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The maximum stress criterion assumes that a material fails when the maximum principal stress σ 1 is the crack length for plane cracks. The failure criteria that were developed for brittle solids were the maximum stress/ strain criteria. An efficient deformation and failure model should be consistent at every level.īrittle material failure criteria įailure of brittle materials can be determined using several approaches: The material behavior at one level is considered as a collective of its behavior at a sub-level. Energy type failure (S-criterion, T-criterion)įive general levels are considered, at which the meaning of deformation and failure is interpreted differently: the structural element scale, the macroscopic scale where macroscopic stress and strain are defined, the mesoscale which is represented by a typical void, the microscale and the atomic scale.Li presents a classification of macroscopic failure criteria in four categories: Macroscopic material failure is defined in terms of load carrying capacity or energy storage capacity, equivalently. Both models form a modification of the von Mises yield potential by introducing a scalar damage quantity, which represents the void volume fraction of cavities, the porosity f. Another approach, proposed by Rousselier, is based on continuum damage mechanics (CDM) and thermodynamics. Such a model, proposed by Gurson and extended by Tvergaard and Needleman, is known as GTN.
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Such models are based on the concept that during plastic deformation, microvoids nucleate and grow until a local plastic neck or fracture of the intervoid matrix occurs, which causes the coalescence of neighbouring voids. Some of the most popular failure models in this area are the micromechanical failure models, which combine the advantages of continuum mechanics and classical fracture mechanics. Failure criteria in this case are related to microscopic fracture. Microscopic failure considers the initiation and propagation of a crack. Such methodologies are useful for gaining insight in the cracking of specimens and simple structures under well defined global load distributions. Microscopic material failure is defined in terms of crack initiation and propagation. Material failure can be distinguished in two broader categories depending on the scale in which the material is examined: On the other hand, due to the lack of globally accepted fracture criteria, the determination of the structure's damage, due to material failure, is still under intensive research. In structural problems, where the structural response may be beyond the initiation of nonlinear material behaviour, material failure is of profound importance for the determination of the integrity of the structure. This definition introduces to the fact that material failure can be examined in different scales, from microscopic, to macroscopic. In materials science, material failure is the loss of load carrying capacity of a material unit. 4 Ductile material failure (yield) criteria.Quite often, phenomenological failure criteria of the same form are used to predict brittle failure and ductile yields. A precise physical definition of a "failed" state is not easily quantified and several working definitions are in use in the engineering community. Failure criteria are functions in stress or strain space which separate "failed" states from "unfailed" states.
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In mathematical terms, failure theory is expressed in the form of various failure criteria which are valid for specific materials. However, for most practical situations, a material may be classified as either brittle or ductile. Depending on the conditions (such as temperature, state of stress, loading rate) most materials can fail in a brittle or ductile manner or both. The failure of a material is usually classified into brittle failure ( fracture) or ductile failure ( yield). Material failure theory is an interdisciplinary field of materials science and solid mechanics which attempts to predict the conditions under which solid materials fail under the action of external loads.