Fatigue Resistance Curves Research Articles

Mechanical Properties of Additively Manufactured Polymeric Materials-PLA and PETG-For Biomechanical Applications.

The study presented herein concerns the mechanical properties of two common polymers for potential biomedical applications, PLA and PETG, processed through fused filament fabrication (FFF)-Material Extrusion (ME). For the uniaxial tension tests carried out, two printing orientations-XY (Horizontal, H) and YZ (Vertical, V)-were considered according to the general principles for part positioning, coordinates, and orientation typically used in additive manufacturing (AM). In addition, six specimens were tested for each printing orientation and material, providing insights into mechanical properties such as Tensile Strength, Young's Modulus, and Ultimate Strain, suggesting the materials' potential for biomedical applications. The experimental results were then compared with correspondent mechanical properties obtained from the literature for other polymers like ASA, PC, PP, ULTEM 9085, Copolyester, and Nylon. Thereafter, fatigue resistance curves (S-N curves) for PLA and PETG, printed along 45°, were determined at room temperature for a load ratio, R, of 0.2. Scanning electron microscope observations revealed fibre arrangements, compression/adhesion between layers, and fracture zones, shedding light on the failure mechanisms involved in the fatigue crack propagation of such materials and giving design reference values for future applications. In addition, fractographic analyses of the fatigue fracture surfaces were carried out, as well as X-ray Computed Tomography (XCT) and Thermogravimetric (TGA)/Differential Scanning Calorimetric (DSC) tests.

Temperature effects on fatigue delamination behavior in thermoset composite laminates

Temperature can significantly affect fatigue delamination growth (FDG) behavior in composites, while fiber bridging has been frequently reported during FDG. The focus of this study was therefore on investigating temperature effects on FDG behavior with fiber bridging. Mode I fatigue delamination experiments were conducted on a thermoset composite laminates M30SC/DT120 at different temperatures. The Paris relation and fatigue resistance curve (i.e. fatigue R-curve) were used to interpret bridging effects on FDG behavior and to explore temperature effects on fiber bridging development. A modified Paris relation was employed to determine the effects of temperature on the intrinsic FDG behavior at the crack front excluding fiber bridging. The Paris interpretations clearly demonstrate that fiber bridging can significantly retard FDG behavior at different temperatures. Temperature can have different effects on fiber bridging development and the intrinsic FDG behavior. Particularly, elevated temperature can promote more bridging fibers, whereas decreased temperature has negligible influence on fiber bridging. When looking at the intrinsic delamination resistance, mode I FDG can accelerate at elevated temperature but decrease at freezing temperature. Fractographic examinations indicate that fiber/matrix interface debonding is the dominant damage mechanism in mode I FDG at different temperatures. Elevated temperature can lead to the weakening of interface adhesion, contributing to faster intrinsic mode I FDG behavior and more fiber bridging development. And a semi-empirical fatigue model based on normalization was finally proposed to determine mode I intrinsic FDG behavior at different temperatures for engineering applications.

Fatigue verification of orthotropic bridge decks with the hot‐spot method – Background to TS 1993‐1‐901

AbstractThe design of orthotropic bridge decks (OBD) is driven by fatigue. The Eurocode on fatigue of steel structures – prEN 1993‐1‐9:2023 – provides fatigue resistance (S‐N) curves for relevant details in OBD. These curves are to be used with the far field (nominal) stress. However, due to the complex geometry and loading of OBD, the nominal stress is not well defined for many details. In addition, cracks have been found in practice in OBD at locations for which S‐N curves are not provided. In order to overcome these issues, experimental and numerical studies are carried out on the use of local stresses (hot‐spot stresses where possible) for the fatigue design of OBD. The different stress extraction method also implies the use of different S‐N curves. A large number of fatigue tests carried out in the past have been re‐evaluated to determine the hot‐spot stress S‐N curves. Additional fatigue tests have been carried out for details lacking data. The study has resulted in a guideline to design OBD for fatigue with the hot‐spot stress method. This guideline, TS 1993‐1‐901:2023, will be published as a Technical Specification (TS) to the standard prEN 1993‐1‐9:2023.This paper provides a short background to the newly created TS. It demonstrates the derivation of S‐N curves based on available tests for a number of details. It highlights fatigue relevant details that are missing in prEN 1993‐1‐9:2023 and that are added to TS 1993‐1‐901. It explains how to evaluate cracks starting from the root of the weld, for which the hot‐spot stress method is traditionally not applicable. Finally, the paper demonstrates how the method can be applied in the fatigue design, including the application of the load in finite element models.

