On Fractal Cracks in Micropolar Elastic Solids

2001 ◽  
Vol 69 (1) ◽  
pp. 45-54 ◽  
Author(s):  
A. Yavari ◽  
S. Sarkani ◽  
E. T. Moyer,
Keyword(s):  
Fracture Mechanics ◽  
Dimensional Analysis ◽  
Asymptotic Method ◽  
Couple Stress ◽  
Stress Singularity ◽  
Stress Singularities ◽  
Elastic Solids ◽  
Fracture Theory ◽  
Fractal Crack ◽  
Fractal Cracks

In this paper we review the fracture mechanics of smooth cracks in micropolar (Cosserat) elastic solids. Griffith’s fracture theory is generalized for cracks in micropolar solids and shown to have two possible forms. The effect of fractality of fracture surfaces on the powers of stress and couple-stress singularity is studied. We obtain the orders of stress and couple-stress singularities at the tip of a fractal crack in a micropolar solid using dimensional analysis and an asymptotic method that we call “method of crack-effect zone.” It is shown that orders of stress and couple-stress singularities are equal to the order of stress singularity at the tip of the same fractal crack in a classical solid.

GENERALIZATION OF BARENBLATT'S COHESIVE FRACTURE THEORY FOR FRACTAL CRACKS

Fractals ◽  
2002 ◽  
Vol 10 (02) ◽  
pp. 189-198 ◽  
Author(s):  
ARASH YAVARI
Keyword(s):  
Driving Force ◽  
A Priori ◽  
Stress Singularity ◽  
Local Theory ◽  
Fractal Surface ◽  
Cohesive Fracture ◽  
Fracture Theory ◽  
Griffith’S Theory ◽  
Fractal Crack ◽  
Fractal Cracks

In this paper, we generalize Barenblatt's cohesive fracture theory for fractal cracks. We discuss the difficulties of generalizing the concept of traction on a fractal surface. Borodich's modification of Griffith's theory for fractal cracks is reviewed. Irwin's driving force is generalized for fractal cracks and a fractal driving force (Gf) is defined. It is shown that to generalize Barenblatt's theory for fractal cracks it is necessary to introduce a new quantity, D-fractal cohesive pseudo-stress. This new quantity is cohesive force per unit of a fractal measure. Fractal modulus of cohesion is seen to be a function of both the material and the fractal dimension of the crack. Equivalence of fractal Barenblatt's and Griffith's theories is discussed. It is seen that the order of stress singularity at the tip of a fractal crack cannot be obtained using modified Barenblatt's theory because this theory is a local theory and assumes the order of stress singularity a priori.

Stress Singularity of Edge Delamination in Angle-Ply and Cross-Ply Laminates

1997 ◽  
Vol 64 (3) ◽  
pp. 525-531 ◽  
Author(s):  
Wen-Hwa Chen ◽  
Tain-Fu Huang
Keyword(s):  
Transverse Shear ◽  
Axial Strain ◽  
Stress Singularity ◽  
Shear Stresses ◽  
Explicit Solutions ◽  
Real Constant ◽  
Stress Singularities ◽  
General Solutions ◽  
Transverse Shear Stresses ◽  
Edge Delamination

By utilizing the general solutions derived for the plies with arbitrary fiber orientations under uniform axial strain (Huang and Chen, 1994), the explicit solutions of the edge-delamination stress singularities for the angle-ply and cross-ply laminates are obtained. The dominant edge-delamination stress singularities for the angle-ply laminates are found to be a real constant, −1/2, and a pair of complex conjugates, −1/2±i/2πln{(b+b2−a2)/a}. For the cross-ply laminates, the significant effect of transverse shear stresses of the laminate is considered and the dominant edge-delamination stress singularities are shown as −1/2 and −1/2±i/2πln{(c2+c22−4c1c3)/2c1}. a, b, cl, c2, and c3 are the corresponding combined complex constants. In addition, two elementary forms of edge-delamination stress singularity, say, r−1/2 and rδr(lnr)n(δr=n−3/2,n=1,2...) exist for both the angle-ply and cross-ply laminates. Excellent correlations between the present results and available solutions show the validity of the approach. The deficiencies of the solutions available in the literature are compensated. New results for other angle-ply and cross-ply laminates are also provided.

Finite Element Analysis of Stress Singularities in Attached Flip Chip Packages

2000 ◽  
Vol 122 (4) ◽  
pp. 301-305 ◽  
Author(s):  
A. Q. Xu ◽  
H. F. Nied
Keyword(s):  
Contact Angle ◽  
Finite Element ◽  
Glass Fiber ◽  
Flip Chip ◽  
Three Dimensional ◽  
Stress Singularity ◽  
Local Stress ◽  
Stress Singularities ◽  
Element Analysis ◽  
Three Dimensional Finite Element

