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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    International journal of fracture 105 (2000), S. 367-389 
    ISSN: 1573-2673
    Keywords: Stress intensity factor ; tribology ; contact problem ; friction coefficient ; fracture mechanics ; rolling contact fatigue ; surface crack ; body force method.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract In rolling/sliding contact fatigue, it is known that the crack propagates at a characteristic angle θ=15–30 deg to the surface. To analyze the mechanism, however, the body force method has been widely used assuming 3D crack models for θ=45–90. In this study, therefore, the unknown body force densities are newly approximated by using fundamental density functions and polynomials. Then, a semi-elliptical crack model is analyzed for θ=15–90 under compressive residual stresses and Hertzian contact loads. The stress intensity factors K II, K III are calculated with varying the crack shape b/a, inclination crack angle θ, and crack face friction coefficient μ. The calculations show that the present method is useful for the analysis for θ=15–30 deg with high accuracy. It is seen that the K II-values when b/a→0 are larger than the ones when b/a=1 by 0–24% for both under compressive residual stress and Hertzian contact load. Regarding the maximum K II values under Hertzian contact load, the results of θ=15 deg are smaller than the ones of θ=45 deg by 23–34%. Regarding the amplitude of (K II max−K II min), the results of θ=15 deg are smaller than the ones of θ=45 deg by 4–24%. With increasing the value of friction coefficient μ for crack faces the value of K II decreases significantly. When the crack is short and the inclination angle θ is small, the value of friction coefficient f for Hertzian contact load largely affect the K II value.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    International journal of fracture 102 (2000), S. 371-392 
    ISSN: 1573-2673
    Keywords: Elasticity ; body force method ; singular integral equations ; numerical analysis ; three-dimensional analysis ; stress concentration factor ; ellipsoidal inclusion.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract In this paper the interaction among a row of N ellipsoidal inclusions of revolution is considered. Inclusions in a body under both (A) asymmetric uniaxial tension in the x-direction and (B) axisymmetric uniaxial tension in the z-direction are treated in terms of singular integral equations resulting from the body force method. These problems are formulated as a system of singular integral equations with Cauchy-type or logarithmic-type singularities, where unknowns are densities of body forces distributed in the r,θ,z directions. In order to satisfy the boundary conditions along the ellipsoidal boundaries, the unknown functions are approximated by a linear combination of fundamental density functions and polynomials. The present method is found to yield rapidly converging numerical results for interface stresses. When the elastic ratio E 1⇒E I/E M〉1, the primary feature of the interaction is a large compressive or tensile stress σn on the interface θ=0. When E 1⇒E I/E M〈1, a large tensile stress σθ or σt on the interface θ=1/2π is of interest. If the spacing b/d and the elastic ratio E I/E M are fixed, the interaction effects are dominant when the shape ratio a/b is large. For any fixed shape and spacing of inclusions, the maximum stress is shown to be linear with the reciprocal of the squared number of inclusions.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    International journal of fracture 106 (2000), S. 81-93 
    ISSN: 1573-2673
    Keywords: Body force method ; elasticity ; elliptical inclusion ; interaction effect ; longitudinal shear ; numerical analysis ; singular integral equation stress concentration.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract This paper deals with an interaction problem of arbitrarily distributed elliptical inclusions under longitudinal shear loading. The problem is formulated as a system of singular integral equations with Cauchy-type or logarithmic-type singularities, where unknown functions are the densities of body forces distributed in the longitudinal directions of infinite bodies having the same elastic constants as those of the matrix and inclusions. In order to satisfy the boundary conditions along the elliptical inclusions, four kinds of fundamental density functions are introduced in a similar way of previous papers treating plane stress problems. Then the body force densities are approximated by a linear combination of those fundamental density functions and polynomials. In the analysis, elastic constants of matrix and inclusion are varied systematically; then the magnitude and position of the maximum stress are shown in tables and the stress distributions along the boundary are shown in figures. For any fixed shape, size and elastic constant of inclusions, the relationships between number of inclusions and maximum stress are investigated for several arrangements.
    Type of Medium: Electronic Resource
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