Life Curves Research Articles

Fatigue life curve – A continuous Wöhler curve from LCF to VHCF

Abstract In order to consider cyclic material behavior in the course of the design process of cyclically loaded components and safety relevant parts, the importance of local strain-based fatigue design approaches has been growing continually. For the damage impact of load-time histories on components such as chassis parts, standard service loads with amplitudes settled in the high cycle fatigue and very high cycle fatigue regimes as well as overloads and misuse with load amplitudes from the low cycle fatigue regime, have to be considered, in order to perform a reliable fatigue life estimation. Therefore, a continuous fatigue life curve from the LCF to the VHCF regime, which covers all relevant damage mechanisms, is required. Hence, a fatigue life curve from low cycle fatigue (LCF) across to high cycle fatigue (HCF), and culminating at very high cycle fatigue (VHCF), derived from a combined method using strain- and load-controlled fatigue tests, will be discussed. This continuous fatigue life curve for aluminum wrought alloys, based on the evolution of the behavior of elastic-plastic material as well as the results of high frequency testing up to VHCF, will be presented.

Low-cycle fatigue test and life assessment of carbon structural steel GB Q235B butt joints and cruciform joints

Axial low-cycle fatigue tests are conducted on transverse butt joint specimens and cruciform joint specimens made of carbon structural steel GB Q235B. The effect of slip between the specimens and the grips of the test machine is considered by the proposal of a linear slip model. The cyclic softening properties are studied by observing the variation of stress amplitude with cycles. The cyclic stress–strain curve and the strain–life curve for both kinds of specimens are obtained based on the fatigue test data, and the corresponding coefficients are fitted. In order to verify the fatigue test results, finite element models of specimens are established and the corresponding fatigue life assessment is conducted using the local stress–strain approach and the equivalent structural stress approach, respectively. The results show that the effect of slip is unneglectable and the established linear slip model is reasonable. The two kinds of specimens both show a strain softening property, but cruciform joint specimens experience sudden falls of stress amplitude during the test due to the damage of welded lines; cruciform joint specimens show an either one-side failure mode or two-side failure mode while butt joint specimens only show a one-side failure mode; the two-side failure mode tends to lead to shorter fatigue life, so in the design of cruciform joint, such failure mode should be avoided.

Continuous fatigue damage prediction of a rubber fibre composite structure using multiaxial energy‐based approach

AbstractThis paper details an advanced method of continuous fatigue damage prediction of rubber fibre composite structures. A novel multiaxial energy‐based approach incorporating a mean stress correction is presented and also used to predict the fatigue life of a commercial vehicle air spring. The variations of elastic strain and complementary energies are joined to form the energy damage parameter. Material parameter α is introduced to adapt for any observed mean stress effect as well as being able to reproduce the well‐known Smith‐Watson‐Topper criterion. Since integration to calculate the energies is simplified, the approach can be employed regardless of the complexity of the thermo‐mechanical load history. Several numerical simulations and experimental tests were performed in order to obtain the required stress‐strain tensors and the corresponding fatigue lives, respectively. In simulations, the rubber material of the air spring was simulated as nonlinear elastic. The mean stress parameter α, which controls the influence of the mean stress on fatigue life, was adjusted with respect to those energy life curves obtained experimentally. The predicted fatigue life and the location of failure are in very good agreement with experimental observations.

Microstructure and fatigue behavior of novel Multi-Ring Domed resistance spot welds for thin X626-T4 aluminum sheets

Resistance spot welding of aluminum alloys is increasingly used in the automotive industry for vehicle lightweighting and better fuel efficiency. In this contribution, General Motor’s aluminum spot welding process including Multi-Ring Domed (MRD) electrodes and Conditioning, Shaping, and Sizing (CSS) weld schedule were used for welding of 0.8-mm thick X626-T4 aluminum alloy sheet. The resultant spot welds had an equiaxed grain structure adjacent to the weld nugget periphery. Within the weld nugget, fine columnar grains were found at the nugget perimeter, while welding defects were concentrated in the centre of the nugget. Using modified shear specimens, it was determined that the weld nugget is the weakest location while the heat affected zone is enhanced by precipitation aging due to a combination of welding and paint bake thermal cycles. We then derived a new equation for calculating minimum weld nugget diameters to ensure that interfacial fracture would not occur during tensile and fatigue testing. Load controlled fatigue test results showed that using structural stress analysis, fatigue life curves for both lap-shear and coach-peel configurations fell onto a single master curve indicating that the weld nugget size is the controlling parameter for fatigue life. While fracture mode varied with load amplitude from full button pullout at high amplitude to eyebrow-like fracture with kinked crack paths at low amplitude, no interfacial fracture occurred during fatigue testing due to the large size of the weld nugget even though the weld nugget is the weakest location.

