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Inclined circular punch with one or two ends in smooth contact with a cracked half plane.pdf
Engineering Fracture Mechanics 172 (2017) 126–138
Contents lists available at ScienceDirect
Engineering Fracture Mechanics
journal homepage: /locate/engfracmech
Inclined circular punch with one or two ends in smooth contact with a cracked half plane
Norio Hasebe a,?, Jun Qian b
a Department of Civil Engineering and System Management, Nagoya Institute of Technology, Gokiso-cho, Showa-ku, Nagoya 466-8555, Japan b Clarivate Analytics, 1500 Spring Garden, Philadelphia, PA 15102, USA
article info
Article history: Received 13 November 2016 Received in revised form 12 January 2017 Accepted 12 January 2017 Available online 16 January 2017
Keywords: Circular rigid punch Contact Edge crack Stress intensity factor Half plane Inclined punch Resultant moment Mapping function Complex stress function
abstract
An inclined circular punch with one or two ends in smooth contact (incomplete contact) with a half plane with a vertical edge crack is considered. The solution is analytically derived, and the conditions of smooth contact with the edge-cracked half plane are expressed as the restraining conditions. The inclined angle is related to the restraining condition at the smooth end of the punch. Because the restraining conditions belong to nonlinear equations, the problem cannot be simply solved using the method of superposition. Different inclined angles are assumed to iterate the corresponding stress intensity factors of the crack, resultant moment on the contact region and length of the contact region in different cases. The relations among the contact length, resultant moment about the origin, stress intensity factor and inclined angle of the punch are shown in the ?gures.
ó 2017 Elsevier Ltd. All rights reserved.
1. Introduction
The contact problem is an important problem in engineering and interesting in applied mechanics and mathematics. Many classical problems have been solved in the ?ne books [1–6], and many references were mentioned. The rigid-punch problem is also an impor
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