Static and Cyclic Strength of Laminates composedof Uni-directional, Endless Fibre reinforced Plies

- The lighter, the more difficult -

by Prof. Dr. Ralf Cuntze

Basic features: The paper presents some background, including views on isotropic materials, in order to find methods to predict the strength of multi-layered laminates composed of UD laminas (plies) and manufactured of fibre-reinforced plastics (FRP). At first a view of the state of the art of static and cyclic strength is presented. Then, the paper depicts the basics of the author's failure mode concept (FMC) generally applicable to materials that can be homogenized for their analysis. The concept is applied in the following section to static strength conditions of uni-directional (UD) material. Differences between the use of the classical 'global' or interactive conditions and the derived 'modal' conditions are addressed. Of benefit for the design judging engineer is the introduction of the 'material stressing effort' and its associated equivalent stress. On the FMC also builds the proposed life time prediction method for the most often 'fibre-dominated' designed laminates of structural walls. Basic intention of the paper is to show the red line of some new ideas including the use of material symmetry facts, as well as to draw attention to the material behaviour (ductile, brittle, intermediate), tomaterial consistency (dense, porous), and to material element behaviour (volume change, shapechange, friction). FMC-based Static Strength: The depicted FMC-based UD strength failure conditions were successful in the World-Wide-Failure-Exercises. In the WWFE-I the courses of multi-axial 2D UD fracture stress test data could be mapped without any difficulties whenever 'clear' data could be provided. In the running WWFE-II, the provision with reliable 3D UD fracture stress data is a very challenging task. Additionally, a lot of multi-axial fracture stress domains are still not covered by the available test data. Therefore just the remaining 'clear' test data sets have been successfully mapped. As the FMC is based on a very strict thinking in independent failure modes equivalent stresses can be formulated for UD-material, too, which is of benefit for engineering assessment.The applicability of the conditions is confirmed here by mapping some static test data sets. FMC-based Cyclic Strength (lifetime prediction): As the determination of a S-N curve is costly, a proposal is made for a so-called master S-N curve which enables the engineer in pre-dimensioning to build life time predictions for variable loading on aphysically-founded and thereby cheaper basis. Above master S-N curve represents the basic R-ratioS-N curve associated to a failure mode, which may be a normal fracture or a shear fracture mode. Further S-N curves for the same failure mode, required in fatigue analysis, can be predicted from the master curve by utilizing the equivalent strain energy principle. The prediction method uses fracture failure modes, is lamina-oriented, and applies the well-knownstress ratio-dependent S-N curves but failure mode linked. This results in a new failure mode related damage accumulation. With respect to the FMC the cyclic loading has to be 'rainflowed' failure mode-linked. This is a new procedure. By the proposed method the traditional fatigue life demonstration with its mean stress correction is very much changed. The damaging portions are related to the material stressing efforts that the material experiences under variable loading. As accumulation model for the damaging portions the ’Relative Miner rule’ is still recommended. The method is schematically applied to one set of S-N data, master curve R = 0.1.