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The net section limit load FY is a key input parameter for the accuracy of any
elastic-plastic flaw assessment procedure of the R6 type. Unfortunately available limit load
solutions are of variable quality since they have been obtained over decades by different
methods. As a consequence the results of the fracture analyses such as the critical load or
crack size are limited in their accuracy and are often significantly conservative. A further
problem is that common limit load solutions based on ligament yielding are inadequate in a
number of cases even for through crack configurations and should be replaced by some
kind of local yielding solutions. In the present paper a simple and straightforward reference
load definition is proposed instead of the limit load which strictly corresponds to a ligament
yielding parameter Lr = 1 in the R6 Routine and similar approaches such as SINTAP and
FITNET. This can be determined by finite element simulation for any geometry. In addition to
a previous study on thin wall notched plates the method is applied to plates containing
shallow semi-elliptical surface cracks. The results demonstrate that the approach provides a
suitable extension and improvement of the existing methods.
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.
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.
Recently three of the authors of this paper presented analytical solutions for reference loads of plate geometries with semi-elliptical surface cracks subjected to tension, bending, combined tension-bending and biaxial tension. These solutions were shown to provide more accurate crack driving force estimates than the conventional limit load solutions available in the literature, and the method behind them allowed for a wider application range. Within the present paper a methodology for the fracture analysis of thick-wall pressurized pipes using the R6 assessment method and considering both, biaxial and combined tension-bending loading is developed and validated. The analyses are carried out analytically, and the comparison between the predicted critical loads and experimental burst test failure loads shows satisfying agreement, this way demonstrating the potential of the proposed method.
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.
The burst of a disc in rotating machinery can cause catastrophic damage of the equipment and, more importantly, it can represent a mortal threat to anyone in the sphere of influence of the event. In order to minimize the danger associated to a rotating component failure, burst testing is required by the authorities in order to set safety margins to the normal operating speeds. Moreover more accurate predicting tools are required for designing the components. This paper presents the results of a numerical and analytical study on the assessment of the crack driving force for discs containing surface flaws. The aim is to provide a simple, though reliable, tool in order to be able to calculate the possible dangerous in-service speed for a rotating component and, therefore, to set burst margins above the normal operating conditions of the equipment. An R6-like flaw assessment procedure is adopted considering different assumptions in the definition of the critical speed and the analytical predictions are compared with the results of elastic-plastic finite element analysis of disc. In particular, the validity and potentiality of the method is proved for surface flaws in different positions in the disc.
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 presentation provides a brief overview on results obtained in the context of fracture mechanics based flaw assessment particularly in the context of short crack propagation. Background is the planned updating of international fitness-for-service procedures such as BS 7910. Specific topics addressed are the determination of the cyclic elastic-plastic crack driving force, the description of the gradual build-up of the crack closure phenomenon at the short crack stage, cyclic R curve analysis and residual stresses.
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.
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.
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.
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.
On July 9, 2008 a high speed train derailed in Cologne main Station, Germany at a low speed because an axle was broken. Fortunately, the derailment happened at a low speed so that nobody was injured. The reason for the broken axle was investigated and it turned out that most likely large inclusions located shortly undemeath the surface in a T-transition were the origin of the final crack. Basing on that result, a systematic investigation on existing safety assessments of railway axles was performed. This results in an analysis of the production process of axles and in a critical review of existing of existing assessments. Improvements and future developments are outlined.
The safety assessment of railway axles is based on a two-stage approach: fatigue strength design and regular inspections which, in terms of a general safety philosophy refer to safe-life and damage tolerance concepts. Starting with a recent failure case, a broken axle of a German high speed train, a discussion is presented on issues of both safety levels. These include ideas for finite life design, the treatment of in-service effects on the fatigue strength due to flying ballast damage and corrosion pits, the effect of corrosion on fatigue crack initiation and propagation, potential effects of non-metallic inclusions in steels, the way to detect them by quality control measures and reliability aspects of non-destructive testing with respect to the detection of fatigue cracks. Proposals are made how the safety level could be further improved.
The paper gives an overview on safe life and damage tolerance methods applied to railway axles. It describes failure scenarios due to fatigue crack initiation and propagation. Besides common aspects of design, specific features such as corrosion and impact damage from flying ballast are discussed which may reduce the fatigue strength of axles during service. Potential effects of non-metallic inclusions from the steel manufacturing process are addressed in the context of the very high number of loading cycles railway axles are designed for. With respect to damage tolerance general lines of fracture mechanics residual lifetime analyses are introduced. More specific discussion is provided on aspects such as the threshold value of fatigue crack propagation and reliability aspects of non-destructive inspection.
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.