On the complex geometry of individuality and growth: Cook’s 1914 “Curves of Life” and reading measurement

Growth in reading ability varies across individuals in terms of starting points, velocities, and decelerations. Reading assessments vary in the texts they include, the questions asked about those texts, and in the way responses are scored. Complex conceptual and operational challenges must be addressed if we are to coherently assess reading ability, so that learning outcomes are comparable within students over time, across classrooms, and across formative, interim, and accountability assessments. A philosophical and historical context in which to situate the problems emerges via analogies from scientific, aesthetic, and democratic values. In a work now over 100 years old, Cook’s study of the geometry of proportions in art, architecture, and nature focuses more on individual variation than on average general patterns. Cook anticipates the point made by Kuhn and Rasch that the goal of research is the discovery of anomalies—not the discovery of scientific laws. Bluecher extends Cook’s points by drawing an analogy between the beauty of individual variations in the Parthenon’s pillars and the democratic resilience of unique citizen soldiers in Pericles’ Athenian army. Lessons for how to approach reading measurement follow from the beauty and strength of stochastically integrated variations and uniformities in architectural, natural, and democratic principles.

The role of the shear and normal stress gradients on life estimation of notched Al7050-T7451 under multiaxial loadings

The aim of this work was to investigate the role of the normal and shear stress gradients on the life estimation of notched Al 7050-T7451 components under multiaxial stress states. In this setting, a new concept of an equivalent critical distance, Leq, was proposed. To validate the analysis a wide number of experimental fatigue data were generated for smooth and notched specimens under push–pull, torsion and combined in phase axial–torsional loadings. From these data, critical distance versus life curves (L-Nf) were obtained under torsion and push–pull loading conditions. The Modified Wöhler Curve Method (MWCM) critical plane based multiaxial model was used in conjunction with these curves and with the new Leq-Nf relationship to estimate lives. The results showed that the L-Nf curves obtained from the fully reversed torsion and push–pull tests had opposite behaviours. The best life estimates for the notched specimens under combined in phase axial–torsional loadings were obtained considering the new Leq-Nf relationship curve proposed in this work.

Tool life and workpiece surface integrity when turning an RR1000 nickel-based superalloy

Following a brief review on the turning of nickel-based superalloys, the paper evaluates the machinability and workpiece surface integrity of a powder metallurgy HIP-ed (PHIP) RR1000 alloy, involving two phases of turning experiments using TiN/Al2O3/Ti(C,N) coated carbide inserts. Based on a maximum flank wear criteria of 200 μm, tool life exceeded 40 min when operating at or below 100 m/min; however, Taylor tool life curves were extremely steep. At a feed rate of 0.08 mm/rev, workpiece surface roughness was ~ 0.5 μm Ra. Tests at cutting speeds of 80 m/min or less with new tools showed the ‘best/acceptable’ surface integrity with no visible white layer or plucking and a maximum distorted layer of ~ 6 μm deep. In contrast, the surfaces produced using worn tools at a cutting speed of 100 m/min showed a distorted layer of ~ 20 μm deep with evidence of surface laps and plucking to a depth of ~ 15 μm.

