Energy Release Rate Prediction in Stiffened-skin Structure Using a Three-dimensional Crack Tip Element Analysis

2005 ◽  
Vol 39 (20) ◽  
pp. 1819-1842 ◽  
Author(s):  
Barry D. Davidson ◽  
Lijie Yu
Keyword(s):  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Three Dimensional ◽  
Crack Tip ◽  
Element Analysis ◽  
Skin Structure ◽  
Rate Prediction ◽  
Crack Tip Element

Application of the Θ-Method to 3D BEM Analysis of Cracks in Piezoelectric Components

2011 ◽  
Vol 488-489 ◽  
pp. 363-366
Author(s):  
Karsten Wippler ◽  
Meinhard Kuna
Keyword(s):  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Three Dimensional ◽  
Crack Tip ◽  
General Purpose ◽  
Virtual Crack Extension ◽  
Crack Problems ◽  
Continuous Crack ◽  
Piezoelectric Structures

A general purpose direct BEM code has been developed for three-dimensional crack problems in piezoelectric structures. Special 3D non-continuous crack tip elements and several techniques for determining crack tip parameters were implemented. To calculate the electromechanical energy release rate for a virtual crack extension, the θ-method is employed, which was originally suggested by BONNET for linear elastic materials. The paper presents the generalization and numerical realization of the θ-method to 3D piezoelectric cracks. The great advantage of the θ-method is the direct computation of energy release rate, whereas the way via K-factors and the IRWIN matrix is more complicated. The efficiency and accuracy of the technique are shown for various example problems by comparing with analytical solutions.

An Analytical Crack-Tip Element for Layered Elastic Structures

1995 ◽  
Vol 62 (2) ◽  
pp. 294-305 ◽  
Author(s):  
B. D. Davidson ◽  
Hurang Hu ◽  
R. A. Schapery
Keyword(s):  
Total Energy ◽  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Plate Theory ◽  
Crack Tip ◽  
Total Energy Release ◽  
Linear Elastic ◽  
Crack Tip Element ◽  
Total Energy Release Rate

A previously developed linear elastic crack-tip element analysis is reviewed briefly, and then extended and refined for practical applications. The element provides analytical expressions for total energy release rate and mode mix in terms of plate theory force and moment resultants near the crack tip. The element may be used for cracks within or between homogeneous isotropic or orthotropic layers, as well as for delamination of laminated composites. Classical plate theory is used to derive the equations for total energy release rate and mode mix; a “mode mix parameter,” Ω, as obtained from a separate continuum analysis is necessary to complete the mode mix decomposition. This parameter depends upon the elastic and geometrical properties of the materials above and below the crack plane, but not on the loading. A relatively simple finite element technique for determining the mode-mix parameter is presented and convergence in terms of mesh refinement is studied. Specific values of Ω are also presented for a large number of cases. For those interfaces where a linear elastic solution predicts an oscillatory singularity, an approach is described which allows a unique, physically meaningful value of fracture mode ratio to be defined. This approach is shown to provide predictions of crack growth between dissimilar homogeneous materials that are equivalent to those obtained from the oscillatory field solution. Application of the approach to delamination in fiber-reinforced laminated composites is also discussed.

On the Fracture Toughness of Pseudoelastic Shape Memory Alloys

2013 ◽  
Vol 81 (4) ◽  
Author(s):  
Theocharis Baxevanis ◽  
Chad M. Landis ◽  
Dimitris C. Lagoudas
Keyword(s):  
Fracture Toughness ◽  
Phase Transformation ◽  
Shape Memory Alloys ◽  
Energy Release Rate ◽  
Shape Memory ◽  
Energy Release ◽  
Release Rate ◽  
Crack Tip ◽  
Reverse Phase ◽  
Element Analysis

A finite element analysis of quasi-static, steady-state crack growth in pseudoelastic shape memory alloys is carried out for plane strain, mode I loading. The crack is assumed to propagate at a critical level of the crack-tip energy release rate. Results pertaining to the influence of forward and reverse phase transformation on the near-tip mechanical fields and fracture toughness are presented for a range of thermomechanical parameters and temperature. The fracture toughness is obtained as the ratio of the far-field applied energy release rate to the crack-tip energy release rate. A substantial fracture toughening is observed, in accordance with experimental observations, associated with the energy dissipated by the transformed material in the wake of the growing crack. Reverse phase transformation, being a dissipative process itself, is found to increase the levels of toughness enhancement. However, higher nominal temperatures tend to reduce the toughening of an SMA alloy—although the material's tendency to reverse transform in the wake of the advancing crack tip increases—due to the higher stress levels required for initiation of forward transformation.

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.

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