Two of the authors of the present paper proposed a definition of a reference load F0 which can be used as an alternative option to the common limit load for cases where the definition of the latter might be problematic in the frame of flaw assessment procedures such as R6, BS 7910, SINTAP or FITNET. The reference load is defined as that load at which the ligament yielding parameter Lr approaches one. F0, in general, varies along the crack front. It has to be obtained by finite element analyses but the results can be approximated by analytical expressions. In a previous study of the authors such a solution was presented for tension loaded plates with semi-elliptical surface cracks. In the present paper it is extended to pure bending and to combined bending and tension.
The acronym IBESS stands for "Integrale Bruchmechanische Ermittlung der Schwingfestigkeit von Schweißverbindungen" which, translated from German, means "integral fracture mechanics determination of the fatigue strength of welds". the method introduced in this study is the outcome of a German Research cluster in which eight partners were involved. A list of them is found at the end this study. The IBESS method is characterized by a number of partially novel aspects and elements of fracture mechanics applied to the evaluation of fatigue stength of welds. The most important ones are: (a) Determination of fatigue crack propagation for mechanically/physically short and long cracks. (b) Determination of an elastic-plastic crack driving force for the treatment of mechanically short cracks. To that purpose an analytical expression for the cyclic J-integral was developed and validated against finite element results. (c) The gradual build-up of the crack closure phenomenon is determined by using cyclic R-curves which describe the crack size dependency of the fatigue crack propagation threshold in the physically short crack growth regime. (d) A physically meaningful initial crack size is defined for total life consideration. It is based on a two-criteria approach. Based on a cyclic R-curve analysis, the crack size at crack arrest is determined as a lower bound. If, however, a pre-existing crack-like defect is larger than this, its dimensions define the initial crack size. (e) Multiple crack propagation at the weld toe is considered. (f) In conjunction with this, the variation of the weld toe geometry is considered in a stochastic model. (g) As a result, both the fatigue limit (defined for 107 loading cycles) and the finite life (high cycle) fatigue S-N curve are obtained statistically. (h) At various analysis steps, parametric equations have been developed which allow for analytical calculations instead of complete stochastic analyses based on finite elements which are unrealistic even at present. (i) The method has been validated with a large number of S-N curves including two materials, three weldment types with two geometries, each referring to differnt manufacturing technologies and the as-welded and stressrelieved state. (j) Althrough not finally solved, an extended discussion is provided on the issue of welding residual stresses including their redistribution under cyclic loading. (k) A number of simplifications is proposed at lower analyses levels which, however, partly lack complete validation by now.
Any fracture mechanics based determination of the fatigue strength of weldments requires different input information such as the local weld geometry and material data of the areas the crack is passing through during its propagation. The latter is so far not a trivial task as the fatigue crack is usually initiated at the weld toe at the transition from the weld metal to the heat affected zone and it subsequently propagates through the different microstructures of the latter to eventually grow into the base material and to cause final fracture. This paper describes how the material input information has gained particularly for heat affected zone material by thermo-mechanically simulated material specimens for two steels of quite different static strength. The data comprise the cyclic stress-strain curve, the crack closure effect-corrected crack growth characteristics, long crack fatigue crack propagation thresholds, the dependency of the parameter on the crack length and monotonic fracture resistance. The substantial experimental effort was necessary for the validation exercises of the IBESS approach, however, within the scope of practical application more easily applicable estimating methods are required. For that purpose the paper provides a number of appropriate proposals in line with its check against the reference data from the elaborate analyses.
The so-called cyclic R curve, i.e. the crack size dependence of the fatigue crack propagation threshold in the physically short crack regime, is a key parameter for bringing together fatigue strength and fracture mechanics concepts. Its adequate determination is of paramount importance. However, notwithstanding this relevance, no test guideline is available by now and only very few institutions have spent research effort on cyclic R curves so far. The aim of the present paper is to give an overview on the state-of-the-art. Besides an introduction into the basic principles, the discussion will concentrate on the experimental determination on the one hand and questions of its application on the other hand.
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.
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.
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 present paper provides a discussion on all these topics and it offers solutions for it. The authors present an analytical solution of a Delta J based crack driving force based on an R6 type approach but modified for cyclic loading. The gradual build-up of the crack closure effect is modelled by the so-called cyclic R curve which describes the crack size dependency of the fatigue crack propagation threshold in the short crack regime. It is explained how the cyclic R curve is experimentally determined and how it can be estimated by a modified Kitagawa-Takahashi approach.
