Plastic Strain Amplitude Research Articles

Proposal of an alternating bending technique for evaluating low‐to‐high cycle fatigue of structural steels

AbstractThis paper proposes an alternating bending technique for evaluating fatigue life in the low‐to‐high cycle fatigue regime. A method was developed for estimating the stress, elastic strain, and plastic strain ranges of a plastically deformed specimen subjected to alternating bending with consideration of stress and strain distributions. To evaluate its effectiveness, fatigue testing was conducted using a specimen made of a steel used for pressure vessels. The stress, elastic strain, and plastic strain ranges could be obtained during cyclic bending. The elastic strain amplitude life and plastic strain amplitude life curves were linear in a log–log plot in the low‐to‐high cycle fatigue regime. Hence, the fatigue life under alternating bending could be evaluated using the proposed strain‐based approach. However, these curves could not be predicted using equations with parameters obtained from tensile testing, such as the universal slope method, due to the strain gradient in the specimen.

A nonlinear fatigue damage model: Comparison with experimental damage evolution of S355 (SAE 1020) structural steel and application to offshore jacket structures

Miner’s rule is commonly used in fatigue life estimations and is also recommended by design standards. Recently, a few models have been proposed, to capture loading sequence effects more precisely than Miner’s rule. However, practical applications of these models have not been found, due to the requirement for additional material parameters. The authors have recently proposed a nonlinear fatigue damage model, which does not require any additional material parameters, other than the S-N curve. It can be applied by practicing engineers, using partially known S-N curves given in design standards, including the corresponding detail categories. The model has been verified with several materials for both damage evolution curves and fatigue life estimations. Verification of this model for S355 (SAE 1020) structural steel used in offshore structures is desirable for the industry. Experimental techniques, based on characterizing fatigue damage using physical quantities, have also recently been developed by the authors and are used for this verification. Subsequently, damage evolution curves under load increase test and constant amplitude tests are developed by observing the changes in plastic strain amplitude, electrical resistance and temperature. The corresponding fatigue strength curve is developed. This curve is used, together with the proposed damage index, for further verification of the proposed model for S355 (SAE 1020) structural steel. Finally, application of the proposed model is shown for an existing offshore jacket structure, and the results are compared with those of the conventional approach. Hence, the importance and significance of the proposed model is further established.

Load-carrying performance and design of BRBs confined with longitudinal shuttle-shaped-trusses

This paper presents load-carrying performance and design method for a Shuttle-Shaped Truss-Confined Buckling-Restrained Brace (SSTC-BRB). Such external restraining system (ERS) innovation through adopting longitudinally variable cross-sectional trusses in the BRB significantly enhances axial load-carrying efficiency of SSTC-BRB that could carry very large axial applied load for over long BRB design when used on exposed purpose externally. Firstly, the elastic buckling performance of the SSTC-BRB is comprehensively investigated by adopting a beam element Finite Element (FE) model, and this leads to an explicit expression of the elastic buckling load of the SSTC-BRB that is adopted to define the restraining ratio of the SSTC-BRB for its strength and stiffness design. Consequently, the load resistance of SSTC-BRBs under monotonic axial compression is numerically analyzed. Accordingly, the lower limit of restraining ratio of the SSTC-BRBs subjected to monotonic axial load is recommended for their load resistance design, where the core could be fully yielded with the plastic strain amplitude reaches 2% without global instability of the SSTC-BRBs. Finally, the hysteretic responses of SSTC-BRBs subjected to axial compressive-tensile cyclic loads are studied numerically, and the corresponding lower limit of restraining ratio of SSTC-BRBs is proposed for their energy-dissipation design. Those two lower limits of restraining ratios of the SSTC-BRBs obtained in this study provide fundamentals for preliminary static and seismic designs of SSTC-BRBs.

Influence of Temperature on Low Cycle Fatigue and Ratcheting Behavior of SA333 Gr-6 C-Mn Steel

The aim of this investigation is to study the influence of temperature on the cyclic plastic deformation behavior of SA333 Gr-6 steel at two loading conditions. Strain-controlled cyclic loading experiments were carried out at ± 0.5% total strain amplitude, 1×10-3 s-1 strain rate, and temperature varied from RT to 400°C, whereas stress controlled ratcheting experiments were conducted at fixed mean stress (σm) of 50 MPa and stress amplitude (σa) of 400 MPa, 115 MPa s-1 stress rate, and in the temperature range of RT to 350°C. The investigated steel shows cyclic hardening characteristic at DSA temperature regime in both the loading condition. The steel shows lower fatigue lives at 250°C and 300°C temperatures even though plastic strain amplitude is smaller. The ratcheting life of the steel increases and strain accumulation decreases with the increase in temperature up to 300°C and on further increment in temperature ratcheting life get decreased. The steel shows greater cyclic hardening at both the loading conditions at 300°C.

