Fatigue Crack Growth Analysis and Damage Prognosis in Structures

Fatigue Crack Growth Analysis and Damage Prognosis in Structures

Shankar Sankararaman (SGT Inc., USA & NASA Ames Research Center, USA), You Ling (General Electric Global Research Center, USA) and Sankaran Mahadevan (Vanderbilt University, USA)
Copyright: © 2015 |Pages: 27
DOI: 10.4018/978-1-4666-8490-4.ch010
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This chapter describes a computational methodology for fatigue crack growth analysis and damage prognosis in structures. This methodology is applicable to a variety structural components and systems with complicated geometry and subjected to variable amplitude multi-axial loading. Finite element analysis is used to address complicated geometry and calculate the stress intensity factors. Multi-modal stress intensity factors due to multi-axial loading conditions are combined to calculate an equivalent stress intensity factor using a characteristic plane approach. Crack growth under variable amplitude loading is modeled using a modified Paris law that includes retardation effects. During cycle-by-cycle integration of the crack growth law, a Gaussian process surrogate model is used to replace the expensive finite element analysis, thereby significantly improving computational effort. The effect of different types of uncertainty – physical variability, data uncertainty and modeling errors – on crack growth prediction is investigated. The various sources of uncertainty include, but not limited to, variability in loading conditions, material parameters, experimental data, model uncertainty, etc. Three different types of modeling errors – crack growth model error, discretization error and surrogate model error – are included in analysis. The different types of uncertainty are incorporated into the framework for calibration and crack growth prediction, and their combined effect on crack growth prediction is computed. Finally, damage prognosis is achieved by predicting the probability distribution of crack size as a function of number of load cycles, and this methodology is illustrated using a numerical example of surface cracking in a cylindrical component.
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Structural systems and their components are often subjected to cyclic loads, leading to fatigue, crack initiation and crack growth. System models are coupled with crack growth models to study crack growth propagation and thereby predict the crack growth as a function of number of loading cycles. This, in turn, can be used in life prediction and reliability evaluation of the system. The process of fatigue crack growth is affected by many sources of variability, such as loading, material properties, geometry and boundary conditions. Therefore it is appropriate to describe the crack size after a certain number of load cycles through a probability distribution that accounts for these different sources of uncertainty.

Fracture mechanics and probabilistic fracture mechanics are extensive areas of research and numerous studies have focused on developing computational techniques probabilistic crack growth and life prediction. Probabilistic crack growth analysis has been applied to both metals (e.g. Johnson and Cook (Johnson & Cook, 1985), Maymon (Maymon, 2005)) and composites (Hwang & Han, 1986; Peng et al., 2013)). Practical applications of these methods include nuclear structural components (Yagawa, Kanto, Yoshimura, Machida, & Shibata, 2001), helicopter gears (Patrick et al., 2007), gas turbine engines (Tryon, Cruse, & Mahadevan, 1996), and aircraft components (S Sankararaman, Ling, & Mahadevan, 2011). These developments have led to software for probabilistic fracture mechanics (McClung, Enright, Millwater, Leverant, & Hudak Jr, 2004), and several commercial software tools such as DARWIN (Wu, Enright, & Millwater, 2002), and other software tools that build probabilistic analysis around well-established codes such as AFGROW (Grell & Laz, 2010) and FASTRAN (Newman Jr, Brot, & Matias, 2004).

This chapter a presents a computational methodology for modeling fatigue crack growth analysis and predicting crack growth in order to aid damage prognosis and life prediction in structural metallic systems. This methodology is directly useful for system design since it is ideal to choose design parameters that maximize the life expectancy of the system. Further, the methodology also facilitates risk assessment and management, inspection and maintenance scheduling and operational decision-making.

Researchers have pursued two different kinds of methodologies for fatigue life prediction. The first method is based on material testing (to generate S-N, ε – N curves) and use of an assumed damage accumulation rule. In this method, specimens are subjected to repeated cyclic loads under laboratory conditions. Hence the results are specific to the geometry of the structure as well as the nature of loading. Further, the performance of these components under field conditions is significantly different from laboratory observation, due to various sources of uncertainty accumulating in the field that render experimental studies less useful. Hence, this methodology cannot be used directly to predict the fatigue life of practical applications wherein complicated structures subjected to multi-axial loading.

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