The Topic of the presentationis a discussion on defects which can cause failure in cyclically loaded metallic components. Although also touching Features such as material defects such as pores or micro-shrinkages, etc. and geometric defects such as surface roughness and secondary notches (which are not considered in the design process) which origin in manufacturing, and others the presentation concentrates on non-metallic inclusions. It is prefaced by an introduction to the life cycle of a fatigue crack from initiation up to fracture. Special emphasis is put on the fact that only cracks which are not arrested during one of their distinct Propagation stages can grow to a critical size.
According to the definition of the ASM handbook [1,3], a defect is "an imperfection. that can be shown to cause failure by a quantitative analysis and that would not have occurred in the absence of the imperfection". The topic of the present three-part review is a discussion of defects which can cause failure in cyclically loaded structures. The features discussed comprise material defects such as non-metallic inclusions, pores or micro-shrinkages, etc. and geometric defects such as surface roughness and secondary notches which have their origin in manufacturing, and defects such as surface damage due to scratches, impact events or contact fatigue as well as corrosion pits which arise in service. In this first part, the discussion is prefaced by an introduction to basic aspects which are essential for a deeper understanding of the characteristics and mechanisms how the defects influence fatigue crack initiation and propagation. These include the life cycle of a fatigue crack from initiation up to fracture, crack arrest, multiple crack initiation and coalescence, and the material and geometrical properties affecting these.
This third part of the review on defects as root cause of fatigue failure addresses cavities (pores, micro-shrinkages, unmelted regions), defective microstructures and microcracks as material defects and defects due to local damage during manufacturing, service and maintenance such as dents, scratches and localized corrosion. In addition, damage due to contact fatigue and the effect of surface roughness are discussed in the context of fatigue failure. Also addressed is the competition between different kinds of defects in controlling the initiation and early growth of fatigue cracks.
Defects as a root cause of fatigue failure of metallic components. II: Non-metallic inclusions
(2019)
This second part of the review on defects as root cause of fatigue failure comprises the origin, the nature and the effects of non-metallic inclusions. Topics addressed are the different kinds of inclusions formed during the manufacturing process, various types of mis-match causing local stresses and, as a consequence, fatigue crack initiation, and effects of characteristics such as size, morphology, localization, spatial distribution and orientation of the defects on the fatigue behavior. Methods for inclusion counting and sizing are discussed along with statistical aspects necessary to be considered when evaluating structural components.
This book provides a comprehensive and thorough guide to those readers who are lost in the often-confusing context of weld fatigue. It presents straightforward information on the fracture mechanics and material background of weld fatigue, starting with fatigue crack initiation and short cracks, before moving on to long cracks, crack closure, crack growth and threshold, residual stress, stress concentration, the stress intensity factor, J-integral, multiple cracks, weld geometries and defects, microstructural parameters including HAZ, and cyclic stress-strain behavior. The book treats all of these essential and mutually interacting parameters using a unique form of analysis.
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.
Analytical flaw assessment
(2018)
The paper provides a review on analytical flaw assessment methods with the focus on fracture under monotonic loading and fatigue crack propagation. The first topic comprises linear elastic as well as elastic-plastic fracture mechanics approaches. It essentially follows their historical development. Topics which are separately discussed are reference/Limit loads, the treatment of secondary stresses, strength mismatch, constraint, unstable crack propagation (monotonic R-curve analyses) and statistical aspects. With respect to fatigue crack propagation the analytical treatment of crack closure and constraint and the Determination of the cyclic elastic-plastic crack driving force is discussed. Finally, cyclic Rcurve analyses are briefly addressed.
The yield or limit load is a key parameter with respect to the accuracy of flaw assessment based on R6 type procedures such as the R6 routine, the SINTAP and FITNET method, the standard BS 7910 and others. In a number of previous papers two of the present authors proposed the use of a reference load instead of the common limit load, which not only provided more exact fracture mechanics predictions, but showed also a wider and more general application range than the conventional parameter. Here the method has been extended to biaxial tensile loading and it has been successfully validated by a thorough comparison with finite element results and alternative solutions available in the literature.
The determination of the fatigue life in technical alloys containing large and small defects must rely on a propagation model which accounts for short and long crack growth. Recently an analytical model which incorporates propagation in the short crack regime and plastic correction for the crack driving force has been presented by two of the authors.
This work is intended to show further validation of the model, taking into account data sets for different materials with different testing conditions.
Despite the assumptions about missing parameters, the value of which had to be taken from the literature, the predictions showed a fairly good approximation of the fatigue lives. A possible interpretation of the results in terms of multiple crack initiation and propagation at higher loads is proposed.
