Self-Similar Crack Expansion Method for Three-Dimensional Cracks Under Mixed-Mode Loading Conditions

1998 ◽  
Vol 65 (3) ◽  
pp. 557-565 ◽  
Author(s):  
Yonglin Xu ◽  
B. Moran ◽  
T. Belytschko
Keyword(s):  
Numerical Method ◽  
Mixed Mode ◽  
Three Dimensional ◽  
Expansion Method ◽  
Shear Loading ◽  
Boundary Integral ◽  
Normal Displacement ◽  
Loading Conditions ◽  
Mixed Mode Loading ◽  
Self Similar

Three-dimensional planar cracks under mixed-mode loading conditions are investigated by using the selfsimilar crack expansion method with the boundary integral equation technique. For a planar crack under general loading (tensile and shear) conditions, the normal displacement and tangential displacements on the crack surface exhibit uncoupled characteristics. However, the tangential displacements in the two directions are generally coupled. In this paper, two coupled boundary integral equations for a crack subject to shear loading are solved using the analytically numerical method, where the integrals on elements’ are estimated by using the explicit expression of the close form of the integrals. Combination of the self-similar crack expansion method and the analytically numerical method results in good accuracy, with errors in stress intensity factors of penny-shaped cracks and elliptical cracks less than one percent. This numerical analysis is applicable to the analysis of cracks with arbitrary geometry.

Nonplanar Crack Growth Using the Surface Integral Method

1997 ◽  
Vol 119 (4) ◽  
pp. 964-968 ◽  
Author(s):  
S. C. Forth ◽  
W. D. Keat
Keyword(s):  
Crack Growth ◽  
Integral Method ◽  
Mixed Mode ◽  
Circumferential Stress ◽  
Three Dimensional ◽  
Coefficient Matrix ◽  
Loading Conditions ◽  
Mixed Mode Loading ◽  
Surface Integral ◽  
Paris Law

A surface integral formulation, based on representing a crack as a distribution of force dipoles, has been developed for modeling the propagation of a three-dimensional nonplanar fracture. The minimum strain energy density and maximum circumferential stress theories were used to determine the direction of crack growth. The extension of the fracture surface was based on the Paris law for fatigue. Remeshing of the fracture during growth was accomplished by adding a ring of elements to the existing mesh at the conclusion of each increment of crack growth. This promoted the efficiency of the algorithm by eliminating the need to recalculate the entire coefficient matrix. Use of the surface integral method, coupled with growth criteria, has yielded an accurate model for three-dimensional nonplanar crack growth under mixed mode loading conditions. The study of several penny-shaped precracks under mixed-mode loading conditions produced the expected growth trajectory, and compared favorably to existing two-dimensional, three-dimensional, and experimental results found in the literature.

Self-Similar Crack Expansion Method for Three-Dimensional Crack Analysis

1997 ◽  
Vol 64 (4) ◽  
pp. 729-737 ◽  
Author(s):  
Yonglin Xu ◽  
B. Moran ◽  
T. Belytschko
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Numerical Solutions ◽  
Crack Surface ◽  
Three Dimensional ◽  
Expansion Method ◽  
Infinite Medium ◽  
Boundary Integral ◽  
Intensity Factors ◽  
Self Similar

The self-similar crack expansion method is developed to calculate stress intensity factors for three-dimensional cracks in an infinite medium or semi-infinite medium by the boundary integral element technique. With this method, the stress intensity factors at crack tips are determined by calculating the crack-opening displacements over the crack surface, and the crack expansion rate, which is related to the crack energy release rate, is estimated by using a technique based on self-similar (virtual) crack extension. For elements on the crack surface, regular integrals and singular integrals are evaluated based on closed-form expressions, which improves the accuracy. Examples show that this method yields very accurate results for stress intensity factors of penny-shaped cracks and elliptical cracks in the full space, with errors of less than one percent as compared with exact solutions. The stress intensity factors of subsurface cracks are in good agreement with other numerical solutions.

scholarly journals Nonplanar Crack Growth Using the Surface Integral Method

1996 ◽  
Author(s):  
Scott C. Forth ◽  
William D. Keat
Keyword(s):  
Crack Growth ◽  
Integral Method ◽  
Mixed Mode ◽  
Circumferential Stress ◽  
Three Dimensional ◽  
Coefficient Matrix ◽  
Loading Conditions ◽  
Mixed Mode Loading ◽  
Surface Integral ◽  
Paris Law

A surface integral formulation, based on representing a crack as a distribution of force dipoles, has been developed for modeling the propagation of a three-dimensional nonplanar fracture. The minimum strain energy density, and maximum circumferential stress theories were used to determine the direction of crack growth. The extension of the fracture surface was based on the Paris Law for fatigue. Remeshing of the fracture during growth was accomplished by adding a ring of elements to the existing mesh at the conclusion of each increment of crack growth. This promoted the efficiency of the algorithm by eliminating the need to recalculate the entire coefficient matrix. Use of the surface integral method, coupled with growth criteria, has yielded an accurate model for three-dimensional nonplanar crack growth under mixed mode loading conditions. The study of several penny-shaped precracks under mixed mode loading conditions produced the expected growth trajectory, and compared favorably to existing 2D, 3D, and experimental results found in the literature.

Loading Direction Versus Crack Propagation Path in a Lead-Free Single Solder Joint Sample

2008 ◽  
Author(s):  
Feng Gao ◽  
Jianping Jing ◽  
Janine Johnson ◽  
Frank Z. Liang ◽  
Richard L. Williams ◽  
...  
Keyword(s):  
Solder Alloy ◽  
Mixed Mode ◽  
Shear Fracture ◽  
Pure Shear ◽  
Shear Loading ◽  
Propagation Path ◽  
Mixed Mode Loading ◽  
Cohesive Failure ◽  
Loading Direction ◽  
Shear Component

In this paper, single solder joints (SSJs) were subjected to moderate speed loading (5mm/sec) in different directions, from pure tensile, mixed mode to pure shear. Fracture surfaces from different loading directions were examined both experimentally and numerically. It is observed that intermetallic compound (IMC) is formed between the solder alloy and the Cu pad, and failure typically occurs at or near the solder/IMC/Cu interfaces on the board side. Pure tensile loading typically leads to interfacial fracture along the IMC/Cu interface. Mixed mode loading usually results in a mixture of interfacial and cohesive failure with crack propagating in a zigzag fashion between the solder/IMC interface and the solder alloy. Loading with higher shear component tends to result in more cohesive failure of the solder alloy near the solder/IMC interface. Under pure shear loading, failure is almost always cohesive within the solder alloy near the solder/IMC interface.

scholarly journals On crack propagation in homogeneous and composite materials under mixed mode loading conditions

2019 ◽  
Vol 23 ◽  
pp. 203-208 ◽  
Author(s):  
Martin Lederer ◽  
Agnieszka Betwar Kotas ◽  
Golta Khatibi ◽  
Herbert Danninger
Keyword(s):  
Composite Materials ◽  
Crack Propagation ◽  
Mixed Mode ◽  
Loading Conditions ◽  
Mixed Mode Loading
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