**Kuntimaddi Sadananda 1,\*, Ilaksh Adlakha 2, Kiran N. Solanki <sup>3</sup> and A.K. Vasudevan <sup>1</sup>**


Received: 19 March 2020; Accepted: 26 April 2020; Published: 1 May 2020

**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.

**Keywords:** crack growth; dislocation models; pile-ups; kitagawa-takahashi diagram; fracture mechanics; internal stresses