Development of a High Cycle Fatigue Life Prediction Model for Thin Film Silicon Structures

The fatigue characteristics of microelectromechanical systems (MEMS) material, such as silicon or polysilicon, have become very important. Many studies have focused on this topic, but none have defined a good methodology for extracting the applied stress and predicting fatigue life accurately. In this study, a methodology was developed for the life prediction of a polysilicon microstructure under bending tests. Based on the fatigue experiments conducted by Hocheng et al. (2008, “Various Fatigue Testing of Polycrystalline Silicon Microcantilever Beam in Bending,” Jpn. J. Appl. Phys., 47, pp. 5256–5261) and (Hung and Hocheng, 2012, “Frequency Effects and Life Prediction of Polysilicon Microcantilever Beams in Bending Fatigue,” J. Micro/Nanolithogr., MEMS MOEMS, 11, p. 021206), cantilever beams with different dimensions were remodeled with mesh control technology using finite element analysis (FEA) software to extract the stress magnitude. The mesh size, anchor boundary, loading boundary, critical stress definition, and solution type were well modified to obtain more correct stress values. Based on the new stress data extracted from the modified models, the optimized stress-number of life curve (S–N curve) was obtained, and the new life-prediction equation was found to be referable for polysilicon thin film life prediction under bending loads. After comparing the literature and confirming the new models, the frequency effect was observed only for the force control type and not for the displacement control type.

Experimental investigation on safety and reliability of ball‐eye under bending load in electrical systems

In view of the frequent failure of the ball-eye (BE) in the transmission line, the force analysis of BE in extreme weather is carried out, and a set of bending fatigue test equipment was designed. It is the first time to carry out the fatigue test of BE treated by normalising, annealing and quenching and tempering process under bending loads of 2330, 3495 and 4560 N. Meanwhile, the bending fatigue life curve is plotted. From the macro and micro point of view, the characteristics and the content of the elements of the fracture, and the influence of the internal structure on the mechanical properties of three samples of different heat treatment processes are analysed. Conclusion indicates that the mechanical properties of the BE treated by normalising process are best, whose microstructure is fine and uniform ‘ferrite + pearlite’. Comparing the life of BE withstood tension load, it is revealed that bending load is the main reason to accelerate the failure of BE.

Discounted cash flow (DCF) model detection based on goodwill impairment test

In the case of goodwill impairment test, the DCF model is often used when estimating the present value of the expected future cash flow of assets. In recent years, the use of DCF model in goodwill impairment test has made great progress, but the overall level has yet to be improved, especially the latest research results are not timely adopted. This paper studies the DCF model based on life curve analysis, the research results can provide reference for goodwill impairment test method and DCF model.

Investigation on vibration scuffing life curves

The printing images on products and packaging play an important role in increasing the business value, adding artistic quality, and sending information. During transportation, scuffing of the printing images will emerge due to vibrations and impacts induced by rough roads and vehicles. This paper investigates experimentally the vibration scuffing through an ink transfer device. The scuffing value–time curves are obtained. Then the scuffing life curves Grms,e‐Na,e based on excitation acceleration root‐mean‐square (RMS) and Grms,r‐Na,r based on relative acceleration RMS are developed. Both Basquin‐type and exponential‐type curves may be applied to describe the scuffing life in this case. The excitation frequency width covering the resonance frequency has a significant effect on the scuffing life curve Grms,e‐Na,e based on excitation acceleration RMS; however, it is not obvious on the scuffing life curve Grms,r‐Na,r based on relative acceleration RMS. The vibration system filters out the broadband excitation vibration frequencies away from the resonance zone and makes the relative acceleration signal a narrow one. The scuffing life curve in the resonance scuffing state is very different from that in the nonresonance scuffing state, and they should be distinguished in practical application. The scuffing life equations and curves obtained in this paper may provide a reference to the further research on packaging scuffing and its test evaluation and accelerated vibration test in laboratory.

Study of rolling contact fatigue behavior of a wind turbine gear based on damage-coupled elastic-plastic model

Gear contact fatigue has a significant influence on the reliabilities of heavy-duty gear-driven machines such as wind turbines. In the present work, an elastic-plastic contact fatigue model in conjunction with damage is developed to study the fatigue performance of a megawatt wind turbine gear. In this model, damages caused by both elasticity and plasticity are considered based upon the continuous damage mechanics (CDM) in the frame of ABAQUS using a user material subroutine. Damage accumulation and the evolution of the material mechanical properties are recorded during the fatigue crack initiation life. The contributions of elastic damage and plastic damage are distinguished. The effect of applied load on the contact fatigue life is studied and the stress–life curve is fitted based upon the numerical data. Results show that under a wide range of load conditions, the contact fatigue of the gear is always dominated by the elastic damage.

