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An analytical fracture mechanics model for predicting the finite life fatigue strength of components is presented which Combines a number of well established and newly developed approaches such as Murakami’s and McEvily's approach for describing the transient behaviour of crack closure of short cracks, the analytical (long) crack closure function of Newman, the R6 procedure modified by a method for improving the ligament yielding correction proposed by the authors and other elements. Basic assumption is the preexistence of initial flaws such that the crack initiation or nucleation stage is small and can be neglected. The application of the model is demonstrated for small tension plates of aluminium Al 5380 H321 with artificial initial defects generated by FIB technology, the size of which was fixed on the basis of fractographic investigations on broken, smooth specimens.
The fracture mechanics-based IBESS approach is applied to the determination of FAT classes of butt welds with crack Initiation along the weld toe. The aim is an investigation of the effect of the geometrical parameters toe radius, flank angle, reinforcement and secondary notches such as roughness or undercuts. The influence of these parameters is discussed both individually and in combination; however, excluding statistical distributions of them and the material data. The results, when compared with conventional FAT classes for butt welds, are encouraging with respect to a potential contribution of IBESS to the discussion of more advanced quality criteria for welds. To that purpose, demands for further research are proposed.
The paper provides an overview on the results of a German cluster project on the use of fracture mechanics to the determination of the fatigue strength of weldments with fatigue cracks originating at the weld toes. The approach includes (a) a concept for short crack propagation for which the common ΔK concept is not applicable and the crack closure effects are still being gradually build-up, (b) a method for determining fatigue life relevant initial crack sizes as they are needed in any fracture mechanics analysis and (c) multiple cracking and crack coalescence at load levels higher than the endurance limit. The analyses are stochastically performed. Both, the endurance limit and the finite life branch of the S-N curve are determined.
Besides a brief introduction into the approach, validation examples are presented. These comprise different weldment types (butt welds, cross joints and longitudinal stiffened plates), two steels (S355NL and S960QL) of quite different strengths, different weld geometries due to different welding techniques (WIG, MAG), as-welded and stress relieved welds and different stress ratios varying from R = -1 to R = 0.5.
Although fatigue crack propagation and fracture cause a large part of failure events in industrial practice, fracture mechanics in failure analysis seems to be still a side issue. Starting from an introduction into important basic questions of failure analysis and fracture mechanics, the authors specify what kind of questions in failure analysis can be effectively solved by fracture mechanics (and which can't). They illustrate their discussion with a number of 13 case studies from the literature. Much more pronounced than in the design stage the benefit of fracture mechanics in failure analysis depends on its accuracy. This is limited by both, intrinsic factors of the method and the availability and quality of the input information. The authors discuss the various aspects and provide the reader with some background information which, as they believe, will be helpful for better understanding the prospects and limitations of fracture mechanics in failure analysis and the conditions of its application.
The idea to determine the fatigue strength of weldments by means fracture mechanics was originally based on the empirical observation that the major portion of the fatigue life in weldments is frequently spent in crack propagation. The present paper gives a brief overview on the basic principles of fracture mechanics-based determination of fatigue strength and on special features which have to be considered for weldments. Based on this information, the ongoing research project IBESS is introduced and briefly reviewed.
Recently two of the authors of the present paper proposed a model for a fracture mechanics
based prediction of the S–N characteristics of metallic components with large microstructural
defects and supported this by a validation exercise on tensile plates made of an aluminium
alloy AL5380 H321. Here the authors extend the study using a number of further
data sets from the literature for which data were available at different R ratios. These data
include two aluminium alloys, Al 2024-T3 and Al 7075-T6, and a ductile cast iron, EN-GJS-
400-18-LT. Despite of necessary assumptions for the compensation of partially missing
input information the results were fairly reasonable with the exception of one data set.
The authors identify high applied stress levels in combination with potential multiple crack
initiation as the probable root of the problem and propose a scheme how the model can be
extended for taking into account crack initiation.
Railway structures such as rails and axles are safety relevant components since any failure includes the risk of catastrophic derailment. This paper gives a brief overview on the most important potential failure scenarios driven by fatigue crack initiation and propagation and discusses the effects of important influencing factors such as vehicle weight and speed, track quality and environmental conditions. The present paper summarizes earlier work of the authors in this field.
