Stress-strain Hysteresis Loops Research Articles

A new damage-coupled cyclic plastic model for whole-life ratchetting of heat-treated U75V steel

In the framework of continuum damage mechanics, a new damage-coupled cyclic plastic model is proposed to describe the nonlinear evolution of whole-life ratchetting and its dependence on the stress level. The characteristic that the damage evolution rate of U75V heat-treated steel decays in the initial load cycles is considered by introducing a modified term into classic damage evolution equation. A hybrid fatigue failure criterion considering both the fatigue and ratchetting strain-induced failures is established based on the fatigue failure rule concluded from experiments. Comparisons between simulated and experimental stress–strain hysteresis loops, ratchetting strains, damage evolutions, and fatigue lives are performed to validate the proposed model.

Comprehensive Assessment of Low Cycle Fatigue Behavior of Nickel-Base Superalloy Superni 263 in the Range 298–1023 K

The effects of temperature on low cycle fatigue (LCF) behavior of Superni 263 superalloy in the solution annealed plus aged state were examined between 298 and 1023 K. The initial microstructure consisted of intragranular spherical γʹ (22 nm), intergranular M23C6 carbides and a few un-dissolved primary MC particles. Strain-controlled LCF tests were performed at a strain rate of 10−3 s−1. Correlations between the initial microstructure, macroscopic cyclic deformation, fatigue life, crack initiation and propagation modes, evolving deformation substructure and phase changes have been attempted. Cyclic stress response displayed a marked variation in its temperature dependence. In general, the alloy exhibited initial hardening followed by very slight softening up to 473 K, continuous hardening to a maximum stress in between 573 and 873 K, and initial hardening succeeded by rapid softening at and above 923 K. Dynamic Strain Ageing (DSA) was noticed during 573–923 K. In the DSA domain, the alloy exhibited pronounced cyclic hardening at 673 K, displayed planar slip, stacking faults, high dislocation density and shearing of γʹ. The macroscopic features revealed serrated flow in the plastic deformation portions of stress–strain hysteresis loops and inverse temperature dependence of maximum stress and inelastic strain generated at half-life. Fresh precipitation of γʹ occurred at 973 K and 1023 K during LCF testing while prior existing γʹ coarsened marginally above 923 K. The operating deformation mechanisms of γʹ were identified and correlated with microscopic and macroscopic aspects. LCF life displayed a maximum at ~ 473 K and the reduction in life above 473 K was attributed to the deleterious effects of DSA and oxidation.

Correlation between endurance limit and cyclic yield stress determined from low cycle fatigue test

Cyclic plastic deformation is an essential condition for fatigue crack initiation. The experimental result shows that the cyclic plastic deformation takes place at the micro-level for applied stress amplitude equal to the cyclic yield stress of the metal. Physics of fatigue crack initiation justifies the fatigue crack initiation in cyclic yield stress, which is far below the tensile yield stress of the metal. Cyclic yield stress is determined from a stable stress–strain hysteresis loop of low cycle fatigue test. The author demonstrates from the experimental result of different metals collected from the literature that endurance limit and cyclic yield stress are alike.

Multiscale analysis of the effect of interfacial energy on non-monotonic stress–strain response in shape memory alloys

The effect of formation and evolution of stress-induced martensitic microstructures on macroscopic mechanical properties of shape memory alloys in the pseudoelastic regime is investigated with account for size-dependent energy of interfaces. A quantitative relationship is established between the changes in free energy and dissipation on the interfaces at three microstructural scales and the overall mechanical characteristic of the material under tensile loading. The multiscale analysis carried out for a polycrystalline NiTi shape memory alloy has revealed that the interfacial energy storage and dissipation can strongly affect the shape and width of the stress–strain hysteresis loop. The predicted non-monotonic stress–strain response for the material of a selected grain size shows a remarkable similarity to the experimental one extracted from a tensile test of a laminate by Hallai and Kyriakides (2013). By the classical Maxwell construction, the non-monotonic response for a material element results in a commonly observed stress plateau for a tensile specimen, which is associated with the propagation of phase transformation fronts. This behaviour is confirmed with striking accuracy by 3D finite-element computations performed for a macroscopic tensile specimen, in which propagating instability bands are treated explicitly.

Microstructure-sensitive critical plastic strain energy density criterion for fatigue life prediction across various loading regimes.

