Critical Stress Amplitude Research Articles

An improved constitutive model for rapid fatigue properties evaluation based on fatigue damage entropy

A constitutive model, which reflects the non-linear response association between microstructural motion and thermodynamic entropy production, is improved in this study. Two critical stress amplitudes associated with two microstructural movement mechanisms are considered in the improved constitutive model. The determination procedures for the parameters of the presented model are developed. Entropy generation data from three materials computed by two calculation methodologies, collected from the experiment and literature, are used to validate the improved model. Subsequently, a rapid fatigue life estimation method is proposed by using the accumulated entropy corresponding to fatigue damage, i.e. FFE, related to irreversible inelastic microstructural motion. Fatigue tests of welded joints fabricated by Q310NQL2 and Q345NQR2 steels, Q235 steel specimens, as well as experimental data, stainless steel specimens, collected from the literature, are employed to determine the values of the parameters of the developed model. The model is then used to forecast the S–N curve of butt joints with a 50% survival probability, and on this basis, the S–N curve with a certain confidence level is well estimated by the improved statistical method. This enhanced model may offer a fast forecast of the P–S–N curve at a certain confidence level within a limited set of tested data ranges.

Assessment of cyclic deformation and critical stress amplitude of jointed rocks via cyclic triaxial testing

Jointed rock specimens with a natural replicated joint surface oriented at a mean dip angle of 60° were prepared, and a series of cyclic triaxial tests was performed at different confining pressures and cyclic deviatoric stress amplitudes. The samples were subjected to 10,000 loading-unloading cycles with a frequency of 8 Hz. At each level of confining pressure, the applied cyclic deviatoric stress amplitude was increased incrementally until excessive deformation of the jointed rock specimen was observed. Analysis of the test results indicated that there existed a critical cyclic deviatoric stress amplitude (i.e. critical dynamic deviatoric stress) beyond which the jointed rock specimens yielded. The measured critical dynamic deviatoric stress was less than the corresponding static deviatoric stress. At cyclic deviatoric stress amplitudes less than the critical dynamic deviatoric stress, minor cumulative residual axial strains were observed, resulting in hysteretic damping. However, for cyclic deviatoric stresses beyond the critical dynamic deviatoric stress, the plastic strains increased promptly, and the resilient moduli degraded rapidly during the initial loading cycles. Cyclic triaxial test results showed that at higher confining pressures, the ultimate residual axial strain attained by the jointed rock specimen decreased, the steady-state dissipated energy density and steady-state damping ratio per load cycle decreased, while steady-state resilient moduli increased.

Large amplitude oscillatory shear stress (LAOStress) analysis for an acid-curd Spanish cheese: Afuega'l Pitu atroncau blancu and roxu (PDO)

Large amplitude oscillatory shear stress (LAOStress) was used to study the nonlinear rheological properties of Afuega'l Pitu (PDO) cheese atroncau blancu and roxu, a Spanish acid-curd cheese made from cow's milk, from nine manufacturers. Composition, physicochemical and lipolytic parameters were determined. The moisture content varied between (23.60 ± 0.75)% and (45.84 ± 0.01)% and the percentage of salt-in-moisture was <(8.17 ± 0.86)%. Stress amplitude sweeps were conducted at 20 °C, 50 °C and 75 °C at frequencies of 0.628 rad/s, 6.28 rad/s and 31.4 rad/s, for each temperature. Experiments were analyzed using the MITlaos software modified to extract LAOStress quantitative material functions. The large number of experiments and the high dimensionality of the LAOS signals were carefully analyzed and reduced to understand the material response and extract the relevant properties. All cheeses showed a distinct signature that motivates us to introduce the concept of “pseudo-linear LAOS” where nonlinear rheology is evident in only some measures while others minimally change from the linear regime. We geometrically interpret these different LAOS measures as rotation and distortion of Lissajous curves; all cheeses showed pseudo-linear LAOS regimes where rotation is strong and distortion is minimal, i.e. first-harmonics change dramatically in a regime where higher-harmonics are small enough that Lissajous curves are nearly elliptical. The pseudo-linear behavior enabled low-dimensional data reduction and three metrics were discovered to be the most relevant: linear elastic modulus (G′), critical stress (σcrit) and strain (γcrit) amplitudes. All Afuega'l Pitu cheese samples softened as stress amplitude increased while maintaining a solid-like behavior (tanδ^1∼ 0.3), regardless of frequency and temperature. Moreover, the difference between blancu and roxu was statistically insignificant compared to difference between manufacturers. Linear G′ and nonlinear σcrit decreased with increasing temperature, while the nonlinear γcrit maintained a constant value at 50 °C and 75 °C. Although G′, σcrit and γcrit metrics establish comparison between cheeses, more metrics are still required to fully connect rheology to cheese texture and sensory profiles.