In the design approval of transport packages for radioactive materials, the mechanical and thermal safety assessment is carried out in Germany by competent authority BAM. In recent years BAM was involved in several licensing procedures of new spent fuel and HLW package designs, where the cask body is of Ductile Cast Iron (DCI). According to IAEA regulations package designs have to fulfill requirements for specific conditions of transport. Type B(U) packages must withstand the defined accident conditions of transport. The temperature range from -40°C up to the operational temperature has to be considered. For the cask material DCI, it is necessary to determine safety against brittle fracture. The German guideline BAM-GGR 007 defines requirements for fracture mechanics of packagings made of DCI. Due to complex cask body structure and the dynamic loading a fracture mechanical assessment by analytical approaches is not always possible. Experience of recent design approval procedures show that the application of numerical calculations are applicable to determine the stresses and stress intensity factors in the cask body. At the first step a numerical analysis has to be done to identify
the loading state at the whole cask body. Secondly an analysis of a detail of the cask body is made considering the displacement boundary conditions of the global model. An artificial flaw is considered in this detailed model to calculate the fracture mechanical loading state. The finite element mesh was strongly refined in the area of the flaw. The size of the artificial flaw is based on the ultrasonic inspection acceptance criteria applied for cask body manufacture. The
applicant (GNS) developed additional analysis tools for calculation of stress intensity factor and/or J-Integral. The assessment approach by BAM led to the decision to develop own tools to the possibility for independent proof of the results.
The paper describes the authority assessment approach for DCI fracture mechanics analysis. The validation procedure incl. the development of own tools is explained. BAM developed a postprocessor to determine the fracture mechanical loads. A horizontal 1 m puncture bar drop test is used to give a detailed description of the assessment procedure.
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.
In a number of previous papers, the authors have proposed a model for fracture mechanics based prediction of the S-N characteristics of metallic components with large microstructural defects. Here, an extension to materials that do not show large defects onto the fracture surfaces is provided. In such cases, an approach based on a so-called cyclic R-curve analysis is proposed for the determination of the initial flaw size, which has to be used in the calculation of fatigue crack propagation. The principle is explained and demonstrated by a first application to a welded joint.
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.
A discussion is provided on the relation between non-destructive testing (NDT) and fracture mechanics. The basic tasks behind this are to guarantee the safety of a component at a potential hazard loading event, to specify inspection intervals or, alternatively, of demands on NDT for a fixed inspection regime, to plan accompanying measures for cases of temporary continued operation of structures in which cracks have been detected, and, finally, fatigue strength considerations which take into account initial defects.
A fracture mechanics model which shall be applied to the fatigue strength determination of weldments has to focus on various aspects such as: (a) the description of mechanical and physical short fatigue crack extension which is characterised by yielding conditions which do not permit the application of the common ΔK concept and by the gradual build-up of the crack closure effect, (b) a consistent methodology for determining the initial crack size, (c) based on this, the determination of a fatigue limit, (d) the treatment of multiple crack propagation at load levels above this limit, (e) the variation of the local geometry along the weld toe, and (f) statistical effects.The paper gives alimited overview of the work the authors did in this field during the last years within the German project cluster IBESS. A model is presented and briefly discussed which covers the questions above.
In the approval procedure of transport packages for radioactive materials, the mechanical and thermal safety assessment is carried out in Germany by competent authority BAM. In recent years BAM was involved in several licensing procedures of new spent fuel and HLW package designs, where the cask body was made of Ductile Cast Iron (DCI). According to IAEA regulations package designs have to fulfill requirements for specific conditions of transport. Type B(U) packages must withstand the defined accident conditions of transport. The temperature range from -40°C up to the operational temperature has to be considered. For the cask material DCI, it is necessary to determine the brittle fracture behavior. The German guideline BAM-GGR 007 defines requirements for the fracture mechanics of DCI. Due to complex structure of the cask body and the dynamic loading a fracture mechanical assessment in an analytical kind is not always possible. Experience of recent design approval procedures show that the application of numerical calculations are applicable to determine the fracture mechanical load in the cask body. At the first step a numerical analysis has to be done to identify the loading state at the whole cask body. Secondly an analysis of a detail of the cask body is made considering the displacement boundary conditions of the global model. An artificial flaw is considered in this detailed model to calculate the fracture mechanical loading state. The finite element mesh was strongly refined in the area of flaw. The size of the artificial flaw is characterized by the ultrasonic inspection used for the quality assurance of the package. The applicant developed additional analysis tools for calculation of stress intensity factor and/or J-Integral. The assessment approach by BAM led to the decision to develop own tools to the possibility for independent check of the results.
The paper describes the authority assessment approach for the DCI fracture mechanics analysis. The validation procedure incl. the development of own tools is explained. BAM developed a post-processor called JINFEM to determine the fracture mechanical loads. The regulatory 1 m puncture bar drop test is used to give an example of the assessment procedure.
