Three-dimensional mode I fundamental fields for circular and elliptical cracks in isotropic, finite bodies with prescribed displacement and traction boundaries are analyzed by a previously introduced finite element method [1]. For the circular crack, we present a procedure for determining the Fourier coefficients of the stress intensity factor by using the ordinary fundamental fields.

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Three-dimensional shear mode fundamental fields in finite bodies with mixed boundary conditions are analyzed by a special finite element method for circular and elliptical cracks. A procedure for determining the Fourier coefficients of the stress intensity factor for circular cracks is presented. A special series is proposed to represent the computed crack face weight functions for elliptical cracks.

Crystallographic texture is related to the anisotropy or isotropy of material physical properties, including mechanical performance. The crystallographic effect in micromachining is more significant than that in macro-processing owing to that the depth of the cut and the grain size are in the same order. It is of great significance to model the crystallographic texture evolution induced by mechanical and thermal load during micro-machining to investigate the surface integrity and performance of the finished product. This study performed hot deformation experiments of Al alloy 7075 (AA7075) under various input parameters, including the temperature, temperature rate, stain rate, and strain, which was designed using the Taguchi method. Following that, crystallographic orientation of the samples before and after the deformation was tested using electron back-scattered diffraction (EBSD). Then, the crystallographic texture evolution was modeled with the parameters obtained by fitting a part of the experimental data. The crystallographic texture evolution of AA7075 under different levels of input parameters is studied and analyzed. Finally, the sensitivity of crystallographic orientation evolution to the process parameter is analyzed. The results indicate that these four input parameters have a significant impact on some crystallographic texture of the specimens. The proposed model is instructive in the future investigation of micromachining and microstructure evolution.