Abstract
Crack growth kinetics in crystalline materials is examined both from the point of continuum mechanics and discrete dislocation dynamics. Kinetics ranging from the Griffith crack to continuous elastic-plastic cracks are analyzed. Initiation and propagation of incipient cracks require very high stresses and appropriate stress gradients. These can be obtained either by pre-existing notches, as is done in a typical American Society of Testing and Materials (ASTM) fatigue and fracture tests, or by in situ generated stress concentrations via dislocation pile-ups. Crack growth kinetics are also examined using the modified Kitagawa–Takahashi diagram to show the role of internal stresses and their gradients needed to sustain continuous crack growth. Incipient crack initiation and growth are also examined using discrete dislocation modeling. The analysis is supported by the experimental data available in the literature.
Highlights
Mechanical failure of materials occurs by crack initiation and growth
We examine the crack initiation and growth process in crystalline materials to extract some of the basic concepts involved
Thethey shortare crack grows to the presence of both applied and in situ generated internal stresses arising from inhomogeneous deformations in the polycrystalline materials
Summary
Mechanical failure of materials occurs by crack initiation and growth. Griffith [1] provided the first crack growth analysis using the change in the strain energy of the cracked body in comparison to uncracked bodies, in generating new surfaces by crack initiation and the growth process. Crystals 2020, 10, 358; doi:10.3390/cryst10050358 www.mdpi.com/journal/crystals size for its continuous expansion are determined as a function of applied stress and lattice friction stress In this model for mathematical simplicity, each crack with its plastic zone is treated separately. The problem is discussed both from the point of continuum mechanics principles plastic crack, the slope is less than 0.5, and depends on the relative ratio of friction stress The conditions for a critical crack size for its continuous expansion are determined as a function of applied stress and lattice friction stress The fundamental concepts remain the same, as will be shown here
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