failure mode concept (FMC) which provides failure conditions formulated on UD lamina level that allows for a prediction of the critical lamina failure mode, and finally of laminate failure. Following the FMC there are five independent conditions: for inter fibre failure (IFF) three and for fibre failure (FF) two conditions. These are based on averaged lamina stresses. The IFF conditions were basically developed in 1996 and later contributed [Cuntze RG, Freund A. The predictive capability of failure mode concept-based strength criteria for multidirectional laminates. Part A. Compos Sci Technol 2004;64:343–77; Cuntze RG. The predictive capability of failure mode concept-based strength criteria for multidirectional laminates. Part B. Compos Sci Technol 2004;63:487–516] to a ‘World-Wide Failure Exercise (WWFE) on failure theories’ [Hinton MJ, Soden PD. Predicting failure in composite laminates: the background to the exercise. Compos Sci Technol 1998;58(7):1001–10]. In this paper a single but effective modification of one IFF condition is highlighted. It consists in the replacement of the ‘shear mode IFF 2’ by a numerically advantageous simplified formulation for the 3D and for the 2D case. A very satisfying verification of the 3D IFF2 condition, reduced to 2D, as well as for a directly formulated 2D IFF2 condition has been achieved when judging them versus the 2D experiments provided by the WWFE and other sources. As design verification demands for an accurate determination of the reserve factor. Its determination is presented for both the linear and the non-linear case. Values are given for one example.