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The Kitagawa-Takahashi (KT) diagram is a well-established tool in the fatigue community for the prediction of the fatigue limit of metallic materials in presence of defects. Nevertheless, its determination is associated with a large number of fatigue tests carried out on specimens with artificial defects (notches) to describe the fatigue limit-defect size relationship in the short crack regime. The preparation of the specimens and the execution of the tests is time expensive. Therefore, few phenomenological models have been introduced in the past to provide a first approximation of the KT diagram based solely on the fatigue limit for smooth specimen and the fatigue crack propagation threshold for long cracks. Despite the use of such models is widely spread, these suffer from problems related to the uncertainties of the material parameters. Furthermore, the mechanics of short cracks, which is the physical mechanism behind the concept of the fatigue limit, is not considered. This work discusses the advantages and drawbacks of using short fatigue crack propagation models for predicting the fatigue limit of flawed metallic materials. The KT diagrams for a EA4T railway axle steel in as-received and full-hardened condition are approximated by means of the cyclic R-curve method.
Fracture mechanics-based methods can be applied to the fatigue assessment of mechanical components containing defects or cracks subjected to cyclic loading. The knowledge of the crack growth behavior for short and long cracks enables the determination of both finite and infinite life regimes. Nevertheless, a first problem arises from the empirical determination of the fatigue data, which vary according to the test conditions, e.g., the test method, frequency and the stress ratio R. This is due to crack closure and further environmental phenomena affecting crack propagation behavior. A second issue regards the lack of standard experimental procedures for the determination of the fatigue crack propagation threshold ΔKth dependency on the crack size. This is problematic, since ΔKth increases with the build-up of the closure effects in the short crack regime and its inaccurate experimental determination leads to large deviations in the assessment and, even more critical, to non-conservative predictions. Aiming at providing more reliable and safer assessment procedures, the present work proposes a method based on effective crack growth data obtained at high stress ratios (R ≈ 0.8). A short-crack model based on the cyclic R-curve and CPLR data is employed for describing the development of the closure effects. The predictions are compared to established methods and validated by experimental tests.
A new simplified and effective method has been formalised to estimate the Constant Amplitude Fatigue Limit (CAFL) of stress-relieved steel welded joints subjected to uniaxial push–pull loading and failing from the weld toe. Starting from the sharp V-notch assumption of the NSIF approach and the cyclic R-curve of the material in the heat affected zone, the proposed method identifies the CAFL as threshold level of the local stress field at the V-notched weld toe in the uncracked configuration. Such threshold stress field assures the crack arrest at the V-notched weld toe, according to the cyclic R-curve analysis. The method has been validated against experimental results and proved effective for a straightforward assessment of the CAFL of welded joints, as the stable crack propagation analysis of classical fracture mechanics approaches can be avoided.
The role of defects in the fatigue strength of Wire Arc Additively Manufactured (WAAMed) Ti-6Al-4V is analysed by means of the IBESS model, a fracture mechanics short crack growth approach based on the cyclic R-curve. Pores and crack-like defects are analysed. Estimations of the role of pore shape and size agree well with published fatigue data of WAAM Ti-6Al-4V with pores. The model is also used to explain the effect of fabrication defects on the scatter of experimental data. This demonstrates that short crack growth models represent a suitable engineering tool for the fatigue assessment of defective AM materials.
The microstructure has a great influence on short fatigue crack growth in metallic materials. Laser-based Powder Bed Fusion AlSi10Mg alloys exhibit in the as-built condition a fine fibrous Si structure and a supersaturated solid solution of Si in the α-Al matrix, which is significantly modified by heat treatments starting already at temperatures under 260 °C. This study focuses on the influence of post-process heat treatments on the microstructural evolution and the resulting fatigue crack growth resistance. As compared to the as-built condition, two heat treatments at 265 °C/1 h and at 300 °C/2 h are found to be beneficial to the fatigue crack growth resistance of the investigated material.