Ускоренная оценка влияния технологических факторов на прочностные характеристики Ti-6Al-4V И Al-Cu-Mg

Introduction. The strength of construction materials when used under cyclic loads is of great importance in design engineering. A significant number of factors that affect the fatigue resistance have predetermined the creation of numerous methods that consider such influence. Nondestructive methods that are based on the connection of the physical degradation of material with strain properties enable evaluating experimentally the fatigue properties of materials. Purpose of study: the analysis of the processes of energy dissipation and strain accumulation during the inelastic cyclic strain of samples, using the VT6 (Ti-6Al-4V) titanium alloy and the D16 (Al-Cu-Mg) aluminum alloy before and after the technological impact. The work experimentally investigates the physical processes of degradation of the VT6 and D16 alloy samples that accompany the process of fatigue failure in materials with homogeneous and inhomogeneous stress-strain states in the concentrator (in the form of a hole and a weld). Typical modes are used to reach the fatigue testing that determine the critical stress in a material sample – the stress at which physical properties (temperature, strain) change without reaching the fatigue failure of samples. Critical stress amplitudes in the cycle, based on the data obtained during the experiment and the results of mathematical simulation, are compared. The effect of stress concentrators on critical loads that a detail can withstand after a unit operation is estimated by the finite-element method (FEM). As a result, the effect of the operational and technological factors on critical stress determined by strain and temperature is estimated. Comparative tests of the VT6 and D16 alloy samples with and without stress concentrators showed that the amplitudes of critical stress decrease by more than 30% in comparison with the ones that are without stress concentrators. The low-cycle fatigue tests of the D16 alloy samples are carried out. Mathematical simulation of the cyclic strain of the samples is carried out using MSC.Marc package. The results of the cyclic loading tests, which show that the characteristics of the technological process reduce the amplitudes of the critical stress of the VT6 and D16 alloys and affect the fatigue properties of the D16 aluminum alloy, are discussed. Mathematical simulation corresponded positively to the experimental data. Such correspondence indicates the possibility of conducting qualitative numerical assessments of the beginning of the inelastic strain accumulation process in structures with stress concentrators under the cyclic stress and the increasing stress amplitude, using the typical sample made of hardening elastoplastic material.

Three-dimensional stress-controlled cyclic behavior of the interface between gravel and steel

Three-dimensional (3D) stress-controlled cycling is arguably reflective for soil–structure interfaces under in-situ loading conditions. The 3D stress-controlled cyclic behavior of a gravel–steel interface and its influencing factors were explored by conducting several series of tests. Distinct tangential displacement is induced and shows a noticeable coupling effect when subjected to 3D cycling of shear stress. The stress-controlled behavior differs significantly from the displacement-controlled behavior, and presents obvious 3D features which are influenced by the shear path, shear stress amplitude, and unequal stress amplitudes. The shear path affects the magnitude and relationship pattern of the performance parameters, while the shear stress amplitude primarily impacts the magnitude. The shear stress-displacement curves exhibit elliptical and hyperbolic formations in circular and linear shear paths, respectively. The peak reversible normal displacement remains constant with cycling in two-way shear paths, but is negligible in one-way shear path. Increased shear stress amplitude results in magnified tangential displacement and migration, peak shear flexibility, irreversible and peak reversible normal displacements, and decreased non-coaxial angle. The critical shear stress amplitude is approximately 240 kPa, at which the peak shear flexibility remains constant with cycling. Induced aeolotropy of the interface occurs in the reversible normal displacement subjected to unequal stress amplitudes.

