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About this book

This volume contains the proceedings of the XIX International Colloquium on Mechanical Fatigue of Metals, held at the Faculty of Engineering of the University of Porto, Portugal, 5-7 September 2018. This International Colloquium facilitated and encouraged the exchange of knowledge and experiences among the different communities involved in both basic and applied research in the field of the fatigue of metals, looking at the problem of fatigue exploring analytical and numerical simulative approaches.

Fatigue damage represents one of the most important types of damage to which structural materials are subjected in normal industrial services that can finally result in a sudden and unexpected abrupt fracture. Since metal alloys are still today the most used materials in designing the majority of components and structures able to carry the highest service loads, the study of the different aspects of metals fatigue attracts permanent attention of scientists, engineers and designers.

Table of Contents


Microstructural Aspects of Fatigue and Thermal and Environmental Fatigue


Chapter 1. Microscopic Strain Localization of Ti-6Al-4V Alloy Under Uniaxial Tensile Loading

In this paper, Plate specimens for tensile tests with two different microstructures (as-received and heat treated) were studied. Micromechanical modelling by using a representative volume element has been adopted to investigate the tensile flow behavior of Ti-6Al-4V alloy. Voronoi tessellation model and actual microstructure model were developed to predict the macroscopic stress versus strain behavior. Kinematic hardening rule was used to simulate the nonlinear hardening. Results showed that Both VT model and actual microstructure model had good ability to predict the stress-strain response. The stress and strain distribution showed that VT model agreed with the microstructure-based model well. Simulation result was consistent with experimental result that measured by digital image correlation test. In addition, the microstructure-level inhomogeneity and incompatible deformation between the hard and soft phases were the main reason for damage.

Guang-Jian Yuan, Peng-Cheng Zhao, Xian-Cheng Zhang, Shan-Tung Tu, Xiao-Gang Wang, Cheng-Cheng Zhang

Chapter 2. Characterization of the Fatigue and Damage Behavior of Extruded AW6060 Aluminum Chip Profiles

Due to a great potential for conserving resources, the direct recycling of aluminum chips by hot extrusion is a promising alternative to energy-intensive remelting process. The mechanical properties of cast-based and chip-based specimens of AW6060 aluminum alloy were characterized by means of mechanical quasi-static and cyclic experiments. The response of the material was followed by means of hysteresis, thermometric and resistometric measurements, whereby the fatigue strength could be estimated by alternating current potential drop-technique. The effects deriving from defects in the microstructure, in the form of cavities and seam welds between the chips, could be correlated with the fatigue properties by means of optical and scanning electron micrographs.

Alexander Koch, Philipp Wittke, Frank Walther

Chapter 3. Micromagnetic-Based Fatigue Life Prediction of Single-Lip Deep Drilled AISI 4140

Non-destructive testing based on micromagnetic techniques, for example magnetic Barkhausen noise analysis, are quick and reliable possibilities to detect and classify material parameters like hardness and residual stresses. High-strength steels, like AISI 4140 (42CrMo4 + QT), are commonly used for highly dynamically loaded parts. Increasing requirements on weight, performance and efficiency of automotive industry claim increasing demands on material properties. The aim of this study is to evaluate the surface conditions of deep drilled round specimens due to drilling parameters and to predict the resulting fatigue strength by micromagnetic measurements. Furthermore, modified process parameters should enhance fatigue life without the need for expensive processing steps, e.g. autofrettage.

N. Baak, J. Nickel, D. Biermann, F. Walther

Chapter 4. Relationship Between Microstructural Features and Fatigue Behavior of Al-Based Alloy in Green Chemical Processing

In this study, a green chemical milling, Green Etching (Patent pending), is applied to B356.2 Aluminum alloy with the aim to remove a controlled thickness layer from the surface with no buckling and maintaining excellent dimensional tolerances. Comparison of the fatigue life of un-treated and chemically treated samples is performed, with the aim to determine how the above mentioned chemical treatment influences the fatigue resistance of the Al alloy to be used in automotive/aircraft industrial application. The results revealed that the fatigue properties of Al casting alloy are influenced by the presence of casting defects and the fatigue resistance can not be significantly compromised by the milling treatment despite the surface roughness induced by the treatment.

Ildiko Peter, Raffaella Sesana, Roberto Maiorano

Chapter 5. Influence of Heat Treatment Process to the Fatigue Properties of High Strength Steel

This paper is devoted to the analysis of static and cyclic properties of two high strength steels (AS 4340). The reason for this analysis was the need to select suitable materials for the power engineering. Analyzed materials had a practically identical chemical composition. The heat treatment process declared by the inspection certificate was very similar too. By the measurements of mechanical properties there were differences in static strength and especially in cyclic properties of compared materials. To explain the significant differences in fatigue properties between materials, it was necessary to analyze their microstructure. The results have shown that a relatively small change in the heat treatment process has a significant effect on the fatigue properties of the steel.

V. Chmelko, I. Berta, M. Margetin

Chapter 6. Effect of Heat Treatment on High-Temperature Low-Cycle Fatigue Behavior of Nickel-Based GH4169 Alloy

The effect of heat treatment on the strain-controlled fatigue behavior of Nickel-based GH4169 alloy at 650 °C was investigated. The volume fraction of δ phase increases as the longer solution annealing time. The maximum phase fraction reaches 13.79% after double-aging heat treatment. At the same time the yield strength and the tensile strength of GH4169 alloy decrease gradually. The heat treatment had almost no effect on fatigue life at strain amplitude higher than 0.6%. However, the fatigue life slightly increased with increasing the solution annealing time at strain amplitude lower than 0.5%. The alloy does not exhibit dual-slope Coffin-Manson relationships at 650 °C. The needle-like δ phase obstruct movement of dislocations. This makes the alloy exhibited the high-temperature fatigue life higher than the room-temperature fatigue life at low strain amplitude.

