Partial Slip Rolling Wheel-Rail Contact With a Slant Rail Crack

2004 ◽  
Vol 126 (3) ◽  
pp. 450-458 ◽  
Author(s):  
Yung-Chuan Chen ◽  
Jao-Hwa Kuang
Keyword(s):  
Stress Intensity ◽  
Contact Stress ◽  
Stress Intensity Factors ◽  
Crack Problem ◽  
Crack Edge ◽  
Contact Model ◽  
Partial Slip ◽  
Stress Distributions ◽  
Intensity Factors ◽  
Normal Contact

This paper investigates the tip characteristics of an oblique crack in the wheel-rail contact problem. The wheel-rail normal contact pressure and interfacial shear stress distributions, and the stress intensity factors (SIF), are studied for oblique cracks of different inclinations, and the variations in both contact stress distributions near the crack edge are simulated under normal and traction loads, respectively. Contact elements are employed to model the interactions between the wheel-rail contact surfaces and the crack surfaces, respectively. The effects of crack orientation, crack length, and contact distance on the contact stress distributions and stress intensity factors, KI and KII, are investigated. The results indicate that a wheel-rail traction force reduces KII significantly as the contact point travels over the crack edge. Furthermore, fluctuations in KI and KII are very significant with regard to early squat propagation of cracks. The results also demonstrate that applying Carter’s contact model or the full slip contact model to the same wheel-rail contact crack problem yields significantly different stress intensity factor values.

Analysis of Branched Interface Cracks Between Dissimilar Anisotropic Media

1989 ◽  
Vol 56 (4) ◽  
pp. 844-849 ◽  
Author(s):  
G. R. Miller ◽  
W. L. Stock
Keyword(s):  
Stress Intensity ◽  
Singular Integral ◽  
Stress Intensity Factors ◽  
Crack Problem ◽  
Singular Integral Equations ◽  
Crack Branching ◽  
Intensity Factors ◽  
Function Solution ◽  
Special Cases ◽  
Branch Crack

A solution is presented for the problem of a crack branching off the interface between two dissimilar anisotropic materials. A Green’s function solution is developed using the complex potentials of Lekhnitskii (1981) allowing the branched crack problem to be expressed in terms of coupled singular integral equations. Numerical results for the stress intensity factors at the branch crack tip are presented for some special cases, including the no-interface case which is compared to the isotropic no-interface results of Lo (1978).

Analysis of Multiple Rigid-Line Inclusions for Application to Bio-Materials

2007 ◽  
Author(s):  
Pawan S. Pingle ◽  
Larissa Gorbatikh ◽  
James A. Sherwood
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Crack Problem ◽  
Building Blocks ◽  
Duality Principle ◽  
Inclusion Problem ◽  
Multiple Cracks ◽  
Intensity Factors ◽  
Aspect Ratios ◽  
Rigid Line

Hard biological materials such as nacre and enamel employ strong interactions between building blocks (mineral crystals) to achieve superior mechanical properties. The interactions are especially profound if building blocks have high aspect ratios and their bulk properties differ from properties of the matrix by several orders of magnitude. In the present work, a method is proposed to study interactions between multiple rigid-line inclusions with the goal to predict stress intensity factors. Rigid-line inclusions provide a good approximation of building blocks in hard biomaterials as they possess the above properties. The approach is based on the analytical method of analysis of multiple interacting cracks (Kachanov, 1987) and the duality existing between solutions for cracks and rigid-line inclusions (Ni and Nasser, 1996). Kachanov’s method is an approximate method that focuses on physical effects produced by crack interactions on stress intensity factors and material effective elastic properties. It is based on the superposition technique and the assumption that only average tractions on individual cracks contribute to the interaction effect. The duality principle states that displacement vector field for cracks and stress vector-potential field for anticracks are each other’s dual, in the sense that solution to the crack problem with prescribed tractions provides solution to the corresponding dual inclusion problem with prescribed displacement gradients. The latter allows us to modify the method for multiple cracks (that is based on approximation of tractions) into the method for multiple rigid-line inclusions (that is based on approximation of displacement gradients). This paper presents an analytical derivation of the proposed method and is applied to the special case of two collinear inclusions.