The net section limit load FY necessary for assessment at static loading is a key input for the accuracy of any elasticplastic flaw assessment procedure of the R6 type. Unfortunately available limit load solutions are of variable quality since they have been obtained over decades by different methods. As a consequence the results of the fracture analyses such as the critical load or crack size are limited in their accuracy and are often significantly conservative. Further, common limit load solutions based on ligament yielding are inadequate in a number of cases even for through crack configurations and should be replaced by some kind of local yielding solutions. In the present paper a simple and straightforward reference load definition is proposed instead of the limit load which strictly corresponds to a ligament yielding parameter Lr = 1 in the R6 Routine and similar approaches such as the European SINTAP and FITNET methods. This can be determined by finite element simulation for any geometry. In addition to a previous study on thin wall notched plates the method is applied to plates containing shallow semi-elliptical surface cracks. The results demonstrate that the approach provides a suitable extension and improvement of the existing methods.
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.
Based on a large set of 2D finite element analyses, parametric equations for weld toe stress concentration factors and through-thickness stress profiles are provided for butt-welded plates. These cover Single-Vand Double-V joints subject to tensile and bending loading. Compared to the most widespread solutions in the literature, which have also been tested against the finite element data in this work, the application range is extended particularly with respect to the weld toe radius(0.1≤ρ≤4 mm)andangle(10 °≤α≤60 °). Furthermore, two values of excess weld metal are considered (h=0.75;2.5mm). The analyses are performed for a plate thickness of 10 mm. Besides the extended validity range, the proposed equations show also an improved accuracy compared to the existing solutions.
Semi-probabilistic method for residual lifetime of aluminothermic welded rails with foot cracks
(2016)
One of the most frequent and dangerous failure modes in continuous welded rails is fatigue crack Propagation terminated by brittle fracture. Due to the brittleness of the weld material and HAZ and the scatter in its mechanical properties, a statistical approach is necessary. The paper deals with surface cracks at the foot base of aluminothermic welded rails, developing a probabilistic methodology for determining the day by day prospective failure probability. The investigations presented here comprise weld material characterization, simulation of fatigue crack propagation and finally the determination of the failure probability using the Monte Carlo method. The effect of various parameters, such as axle weight, Initial crack size, residual stresses, fatigue crack propagation threshold and date of inspection were analyzed.
The results show that, independent of the date of the last inspection, almost any failure event happens in wintertime. This is in accordance with practical experience. However, from the proposed analysis it is evident that the main parameter controlling rail fracture is not only the minimum local temperature, but the temperature range over the whole year. Finally, the results are compared to the standard rail classification method.
Starting from an introduction into important Basic questions of failure analysis and fracture mechanics, the author specifies what kind of questions in failure analysis can be effectively solved by fracture mechanics (and which can't). He illustrates his discussion with a number of case studies. Much more pronounced than in the design stage the benefit of fracture mechanics in failure analysis depends on ist accuracy. This is limited by both, intrinsic factors of the method and the availability and quality of the input information. The author discusses the various aspects and provides the participants with background information helpful for better understanding the prospects and limitations of fracture mechanics in failure analysis and the conditions of its application.
The paper provides a discussion on damage tolerance options applied to railway axles and factors influencing the residual lifetime as well as the required inspection interval. These comprise material properties such as the scatter of the da/dNΔK curve, the fatigue crack propagation threshold ΔKth and the toughness of the material. Parameters affecting axle loading such as the press fit, rotating bending, load history and mixed crack opening modes are discussed. Finally the influence of the initial crack geometry on residual lifetime is simulated.
The aim of this paper is a collection of stress intensity factor solutions for cracks in railway axle geometries which the authors of the present special issue developed and/or used for damage tolerance analyses. These solutions comprise closed form analytical as well as tabled geometry functions and they refer to solid as well as hollow axles and various crack sites such as the T- and V-notch and the axle body.
The fatigue crack propagation threshold ΔKth is of paramount importance for any kind of damage tolerant design, but in contrast to this importance, the determination and application of the parameter is not on the firm ground as previously assumed. The paper discusses questions of its experimental determination as well as of its application to components. In both fields, new questions have been raised with the potential to challenge or modify long-standing knowledge. Against this background, the paper is an attempt to systematize the established knowledge as well as questions and open issues.
The paper deals with the prediction of the fatigue Limit of notched specimens. Some authors in the literature have shown that this issue can be solved by employing an approach based on critical distances, others used elastic fracture mechanics. In this paper the fatigue limit of notched specimens is given by the non-propagating condition of mechanically small surface cracks. According to the so-called cyclic R-curve method, the crack driving force of a growing small crack is compared to its resistance force, which incorporates the gradual build-up of crack closure. The fatigue limit is determined by that applied nominal stress, for which the tangency condition of crack driving and resistance force is satisfied. The approach has been modified to incorporate plasticity effects in the mechanically short crack Regime and it has been applied to a mild and a high-strength steel, in case of an infinite plate with circular hole under remote tensile stress. The method has been successfully applied to the evaluation of fatigue notch-sensitivity in case of surface roughness.