Xu-Min Zhu, Xian-Cheng Zhang, Shan-Tung Tu, Run-Zi Wang, Xu Zeng

Chapter 7. High Temperature Fatigue Behaviour of Secondary AlSi7Cu3Mg Alloys

The high temperature fatigue behaviour of secondary AlSi7Cu3Mg alloys has been investigated. The alloy has been solubilized and aged for different times to obtain the age-hardening profile. The peak hardness is reached at 180 °C after 4 h ageing treatment. Further, the hardness stabilizes showing a plateau in the range between 5 and 10 hours of ageing treatment. The heat treatment leads to a complete dissolution of Cu-rich phases, spheroidization of eutectic Si particles and precipitation inside the α-Al matrix. Several fatigue tests have been carried out on selected heat-treated specimens both at room and elevated temperatures (200 and 300 °C). The obtained results show how the fatigue strength decreases with increasing the testing temperature.

Alessandro De Mori, Giulio Timelli, Filippo Berto

Chapter 8. Mean Stress Effect on Fatigue Behavior of Austenitic Stainless Steel in Air and LWR Conditions

In this paper, mean stress influence and cooperative effects associated with light water reactor (LWR) environmental factors were studied through load-controlled fatigue tests with cylindrical hollow specimens. Positive (+10, +50 MPa) and negative (−10, −20 MPa) mean stresses were applied and both showed beneficial influence on fatigue life due to cyclic hardening, which results in smaller strain amplitude under the same stress amplitude. The increase in fatigue life was found to depend on mean stress and testing environments. The increase (1.8–2.2x) in fatigue life with +50 MPa mean stress in boiling water reactor/hydrogen water chemistry (BWR/HWC) is smaller than that in air (3.0–3.4x), while the increase with −20 MPa mean stress in both environments is approximately similar. −20 MPa mean stress enhances the resistance to crack initiation as observed with optical microscopy (OM) observations of fracture surfaces and wall cross-sections of tested specimens.

W. Chen, P. Spätig, H. P. Seifert

Chapter 9. Characterization of the Fatigue Behavior of Mechanical and Thermal Aged Austenitic Power Plant Steel AISI 347

For the comprehensive understanding of the fatigue mechanisms of mechanical and thermally aged materials in power plant reactors, an innovative, resource- and time-optimized approach based on non-destructive testing methods is used. Beside investigations on AISI 347 austenitic stainless steel under cyclic loading, magnetic, resistometric and electrochemical measurement techniques were applied to monitor the proceeding fatigue behavior. Qualitative values indicate surface passivation effects and microstructural changes, which are directly related to fatigue states. In total strain-controlled increase tests, cyclic investigations for the initial and a mechanically and thermal aged condition were carried out under distilled water environment at ambient temperature. In comparison to the initial state, the aging process shows a significant influence on the fatigue behavior with a reduction of the stress amplitude at failure down to 75%.

F. Maci, M. Jamrozy, R. Acosta, P. Starke, C. Boller, K. Heckmann, J. Sievers, T. Schopf, F. Walther

Fatigue of Additive Manufacturing Metals


Chapter 10. As-Built Sharp Notch Geometry and Fatigue Performance of DMLS Ti6Al4V

Metal parts obtained by the layer-wise selective melting of a powder bed are characterized by surfaces that are considerably rougher than conventionally machined parts. Application of lightweight design tools results in complex part geometries with notches, reentrant corners, internal surfaces that are difficult to inspect and whose surface finish may not be improved. To efficiently investigate the fatigue response of as-built DMLS Ti6Al4V in the presence of as-built notches a miniature specimen approach is adopted. Sets of directional mini specimens were manufactured with the long axis parallel and perpendicular to the build direction and heat treated. The sharp notched bar geometry is subjected to cyclic bending. The interaction of directional notch generation, surface quality and geometrical accuracy on the notch fatigue behavior is quantified and discussed.

Martin Frkáň, Gianni Nicoletto, Radomila Konečná

Chapter 11. Impact of Various Surface Treatments on the S-N Curve of Additive Manufactured AlSi12

Objective of this work is to investigate the behavior of AlSi12 specimens under fatigue loading. It describes the impact of various surface treatments like turning, polishing, shot peening and deep rolling on the S-N curve. Surface treatments, which create compressive residual stresses in near-surface regions show an improved fatigue strength. Deep rolling leads to the best results. Furthermore, the scatter of the S-N curves is discussed. Crack initiation seems to be sensitive to surface treatment. It is concluded, that in the case of rough surfaces the crack starts at surface defects whereas for improved surface conditions, for example polishing, the crack may start at pores in near-surface regions.

Steffen Greuling, Wolfgang Weise, Dieter Fetzer, Klaus Müller-Lohmeier, Mattias-Manuel Speckle

Chapter 12. Fatigue Properties of Powder Bed Fused Inconel 718 in As-Built Surface Condition

The aim of this study was to investigate the fatigue properties of Selective Laser Melted (SLM) processed Inconel 718 (IN718). The joint research activity between the European Space Agency and the company Renishaw, chose IN718 for its suitability in applications for launcher engine components and for Additive Manufacturing (AM) processing. The high-cycle fatigue properties of vertically and horizontally built specimens in as-built condition were investigated and a stress-life (S-N) curve constructed. The fatigue specimens were characterized by X-Ray Computed Tomography (XRCT) and the fracture surfaces analysed by Scanning Electron Microscopy (SEM). The analysis performed shows similar fatigue properties of vertically and horizontally built specimens below 106 cycles, despite significant differences in surface roughness.

M. Sprengel, A. Baca, J. Gumpinger, T. Connolley, A. Brandao, T. Rohr, T. Ghidini

Chapter 13. Application of Data Science Approach to Fatigue Property Assessment of Laser Powder Bed Fusion Stainless Steel 316L

The adaptive neuro-fuzzy inference system (ANFIS) was applied for fatigue life prediction of laser powder bed fusion (L-PBF) stainless steel 316L. The model was evaluated using a dataset containing 111 fatigue data derived from 14 independent S-N curves. By using porosity fraction, tensile strength and cyclic stress as the inputs, the fuzzy rules defining the relations between these parameters and fatigue life were obtained for a Sugeno-type ANFIS model. The computationally derived fuzzy sets agree well with understanding of the fatigue failure mechanism, and the model demonstrates good prediction accuracy for both the training and test data. For parts made by the emerging L-PBF process where sufficient knowledge of the material behavior is still lacking, the ANFIS approach offers clear advantage over classical neural network, as the use of fuzzy logics allows more physically meaningful system design and result validation.

