Cyclic Stress-strain Hysteresis Loops Research Articles

An experimental and numerical study on strain controlled fatigue response of TRIP steel under influence of hydrogen

The present work aims to study the influence of hydrogen charging on the transformation induced plasticity steel under strain-controlled low cycle fatigue (LCF). Hydrogen charging had detrimental effect on strain-controlled LCF lives. Cyclic hardening in un-charged specimen due to strain-induced martensitic transformation (SIMT) dominated over cyclic softening. In contrast, generation of large fraction of low angle grain boundaries in hydrogen charged specimen leads to cyclic softening and supresses cyclic hardening due to SIMT. Additionally, Cyclic plasticity modelling using Ohno-Wang kinematic hardening model is validated by simulating cyclic stress–strain hysteresis loop and cyclic softening curve of uncharged and hydrogen charged specimens.

Fatigue assessment of additively-manufactured C-18150 copper alloy at room and elevated temperatures via a microstructure-sensitive algorithm

The efficacy of a recently developed microstructure-sensitive fatigue framework is assessed for additively manufactured materials at different environmental temperatures. C-18150 copper alloy samples additively manufactured using the Laser Powder Bed Fusion process (L-PBF) are fatigue tested at the room, 204 °C, and 426 °C temperatures. Plastic strain energy as the damage representative is studied via the cyclic stress–strain hysteresis loop area measurements and analyzed via a microstructure-sensitive algorithm. A thermodynamics-based framework is used to calculate Fracture Fatigue Entropy (FFE) to assess the material’s fatigue performance. The results based on the hysteresis loop and the microstructure-sensitive method agree both in trend and magnitude.

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).

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.

Description of non-linear unloading curve and closure of cyclic stress-strain loop based on Y-U model

This paper proposes a cyclic elasto-plasticity model to describe non-linear unloading-reloading curves and closure of a cyclic stress-strain hysteresis loop based on the Yoshida-Uemori (Y-U) model. The nonlinear unloading stress-strain response is expressed by an equation for the stress-dependent Young’s modulus in the yield surface. The closure of a cyclic stress-strain curve is described by automatically changing Y-U material parameters. The great advantage of the above approaches is that no additional parameters are needed.

A finite cyclic elasto-plastic constitutive model to improve the description of cyclic stress-strain hysteresis loops

Plenty of cyclic constitutive models have been developed to describe the cyclic hardening/softening feature and ratchetting behavior of metals and good descriptions can be obtained. The cyclic stress-strain hysteresis loops, however, cannot be well predicted by most of the existing models since the different plastic moduli between monotonic and cyclic deformations have rarely been considered. In this work, a finite cyclic elasto-plastic constitutive model is developed to improve the description of the cyclic stress-strain hysteresis loops by introducing a new proposed kinematic hardening rule and an exponential isotropic hardening rule. In the proposed kinematic hardening rule, the back stress is decomposed into long-range, middle-range and short-range components with each addressing an “Armstrong-Frederick” evolution rule consisting of a linear hardening and a dynamic recovery term (Armstrong and Frederick, 1966). For the long-range and middle-range components, the dynamic recovery coefficients are postulated to decrease with the increase of plastic deformation and each contains a ratchetting coefficient. For the short-range component, the linear hardening and dynamic recovery terms are further divided into two parts, respectively, with one part in each activating only when the reverse loading occurs. The capability of the proposed model is demonstrated by benchmarking its predictions against experimental data. It is shown that the monotonic stress-strain response, cyclic hardening with both small and large strain amplitudes, ratchetting and, particularly, the cyclic stress-strain hysteresis loops of metallic materials can be well described by the proposed model.

Sensitivity of polycrystal plasticity to slip system kinematic hardening laws for Al 7075-T6