Most of the in-service failures of welded structures are due to fatigue damage occurring in the joints. Damage tolerant approaches based on the principles of Fracture Mechanics have been shown to play a key role in this framework, as the fatigue limit is defined by the non-propagating condition of multiple defects at the weld toe. The fatigue limit assessment can be performed using the cyclic R-curve analysis which consists in comparing the driving force of a crack propagating into a component, which depends on the geometry, material and external loads, with its resistance curve, i.e. the cyclic R-curve. The crack propagation occurs whenever the crack driving force is higher than the resistance to fatigue crack propagation, while the crack is arrested in the opposite case. Consequently, this suggests that the fatigue limit of a component is defined as that stress level at which the crack driving force curve is tangent to the crack resistance curve. In the present work, the cyclic R-curve analysis has been adopted for determining the fatigue limit of stress-relieved transverse non-load-carrying joints made of S355 structural steel and subjected to fatigue axial loadings. Experimental tests have been performed to evaluate the fatigue limit of the joints. The driving force, identified by the applied Stress Intensity Factor (SIF), has been evaluated by means of linear elastic finite element analysis taking advantage of the Peak Stress Method for its rapid estimation. Based on the experimental observations that the crack initiation and early crack growth phases in welded joints occur within the Heat Affected Zone (HAZ) the cyclic R-curve has been experimentally derived for both the base metal and HAZ material.
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.
The cyclic R-curve describes the resistance of a material to fatigue crack propagation fromthe short to the long crack regimes and it is therefore an essential ingredient in any fracturemechanics-based fatigue assessment procedure. This work presents different testing proceduresemployed in the experimental determination of the cyclic R-curve, especially focusing onthe comparison with long fatigue crack propagation thresholds obtained by means of thecompression precracking load reduction (CPLR) procedure. The tests were performed on theEA4T steel considering different stress ratios. The results show a good reproducibility of thecyclic R-curves at every stress ratio and for any testing procedure. In addition, the cyclicR-curves were used in a fracture mechanics-based assessment to predict the fatigue limits ofspecimens containing micro-notches.
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.
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.
The fatigue design of metallic components is usually based on two different approaches, namely total life and damage tolerance. The former takes into account both the initiation and propagation stages. The latter is based on fracture mechanics and needs an initial defect, which propagates until the critical size under cyclic loading, provided it is large enough. In this case, a residual life rather than a total life is obtained. The overall lifetime of a cyclically loaded structure involves four consecutive stages: a) crack initiation; b) propagation of microstructurally short cracks; c) propagation of physically/mechanically short cracks; d) propagation of long cracks. Considering the propagation from the short crack regime, the damage tolerance approach can be extended to adequately calculate the total life of a component.
The fatigue strength of metallic materials containing defects depends on the non-propagation condition of small cracks emanating from these defects. In this work, the presence of mechanically short cracks from the beginning of the component's life is considered. Consequently, the methodology of analysis must be able to treat adequately local ligament yielding effects typical for short cracks and must include the thorough description of the crack closure effect up to the long-crack regime. In the analysis based on long cracks, the linear-elastic condition is mostly satisfied which allows the use of the linear elastic parameter ΔK for describing the crack driving force. On the contrary, this assumption is not adequate for mechanically short cracks because the crack depth is in the order of the plastic zone. Instead, an elastic-plastic driving force should be considered. Furthermore, the gradual build-up of the plasticity-induced crack closure effect must be considered, which implies a transition from the intrinsic (effective) threshold value, ΔKth,eff, to the long-crack threshold, ΔKth,LC.
The effective component is a material parameter which is dependent on the elastic properties and crystal lattice. The gradual build-up of crack-closure is described by ΔKth,op which is a function of the plastic properties, grain-size, environment conditions, load ratio and crack-depth. The crack closure can be characterized experimentally by the so-called cyclic R-curve. Some other crack closure effects, such as roughness or oxide-debris induced, might be incorporated as well.
The knowledge of the cyclic R-curve can be useful to determine the largest non-propagating crack size at the material fatigue limit. This is realised by means of the so-called cyclic R-curve analysis: The tangent criterion between the driving force and the cyclic R-curve define the transition between crack arrest and propagation. In this regard, a0 is defined as that crack depth which will only grow into a non-propagating crack due to the development of crack closure.
