Optimal Cruciform Specimen Design Using the Direct Multi-search Method and Design Variable Influence Study

Abstract

Nowadays the development of new testing machines and the optimization of new specimen geometries are two very demanding activities. In order to study complex material stress and strain distributions, as in-plane biaxial loading, one must develop new technical solutions. A new type of testing machine has been developed by the present authors, for the fatigue testing of cruciform specimens, but the low capacity of the testing machine requires the optimization of the specimen in order to achieve higher but uniform stress and strain distributions on the specimen center. In this paper, the authors describe the procedure to optimize one possible geometry for cruciform specimens, able to determine the fatigue initiation life of material subjected to out of phase in plane biaxial fatigue loadings. The high number of design variables were optimized using the direct multi-search method, considering two objective functions, the stress level on the specimen center and the uniformity of the strain distribution on a 1.0mm radius of the specimen center. Several Pareto Fronts were obtained for different material thickness, considering the commercially available sheet metal thickness. With the optimal solution, the influence of every design variable was studied in order to provide others with a powerful tool that allows selecting the optimal geometry for the desired application. The results are presented in the form of design equations considering that the main design variable, the material thickness, was chosen from a Renard series of preferred numbers. The end user is then able to configure the optimal specimen for the required fatigue test.