A genetic algorithm for unified approach-based predictive modeling of fatigue crack growth

This paper presents a framework to derive models of fatigue crack growth in real-life applications based on the unified approach.The unified approach enunciates that two parameters-namely, the stress intensity amplitude ΔK and the peak stress intensity K_max-drive fatigue crack growth. It captures and explicates the various fatigue phenomena coherently. However, its application for damage prediction is still in its infancy. Mathematical models that are consistent with the approach and the various observed characteristics under various environments are imperative for fatigue damage life prediction. These models will reduce cumbersome experimentation that is usually needed for the fatigue crack growth analysis. The framework presented in this paper consists of using the unified approach to design the structure of a model that relates fatigue crack growth with the specified microstructure, applied stress and environmental conditions. The fatigue growth model is derived by parametrizing, using a genetic algorithm, these structural relationships from the known experimental data. This model can quantitatively estimate crack growth rate under the given combination of microstructure, applied stress and environmental conditions. The initial research on modeling fatigue crack growth dynamics in Al-5052 under vacuum and air has revealed that the models resulting from the framework can capture the actual crack growth pattern to within 12% accuracy, and that an automatic rendering of ΔK^* vs. trajectories is possible for a given material and environmental conditions.     

A unified approach to damage accumulation and fatigue crack growth

An approach is proposed to the theory of fatigue cracks propagation based on the following postulate: a growing crack at least once in a cycle becomes a nonequilibrium one (in the Griffith's sense) under the condition that the resistance to crack growth is calculated with an account of damage accumulated at the crack tip during the loading history. The theory is used for nonuniaxial stress states including jumplike growth, stops, kinking and branching phenomena. The general structure of differential equations is discussed for the averaged crack growth rate under nonuniaxial loading.     

A unified theory of fatigue crack growth: a statistical approach

Treating the local fracture toughness of a material as a random value, a general relationship between the applied fracture parameter and the stable crack growth distance is developed. The result is applied to a study of the fatigue crack growth and a general expression connecting fatigue crack growth rate and the applied loading is rendered. Several empirical fatigue crack growth models can be derived on the basis of this unified view, and the valid ranges of these models are established. The conclusions are found to be in agreement with experimental evidence.     

Reproducibility of the fatigue crack growth resistance of materials and its consequences

We analyze the reproducibility of the results of mechanical testing of materials aimed at the evaluation of their fatigue crack resistance under quasistatic or cyclic loading. Numerical results are presented for several types of welded joints. It is suggested to estimate the crack growth resistance of structural elements by the slope of the dependence of the logarithm of residual durability lnN _k on the length of the cracka. Department of Mechanical Engineering, University of Miskolc, Hungary. Published in Fizyko-Khimichna Mekhanika Materialiv, Vol. 32, No. 2, pp. 89–93, March–April, 1996.     

A fracture mechanics analysis of fatigue crack growth data for various materials

A large amount of previously published fatigue crack growth data obtained from 10 in. wide centre-cracked sheet specimens of various materials has been re-analysed in terms of the range of stress intensity factor (ΔK) and the results presented as master curves of crack growth rate against ΔK. In addition, data obtained previously from fatigue tests on edge-cracked plate specimens concerning the minimum cyclic stress that would just not cause a crack of a given length to grow have been similarly analysed.     

A convenient way to represent fatigue crack growth in structural adhesives

The present paper examines crack growth in a range of aerospace and automotive structural adhesive joints under cyclic‐fatigue loadings. It is shown that cyclic‐fatigue crack growth in such materials can be represented by a form of the Hartman–Schijve crack‐growth equation, which aims to give a unique and linear ‘master’ representation for the fatigue data points that have been experimentally obtained, as well as enabling the basic fatigue relationship to be readily computed. This relationship is shown to capture the experimental data representing the effects of test conditions, such as R‐ratio and test temperature. It also captures the typical scatter often seen in the fatigue crack‐growth tests, especially at low values of the fatigue crack‐growth rate. The methodology is also shown to be applicable to both Mode I (opening tensile), Mode II (in‐plane shear) and Mixed‐Mode I/II fatigue loadings. Indeed, it has been demonstrated that the fatigue behaviour of structural adhesives under both Mode I and Mode II loadings may be described by one unique ‘master’ linear relationship via the Hartman–Schijve approach.     