M. Zhang, C. N. Sun, X. Zhang, P. C. Goh, J. Wei, D. Hardacre, H. Li

Chapter 14. Influence of Surface Orientation and Segmentation on the Notch Fatigue Behavior of as-Built DMLS Ti6Al4V

Design and qualification of load-bearing metal parts produced by the additive manufacturing technology is a critical issue. Such metal parts are complex in geometry with notches that are critical locations under fatigue loading. Notch surfaces are typically in the as-built state because post-fabrication surface finishing is not a viable approach in most applications. Here fatigue experiments using notched specimens produced according to different orientations with respect to build direction are presented and used to discuss the notch fatigue behavior of DMLS Ti6Al4V. Notch fatigue factors depend on the process itself and on fabrication details such as up-skin versus down-skin surface orientation, stair-stepping of the notch surface due to the layer-by-layer segmentation and intrinsic as-built surface roughness.

Gianni Nicoletto, Radomila Konečná

Chapter 15. Characterization of the Cyclic Material Behavior of AlSi10Mg and Inconel® 718 Produced by SLM

The flexibility in design offered by advanced additive manufacturing technologies makes this process more and more attractive for the automotive as well as the aircraft industry, especially for the production of metal components. Nevertheless, while, on the one hand, additive manufacturing paved the way for new design solutions which were not possible before, on the other hand, it represents a new process, which has still not been standardized and, therefore, made exploitable. In this work, the cyclic material behavior of two different metals used for additive manufacturing technologies were evaluated. Small-scale specimens, produced by Selective Laser Melting (SLM) of the Aluminum alloy AlSi10Mg and Inconel® 718 powder, were subjected to Incremental Step Tests (IST) in order to evaluate the cyclic stress-strain behavior of the material. The effects of removed support structures, four building orientations, surface conditions and an additional heat treatment on the cyclic stress-strain behavior of the material were evaluated.

M. Scurria, B. Möller, R. Wagener, T. Bein

Fatigue Crack Propagation


Chapter 16. Review of Current Progress in 3D Linear Elastic Fracture Mechanics

The aim of this contribution is to provide a brief review of the latest developments in the area of 3D Linear-Elastic Fracture Mechanics. The primary focus of this contribution is on the situations where the classical results, which are normally obtained within the framework of plane theory of elasticity, lead to peculiar results. These situations include analysis of stress and displacement fields near vertex points, generation of the coupled fracture mode under shear loading, application of Williams series expansion to 3D problems as well as fracture scaling.

Andrei Kotousov, Aditya Khanna, Ricardo Branco, Abílio M.P. De Jesus, José A.F.O. Correia

Chapter 17. An Improved Prediction of the Effective Range of Stress Intensity Factor in Fatigue Crack Growth

This paper will summarise the results obtained to date and which demonstrate that the mesoscale CJP model of crack tip fields is capable of providing an improved correlation of fatigue crack growth rates across a range of stress ratios and specimen geometries, compared with the standard stress intensity factor calculations.

Bing Yang, M. N. James, Yongfang Huang, J. M. Vasco-Olmo, F. A. Díaz

Chapter 18. Short and Long Crack Growth of Aluminium Cast Alloys

Fatigue design of AlSi-alloy cast components is a challenging issue due to a great variety of the microstructure depending on the local cooling conditions, which majorly affects the local fatigue behaviour. Therefore, this paper contributes with an experimental evaluation of the short and long crack growth of aluminium cast alloys. At first, single edge notched bending (SENB) crack propagation tests show a distinctive transition of the crack resistance from the small to the long crack regime. At second, in situ fatigue experiments with an optical measurement of the surface crack length augment the crack growth data of the SENB-tests. In addition, the observations reveal that the local material condition, such as micro shrinkage pores or variation in local microstructure, affect the crack propagation as well as the crack path. Summarized, the presented work highlights that the short and long crack behaviour including the influence of microstructural properties needs to be considered thoroughly in order to properly assess the fatigue life of AlSi-alloy cast components.

Martin Leitner, Roman Aigner, Sebastian Pomberger, Michael Stoschka, Christian Garb, Stefan Pusterhofer

Chapter 19. Evaluation of Strain Controlled Fatigue and Crack Growth Behaviour of Al–3.4Mg Alloy

Present study focuses on fatigue performance of Al–3.4Mg (AA5754) aluminium alloy. Fatigue crack growth (FCG) and strain controlled low cycle fatigue (LCF) tests are performed for as received and precipitation strengthened AA5754 alloy. Precipitation strengthening heat treatment (PSHT) process significantly alters the mechanical and fatigue strength of Al–3.4Mg alloy. Fatigue crack growth (FCG) test is performed at load ratio (R-ratio = Pmax/Pmin) of 0.1 and 0.5 using compact tension (CT) specimens. Strain controlled low cycle fatigue (LCF) tests are performed at 1.2 and 1.0% strain ranges. FCG test results depict that PSHT alloys offer higher resistance against crack growth and improvement in fatigue life. LCF test reveals the cyclic hardening behaviour for both as received and PSHT AA5754 alloys. Improvement in fatigue life at both strain ranges is observed for PSHT alloys. Numerical simulations for crack growth analysis are performed by using eXtended Finite Element Method (XFEM). Chaboche kinematic hardening model coupled with finite element method (FEM) is used to simulate the experimental hysteresis loops and fatigue life obtained during strain controlled LCF tests. The present study concludes that lower crack growth rate by FCG test and higher fatigue strength during LCF test is obtained for precipitation strengthened AA5754 alloy as compared with as received alloy. The crack growth simulations by XFEM have good convergence with experimental results. The simulations performed by kinematic hardening model have good agreement with experimental results.