The paper provides an overview on material defects which may serve as fatigue crack initiation sites and can cause final fatigue failure of a component. These comprise nonmetallic inclusions in Steel and aluminum alloys, cavities such as pores, micro-shrinkages and un-welded regions in cast, sinter and additively manufactured alloys, graphite nodules, shrinkages and other items in modular cast iron, regions of defective microstructure, microcracks and secondary notches such as undercuts and surface roughness. Besides their origin, the effect and mechanisms on fatigue crack initiation and propagation are discussed.
The considerations are proceeded and accompanied by a Brief discussion of some Basic aspects such as the stages of crack propagation along their length scale, the overcoming of crack arrest and the question when a secondary notch can be treated as a crack.
The two-part paper provides an overview on the state-of-the-art in the application of engineering fracture mechanics to weldments. This, of course, cannot be exhaustive but is limited to butt and fillet welds with crack initiation at weld toes. In the present first pari, the authors briefly focus on the susceptibility of welds to cracks and other defects. Following this, they discuss in more detail the consequences of material inhomogeneity across the weld for fracture mechanics. Inhomogeneity causes scatter in fracture toughness and strength mis-match effects which both have to be considered in fracture toughness testing, crack driving force determination and fracture assessment of welded components. Part 2 of the paper series will add a discussion of welding residual stresses and questions of applying fracture mechanics to residual as well as total lifetime estimation of welds under cyclic loading.
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.
In the framework of the fatigue assessment of welded components, several methods are available in design standards such as the nominal stress, hot-spot stress, notch stress and linear elastic fracture mechanics approaches. The present paper aims at comparing two advanced local approaches for the fatigue strength assessment of different welded joints made of steel. The first one is IBESS which is based on short crack fracture mechanics. The second one is the PSM which instead involves the strain energy density approach. Both methods will be briefly presented, and the fatigue life prediction results discussed. The results obtained for the joint geometries considered in this work show advantages and drawbacks of the approaches, which are thoroughly analysed as well.
The effect of the environmental conditions on the threshold against fatigue crack propagation
(2022)
The threshold against fatigue crack propagation (ΔKth) is a crucial parameter for the damage tolerance assessment of engineering components subjected to cyclic loading and it is composed by two distinct components, one intrinsic, dependent on the elastic material properties and the lattice type, and one extrinsic, related to the occurrence of crack closure effects. An important issue is that several factors can influence ΔKth and, in general, the fatigue crack propagation behavior. In this work, the influence of the experimental procedure, air humidity, stress ratio and test frequency on da/dN-ΔK data has been investigated. Results are discussed with their potential causes and consequences on the calculations of the residual lifetime.
The Kitagawa-Takahashi (KT) diagram is a proven concept for describing the fatigue limit in presence of a defect or crack. It can be determined empirically with great experimental effort. It can also be estimated by means of the El Haddad relationship if the endurance limit and the long fatigue crack propagation threshold are available in reasonable accuracy. A third option is the determination using the cyclic R-curve, which describes the dependency of the fatigue crack propagation threshold on the crack growth at the short crack propagation stage. This can be experimentally determined using a closure-free initial pre-crack. It can then be applied to the determination of crack arrest for a given applied load and a given defect or crack size. Compared to the other two methods mentioned above, this option has considerable advantages: It can be applied to any component and any stress ratio. It allows the treatment of multiple cracks and provides estimations of the S-N curve in the finite life regime as well as at the endurance limit. Compared to the empirical determination of the KT diagram, the experimental effort is significantly lower and compared to the El Haddad approach it avoids problems such as the use of non-conservative long fatigue crack propagation thresholds (when the conventional load reduction method is applied to materials prone to corrosion) and the mathematical predetermination of the curve shape. The work introduces the method and provides a critical discussion as well as quantitative comparison between the different methods.
