Investigation of the Process Zone Near the Tip of an Interface Crack in the Elastic Body in Shear Within the Framework of the Complex Model

• Published in: Journal of mathematical sciences (New York, N.Y.) N.Y.), 2017-01, Vol.220 (2), p.117-132
• Main Authors: Kamins’kyi, A. O., Dudyk, M. V., Kipnis, L. A.
• Format: Article
• Language: English
• Subjects: Analysis; Interfacial cracks; Investigations; Mathematics; Mathematics and Statistics; Methods; Numerical analysis
• ISSN: 1072-3374; 1573-8795
• DOI: 10.1007/s10958-016-3171-9

Under the conditions of plane deformation, by using the Wiener–Hopf method, we perform the numerical analysis of a narrow small-scale process zone in the elastic body subjected to shear near the tip of an interface crack whose faces are in contact with friction. The process zone originates at the crack tip and makes a certain angle with the interface of the media. It is modeled by the straight line of discontinuities of displacements and consists of two segments. In the segment adjacent to the crack tip, which models the region of destruction of the material, both normal and tangential displacements have discontinuities. At the same time, in the second segment, only the normal component of displacements suffers discontinuities. The angle between the process zone and the interface of the media is determined from the condition of maximum of circumferential tensile stresses. We determine the sizes of the entire process zone and the region of destruction, the crack-tip opening displacements, and maximum opening displacement of the initial process zone. We also investigate the influence of the friction coefficient on the parameters of the process zone. By using the deformation criterion of fracture, we analyze the role played by the zone of destruction in the onset of crack propagation. It is shown that the crack starts as a result of the relative shear of its faces near the tip. The comparison of the obtained results with the data of other researchers is presented.