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.

Analysis of Potential Energy Release Rate of Composite Laminate Based on Timoshenko Beam Theory

2007 ◽  
Vol 334-335 ◽  
pp. 513-516
Author(s):  
Kyohei Kondo
Keyword(s):  
Potential Energy ◽  
Energy Release Rate ◽  
Energy Release ◽  
Timoshenko Beam ◽  
Release Rate ◽  
Double Cantilever Beam ◽  
Beam Theory ◽  
Timoshenko Beam Theory ◽  
Beam Specimen ◽  
Cracked Beam

The Timoshenko beam theory is used to model each part of cracked beam and to calculate the potential energy release rate. Calculations are given for the double cantilever beam specimen, which is simulated as two separate beams connected elastically along the uncracked interface.

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.

Vector J -integral analysis of crack initiation at the edge of complete sliding contact

2006 ◽  
Vol 462 (2070) ◽  
pp. 1805-1820 ◽  
Author(s):  
Lifeng Ma ◽  
Alexander M Korsunsky
Keyword(s):  
Crack Initiation ◽  
Potential Energy ◽  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Fretting Fatigue ◽  
Maximum Energy ◽  
Integral Vector ◽  
Crack Initiation Angle ◽  
Independent Integral

In this paper, the crack initiation at contact surface of solids is investigated on the basis of the concept of potential energy release rate. The expressions for path-independent integral vector J i ( i =1, 2) are derived and applied to the consideration of the process of crack initiation. The relationship is then established between the value of the path-independent integral vector J i and the potential energy release rate for crack initiation in an arbitrary orientation. This allows the prediction of crack initiation angle on the basis of the maximum energy release rate criterion. The surface crack initiation angle in fretting fatigue is determined analytically as a function of the friction coefficient of the edge contact. This theoretical result is compared with the existing experimental results reported in the literature and a good agreement is found. The formulation provides a novel basis for numerical modelling of the complex process of fretting fatigue.

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