Energy-Release Rate in Elastic-Plastic Fracture Problems

1981 ◽  
Vol 48 (4) ◽  
pp. 825-829 ◽  
Author(s):  
S. Aoki ◽  
K. Kishimoto ◽  
M. Sakata
Keyword(s):  
Plastic Deformation ◽  
Energy Release ◽  
Release Rate ◽  
Fracture Process ◽  
Release Rates ◽  
Process Region ◽  
Special Cases ◽  
Energy Release Rates ◽  
Self Similar ◽  
Inertia Forces

It is shown that the energy-release rates associated with the translation, rotation, self-similar expansion and distortion of the fracture process region are expressed by the newly introduced integrals, Jˆ, Lˆ, Mˆ, and Iˆ. These integrals can be defined even if there exist plastic deformation, thermal strains, body forces, and inertia forces. They include as special cases the J, L, and M integrals which have been defined by Knowles and Sternberg and discussed by Budiansky and Rice.

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.

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.

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.

A review of the determination of energy release rates for strips in tension and bending. Part II – dynamic solutions

1993 ◽  
Vol 28 (4) ◽  
pp. 247-256 ◽  
Author(s):  
J G Williams
Keyword(s):  
Steady State ◽  
Kinetic Energy ◽  
Energy Release ◽  
Release Rate ◽  
Moving Loads ◽  
Release Rates ◽  
Wave Speeds ◽  
Transient Solutions ◽  
Energy Release Rates

Energy release rate calculations are performed for a flexible strip peeling from a substrate and including the effects of kinetic energy. The effects of various wave speeds are demonstrated. Solutions for an axially loaded strip are then explored, including the transient solutions and those for steady-state conditions. The methods developed are then used for cases involving the bending of strips, including those of moving loads. It is demonstrated that these methods of analysis are of value in the analysis of test specimens and of use in design.

Energy Release Rates for an Interface Crack Embedded in a Laminated Beam Subjected to Three-Point Bending

1997 ◽  
Vol 64 (2) ◽  
pp. 375-382 ◽  
Author(s):  
M. Toya ◽  
M. Aritomi ◽  
A. Chosa
Keyword(s):  
Energy Release Rate ◽  
Energy Release ◽  
Interface Crack ◽  
Release Rate ◽  
Mode I ◽  
Mode Ii ◽  
Release Rates ◽  
Three Point Bending ◽  
Axial Forces ◽  
Energy Release Rates

Asymmetric three-point bending of a layered beam with an interface crack is analyzed on the basis of the classical beam theory. Axial forces induced by bending in the parts of the beam above and below the delamination are determined by regarding the cracked part as two lapped beams hinged at both ends. The compliance and the energy release rate are then derived. Numerical analyses based on the finite element method are carried out, which show that delamination growth occurs in mixed mode, i.e., both the normal separation (mode I) and mutual sliding (mode II) of the crack surfaces contribute to the fracturing process. Finally the decomposition of the energy release rate into mode I and mode II components is made by combining the analysis of the energy release rates by Toya (1992) and the two-dimensional linear beam solutions by Suo and Hutchinson (1990).

Stress Intensity Factors for Interfacial Cracks in Thick Thermal Barrier Coatings

1998 ◽  
Author(s):  
C. Bjerken ◽  
C. Persson
Keyword(s):  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Thermal Barrier ◽  
Intensity Factors ◽  
Mode Mixity ◽  
Release Rates ◽  
Edge Angle ◽  
Interfacial Cracks ◽  
Energy Release Rates

Abstract A straight-forward method for calculating the stress intensity factors (or the energy release rate and mode mixity) for interfacial cracks in bi-materials has been developed. An existing method for homogeneous materials, based on the computation of the energy release rate from the nodal forces and displacements given by a finite element analysis, was modified to include the mismatch in material properties. Thick thermal barrier coatings usually fail as a result of cracking near the interface. The influence of the thickness and the edge angle of the coating on the energy release rate and mode mixity for a small edge crack at the interface of a TBC system subjected to thermal loading was investigated. It was established that the high energy release rates obtained for thick coatings can be reduced by decreasing the edge angle of the coating. Additionally a comparison with energy release rates given by J-integral computations has been done.

scholarly journals Modeling snow slab avalanches caused by weak layer failure – Part I: Slabs on compliant and collapsible weak layers

2019 ◽  
Author(s):  
Philipp L. Rosendahl ◽  
Philipp Weißgraeber
Keyword(s):  
Closed Form ◽  
Energy Release ◽  
Analytical Model ◽  
Failure Criterion ◽  
Fracture Process ◽  
Slope Angle ◽  
Release Rates ◽  
Weak Layer ◽  
Proposed Model ◽  
Energy Release Rates

Abstract. Dry-snow slab avalanche release is preceded by a fracture process within the snowpack. Recognizing weak layer collapse as an integral part of the fracture process is crucial and explains phenomena such as whumpf sounds and remote triggering of avalanches from low-angle terrain. In this two-part work we propose a novel closed-form analytical model for a snowpack under skier loading and a mixed-mode failure criterion for nucleation of weak layer failure. In the first part of this two-part series we introduce a closed-form analytical model of a snowpack accounting for the deformable layer. Despite the importance of persistent weak layers for slab avalanche release, no simple analytical model accounting for weak layer deformations is available. The proposed model provides deformations of the snow slab, weak layer stresses and energy release rates of cracks within the weak layer. It generally applies to skier-loaded slopes as well as stability tests such as the propagation saw test. A validation with a numerical reference model shows very good agreement of the stress and energy release rates results in several parametric studies including analyses of the bridging effect and slope angle dependence. The proposed model is used to analyze 93 propagation saw tests. Computed weak layer fracture toughness values are physically meaningful and in excellent agreement with finite element analyses. In the second part of the series we make use of the present mechanical model to establish a novel failure criterion crack nucleation in weak layers. The code used for the analyses in both parts is publicly available.

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.

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