Additive manufacturing (AM) is becoming increasingly important in engineering applications due to the possibility of producing components with a high geometrical complexity allowing for optimized forms with respect to the in-service functionality. Despite the promising potential, AM components are still far from being used in safety-relevant applications, mainly due to a lack of understanding of the feedstock-process-properties-performance relationship. This work aims at providing a full characterization of the fatigue behavior of the additively manufactured AISI 316L austenitic stainless steel and a direct comparison with the fatigue performance of the wrought steel. To this purpose, a set of specimens has been produced by laser powder bed fusion (L-PBF) and subsequently heat treated at 900 °C for 1 hour for complete stress relief, whereas a second set of specimens has been machined out of hot-rolled plates. Low cycle fatigue (LCF) and high cycle fatigue (HCF) tests have been conducted for characterizing the fatigue behavior. The L-PBF material had a higher fatigue limit and better finite life performance compared to wrought material. Both, LCF and HCF-testing revealed an extensive cyclic softening.
The application of fracture mechanics to the determination of the fatigue behavior of weldments is discussed with the focus on classic fatigue, i.e., the overall fatigue life and the fatigue strength in terms of an S-N curve and the endurance limit. The following issues are addressed: specific features of short fatigue crack propagation, an adequate initial crack size, multiple crack propagation and its statistical treatment as well as welding residual stresses. As an example, an approach of the authors is applied to the determination of FAT classes for a butt weld with varying weld toe geometry.
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.
This article is an outcome of a workshop on Fatigue of Additive Manufactured Metallic Components jointly organized by the Federal Institute for Materials Research and Testing (BAM) Berlin, Germany and the National Institute of Standards and Technology (NIST) Boulder, CO, U.S.A. The aim of the workshop was a comprehensive discussion of the specific aspects of additively manufactured (AM) components in regard to failure under cyclic loading. Undoubtedly, a better understanding and the further development of approaches for damage tolerant component design of AM parts are among the most significant challenges currently facing the use of these new technologies.
This article presents a thorough overview of the workshop discussions. It aims to provide a review of the parameters affecting the damage tolerance of AM parts with special emphasis on the process parameters intrinsic to the AM technologies, the resulting defects and residual stresses. Based on these aspects, concepts for damage tolerant component design for AM are reviewed and critically discussed.
The safe fatigue design of metallic components fabricated by additive manufacturing (AM) is still a largely unsolved problem. This is primarily due to (a) a significant inhomogeneity of the material properties across the component; (b) defects such as porosity and lack of fusion as well as pronounced surface roughness of the asuilt components; and (c) residual stresses, which are very often present in the as‐built parts and need to be removed by post‐fabrication treatments. Such morphological and microstructural features are very different than in conventionally manufactured parts and play a much bigger role in determining the fatigue life. The above problems require specific solutions with respect to the identification of the critical (failure) sites in AM fabricated components. Moreover, the generation of representative test specimens characterized by similar temperature cycles needs to be guaranteed if one wants to reproducibly identify the critical sites and establish fatigue assessment methods taking into account the effect of defects on crack initiation and early propagation. The latter requires fracture mechanics‐based approaches which, unlike common methodologies, cover the specific characteristics of so‐called short fatigue cracks. This paper provides a discussion of all these aspects with special focus on components manufactured by laser powder bed fusion (L‐PBF). It shows how to adapt existing solutions, identifies fields where there are still gaps, and discusses proposals for potential improvement of the damage tolerance design of L‐PBF components
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.
This paper presents the application of short crack propagation models based on the cyclic R-curve for assessing the fatigue strength of additively manufactured (AM) materials containing fabrication defects. Chapetti’s and IBESS models were implemented in combination with Murakami’s √area parameter, considering recently published data on laser powder bed fusion processed AISI 316L stainless steels. Estimated S-N curves and Kitagawa-Takahashi diagrams predict fairly well the experimental data, especially the origin of the failure from internal or surface defects. These results provide an indication that the methods based on the cyclic R-curve constitute suitable tools for fatigue behavior assessment of AM materials.
Determination of fatigue crack propagation thresholds for steel in presence of environmental effects
(2021)
The experimental determination of the resistance to fatigue crack propagation in steel, particularly in the socalled near-threshold regime, is a crucial issue for safety-relevant components which are designed to operate for a large number of loading cycles before undergoing periodic inspections. This work summarizes the most relevant results of extensive experimental campaigns conducted at BAM and IPM over the last years, which have been devoted to the determination of fatigue crack propagation characteristics on medium and high strength steels. The influence of environment, oxide-induced crack closure and test methodologies in the near-threshold regime are discussed.
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.
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.
The presentation provides a discussion and damage tolerant assessment of metallic AM components. In the focus are problems of the determination of representative material data, the effect of material defects and residual stresses. Starting with the actual state-of-the-art in the field, options and possibilities of a damage tolerant design for AM are discussed.