In the present work, we postulate that a critical value of the stored plastic strain energy density (SPSED) is associated with fatigue failure in metals and is independent of the applied load. Unlike the classical approach of estimating the (homogenized) SPSED as the cumulative area enclosed within the macroscopic stress–strain hysteresis loops, we use crystal plasticity finite element simulations to compute the (local) SPSED at each material point within polycrystalline aggregates of a nickel-based superalloy. A Bayesian inference method is used to calibrate the critical SPSED, which is subsequently used to predict fatigue lives at nine different strain ranges, including strain ratios of 0.05 and −1, using nine statistically equivalent microstructures. For each strain range, the predicted lives from all simulated microstructures follow a lognormal distribution. Moreover, for a given strain ratio, the predicted scatter is seen to be increasing with decreasing strain amplitude; this is indicative of the scatter observed in the fatigue experiments. Finally, the lognormal mean lives at each strain range are in good agreement with the experimental evidence. Since the critical SPSED captures the experimental data with reasonable accuracy across various loading regimes, it is hypothesized to be a material property and sufficient to predict the fatigue life.

Cyclic Plasticity of the As-Built EOS Maraging Steel: Preliminary Experimental and Computational Results

This short communication offers a preliminary view on ongoing research conducted on the as-built EOS maraging steel 300. The material’s cyclic elastoplastic characteristics under strain-controlled loading have been investigated experimentally. Specimens fabricated under two primary orientations, horizontally and vertically to the build plate, have been tested. The obtained stress–strain hysteresis loops exhibited symmetry, with the vertical specimen showing a higher plastic strain energy dissipation capability than the horizontal specimen. Modelling of the material’s elastoplastic behaviour was performed with a commonly used kinematic hardening rule, combined with both isotropic and anisotropic yield functions and elasticity moduli. The obtained simulations of the hysteresis loops, from the implementation of these two plasticity models, indicate the advantage of the anisotropic modelling approach over the isotropic approach. The anisotropic plasticity model describes in a more representative way the inherent elastic and plastic anisotropy of the as-built material. Further research is underway to explore the low cycle fatigue performance of this additively manufactured metal.

Uniaxial Ratcheting Assessment of 304 Stainless Steel Samples Undergoing Step-Loading Conditions at Room and Elevated Temperatures

AbstractThe present study evaluates ratcheting response of 304 stainless steel samples subjected to various step-loading conditions at room and elevated temperatures using the kinematic hardening rules of Ohno–Wang (O–W), AbdelKarim–Ohno (AK–O), and Ahmadzadeh–Varvani (A–V). The hardening rules were employed along with the visco-plastic flow rule to account for the time-dependent response of 304 stainless steel samples. Ratcheting over low–high–low loading sequences consistently showed a small drop in ratcheting strain over the third loading step. This is mainly due to plastic strain accumulation over the first two loading steps preventing ratcheting strain to drop significantly with a drop in the mean stress. Moreover, dynamic recovery terms in these models were further modified through the inclusion of an exponential function developed by Kang to address the dynamic strain aging phenomenon. Low ratcheting rate and shakedown shortly after a few stress cycles within loading steps as operating temperatures varied between 400 and 600 °C were attributed to dynamic strain aging phenomenon in SS304 steel alloy. Progressive ratcheting response and their stress–strain hysteresis loops were highly influenced at various operating temperatures, stress levels, and stress rates. Coefficients in the dynamic recovery term of the A–V model controlled ratcheting progress and hysteresis loops agreeable with those of experimental data over consecutive loading steps. Choices of material constants and the number of segments defined from stress–strain curve based on the O–W and AK–O models noticeably influenced the ratcheting response of steel samples. Predicted ratcheting values by means of the A–V, O–W, and AK–O models were discussed and compared with those of the experimental data.

Shaking Table Experiments to Evaluate the Boundary Effects on Seismic Response of Saturated and Dry Sands in Level Ground Condition

The laminar shear boxes (LSBs) are commonly preferred for geotechnical physical modeling over the fixed wall boxes; the latter may suffer from problems associated with wave reflection. This paper mainly describes the seismic response of a uniform layer of loose saturated and dry sands in rigid and flexible boundary conditions. A lightweight LSB was recently designed and fabricated by the authors for physical modeling of geotechnical earthquake engineering problems. To investigate the boundary effect on the seismic response of level ground, a series of shaking table tests were conducted with both LSB and rigid wall containers in identical conditions. The seismic performance of the free-field ground in the experiments is evaluated in terms of time histories, shear stress–strain hysteresis loop, and dynamic soil properties. The dynamic movements of all layers in the LSB, captured by image processing techniques, are compared with that of the rigid end-wall condition. The results demonstrate that acceleration and settlement of the ground surface are highly affected by artificial boundaries in both dry and saturated sands. It is shown that the hysteresis loops estimated from the LSB tests are more compatible with the cyclic behavior of sands, compared with those of the rigid box tests.