The procedure outlined briefly here has been successfully applied to the determination of the fatigue limits of steel weldments. Considering the stochastic distribution of the weld geometric parameters (namely, weld toe radius, the flank angle, and the excess weld metal) it is possible to perform a full probabilistic cyclic R-curve analysis and determine this way the statistical distribution of the initial crack size at the weld toe at the fatigue limit.
The present study deals with the experimental characterization of short crack propagation in SLM (selective-laser-melting) manufactured stainless steel. More specifically, the determination of cyclic R-curves is discussed. This describes the dependency of the crack propagation threshold on crack growth during the short crack propagation stage. For metals, the threshold, starting at a material-intrinsic value, increases until it reaches a value independent of the crack length due to crack closure phenomena which build up at that stage. The cyclic R-curve, when used in the frame of a cyclic R curve analysis, characterizes the resistance of a material to fatigue crack growth and the ability to arrest a physically short crack. Thus, it is the link between classical fatigue and fracture mechanics. In the high-cycle-fatigue range, the short crack propagation stage dominates the overall lifetime, i.e., the number of cycles until failure. Below the fatigue limit crack arrest of hitherto propagable micro-cracks will occur. The effort for the experimental characterization of the short fatigue crack propagation behavior and the cyclic R-curve is very high compared to experiments on long crack propagation. A very exact measurement of crack extension is required, since small increments need to be depicted. Pre-cracking must leave a closure free initial crack, since closure must be build up only by the cyclic R-curve. The closure-free status is achieved by compression pre-cracking. The aim of the present study is an insight into the influence of an AM process on the short crack propagation threshold. Cyclic R-curves are experimentally determined at different load-ratios for 316L austenitic steel specimens produced by SLM and conventional manufacturing. Residual stresses are measured in the crack plane and their influence on the cyclic R-curve is discussed.
The assessment of high cycle fatigue in additive manufactured (AM) components is a challenge due to complex microstructure, anisotropic material behavior, residual stresses and porosity / lack-of-fusion defects. Due to the statistical distribution of defects, a high scatter band of S-N-curves is expected. The fracture mechanics-based fatigue assessment of additive manufactured components must consider the propagation of short cracks emanating from defects.
In this work, the fatigue crack propagation resistance in the short and large crack regimes of additive and conventionally manufactured AISI 316L stainless steel is examined experimentally based on the cyclic R-curve. However, remaining residual stresses in the AM specimen lead to unexpected and dramatic crack-growth during the pre-cracking procedure.
The present study deals with the experimental characterization of short crack propagation in SLM (selective-laser-melting) manufactured stainless steel. More specifically, the determination of cyclic R-curves is discussed. This describes the dependency of the crack propagation threshold on crack growth during the short crack propagation stage. For metals, the threshold, starting at a material-intrinsic value, increases until it reaches a value independent of the crack length due to crack closure phenomena which build up at that stage. The cyclic R-curve, when used in the frame of a cyclic R curve analysis, characterizes the resistance of a material to fatigue crack growth and the ability to arrest a physically short crack. Thus, it is the link between classical fatigue and fracture mechanics. In the high-cycle-fatigue range, the short crack propagation stage dominates the overall lifetime, i.e., the number of cycles until failure. Below the fatigue limit crack arrest of hitherto propagable micro-cracks will occur. The effort for the experimental characterization of the short fatigue crack propagation behavior and the cyclic R-curve is very high compared to experiments on long crack propagation. A very exact measurement of crack extension is required, since small increments need to be depicted. Pre-cracking must leave a closure free initial crack, since closure must be build up only by the cyclic R-curve. The closure-free status is achieved by compression pre-cracking. The aim of the present study is an insight into the influence of an AM process on the short crack propagation threshold. Cyclic R-curves are experimentally determined at different load-ratios for 316L austenitic steel specimens produced by SLM and conventional manufacturing. Residual stresses are measured in the crack plane and their influence on the cyclic R-curve is discussed.
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 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.