Fatigue and Creep Failure Models for Variable Amplitude Loading Programs

A new section on fatigue and creep rupture has been added to the website:    http://www.FailureCriteria.com. 

This is Section IV entitled “Cumulative Damage Leading to Fatigue and Creep Failure for General Materials”.  It is shown that a general formalism can be taken which applies to either fatigue or creep rupture through suitable notational changes.  The basic problem is to predict the lifetimes under variable amplitude loading programs based upon knowledge of the data base of lifetimes under constant amplitude loading conditions.  The problem is analogous to that of viscoelasticity where creep or relaxation functions combined with convolution integrals can be used to predict the response for a general loading history.  However, the viscoelasticity problem admits a linear constitutive formulation, whereas the failure problems of interest here are by definition nonlinear.

Four different cumulative damage models are compared.  Three of them are long standing forms.  One of these is that of Miner’s rule, which although completely empirical remains the most  widely used form.  The fourth model is of micromechanical origin.  It is shown that the idealization of a single, non-interactive, but growing crack is of limited value in this problem and it is necessary to generalize to a more inclusive flaw growth methodology.  All four models are completely calibrated by  constant amplitude failure data bases and do not contain any adjustable parameters.

A program of evaluation is based upon three  critical problems: residual strength, residual life, and life after damage.  It is shown that the models make enormously different predictions for these problems, sometimes different by orders of magnitude.  The  flaw growth model is the only one without objectionable  predictions in the evaluations.

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   Recently a new section has been added to the homepage of FailureCriteria.com summarizing  the work objectives for the entire website.  Part of it is repeated below:

Failure Characterization

   It is highly advisable that the failure characterization for any one materials type, epoxy polymers for example, follow directly as a specialization from a comprehensive form applicable to all homogeneous and isotropic materials. Success across the spectrum of all materials types, from very ductile to very brittle, would be much more likely to assure success for any one particular class of interest.

   In the present work it first will be required that the general characterization admit the one property Mises criterion at one extreme, since it gives the most nearly correct results for ductile metals.  Then at the other end of the scale, realistic specializations must occur for the cases of brittle ceramics, glasses and geological materials, which surely would require more than one property.

   It is furthermore required that the general theory be calibrated by only a few (preferably two) failure properties.  If many properties appeared to be needed, the situation would inevitably degenerate to being just that of adjusting or fitting parameters rather than that of an evaluation from mechanical properties.  The same unsatisfactory situation would usually occur in merely fitting data for a single materials type with no regard for anything else.  

   The mainstream topics of traditional interest have mostly been composed of isotropic materials.  However, anisotropic materials in general and fiber composite materials in particular are of great contemporary interest and relevance.  These broader classes of materials will also be covered.  Beyond the idealization of quasi-static failure lie the even more difficult classes of fatigue and rate dependent failure.  These too should be and will be included.  Nevertheless, the priority order taken here is that a consistent and self contained formulation of quasi-static, isotropic material failure must come first.  If this most basic aspect of failure cannot be correctly treated, then there is little likelihood for succeeding with the even more difficult problems.

   Despite the historically slow and sometimes convoluted path of progress, modern developments for failure criteria have confronted the basic problems and yielded tractable and cohesive results.  The main body of these failure criteria for homogeneous materials along with the complementary field of fracture mechanics go far toward providing a general framework for materials failure characterization.