Pankaj Kumar, Akhilendra Singh

Chapter 20. Numerical Analysis of the Influence of Crack Growth Scheme on Plasticity Induced Crack Closure Results

Plasticity Induced Crack Closure (PICC) has been studied by means of finite element method for a long time. Most of previous work was developed considering bi-dimensional models. During last years, the use of three-dimensional models has been extended. Nevertheless, the methodology employed has been inherited from bi-dimensional analyses. Many previous bi-dimensional analyses studied different numerical parameters and optimized them. Present computational capabilities allow a comprehensive study of the influence of different modelling parameter in a similar way to those bi-dimensional analyses. Moreover, the influence of these parameters on the obtained results along the thickness can be taken into consideration. In particular, one of the key issues is related to the crack growth scheme. A fatigue analysis implies a crack growth. Each change in loading and boundary conditions implies solving a nonlinear problem. It is not feasible to consider all the cycles involved in a real fatigue problem when running a finite element analysis. The computational cost is not acceptable. In the present work, a CT aluminium specimen has been modelled three-dimensionally and several calculations have been made in order to evaluate the influence of the number of load cycles between node releases. The results are analysed in terms of crack closure and opening values.

D. Camas, J. Garcia-Manrique, F. V. Antunes, A. Gonzalez-Herrera

Chapter 21. Towards Quantitative Explanation of Effective Thresholds of Mode III Fatigue Crack Propagation in Metals

The article presents the state-of-the art of tools for prediction of mode I, II and III effective thresholds for metallic materials. The effective threshold is independent of the stress ratio as well as the yield strength and is, therefore, a universal parameter for a particular metal. It can also be also used to separate the effective and crack closure components of resistance to fatigue crack growth. Results of recent research provided relationships for quantification of mode II and mode III effective thresholds for a wide range of metallic materials which are in a good agreement with experiments. The local crack growth mode has to be taken into account which depends on crystal lattice type and secondary phase type. The mode III cracks propagate by local crack front advances under mode I or mode II which was taken into account in numerical calculation of local stress intensity factors. It allowed explanation of the experimentally obtained values of the mode III effective thresholds.

Tomáš Vojtek, Stanislav Žák, Jaroslav Pokluda

Chapter 22. Crack Propagation Under Cyclic Bending in Welded Specimens After Heat Treatment

The paper presents the tests results on the fatigue crack growth under cyclic bending specimens at constant moment amplitude made of S355 steel with fillet welds. Rectangular specimens with stress concentrators in form of the external two-sided blunt notches and fillet welded joints were tested. The tests were performed under constant value of the stress ratio R = −1 without and after heat treatment. This research also presents the test results of the microstructure of welded joints taking into account changes in the material after heat treatment and the impact of these changes on the fatigue life of specimens.

Dariusz Rozumek, Janusz Lewandowski, Grzegorz Lesiuk, José A.F.O. Correia

Chapter 23. Crack Propagation in the Threshold Stress Intensity Region a Short Review

This work presents a short review of fatigue crack propagation with emphasis on the parameters that influence the threshold stress intensity, ΔKth. This threshold value is dependent on such variables as the material itself, the test conditions, the R-ratio, the environment and crack closure. The crack geometry effects are discussed as well as some crack closure models. A discussion of other parameters that influence the threshold stress intensity regime including short crack thresholds and their respective models and their application will be the subject of a near-future review.

Luiz Felipe F. Ricardo, Timothy H. Topper, Luiz Carlos H. Ricardo, Carlos Alexandre J. Miranda

Chapter 24. A Stress Intensity Factor Study for a Pressure Vessel CT Specimen Using Finite Element Method

This study aims to determine the mode I Stress Intensity Factor, KI, for a steel alloy specimen extracted from a pressure vessel, so-called P355NL. The geometric and mechanical properties are derived from Compact Tension, CT, specimens available in the relevant literature. The theoretical value of KI is evaluated through the formulation reported in ASTM E 647-15 ASTM International (Standard test method for measurement of fatigue crack growth rates. West Conshohocken, PA, 2015, [1]) for the geometric properties used in the previous study. Numerically, to solve the CT specimen problem, a Finite Element code software, ABAQUS© is used. Therefore, obtained numerical results are then compared to the theoretical ones, leading to assess the numerical analyses’ performance. In this study, distinct crack lengths are considered as; a = {8, 9, …, 20 mm}. Overall, encouraging results were obtained possessing a satisfactory agreement compared to theoretical solution.

Patrícia Raposo, Behzad V. Farahani, José A.F.O. Correia, Jorge Belinha, Abílio M.P. De Jesus, Renato N. Jorge, Rui Calçada

Chapter 25. Micro-notch Size Effect on Small Fatigue Crack Propagation of Nickel-Based Superalloy GH4169

Nickel based superalloys are used extensively in the hot sections of gas turbines in the aerospace and power generation industries. Some of them are submitted to fatigue circumstances, which may restrict their service lives. Moreover, almost all the structural components have defects. In the past years, the disasters caused by fatigue have aroused consensus. And the safety life design methods have been widely used in the service time design for structures under fatigue load. However, most of those design methods considered the structures were integrated with no defects such as cavities and micro-cracks. While the cracks would initiate and propagate from these defects, which might limit the fatigue life largely. Therefore, a profound understanding of the notch effect on fatigue progress is necessary to build models which can assess the failure period of components in these harsh operating conditions. This paper will discuss notch size effect on fatigue progress in nickel-based superalloys.

J. Wang, R. Wang, Y. Wang, Y. Ye, X. Zhang, S. Tu

Probabilistic Methods


Chapter 26. The Interactive Method—Reliable and Reproducible S-N-Curves for Materials

Based on a new developed research method—the Interactive Procedure—the characteristic fatigue strength curve (e.g. 5%-quantile obtained at a level of confidence of 90%) was determined directly by test results. As an example new experimental investigations on reinforcing steel were conducted on pure single bars as well as on bars embedded in concrete. The lower stress level was kept constant according to the usual design situation. Another example with a shear loaded fastener system—steel element in concrete—shows that the load bearing capacity increases, if the concrete strength increases. A third example shows the differences between prestressing steel tested without embedment and casted in concrete. For the development of a complete whole S-N-curve for steel 3–5 static and 20–25 cyclic tests are necessary.

Klaus Block

Chapter 27. Probability Distribution Type for the Accumulated Damage from Miner’s Rule in Fatigue Design

Variability is present within the stress-life (S-N) fatigue analysis process. This variability propagates through the analysis process into the accumulated damage computed using Miner’s Rule. This paper aims to characterise the probability distribution type of the accumulated damage from Miner’s rule when accounting for variability in fatigue design parameters using a case study. Whilst the distribution type could not be conclusively selected, considerations regarding the future application of probabilistic methods for fatigue design are presented.

