Vector J-Integral Analysis of Crack Interaction With Pre-existing Singularities

2005 ◽  
Vol 73 (5) ◽  
pp. 876-883 ◽  
Author(s):  
Lifeng Ma ◽  
Tian Jian Lu ◽  
Alexander M. Korsunsky
Keyword(s):  
Potential Energy ◽  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Crack Tip ◽  
Crack Interaction ◽  
Amplification Effect ◽  
Crack Problems ◽  
Remote Loading ◽  
New Criterion

In this paper, the mechanics of a semi-infinite crack interacting with near crack-tip singularities (e.g., dislocations) in two-dimensional solids is investigated using the concept of potential energy release rate. The spontaneous relationship between the crack potential energy release rate and the well-known vector conservative integral Ji(i=1,2) is derived. It is demonstrated that J1 and J2 integrals are equally important in solving crack problems. This allows a more rational criterion to be proposed, based on the criterion of maximum energy release rate, to assess the so-called shielding/amplification effect on the crack tip due to the presence of the singularities. It is shown that the new criterion can not only assess the shielding/amplification effect under pure mode I or mode II remote loading, but also efficiently assess crack-singularity interaction under mixed mode remote loading. Simultaneously, it is found by re-examining the Ji integrals that there exists a simple but universal relation among the three values of the vector Ji integral corresponding separately to the contributions induced from the semi-infinite crack tip, the singularity, and the remote loading. Next, a multi-singularity-crack interaction model is addressed, and the closed-form solution is obtained. Finally, as an example, the problem of a single dislocation interacting with a main crack is solved to demonstrate the validity of the proposed model and the new criterion.

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.

Integral Representation of Energy Release Rate in Graded Materials

2006 ◽  
Vol 74 (5) ◽  
pp. 1046-1048 ◽  
Author(s):  
Z.-H. Jin ◽  
C. T. Sun
Keyword(s):  
Potential Energy ◽  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Plastic Material ◽  
Contour Integral ◽  
Material System ◽  
Graded Materials ◽  
Elastic Plastic Material ◽  
Graded Interlayer

It is well known that, for homogeneous materials, the path-independent J contour integral is the (potential) energy release rate. For general nonhomogeneous, or graded materials, such a contour integral as the energy release rate does not exist. This work presents a rigorous derivation of the extended J integral for general graded materials from the potential energy variation with crack extension. Effects of crack shielding and amplification due to a graded interlayer in an elastic-plastic material system are discussed in terms of this integral.

scholarly journals Crack Growth and Energy Release Rate for an Angled Crack under Mixed Mode Loading

2020 ◽  
Vol 10 (12) ◽  
pp. 4227
Author(s):  
Yali Yang ◽  
Seok Jae Chu ◽  
Wei song Huang ◽  
Hao Chen
Keyword(s):  
Energy Release Rate ◽  
Numerical Method ◽  
Energy Release ◽  
Release Rate ◽  
Mixed Mode ◽  
Crack Tip ◽  
Theoretical Expression ◽  
Propagation Mechanism ◽  
Mode I ◽  
Theoretical Derivation

The evaluation of energy release rate with angle is still a challenging task in metal crack propagation analysis, especially for the mixed Mode I-II-III loading situation. In this paper, the energy release rate associated with stress intensity factors at an arbitrary angle under mixed mode loadings has been investigated using both a numerical method and theoretical derivation. A relatively simple and precise numerical method was established through a series of spatial-inclined ellipses in Mode I-II and ellipsoids in Mode I-II-III, with different propagation angles computed from simulation. Meanwhile, a theoretical expression of the energy release rate with angle for a crack tip under a I-II-III mixed mode crack was deduced based on the propagation mechanism of the crack tip under the influence of a stress field. It is confirmed that the theoretical expression deduced could provide results as accurately as the present numerical method. The present results were confirmed to be effective and accurate by comparison with experimental data and other literature.

The Relationship between Strain Energy Release Rate with Crack-to-Width Ratio of Human Phalanx Bone

2015 ◽  
Vol 786 ◽  
pp. 141-146 ◽  
Author(s):  
Siti Aisyah Abdul Halim ◽  
Ruslizam Daud ◽  
Yazid Bajuri ◽  
S.K. Zaaba ◽  
Khairul Salleh Basaruddin ◽  
...  
Keyword(s):  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Bone Fracture ◽  
Strain Energy ◽  
Strain Energy Release Rate ◽  
Stress Shielding ◽  
Strain Energy Release ◽  
Width Ratio ◽  
Crack Interaction

Bone fracture can occur in all parts of human skeletal cortical bone including phalanx bone of finger bone. Sometime, it leaves permanent damage and a long period of recovery. This situation can be prevented if we understand the mechanics and the process of the bone fracture. This study aims is to evaluate stress shielding induced by crack interaction using a simple model on Linear Elastic Fracture Mechanics (LEFM). Numerical simulation had been carried out in this study to understand the stress shielding induced by crack interaction. The results revealed that the interaction of two cracks is directly proportional to the stress intensity factor (SIF) magnitude at crack tips. Finally, as the crack-to-width ratio increase and the strain energy release rate also increased.