Special aspects of welded components such as geometrical imperfections, inhomogeneity, strength mismatch and welding residual stresses have to be taken into account in a fracture mechanics analysis since they affect the crack driving force in the component as weil as the fracture resistance of the material. The treatment of components subjected to static loading is based on methods such as the European SINT AP procedure, which has been validated in a nurober of case studies. In the present paper the influence of strength mismatch and residual stresses on the fracture resistance and the assessment of a component are discussed.
Welding is one of the most common methods in industrial practice for joining components. Its main advantages are high speed in manufacturing combined with low costs and, usually, a high degree of flexibility, integrity and reliability. Nevertheless, welding is a highly complex metallurgical process and, therefore, weldments are susceptible to material discontinuities, flaws and residual stresses which may lead to structural failure and life time reduction. As a consequence weldments are an important field of fracture mechanics methods although its application is more complex than for homogeneous or non-welded structures. The aim of the paper is to provide an overview on the current state of fracture mechanics application to weldments. It starts by discussing the specific features which any fracture mechanics analysis of weldments has to take into account. Then, the experimental determination of fracture toughness, fatigue crack propagation and tensile properties of weldments is addressed. Finally, the analytical determination of the crack driving force in components and structural integrity assessment approaches for weldments are presented.
The paper provides an overview on the results of a German cluster project on the use of fracture mechanics to the determination of the fatigue strength of weldments with fatigue cracks originating at the weld toes. The approach includes (a) a concept for short crack propagation for which the common K concept is not applicable and the crack closure effects are still being gradually build-up, (b) a method for determining fatigue life relevant initial crack sizes as they are needed in any fracture mechanics analysis and (c) multiple cracking and crack coalescence at load levels higher than the endurance limit. The analyses are stochastically performed. Both, the endurance limit as defined for 107 loading cycles and the finite life branch of the S-N curve are determined.
Besides a brief introduction into the approach, a wide range of validation examples is presented. These comprise different weldment types (butt welds, cross joints and longitudinal stiffened plates), two steels of quite different strengths, different weld geometries due to different welding techniques (TIG, MAG), as-welded and stress relieved welds and different stress ratios varying from R = -1 to R = 0.5.
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.
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 additive manufacturing technology of Selective Laser Melting (SLM) experiences a rapid development within an increasing marked of quite different application fields. The properties of SLM materials and structures are influenced by a number of tech-nological parameters such as the metal powder (particle size, homogeneity, cleanliness), the laser tool (power, beam diameter, pulse lengths), the scanning operation (speed, sequence and orientation of melting paths), parameters of the over-all equipment (design and preheating of the base plate, currents and turbulence in the protective gas atmosphere) and, last not least, the hatching strategy including the build-up direction of the structure with respect to the loading direction of the component.
For the perspective use of SLM structures as load carrying, safety-relevant components the knowledge of their mechanical properties is necessary. It is essential to understand these in the context of the manufacturing-related features and at the back-ground of the basic characteristics of metallic materials: crystal lattice, microstructure and material defects. The paper provides an overview on factors which affect the mechanical parameters stiffness, strength, ductility, toughness, fatigue crack propagation and fatigue strength in the context of selective laser melting.
Damage development and damage tolerance of structures manufactured by selective laser melting
(2017)
The additive manufacturing technology of Selective Laser Melting (SLM) experiences a rapid development within an increasing marked of quite different application fields. The properties of SLM materials and structures are influenced by a number of tech-nological parameters such as the metal powder (particle size, homogeneity, cleanliness), the laser tool (power, beam diameter, pulse lengths), the scanning operation (speed, sequence and orientation of melting paths), parameters of the over-all equipment (design and preheating of the base plate, currents and turbulence in the protective gas atmosphere) and, last not least, the hatching strategy including the build-up direction of the structure with respect to the loading direction of the component.
For the perspective use of SLM structures as load carrying, safety-relevant components the knowledge of their mechanical properties is necessary. It is essential to understand these in the context of the manufacturing-related features and at the back-ground of the basic characteristics of metallic materials: crystal lattice, microstructure and material defects. The paper provides an overview on factors which affect the mechanical parameters stiffness, strength, ductility, toughness, fatigue crack propagation and fatigue strength in the context of selective laser melting.