Microstructure and Low-Cycle Fatigue Behavior of Al-9Si-4Cu-0.4Mg-0.3Sc Alloy with Different Casting States.

The low-cycle fatigue behavior of Al-9Si-4Cu-0.4Mg-0.3Sc alloy with different casting states was investigated by performing low-cycle fatigue tests and by means of observations and analysis with a scanning electron microscope (SEM) and a transmission electron microscope (TEM). It was found that the metal-mold cast and die-cast Al-9Si-4Cu-0.4Mg-0.3Sc alloys exhibited the cyclic stress response of strain hardening under all imposed total strain amplitudes. The cyclic deformation resistance and fatigue life of the metal-mold cast Al-9Si-4Cu-0.4Mg-0.3Sc alloy were lower than those of the die-cast Al-9Si-4Cu-0.4Mg-0.3Sc alloy. The plastic strain and elastic strain amplitudes of the metal-mold cast and die-cast Al-9Si-4Cu-0.4Mg-0.3Sc alloys were linearly related to the number of reversals to failure, which obeyed the Coffin-Manson and Basquin formulas, respectively. The results of TEM observation revealed that at all imposed total strain amplitudes, the cyclic deformation mechanisms of the metal-mold cast and die-cast Al-9Si-4Cu-0.4Mg-0.3Sc alloys were planar slip and wavy slip at the lower and higher strain amplitudes, respectively.

Low Cycle Fatigue Properties of Sc-Modified AA2519-T62 Extrusion.

This investigation presents the results of research on low cycle fatigue properties of Sc-modified AA2519-T62 extrusion. The basic mechanical properties of the investigated alloy have been established in the tensile test. The low cycle fatigue testing has been performed on five different levels of total strain amplitude: 0.4%; 0.5%; 0.6%; 0.7% and 0.8% with cycle asymmetry coefficient R = 0.1. For each level of total strain amplitude, the graphs of variations in stress amplitude and plastic strain amplitude in the number of cycles have been presented. The obtained results allowed to establish Ramberg-Osgood and Manson-Coffin-Basquin relationships. The established values of the cyclic strength coefficient and cyclic strain hardening exponent equal to k’ = 1518.1 MPa and n’ = 0.1702. Based on the Manscon-Coffin-Basquin equation, the values of the following parameters have been established: the fatigue strength coefficient σ’f = 1489.8 MPa, the fatigue strength exponent b = −0.157, the fatigue ductility coefficient ε’f = 0.4931 and the fatigue ductility exponent c = −1.01. The fatigue surfaces of samples tested on 0.4%, 0.6% and 0.8% of total strain amplitude have been subjected to scanning electron microscopy observations. The scanning electron microscopy observations of the fatigue surfaces revealed the presence of cracks in striations in the surrounding area with a high concentration of precipitates. It has been observed that larger Al2Cu precipitates exhibit a higher tendency to fracture than smaller precipitates having a higher concentration of scandium and zirconium.

Plastic Strain Amplitude Dependence of Cyclic Deformation Behavior in Ultrafine Grained Cu Alloys Containing Fe Precipitates

Plastic Strain Amplitude Dependence of Cyclic Deformation Behavior in Ultrafine Grained Cu Alloys Containing Fe Precipitates

Justification of post-ratcheting hardening behavior of annealed Copper through hardening coefficient and hardening factor

The present research work has been carried out to investigate the ratcheting behavior at different stress ratios under constant maximum stress and changes in post-ratcheting tensile properties of commercially pure (99.97%) polycrystalline Copper. All the ratcheting tests were done at room temperature upto 25% true ratcheting strain accumulation. After ratcheting deformation tensile tests were performed on ratcheted specimens at strain rate of 10−3 s−1 up to complete fracture. Post-ratcheting hardening behaviors were analyzed by the variation of plastic strain amplitude and hardening factors with respect to number of cycles. It is observed that the number of cycles over which a constant amount of ratcheting deformation occurs exponentially increases with increase of stress ratio. It is also observed that post ratcheting tensile properties of annealed copper linearly increases with increase of stress ratio. Such observations of post-ratcheting hardening behavior have been successfully justified by the variation of hardening coefficient and hardening factor.

