scholarly journals Computation of Energy Release Rates for a Nearly Circular Crack

2011 ◽  
Vol 2011 ◽  
pp. 1-17 ◽  
Author(s):  
Nik Mohd Asri Nik Long ◽  
Lee Feng Koo ◽  
Zainidin K. Eshkuvatov
Keyword(s):  
Integral Equation ◽  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Linear Equations ◽  
Circular Crack ◽  
Plane Elasticity ◽  
Hypersingular Integral Equation ◽  
Hypersingular Integral ◽  
Energy Release Rates

This paper deals with a nearly circular crack, in the plane elasticity. The problem of finding the resulting shear stress can be formulated as a hypersingular integral equation over a considered domain, and it is then transformed into a similar equation over a circular region, , using conformal mapping. Appropriate collocation points are chosen on the region to reduce the hypersingular integral equation into a system of linear equations with unknown coefficients, which will later be used in the determination of energy release rate. Numerical results for energy release rate are compared with the existing asymptotic solution and are displayed graphically.

Energy-based approach to fracture

2020 ◽  
pp. 506-528
Author(s):  
Lallit Anand ◽  
Sanjay Govindjee
Keyword(s):  
Fracture Mechanics ◽  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Momentum Tensor ◽  
Linear Elastic Fracture Mechanics ◽  
J Integral ◽  
Linear Elastic ◽  
Energy Release Rates ◽  
Elastic Fracture

This chapter introduces the concept of energy release rates for linear elastic fracture mechanics. The concept of an energy release rate is defined and related to the criteria of Griffith with application in the context of bodies with point loads. Eshelby’s energy momentum tensor is also introduced and Rice’s path independent J-integral is derived, related to energy release rate, and applied to fracture problems.

Energy Release Rates for an Edge Delamination of a Laminated Beam Subjected to Thermal Gradient

2004 ◽  
Vol 72 (5) ◽  
pp. 658-665 ◽  
Author(s):  
M. Toya ◽  
M. Oda ◽  
A. Kado ◽  
T. Saitoh
Keyword(s):  
Energy Release Rate ◽  
Energy Release ◽  
Temperature Difference ◽  
Release Rate ◽  
Mode Ii ◽  
Pure Mode ◽  
Release Rates ◽  
Laminated Beam ◽  
Energy Release Rates ◽  
Edge Delamination

Energy release rates for an edge delamination of a laminated beam subjected to through-thickness temperature gradient are analyzed on the basis of the classical beam theory. The decomposition of the energy release rate into mode I and mode II components is made by combining the analyses of the energy release rates by Toya (1992) and the two-dimensional elasticity solutions for a split-beam element by Suo and Hutchinson (1990). The energy release rate is a quadratic function of the temperatures of the top and bottom surfaces of the beam. The transition of the type of crack growth between pure mode II and mixed mode type occurs at the temperature difference corresponding to the minimum energy release rate. Numerical analyses based on finite-element method are also carried out, which show that the theory agrees well with numerical results when temperature jump across the delaminated surfaces is relatively small as compared with the temperature difference between the top and bottom surfaces of the layered beam.

Strain energy release rates and the fatigue growth of matrix cracks in model arrays in composite laminates

1991 ◽  
Vol 432 (1886) ◽  
pp. 427-444 ◽  
Keyword(s):  
Energy Release Rate ◽  
Energy Release ◽  
Crack Growth ◽  
Release Rate ◽  
Composite Laminates ◽  
Strain Energy ◽  
Strain Energy Release Rate ◽  
Strain Energy Release ◽  
Matrix Cracks ◽  
Energy Release Rates

Crack growth in the transverse plies of cross-ply composite laminates has been investigated both experimentally and theoretically. Expressions for the strain energy release rate associated with the growth of cracks in model arrays have been obtained using both the compliance approach and the energy method. Measurements of compliance change with crack length were obtained using glass-epoxy laminates and compared with various predictions. Correlations between the crack growth rate and the strain energy release rate range indicate that a Paris law is applicable.

The Energy Release Rate for Decohesion in Thin Multilayered Films on Substrates

1997 ◽  
Vol 473 ◽  
Author(s):  
Ming. Y. He ◽  
Guanghai Xu ◽  
David R. Clarke ◽  
Qing Ma ◽  
H. Fujimoto
Keyword(s):  
Energy Release Rate ◽  
Energy Release ◽  
Line Width ◽  
Release Rate ◽  
Metal Layer ◽  
Strain Energy Release ◽  
Intrinsic Stress ◽  
The Finite Element Method ◽  
Energy Release Rates ◽  
Strain Energy Release Rates

ABSTRACTThe strain energy release rates for the converging decohesion crack in a multilayered film on a substrate have been calculated using the finite element method. The results for the energy release rate as a function of the intrinsic stress, the thickness of the superlayer and the modulus ratio will be presented. A simple functional form for the results will be shown. The effects of plasticity of the thin metal layer on the energy release rate have been examined. The results show that the effect of plastic deformation is not significant for the converging decohesion crack. The effects of the line width have also been addressed. The results show that for two-layer films the energy release rate for steady-state decohesion cracks decreases dramatically as B/h decreases, in the range B/h<40, where B is the line width and h is the thickness of the superlayer. For narrow lines the plane strain solutions overestimate the energy release rate. The numerical results are consistent with the experimental observations on lines with different width.