Ratcheting Prediction at the Notch Root of Steel Samples Over Asymmetric Loading Cycles

Abstract The present study intends to evaluate local ratcheting and stress relaxation of medium carbon steel samples under various asymmetric load levels by means of two kinematic hardening rules of Chaboche (CH) and Ahmadzadeh-Varvani (A-V). The Neuber's rule was coupled with the hardening rules to predict ratcheting and stress relaxation at the vicinity of the notch root. Stress-strain hysteresis loops generated by the CH and A-V models were employed to simultaneously control ratcheting progress over stress cycles and stress relaxation at notch root while strain range kept constant in each cycle. The higher cyclic load levels applied at the notch root accelerated shakedown over smaller number of cycles and resulted in lower relaxation rate. The larger notch diameter of 9 mm on the other hand induced lower stress concentration and smaller plastic zone at the notch root promoting ratcheting progress with less materials constraint over loading cycles compared with notch diameter d = 3 mm. Predicted ratcheting results through the A-V and CH models as coupled with the Neuber's rule were found in good agreements with the experimental data. The choice of the A-V and CH hardening rules in assessing ratcheting of materials was attributed to the number of terms/coefficients and complexity of their frameworks and computational time/central processing unit (CPU) required to run a ratcheting program.

Investigation on fatigue crack resistance of Q370qE bridge steel at a low ambient temperature

The Q370qE steel has a wide application in the medium and long span railway steel bridges in China, due to its excellent material characteristics including high strength, high toughness and good weldability at room temperature. Nevertheless, the limited research work on the fatigue properties of the Q370qE steel challenges the safety of steel bridges in cold and severe cold regions under the cyclic actions. This study first conducts a series of strain-controlled fatigue tests of coupon specimens at room temperature and −60 °C to characterize the cyclic stress-strain curve, hysteresis loops, Masing behavior and fatigue crack initiation resistance by Coffin-Manson relationship. Thereafter, the fatigue crack propagation tests of the compact tension specimens under different stress ratios and different temperatures reveal the effect due to stress ratios and temperatures on the fatigue crack propagation resistance of the Q370qE steel through the Paris formula. Results demonstrate that the low temperatures enhance the resistance to the fatigue crack initiation and propagation of the Q370qE steel. Finally, to better quantify the performance of the Q370qE steel, this paper collects different bridge steels and compares the fatigue crack initiation resistance and fatigue crack propagation between the Q370qE steel and other bridge steels. The results quantify the excellent higher fatigue resistance of Q370qE steel in comparison with other bridge steels.

Descriptions of stress-strain responses of non-linear unloading and closure of stress-strain hysteresis loop based on the Yoshida-Uemori model

This paper proposes models to describe a non-linear unloading-reloading stress-strain response and closure of a cyclic stress-strain hysteresis loop based on the Yoshida-Uemori (Y-U) model. The average stress-strain slope given by the non-linear model is consistent with the Y-U model of Young’s modulus degradation. The closure of a cyclic stress-strain curve is described by automatically changing one of the Y-U material parameters. An advantage of the above approaches is that no additional parameters are needed for modeling.

Effect of laser shock peening on high cycle fatigue characteristics of 316LN stainless steel

The influence of ‘laser shock peening’ (LSP) on fatigue behavior of 316LN stainless steel has been studied at 298 K by conducting fully reversed stress controlled fatigue tests in the range 200–300 MPa. A triangular wave form with a constant frequency of 5 Hz was employed for all the tests conducted below 107 cycles on the virgin and laser shock peened samples. The run out tests at 107 cycles were performed at a frequency of 60 Hz. The studies have clearly revealed that the fatigue life is dependent on surface condition of the material and stress amplitude employed. A comparison is made of cyclic stress-strain hysteresis loops and fatigue lives between virgin and peened material. The peened material showed better fatigue strength and life at low stress amplitudes pertaining to high cycle fatigue regime, and exhibited lower density of surface microcracks. The improved fatigue resistance of peened material is attributed to the presence of residual compressive stresses to a depth of ~100 μm from the surface. The beneficial effect of compressive stresses is perceived both in the reduction in number density of Stage-I microcracks and retarded stage-II crack growth in the initial stages (that revealed striations with lesser spacing compared to un-peened samples).