On the Effect of Latent Heat on the Fracture Toughness of Pseudoelastic Shape Memory Alloys

2014 ◽  
Vol 81 (10) ◽  
Author(s):  
Theocharis Baxevanis ◽  
Chad M. Landis ◽  
Dimitris C. Lagoudas
Keyword(s):  
Fracture Toughness ◽  
Shape Memory Alloys ◽  
Energy Release Rate ◽  
Shape Memory ◽  
Energy Release ◽  
Latent Heat ◽  
Release Rate ◽  
Crack Tip ◽  
Thermomechanical Coupling ◽  
Adiabatic Conditions

A finite element analysis of steady-state crack growth in pseudoelastic shape memory alloys under the assumption of adiabatic conditions 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 and the fracture toughness is obtained as the ratio of the far-field applied energy release rate to the crack-tip critical value. Results related to the influence of latent heat on the near-tip stress field and fracture toughness are presented for a range of parameters related to thermomechanical coupling. The levels of fracture toughness enhancement, associated with the energy dissipated by the transformed material in the wake of the growing crack, are found to be lower under adiabatic conditions than under isothermal conditions [Baxevanis et al., 2014, J. Appl. Mech., 81, 041005]. Given that in real applications of shape memory alloy (SMA) components the processes are usually not adiabatic, which is the case with the lowest energy dissipation during a cyclic loading–unloading process (hysteresis), it is expected that the actual level of transformation toughening would be higher than the one corresponding to the adiabatic case.

On Conservative CTOD Estimation Using Far Crack Deformation Field

2013 ◽  
Author(s):  
Piotr Bednarz ◽  
Jaroslaw Szwedowicz
Keyword(s):  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Crack Tip ◽  
Material Behavior ◽  
Deformation Field ◽  
Nonlinear Material ◽  
Small Scale ◽  
Engineering Practice ◽  
Nonlinear Energy

In general engineering practice, crack tip opening displacement (CTOD) is very convenient approach for prediction of the components fracture mechanics (FM) lifetime. FM lifetime calculations are defined very well in industry and the lifetime prediction methods based on the CTOD resolve linear and nonlinear material behavior for monotonic and cyclic responses. The experiments confirm that under plasticity conditions the crack tip blunts for small scale or large scale yielding while, crack flanks open against each other only under elastic conditions. However, the CTOD application requires a very fine mesh in order to predict a crack tip deformation in reliable manner. Therefore, much more engineering work have to be involved in fine FE modeling. The crack tip flank deformation is crucial parameter responsible for reliable prediction of the nonlinear energy release rate, which is obtained from Hutchinson-Rice-Rosengren solution and the Shih rule. In accordance with design guidelines, the nonlinear energy release rate obtained from the CTOD must be evaluated conservatively to meet demands of RAM (Reliability, Availability and Maintainability). By using far crack deformation field, the paper proposes an engineering approach, which predicts the CTOD in a conservative manner under elastic-plastic conditions. This novel method is validated numerically by applying the well-known J-integral approach.

Effect of Solvent Diffusion on Crack-Tip Fields and Driving Force for Fracture of Hydrogels

2015 ◽  
Vol 82 (8) ◽  
Author(s):  
Nikolaos Bouklas ◽  
Chad M. Landis ◽  
Rui Huang
Keyword(s):  
Boundary Conditions ◽  
Energy Release Rate ◽  
Energy Release ◽  
Crack Growth ◽  
Release Rate ◽  
Crack Tip ◽  
Far Field ◽  
Solvent Diffusion ◽  
Effect Of Solvent ◽  
Transient Energy

Hydrogels are used in a variety of applications ranging from tissue engineering to soft robotics. They often undergo large deformation coupled with solvent diffusion, and structural integrity is important when they are used as structural components. This paper presents a thermodynamically consistent method for calculating the transient energy release rate for crack growth in hydrogels based on a modified path-independent J-integral. The transient energy release rate takes into account the effect of solvent diffusion, separating the energy lost in diffusion from the energy available to drive crack growth. Numerical simulations are performed using a nonlinear transient finite element method for center-cracked hydrogel specimens, subject to remote tension under generalized plane strain conditions. The hydrogel specimen is assumed to be either immersed in a solvent or not immersed by imposing different chemical boundary conditions. Sharp crack and rounded notch models are used for small and large far-field strains, respectively. Comparisons to linear elastic fracture mechanics (LEFM) are presented for the crack-tip fields and crack opening profiles in the instantaneous and equilibrium limits. It is found that the stress singularity at the crack tip depends on both the far-field strain and the local solvent diffusion, and the latter evolves with time and depends on the chemical boundary conditions. The transient energy release rate is predicted as a function of time for the two types of boundary conditions with distinct behaviors due to solvent diffusion. Possible scenarios of delayed fracture are discussed based on evolution of the transient energy release rate.

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