Numerical Study on Fatigue Propagation of Surface Cracks

Through FRANC3D software, the life curves of samples containing surface crack and through crack are analyzed respectively under the same stress ratio, whose life results are calculated when reaching each critical condition. The test results show that the sample containing surface crack whose life N3D is 65870, and the sample containing through crack whose life N2D is 6434, N3D is about 10.4 times of N2D. In addition, the life test results of samples with different initial surface crack sizes under the stress ratio R=0.1, 0.2, 0.3, 0.4, 0.5 cyclic load are also studied. Results show that the life N3D and the stress ratio R are obvious nonlinear relationship. Similarly, the life N3D and the initial crack half length c also show obvious nonlinear relationship.

Wear and Tool Life Investigation of Carbide Inserts while Hard Machining of Armox 500 Steel

Presented article deals about the experimental investigation of PVD coated cutting inserts of type SNHF 120408EN-SR-M1while hard face milling of steel Armox 500. This study was supported by the Slovak Research and Development Agency under the contract No. APVV-15-0710. All realized measurements and tests have been performed at Department of Engineering in Trencin. It also includes support and cooperation with the University of Defence in Brno, Department of mechanical engineering. The main aim of this experimental work is to focus measurement on the influence of the various values of feed rates per tooth during the hard machining experiments of steel Armox 500. All tested workpiece material is investigated with variable cutting conditions of feed rate per tooth, whereas the cutting speed and depth of cut were specified as the constant cutting parameters. Practical part of presented work also includes some figures of worn flank faces of carbide cutting inserts, microstructure of workpiece material and graphical dependences of tool wear and tool life curve in logarithm graph as the results of these realized experimental investigation.

Low cycle fatigue performance of Ni-based superalloy coated with complex thermal barrier coating

Thermal barrier coatings (TBCs) are widely applied to protect high-temperature components against high temperatures in harsh environments. Nineteen cylindrical specimens of Inconel 713LC were manufactured using the investment castings technique, and 10 specimens were subsequently coated with a novel complex thermal barrier coating (TBC) system. The TBC system comprises a metallic CoNiCrAlY bond coat (BC) and a complex ceramic top coat (TC). The TC is a mixture of a near eutectic nanocrystalline ceramic made of zirconia (ZrO2), alumina (Al2O3), silica (SiO2) and conventional yttria stabilized zirconia (YSZ) ceramic in the ratio of 50/50 in wt%. Low cycle fatigue (LCF) tests were carried out in a symmetrical push-pull cycle under strain control at 900 °C. Cyclic hardening/softening curves, cyclic stress-strain curves and fatigue life curves of the TBC-coated and uncoated material were assessed. Fatigue life curves in total strain representation showed transient behaviour. Fracture surfaces and polished sections parallel to the loading axis of the TBC-coated and uncoated specimens prior and after cyclic loading were observed by means of scanning electron microscopy (SEM) to study the degradation mechanisms during high-temperature LCF. TBC delamination was observed at the TC/BC interface, and rafting of precipitates occurred after high-temperature exposure. The microstructural investigations further the discussion of the differences in the stress-strain response and the fatigue life of the TBC-coated and uncoated superalloy.

Evaluating the development of life and progress of heavy vehicles based on Analytical Hierarchy Process (AHP) in main subsystems

The development of automotive products considering product lifecycle is considered as one of the automotive strategic key issues. In this article, Analytical Hierarchy Process (AHP) is used to evaluate the lifetime of heavy vehicles. To do this research, subsystems of weighted Titan heavy vehicle and the position of desired vehicle compared to other vehicles in the various subsystems and in general by the technical standards, new technologies and aesthetic appearance is evaluated. Finally, the curve of progress and technology life of Titan vehicle is provided . The results show that technical standards in automotive technology growth curve has the greatest impact in comparison with other properties. About Titan vehicle according to the technology lifecycle should be considered this issue that the technology of this vehicle because spending their maturity era is in decline. Regarding the investigation of new technologies, we have to think to make changes in vehicle technology or finding alternative technology. According to the first priority, criteria and the weight of analytic hierarchy process, the technical criteria, first the action should be done in technical improvements of the vehicle, and also considering that the sub-criteria of engine performance assigned the highest weight to itself, most of the studies should be placed in order to improve Titan automotive technology in terms of vehicle performance.