The prediction of formation and early growth of microstructurally small fatigue cracks requires use of constitutive models that accurately estimate local states of stress, strain, and cyclic plastic strain. However, few research efforts have attempted to systematically consider the sensitivity of overall cyclic stress-strain hysteresis and higher order mean stress relaxation and plastic strain ratcheting responses introduced by the slip system back-stress formulation in crystal plasticity, even for face centered cubic (FCC) crystal systems. This paper explores the performance of two slip system level kinematic hardening models using a finite element crystal plasticity implementation as a User Material Subroutine (UMAT) within ABAQUS (Abaqus unified FEA, 2016) [1], with fully implicit numerical integration. The two kinematic hardening formulations aim to reproduce the cyclic deformation of polycrystalline Al 7075-T6 in terms of both macroscopic cyclic stress-strain hysteresis loop shape, as well as ratcheting and mean stress relaxation under strain- or stress-controlled loading with mean strain or stress, respectively. The first formulation is an Armstrong-Frederick type hardening-dynamic recovery law for evolution of the back stress [2]. This approach is capable of reproducing observed deformation under completely reversed uniaxial loading conditions, but overpredicts the rate of cyclic ratcheting and associated mean stress relaxation. The second formulation corresponds to a multiple back stress Ohno-Wang type hardening law [3] with nonlinear dynamic recovery. The adoption of this back stress evolution law greatly improves the capability to model experimental results for polycrystalline specimens subjected to cycling with mean stress or strain. The relation of such nonlinear dynamic recovery effects are related to slip system interactions with dislocation substructures.

Description of Closure of Cyclic Stress-Strain Loop and Ratcheting Based on Y-U Model

This paper proposes a cyclic plasticity model to describe the closure of a cyclic stress-strain hysteresis loop based on the Y-U model. In this model, the backstress moves in a cyclic memory surface following a newly proposed kinematic hardening law. For this model just the same Y-U parameters can be used, and no additional material parameters are needed. By using a supplementary rule, this model is also able to describe ratcheting.

Microstructural, compositional and mechanical investigation of Shielded Metal Arc Welding (SMAW) welded superaustenitic UNS N08028 (Alloy 28) stainless steel

Shielded Metal Arc Welding (SMAW) was performed on UNS N08028 (Alloy 28) superaustenitic stainless steel sheets. In the present work, the microstructure and the mechanical properties of base metal (BM), weld metal (WM), and welded joint (WJ) are investigated. Optical micrographs show that the base metal presents austenitic grains, and the weld metal exhibits a fully austenitic dendritic structure, confirming the Schaeffler diagram estimations. Microhardness measurements indicate that the hardness increases in the weld bead due to the rapid cooling and thermal cycle during welding procedure. The measured mechanical properties and the analysis of the fracture profiles show that the two materials are ductile but the ductility is less pronounced in the weld metal. Consistently the yield stress, the plastic strength and the impact toughness are lower than in the base metal. In addition, the BM presents a higher cyclic hardening and plastic strain compared to those of WM. Cyclic stress–strain hysteresis loops show that WM and WJ have almost the same cyclic behavior and especially at high imposed strain levels.

Disappearance and reappearance of serrated plastic flow under cyclic loading: A study of dislocation substructures

Serrated plastic flow was observed in cyclic stress–strain hysteresis loops both in tensile and in compressive components during strain controlled low cycle fatigue of annealed Zircaloy-2 at a strain rate of 10−4s−1 and different strain amplitudes, at room temperature. Although there were only D-type serrations at higher strain amplitudes (>±0.75%) there were mixed serrations of D, A, B and C type at lower strain amplitudes (≤±0.75%). Depending on the cyclic stress response, transitions in dislocation structure from dislocation pile-ups to cell structure and cells to Corduroy structure were observed in the region of softening and secondary hardening. Disappearance and reappearance of serrated flow in the hysteresis loops were observed with number of cycles and it was proposed to be associated with transition in dislocation structure from planar to cell walls and finally from cell wall to Corduroy structure.

Low cycle fatigue behavior of Zircaloy-2 at room temperature

Fuel cladding and pressure tubes of Zircaloy-2 in pressurized light and heavy water nuclear reactors experience plastic strain cycles due to power fluctuations in the reactor, such strain cycles cause low cycle fatigue (LCF) and could be life limiting factor for them. Factors like strain rate, strain amplitude and temperature are known to have marked influence on LCF behavior. The effect of strain rate from 10−2 to 10−4s−1 on LCF behavior of Zircaloy-2 was studied, at different strain amplitudes between ±0.50% and ±1.25% at room temperature. Fatigue life was decreased with lowering of strain rate from 10−2 to 10−4s−1 at all the strain amplitudes studied. While there was cyclic softening at lower strain amplitudes (Δεt/2⩽±0.60%) cyclic hardening was exhibited at higher strain amplitudes (Δεt/2⩾±1.00%) at all the strain rates. Further, there was secondary cyclic hardening during the later stage of cycling at all the strain amplitudes and the strain rates. Cyclic stress–strain hysteresis loops at the lowest strain rate of 10−4s−1 were found to be heavily serrated, resulting from dynamic strain aging (DSA). There was significant effect of strain rate on dislocation substructure. The results are discussed in terms of high concentration of point defects generated during cyclic straining and their role in enhancing interaction between solutes and dislocations.

