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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.
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.
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.
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 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.
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.
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.
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 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 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.
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 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.
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.
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.
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.
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 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.
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.
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.
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 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.
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.
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.
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.
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 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.
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.
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.
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.
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.
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.
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 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.
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 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.
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.
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 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.
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.
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 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.
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 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 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 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.
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.
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.