Isothermal and thermomechanical fatigue behaviour of type 316LN austenitic stainless steel base metal and weld joint

Thermomechanical fatigue (TMF) studies were carried out on type 316 LN austenitic stainless steel (SS) base metal (BM) and its weld joint (WJ) with a temperature interval of 623–873 K under in-phase (IP) and out-of-phase (OP) combinations of mechanical strain and temperature. Tests were performed under mechanical strain control mode using the strain amplitudes in the range, ±0.25% to ±0.6%. Besides, isothermal low cycle fatigue (IF) tests were also conducted on the weld joint at 873 K. TMF cycling resulted in a slightly higher cyclic stress response (CSR) compared to IF loading for the weld joint. The IP TMF cycling yielded a higher plastic strain amplitude in comparison to OP TMF for both the base metal and the weld joint. Cyclic life of the weld joint is found to be inferior to that of the base metal. The fatigue lives exhibited by the base metal and the weld joint varied in the following sequence: IP TMF < IF < OP TMF. Preferential crack initiation in the weld region owing to embrittlement of transformed δ-ferrite was noticed with an increase in the mechanical strain amplitude under both TMF and IF cycling conditions. Crack initiation and propagation generally occurred in transgranular mode under IF and OP TMF and mixed (trans-plus intergranular) mode under IP TMF cycling. Electron back scattered diffraction (EBSD) measurements were employed to investigate the substructural development in terms of local misorientation distribution, inverse pole figure (IPF) maps and boundary dislocation density (ρ) in the weld metal region, under IF and IP TMF cycling. The dislocation density was found to decrease for both IF and IP TMF cycling compared to the as-welded condition, with the decrease being higher for IF cycling. The TMF data generated for the type 316LN SS base metal and weld joint at different strain ranges in the present study clearly demonstrated a lack of conservatism associated with the current design practice which is based on the IF data at the maximum temperature (Tmax) of the service cycle.

The influence of hydrogen on cyclic plasticity of oriented nickel single crystal. Part I: Dislocation organisations and internal stresses

The present paper discussed the impact of hydrogen on the mechanical response of cyclically strained nickel single crystal oriented for multi-slips at different length scales. At macroscale, hydrogen seems to induce competition between softening and hardening of the metal as a function of the plastic strain amplitude. Then, by separating internal stresses induced by long-range and short-range interactions between dislocations (represented by back and effective stresses, respectively), we noted that hydrogen reduces the effective stress but has a more complex behaviour with the back stress. Therefore, observations with transmission electron microscope and nano-indentation tests have been performed on cyclically pre-strained nickel single crystal with and without hydrogen. The dislocation organisation induced by the cyclic tests is similar for nickel with and without hydrogen. In both cases, the dislocation arrangement can be affiliated to a composite structure with a wall phase containing mainly edge dislocation dipoles and a channel phase where the mobility and cross-slip events of screw dislocations occurred. From both approaches, we observed that hydrogen hardens the wall phase while it softens the channel phase. These results are discussed on the base of plasticity mechanisms.

On the numerical modeling of nucleation and growth of microstructurally short cracks in polycrystals under cyclic loading

Abstract

Fatigue damage analysis of reinforced concrete column considering low‐cycle behavior of HRB400 steel

SummaryIn this study, a damage model‐based fatigue behavior is proposed. To consider the fatigue behavior of steel in the damage model, the experimental research on reinforcing steel bar grades HRB400 was presented. The monotonic tension test and low‐cycle fatigue test were carried out. The plastic strain amplitude–fatigue cycle (εp–2Nf) curve and plastic strain amplitude–strength loss factor (εp–ϕSR) curve were obtained. The fatigue parameters (Cf, Cd, and α) were proposed by nonlinear fitting. The specimens were simulated using the “Reinforcing Steel” material in “OpenSees” program. These fatigue parameters were proved to accurately describe the fatigue behavior of HRB400 rebar. Moreover, to verify the application of fatigue damage model in RC column, fiber‐based element models were established based on the quasi‐static cyclic test on RC columns. The calculated results agreed well with those of the tests. The damage degree of RC column was calculated by the recorded stress–strain curves of material. The proposed fatigue parameters could be referred in damage model based on material fatigue behavior.