Cracking and delamination at the interfaces of different materials in plastic IC packages is a well-known failure mechanism. The investigation of local stress behavior, including characterization of stress singularities, is an important problem in predicting and preventing crack initiation and propagation. In this study, a three-dimensional finite element procedure is used to compute the strength of stress singularities at various three-dimensional corners in a typical Flip-Chip assembled Chip-on-Board (FCOB) package. It is found that the stress singularities at the three-dimensional corners are always more severe than those at the corresponding two-dimensional edges, which suggests that they are more likely to be the potential delamination sites. Furthermore, it is demonstrated that the stress singularity at the upper silicon die/epoxy fillet edge can be completely eliminated by an appropriate choice in geometry. A weak stress singularity at the FR4 board/epoxy edge is shown to exist, with a stronger singularity located at the internal die/epoxy corner. The influence of the epoxy contact angle and the FR4 glass fiber orientation on stress state is also investigated. A general result is that the strength of the stress singularity increases with increased epoxy contact angle. In addition, it is shown that the stress singularity effect can be minimized by choosing an appropriate orientation between the glass fiber in the FR4 board and the silicon die. Based on these results, several guidelines for minimizing edge stresses in IC packages are presented. [S1043-7398(00)00904-X]

Advances in Three-Dimensional Fracture Mechanics

2006 ◽  
Vol 312 ◽  
pp. 27-34 ◽  
Author(s):  
Wan Lin Guo ◽  
Chongmin She ◽  
Jun Hua Zhao ◽  
Bin Zhang
Keyword(s):  
Fracture Mechanics ◽  
Deformation Theory ◽  
Three Dimensional ◽  
Unified Theory ◽  
Constraint Factor ◽  
Engineering Structures ◽  
The Past ◽  
Fatigue And Fracture ◽  
Fracture Theory ◽  
Historical Developments

The historical developments of the fracture mechanics from planar theory to threedimensional (3D) theory are reviewed. The two-dimensional (2D) theories of fracture mechanics have been developed perfectly in the past 80 years, and are suitable for some specific cases of engineering applications. However, in the complicated 3D world, the limitation of the 2D fracture theory has become evident with development of the structure toward complication and micromation. In the 1990’s, Guo has proposed the 3D fracture theory with a 3D constraint factor based on the deformation theory and energy theory. The proposed 3D theory can predict accurately the fracture problems for practical and complicated engineering structures with defects, by integrating the 3D theory of fatigue, which has been developed to unify fatigue and fracture. Our efforts to develop the 3D fracture mechanics and the unified theory of 3D fatigue and fracture are summarized, and perspectives for future efforts are outlined.

Dynamical Behaviour of Orthotropic Micropolar Elastic Medium

2002 ◽  
Vol 8 (8) ◽  
pp. 1053-1069 ◽  
Author(s):  
Rajneesh Kumar ◽  
Suman Choudhary
Keyword(s):  
Elastic Medium ◽  
Couple Stress ◽  
Normal Force ◽  
Numerical Technique ◽  
Integral Transforms ◽  
Dynamical Behaviour ◽  
Normal Displacement ◽  
Physical Domain ◽  
Elastic Solids ◽  
Eigenvalue Approach

The present paper is concerned with the plane strain problem in homogeneous micropolar orthotropic elastic solids. The disturbance due to continuous normal and tangential sources are investigated by employing eigenvalue approach. The integral transforms have been inverted by using a numerical technique to obtain the normal displacement, normal force stress and tangential couple stress in the physical domain. The expressions of these quantities are given and illustrated graphically.

Stress Singularity Effect on Beam Flanges in Moment Connections

2005 ◽  
Vol 8 (2) ◽  
pp. 143-156 ◽  
Author(s):  
J. Kent Hsiao ◽  
Janice J. Chambers ◽  
William J. Schultz
Keyword(s):  
Finite Element ◽  
Steel Plate ◽  
Stress Singularity ◽  
Northridge Earthquake ◽  
Finite Element Analyses ◽  
Stress Singularities ◽  
Moment Connections ◽  
Nonlinear Static ◽  
Ductility Capacity ◽  
Free Edges

The ductility capacity of the directly welded flange connection was found to be insufficient after the 1994 Northridge earthquake. The Enlarged End Section (EES) connection which considers the stress singularity effect on beam flanges can be utilized as a means to improve the performance of welded moment connections. The corner of a steel plate contains stress singularities (unbounded stresses) when the corner is bounded by free-free edges and when the angle of the corner is larger than 180°. Also, the corner of a steel plate contains stress singularities when the corner is bounded by fixed-free edges and when the angle of the corner is larger than 61.3°. Nonlinear static finite element analyses of two types of beam-to-column moment connections were conducted. These two types of connections are (1) the constant-beam-section connection, and (2) the Enlarged End Section connection. The result of the finite element analyses shows that the Enlarged End Section connection exhibits much higher strength and ductility capacities.

Nature of Stress Singularities at the Reentrant Wedge Corner for a Branched Crack Problem

1999 ◽  
Vol 66 (1) ◽  
pp. 278-280 ◽  
Author(s):  
A. S. Selvarathinam and ◽  
J. G. Goree
Keyword(s):  
Integral Equation ◽  
Singular Integral Equation ◽  
Isotropic Material ◽  
Main Crack ◽  
Crack Opening ◽  
Crack Problem ◽  
Stress Singularity ◽  
Stress Singularities ◽  
Opening Displacement ◽  
Reentrant Corner

The solution of the branched crack problem for an isotropic material, employing the dislocation method as developed by Lo (1978), results in a singular integral equation in which the slope of the crack-opening displacement is the unknown. In this brief note, using the function-theoretic method, the behavior of this unknown function is investigated at the corner where the branched and main crack meet and it is shown that the order of stress singularity obtained at the reentrant corner of the branched crack is given by the Williams’ (1952) characteristic equation for the isotropic wedge.

Sign in / Sign up

Export Citation Format

Share Document