An Analysis of a Near-Surface Crack Branching Under a Rigid Indenter

1999 ◽  
Vol 122 (1) ◽  
pp. 23-29 ◽  
Author(s):  
David J. Mukai
Keyword(s):  
Coulomb Friction ◽  
Crack Depth ◽  
Hertzian Contact ◽  
Crack Branching ◽  
Mode I ◽  
Subsurface Crack ◽  
Intensity Factors ◽  
Near Surface ◽  
Straight Crack ◽  
Surface Conditions

A near surface branching subsurface crack under a rigid cylindrical indenter is analyzed by a complex variable 2-D elasticity formulation. This analysis focuses on the mode II stress intensity factors (SIF) of a straight crack vs. the mode I SIF of a branched crack. The contact portion of the analysis is limited to a Hertzian contact under simple Coulomb friction. The effects of crack depth and length are examined and it is found that for small indenter footprints, as a crack grows parallel to the surface, conditions favor mode I branching toward the surface. [S0742-4787(00)00401-X]

scholarly journals Subsurface Cracks Under Conditions of Slip, Stick, and Separation Caused by a Moving Compressive Load

1987 ◽  
Vol 54 (2) ◽  
pp. 393-398 ◽  
Author(s):  
S. D. Sheppard ◽  
J. R. Barber ◽  
M. Comninou
Keyword(s):  
Integral Equation ◽  
Stress Intensity ◽  
Coulomb Friction ◽  
Compressive Load ◽  
Mode I ◽  
Subsurface Crack ◽  
Intensity Factors ◽  
Subsurface Cracks ◽  
Load Location ◽  
Crack Faces

The Mode I and II stress intensity factors (KI, KII) at the two tips of a subsurface crack subjected to a moving compressive load are studied. Coulomb friction along the crack faces results in a number of history dependent slip-stick configurations and nonsymmetric variation in KI and KII. The formulation used to study this variation involves a singular integral equation in two variables which must be solved numerically, and because of the history dependence, requires an incremental solution. Crack lengths and coefficients of friction that result in as many as three zones for any load location are considered in this paper, while a previous paper (Sheppard et al., in press) was limited to configurations involving two zones only.

Behavior of a Horizontal Fluid Filled Crack Under Moving Hertzian Load

2005 ◽  
Author(s):  
X. Jin ◽  
L. M. Keer ◽  
E. L. Chez
Keyword(s):  
Half Plane ◽  
Continuous Distribution ◽  
Contact Stresses ◽  
Hertzian Contact ◽  
Subsurface Crack ◽  
Intensity Factors ◽  
Crack Volume ◽  
Rolling Body ◽  
Soft Inclusion ◽  
Edge Dislocations

Numerical analysis is presented for a fluid filled subsurface crack in an elastic half plane loaded by Hertzian contact stresses. The opening volume of the horizontal Griffith crack is fully occupied by an incompressible fluid. In the presence of friction, a moving Hertzian line contact load is applied at the surface of the half plane. The stress intensity factors at the tips of the fluid filled crack are analyzed on condition that the change of the opening crack volume vanishes due to the fluid incompressibility. The method used is that of replacing the crack by a continuous distribution of edge dislocations. As a cycle of rolling can be viewed as shifting the Hertzian contact stresses across the surface of the half plane, the results of this analysis may prove useful in the prediction of rolling fatigue of an elastic rolling body containing a soft inclusion.

Elastodynamic Stress-Intensity Factors for a Crack Near a Free Surface

1981 ◽  
Vol 48 (3) ◽  
pp. 539-542 ◽  
Author(s):  
J. D. Achenbach ◽  
R. J. Brind
Keyword(s):  
Stress Intensity ◽  
Half Space ◽  
Stress Intensity Factors ◽  
Elastic Half Space ◽  
Mode I ◽  
Dimensionless Frequency ◽  
Subsurface Crack ◽  
Intensity Factors ◽  
Time Harmonic ◽  
Crack Tips

Elastodynamic Mode I and Mode II stress-intensity factors are presented for a subsurface crack in an elastic half space. The plane of the crack is normal to the surface of the half space. The half space is subjected to normal and tangential time-harmonic surface tractions. Numerical results show the variation of KI and KII at both crack tips, with the dimensionless frequency and the ratio a/b, where a and b are the distances to the surface from the near and the far crack tips, respectively. The results are compared with corresponding results for a crack in an unbounded solid.

The Hertzian Cone Crack

1991 ◽  
Vol 58 (1) ◽  
pp. 120-127 ◽  
Author(s):  
Li Yingzhi ◽  
D. A. Hills
Keyword(s):  
Finite Element ◽  
Stress Intensity ◽  
Hertzian Contact ◽  
Mode I ◽  
Mode Ii ◽  
Element Solution ◽  
Contact Pressure Distribution ◽  
Intensity Factors ◽  
Indentation Tests ◽  
Hertzian Cone

Stress intensity factors are determined for cracks in the form of a frustum of a cone, and loaded by a Hertzian contact pressure distribution using a global-local finite element solution. These will be helpful in interpreting blunt indentation tests quantitatively, and it is shown that for most crack geometries occurring in practice, the mode II component is about a tenth of the mode I contribution.

scholarly journals Flaking of PEEK under one-point rolling contact fatigue using Al2O3 ball

2019 ◽  
Vol 264 ◽  
pp. 01004
Author(s):  
Hitonobu KOIKE ◽  
Genya YAMAGUCHI ◽  
Koshiro MIZOBE ◽  
Katsuyuki KIDA
Keyword(s):  
Fatigue Cracks ◽  
Rolling Contact Fatigue ◽  
Contact Fatigue ◽  
Rolling Contact ◽  
Hertzian Contact ◽  
Surface Cracks ◽  
Subsurface Crack ◽  
Near Surface ◽  
The One ◽  
Point Type

The growth of flaking as tribological fatigue failure in PEEK was investigated through the one-point type rolling contact fatigue test between a machined PEEK polymer shaft and an alumina bearing's ball. Due to Hertzian contact of cyclic compressive stress, the subsurface fatigue cracks in the PEEK shaft propagated in rolling and axial directions. When the rolling fatigue life of the PEEK shaft reached 106 fatigue cycles, many narrow angled cracks occurred in the near-surface of the rolling track without flaking. On the other hand, when the flaking ocuurred on the PEEK shaft before 106 fatigue cycles, semicircular surface and subsurface crack propagations were observed. From these observations, it was found that micro-flaking occurred due to the linkages between subsurface and surface cracks. Flakingdeveloped due to the accumulation of these micro-flakings.

Motion of a Ball in a Ball Bearing

1973 ◽  
Vol 95 (1) ◽  
pp. 263-268
Author(s):  
H. Portig ◽  
H. G. Rylander
Keyword(s):  
Deformation Theory ◽  
Coulomb Friction ◽  
Ball Bearing ◽  
Digital Simulation ◽  
Equations Of Motion ◽  
Unsteady Motion ◽  
Hertzian Contact ◽  
Contact Deformation ◽  
Normal Forces ◽  
Simulation Language

A method is developed which allows the digital simulation of the unsteady motion of a single ball constrained only by two moving bearing races. Any desired motion of the races can be simulated. Normal forces acting on the ball are calculated by Hertzian contact deformation theory. If there is slippage between ball and races, Coulomb friction is assumed to occur. Solutions to the differential equations of motion were obtained on a computer with the digital simulation language MIMIC. The phenomenon of ball control as well as the behavior of the ball as it reached a controlled state from rest were observed. This analysis can produce more realistic results than methods that assume that the ball is controlled at all times, especially when the races are radially or angularly displaced with respect to each other.

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