Weight Functions for an External Longitudinal Semi-Elliptical Surface Crack in a Thick-Walled Cylinder

1997 ◽  
Vol 119 (1) ◽  
pp. 74-82 ◽  
Author(s):  
A. Kiciak ◽  
G. Glinka ◽  
D. J. Burns
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Surface Crack ◽  
Complex Stress ◽  
Weight Functions ◽  
Stress Distributions ◽  
Intensity Factors ◽  
Reference Stress ◽  
Pressurized Cylinder ◽  
Walled Cylinder

Mode I weight functions were derived for the deepest and surface points of an external radial-longitudinal semi-elliptical surface crack in a thick-walled cylinder with the ratio of the internal radius to wall thickness, Ri/t = 1.0. Coefficients of a general weight function were found using the method of two reference stress intensity factors for two independent stress distributions, and from properties of weight functions. Stress intensity factors calculated using the weight functions were compared to the finite element data for several different stress distributions and to the boundary element method results for the Lame´ hoop stress in an internally pressurized cylinder. A comparison to the ASME Pressure Vessel Code method for deriving stress intensity factors was also made. The derived weight functions enable simple calculations of stress intensity factors for complex stress distributions.

A Method to Extract Interface Stress Intensity Factors Using Interlayers

2005 ◽  
Author(s):  
Sridhar Santhanam
Keyword(s):  
Stress Intensity ◽  
Interface Crack ◽  
Stress Intensity Factors ◽  
Crack Problem ◽  
Interface Stress ◽  
Mode I ◽  
Universal Relation ◽  
Intensity Factors ◽  
Infinite Blocks

A method is presented here to extract stress intensity factors for interface cracks in plane bimaterial fracture problems. The method relies on considering a companion problem wherein a very thin elastic interlayer is artificially inserted between the two material regions of the original bimaterial problem. The crack in the companion problem is located in the middle of the interlayer with its tip located within the homogeneous interlayer material. When the thickness of the interlayer is small compared with the other length scales of the problem, a universal relation can be established between the actual interface stress intensity factors at the crack tip for the original problem and the mode I and II stress intensity factors associated with the companion problem. The universal relation is determined by formulating and solving a boundary value problem. This universal relation now allows the determination of the stress intensity factors for a generic plane interface crack problem as follows. For a given interface crack problem, the companion problem is formulated and solved using the finite element method. Mode I and II stress intensity factors are obtained using the modified virtual crack closure method. The universal relation is next used to obtain the corresponding interface stress intensity factors for the original interface crack problem. An example problem involving a finite interface crack between two semi-infinite blocks is considered for which analytical solutions exist. It is shown that the method described above provides very acceptable results.

Numerical Method for Determining Stress Intensity Factors of an Interior Crack in a Finite Plate

1971 ◽  
Vol 93 (4) ◽  
pp. 685-690 ◽  
Author(s):  
W. K. Wilson
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Stress Function ◽  
Outer Boundary ◽  
Normal Derivative ◽  
Crack Edge ◽  
Rectangular Plates ◽  
Airy Stress Function ◽  
Intensity Factors ◽  
Plate Edge

A boundary collocation method for estimating the stress intensity factors for a through-thickness interior crack in a plate of arbitrary geometry and arbitrary in-plane loading on the plate outer-boundary and crack surfaces is presented. The collocation is carried out on an Airy stress function which is derived from a previously given complex stress function. Various types of boundary collocation procedures are investigated. It is shown that collocation on the Airy stress function and its normal derivative gives the most accurate results. The method is applied to rectangular plates containing center cracks of arbitrary angular orientation. A number of plate edge and crack edge loading conditions are analyzed. The stress intensities calculated by this method compare very favorably with existing solutions for cases in which such solutions are available.

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