Research on extending the fatigue life of railway steel bridges by using intelligent control

This paper investigates the potential of a vibration control-inspired method towards extending the fatigue life of railway steel bridges. Based on coupled thermal-mechanical and vehicle-track analysis, both the residual stresses from welding and these from traffic on the bridge are obtained. Subsequently, a multi-scale approach with a shell Finite Element (FE) model of the whole bridge and a solid FE model of its critical joints is put forward. The equation of motion is established for the controlled bridge, equipped with a Magnetorheological-Tuned Mass Damper (MR-TMD) system, while the combination of excitation, welding and control effects is practiced through own-developed packages and commercial software sub-model routines. The framework is showcased for the study of the Poyang Lake Railway Bridge in China. After obtaining the controlled stress states at the critical welded joint, the fatigue crack initial life is evaluated by using the critical plane method and the linear cumulative damage theory. Simulation results indicate that the multi-scale modelling approach followed, meets the accuracy needs for capturing the cracking process of the welded joint with high computational efficiency. The MR-TMD system, even when moderately reducing the critical joint stress amplitudes, can improve substantially the overall bridge fatigue resistance over the uncontrolled structure.

An intrinsic dissipation model for high-cycle fatigue life prediction

This paper introduces a new intrinsic dissipation model for high-cycle fatigue life prediction of metallic materials. A general constitutive model with internal state variables, in accordance with the thermodynamic principles, is firstly formulated to describe the thermo-mechanical response of metallic materials under high-cycle fatigue loading. The model formulation considers two types of micro-mechanisms, i.e. the recoverable microstructure motion inducing anelasticity and the unrecoverable microstructure motion inducing damage. The intrinsic dissipation model is then derived taking into account two critical stress amplitudes related to the corresponding microstructure motion. Finally, a fatigue life prediction model is obtained by taking as a fatigue damage indicator, the intrinsic dissipation part induced solely by the unrecoverable microstructure motion, and as a failure criterion, the concept of energy dissipation threshold. The application is made on a FV520B stainless steel. Stepwise-amplitude and constant-amplitude experiments are used to identify the model parameters and the model prediction capabilities are verified by comparing the model-predicted S–N curve with the experimental results issued from traditional fatigue measurements. The underlying physical mechanisms are discussed by analyzing the stress amplitude and plastic pre-strain effects on the intrinsic dissipation.

Kinking Behavior of S-N Curve for Ti6Al4V Alloy Notched Specimen under a Load-Controlled High Cycle Fatigue Test

Notch fatigue behavior of Ti-6Al-4V titanium alloy has been investigated under a load-controlled high cycle fatigue test. The S-N curve was kinked at the critical nominal stress amplitude, where the plastic deformation nucleated at notch root. The plastic zone size at the critical nominal stress amplitude was almost equal to the size of 4 grains of the present Ti-6Al-4V alloy, which were the same findings as in the 2024-T4 alloy used in the previous study. Above the critical nominal stress amplitude, the local stress ratio at notch root decreased with increasing nominal stress amplitude. The critical nominal stress amplitudes normalized by the cyclic yield stress were almost the same for Ti-6Al-4V alloy and the 2024-T4 alloy. The significant decrease of the local stress ratio with increasing nominal stress amplitude was observed in the 2024-T4 alloy with low cyclic yield stress and low cyclic hardening coefficient compared to the Ti-6Al-4V alloy with high cyclic yield stress and high cyclic hardening coefficient.

Variation of local stress ratio and its effect on notch fatigue behavior of 2024-T4 aluminum alloy

Fatigue tests and finite element analysis of notched specimen were carried out to investigate the variation of local stress ratio at notch root and its influence on fatigue strength. The S–N curve of 2024-T4 aluminum alloy was kinked at the critical nominal stress amplitude, above which the local stress ratio became low due to the development of local plastic deformation at notch root. The predicted fatigue lives based on linear fracture mechanics approach were in agreement with the experimental results below the critical nominal stress amplitude. The predicted fatigue lives based on the SWT parameter, where the variation of local stress ratio was taken into account, were in good agreement with the experimental results above the critical nominal stress amplitude.