J. Hoole, P. Sartor, J. D. Booker, J. E. Cooper, X. V. Gogouvitis, R. K. Schmidt

Chapter 28. Evaluation of Fatigue Properties of S355 J2 and S355 J0 by Using ProFatigue Software

The use of S355 high strength steel in civil engineering to design structures of bridges, cranes or simple engineering parts allows material and economical savings to be achieved meeting the strict construction requirements. The knowledge of the fatigue resistance of material plays the key role during design and maintenance of the bridge structures. In the paper the fatigue behavior of S355 J2 and S355 J0 steels are analyzed using statistical models. The data consist of results from low cycle and high cycle fatigue for a variety of specimens. In particular, the software ProFatigue is used for derivation of the probabilistic S–N field from experimental fatigue data. The program, based on a former regression Weibull model, allows the estimation of the parameters involved in the S–N field, providing an advantageous application of the stress based approaches in the fatigue design of mechanical components. The results obtained are compared with the usual used Wöhler-curve, usually used, represented as a straight line in a double-logarithmic scale.

Stanislav Seitl, Petr Miarka, Sergio Blasón, Alfonso F. Canteli

Chapter 29. Updating the Failure Probability of Miter Gates Based on Observation of Water Levels

Hydraulic steel structures, especially lock gates play a significant role in keeping navigation traffic uninterrupted. After a few decades of operation, many of the welded joints may suffer various degrees of deterioration, primarily due to fatigue. To economically combining crack inspection with a scheduled maintenance of the movable parts of the gate, it is valuable to predict inspection time of the welded joints using the historical operations of the gate, i.e. the variation of water levels. Updating failure probability of welded joint is mature in the offshore industry, but it is rarely applied for inland navigation lock gates where the contribution to fatigue failure comes from the variation of water pressures during operation of the lock gates. The scope of this paper is to predict the inspection time of a welded joint using the observed water levels from the operational history. The updating of the failure probability is done for three inspection techniques, considering annual probability and repair decisions. The results show the effects of critical annual probability and the probability of detections (PODs) on the update failure probability for a welded joint.

Thuong Van Dang, Quang Anh Mai, Pablo G. Morato, Philippe Rigo

Fatigue Modelling


Chapter 30. Comparison of Several Optimized Methods for Mean Stress Effect Evaluating the Stress-Life Prediction

Four methods for computing the equivalent stress amplitude as the response to the mean stress effect are compared. They all include one additional parameter, which was optimized for 19 different data sets. Trends of the optimized parameters were analyzed, and their estimates were recommended. These recommended values were then checked on the same test set. The final results favor use of the Bergmann and the Walker methods, while the Linear method built as a generalization of the Goodman formula results in a weak output.

Jan Papuga, Ivona Vízková, Maxim Lutovinov, Martin Nesládek

Chapter 31. Application of the Nonlinear Fatigue Damage Cumulative on the Prediction for Rail Head Checks Initiation and Wear Growth

The nonlinear fatigue damage cumulative model was presented by combining the damage curve method considering the wheel-rail loading sequence and the fatigue damage method considering the interaction of the loads. Based on above model and the prediction method for coexistence of fatigue crack initiation and wear of rail, the results for rail head checks (HC) prediction by the linear and nonlinear fatigue cumulative models was analyzed. It was found that the cumulative fatigue damage at the rail material point by the modified nonlinear fatigue damage cumulative model was higher than that of the linear one. Therefore, the HC initiation life was the short. Comparing with the field tests, the results by linear fatigue cumulative model and modified nonlinear fatigue damage cumulative model were close to the upper range value and median of the field test result respectively.

Y. Zhou, D. S. Mu, Y. B. Han, X. W. Huang, C. C. Zhang

Chapter 32. Fatigue Life Prediction for Component with Local Structural Discontinuity Based on Stress Field Intensity

The impact of notch is one of the major problems that remain to be solved when predicting fatigue life. The zone of notch root has serious stress concentration condition. Stress field intensity (SFI) approach is an advanced volumetric method for fatigue life prediction. This paper makes further research and puts forward a modified approach based on it. A numerical example and an engineering notched specimen are analyzed by finite element approach to prove the validity of new approach. The modified SFI approach shows good fatigue life prediction and is convenient for practical use.

Tianyang Lu, Peng Zhao, Fu-Zhen Xuan

Chapter 33. Low Cycle Fatigue Life Estimation of P91 Steel by Strain Energy Based Approach

In the present study strain energy based analytical models are used to predict the fatigue life of P91 steel subjected to strain controlled loading. P91 steel being used in pressure vessel and many other components for ultra-supercritical fossil fired and nuclear power plants are subjected to repeated thermal stresses. In low cycle fatigue regime plastic strain range significantly affects the energy dissipation process during the course of loading. Thus, models based on energy dissipation during first cycle and averages of cycles are developed to assess the fatigue life. Uniaxial strain controlled low cycle fatigue tests at ambient temperature are conducted on P91 steel in the normalized and tempered condition. The material depicted near masing type behaviour as evaluated in terms of variation in bauschinger strain with plastic strain range. The analytically predicted results for fatigue life showed good agreement with experimental fatigue life. The cumulative plastic strain energy or fatigue toughness to failure is seen to increase with increasing number of cycles to failure.

Bimal Das, Akhilendra Singh

Chapter 34. Evaluation of Regression Tree-Based Durability Models for Spring Fatigue Life Assessment

This paper presents an evaluation of pruned regression decision tree for spring fatigue life predictions. The inputs for this regression decision tree models are vehicle ISO 2631 vertical vibrations and suspension frequencies. The design process of a coil spring involved many steps which consume many time and efforts. Hence, there is a need to generate a prediction model to assist spring design. Loading time histories were obtained from a quarter car model simulation for spring fatigue life assessment and ISO 2631 vertical vibrations calculations. The obtained force time histories were used to predict fatigue life of spring using strain-life approaches while acceleration time histories were used to obtain ISO 2631 vertical vibration. Together with spring stiffness sensitivities, the spring fatigue life was modelled using regression decision tree and mean squared error of the generated regression decision tree residuals were analysed. Five sets of independent experimental measurement strain time histories were used to validate the fatigue life predictions using a conservative approach. Most of the validation data points have lied beyond the acceptable region. Therefore, these proposed regression tree models are providing a good prediction on spring fatigue life which could shorten the spring design process.