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. The aim of this work is to present part of a fracture mechanics-based procedure under development which aims at replacing the tests on production-similar disks with lab tests on fracture mechanics specimens. The finite element simulation of the cracked disk considers the real thermal and mechanical loading conditions. In order to design a lab representative specimen, beside the crack driving force, expressed in terms of 𝐽-integral, also the constraint to plastic deformation e.g., stress triaxiality, at the crack-tip must be similar for the same crack in the specimen and in the disk. This has been achieved and as expected, both the highest 𝐽 -integral and constraint factor are calculated at the same location along the crack front for both disk and specimen. The results of the structural integrity assessment in the form of a Failure Assessment Diagram (FAD) show good agreement between designed specimen and disk both in terms of expected failure mode and value of the critical speed. In addition, probabilistic aspects are also considered in the calculations.
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 productionsimilar 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 part of a fracture mechanics-based procedure under development which aims at replacing the tests on production-similar disks with lab tests on fracture mechanics specimens. In particular, the rimpeeling failure mode is considered as case study. A semi-circular surface crack is modelled at the most stressed region at the diaphragm of a turbine disk, with the crack plane perpendicular to the radial direction. The crack is therefore subjected to a biaxial stress state and grows under increasing rotational speed until it triggers the rim-peeling failure. The finite element simulation of the cracked disk considers the real thermal and mechanical loading conditions. In order to design a lab representative specimen, beside the crack driving force, expressed in terms of -integral, also the constraint to plastic deformation e.g., stress triaxiality, at the crack-tip must be similar for the same crack in the specimen and in the disk. This has been achieved and as expected, both the highest -integral and constraint factor are calculated at the same location along the crack front for both disk and specimen. The results of the structural integrity assessment in the form of a Failure Assessment Diagram (FAD) show good agreement between designed specimen and disk both in terms of expected failure mode and value of the critical speed. Probabilistic aspects are also considered in the calculations.
If a component is cyclically loaded, its load carrying capacity is considerably lower than in the monotonic loading case. This general observation applies in particular to L-PBF parts. The causes of this are mainly material defects such as pores and unwelded regions (Chapter 8) and a pronounced surface roughness in the as-built condition (Chapter 9). In addition, effects due to the anisotropy of the microstructure (Chapter 6) and a complex residual stress pattern (Chapter 7) play an important role. A consequence is that common strategies of fatigue assessment cannot be transferred to L-PBF applications without modifications. Due to the inhomogeneity of the material, the determination of representative material properties and the transfer to the component is a problem, and this is also the case with regard to the consideration of defects, surface roughness and residual stresses. The chapter gives a brief introduction to these problem areas.
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.
The two-part paper series provides an overview on the state-of-the-art in the application of engineering fracture mechanics to weldments limited to butt and fillet welds with crack initiation at weld toes. In the present second part, one focus is on welding residual stresses, their characteristics and stability under cyclic loading and their effect on structural integrity. Subsequently, features will be addressed which are essential for applying fracture mechanics to overall fatigue life and fatigue strength considerations of weldments. These comprise fatigue life relevant initial crack sizes and multiple crack initiation and Propagation due to various stress peaks along the weld toe. A concept is briefly introduced which covers all these aspects.
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.
A discussion is provided on demands that must be met in order to apply fracture mechanics to the determination of overall fatigue lifetime and strength, i.e., S-N curves and fatigue limits. These comprise the determination of the cyclic crack driving force for all stages of fatigue crack propagation, in particular for the short crack stage where the crack driving force has to be determined for elastic-plastic deformation and the gradual build-up of the crack closure phenomenon. Special emphasis is put on a fatigue damage relevant specification of the initial crack size. Different approaches in the literature are discussed. Another important aspect is the adequate treatment of multiple crack propagation. Finally, the discussion is illustrated by an example of a butt weld made of a medium strength steel.
Foreword
(2018)
The subject of this Special Issue is the fracture mechanics-based determination of the fatigue strength of weldments. Except for one, all papers were written in closer or wider relation to a methodology developed within the framework of the German Project cluster IBESS. Some of them provide background or supplementary information needed in that context but which is also relevant in a wider frame of research activities. The acronym IBESS stands for the topic of this Special Issue (in German: „Integrale Methode zu Bruchmechanischen Ermittlung der Schwingfestigkeit von Schweißverbindungen). Eight partners were involved. The cluster was cooperatively founded by the German Research Foundation (Deutsche Forschungsgemeinschaft) and by the German AiF Network (Arbeitsgemeinschaft industrieller Forschungsvereinigungen) for industrial research.