Frictional Punch and Crack in Plane Elasticity

A general solution to the frictional punch problem is obtained for any shape, but the part of the punch is a straight boundary. As an example, a crack initiating from an end of the punch in an elastic half‐plane is analyzed. A rational mapping function and complex stress functions are used for the analysis. The stress distributions, the stress intensity factors and the resultant moment to keep the punch horizontal are evaluated for some Poisson's ratio and frictional coefficient. For a short crack, the effect of the frictional coefficient to the stress intensity factor is investigated.

[1]  G. Gladwell.  Contact Problems in the Classical Theory of Elasticity , 1980 .

[2]  Norio Hasebe.  Mixed Boundary Value Problem of Plate with Crack , 1984 .

[3]  Y. Murakami.  Stress Intensity Factors Handbook , 2006 .

[4]  Iida Jiro,et al.  A crack originating from a triangular notch on a rim of a semi-infinite plate , 1978 .

[5]  M. D. Bryant,et al.  A Pitting Model for Rolling Contact Fatigue , 1983 .

[6]  Leon M Keer,et al.  SUBSURFACE AND SURFACE CRACKING DUE TO HERTZIAN CONTACT. , 1982 .

[7]  M. Kaneta,et al.  Mechanism of Crack Growth in Lubricated Rolling/Sliding Contact , 1985 .

[8]  N. Muskhelishvili.  Some basic problems of the mathematical theory of elasticity , 1953 .

[9]  N. Hasebe.  AN EDGE CRACK IN A SEMI-INFINITE PLATE WELDED TO A RIGID STIFFENER , 1981 .

[10]  M. Kaneta,et al.  Analysis of Surface Crack Propagation in Lubricated Rolling Contact , 1985 .

[11]  Anton Dammes de Pater,et al.  The Mechanics of the contact between deformable bodies : proceedings of the symposium of the International Union of Theoretical and Applied Mechanics (IUTAM), Enschede, Netherlands, 20-23 August 1974 , 1975 .

[12]  Yukitaka Murakami,et al.  Mechanism of Surface Crack Growth in Lubricated Rolling/Sliding Spherical Contact , 1986 .

[13]  N. Hasebe,et al.  Stress analysis of a semi-infinite plate with an oblique edge crack , 1980 .

[14]  Norio Hasebe,et al.  Mixed boundary value problem of simple support type in plane elasticity , 1988 .

[15]  Sheri Sheppard,et al.  An analysis of fretting cracks. II: Unloading and reloading phases , 1986 .

[16]  Morton Lowengrub,et al.  Some Basic Problems of the Mathematical Theory of Elasticity. , 1967 .