Dynamic strain aging in low cycle fatigue of duplex titanium alloys

The influence of dynamic strain aging (DSA) on low cycle fatigue (LCF) in duplex Ti-6-4 and SP700 titanium alloys was studied. LCF was performed within the temperature range from 350 °C to 450 °C, at strain rates of 10 −3 s −1 and 10 −4 s −1, and strain amplitudes of 1.25% and 2%. DSA appeared as serrations at the plastic portion of the cyclic stress–strain hysteresis loop, as well as stress humps appearing in the cyclic stress response (CSR) curve of peak tensile stress response versus cycle number. Strain-induced micro twin formation was only observed in the sample after fatigue with 2% strain amplitude under a 10 −4 s −1 strain rate, indicating that it is a DSA induced phenomenon.

Predicting Fatigue Initiation Life of Sn/3.8Ag/0.7Cu Solder using Endochronic Cyclic Damage-Coupled Viscoplastic Theory

AbstractThis paper studied cyclic behavior Sn/3.8Ag/0.7Cu solder with dendritic microstructure. A cyclic damage factor D under constant strain amplitude fatigue tests, was defined by using the reducing rate of maximum cyclic tensile stress σa. The critical cyclic damage DC and it's fatigue initiation life NI were determined very consistently by using separately the experimental σavs. N curves and the percolation theory. The endochronic cyclic damage-coupled viscoplastic theory proposed by the 1st author was used to simulate cyclic stress-strain hysteresis loops with damage under strain amplitude (εa) 0.8% at 298K. The results were in very good agreement with data. Combining the evolution equation of intrinsic damage and the computed cyclic stress-inelastic strain relation, a modified Coffin-Manson relationship was derived. By setting DC = 0.3, it predicted very effectively the NI data under σa from 0.2% to 1.0%.

Inelastic deformation and its related life under cyclic/creep loadings in Si 3N 4-monolithic and Si 3N 4/SiCw-composite ceramics at elevated temperature

Push–pull low cycle fatigue and creep tests were performed in monolithic-Si 3N 4 and composite-Si 3N 4/SiCw materials at 1573 K. Then cyclic stress–strain response and creep strain were measured with a newly developed extensometer. The inelastic strain, which is greatly dependent upon stress/strain rate, was detected in both the materials. It was found from the shape of the cyclic stress–strain hysteresis loop that inelastic strain was easier to generate under tensile than under compressive loading; the width of the hysteresis loop is larger on the tensile stress side than on the compressive stress side. Such a characteristic cyclic stress–strain response is much more enhanced in the composite-Si 3N 4/SiCw than in the monolithic-Si 3N 4. The low cycle fatigue life plotted against inelastic strain range is much longer in the former than in the latter, although the difference is reduced with decreasing the controlled strain range. Moreover, greater creep resistance is attained in the former than in the latter at the lower stress level, while the opposite is the case at the higher stress level.

炭素鋼の繰返し応力―ひずみ特性および疲労挙動に及ぼす水素チャージの影響

Effects of hydrogen charge on fatigue behaviour of two carbon steels, JIS-S10C (SAE1010) and JIS-S45C (SAE1045) were investigated. There was no hydrogen effect in the cyclic stress-strain hysteresis loops of S10C hydrogen-charged with 0.2 ppm. On the other hand, the strain amplitude was decreased in S45C hydrogen-charged with 0.8 ppm. The delayed yielding and the decrease in the saturated value of the strain amplitude were observed in the hydrogen-charged specimen (H : 0.5 ppm) of S45C under the constant stress amplitude tests. It is supposed that the degree of influence of hydrogen on cyclic stress-strain properties depends or material structure and/or hydrogen content. The effect of hydrogen charge (H : 0.5 ppm) on the fatigue life, the fatigue limit and the crack growth curves of S45C were not remarkable, while there was a distinct difference in the morphology of the slip bands between the hydrogen-charged and uncharged specimens. The localized slip bands were observed in the hydrogen-charged specimen of S45C. Therefore, it is presumed that the decrease in the strain amplitude in hysteresis loop by hydrogen charge is caused by the localization of slip bands. More crack initiations from ferrite grains were observed in the hydrogen-charged specimen (H : 0.5 ppm) of S45C. This phenomenon also corresponds to the localization and the formation of slip bands.

