Probabilistic Fatigue Crack Growth Analyses for Critical Structural Details

Abstract

The damage tolerance method requires the assumption that cracks preexist at the critical structural details and that subsequent fatigue crack propagation could cover at least twice the design life before failure occurs. If fatigue crack propagation cannot meet these requirements, an inspection could be arranged to detect cracks at half of the fatigue life to prevent catastrophic failure. Fatigue tests using from coupons up to the whole structure should be performed to complement the damage tolerance analyses. Nevertheless, the damage tolerance method can still not guaranteean economical airframe dueto uncertaintiesin initial fatiguequality, material, usage, and maintenance. Probabilistic analyses are needed to cover major sources of these uncertainties. A procedure is presented based on several novel probabilistic fracture mechanics solutions for the analyses of fatigue crack propagation. A practical example is used in the discussion to illustrate the procedure and to address important issues when uncertainties are considered. It is shown that different consequences may appear if analyses of the fatigue life are based on the probabilistic consideration. O guarantee enough structural strength during the design life span, the damage tolerance is usually considered for critical structural details to achieve the maximum reliability with a mini- mum maintenance requirement. The damage tolerance method re- quiresspecifyingthatcracksshouldbeassumed inalloftheprimary structural details, and that these cracks should not grow to a size to cause loss of the structure within a specie ed service period. The damage tolerance method requires 1 ) a full-scale fatigue test to at least double the design life for an average usage load and 2 ) at least twice the design life for a crack started froma specie ed size to grow into the critical size. The damage tolerance method is often imple- mented by an inspection to detect fatigue cracks at half of the crack growth life. The fracture-mechanics-based damage tolerance method pro- vides information about the average crack growth behavior. It usu- ally does not account for uncertainties involved in the fatigue crack growth process for practical structural problems. Empirical safety factors are often adopted to cover uncertainties in crack propaga- tion.Whentherearenoadequatedatatosupportselectionofasafety factor, a large value is preferred, which may lead to uneconomical heavy structures and to rejection of reliable structures and com- ponents. The consequent maintenance programs are usually poorly dee ned,resultinginuneconomicalinspectionintervalsthatmaystill notguarantee a reliable structure in service. Aprobabilistic analysis ofthefatiguecrackgrowthisdesirableinthereliabilitymanagement of structural problems. The analysis can be used as a guideline for service conditions, where various uncertainties cannot be avoided. When accidental damages such as pilot error, maintenance dam- age, environmental attacks, production faults, etc., are excluded, probabilistic fatigue crack growth analyses should cover the effect ofpredictablevariablessuchasinitiale aws,stochasticcrackgrowth, crack growth threshold, production and loading, failure criteria, in- spection, e eet size, etc. In this paper, a crack growth analytical pro- cedure is developed based on Elber' s fatigue crack closure model 1 for nonstationary stochastic fatigue crack growth analyses under the general loading condition. The experimental data for the fa- tigue crack growth rate against the effective stress intensity factor for constant amplitude loading are used as intrinsic material data to represent the resistance of material to the fatigue crack growth. The