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- Fatigue crack growth (2)
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- Weldments (2)
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Approximation of the crack driving force for cracks at notches under static and cyclic loading
(2017)
The work deals with the efficient calculation of the elastic-plastic crack driving force (J-integral for monotonic loading andΔJ-integral under cyclic loading) for short cracks at notches as essential parameter for the reliable static and fatigue assessment of notched structures. The J- or ΔJ-integral is calculated based on analytical solutions for stress intensity factors, estimated by means of well-known weight function solutions in the case of cracks under power-law stress distributions. A plasticity-correction function is applied to the stress intensity factors to obtain the final expression of the crack driving force. The comparison between analytical solutions and finite element calculations in case of cracks at the weld toe in welded joints shows good agreement.
The cyclic J-integral (∆J-integral) is a crack tip parameter of elastic-plastic fracture mechanics which can be used as governing parameter for the description of fatigue crack growth (FCG) in metallic structures. In this contribution, it is applied for modelling FCG in weldments. The ∆J-integral is determined by means of analytical approximation formulas as well as numerical methods. An analytical solution, which takes into account effects of the local ligament plasticity, was derived. This solution is based on well established methods such as R6, BS7910 and SINTAP which were modified for cyclic loading. It incorporates methods for the description of short crack closure behaviour as well as the well known analytical (long) crack closure function of Newman. A specific code was written to evaluate the ∆J-integral numerically in the course of finite element based crack growth simulations. The code was first validated for an infinite plate with centre crack by applying elastic and elastic-plastic material behaviour. Next, the ∆J-integral was calculated for cracks in various butt and cruciform welded joints. The results were compared with the results of the derived analytical approximation formula. A good accordance was achieved between the results.
Welding residual stresses have an impact on the performance of welded structures, on their fracture resistance, their resistance against fatigue crack propagation and, most important, their fatigue strength and fatigue lifetime. The present paper provides an overview on the issue mainly from the point of view of the application of fracture mechanics to the determination of the fatigue strength as the topic of this Special issue. Besides own experimental and theoretical data a comprehensive discussion is provided in that context which includes the definition and interaction of short- and long-range (or reaction) residual stresses, the effect of cyclic mechanical loading and its treatment in fracture and fatigue analyses.
Common fracture mechanics based fatigue considerations are usually limited to the residual lifetime determination of so-called long cracks. The extension of this concept to the total lifetime, as in the S-N curve approach, requires an adequate description of short crack propagation which cannot be based on the Delta K concept, and it must consider the crack closure phenomenon as well as its gradual build-up at the short crack stage. Further, it has to provide a meaningful definition of initial crack dimensions and a solution for the multiple crack problem at stress levels higher than the fatigue limit as it is specific for some configurations such as weldments. This paper aims at a discussion of all these points and offers possible solutions which are illustrated by examples taken from the German IBESS project on fracture mechanics based determination of the fatigue strength of weldments, the results of which will be discussed in more detail in this Special issue.
The work presents the procedure developed within the German research project IBESS, which allows for the fracture mechanics-based prediction of the fatigue strength of welded joints under constant amplitude loading. Based on the experimental observations of the crucial failure mechanisms, the approach focuses on the short crack propagation, where elastic-plastic fracture mechanics and the build-up of closure effects must be considered as well as the variability of the local geometry at the weld toe and the modelling of multiple crack interaction. Analytical solutions are provided for the approximation of the through-thickness stress profiles at the weld toe and for the determination of the crack driving force in the form of a plasticity-corrected stress intensity factor range ∆K_p. Proposals for the determination of the initial crack size and the crack closure factor are also included.
The approach is validated against a large number of experimental data, which comprises fatigue tests on individual cracks monitored by heat tinting and beach-marking techniques, as well as stress life curves. Three kinds of welded joints, two steels of significant different strengths and three stress ratios are considered. The results show that the procedure provides good estimations of the statistical distribution of the fatigue strength of welded joints both for the finite and infinite life regime. Furthermore, the predictions are compared with available benchmark data for structural steels.