Probabilistic models for the fatigue resistance of welded steel joints subjected to constant amplitude loading

S-N curves found in various rules and regulations are the basic tool for the practicing engineer when carrying out life predictions for welded details in dynamically loaded structures. The present work is investigating the expected fatigue life and associated scatter for welded steel joints subjected to Constant Amplitude (CA) loading. The objective is to obtain more reliable life predictions based on advancements in the probabilistic model fitted to collected life data. A Random Fatigue Limit Model (RFLM) is proposed to obtain fatigue resistance curves at given probability levels of survival. As a distinction to more conventional statistical methods, the model is treating both the fatigue life and the fatigue limit as random variables. The focus is on high cycle fatigue and long-life data and runouts are included in a rational and logical manner by using a maximum likelihood method. Life data for a transverse fillet welded attachment originally designated as a category 71 detail in Eurocode 3 Part 1-9 are collected and analysed. The plate thickness of the specimens ranges from 20 mm to 32 mm and the steel quality is mild and medium strength Carbon-Manganese steel. The results are compared with the results obtained by conventional S-N curves. The compatibility between the fitted probabilistic models and the underlying fatigue damage mechanisms is emphasized.

Numerical investigation on the fatigue life of non‐cracked metallic plates repaired with bonded CFRP

AbstractIn Europe, a large number of old riveted metallic bridges approach the end of their fatigue life. Past research has shown that the application of CFRP can be very efficient in delaying the crack growth rate of deficient structural elements with existing crack. However, little attention is given to the fatigue resistance of non‐damaged metallic members approaching the end of their fatigue life. This is particularly relevant for old metallic riveted bridges, where many critical components do not have existing cracks. This paper presents a numerical investigation on the fatigue behavior of non‐cracked metallic plates bonded with CFRP using epoxy resin. Nonlinear finite element analyses are performed using the commercial software ABAQUS. The cyclic elasto‐plastic behavior and the fatigue strain life of puddle iron metal are obtained from previous experimental results conducted on specimens extracted from Luiz I Bridge (Porto, Portugal). Debonding failure of the adhesive joint is simulated through the use of cohesive zone model with traction separation law. The cohesive behavior was calibrated using fracture mechanic tests results on the adhesive, conducted in a previous related study. The fatigue crack initiation life was estimated using local approach based on material fatigue strain life. Fatigue resistance curves that relate the number of cycles to failure and the applied nominal stress for unreinforced and reinforced elements are derived. The results show that the application of CFRP can significantly increase the fatigue crack initiation life of a metallic structural component significantly.

Fatigue S-N curves of bolts and bolted connections for application in civil engineering structures

Bolts and bolted connections are frequently used in civil engineering steel structures. This paper presents a meta study where a few thousand fatigue tests on these elements are evaluated. The evaluation reveals that current specifications in design standards need updating to account for the relevant stress parameter and production methods. This substantially reduces the scatter of the fatigue resistance. The shape and position of the fatigue resistance (S-N) curves also require updating. The results of this study have been implemented in the new revision of European standard EN 1993-1-9. This paper provides the background for the modifications.

Mechanical fatigue fractures bivalve shells.

Mollusk shells protect against diverse environmental and predatory physical threats, from one-time impacts to chronic, low-magnitude stresses. The effectiveness of shells as armor is often quantified with a test of shell strength: increasing force is applied until catastrophic fracture. This test does not capture the potential role of fatigue, a process by which chronic or repeated, low-magnitude forces weaken and break a structure. We quantified the strength and fatigue resistance of California mussel (Mytilus californianus) shells. Shells were fatigue tested until catastrophic failure by either loading a valve repeatedly to a set force (cyclic) or loading a valve under constant force (static). Valves fatigued under both cyclic and static loading, i.e. subcritical forces broke valves when applied repeatedly or for long durations. Stronger and more fatigue-resistant valves tended to be more massive, relatively wider and the right-hand valve. Furthermore, after accounting for the valves' predicted strength, fatigue resistance curves for cyclic and static loading did not differ, suggesting that fatigue fracture of mussels is more dependent on force duration than number of cycles. Contextualizing fatigue resistance with the forces mussels typically experience clarifies the range of threats for which fatigue becomes relevant. Some predators could rely on fatigue, and episodic events like large wave impacts or failed predation attempts could weaken shells across long time scales. Quantifying shell fatigue resistance when considering the ecology of shelled organisms or the evolution of shell form offers a perspective that accounts for the accumulating damage of a lifetime of threats, large and small.

