Stress Based Failure Criteria for Materials Science and Engineering

Richard M. Christensen
Brief Biography

Stress Based Failure Criteria for
Materials Science and Engineering

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.
Cumulative Damage Leading to Fatigue and Creep Failure for General Materials - Four different cumulative damage models are compared. All four models are calibrated by constant amplitude failure data bases and do not contain any adjustable parameters. Only the flaw growth theory/model shows a consistent and realistic life prediction capability for variable amplitude conditions.
Manuscript of Published Paper
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.
Probablistic Failure - (coming later)