Closed-Path J-Integral Analysis of Bridged and Phase-Field Cracks

2016 ◽  
Vol 83 (6) ◽  
Author(s):  
Roberto Ballarini ◽  
Gianni Royer-Carfagni
Keyword(s):  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Momentum Tensor ◽  
Integral Approach ◽  
J Integral ◽  
Damaged Material ◽  
Energetic Balance ◽  
Material Separation ◽  
Definition Of

We extend the classical J-integral approach to calculate the energy release rate of cracks by prolonging the contour path of integration across a traction-transmitting interphase that accounts for various phenomena occurring within the gap region defined by the nominal crack surfaces. Illustrative examples show how the closed contours, together with a proper definition of the energy momentum tensor, account for the energy dissipation associated with material separation. For cracks surfaces subjected to cohesive forces, the procedure directly establishes an energetic balance à la Griffith. For cracks modeled as phase-fields, for which no neat material separation occurs, integration of a generalized energy momentum (GEM) tensor along the closed contour path that traverses the damaged material permits the calculation of the energy release rate and the residual elasticity of the completely damaged material.

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.

Elastic Foundation Solution for the Energy Release Rate and Mode Partitioning of Face/Core Debonds in Sandwich Composites

2019 ◽  
Vol 86 (12) ◽  
Author(s):  
George A. Kardomateas ◽  
Niels Pichler ◽  
Zhangxian Yuan
Keyword(s):  
Energy Release Rate ◽  
Closed Form ◽  
Energy Release ◽  
Elastic Foundation ◽  
Release Rate ◽  
Sandwich Beam ◽  
Integral Approach ◽  
Closed Form Expression ◽  
Sandwich Composites ◽  
Sandwich Construction

Abstract The goal of this paper is to derive closed form expressions for the energy release rate and mode partitioning of face/core debonds in sandwich composites, which include loading in shear. This is achieved by treating a finite length sandwich beam as having a “debonded” section where the debonded top face and the substrate (core and bottom face) are free and a “joined” section where a series of springs (elastic foundation) exists between the face and the substrate. The elastic foundation analysis is comprehensive and includes the deformation of the substrate part (unlike other elastic foundation studies in the literature) and is done for a general asymmetric sandwich construction. A J-integral approach is subsequently used to derive a closed form expression for the energy release rate. In the context of this elastic foundation model, a mode partitioning approach based on the transverse and axial displacements at the beginning of the elastic foundation (“debond tip”) is proposed. The results are compared with finite element results and show very good agreement.

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.

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.

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