Fatigue design of welded double‐sided T‐joints and double‐sided cruciform joints in steel marine structures: A total stress concept

AbstractFatigue is a governing design limit state for marine structures. Welded joints are important in that respect. The weld notch stress (intensity) distributions contain essential information and formulations have been established to obtain a total stress fatigue damage criterion and corresponding fatigue resistance curve; a total stress concept. However, the involved weld load carrying stress model does not provide the required estimates and trends for varying geometry dimensions and loading & response combinations. A new one has been developed and performance evaluation for T‐joints and cruciform joints in steel marine structures shows that in comparison with the nominal stress, hot spot structural stress and effective notch stress concept based results up to 50% more accurate fatigue design life time estimates can be obtained. Taking advantage of the weld notch stress formulations, the effective notch stress concept performance has improved adopting a stress‐averaged criterion rather than a fictitious notch radius‐based one.

Fatigue resistance curves for single and double shear riveted joints from old portuguese metallic bridges

Abstract The maintenance and safety of ancient bridges is a major concern of governmental authorities. In particular, the safety of old riveted bridges fabricated and placed into service at the end of the 19th century deserves particular attention. These structures are susceptible to exhibit high fatigue damage levels due to their long operational period with increasing traffic intensity associated to an original design not covering the fatigue phenomenon. This paper reviews recent fatigue behaviour investigations on single and double shear riveted joints performed by Universities of Porto (Portugal), Tras-os-Montes e Alto Douro (Portugal), and Wroclaw (Poland), in particular concerning the fatigue characterization of riveted joints extracted from representative Portuguese riveted bridges, namely the Eiffel, Luiz I, Fao, Pinhao and Trezoi bridges. In order to overcome the influence of scatter and establish a reliable assessment for the obtained experimental data, two statistical approaches were used: implement linearized boundaries following the recommendation in ASTM E739 standard and defining probabilistic S N fields using the Castillo & Fernandez-Canteli model. This statistical analysis allows to propose design S N curves for single and double riveted joints and evaluate the applicability (safety) of using the design curves suggested in Eurocode 3 as well as design curves proposed by Taras and Greiner.

Fibre-bridged fatigue delamination in multidirectional composite laminates

The influence of fibre bridging on delamination failure in multidirectional composite laminates with different thickness scales is characterized, and the dependence of fibre bridging significance on laminate thickness as well as loading regime is investigated in this paper. Both quasi-static and fatigue resistance curves (R-curve) are experimentally determined to quantify the significance of fibre bridging in delamination growth. The results clearly demonstrate that thickness has effect on the amount of fibre bridging in quasi-static delamination. And the significance of fibre bridging decreases with the increase in laminate thickness. However, the situation for fatigue delamination growth (FDG) is much more complicated. The difference in fibre bridging generation seems to be insignificant in short fatigue cracks and at the plateau state, whereas more bridging fibres can be present in a thinner laminate in-between state. Loading regimes also have significant effect on the amount of fibre bridging. The results clearly demonstrate that more bridging fibres can be generated in quasi-static delamination compared to fatigue. A modified Paris relation proposed by the authors in previous studies is employed in present study to determine fibre-bridged FDG behaviors in multidirectional composite laminates with various thickness scales. All fatigue data locate in a relatively narrow band region of the resistance graph, resulting in a master resistance curve in determining fatigue delamination behaviors. This clearly demonstrates that neither thickness nor fibre bridging has significant effect on fatigue delamination behaviors, if the similarity is well represented.

Fatigue performance and evaluation of welded joints in steel truss bridges

While welded joints are extensively used in the connections of steel truss bridges, service life of the bridges is largely dependent on the fatigue resistance of the welded joints. Stress concentration and weld residual stress are two primary causes of fatigue damage in the welded joints. In this study, corner-fillet profile (CFP) and ultrasonic impact treatment (UIT) are used to improve the fatigue performance of the welded joints through relieving stress concentration and weld residual stresses, respectively. The fatigue resistance of welded joints is evaluated through experimentation. The results indicate that the use of CFP and/or UIT can alter the initiation location of fatigue crack. The fatigue resistance of welded joints was increased by 24% and 36% by using the CFP and UIT, respectively. The fatigue performance of welded joints was evaluated using three different methods, including the nominal stress method, effective notch stress method, and peak stress method. The peak stress method with a single fatigue resistance curve demonstrated the highest applicability and accuracy.