Effect of HIPing and degassing on the low cycle fatigue behavior of A319 cast alloy

Microstructure and low-cycle fatigue (LCF) behavior of A319 cast alloy were investigated in this work. Microstructure analysis indicated that both degassing and hot isostatic pressing (HIPing) process could help to reduce and eliminate porosity. The strain-controlled low-cycle fatigue tests were conducted at total strain amplitude ranging from 0.2% to 0.4%. The stress-strain hysteresis loops were acquired and the effect of HIPing and degassing on cyclic deformation behavior was analyzed combining the cyclic stress response curves. Moreover, the effect of HIPing and degassing on LCF life was analyzed, and a fatigue life model based on the area fraction of defects was proposed which was found to be suitable to predict life. Finally, the fatigue fractography observation showed that the presence of porosity could accelerate the initiation and propagation of cracks and the fatigue failure of materials.

Electrical resistivity and mechanical properties of cementitious composite incorporating conductive rubber fibres

Conductive cementitious composites with excellent conductivity and piezoresistivity can be potentially used for pavement deicing, concrete corrosion evaluations or structural health monitoring. Inspired by the practice of recycling rubber wastes for concrete manufacturing, the conductive rubbers are first added as enhanced fillers to improve the electrical conductivity of cementitious composite in this study. Based on the experimental investigations on electrical resistivity, mechanical properties and microstructure, the results show that cementitious composites containing conductive rubber fibres exhibit relatively low resistivity with nearly one order of magnitude to approximately 1 × 104 Ω cm. On the other hand, cementitious composites with aluminium/silver filled rubber (AR) exhibit better conductivity than the counterparts with carbon black filled rubber (CR). For CR reinforced composites (CRC) and AR reinforced composite (ARC) with more than 40 rubber fibres (0.64 vol%), the higher the rubber fibre content, the better is the conductivity but the slightly lower the compressive strength. The cementitious composites reinforced by 100 conductive rubber fibres (1.6 vol%) not only display excellent conductivity but also provides acceptable mechanical properties, with up to 30.6% increase in ultimate strain but only 17.3% reduction in compressive strength. Furthermore, cementitious composites with rubber fibres demonstrate better damping capacity by enlarging stress–strain hysteresis loops compared to the counterpart without rubber. Such promising conductivity and damping properties provide the cementitious composites with great potentials for being used as cementitious composite sensors and smart composites to self-monitor the structural health or traffic load of various transportation infrastructures, such as bridges, highways and pavements.

Cubic negative stiffness lattice structure for energy absorption: Numerical and experimental studies

We present a new type of a truly three-dimensional cubic negative stiffness lattice structure that can achieve energy absorption and recover its original configuration under cyclic loading in excess of a strain of approximately 20%. This structure was composed of multiple unit cells exploiting negative stiffness from controlled elastic buckling. Structural properties were designed to be tuned by adjusting geometry. The effective Poisson’s ratio was equal to zero regardless of the constituent material. Geometric parameters that can lead to the desired energy absorption without yielding the structure were determined by finite element analysis. We then fabricated samples representing the lattice structure with different sizes through additive manufacturing and performed cyclic loading experiments to capture stress-strain hysteresis loops. Results clearly showed that the designed structure was capable of absorbing mechanical energy effectively with a full recovery of geometry in three principal directions and that the amount of energy absorbed during cyclic loading increases with its size.

A compact constitutive model to describe the viscoelastic-plastic behaviour of glassy polymers: Comparison with monotonic and cyclic experiments and state-of-the-art models

A number of constitutive models have been developed for solid polymers to describe the large deformation behavior. However, most of the existing models rely on a purely elastic or hyperelastic initial response when they are incapable of accurately predicting the cyclic stress-strain hysteresis loops. In this work, therefore, a compact cyclic viscoelastic-viscoplastic constitutive model is proposed to improve the prediction of the loops below the peak yield stress. The proposed approach is based on the distinguished model by Haward and Thackray (1968) for glassy polymers, which is augmented by a few thermodynamically motivated internal state variables able to predict the missing viscous deformation behavior, including the nonlinear cyclic hardening in three dimensions. Based on the comprehensive uniaxial tension experiments, it is demonstrated that this compact formulation, along with a calibration scheme, enables accurate prediction of the shape of the hysteresis loops, as well as the representation of ratcheting behavior. A comparison is also made with state-of-the-art models that are capable of predicting the cyclic stress-strain hysteresis loops.

