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If fracture mechanics shall be applied to the total lifetime respectively the fatigue limit of components (within the meaning of the S-N curve approach) it has to address four challenges:
(a) It has to adequately describe so-called short crack propagation, which cannot be based on the common long crack concepts for principle reasons. Since the crack size is in the order of the plastic zone size, the modelling of short crack propagation cannot be based on the common linear elastic Delta K concept. Instead, an elastic-plastic parameter such as the cyclic J integral has to be applied. A second point is that the crack closure concept has to be modified in that the crack opening stress is not a constant, crack size- independent parameter but shows a transient behaviour with increasing short crack size.
(b) It has to provide a meaningful definition of the initial crack dimensions as the starting point for an S-N curve relevant (residual) lifetime analysis. This can be based either on the (statistical) size of material defects which can be treated as cracks or by the size of the crack which would arrest subsequent to early crack propagation, whatever is larger.
(c) It has to cope with the problem of multiple cracks for load levels higher than the fatigue limit such as it occurs in many applications in the absence of very large initial defects.
(d) This requires consequent statistical treatment taking into account variations in the local geometry of the area where crack initiation has to be expected as well as the scatter in the initial crack size and in the material data used for the analyses.
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 paper provides an application of the IBESS approach to the investigation of the influence of various parameters of the global and local weld geometry as well as material defects on the fatigue strength of weldments. For this purpose, the global weld parameters, such as the weld toe radius, the flank angle, the excess weld metal, local secondary notches (in the present study as a measure of surface imperfections) and inclusions sizes have been determined as statistical distributions for different joint types and geometries and two steels of different strengths. The results are in line with literature data and reveal the potential of the theoretical approach to predict the correct trends. The combination with an advanced weld quality system has been demonstrated to be possible.
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.
Aero-engine turbine disks are safety-relevant components which are operated under high thermal and mechanical stress conditions. The actual part qualification and certification procedures make use of spin-tests conducted on production-similar disks. While these tests provide, on the one hand, a reliable definition of the critical conditions for real components, on the other hand they represent a relevant cost item for engine manufacturers. The aim of this work is to present two alternative burst speed assessment methods under development based on the Failure Assessment Diagram (FAD) and a global stability criterion, respectively. In the scope of the fracture mechanics assessment, the failure modes hoop-burst and rim-peeling are investigated with semicircular surface cracks modelled at the critical regions on the turbine disk. The comparison of the predicted critical rotational speed shows good agreement between the assessment methods.