Sufficient criterion of fracture in the case with a complex stress state and non-proportional deformation of the material in the pre-fracture zone

A general case of proportional loading with a complex stress state of the material in the pre-fracture zone, which is typical for polycrystalline solids with plastic deformation, is considered. A sufficient criterion of fracture is proposed for the case of a complex stress state with non-proportiona...

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Bibliographic Details
Published in:Journal of applied mechanics and technical physics 2010-12, Vol.51 (6), p.904-912
Main Authors: Kornev, V. M., Kurguzov, V. D.
Format: Article
Language:English
Subjects:
Applications of Mathematics
Classical and Continuum Physics
Classical Mechanics
Cleavage
Crack propagation
Criteria
Deformation
Fluid- and Aerodynamics
Fracture mechanics
Fracturing
Mathematical Modeling and Industrial Mathematics
Mathematical models
Mechanical Engineering
Physics
Physics and Astronomy
Stresses
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Summary:A general case of proportional loading with a complex stress state of the material in the pre-fracture zone, which is typical for polycrystalline solids with plastic deformation, is considered. A sufficient criterion of fracture is proposed for the case of a complex stress state with non-proportional deformation of the material in the pre-fracture zone. Critical parameters of fracture (pre-fracture zone length and load) for cracks propagating in quasi-brittle materials are obtained with the use of a modified Leonov-Panasyuk-Dugdale model. The pre-fracture zone width is determined by solving the problem of the plasticity theory in the vicinity of the crack tip. The proposed modification of the Leonov-Panasyuk-Dugdale model makes it possible to estimate the critical opening of the crack and the critical displacement of the crack flanks. Inequalities that describe different mechanisms of material fracture under proportional loading (predominantly shear fracture mechanism and fracture mechanism through cleavage) are derived.
ISSN:0021-8944
1573-8620
DOI:10.1007/s10808-010-0112-0