Tailoring the Hardening Behavior of 18CrNiMo7‐6 via Cu Alloying

In order to improve the rolling contact fatigue (RCF) behavior of gear steels, a concept to increase their damage tolerance is developed alternatively to the conventional approach of improving the degree of steel cleanliness. For that purpose, Cu is used as a main alloying element in order to trigger the precipitation of nano‐sized Cu precipitates which shall improve the strain‐hardening rate of the martensitic matrix of Cu‐alloyed 18CrNiMo7‐6 steel surrounding a non‐metallic inclusion during plastic deformation. In this way, early component failure may be avoided and the maintenance costs of, e.g., wind energy converters may be kept low. The experimental analysis shows that nano‐sized Cu precipitates influence the material's strength, ductility, and strain‐hardening behavior under tension, depending on their coherence. Among others, the latter is related to strain‐induced martensitic transformation of coherent Cu. The structure of the Cu precipitates is studied by TEM and SANS analysis. The Cu‐alloyed steel also shows an increased hardening‐exponentCHT studied by cyclic hardness test (CHT) PHYBALCHT. Fatigue tests of specimens with coherent precipitates show cyclic hardening until a critical stress amplitude. Above that, stress amplitude cyclic softening is detected. An increased damage tolerance could be obtained for a 1 mass‐% Cu‐alloyed 18CrNiMo7‐6 steel.

Effects of a Single Open Joint on Energy Transmission Coefficients of Stress Waves with Different Waveforms

Open joints have significantly different effects on stress wave propagation across them as compared to closed and filled joints. In the present study, a theoretical model is developed based on the analysis of interaction process between stress waves and a single open joint. The analytical solutions to the energy transmission coefficient are mathematically derived for stress waves across an open joint. Parametric studies are conducted to evaluate the effects of various parameters on the energy transmission coefficient. It is found that the energy transmission coefficient follows a similar trend for all types of stress waves, but stress waves with different waveforms have different values. The energy transmission coefficient increases with the increase in the wave amplitude and duration, but decreases with the gap width. It also increases at the outset, and then decreases gradually with the increase in the incident angle for rectangle, symmetric triangle and ascending triangle waves, but it decreases with the incident angle for sine and descending triangle waves. Furthermore, different-shaped stress waves have different critical gap widths for wave transmission. The optimal incident angle and the critical gap width increase as the wave duration increases, but the critical stress amplitude decreases.

Analysis of Sinusoidal Interfacial Wrinkling of an Anisotropic Film Sandwiched Between Two Compliant Layers

When a stiff film is bonded to a compliant layer and meanwhile encapsulated by another compliant layer on top, the film may form wrinkles under applied compressive stress. Inspired by the recent development of foldable circuit sealed in an encapsulating layer to improve bendability, unlike the wide study of surface wrinkling in a bilayer system, this paper presents a study of possible sinusoidal interfacial wrinkling in such sandwich system. The film is assumed to be anisotropic with arbitrary orientation of elastic axis while both layers are isotropic. A linear perturbation analysis is performed to predict critical membrane stress, wave number and equilibrium amplitude for the onset of interfacial wrinkles. The effect of parameters such as elastic axis orientation of the film and moduli, thicknesses, and Poisson's ratios of the layers on the wrinkling is evaluated in detail. The results show that compared to two compliant layers, the stiffer and thinner the film is, the smaller the values of both the critical stress and wave number for wrinkling will be. Especially, we illustrate three limiting cases: two layers both reach thick-layer limit, two layers both reach thin-layer limit and one layer reaches thick-layer limit while the other layer reaches thin-layer limit. Analytical solutions are obtained for first two cases and numerical solutions are plotted for the third case. It is found that as long as the thin-layer is near incompressible, the interfacial wrinkles can be suppressed. In addition, the equilibrium wave modes for the three limiting cases are also given. The resulting solutions for the sandwich system can be reduced to the classic solutions for a bilayer system.

