Nonlinear Abel type integral equation in modelling creep crack propagation

Copyright @ 2011 Birkhäuser BostonA nonlinear Abel-type equation is obtained in this paper to model creep crack time-dependent propagation in the infinite viscoelastic plane. A finite time when the integral equation solution becomes unbounded is obtained analytically as well as the equation parameters when solution blows up for all times. A modification to the Nyström method is introduced to numerically solve the equation and some computational results are presented

Integral equations of a cohesive zone model for history-dependent materials and their numerical solution

A nonlinear history-dependent cohesive zone (CZ) model of quasi-static crack propagation in linear elastic and viscoelastic materials is presented. The viscoelasticity is described by a linear Volterra integral operator in time. The normal stress on the CZ satisfies the history-dependent yield condition, given by a nonlinear Abel-type integral operator. The crack starts propagating, breaking the CZ, when the crack tip opening reaches a prescribed critical value. A numerical algorithm for computing the evolution of the crack and CZ in time is discussed along with some numerical results

Theoretical backgrounds of durability analysis by normalized equivalent stress functionals

Generalized durability diagrams and their properties are considered for a material under a multiaxial loading given by an arbitrary function of time. Material strength and durability under such loading are described in terms of durability, safety factor and normalized equivalent stress. Relations between these functionals are analysed. We discuss some material properties including time and load stability, self-degradation (ageing), and monotonic damaging. Phenomenological strength conditions are presented in terms of the normalized equivalent stress. It is shown that the damage based durability analysis is reduced to a particular case of such strength conditions. Examples of the reduction are presented for some known durability models. The approach is applicable to the strength and durability description at creep and impact loading and their combination

Local and non-local approaches to fatigue crack initiation and propogation

Copyright @ 2003 Kulwer Academic Publishers.A functional form of local strength conditions under fatigue loading is introduced and employed to formulation and analysis of fatigue crack initiation and propagation. For the strength conditions associated with the Palmgren-Miner linear damage accumulation rule and the power-type S-N diagram, the problem is reduced to a non-linear integral Volterra equation, which can be transformed to a linear one for the case of a single crack. An analytical solution of some simple problems are presented for the latter case and shortcomings of the local approach are pointed out. A non-local approach free from the shortcomings is presented along with an example of its implementation.This work was completed under the research grant GR/M24592 "Non-local approach to high cyclic fatigue: Theoretical basis" of the Engineering and Physical Sciences Research Council, UK

An approach to microstructure modelling in nickel based superalloys

Mechanical properties of components made from nickel based superalloys rely on the microstructure that forms during their thermomechanical processing. The ability for predicting and controlling microstructure during the processing is of the utmost importance for this class of alloys. In this work, the applicability of JMAK-type (Johnson-Mehl-Avrami-Kolmogorov) models is studied in the context of industrial manufacturing processes. The results of FEA (finite element analysis) based predictions of microstructure evolution in ATI 718Plus® alloy during the hot deformation process are presented. The limitations of the JMAK-type approach are discussed in the paper and concepts for an alternative modelling approach for microstructure prediction in nickel based superalloys are presented

Correlation regimes in fluctuations of fatigue crack growth

This paper investigates correlation properties of fluctuations in fatigue crack growth of polycrystalline materials, such as ductile alloys, that are commonly encountered in structures and machinery components of complex electromechanical systems. The model of crack damage measure indicates that the fluctuations of fatigue crack growth are characterized by strong correlation patterns within short time scales and are uncorrelated for larger time scales. The two correlation regimes suggest that the 7075-T6 aluminum alloy, analyzed in this paper, is characterized by a micro-structure which is responsible for an intermittent correlated dynamics of fatigue crack growth within a certain scale. The constitutive equations of the damage measure are built upon the physics of fracture mechanics and are substantiated by Karhunen-Lo\`{e}ve decomposition of fatigue test data. Statistical orthogonality of the estimated damage measure and the resulting estimation error is demonstrated in a Hilbert space setting.Comment: 30 pages, 8 figures, to appear in Physica

A Review of Statistical Failure Time Models with Application of a Discrete Hazard Based Model to 1Cr1Mo-0.25V Steel for Turbine Rotors and Shafts

Producing predictions of the probabilistic risks of operating materials for given lengths of time at stated operating conditions requires the assimilation of existing deterministic creep life prediction models (that only predict the average failure time) with statistical models that capture the random component of creep. To date, these approaches have rarely been combined to achieve this objective. The first half of this paper therefore provides a summary review of some statistical models to help bridge the gap between these two approaches. The second half of the paper illustrates one possible assimilation using 1Cr1Mo-0.25V steel. The Wilshire equation for creep life prediction is integrated into a discrete hazard based statistical model—the former being chosen because of its novelty and proven capability in accurately predicting average failure times and the latter being chosen because of its flexibility in modelling the failure time distribution. Using this model it was found that, for example, if this material had been in operation for around 15 years at 823 K and 130 MPa, the chances of failure in the next year is around 35%. However, if this material had been in operation for around 25 years, the chance of failure in the next year rises dramatically to around 80%