Energy Release Rates and Related Balance Laws in Linear Elastic Defect Mechanics

1987 ◽  
Vol 54 (2) ◽  
pp. 388-392 ◽  
Author(s):  
J. W. Eischen ◽  
G. Herrmann
Keyword(s):  
Conservation Laws ◽  
Energy Release ◽  
Thermal Effects ◽  
Balance Laws ◽  
Release Rates ◽  
Direct Derivation ◽  
Linear Elastic ◽  
Linear Dynamic ◽  
Dynamic Elasticity ◽  
Energy Release Rates

A simple and direct derivation of certain balance (or conservation) laws for linear dynamic elasticity is presented including nonhomogeneities, thermal effects, anisotropy, and body forces. Additionally, the connection between the balance laws and energy release rates for defect motions is established.

scholarly journals Interface Crack Approaching a Three-Material Joint

2020 ◽  
Vol 10 (1) ◽  
pp. 416 ◽  
Author(s):  
Jelena M. Djoković ◽  
Ružica R. Nikolić ◽  
Robert Ulewicz ◽  
Branislav Hadzima
Keyword(s):  
Plastic Zone ◽  
Energy Release ◽  
Interface Crack ◽  
Crack Deflection ◽  
The Other ◽  
Elastic Behavior ◽  
Release Rates ◽  
Linear Elastic ◽  
Energy Release Rates ◽  
Elastic Fracture

The problem of an interface crack that approaches a three-material joint with two interfaces is analyzed in this paper. Two possible cases are considered: the crack that lies at the interface between materials A and B, approaching the joint of materials A, B, and C, deflects into the interface between materials A and C or into the interface between materials B and C. Analysis is performed within restrictions imposed by the linear elastic fracture mechanics (LEFM), linear elastic behavior of materials, and the small plastic zone around the crack tip, based on the crack deflection criterion proposed by He and Hutchinson. That criterion is applied in this paper to a joint of the three homogeneous isotropic materials. The energy release rates for the crack deflection into one interface or the other are compared to each other, and, based on this comparison, a conclusion is drawn as to which of the two interfaces the crack would deflect. If the value of the ratio of the energy release rates GBC/GAC is greater than the ratio of the corresponding fracture toughnesses of the two interfaces, the crack will deflect into the BC interface. If this ratio is smaller than the ratio of the corresponding fracture toughnesses, the crack will deflect into the AC interface. Knowing the ratio of energy release rates for deflection into one interface or the other can be used for designing the interface, namely for prediction of the direction of further crack propagation.

Criteria for Prediction the Interfacial Crack Growth in Concrete

2016 ◽  
Vol 258 ◽  
pp. 514-517
Author(s):  
Jelena M. Djoković ◽  
Ružica R. Nikolić ◽  
Ján Bujňák ◽  
Branislav Hadzima
Keyword(s):  
Fracture Mechanics ◽  
Mechanical Behavior ◽  
Energy Release ◽  
Crack Growth ◽  
Interfacial Crack ◽  
Release Rates ◽  
Linear Elastic ◽  
Deformation And Fracture ◽  
Energy Release Rates ◽  
Elastic Fracture

To understand the mechanical behavior of the concrete structures, one must analyze deformation and fracture of the interfaces between the constituents of the material that the structure is made of. Criteria for predicting the crack growth along an interface, based on the linear elastic fracture mechanics concept, applied for the cement substrate/aggregate interface, are presented in this paper. The two possible directions of the interfacial crack growth – the crack propagation along the interface and the crack kinking away from the interface are considered, with the corresponding energy release rates. For the case of the crack approaching the interface from one of the materials – cement, the competition between the crack deflecting into the interface and the crack penetrating the interface is considered with the corresponding energy release rates.

Conservation Laws and Energy-Release Rates

1973 ◽  
Vol 40 (1) ◽  
pp. 201-203 ◽  
Author(s):  
B. Budiansky ◽  
J. R. Rice
Keyword(s):  
Conservation Laws ◽  
Energy Release ◽  
Complex Variable ◽  
Plane Elasticity ◽  
Special Point ◽  
Stress Distributions ◽  
Isotropic Plane ◽  
Release Rates ◽  
Energy Release Rates ◽  
Plastic Stress

New path-independent integrals recently discovered by Knowles and Sternberg are related to energy-release rates associated with cavity or crack rotation and expansion. Complex-variable forms are presented for the conservation laws in the cases of linear, isotropic, plane elasticity. A special point concerning plastic stress distributions around cracks is discussed briefly.

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