Stress ratio dependence of fibre bridging significance in mode I fatigue delamination growth of composite laminates

This paper aims to investigate stress ratio effect on fibre bridging significance in mode I fatigue delamination growth of composite materials. Fatigue resistance curves (R-curves) of different stress ratios are determined and compared with the quasi-static R-curve. The fatigue R-curve of a high stress ratio is similar to the quasi-static results. However, fatigue resistance of a low stress ratio is smaller than quasi-static resistance. These indicate that fibre bridging significance is stress ratio dependent. More bridging fibres can be generated in delamination of a high stress ratio, as compared to that of a low stress ratio. This can lead to fatigue bridging laws are stress ratio dependent and fatigue delamination is block load sequence dependent.

Factors affecting the fatigue strength of thin-plates in large structures

This paper studies the main factors affecting the fatigue strength assessment of thin plates in large structures. The first part of study includes the influence of initial distortions, joints’ flexibility and surrounding structure on structural stress analysis of welded joint. The second part covers the influence of joint and its geometrical properties on fatigue strength modelling. The third part includes also the material elastic-plastic behaviour and the influence of crack propagation. The results show that if the structural analysis considers secondary bending properly, the local elastic fatigue damage parameters such as J-integral range can be used to model fatigue strength at 2–5million load cycles. However, to explain the slope variation of the fatigue resistance curve, the consideration of material elastic-plastic behaviour and short crack growth is needed. The strain-based crack growth simulations indicate that longer short crack growth period is the reason for the higher slope value. The importance of short crack growth is dependent on the weld notch geometry and plate thickness.

Fitness-for-service assessment of defected welded structural details by experimental evaluation of the fatigue resistance S-N curve

During the fabrication of two different structures (a ship and a bridge), made by mild construction steel, some unacceptable anomalies were detected; the structures were almost completely fabricated and a repair of the defected structural details was impractical due to the extent of the defected zones. A fitness-for-service assessment has therefore been carried out, in both cases, by performing fatigue tests on representative samples, cut off from the structure and by evaluating the fatigue resistance curve. A re-assessment of the structural details in question was undertaken, on the basis of the experimental S-N curve, evaluating the fitness for service of the “defected details”. The experimental tests showed that the detected anomalies had no influence on the fatigue strength of the welded joints and that the examined details (a butt joint and a cruciform joint) behave in accordance with the relevant FAT classes. The experimental program has also given the opportunity to compare different methodologies for fatigue assessment: the Effective Notch Stress Method, the Fracture Mechanics Method and the Peak Stress Method. The different procedures have been applied to the tested specimens, and the expected fatigue life was compared with the experimental one.

Fatigue strength assessment of laser stake‐welded T‐joints subjected to reversed bending

AbstractThe paper investigates the fatigue strength of laser stake‐welded T‐joints subjected to reversed bending. The fatigue tests are carried out with the load ratio, R ≈ −0.8. The experimental data is firstly analysed using the nominal stress approach and then by the J‐integral as the local fatigue strength parameter in the finite element (FE) assessment.The nominal stress approach demonstrated that the fatigue strength of the investigated T‐joints is lower than encountered for any other steel joint under reversed tensile loading. The results also showed that the fatigue strength of this joint under the load ratio R ≈ −0.8 increases with respect to R = 0 bending by 22.6% in the case of the nominal stress approach and 13% in the case of the J‐integral approach. However, the slopes of the fatigue resistance curves for different load ratios appear very similar, suggesting that the load ratio has an insignificant influence to the slope. In contrast to the similar slopes, the scatter indexes were different. The nominal stress approach shows that the scatter index is 3.4 times larger for R ≈ −0.8 than R = 0 bending. The J‐integral approach showed that the scatter index for R ≈ −0.8 is only 67% larger than in the R = 0 case because the weld geometry is modelled in the FE analysis.

Fatigue strength assessment of laser stake-welded T-joints using local approaches

This study investigates the applicability of local stress- and energy-based approaches to the fatigue strength assessment of laser stake-welded T-joints. The T-joint has two crack-like notches with infinitesimal tip rounding on each side of the weld. The local approaches used are fictitious tip rounding of 1 and 0.05mm and the approaches that assume zero rounding within this study, namely the stress intensity factor, the average strain energy density and the J-integral.It is shown that the slopes of the fatigue resistance curves vary between 4 and 8 under different loading conditions imposed on the joint. The slope value exhibits a linear relation with the dimensionless gradient of the maximum principal stress evaluated at the critical notch tip. The same linear relation between the slope and the gradient is valid for all approaches. Because of the slopes, which differ from the usual 3, the agreement of the T-joints with other steel joints is obtained at five million load cycles. The exception is the fictitious rounding concept of 0.05mm, in which case the recommended design S–N curve with a slope of 3 appears overly conservative in a high-cycle regime.