Using the case study of a fail-safe design criterion for a steering knuckle of a commercial vehicle, the effect of stiffness/constraint on the crack driving force in the component is discussed. The problem arises when assessment procedures such as R6, BS 7910 or SINTAP/FITNET are applied in conjunction with substitute geometries for determining the model parameters K-factor and limit load (or a substitute for the latter), as it is common practice. In the example, the conservatism was so pronounced that this procedure was in fact unusable. A way out could be the finite element-based determination of the model parameters and their use in the analytical framework. This procedure is useful and effective if the finite element-based calculations are used in parameter sensitivity analyses.
The impact of crack closure and environmental effects on the experimental determination of the fatigue crack propagation threshold is a major problem for the assessment of cyclically loaded components, especially at low stress ratios 𝑅. In this work, the influence of the experimental procedure and air humidity on d𝑎∕d𝑁 − 𝛥𝐾 data at different 𝑅 is discussed. Unlike the results at 𝑅 = −1, the threshold values obtained at 𝑅 ≈ 0.8, i.e. under negligible crack closure levels, show a very small scatter band regardless of the variation of the test parameters and environmental conditions.
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.
In 2015, the University of Manchester hosted a workshop (‘Mind the Gap’) aimed at identifying gaps in a number of structural integrity fitness-for-service procedures, including R5, R6, BS 7910 and API/ASME. The findings were subsequently summarised in a journal paper and shared with the relevant stakeholders. A second workshop, this time hosted by the University of Bristol in 2017, was intended to build on the findings of the earlier event, identifying which gaps had been filled, which remain and whether new ones have been identified in the meantime. ‘Mind the Gap 2’ was wide-ranging, including consideration of failure by fracture, fatigue crack growth, hightemperature creep and environmentally assisted crack growth, along with the use of innovative techniques to follow the progress of crack growth from the atomic to the macroscopic scale. A summary of the whole event is thus outside the scope of a single paper, so here we concentrate mainly on advances in fracture assessment, on the interface between inspection and ECA, and on how developments are being incorporated into structural integrity procedures. There is a particular emphasis on the energy transition in the UK, where the planned energy mix will include both nuclear power and offshore wind.
The knowledge of fatigue crack propagation data in terms of their effective values is important for a conservative and safe life assessment of components subjected to cyclic loading. To overcome issues related to the precise consideration of the crack-closure effects on experimental data obtained at small R ratios, closure-free data have been obtained at R ≈ 0.8 by different experimental procedures. The statistical analysis of the intrinsic fatigue crack propagation threshold obtained experimentally has shown a small data scatter and good agreement between procedures. When compared with effective values obtained from analytical corrections of closure-affected data, the data obtained at R ≈ 0.8 should lead to a conservative life estimation.
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.
Design methodology of vessel produced by L PBF stainless steel using representative specimens
(2022)
This work presents the preliminary results of an ongoing project with a double objective: on the one hand, the characterisation of the mechanical properties against fatigue damage of an additively manufactured 316 stainless steel produced by laser powder bed-based (L-PBF) technology; on the other hand, the implementation of numerical simulation techniques able to predict the mechanical behaviour of the material in order to optimise and reduce the design costs of vessels used in the chemical sector. The current state of the work developed in this research framework allows showing the first batch of experimental results of crack propagation rate (FCGR) and high cycle fatigue (HCF) tests. The geometry of the vessels studied presents three clearly differentiated regions, either in terms of thickness (11-15 mm) or concerning the inclination of the walls to the direction of manufacturing (0º - 45º). The experimental campaign carried out so far allows identifying the differences in behaviour when comparing different extraction locations around the vessel. This is due to the variations in thermal cycles that the deposited material undergoes during the manufacturing process. Therefore, this causes variations in the microstructure which lead to changes in the response of the material. In this work, these differences are analysed qualitatively and quantitatively from the results of FCGR and HCF, thus allowing to locate the regions with the highest risk in terms of structural integrity against fatigue. This preliminary phase together with the numerical simulation of the additive manufacturing process are key to achieving a reliable description and modelling of the material. The latter will make it possible to address the priority aim of this project, involving the manufacture of independent samples whose properties are representative of the original material extracted from the reference vessels. It is, therefore, a comprehensive methodology for the design of additively manufactured components based on the localised fatigue mechanical properties of representative specimens.
The robust determination of the threshold against fatigue crack propagation DKth is of paramount importance in fracture mechanics based fatigue assessment procedures. The standards ASTM E647 and ISO 12108 introduce operational definitions of DKth based on the crack propagation rate da/dN and suggest linear fits of logarithmic DK– da/dN test data to calculate DKth. Since these fits typically suffer from a poor representation of the actual curvature of the crack propagation curve, a method for evaluating DKth using a nonlinear function is proposed. It is shown that the proposed method reduces the artificial conservativeness induced by the evaluation method as well as the susceptibility to scatter in test data and the influence of test data density.
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.