Strain controlled isothermal low cycle fatigue life, deformation and fracture characteristics of Superni 263 superalloy

The total axial strain controlled low-cycle fatigue (LCF) behaviour of a wrought nickel-base superalloy Superni 263 has been evaluated at 298 K, 673 K, and 923 K employing the strain amplitudes in the range ± 0.25% to ± 0.80%. All the tests were performed using a triangular wave form at a constant strain rate of 10−3 s−1. The Superni 263 alloy was subjected to a solutionizing treatment at 1373 K/1.5 h followed by water quenching. An ageing treatment of 1073 K/8 h was given to the solutionized samples. The microstructure of the alloy is composed of γʹ in the intragranular regions and discrete M23C6 precipitates on the grain boundaries. Few undissolved (Ti, Mo)C and TiN precipitates were also noticed in the matrix. The strain amplitude and temperature played a significant role in the evolution of macroscopic cyclic stress response and the development of deformation substructure. The alloy displayed serrated flow in the plastic portions of stress-strain hysteresis loops in the tests conducted at 673 K and 923 K, predominantly at strain amplitudes higher than ±0.40%. Several manifestations depicting the occurrence of dynamic strain ageing (DSA) were derived by analysing both the macroscopic and micro-mechanistic information generated. The comparative evaluation of monotonic and cyclic stress-strain curves was conducted and the factors responsible for rapid cyclic hardening during DSA were identified. The fatigue life decreased drastically with increasing temperature, particularly at low strain amplitudes. The strain-life data could be represented well by using Basquin and Coffin-Manson relationships. The slope in Coffin-Manson relationship revealed more negative values under the influence of DSA. The crack initiation and propagation modes at all the test conditions remained transgranular without the indications of interference from creep and oxidation effects. The deformation substructure at elevated temperatures was characterized by the occurrence of co-planar slip, stacking faults, micro twinning and high dislocation density in between the slip bands.

Fatigue and cyclic plasticity of 304L stainless steel under axial-torsional loading at room temperature

This work investigates the axial-torsional fatigue and cyclic deformation behaviour of 304L stainless steel at room temperature. The testing programme included four fully reversed strain-controlled loading paths (axial, torsional, proportional axial-torsional, and 90° out-of-phase axial-torsional) and a fully reversed shear strain-controlled with static axial stress. The experiments were carried out at equivalent strain amplitudes ranging from 0.20% to 1.00%, resulting in fatigue lives from 102 to 106 cycles. For axial, torsional, and torsional with axial static stress loading, secondary hardening related to martensitic transformation was observed, while it did not occur for nonproportional loading. For proportional loading, secondary hardening occurred only for an equivalent strain amplitude equal to or greater than 0.80%. Neither the accumulated plastic strain nor the equivalent plastic strain amplitude could predict whether secondary hardening would occur for the investigated loading conditions. Almost no variation in the cyclic Young’s and shear moduli with the number of loading cycles was observed even for the tests that exhibited considerable secondary hardening. Fatigue life estimates calculated using the stress-strain hysteresis loops at maximum softening and at half-life were similar for the Smith–Watson–Topper, Fatemi–Socie, and Jiang models. It was observed that macroscopic surface crack orientation depends on the equivalent strain amplitude for torsional, proportional, nonproportional and torsional with static stress loading. The capability of the models to estimate the observed crack orientations is discussed.

소성변형률 에너지밀도를 이용한 In738LC의 고온저주기피로수명 예측

Gas turbine blades are important parts of a power plant, and thus, it is necessary to be able to predict the low-cycle fatigue life of the blades. In this study, a low-cycle fatigue test of In738LC, which is used primarily in gas turbine blade manufacture, was performed at various high temperatures (750oC, 800oC, and 850oC). From the test results, the stressstrain curve and the stress-strain hysteresis loop were obtained. It was established that In738LC has no strain hardening or softening. The life prediction equations for low-cycle fatigue were derived using the Coffin-Manson equation and the energy model. In conclusion, one equation for predicting the life low-cycle fatigue was obtained using the energy level with temperature as the varying factor.

High temperature stiffening of ferroelastic LaCoO3

The cyclic ferroelastic hysteretic behavior of pure LaCoO3 perovskite ceramic has been studied at different temperatures in four point bending. The stress-strain deformation behavior of LaCoO3 was analyzed both in the term of the maximum stress in the cycle and in terms of the temperature used when the cyclic testing was performed. The characteristics of the stress-strain hysteresis loops, such as hysteresis loop area and irreversible strain, as well as effective Young’s modulus, were analyzed, and it was established that both the loading and the temperature history have a significant influence on the mechanical behavior of LaCoO3. Young’s modulus values are reported to be much higher in the 700–900 °C temperature range as compared to the measurements performed in the RT-400 °C temperature range.