Asymmetric cyclic response of tensile pre-deformed Cu with highly oriented nanoscale twins

History-independent, stable and symmetric cyclic response has been detected in as-deposited bulk polycrystalline Cu with highly oriented nanotwins [Nature 551 (2017) 214–217]. In this study, to deepen the understanding of cyclic deformation in nanotwinned (NT) structures, small levels of tensile pre-strains were applied on NT-Cu, followed by strain-controlled symmetric tension-compression cyclic tests. Distinct from the symmetric cyclic response of as-deposited NT-Cu, the magnitude of the maximum stress in tension is much larger than that of the minimum stress in compression, indicating that the cyclic response of tensile pre-deformed NT-Cu is highly asymmetric. The degree of its cyclic asymmetry gradually decays as the number of cycles or the plastic strain amplitude is increased. The tensile pre-deformed NT-Cu recovers to its symmetric cyclic response after cyclic deformation at sufficiently large plastic strain amplitude, analogous to that detected in as-deposited NT counterparts. Molecular dynamics simulations and microstructural observations revealed that the observed asymmetric cyclic response is mainly related to the activation and movement of threading dislocations with extended misfit dislocation tails lying on the twin boundaries (TBs) during tensile pre-deformation. During cyclic deformation, threading dislocations in adjacent twin interiors tend to link their long tails with one another to form correlated necklace dislocations (CNDs) with a symmetric structure. The CNDs move back-and-forth along the twin boundaries without directional slip resistance, contributing to the transition from asymmetric to symmetric cyclic response of NT-Cu.

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.

Asymmetric cyclic deformation behavior of SA 333 steel at elevated temperatures

Purpose The purpose of this paper is to study the effect of mean stress and stress amplitude on the asymmetric cyclic deformation behavior of SA333 Gr-6 C-Mn steel. Such type of loading may arise during the service period because of the load fluctuations, thermal gradients and sudden loading like seismic events. Tests were also carried out at different temperatures to understand the effect of it on sensitiveness of the materials deformation behavior. Design/methodology/approach Cylindrical specimen of 8-mm gauge diameter and 15-mm gauge length was fabricated from the pipe section along its axis. Stress controlled ratcheting tests were carried out by using triangular waveform for cyclic loading. The strain accumulations were measured using 12.5-mm gauge length extensometer. Ratcheting tests were carried out at fixed stress amplitude of 400 MPa and mean stress varying from 0 to 75 MPa, whereas at the fixed mean stress of 100 MPa and stress amplitude varies from 300 to 400 MPa at 300°C. To study the effect of temperature on ratcheting behavior, tests were carried out at a load of 100 MPa mean stress and 350 MPa stress amplitude, with a varying temperature between room temperature and 350°C. The stress rate of 115 MPas-1 was kept constant for all the tests. Findings Increase in mean stress and stress amplitude, ratcheting strain and plastic strain amplitude increases, whereas ratcheting life decreases. With an increase in temperature, ratcheting life increases and strain accumulation decreases up to 300°C, whereas on further increase in temperature, strain accumulation increases with reduction in ratcheting life. Minimum ratcheting rate was observed at 250°C and 300°C. The dynamic strain aging (DSA) phenomena lead to the hardening of the material. The investigated steel shows DSA temperature regime lies between 250°C and 300°C. The failure modes at 250°C and 300°C temperature was transgranular, whereas at 350°C complete ductile. Research limitations/implications The stress rate and loading condition may vary to study the ratcheting behavior. Practical implications From this study, the critical cyclic load may be determined. The DSA temperature regime of this material is determined at this stress rate. This could help to evaluate the cyclic deformation behavior of the material with temperature changes. Originality/value In this investigation, the DSA temperature regime has been determined where maximum ratcheting life, minimum strain accumulation and ratcheting rate were observed. The critical load where the minimum life of the material occurred at elevated temperature is 100 MPa mean stress and 400 MPa stress amplitude.

The effect of strain rate under multiple forging on the mechanical and microstructural properties

The flow stress of aluminum alloy 6082M under cyclic, non-monotonic plastic deformation has been determined by multiaxial forging experiments, using the MaxStrain system on a Gleeble 3800 thermo-physical simulator. The simulations were done at ambient temperature with different strain rates of 0.1, 1.0 and 10 1/s. The plastic strain amplitude per forging pass was 0.4. The accumulated equivalent strain was around 4 in each forging simulation.For the mechanical modeling of the cyclic, non-monotonic plastic deformation characteristic of the forming process, a control program and measurement arrangements have been developed. These controlled the equivalent logarithmic strain and the equivalent strain rate implemented in each forming step. It was also suitable for measuring the dimensions of the deformed material volume between the tools. These parameters and the measured force data were applied in the mechanical model, based on the principle of virtual velocities.In parallel with the cyclic experiments, monotonic plane-strain Watts-Ford compression tests were also performed. Strain rate influence for material properties has been investigated. Monotonous and cyclic flow curves were compared, and significant differences were found. Contrary to the monotonous flow curve, the cyclic flow stress showed the Bauschinger effect, occurring when the load direction was changed. Concerning the effect of strain rate it can be concluded that the applied strain rate influences the strain hardening, the resultant hardness and the characteristic properties of the generated ultrafine-grained microstructure.

