Current state and historical evolution of theoretical strength calculations is presented as a brief overview completed by a database of selected theoretical and experimental results. Principles of a sophisticated analysis of mechanical stability of crystals are elucidated by means of a schematic example. Stability conditions and Jacobian matrixes are presented for selected crystalline symmetries and deformation paths. The importance of this analysis for understanding micromechanics of fracture is shown against the background of the influence of crystal defects. Differences between theoretical and experimental theoretical strength (TS) values are discussed and some challenging tasks are outlined for the near future.
Influence of biaxial stresses applied perpendicularly to the ͓100͔ loading axis on the theoretical tensile strength is studied from first principles. Ten crystals of cubic metals and three crystals of diamond ceramics were selected as particular case studies. Obtained results show that, within a limited range of biaxial stresses, the tensile strength monotonously increases with increasing biaxial tensile stress for most of the studied metals. Within the range, the dependence can be approximated by a linear function. Beyond the range, the dependence shows a maximum that usually appears in the tensile range of biaxial stresses. On the other hand, some of the materials ͑Si, Ni, Cu, and Ge͒ exhibit a maximum tensile strength at nearly uniaxial stress state, and the superposition of both tensile and compressive biaxial stresses reduces the tensile strength. Unlike the other crystals, diamond revealed a maximum under compressive biaxial stress.
A simulation of a tensile test of copper crystal along the [001] direction is performed using the Vienna ab initio simulation package (VASP). Stability conditions for a uniaxially loaded system are presented and analysed and the ideal (theoretical) tensile strength for the loading along the [001] direction is determined to be 9.4 GPa in tension and 3.5 GPa in compression. A comparison with experimental values is performed.
This review paper presents a brief state‐of‐the art of the research on long fatigue shear‐mode cracks and describes some recent results on effective crack growth thresholds and mode I branching conditions achieved by the authors for ARMCO iron, titanium with two different microstructures, nickel and stainless steel. A special technique for preparation of fatigue precracks enabled us to substantially suppress the crack closure (friction) effects at the beginning of the experiment, and the measured threshold values could be considered to be very close to the effective ones. In all investigated materials, the effective thresholds under the remote mode II loading were found to be about 1.7 times lower than those under the remote mode III loading. Effective thresholds under mode II loading of investigated materials were found to follow a simple formula assembled by the shear modulus G, the magnitude of Burgers vector b and a goniometrical function nα of the mean deflection angle that depends on the number of available crystallographic slip systems. These quantities determine the intrinsic material resistance to mode II crack propagation at the threshold. A simple criterion for mode I branching in terms of effective threshold values well reflects a transition from the shear‐mode to the opening‐mode controlled crack propagation at the threshold. The associated transition deflection angle of 40° is a material independent constant.
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