Y. S. Kong, S. Abdullah, D. Schramm, M. Z. Omar, S. M. Haris

Multiaxial Fatigue


Chapter 35. Prediction of Fatigue Crack Initiation Life in Notched Cylindrical Bars Under Multiaxial Cycling Loading

This paper addresses the determination of fatigue crack initiation lifetime in notched round bars under multiaxial loading on the basis of a total strain energy density approach. The modus operandi consists of developing a fatigue master curve relating the total strain energy density and the number of cycles to failure from the outcomes of a set of standard strain-controlled fatigue tests. In a second stage, the total strain energy density of the notched sample is computed from representative hysteresis loops obtained via linear-elastic finite-element models. The proposed methodology is tested in cylindrical bars with lateral U-shaped notches and cylindrical bars with blind transverse holes subjected to different constant-amplitude proportional bending-torsion loading. After fatigue testing, specimen surfaces are examined by scanning electron microscopy to identify the main failure micro-mechanisms.

R. Branco, J. D. Costa, F. Berto, A. Kotousov, F. V. Antunes

Chapter 36. Multiaxial Fatigue Analysis of Stainless Steel Used in Marine Structures

This work investigates the fatigue behaviour under multiaxial loading conditions of 316 stainless steel commonly used in offshore and marine structures. Cylindrical hollow specimens were tested under uniaxial tensile stress, hoop stress and different combinations of tensile and hoop stresses. Both proportional and non-proportional loading were studied in the experiments. Prediction of the fatigue life was performed with Wang-Brown, Fatemi-Socie and Liu critical plane models. A detailed analysis and discussion of the performance of the different models is presented with an emphasis on the versatility for different situations.

A. S. Cruces, P. Lopez-Crespo, B. Moreno, S. Bressan, T. Itoh

Chapter 37. On the Application of SK Critical Plane Method for Multiaxial Fatigue Analysis of Low Carbon Steel

In this work Suman-Kallmeyer critical plane model is assessed and compared to few other critical plane models. The analysis is based on both in-phase proportional loading and out-of-phase non-proportional loading applied to a low carbon steel. A wide range of loading scenarios were studied by combining axial and torsional loads, producing fatigue lives in the range of 103 to 106 cycles. The study allowed low and high cycle fatigue regimes to be assessed. In addition, the hardening effect was also investigated. Finally, a comparison with well established critical plane models is also performed.

A. S. Cruces, P. Lopez-Crespo, S. Sandip, B. Moreno

Very High Cycle Fatigue


Chapter 38. Fatigue Testing at 1000 Hz Testing Frequency

In 2014 RUMUL could present a new resonant fatigue testing machine, with a testing frequency of 1000 Hz. The dynamic load of maximum 50 kN peak-peak is produced with an electromagnetic system. Similar to established resonant systems which run on testing frequencies from about 40 up to 250 H. The static portion of the load is provided by a mechanical spindle, the maximum load of the system is ±50 kN. Any load ratio can be selected. Flat and round specimen types that are normally used in fatigue testing can be used. The new testing machine offers new possibilities for investigations of material properties in the very high cycle fatigue (VHCF) regime. Compared to other systems used in the field of VHCF testing the RUMUL GIGAFORTE provides several advantages. The size of the machine is smaller and energy consumption less compared to a servo hydraulic system. The actually tested material volume is larger than the material volume that is tested on ultrasonic systems. The testing frequency of 1000 Hz allows normally continuous testing, without stopping for cooling down the specimen. In the past three years the new testing machine was intensively used for example at the laboratory of the Fraunhofer institute IWS Dresden in Germany. Effects of the 1000 Hz testing frequency on the fatigue behaviour of the material were observed. This talk shows some example of heating up of the specimen related to the 1000 Hz testing frequency and highlights some of the found frequency related effects on fatigue strength.

Markus Berchtold

Chapter 39. Influence of Microstructural Inhomogeneities on the Fatigue Crack Growth Behavior Under Very Low Amplitudes for Two Different Aluminum Alloys

In the present paper the aluminum alloys EN AW-6082 (peak-aged and overaged) and EN AW-5083 (solution annealed) were investigated regarding the long fatigue crack growth behavior in the range of very low amplitudes and therefore very high number of load cycles. The cracks were initiated at micro notches, prepared by means of focused ion beam technology and examined in situ by a long distance microscope. In first experiments the threshold for each material condition was defined. Subsequently the tests were carried out at constant ΔK values. Further analysis such as electron backscatter diffraction (EBSD) and confocal microscopy were executed to analyze the fatigue crack growth behavior. A microstructural barrier function of the primary precipitates could be detected for each material condition. Grain boundaries seem to influence the crack growth only in case of the work hardening alloy (EN AW-5083), which is the material with smaller average grain size compared to EN AW-6082.

T. Kirsten, M. Kuczyk, M. Wicke, A. Brückner-Foit, F. Bülbül, H.-J. Christ, M. Zimmermann

Chapter 40. Effect of Ultrasonic Deep Rolling on High-Frequency and Ultrasonic Fatigue Behavior of TC4

A gradient nanostructured (GNS) surface layer was produced on TC4 samples by means of ultrasonic deep rolling (UDR). Grain size refined to nano-scale and increased to macro-scale with the increasing depth. The microstructure of the UDRed sample was observed and the mechanical properties of UDRed samples were measured. The Roughness of samples after rolling is reduced by 60% with the comparison of un-treated sample. The micro-hardness increased with the increasing rolling passes. After the measurement of mechanical properties, the fatigue tests were carried out and the fatigue life of UDRed samples shows were lower than that of un-UDRed samples on high-frequency and ultrasonic fatigue. The fatigue fracture and the initiation of cracks have been investigated to clarify the fatigue mechanism of the UDRed samples. The results showed that the decrement of fatigue life of UDRed samples compared with coarse-grain samples was attributed to the fever in cyclic loading induced by the heterogeneity of the material.

