scholarly journals Fracture Mechanics and Beam Theory Analyses of Semi-Elliptical Cracks Originating in the Base of Rail

2012 ◽  
Author(s):  
David Y. Jeong ◽  
Michael E. Carolan ◽  
Hailing Yu ◽  
Benjamin Perlman ◽  
Jeffrey E. Gordon
Keyword(s):  
Stress Intensity ◽  
Fracture Mechanics ◽  
Stress Intensity Factors ◽  
Beam Theory ◽  
The United States ◽  
Intensity Factors ◽  
Northeast Region ◽  
Aspect Ratios ◽  
Serious Injuries ◽  
Elliptical Cracks

In May 2011, a derailment of a passenger train occurred in a tunnel in the northeast region of the United States. Fortunately, no serious injuries or fatalities resulted from this derailment. The probable cause of the derailment was determined to be a broken rail from a defect originating in the base of the rail. This internal rail base defect is characterized as having a crescent, thumbnail, or semi-elliptical shape. In addition, the formation and growth of this defect may have been exacerbated by corrosion. This paper describes engineering calculations to estimate the growth rate of this type of rail base defect. These engineering calculations are based on applying the principles of fracture mechanics and beam theory. Fracture mechanics principles are applied to determine stress intensity factors for the semi-elliptical shaped defect with different aspect ratios. Stress intensity factors are then used to estimate the growth of the defect under the accumulation of tonnage from repeated wheel passages. For this purpose, the rail is assumed to behave as a beam in bending.

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.

An Integral Technique to Evaluate Opening Mode Stress Intensity Factors for Embedded Planar Cracks of Arbitrary Shape

1985 ◽  
Vol 9 (1) ◽  
pp. 1-10 ◽  
Author(s):  
M.A.A. Khattab ◽  
D.J. Burns ◽  
R.J. Pick ◽  
J.C. Thompson
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Arbitrary Shape ◽  
Intensity Factors ◽  
Simple Method ◽  
Aspect Ratios ◽  
Opening Mode ◽  
Integration Techniques ◽  
Mode Stress ◽  
Coarse Grids

In this paper, techniques are developed to handle the integrable singularities of the integral proposed by Burns and Oore for the estimation of opening mode stress intensity factors for embedded planar defects of arbitrary shape. The hybrid numerical-analytical integration techniques developed consider separately two crack front zones and one interior zone of the crack surface. Parameters are established for the sizing of the integration elements within each zone. Studies of elliptical defects with aspect ratios between 1 and 10 demonstrate the accuracy and efficiency of this procedure for computing opening mode stress intensity factors. A simple method which compensates for the quadrature error associated with computationally inexpensive, coarse grids is outlined.

Part-Elliptical Cracks Emanating From Open and Loaded Holes in Plates

1979 ◽  
Vol 101 (1) ◽  
pp. 12-17 ◽  
Author(s):  
T. E. Kullgren ◽  
F. W. Smith
Keyword(s):  
Finite Element ◽  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Crack Opening ◽  
Plate Thickness ◽  
Hole Diameter ◽  
Elastic Analysis ◽  
Intensity Factors ◽  
Linear Elastic ◽  
Elliptical Cracks

A linear elastic analysis using the finite element-alternating method is conducted for problems of single semi-elliptical and double quarter-elliptical cracks near fastener holes. Mode-one stress intensity factors are presented along the crack periphery for cases of open and loaded holes and crack opening displacements are calculated. Results are shown for a variety of crack geometries and loading conditions and for two ratios of hole diameter to plate thickness.

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