Three-Dimensional Interface Cracks in Anisotropic Bimaterials: The Non-Oscillatory Case

1998 ◽  
Vol 65 (4) ◽  
pp. 1048-1055 ◽  
Author(s):  
Jianmin Qu ◽  
Yibin Xue
Keyword(s):  
Stress Intensity ◽  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Formal Solution ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Interface Cracks ◽  
Penny Shaped Crack ◽  
Anisotropic Bimaterials

Two-dimensional interface cracks in anisotropic bimaterials have been studied extensively in the literature. However, solutions to three-dimensional interface cracks in anisotropic bimaterials are not available. In this paper, a penny-shaped crack on the interface between two anisotropic elastic half-spaces is considered. A formal solution is obtained by using the Stroh method in two-dimensional elasticity in conjunction with the Fourier transform method. Fracture mechanics parameters such as the stress intensity factor, crack-opening displacement, and energy release rate are obtained in terms of the interfacial matrix M. To illustrate the solution procedure, a circular delaminations in a unidirectional and a cross-ply composite are considered. Numerical results for the stress intensity factors and energy release rate along the crack front are presented.

scholarly journals Energy Release Rate Approximation for Small Surface Cracks in Three-Dimensional Domains Using the Topological Derivative

2020 ◽  
Vol 87 (4) ◽  
Author(s):  
Kazem Alidoost ◽  
Meng Feng ◽  
Philippe H. Geubelle ◽  
Daniel A. Tortorelli
Keyword(s):  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Three Dimensional ◽  
Topological Derivative ◽  
Two Dimensional ◽  
Surface Cracks ◽  
Small Surface ◽  
Refined Meshes ◽  
Boundary Location

Abstract The topological derivative describes the variation of a response functional with respect to infinitesimal changes in topology, such as the introduction of an infinitesimal crack or hole. In this three-dimensional fracture mechanics work, we propose an approximation of the energy release rate field associated with a small surface crack of any boundary location, direction, and orientation combination using the topological derivative. This work builds on the work of Silva et al. (“Energy Release Rate Approximation for Small Surface-Breaking Cracks Using the Topological Derivative,” J. Mech. Phys. Solids 59(5), pp. 925–939), in which the authors proposed an approximation of the energy release rate field which was limited to two-dimensional domains. The proposed method is computationally advantageous because it only requires a single analysis. By contrast, current boundary element and finite element-based methods require an analysis for each crack length-location-direction-orientation combination. Furthermore, the proposed method is evaluated on the non-cracked domain, obviating the need for refined meshes in the crack tip region.

Stress Intensity Factor and Energy Release Rate for Interfacial Cracks Between Dissimilar Anisotropic Materials

1990 ◽  
Vol 57 (4) ◽  
pp. 882-886 ◽  
Author(s):  
Kuang-Chong Wu
Keyword(s):  
Stress Intensity ◽  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Stress Intensity Factors ◽  
Real Form ◽  
Intensity Factors ◽  
Interface Cracks ◽  
Interfacial Cracks ◽  
Homogeneous Materials

The framework of fracture mechanics analysis for interface cracks as outlined by Willis (1971) is recast into a form resembling the customary framework for cracks in homogeneous materials. Based on the complex-valued “stress concentration vector” introduced by Willis, a new definition of real-valued stress intensity factors is introduced. The definition is an extension to that for cracks in homogeneous materials and reduces to the one given recently by Rice for isotropic interface cracks. In terms of the new stress intensity factors, tractions ahead of the crack and the relative crack face displacements given by Willis are rewritten into real-form expressions. The energy release rate obtained by Willis is also expressed into a real form in terms of the stress intensity factors. The validity of using the stress intensity factors as parameters controlling fracture is discussed along the line advanced by Rice (1988).

Shape and energies of a dynamically propagating crack under bending

2003 ◽  
Vol 18 (10) ◽  
pp. 2379-2386 ◽  
Author(s):  
Dov Sherman ◽  
Ilan Be'ery
Keyword(s):  
Crack Propagation ◽  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Crack Front ◽  
Three Dimensional ◽  
Strain Energy Release ◽  
Governing Parameter ◽  
Propagating Crack ◽  
Front Shape

We report on the exact shape of a propagating crack in a plate with a high width/thickness ratio and subjected to bending deformation. Fracture tests were carried out with brittle solids—single crystal, polycrystalline, and amorphous. The shape of the propagating crack was determined from direct temporal crack length measurements and from the surface perturbations generated during rapid crack propagation. The shape of the crack profile was shown to be quarter-elliptical with a straight, long tail; the governing parameter of the ellipse axes is the specimen's thickness at most length of crack propagation. Universality of the crack front shape is demonstrated. The continuum mechanics approach applicable to two-dimensional problems was used in this three-dimensional problem to calculate the quasistatic strain energy release rate of the propagating crack using the formulations of the dynamic energy release rate along the crack loci. Knowledge of the crack front shape in the current geometry and loading configuration is important for practical and scientific aspects.