Yi-Xin Liu, Yun-Fei Jia, Xian-Cheng Zhang, H. Li, Run-Zi Wang, Shan-Tung Tu

Applications/Case Studies


Chapter 41. Microinclusion and Fatigue Performance of Bearing Rolling Elements

Many phenomena are involved in damage of rolling elements of bearings. Rolling contact fatigue is the main cause of failure, along with contact pressure related fatigue and dimensional instabilities effect. Most of those are well known, and are described by wide experimental, analytical and numerical literature. Damage phenomena are related to material properties and manufacturing processes, respectively. Particularly, the damage evolution might be affected by some microinclusions present in the material. This influence is related to mechanical properties, dimension, composition, shape and location of inclusions. This research activity is focused on the 100Cr6 steel alloys. Relation between microinclusions and fatigue life is here investigated. Results of experimental testing run on some test bench are compared to some analytical models for given set of operation conditions. Failures are then analysed to relate life of rolling elements to the microinclusion parameters. The research activity is aimed to investigate whether a microinclusion threshold parameter could be defined, to be related to the life bearing requirements. This analysis is performed by comparing analytical and experimental results of several models and different alloys.

E. Ossola, S. Pagliassotto, S. Rizzo, R. Sesana

Chapter 42. Strength Analysis of Tramway Bogie Frame

The aim of this contribution is to present the development of bogie frames for rail vehicles from the viewpoint of their strength and fatigue life. The manufacturer of the frames described here pays major attention to these aspects during the design, testing and test runs of vehicles. The manufacturer also collaborates with other specialised research facilities. In practice, the development process consists of three stages. The first stage involves stress calculations, the second stage comprises static and fatigue tests and the third one is focused on validating fatigue life data by stress monitoring during test runs on an actual track.

Vaclav Kraus, Miloslav Kepka, Daniel Doubrava, Jan Chvojan

Chapter 43. A Study of the Shot Peening Effect on the Fatigue Life Improvement of Al 7475-T7351 3PB Specimens

Shot peening is a widely used mechanical surface treatment in the automotive and aerospace industries to improve the fatigue life of metallic components. This work aims to further improvement of the fatigue life on AA7475-T7351 alloy specimens by applying shot peening process using different beads size and bead materials. A systematic study was carried out on the roughness, surface hardening, residual stress profiles and fatigue life. Three point bending (3PB) fatigue tests were conducted. Residual stresses were evaluated by X-Ray diffraction, and the fracture surface was observed and analyzed with a Scanning Electron Microscope. The fatigue test results were plotted in terms of the stress amplitude versus the number of cycles to failure. Since, for this type of loading the initiation of the fatigue process is much localized, the roughness is as or more important than the residual stresses resulting from the shot peening. It was concluded that shot peening does not introduce significant improvement on fatigue life and that the use of glass beads is potentially beneficial.

N. Ferreira, J. A. M. Ferreira, J. Jesus, C. Capela, J. D. Costa

Chapter 44. Investigation of Mechanical Properties and Fatigue of Friction Stir Spot Welded Light Metals

The Light metals such as aluminum and magnesium alloys find extensive use in land and air transport vehicles, electronics, computer and sporting goods industries. In order to reduce weight and thus save fuel, many studies are carried out on the development of new engineering materials, which have lightweight and high fatigue strength, especially for the automotive and aviation industry. One of the first metals remembered in this field is magnesium, which has lower density. In contrary to these advantages, joining of light metal alloys with fusion based welding methods have some problems. Since the fusion welding of light metal sheets is difficult, friction stir welding (FSW) method frequently used for joining of these. Studies has shown that shoulder profile of welding tool, which apply pressure on material, affects the welding quality in FSW method. In order to understand these effects various shoulder profile has been studied and understood. FSW method has been investigated and used for joining of materials since about 50 years. In this paper, the pinless shoulder profile designs of stir tool and the mechanical properties and fatigue strength of magnesium and aluminum alloy sheets, which are joined with these stir tools, are aimed to investigate. In order to realize this, shoulder profiles were designed and manufactured accordingly. Subsequently, magnesium and aluminum alloy sheets for automotive and aviation applications were joined with friction stir spot welding (FSSW). Finally, mechanical properties of joined materials such as tensile, tensile shear, bending and fatigue strength were tested. As a result, it has been verified that light metal alloys such as magnesium alloy AZ31B with good ductile and fatigue strength can easily be joined with FSSW. Moreover, joining of light metals with FSSW method has been demonstrated with comparative test and analysis in engineering applications.

Ahmet Atak, Aydin Şik

Chapter 45. Advanced Development of Hysteresis Measurement Characteristics for Early Detection of Fatigue Damages on Fasting Systems in Concrete

This paper presents an advanced hysteresis measurement model for the characterization of fatigue failures and corresponding, time-dependent damage processes until final failure of fastening systems in concrete. The developed hysteresis model is based on analytical-physical principals with viscoelastic material properties, four adjustment parameters in combination to secondary additive function components (determined through regression analysis) and uses the measurement data, respective hysteresis loops, in accordance with defined conformation criteria for the first step of approximation. Thus conventional characteristic values of the hysteresis measurement procedure, displacement, cyclic stiffness’s and energies could also be defined, even for certain incorrectly and local limited faulty courses, e.g. measurement errors. In a first step, the suitable predictive hysteresis model was applied to experimental fatigue tests of anchor channels in concrete. Further investigations of the four variable parameters led to the potential to identify an indicator for experimental predictions, in relation to specific changes and processes in the shape and area of hysteresis loops at an early stage during the test.

Marvin Hoepfner

Chapter 46. Mechanics and Evaluation of Early Damage

This chapter describes the microstructural mechanisms leading to damage and the formation of fatigue cracks as well as the methods available to monitor these processes. The evaluation of early damage is especially important for structures with long service life spans, where the crack nucleation stage can dominate the total fatigue life.