Discussion of “Empirical Design Rules for Effective Utilization of Orthotropic Decks” by Roman Wolchuk

The author’s statement that there is no stress-strain proportionality of welded connections because there are residual stresses that are at the yield point at the weld toes or in the weld, and therefore that linear-elastic analysis is not applicable at such locations, is in error as worldwide research has shown in published experimental fatigue studies of welded steel details provided in detailed National Cooperative Highway Research Program (NCHRP) reports (Fisher et al. 1970, 1974; Keating and Fisher 1986) and several books (Fisher 1984; Barsom and Rolfe 2001; Maddox 1991; Fisher et al. 1998; Gurney 2006). These results are also incorporated into design specifications around the world (every edition of the AASHTO standards from 1974 to the current version (AASHTO 2002); every edition of the AASHTO LRFD bridge design specifications from 1994 to the current version (AASHTO 2012); every edition of the American Railway Engineering and Maintenance-of-Way Association (AREMA) specification from 1978 to the current version [AREMA 2014; British Standards Institution 1980; European Convention for Constructional Steelwork (ECCS) 1985; European Committee for Standardization (CEN) 2006; Japanese Society of Steel Construction 1993]). There is no cumulative plasticity at these welded details as the author implies in Fig. 3 of the paper; plasticity mostly occurs at gross section yielding. At the weld toe section, the residual stresses are in equilibrium on the cross section, and the surrounding material remains elastic under subsequent dead and live loads. The flowwithin the high tensile residual stress region at the weld toe is contained by the surrounding, primarily elastic, material, which prevents cumulative plasticity at these regions. This has been verified in the experimental and analytical studies cited previously. Accordingly, the nominal elastic stress in the gross section is used for fatigue design, without any explicit consideration for the local residual stresses, which are implicitly considered by experimentally obtained fatigue resistance curves. This approach to fatigue design has been accepted universally; the phenomenon of metal fatigue was formally acknowledged in the 1860s (Barsom and Rolfe 2001; Bannantine et al. 1990). Only loads that create yielding on the entire cross section, such as that which occurs in cyclic hysteresis loops (or gross section yielding), as applied in seismic loading, redistribute the residual stress states. This does not occur in the orthotropic deck, nor in other welded bridge elements,which are designed for nominal elastic stresses under service conditions. Measurements on full-scale orthotropic decks and other bridge members have verified this finding in the laboratory and in the field (Fisher 1984; Connor and Fisher 2000; Tsakopoulos and Fisher 2005a, b; Connor et al. 2003). These measurements have also verified the analytical evaluation of orthotropic decks (Fanjiang et al. 2004).

Bridging effect on mode I fatigue delamination behavior in composite laminates

This paper discusses the bridging effect of fibres on mode I fatigue delamination growth in unidirectional and multidirectional polymer composite laminates based on a series of double cantilever beam (DCB) tests. From the results, there is sufficient evidence that fibre bridging can decrease the crack growth rate da/dN significantly, and using only one fatigue resistance curve to determine the delamination behavior in composite materials with large-scale fibre bridging may be inadequate. The bridging created in fatigue delamination is different from that of quasi-static delamination at the same crack length. So it is incorrect to use the resistance curve (R-curve) from quasi-static delamination tests to normalize fatigue delamination results.

Accurate Prediction of Fatigue Life under Random Loading

This study focuses on the method of predicting the fatigue life of materials subjected to random loading. Since random stress caused by random loading is rigorously expressed in the frequency domain as stress power spectral density (PSD), fatigue life should be predicted using stress PSD. We propose two adjustment methods of improving the accuracy of fatigue life prediction using stress PSD in the frequency domain. The method proposed by Dirlik is widely used for predicting the fatigue life in the frequency domain; however, it overestimates fatigue damage caused by large stress amplitude when the slope of the fatigue resistance curve is large. To prevent this overestimation, we applied our two adjustment methods to fatigue life prediction for typical random stresses observed on mechanical products. As a result, the adjustment methods worked well in improving prediction accuracy. Lightweight and reliable products can be therefore designed by applying the proposed methods to the evaluation of fatigue life under random loading.

Assessment of the service life of steel welded structures of offshore oil and gas installations

A method for calculating the fatigue of tubular welded sections, for evaluating the excessive increase in service life and for correcting the parameters of fatigue resistance curve, developed jointly with the E.O. Paton Electric Welding Institute, Kiev, is described.