scholarly journals Research on Multiple Griffith Cracks at the Interface of Fine-Grained Piezoelectric Coating/Substrate

2019 ◽  
Vol 2019 ◽  
pp. 1-14
Author(s):  
Shuaishuai Hu ◽  
Jiansheng Liu ◽  
Junlin Li
Keyword(s):  
Energy Release Rate ◽  
Energy Release ◽  
Singular Integral ◽  
Release Rate ◽  
Electric Displacement ◽  
Singular Integral Equations ◽  
Interface Cracks ◽  
Fine Grained ◽  
Piezoelectric Structure ◽  
Bimaterial Structure

The behavior of a fine-grained piezoelectric coating/substrate with multiple Griffith interface cracks under electromechanical loads is investigated. In this work, double coupled singular integral equations are proposed to solve the fracture problems. Both the singular integral equation and single-valued conditions are simplified into an algebraic equation and solved by numerical calculation. Thereby, the intensity factors of electric displacement and stress obtained are used to obtain the expression of the energy release rate. Furthermore, numerical results of the energy release rate with material parameters are demonstrated. Based on the obtained results, it could be concluded that the energy release rate is closely related to the size of the interface cracks and the mechanical-electrical loading. For a bimaterial structure, the fine-grained piezoelectric structure exhibited better material performance compared to the large one.

An Investigation of Moisture-Induced Interfacial Delamination in Plastic IC Package During Solder Reflow

2017 ◽  
Author(s):  
Jing Wang ◽  
Yuling Niu ◽  
Seungbae Park
Keyword(s):  
Stress Intensity ◽  
Vapor Pressure ◽  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Strain Energy ◽  
Strain Energy Release Rate ◽  
Strain Energy Release ◽  
Solder Reflow ◽  
Delamination Behavior

In this study, the moisture induced delamination behavior of a plastic ball grid array package under the solder reflow process was investigated by the finite element analysis. The entire moisture history of the PBGA package was simulated for preconditioning at moisture sensitivity level 1 and the subsequent exposure to a soldering reflow. A fracture mechanics based analysis was used to investigate the combined effects of temperature, moisture and vapor pressure on the delamination behavior at the die/molding compound and die/die attach interfaces during solder reflow. For determining the total strain energy release rate and total stress intensity factor under a multiphysics environment like reflow, researchers commonly used the principle of superposition to combine the results from individual thermal stress, hygroscopic stress and vapor pressure induced stress analyses. In this study, a new method was proposed to obtain the total strain energy release rate and total stress intensity factor under the multi-physics environment in a single fracture analysis instead of three. Two different methods-virtual crack closure technique (VCCT) and crack tip opening displacement method (CTOD) were employed and compared in studying the variation of strain energy release rates during lead-free solder reflow. The relationship between the strain energy release rate and crack length was also obtained. The developments of the stress intensity factors due to individual effect of thermal mismatch, hygroscopic swelling and vapor pressure were calculated. The mode mixity was also determined under different temperatures and crack length.

Analytical Study of Delamination in Multilayered Two-Dimensional Functionally Graded Non-Linear Elastic Beams

2017 ◽  
Vol 34 (4) ◽  
pp. 495-504
Author(s):  
V. I. Rizov
Keyword(s):  
Energy Release Rate ◽  
Energy Release ◽  
Cross Section ◽  
Release Rate ◽  
Strain Energy ◽  
Strain Energy Release Rate ◽  
Strain Energy Release ◽  
Functionally Graded ◽  
Two Dimensional ◽  
Delamination Fracture

AbstractThe present paper is focused on the delamination fracture in a multilayered two-dimensional functionally graded beam configuration which exhibits non-linear behavior of the material. The beam is loaded by two longitudinal forces applied at the beam free ends. The beam contains a delamination crack which is located symmetrically with respect to the beam mid-span. The delamination is studied analytically in terms of the strain energy release rate. TheJ-integral approach is applied for verification of the analysis of the strain energy release rate. The solution derived is valid for a beam made of an arbitrary number of layers. It is assumed that each layer has individual thickness and material properties. Also, the material is two-dimensional functionally graded in the cross-section of each layer. The solution obtained can be applied for a delamination crack located arbitrary along the height of the beam cross-section. It is shown that the solution is very convenient for investigating the influences of material gradients and crack location on the delamination fracture behavior. The results obtained can be used for optimization of multilayered two-dimensional functionally graded structural members and components with respect to their delamination fracture performance.

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