Andrei Kotousov, James Vidler, James Hughes, Aditya Khanna, Ching-Tai Ng, Munawwar Mohabuth

Risk Analysis and Safety of Large Structures and Structural Details


Chapter 47. Fatigue Damage Factor Calibration for Long-Span Cable-Stayed Bridge Decks

Part 2 of the Eurocode 3 (EN 1993-2) proposes a straight forward fatigue verification method using a single heavy vehicle model (FLM3) and a damage equivalent factor, λ, to represent the fatigue damaging effects of the real traffic on road bridges. The method is very appealing for bridge design. However, the λ-factor has limitations and is not defined in the EN1993-2 for some load cases or “span lengths” above 80 m, renamed here as “critical lengths”. This is the case of cable-stayed bridge decks, where a combination of two internal forces—bending and compression (induced by the stays)—is a characteristic of this bridge system, and stay-cables, with specific shapes of influence lines. To address the above issues a variant solution of the Vasco da Gama Bridge is taken as the case study. In this paper, the results of the λ-factor computed for different critical lengths are compared with previous studies and the original work that led to the current EN formulas for λ. Based on these results, a constant λ value for critical lengths above 80 m is proposed to update the EN for the “mid-span case”. For the fatigue design of stays and steel girders, recommendations are given for determining the critical length based on the influence line of the bending moments.

A. Nussbaumer, J. Oliveira Pedro, C. A. Pereira Baptista, M. Duval

Chapter 48. Fatigue Analysis of a Concrete Chimney Under Wind Loads

In most cases, tall structures are slender, demonstrating flexible behavior and, consequently, weather-related loads such as wind become a major component. Since these structures are flexible, they may become susceptible to wind induced fatigue. The effect of wind presents itself as dynamic load and can affect structures randomly in an infinite number of cycles, producing significant stress variations. The aim of this work is to present an evaluation of fatigue of a reinforced 180-meter-concrete chimney, at its most critical section, through a non-linear dynamic analysis. The method provides a full dynamic analysis which takes into account the geometric nonlinearities, the aerodynamic and structural damping. The numerical results were evaluated according to the fatigue limit specified by ABNT NBR 6118:2014.

Hermes Carvalho, Victor Roberto Verga Mendes, Sebastião Salvador Real Pereira, José A.F.O. Correia

Chapter 49. On the Calculation of Offshore Wind Turbine Load Spectra for Fatigue Design

The present work researches on the definition of the load spectra used for offshore wind turbine low SN slope materials’ fatigue design. Uncertainty in the sample sized used to scale fatigue life is analyzed for the tower component. Damage density is investigated for different environmental conditions in order to understand the importance of the different regimes of operation. Damage density is identified to be a heterogeneous function of the loading environmental conditions. In some cases, even for low SN slope materials, most of the damage occurs due to high load ranges. To study on the influence of this heterogeneity, different statistical tail fits are used to compare the influence of accurately defining the tail region on a reference design time (T). Results show that OWT fatigue is highly dependent on the t shorter that T time used to approximate T. This is mainly related to the fact that fatigue design depends not only on scaling stress ranges, but also cycle counts. Effort on the design phase should be applied in the definition of the uncertainty of the load spectra due to the limitation imposed by using low sample sizes to cover the extensive joint distribution of environmental parameters.

Rui Teixeira, Maria Nogal, Alan O’Connor

Numerical Methods


Chapter 50. The Natural Neighbour Radial Point Interpolation Method to Predict the Compression and Traction Behavior of Thermoplastics

Nowadays, the Finite Element Method is the most used discretization technique in structural computational mechanics. However, recently, new discretization techniques—such as meshless methods (Belinha in methods in biomechanics: bone tissue remodelling analysis. Springer International Publishing, Porto, Portugal, 2014 [1])—have been proposed. These numerical techniques are able to efficiently handle some of the FEM’s drawbacks, such as the re-meshing requirement in crack propagation or large deformations problems. Meshless methods only require an unstructured nodal mesh to discretize the problem domain, and the numerical integration of the discrete system of equations obtained from the Galerkin weak form is performed using a background integration mesh. Additionally, the nodal connectivity is imposed using the influence-domain concept, which allows to construct the interpolation functions. The Natural Neighbor Radial Point Interpolation Method (NNRPIM) is a recently developed truly meshless method, which in this work is used to analyze a thermoplastic assuming an elasto-plastic behavior. Benchmark numerical examples are solved in both traction and compression, and in the end, the NNRPIM results obtained are compared with FEM solutions.

D. E. S. Rodrigues, J. Belinha, R. M. Natal Jorge, L. M. J. S. Dinis

Chapter 51. The Elasto-plastic Analysis of Polymers Subject to Traction and Compression Using Advanced Discretization Techniques

Materials such as thermoplastics often have different behaviors when subjected to traction and compression. In those cases, yield criterions for nonlinear behavior need to be appropriately selected. In this work, a thermoplastic for a particular additive manufacturing process—the fused filament fabrication (FFF)—is investigated. Traction and compression tests are performed using two numerical tools and two variations of the Newton-Raphson method for the elasto-plastic incremental-iterative process. The stress-strain curves are compared with experimental data provided in the literature. The numerical tools used are the Finite Element Method (FEM) and the Radial Point Interpolation Method (RPIM), which is a meshless method [1]. In order to discretize the problem domain, meshless methods only require an unstructured nodal distribution. The numerical integration of the Galerkin weak form is performed using a background integration mesh and the nodal connectivity is enforced by the overlap of influence-domains defined in each integration point. In the end, a comparison study is performed between the results obtained using the meshless method and the finite element method.

D. E. S. Rodrigues, J. Belinha, R. M. Natal Jorge, L. M. J. S. Dinis

Chapter 52. Fracture Analysis of Semi-circular Bend (SCB) Specimen: A Numerical Study

A variety of numerical analysis has been carried out by Finite Element Method (FEM), and Extended FEM (XFEM) on Semi-circular Bend (SCB) specimens to evaluate its material behavior, in particular fracture characterization. This work concentrates on calculating stress intensity factor (SIF) assuming an elastic brittle behavior. In order to obtain the required variable fields, FEM formulation was extended to the linear elastic fracture mechanics (LEFM) for the plane stress status. The problem is solved using standard FEM formulation in ABAQUS© to obtain the numerical solution of SIFs, the results are compared to the previous work available in the literature. An acceptable agreement was accomplished leading to verify the proposed computational methodology.

Farid Mehri Sofiani, Behzad V. Farahani, J. Belinha
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