scholarly journals The path-independent J-integral and the crack-extension energy-release rate

2021 ◽  
pp. 104419
Author(s):  
Igor A. Beresnev
Keyword(s):  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Crack Extension ◽  
J Integral

Energy-based approach to fracture

2020 ◽  
pp. 506-528
Author(s):  
Lallit Anand ◽  
Sanjay Govindjee
Keyword(s):  
Fracture Mechanics ◽  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Momentum Tensor ◽  
Linear Elastic Fracture Mechanics ◽  
J Integral ◽  
Linear Elastic ◽  
Energy Release Rates ◽  
Elastic Fracture

This chapter introduces the concept of energy release rates for linear elastic fracture mechanics. The concept of an energy release rate is defined and related to the criteria of Griffith with application in the context of bodies with point loads. Eshelby’s energy momentum tensor is also introduced and Rice’s path independent J-integral is derived, related to energy release rate, and applied to fracture problems.

Estimation Method for Evaluating Energy Release Rate of Circumferential Through-Wall Cracks in Dissimilar Metal Welds

2015 ◽  
Author(s):  
Jeong Soon Park ◽  
Richard Olson
Keyword(s):  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Estimation Method ◽  
New Method ◽  
Estimation Methods ◽  
J Integral ◽  
Mixture Ratio ◽  
Dissimilar Metal ◽  
Integral Estimation

In this study, an estimation method is proposed to evaluate the energy release rate (J-integral) of a circumferential through-wall crack in a dissimilar metal (DM) weld subjected to tension and/or bending. In order to evaluate such cracks in a DM weld, the concept of a mixture ratio has been introduced, so that the existing single-material J-integral estimation method can be utilized with effective material strength properties which are the mixture of the two base metal properties with some ratio. The mixture ratio, however, is empirical, and several numerical analyses would be required to determine an appropriate value of mixture ratio. The new J-integral estimation method proposed in this study can take account of three material properties of the two base metals and a weld metal. Following the approach similar to the LBB.ENG2 method, the new method provides closed-form solutions for the J-integral by introducing an equivalent reduced thickness section replacing the cracked section in the DM weld. It is confirmed that the new method successfully degenerates to the existing one- and two-material J-estimation methods, when simulating one- and two-material crack problems. Furthermore, the maximum moments predicted by the proposed method, as a result of crack stability analyses, show good agreements with DM weld test results.

GRIFFITH-FORMULA AND J-INTEGRAL FOR A CRACK IN A POWER-LAW HARDENING MATERIAL

2006 ◽  
Vol 16 (11) ◽  
pp. 1723-1749 ◽  
Author(s):  
DOROTHEE KNEES
Keyword(s):  
Energy Release Rate ◽  
Energy Release ◽  
Nonlinear Model ◽  
Power Law ◽  
Release Rate ◽  
Deformation Energy ◽  
Stress Fields ◽  
J Integral ◽  
Fracture Criteria ◽  
Hardening Material

We consider an elastic body with pre-existing crack which is subjected to external loadings. It is assumed that the constitutive relation is of power-law type (Ramberg/Osgood model). Several fracture criteria are based on the energy release rate, which is the derivative of the potential deformation energy with respect to the crack length. The goal of this paper is to derive the Griffith-formula and the Eshelby–Cherepanov–Rice integral for the energy release rate of this nonlinear model taking into account the actual regularity of the corresponding displacement and stress fields.

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