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Failure Theory for Materials Science and Engineering
Failure Theory for Materials Science and Engineering
Posted by Jugraj Singh Randhawaon 10:12 AMin
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Overview
Three dimensional failure criteria are given for various materials classes. These include both isotropic and anisotropic material symmetries, and are applicable for macroscopic homogeneity. In the isotropic materials form, the properly calibrated failure criteria can distinguish ductile from brittle failure for specific stress states. Although most of the results are relevant to quasi-static failure, some are for time dependent failure conditions as well as for fatigue conditions.
Contents
Purpose and Conditions - Attention is given to many failure related matters, but especially to the physical and mathematical basis for the failure criteria under examination.
Yield and Failure Criteria for Isotropic Materials - Historical and modern failure criteria for isotropic materials are outlined and discussed. A recently developed yield and failure formalism is given which is completely calibrated by the two failure properties in uniaxial tension and compression. It necessarily involves an inherent transition from ductile to brittle failure mechanisms across the range of materials types. Manuscripts of Published Papers
Failure Criteria for Anisotropic Fiber Composite Materials - A physically based failure formulation is given for aligned fiber composite materials. Two coordinated failure criteria are derived, one for the fiber controlled mode and one for the matrix controlled mode. The targeted applications are to carbon fiber, polymeric matrix (or equivalent) types of systems.
Failure of Fiber Composite Laminates: Progressive Damage and Polynomial Invariants - Two distinctly different failure methods are given. The first is that of progressive damage where lamina level failure criteria are used to predict the sequence of damage/failures within the laminate. The second method is that of polynomial invariants which takes the scale of the laminate itself and its symmetry properties as the fundamental basis for failure characterization. The two methods are carefully and thoroughly compared.
Critical Experimental and Theoretical Tests for Failure Criteria - The evaluation procedure for isotropic material failure criteria involves assessing their theoretical basis followed by comparisons with critical data sets (ductile and brittle). All of the long standing commonly used failure forms are found to be fundamentally incapable of functioning as general three dimensional failure criteria. All but one (Mises) cannot even serve for just a single, restricted materials type. Only the recently developed, two property failure theory outlined in Section II correlates well with all the data cases and has complete generality, going from the ductile limit to the brittle limit. Some failure criteria for fiber composites are also evaluated.
The Ductile/Brittle Transition, Gaging Ductility Levels - Under the heading Organizing Principle the isotropic material failure criterion is put into the form that is best for examining ductility and brittleness matters. Starting with the ductile/brittle transition, a failure number index is derived that gages the level of ductility (and brittleness) in failure. The failure number, Fn, is expressed in terms of the uniaxial strength ratio, T/C, and the nondimensionalized first invariant of the stress state at failure. Many examples with detailed explanations are given.
Fracture Mechanics - A sharply focused examination is taken of the two major failure disciplines: fracture mechanics and failure criteria. First, the historical development of the field of fracture mechanics is summarized. Then, typical but revealing examples of the use of each approach are given. Finally, the importance and usefulness of the two failure theories are assessed, both individually and relative to each other.
Micromechanics Failure Analysis - The role of micromechanics in synthesizing macroscopic failure criteria is assessed. Micromechanics is seen as having a special capability beyond just that of predicting micron scale failure. Three examples are given that illustrate how particular failure modes at the micron scale bridge over to provide needed and sometimes critical information for macroscopic failure. Two of the examples are appropriate to carbon fiber composites, while the third one is for particulate composites.
Defining Yield Stress and Failure Stress (Strength) - Historically there have been many different and confusing designations for the yield stress and strength. But for failure criteria purposes it is necessary to specify clear and rigorous definitions of these properties. The yield stress is determined to be given by the maximum of the second derivative of the stress strain curve. Since this is difficult to implement, an easy to use approximation to it is found. The strength property is determined to involve certain integrations over the stress strain curve, and it also is very easy to use with data.