Statistical evaluation of the softening or hardening behaviour of metallic materials

Detailed knowledge of the cyclic behaviour of a material is essential for the design of components which can be plastically deformed by cyclic loads. The design process based on the sole static characteristics could lead, in case of softening behaviour, to a significant underestimation of the plastic strain amplitude and to a consequential overestimation in terms of component life.The experimental determination of cyclic characteristics is onerous compared to static properties, which can be obtained by a simple tensile test. The objective of this study is to derive a model to evaluate, starting from the knowledge of tensile variables alone, whether the material subject to cyclic loads hardens or softens.The proposed approach is statistical, based on a sample of about 240 materials. The predictive model results from a multinomial logistic regression, which allows deriving a relationship between independent input variables (tensile variables of the materials) and a dependent output variable, represented by the material belonging to one of the following behaviour categories: hardening, softening, mixed (hardening or softening depending on the load level), stable (small differences between static and cyclic behaviour).To determine which tensile variables significantly influence the cyclic behaviour, different regressions based on no more than three parameters are compared, to result in a simple and functional calculation tool. Finally, several correlations from the literature are considered, comparing the associated results with those from the derived models. The comparison highlights higher goodness-of-fit for the proposed approach with respect to the state of the art, demonstrating its predictive potential.

Cyclic damage behavior of Sanicro 25 alloy at 700 °C: Dispersed damage and concentrated damage

The damage evolution behavior of a novel Sanicro 25 alloy was investigated based on low-cycle fatigue tests at 700 °C. The results show that at relatively low total strain amplitude (Δεt/2), the dispersed damage was dominant, which led to prolonged fatigue life. However, at relatively high Δεt/2, the concentrated damage was dominant, which led to reduced fatigue life. Based on the damage characteristics, a modified Coffin-Manson equation that accounts for microporosity (f) was derived. The curved surface of plastic strain amplitude (Δεp/2) - f - number of reversals to failure (2Nf) shifts upward with increasing fatigue ductility exponent c. However, this curved surface shifts downward when the cyclic strength coefficient K′ increases. A new model of micro-crack initiation considering the precipitates at the grain boundary was derived. The Gibbs free energy change of crack nucleation (ΔG) decreased with decreasing Δεt/2. Finally, based on the prediction model of energy-based fatigue life, the theoretical formulas of the fatigue toughness Wf and the fatigue cracking exponent β were derived. Wf increases and β decreases with increasing Δεp/2.

Ultrafine versus coarse grained Al 5083 alloys: From low-cycle to very-high-cycle fatigue

The fatigue performance of coarse and ultrafine-grained (UFG) 5083 Al alloy were compared, from low to very high cycle fatigue. The UFG alloy exhibited cyclic hardening and predominant kinematic hardening. At high plastic strain amplitude (and only in this regime), it showed easier crack initiation and a lower fatigue resistance. Its resistance to HCF was hardly better than that of its coarse grained counterpart until 2.106 cycles, but 43% higher in VHCF, until 5.108 cycles. Beyond that point, internal crack initiation occurred, and the fatigue resistance of the UFG material decreased, which was explained using Fracture Mechanics.

Cyclic deformation behavior of friction-stir-welded dissimilar AA5083-to-AA2024 joints: Effect of microstructure and loading history

The microstructural evolution across the friction-stir-welded dissimilar AA5083-H112 to AA2024-T351 aluminum alloy joints was characterized via electron backscatter diffraction (EBSD), aiming to identify the effect of inhomogeneous microstructures on the tensile properties and cyclic deformation behavior along with the influence of loading history. Results show that the top region of the stir zone (SZ) mainly consisted of AA2024 which was initially positioned on the retreating side during welding. On the AA5083 side, the lowest density of the geometrically-necessary dislocations (GNDs) assessed from the local misorientations of 0°–2° appeared in the SZ, while it occurred in the heat-affected zone (HAZ) of the AA2024 side. The fractions of recrystallized grains in the AA5083 SZ and AA2024 SZ were ~73% and ~34%, respectively. Strain localization and the resultant failure occurred in the lowest hardness zone of the AA5083 side. The extent of cyclic hardening increased as the stress amplitude increased. Both plastic strain amplitude and plastic strain energy density decreased with increasing number of cycles at higher total strain amplitudes. In the stepwise cyclic deformation tests in the form of ascending-descending loading, the prior cyclic deformation process tended to generate more stabilized structure and performance.