C. H. Kuo

Cracking in a loaded, brittle elastic half-space

Abstract An approximation giving the relation between the applied load and the crack density in a microscratch test is presented from considerations of sliding contact and fracture analysis. First, the three-dimensional problem of two interacting cracks, with arbitrary shape and configuration, in an elastic half-space is analyzed using the body force method. Then, the analysis is specialized to study the surface cracking which occurs due to the indenter sliding over the rough, brittle half-space. Numerical examples are given for point contact by a spherical indenter sliding over a zirconia ceramic and the shielding effects between two adjacent surface cracks with different spacings are discussed in the context of the determination of crack density.

Surface deformation and energy release rates for constant stress drop slip zones in an elastic half‐space

Free surface displacements, stress intensity factors, and energy release rates are calculated for planar slip zones in an elastic half-space subjected to a prescribed shear stress drop. Although the method can treat arbitrarily shaped planar zones and distributed stress drops, for simplicity, results are presented only for circular and elliptic zones and uniform stress drops. Calculations of the stress intensity factors and energy release rates for various geometries indicate that solutions for the half-space differ by less than 10% from those in the full space if the distance from the slip zone center to the free surface is greater than the downdip width of the slip zone. In addition, the influence of the free surface is greater for decreasing dip angle. For slip zones that are near the free surface and, especially, those that break the surface there is a coupling between slip and normal relative displacement. That is, for a prescribed shear stress drop and zero normal stress change, slip induces relative normal displacement. As example applications, these solutions are used to reexamine the coseismic geodetic data from three earthquakes: 1966 Parkfield, 1983 Borah Peak, and 1987 Whittier Narrows. The geometries, moments, and stress drops are similar to those inferred in previous studies using dislocation methods. However, the stress drop inferred here may be more reliable because stress drop is one of the parameters adjusted to fit the observed surface deformations. In addition, the method makes it possible to estimate the critical energy release rate at the termination of rupture. Values for the Parkfield, Borah Peak, and Whittier Narrows earthquakes are 1.5.×106 J/m2, 1.2×106 J/m2, and 2×108 J/m2, respectively.

Effects of multiple cracking on crack growth and coalescence in contact fatigue

A three-dimensional fracture analysis is applied to investigate the interaction effects of multiple cracking on the crack growth in contact fatigue and to simulate the process of crack coalescence that leads to pitting failure. The rolling contact fatigue is simulated by a cyclic Hertzian contact loading moving across the surface of an elastic half-space containing several planar cracks. The body force method is applied to determine the three modes of stress intensity factors around the three-dimensional crack fronts. The fatigue crock propagation under contact loading is estimated based on the modified Paris law for mixed mode crack growth. For coplanar cracks, the growth rate increases significantly as the adjacent cracks are very close while parallel cracks appear to constrain the cracks from coalescing. A numerical simulation for the propagation of crack fronts versus contact cycles is shown to agree with the pitting cracks observed in gears.

A note on the line spring solution for a part-through crack

The line spring solutions used to solve part-through crack problems in plates are investigated by comparing with the results obtained from an accurate three-dimensional analysis using the body force method. Comparisons are made for the mode I stress intensity of a semi-elliptical crack with various aspect ratios a/b, i.e. the ratio of the width to the depth of the crack. The results indicate that the two methods agree well for cracks that are wider than they are deep (an aspect ratio greater than one).

A simulation of the vertical split head failure in rails

Abstract A two-dimensional analysis is presented to assess a possible mechanism to account for the axial cracking behavior in rails which is usually called a vertical split head failure. This failure is potentially damaging and may eventually lead to derailment. The vertical split head is simulated in the present analysis as a vertical crack in an eccentrically loaded infinite strip, representing the head, loaded on its upper surface and constrained on its lower surface, approximating the web constraint. The vertical crack is modeled as distributed dislocations. By using Fourier tarnsforms, the interior stress field and stress intensity factors at the crack tip are determined from the derived coupled integral equations. The calculated stress field indicates that the initiation of a vertical defect is more likely to be caused by the influence of residual stresses upon an existing rail defect, such as an inclusion. Moreover, the growth of the crack is constrained to within the rail head by the high magnitudes of compressive stresses that occur beneath the contact loading and the head-web juncture.