The Characterization of Mixed-Mode Energy Release Rates in Orthotropic Materials

1996 ◽  
Vol 210 (1) ◽  
pp. 33-42 ◽  
Author(s):  
C A Walker ◽  
Jamasri
Keyword(s):  
Finite Element ◽  
Energy Release Rate ◽  
Energy Release ◽  
Crack Growth ◽  
Release Rate ◽  
Mode I ◽  
Mode Ii ◽  
Finite Element Models ◽  
Release Rates ◽  
Energy Release Rates

The aim of this work was to predict, from the material constants, mixed-mode energy release rates in orthotropic materials, in particular the general cases in which the crack is aligned at a random angle to the principal material direction, normal to the plane of orthotropy. Two-dimensional finite element models with various fibre orientations were generated. The finite element models were validated by comparing two sets of contour plots of deformation, one resulting from the finite element analysis and the other from moiré interferograms of the experimental work. On comparison there was shown to be a strict similarity between experimentally determined and computational deformation fields. Variations of the energy release rates were investigated for both rapid and stable crack growth. This was accomplished by generating two-dimensional stable crack growth finite element models. In general, energy release rates were found to be strongly affected by the fibre orientation. An increase of the angle of the crack growth direction caused a decrease of the mode I energy release rate and, by contrast, an increase of the mode II energy release rate, but the mode II energy release rate was always a small fraction of the mode I value. Crack extension caused a gradual increase of the mode I energy release rate both for coplanar and non-coplanar crack growth. However, there was no significant effect found on the mode II energy release rate.

On Energy-Release Rates for a Plane Crack

1981 ◽  
Vol 48 (3) ◽  
pp. 525-528 ◽  
Author(s):  
A. Golebiewska Herrmann ◽  
G. Herrmann
Keyword(s):  
Stress Field ◽  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Static Stress ◽  
Plane Crack ◽  
J Integral ◽  
Release Rates ◽  
Energy Release Rates ◽  
Natural Description

Considered is a plane crack in a homogeneous, static stress field. The component of the Ji integral normal to the plane of the crack (J2) is shown not to be path-independent in the sense of the well-known J integral (≡ J1) parallel to the plane of the crack. The relation between the energy-release rate for rotation L and the integral J2 is established. It is finally suggested that the integrals L and M may provide a more natural description of energy-release rates (or forces) for plane cracks, rather than the integrals J1 and J2.

Strain-energy release rate for a single-edge-cracked circular bar in tension

1978 ◽  
Vol 13 (2) ◽  
pp. 83-89 ◽  
Author(s):  
O E K Daoud ◽  
D J Cartwright ◽  
M Carney
Keyword(s):  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Strain Energy ◽  
Strain Energy Release Rate ◽  
Circular Cross Section ◽  
Strain Energy Release ◽  
Energy Release Rates ◽  
Circular Bar ◽  
Strain Energy Release Rates

The strain-energy release rate is determined for an edge crack in a uniformly stressed bar of circular cross-section. Values of the strain-energy release rate, obtained using a finite-element representation of the bar and by measuring the compliance of the bar experimentally, are shown to be in close agreement. For crack depths of less than one-half diameter, the strain-energy release rates are found to be lower than existing results on rectangular bars having the same relative crack length.

Three Dimensional Analysis and Resulting Design Recommendations for Unidirectional and Multidirectional End-Notched Flexure Tests

1995 ◽  
Vol 29 (16) ◽  
pp. 2108-2133 ◽  
Author(s):  
B. D. Davidson ◽  
R. Kruger ◽  
M. König
Keyword(s):  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Plate Theory ◽  
Design Procedure ◽  
Local Mode ◽  
Mode Ii ◽  
Mode Iii ◽  
Release Rates ◽  
Energy Release Rates

Results are presented from a theoretical investigation of the effects of stacking sequence on the energy release rate in laminated composite end-notched flexure test specimens. Deflections and energy release rates of unidirectional and multidirectional ENF specimens are obtained by classical laminated plate theory, shear deformable plate theory, and three dimensional finite element analyses. It is shown that the distribution of energy release rate varies across the front of an initially straight delamination. The percentage of mode II and mode III energy release rates for the specimen, as well as the local peak values of the mode II, mode III and total energy release rates that occur at the specimen's free edges are shown to correlate with a nondimensional ratio comprised of the specimen's flexural rigidities. The results of the study are used as a basis for a proposed “ENF test design procedure” that may be used for the determination of appropriate specimen stacking sequences and test geometries for studying delamination growth at interfaces between plies at various orientations. The test design procedure minimizes the contributions to the energy release rate from residual thermal stresses, geometric nonlinearities, local mode II concentrations at the specimen's free edges and local mode III effects.

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