Evaluation of Strain–Life Fatigue Curve Estimation Methods and Their Application to a Direct-Quenched High-Strength Steel

Methods to estimate the strain–life curve, which were divided into three categories: simple approximations, artificial neural network-based approaches and continuum damage mechanics models, were examined, and their accuracy was assessed in strain–life evaluation of a direct-quenched high-strength steel. All the prediction methods claim to be able to perform low-cycle fatigue analysis using available or easily obtainable material properties, thus eliminating the need for costly and time-consuming fatigue tests. Simple approximations were able to estimate the strain–life curve with satisfactory accuracy using only monotonic properties. The tested neural network-based model, although yielding acceptable results for the material in question, was found to be overly sensitive to the data sets used for training and showed an inconsistency in estimation of the fatigue life and fatigue properties. The studied continuum damage-based model was able to produce a curve detecting early stages of crack initiation. This model requires more experimental data for calibration than approaches using simple approximations. As a result of the different theories underlying the analyzed methods, the different approaches have different strengths and weaknesses. However, it was found that the group of parametric equations categorized as simple approximations are the easiest for practical use, with their applicability having already been verified for a broad range of materials.

Predicting Fatigue Damage of Composites Using Strength Degradation and Cumulative Damage Model

This paper discusses the prediction of fatigue response of composites using an empirical strength and stiffness degradation scheme coupled to a cumulative damage accumulation approach. The cumulative damage accumulation approach is needed to account for the non-constant stress levels that arise due to stress distributions from stiffness degradation during the fatigue loading. Degradation of strength and stiffness during fatigue loading of the composite was implemented by following the empirical model presented by Shokrieh and Lessard with some modification and correction to the non-dimensional load parameter definition. The fatigue analysis was performed using ABAQUS™ finite element software using a user-defined material subroutine UMAT developed for the material response. Implementation results were first verified for unidirectional laminate test cases and validated by predicting stress versus life (S-N) curves for several laminate coupons test simulations and residual strengths of Open Hole Tension (OHT) specimens subjected to constant amplitude fatigue loading.

Determination of damage evolution in CFRP subjected to cyclic loading using DIC

AbstractDamage evolution in carbon fibre reinforced plastic subjected to fatigue loading (R = 0.5, −1, 2) has been studied using digital image correlation to obtain full‐field surface strains. Damage initiation being a local phenomenon, its effect on global parameters is not significant. The local transverse strain is a better indicator of delamination which affects transverse strain more than the longitudinal strain. Variation of normalized local transverse strain (ratio of local transverse strain to applied stress) near the initiated delamination indicates that the damage evolution occurs over 2 to 3 stages. Each stage has a stable damage growth with a drastic increase between the stages. The stages correspond to different damage mechanisms (matrix cracking, fibre‐matrix debonding, delamination, and fibre breakage) dominating at different periods during the fatigue life. Scatter in normalized local transverse strain plots due to large relative displacements was eliminated using different reference images for DIC. Waviness due to shift in the time at which the images are captured during the loading cycles was avoided using a sine curve fit to obtain maximum transverse strain in a cycle. Normalized local transverse strain plots were found to qualitatively reflect the physical extent of damage, thereby providing confidence in the methodology. Fatigue life curves were generated and run‐out lives were determined.

Damage mechanism in austenitic steel during high temperature cyclic loading with dwells

Austenitic stainless Sanicro 25 steel has been subjected to high temperature elasto-plastic cyclic straining at 700 °C. The isothermal cyclic tests without and with a dwell in the loading cycle were implemented. Several strain amplitudes and optional dwells of 10 min in tensile part of the loading cycle were applied to the specimens. Cyclic stress-strain response was recorded, cyclic hardening/softening curves and fatigue life curves were obtained. Scanning electron microscopy combined with focused ion beam allowed observing sections containing secondary cracks. They were used to identify the surface damage evolution. In order to investigate the internal damage the longitudinal cross sections parallel to the stress axis of the fatigued specimens were prepared. The crack paths and their relation to the grain and twin boundaries were studied by means of electron back scatter diffraction. Several distinct mechanisms of the crack initiation were found in both types of cyclic loading. The effect of the dwell in the loading cycles on fatigue life is discussed in relation to the surface and internal damage evolution.