Effect of boron on the low-cycle fatigue behavior and deformation structure of INCONEL 718 at 650 °C

Symmetrical push-pull low-cycle fatigue (LCF) tests were performed on INCONEL 718 (IN718) containing 12, 29, 60, and 100 ppm B at 650 °C. The results showed that all the alloys experienced a relatively short period of initial cyclic hardening at low strain amplitudes, followed by a regime of saturation or slightly continuous cyclic softening. The initial cyclic hardening phase decreased with increasing strain amplitudes, and disappeared at the high strain amplitudes. A serrated flow was observed in the plastic regions of cyclic stress-strain hysteresis loops. The saturated cyclic stress amplitude at a given strain amplitude was highest for the alloy with 60 ppm B, and lowest for the alloy with 12 ppm B. The LCF lifetime increased with increasing B concentration up to 60 ppm, and then decreased as the B content increased from 60 to 100 ppm. Fractographic analysis suggested that the fracture mode changed from intergranular to transgranular cracking as the B concentration increased. The characteristic deformation microstructures produced by LCF tests at 650 °C, examined via transmission electron microscopy, were regularly spaced arrays of planar deformation bands on {111} slip planes in all four alloys. A ladderlike structure was observed in some local regions in the alloy with 12 ppm B. Heavily deformed planar deformation bands were observed in the fatigued specimens with 100 ppm B. The mechanism of improvement in the LCF life of IN718 due to B addition is discussed.

Influence of microstructure size on the plastic deformation kinetics, fatigue crack growth rate, and low-cycle fatigue of solder joints

The influence of microstructure size on the plastic deformation kinetics, fatigue crack growth rate and low-cycle fatigue of eutectic Sn-Pb solder joints is reviewed. The principal microstructure feature considered is the average eutectic phase size d=(dPb+dSn)/2. The effect of an increase in reflow cooling rate (which gave a decrease in d) on the flow stress and on fatigue life was irregular at 300K, depending on the stress or strain level and cooling rate. In contrast, a consistent increase in fatigue life with decrease in d occurred for thermomechanical cycling between −30° and 130°C. Constitutive equations for plastic deformation and fatigue crack growth rate are presented which include the microstructure size. It appears that the rate-controlling deformation mechanism is the intersection of forest dislocations in the Sn phase. The mechanism for both static and dynamic phase coarsening appears to be grain boundary diffusion with a t1/4 time law. Some success has been achieved in predicting the cyclic stress-strain hysteresis loops and fatigue life, including the influence of the as-reflowed microstructure size and its coarsening. Additional definitive studies are however needed before we can accurately predict the fatigue life of solder joints over the wide temperature range and conditions experienced by electronic packages.

Cyclic hardening mechanisms in [001] copper single crystals

Friction stress and back stress of [001] Cu single crystals during cyclic deformation were derived from cyclic stress–strain hysteresis loops by using the Cottrell method and the results are compared with those for single slip crystals. The cyclic hardening features of the [001] crystals are described in terms of the friction stress and back stress. Specific, detailed study was carried out on the sample cycled with a plastic strain amplitude of 1.8×10 –3. It has been shown that both the ‘true’ friction stress, i.e. the cyclic yield stress, and the back stress in the [001] crystals increase much more rapidly than those in single slip crystals in the hardening stage. In the saturation stage, however, only the friction stress in the [001] crystal is higher than its correspondent in the single slip crystals, while the back stresses in these two types of crystals are close to each other. The higher friction stress in the [001] crystal is related to the higher density of jogs produced by the dislocation reactions between the primary and critical slip systems, and the existence of secondary dislocations in channels. The higher back stress in the hardening stage is attributed to the higher dislocation density in loop patches introduced by dislocation reactions in the first dozen of cycles. By modifying the Kulhlmann-Wilsdorf and Laird model, it is possible now to express quantitatively both the back stress and the shear stress in a cyclically deformed crystal with a particular orientation as functions of the applied strain amplitude as well as an orientation-dependent factor: the hardening coefficient for the first stage of unidirectional deformation. The predictions from these expressions for multiple slip crystals are in very good agreement with experimental data.