Energy release rate approximation for small surface-breaking cracks using the topological derivative

2011 ◽  
Vol 59 (5) ◽  
pp. 925-939 ◽  
Author(s):  
Mariana Silva ◽  
Philippe H. Geubelle ◽  
Daniel A. Tortorelli
Keyword(s):  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Topological Derivative ◽  
Small Surface

scholarly journals Energy Release Rate Approximation for Small Surface Cracks in Three-Dimensional Domains Using the Topological Derivative

2020 ◽  
Vol 87 (4) ◽  
Author(s):  
Kazem Alidoost ◽  
Meng Feng ◽  
Philippe H. Geubelle ◽  
Daniel A. Tortorelli
Keyword(s):  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Three Dimensional ◽  
Topological Derivative ◽  
Two Dimensional ◽  
Surface Cracks ◽  
Small Surface ◽  
Refined Meshes ◽  
Boundary Location

Abstract The topological derivative describes the variation of a response functional with respect to infinitesimal changes in topology, such as the introduction of an infinitesimal crack or hole. In this three-dimensional fracture mechanics work, we propose an approximation of the energy release rate field associated with a small surface crack of any boundary location, direction, and orientation combination using the topological derivative. This work builds on the work of Silva et al. (“Energy Release Rate Approximation for Small Surface-Breaking Cracks Using the Topological Derivative,” J. Mech. Phys. Solids 59(5), pp. 925–939), in which the authors proposed an approximation of the energy release rate field which was limited to two-dimensional domains. The proposed method is computationally advantageous because it only requires a single analysis. By contrast, current boundary element and finite element-based methods require an analysis for each crack length-location-direction-orientation combination. Furthermore, the proposed method is evaluated on the non-cracked domain, obviating the need for refined meshes in the crack tip region.

Calculating Energy Release Rate as a Function of Crack Length Using a Multiple-Step Crack Closure Technique in Tire Finite Element Models

2018 ◽  
Vol 46 (3) ◽  
pp. 130-152
Author(s):  
Dennis S. Kelliher
Keyword(s):  
Finite Element ◽  
Energy Release Rate ◽  
Crack Length ◽  
Energy Release ◽  
Crack Closure ◽  
Release Rate ◽  
Fatigue Behavior ◽  
Three Dimensions ◽  
Quantitative Prediction ◽  
Closure Technique

ABSTRACT When performing predictive durability analyses on tires using finite element methods, it is generally recognized that energy release rate (ERR) is the best measure by which to characterize the fatigue behavior of rubber. By addressing actual cracks in a simulation geometry, ERR provides a more appropriate durability criterion than the strain energy density (SED) of geometries without cracks. If determined as a function of crack length and loading history, and augmented with material crack growth properties, ERR allows for a quantitative prediction of fatigue life. Complications arise, however, from extra steps required to implement the calculation of ERR within the analysis process. This article presents an overview and some details of a method to perform such analyses. The method involves a preprocessing step that automates the creation of a ribbon crack within an axisymmetric-geometry finite element model at a predetermined location. After inflating and expanding to three dimensions to fully load the tire against a surface, full ribbon sections of the crack are then incrementally closed through multiple solution steps, finally achieving complete closure. A postprocessing step is developed to determine ERR as a function of crack length from this enforced crack closure technique. This includes an innovative approach to calculating ERR as the crack length approaches zero.

scholarly journals Effect of the Characteristic Size and Content of Graphene on the Crack Propagation Path of Alumina/Graphene Composite Ceramics

Materials ◽  
2021 ◽  
Vol 14 (3) ◽  
pp. 611
Author(s):  
Benshuai Chen ◽  
Guangchun Xiao ◽  
Mingdong Yi ◽  
Jingjie Zhang ◽  
Tingting Zhou ◽  
...  
Keyword(s):  
Crack Propagation ◽  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Volume Content ◽  
Phase Interface ◽  
Average Energy ◽  
Characteristic Size ◽  
Composite Ceramics ◽  
Graphene Composite

In this paper, the Voronoimosaic model and the cohesive element method were used to simulate crack propagation in the microstructure of alumina/graphene composite ceramic tool materials. The effects of graphene characteristic size and volume content on the crack propagation behavior of microstructure model of alumina/graphene composite ceramics under different interfacial bonding strength were studied. When the phase interface is weak, the average energy release rate is the highest as the short diameter of graphene is 10–50 nm and the long diameter is 1600–2000 nm. When the phase interface is strong, the average energy release rate is the highest as the short diameter of graphene is 50–100 nm and the long diameter is 800–1200 nm. When the volume content of graphene is 0.50 vol.%, the average energy release rate reaches the maximum. When the velocity load is 0.005 m s−1, the simulation result is convergent. It is proven that the simulation results are in good agreement with the experimental phenomena.

Modified Edge Lift-Off Test: Experimental Modifications for Multifilm Systems

1999 ◽  
Vol 594 ◽  
Author(s):  
J. C. Hay ◽  
E. G. Liniger ◽  
X-H Liu
Keyword(s):  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Strain Energy ◽  
Plate Bending ◽  
Adhesion Test ◽  
Testing Method ◽  
Rate Calculation ◽  
Lift Off ◽  
Microelectronics Fabrication

AbstractIn developing an adhesion test for a microelectronics fabrication facility there are many criteria which must be met. Some of these include (i) sample prep must be simple, (ii) deformations should be elastic so the problem can be easily modeled, (iii) mechanics are ideally analytical, and (iv) the test end-point must be unambiguous and easy to obtain. A testing method in the literature which meets many of these criteria is the modified edge liftoff test (MELT). Delamination is induced through the release of strain energy stored in an elastic superlayer which results from a large mismatch in CTE between the film and substrate. In this work we consider details of the energy release rate calculation, effects of plate bending, and initial flaw size.

On the Axial Rigidity of a Perforated Strip and the Strain Energy Release Rate in a Centrally Notched Strip Subjected to Uniaxial Tension

1964 ◽  
Vol 86 (4) ◽  
pp. 693-697 ◽  
Author(s):  
R. G. Forman ◽  
A. S. Kobayashi
Keyword(s):  
Energy Release Rate ◽  
Energy Release ◽  
Uniaxial Tension ◽  
Release Rate ◽  
Strain Energy ◽  
Strain Energy Release Rate ◽  
Strain Energy Release ◽  
Theoretical Studies ◽  
Correction Factors ◽  
Elasticity Solutions

This paper presents theoretical studies on the axial rigidities in strips with circular and elliptical perforations and subjected to uniaxial tension. Greenspan’s original derivations on these axial rigidities [2] were improved by using the elasticity solutions by Howland [6] and Ishida [7] for infinite strips with circular and elliptical perforations, respectively. Finally, the correction factors for centrally notched strips subjected to uniaxial tension were rederived from the above results following the energy approach by Irwin and Kies [3].

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