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).

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.

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.

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.

Numerical Examination of Mixed Mode Crack in SSY: A Review

2013 ◽  
Vol 275-277 ◽  
pp. 198-202
Author(s):  
Prasad S. Godse ◽  
Sangram A. Gawande ◽  
Sunil Bhat
Keyword(s):  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Mixed Mode ◽  
Small Scale ◽  
Mode I ◽  
Mode Ii ◽  
Fracture Parameter ◽  
Conservation Of Energy ◽  
Mixed Mode Crack

The paper reviews the numerical methodology to investigate fracture parameter namely energy release rate, G, of a mixed mode crack. An inclined, through, centre crack is assumed in a ductile steel plate subjected to bi-axial tension. Applied stress and crack size are suitably selected to simulate small scale yielding (SSY) condition at the crack tips. The cracked plate is modelled by finite element method. Both plane stress and plane strain situations are examined. G value is found from J integral. Equations of transformation are employed to obtain normal and shear stress in the plane of the crack. G is then again determined for Mode I and Mode II cracks by modelling each case separately. The analysis is finally validated by fulfilment of the conservation of energy release rate criterion, G (Mixed mode) = G (Mode I) + G (Mode II).

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.

scholarly journals Geometrically Nonlinear Analysis of Adhesively Bonded Joints

1984 ◽  
Vol 106 (1) ◽  
pp. 59-65 ◽  
Author(s):  
B. Dattaguru ◽  
R. A. Everett ◽  
J. D. Whitcomb ◽  
W. S. Johnson
Keyword(s):  
Energy Release ◽  
Strain Energy ◽  
Strain Energy Release ◽  
Mode I ◽  
Mode Ii ◽  
Geometrically Nonlinear ◽  
Release Rates ◽  
Lap Shear ◽  
Energy Release Rates ◽  
Strain Energy Release Rates

A geometrically nonlinear finite-element analysis of cohesive failure in typical joints is presented. Cracked-lap-shear joints were chosen for analysis. Results obtained from linear and nonlinear analysis show that nonlinear effects, due to large rotations, significantly affect the calculated mode I, crack opening, and mode II, inplane shear, strain-energy-release rates. The ratio of the mode I to mode II strain-energy-release rates (GI/GII) was found to be strongly affected by the adhesive modulus and the adherend thickness. GI/GII ratios between 0.2 and 0.8 can be obtained by varying adherend thickness and using either a single or double cracked-lap-shear specimen configuration. Debond growth rate data, together with the analysis, indicate that mode I strain-energy-release rate governs debond growth. Results from the present analysis agree well with experimentally measured joint opening displacements.

The Effects of In-Service Induced Reduction of Bonding Quality on the Mode I, II, and I-II Fracture Toughness of CNT Nanocomposites

2016 ◽  
Author(s):  
Masoud Yekani Fard ◽  
Brian Raji ◽  
John M. Woodward ◽  
Aditi Chattopadhyay
Keyword(s):  
Fracture Toughness ◽  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Accelerated Aging ◽  
Beam Theory ◽  
Mode I ◽  
Mode Ii ◽  
Initiation And Propagation ◽  
Calibration Methods

Tests were carried out to determine the interlaminar fracture toughness of stitch-bonded biaxial polymer matrix carbon nanotube nanocomposites for mode I, II, and I-II including durability effects. Analysis of the test specimens in terms of mode I energy release rates showed good agreement among Modified Beam Theory, Compliance Calibration, and Modified Compliance Calibration methods. End-Notched Flexure (ENF) and four point End-Notched Flexure (4ENF) tests gave very consistent crack initiation and propagation results for mode II fracture. The results show that the critical mode I energy release rate for delamination decreases monotonically with increasing mode II loading. The effects of accelerated aging (60°C and 90% Rh) on fracture properties were studied. Early accelerated aging (0–12 months) has the dominant diminishing effect on energy release rate initiation and propagation in composites and nanocomposites.

scholarly journals Analysis of Interfacial Cracks in a TBC/Superalloy System Under Thermo-Mechanical Loading

1997 ◽  
Author(s):  
S. Q. Nusier ◽  
G. M. Newaz
Keyword(s):  
Residual Stresses ◽  
Energy Release Rate ◽  
Energy Release ◽  
Circular Plate ◽  
Release Rate ◽  
Bond Coat ◽  
Mode I ◽  
Mode Ii ◽  
Mixed Mode Fracture ◽  
Processing Temperature

In thermal barrier coatings (TBC) residual stresses develop during cool down from processing temperature due to the thermal expansion mismatch between the different layers (substrate, bond coat, and TBC). These residual stresses can initiate micro cracks at the bond coat/TBC interface and can lead to debonding at the bond coat/TBC interface. The effect of voids or crack like flaws at the interface can be responsible for initiating debonding and accelerate the oxidation process. Effect of oxide layer growth between bond coat and ceramic layer (TBC) can be modeled as volume increase. In this work we represent this change in volume as an induced pressure across the interface. Mixed-mode fracture analysis of a thin circular delamination in an-axisymmetrically multi layer circular plate is developed. Geometrical nonlinearity is included in the analysis, since we have a large deflection case. The elastic deformation problem of a circular plate subjected to a clamped boundary condition at the edge of the delamination, an out of plane pressure load, and a compressive stress due to thermal mismatch between different layers, was solved numerically using a Rayleigh-Ritz method. The strain energy release rate was evaluated by means of the path-independent M-integral. The numerical results of this problem based on the energy method were verified using finite element method. Both methods correlate well in predicting the energy release rate for Mode I and Mode II, deflection, and postbuckling solutions. The energy release rates G, for both Mode I and Mode II using virtual crack extension method were evaluated. The specimen was cooled down from processing temperature of 1000 °C to 0 °C. The variation of the properties as a function of temperature was used for analysis. It was found that the use of temperature dependent properties in contrast to constant properties provides significantly different values of J-integral and G.

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