Finite weakest-link model of lifetime distribution of quasibrittle structures under fatigue loading

The design of various engineering structures, such as buildings, infrastructure, aircraft, ships, as well as microelectronic components and medical implants, must ensure an extremely low probability of failure during their service lifetime. Since such a low probability is beyond the means of histogram testing, we must rely on some physically based probabilistic model for the statistics of structural lifetime. Attention is focused on structures consisting of quasibrittle materials. These are brittle materials with inhomogeneities that are not negligible compared with the structure size, as exemplified by concrete, fiber composites, tough ceramics, rocks, sea ice, bone, wood, and many more at the micro- or nano-scale. This paper presents a finite weakest-link model of the fatigue lifetime of quasibrittle structures that fail at the fracture of one representative volume element (RVE). In this model, the probability distribution of critical stress amplitude is first derived by assuming a prescribed number of loading cycles and a fixed stress ratio. The probability distribution of fatigue lifetime is then deduced from the probability distribution of critical stress amplitude through the Paris law for fatigue crack growth. It is shown that the present theory matches well with the experimentally measured lifetime histograms of various engineering and dental ceramics, which systematically deviate from the two-parameter Weibull distribution. The theory indicates that the mean fatigue lifetime of quasibrittle structures must strongly depend on the structure size and geometry. Finally, the present model indicates that the probability distribution of fatigue lifetime can be determined from the mean size effect analysis.

Experimental Study on Dynamic Deformation Characteristics of Weathered Conglomerate under Cyclic Loading

The durability and safety of the subway tunnel structure is contingent on the substrate deformation under the subway operating load, which is a low frequency, long-term repetitive dynamic load. Using dynamic tri-axial cyclic loading test, the dynamic strain for weathered conglomerate under low-frequency cyclic loading was studied, while the influence of factors such as dynamic stress amplitude, static deviator stress, confining pressure impaction and loading frequency on dynamic strain of weathered conglomerate were analyzed. The results showed that, the deformation development of weathered conglomerate was basically stable convergence curves under low frequency cyclic loading, and the deformation could be divided into early stage (characterized by an increase in deformation) and stable stage with accumulative deformation in the early stage accounted for more than 90% of the total deformation. For the case of exceeding the critical stress amplitude, strain development of weathered conglomerate was quadratic curve type, and reached failure state. The results of dynamic test could provide useful reference to the dynamic design of subway tunnel.

Physicochemical and rheological characterization of Prosopis juliflora seed gum aqueous dispersions

The gum from Prosopis juliflora seed was isolated and its protein (0.60%), fat (0.55%) and total carbohydrate (98.46%) percentages, specific rotation (+64.01), intrinsic viscosity (1178 mL/g) and calculated molecular weight were determined. This gum turned out to be a galactomannan with an M/G ratio of 1.74:1. The rheology of concentrated aqueous dispersions of this gum was studied as a function of gum concentration in the (0.6–1.4) %w/v range. The mechanical spectra were consistent with the occurrence of random-coil macromolecular solutions forming entanglement networks. The terminal relaxation time estimated from mechanical spectra increased with gum concentration. The crossover frequency, terminal relaxation time and corresponding viscoelastic moduli of the 1% w/v dispersion were compared to those of commercial and non-traditional galactomannan gums. Steady-shear flow curves showed a low-shear Newtonian region, shear thinning behaviour above a critical shear rate and fitted the 2-parameter empirical model proposed by Morris (1990). The specific viscosity derived from the zero-shear viscosity scaled with C [η] with an exponent of 3.7. An Arrhenius-type equation fitted the temperature dependence of the zero-shear viscosity and of the apparent viscosity at 10 s−1, for the 1% w/v dispersion. The energy of activation for the latter shear rate was much lower than for the former. Decreasing temperatures from 20 °C to 5 °C hardly influence the critical stress amplitude but brought about a small increase in the terminal relaxation time and greater values of G′ and G″. Deviations from the Cox–Merz rule were found to depend on both the gum concentration and temperature.

Compression fatigue behavior of laser processed porous NiTi alloy

Porous metals are being widely used in load bearing implant applications with an aim to increase osseointegration and also to reduce stress shielding. However, fatigue performance of porous metals is extremely important to ensure long-term implant stability, because porous metals are sensitive to crack propagation even at low stresses especially under cyclic loading conditions. Herein we report high-cycle compression–compression fatigue behavior of laser processed NiTi alloy with varying porosities between ∼1% and 20%. The results show that compression fatigue of porous NiTi alloy samples is in part similar to metal foams. The applied stress amplitude is found to have strong influence on the accumulated strain and cyclic stability. The critical stress amplitudes associated with rapid strain accumulation in porous NiTi alloy samples, with varying relative densities, were found to correspond to 140% of respective 0.2% proof strength indicating that these samples can sustain cyclic compression fatigue stresses up to 1.4 times their yield strength without failure.