A new testing method to obtain mode II fatigue crack growth characteristics of hard materials

Flaking type failure in rolling‐contact processes is usually attributed to fatigue‐induced subsurface shearing stress caused by the contact loading. Assuming such crack growth is due to mode II loading and that mode I growth is suppressed due to the compressive stress field arising from the contact stress, we developed a new testing apparatus for mode II fatigue crack growth. Although the apparatus is, as a former apparatus was, based on the principle that the static K_I mode and the compressive stress parallel to the pre‐crack are superimposed on the mode II loading system, we employ direct loading in the new apparatus. Instead of the simple four‐point‐shear‐loading system used in the former apparatus, a new device for the application of a compressive stress parallel to the pre‐crack has been developed. Due to these alterations, mode II cyclic loading tests for hard steels have become possible for arbitrary stress ratios, including fully reversed loading (R=?1); which is the case of rolling‐contact fatigue. The test results obtained using the newly developed apparatus on specimens made from bearing steel SUJ2 and also a 0.75% carbon steel, are shown.     

A unified model of fatigue kinetics based on crack driving force and material resistance

Fatigue in Al-alloys is largely a process of crack growth from pre-existing defects occurring by several different mechanisms, each of which dominates a particular rate-driven segment of fatigue kinetics. These include fatigue void formation through interfacial cracking of secondary particulates, crack extension by brittle micro-fracture (BMF) in near-threshold fatigue, slip driven crack growth in the Paris regime and quasi-static crack extension by the well-known micro-void coalescence (MVC) and the less known fatigue void coalescence (FVC). BMF is mean stress and sequence-sensitive.Mechanism selection for fatigue crack extension in each load cycle occurs on the principle of least resistance to crack driving force represented by ΔK and K_max. Crack extension will switch to a different failure mechanism given reduced resistance to that mechanism by comparison to the current one. Increasing driving force will thus force a switch from BMF to shear and then onto MVC or FVC in that order, over each rising load half-cycle. Higher growth rates will therefore always be associated with a mix of all these mechanisms.     

Studies on fatigue crack growth for airframe structural integrity applications

A review is made of efforts at the National Aerospace Laboratories in the development of fatigue crack growth prediction technology for airframe applications. The research was focused on extension of rainflow techniques for crack growth analysis and development of accelerated crack growth calculation methods for spectrum loading. Fatigue crack closure forms a crucial element of modelling and fractographic techniques were developed for its study. These, combined with binary coded event registration enabled crack growth and closure mapping for part-through cracks in metallic materials. Experimental research on short cracks at notches led to discovery of the hysteretic nature of crack closure, which explains well-known history-sensitive local mean stress effects in notch root fatigue. Optical fractography of failures obtained under simulated service conditions revealed that short cracks do not exhibit any more scatter than long cracks at comparable growth rates. The nature of multi-site crack initiation and growth of small cracks at notches was investigated and the effort extended to lug joints that are widely used in airframe applications. Results from this work suggest the possibility of modelling crack growth from a size smaller than 50 microns through to failure, thereby accounting for a major fraction of total life. The work described in this paper enjoyed the strong support of Dr S R Valluri, Prof R Narasimha and Dr K N Raju. Financial support for the effort was provided by Aeronautical Research & Development Board, Aeronautical Development Agency and Department of Science and Technology.     

Environmentally-assisted fatigue crack growth mechanisms in advanced materials for aerospace applications

This paper addresses the issue of environmentally-assisted fatigue crack propagation in metallic and intermetallic alloys, which is essential to predict the durability of aerospace components. A review of the current understanding of the mechanisms accounting for the detrimental effect of air on fatigue crack growth resistance of conventional alloys is first presented. The adequacy of the two sequential processes identified, namely water vapour adsorption on crack tip surfaces and hydrogen embrittlement of cyclically deformed material within the plastic zone, to account for environmentally-assisted fatigue crack propagation in alloys based on intermetallic compounds is then examined. The last section is devoted to the analysis of environmental effects during creep–fatigue crack growth in an age-hardened aluminium alloy for supersonic aircraft. In particular the influence of environment on the intergranular cavitation damage process is analysed.