Research Papers

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

[+] Author and Article Information
Roberto Ballarini

Department of Civil and
Environmental Engineering,
University of Houston,
Houston, TX 77004
e-mail: rballarini@uh.edu

Gianni Royer-Carfagni

Department of Industrial Engineering,
University of Parma,
Parma 43124, Italy
e-mail: gianni.royer@unipt.it

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received February 26, 2016; final manuscript received March 9, 2016; published online March 29, 2016. Editor: Yonggang Huang.

J. Appl. Mech 83(6), 061008 (Mar 29, 2016) (13 pages) Paper No: JAM-16-1110; doi: 10.1115/1.4032986 History: Received February 26, 2016; Revised March 09, 2016

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.

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Grahic Jump Location
Fig. 2

(a) The body composed of two elastic solids joined by a straight elastic interface. (b) A general constitutive equation relating the interface-stress with the relative displacement.

Grahic Jump Location
Fig. 1

Spatially diffused crack tip region. Circular contour path to calculate the flux of the GEM tensor.

Grahic Jump Location
Fig. 3

(a) Deformed configuration of the body. (b) The closed-path contour for the application of Eshelby energy moment tensor.

Grahic Jump Location
Fig. 4

(a) Closed-path contour for a crack with a tip stress singularity. (b) A special configuration for which the contour integral J can be readily evaluated.



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