Unified nano-mechanics based probabilistic theory of quasibrittle and brittle structures: II. Fatigue crack growth, lifetime and scaling

This paper extends the theoretical framework presented in the preceding Part I to the lifetime distribution of quasibrittle structures failing at the fracture of one representative volume element under constant amplitude fatigue. The probability distribution of the critical stress amplitude is derived for a given number of cycles and a given minimum-to-maximum stress ratio. The physical mechanism underlying the Paris law for fatigue crack growth is explained under certain plausible assumptions about the damage accumulation in the cyclic fracture process zone at the tip of subcritical crack. This law is then used to relate the probability distribution of critical stress amplitude to the probability distribution of fatigue lifetime. The theory naturally yields a power-law relation for the stress-life curve (S-N curve), which agrees with Basquin's law. Furthermore, the theory indicates that, for quasibrittle structures, the S-N curve must be size dependent. Finally, physical explanation is provided to the experimentally observed systematic deviations of lifetime histograms of various ceramics and bones from the Weibull distribution, and their close fits by the present theory are demonstrated.

Ultrasonic fatigue of a high strength steel

At the Institute of Materials Science and Engineering at the University of Kaiserslautern an ultrasonic testing system for the fatigue assessment of metallic materials in the very high cycle fatigue (VHCF) regime was developed. The ultrasonic testing system allows to control the test and to measure detailed fatigue data. The achieved results can be used to describe the cyclic deformation behaviour of wheel steels at ultrasonic frequencies. In load increase tests (LIT), the critical stress amplitude can be determined, which leads to a defined change of process parameters like generator power, dissipated energy and specimen temperature. With SEM investigations it was proved that the change of the process parameters correlates with irreversible changes in the microstructure. It can be shown that the stress amplitude, leading to first irreversible changes in the microstructure, strongly depends on the depth position within the original wheel rim. New and basic results on the fatigue mechanisms of high strength steels in the VHCF-regime can be achieved.

Cyclic deformation behavior of a medium carbon steel in the VHCF regime

At the Institute of Materials Science and Engineering an ultrasonic testing facility (UTF) for the fatigue assessment in the very high cycle fatigue (VHCF) regime was developed. The UTF allows to control the test and to measure process parameters like generator power and specimen temperature. In load increase tests (LIT), the critical stress amplitude leading to a first rise of the measured physical values is determined and can be used to identify suitable amplitudes for single step tests in the VHCF regime. The individual design of the UTF allows a defined interruption of the fatigue experiment for detailed microscopic investigations.

Shock compression behavior of a S2-glass fiber reinforced polymer composite

Synthetic heterogeneous material systems, e.g., layered composite materials with organic matrices reinforced by glass fibers (GRP), are attractive materials for a variety of lightweight armor applications. However, while the dynamic response of homogeneous materials, such as, metals and ceramics, has been well documented, the ballistic response of heterogeneous material systems is poorly understood. In the present study, in an attempt to better understand the shock-induced compression response of GRPs, a series of plate impact experiments were conducted on a S2-glas fiber reinforced polymer composite comprising S2-glass woven roving in a Cycom 4102 polyester resin matrix. The plate-impact experiments were conducted using an 82.5 mm bore single-stage gas-gun at the Case Western Reserve University. The history of the shock-induced free-surface particle velocity at the rear surface of the target plate was monitored using the multibeam VALYN™ VISAR system. The results of the experiments indicate the absence of an elastic front in the shock-induced free-surface particle velocity profile in the GRP. Moreover, in the low impact velocity range, relatively weak late-time oscillations are observed in the particle velocity profiles. Increasing the amplitude of the shock-induced compression resulted in a decrease in the rise-time of the shock wave front. The critical shock stress amplitude at which a clear shock-front is seen to develop during the shock loading was determined to be between 1.5 and 2.0 GPa. The results of the experiments are used to obtain the equation of state of the GRP in the stress range 0.04–20 GPa. Moreover, the Hugoniot curve (Hugoniot stress versus Hugoniot strain) was calculated using the Rankine–Hugoniot relationships; the departure of the Hugoniot stress versus the particle velocity curve from linearity allowed the estimation of the Hugoniot elastic limit of the GRP to be about 1.6 GPa.