Cyclic Stress-strain Response Research Articles

An adaptive fatigue crack growth model at the welded joints of steel bridge

Under the influence of random loads such as those from vehicles, the welded details in steel bridges tend to gradually develop into macrocracks, typically originating from manufacturing defects or stress concentration points. As the service life of the steel bridge increases, the continuous generation and propagation of fatigue cracks lead to a decline in the bridge's service performance, potentially resulting in catastrophic failures such as bridge collapse. Accurately analyzing the fatigue crack growth patterns at welded joints is a prerequisite for reliably assessing the structural service performance. The analysis of fatigue crack propagation depends on both the crack growth step size and the cyclic stress–strain response at the welded joint under loading. Considering the complexity of the material properties and stress concentration at the welded joint, which leads to a lack of analytical solutions for the cyclic stress–strain characteristics at the crack tip, numerical analysis was employed to obtain the cyclic stress–strain response at the crack tip of the welded joints. Using the size of the cyclic plastic zone at the crack tip as an adaptive crack growth step size, a model for fatigue crack growth was developed based on the plastic strain energy of the cyclic plastic zone. Fatigue test specimens extracted from the welded toe of cruciform welded joints were tested, providing cyclic stress–strain (Ramberg-Osgood material parameters) and fatigue damage characteristics (Manson-Coffin material parameters) of the material at the welded toe. High-cycle fatigue tests using cruciform welded joint specimens determined a good correlation between the crack propagation characteristic dimensions obtained from the adaptive numerical analysis model and the experimental results. The experimental findings confirmed the applicability of the established adaptive numerical analysis model for studying fatigue crack growth in cruciform welded joints. The parameters introduced in this model are physically meaningful, easy to obtain, and suitable for engineering applications.

Dislocation density‐based constitutive model for cyclic deformation and softening of Ni‐based superalloys

AbstractA physically‐based constitutive modeling framework is proposed for the cyclic deformation and softening of Ni‐based superalloys. The constitutive model accounts for underlying mechanisms of grain size strengthening, dislocation strengthening, solid solution strengthening, and precipitate strengthening, commonly observed in these alloys. A constitutive model is proposed for the shearing of precipitates on their interaction with glide dislocations during cyclic deformation. This is the primary contributor to the experimentally observed cyclic softening behavior in Ni‐based superalloys. Model predictions of the cyclic stress–strain response and the cyclic softening (quantified in terms of the peak stress) are compared with the experimental counterparts for a range of strain amplitudes under fully‐reversed cyclic loading of Inconel 718 (IN 718). Further, model predictions of precipitate size are also compared with the experimentally measured transmission electron micrographs of precipitate sizes at the end of deformation. Concurrence in the cyclic stress–strain response, peak stress, and precipitate size provides validation for our constitutive modeling framework.

Monotonic tensile and cyclic deformation of a Ni-based single crystal superalloy with anisotropic microstructural rafting patterns at high temperature: Experiment and constitutive modelling

Monotonic tensile and cyclic deformation behaviours are investigated under different microstructural rafting states of a SC Ni-based superalloy, with emphasis on the influences of the rafting extent, type and loading orientation. The deformed microstructures and the dislocation configurations are characterized to give a micro-based understanding on the varying of deformation behaviours due to rafting. It is found that the decreases in the initial yield point and cyclic stress amplitude are only related to the rafting extent. Nevertheless, the rafting type (namely, the plate-like and needle-like morphology) has an undeniable contribution to the shape of hysteresis loops, where the plate-like rafting morphology results in more significant Bauschinger effect than needle-like rafting morphology. The variation of monotonic and cyclic deformation induced by rafting shares affinity with the alteration of internal stress and the movement of dislocations. Afterwards, a microstructure-sensitive constitutive model with two-phase flow rules has been developed. The effect of rafting on the monotonic and cyclic stress-strain responses is captured by introduce a series of microscopic mechanisms and a micromechanics-based back stress model that considers the morphology and size of the γ'/γ two-phase structures. The developed model is used to simulate the macroscopic stress-strain responses of the SC Ni-based superalloy under different rafting states. Model predictions are in good agreement with tests, capturing the reduction of cyclic stress amplitudes and the change in hysteresis loops. Finally, the impacts of the two-phase flow rules and the micromechanics-based back stress on the simulation capability have been discussed.

Quantitative study on the influence of strain amplitude on deformation mechanisms and cracking modes during cyclic torsion of AZ31 magnesium alloy

AbstractThe influence of strain amplitude on deformation mechanisms and cracking modes during cyclic torsion of the AZ31 magnesium (Mg) alloy was quantitatively investigated via EBSD‐SEM characterization. At 0.42% strain amplitude, basal slip was the dominated deformation mechanism throughout the entire fatigue life. At 1.732% strain amplitude, the activation of deformation mechanisms was featured by the periodic transition: tension twinning + basal slip (during counterclockwise torsion) then detwinning + tension twinning + basal slip (during reverse torsion). Moreover, cracking along slip traces (ST) and tension twins (TTW) were the primary cracking modes at 0.42% and 1.732% strain amplitude, respectively. ST cracking and TTW cracking preferentially appeared in soft‐oriented grains for basal slip and tension twinning, respectively. The underlying mechanisms governing the activation of various deformation mechanisms, cracking modes, and cyclic stress–strain responses were systematically discussed.

Twinning–Detwinning-Dominated Cyclic Deformation Behavior of a High-Strength Mg-Al-Sn-Zn Alloy during Loading Reversals: Experiment and Modeling

The deformation behavior of a high-strength Mg-Al-Sn-Zn alloy under loading reversals has been thoroughly examined through a combination of experimental measurements and crystal plasticity modeling. We focused on an age-treated alloy fortified by distributed Mg2Sn particles and Mg17Al12 precipitates, which underwent two distinct loading cycles: tension-compression-tension (TCT) and compression-tension-compression (CTC), aligned with the extrusion direction (ED). The initial and deformed microstructures of the alloy were analyzed using the electron backscattering diffraction (EBSD) technique. Notably, the alloy displays tensile and compressive yield strengths (YS) of 215 MPa and 160 MPa, respectively, with pronounced anelastic behavior observed during unloading and reverse loading phases. Utilizing the elasto-viscoplastic self-consistent model incorporating a twinning–detwinning scheme (EVPSC-TDT), the cyclic stress–strain responses and resultant textures of the alloy were accurately captured. The predicted alternation between various slip and twinning modes during plastic deformation was used to interpret the observed behaviors. It was found that prismatic <a> slip plays an important role during the plastic deformation of the studied alloy, and its relative activity in tensile loading processes accounts for up to ~66% and ~67% in the TCT and CTC cases, respectively. Moreover, it was discerned that detwinning and twinning behaviors are predominantly governed by stresses within the parent grain, and they can concurrently manifest during the reverse tensile loading phase in the TCT case. After cyclic deformation, the area fractions of residual twins were determined to be 7.51% and 0.93% in the TCT and CTC cases, respectively, which is a result of the varied twinning–detwinning behavior of the alloy in different loading paths.

Thermodynamic Entropy-Based Fatigue Life Assessment Method for Nickel-Based Superalloy GH4169 at Elevated Temperature Considering Cyclic Viscoplasticity.

This paper develops a thermodynamic entropy-based life prediction model to estimate the low-cycle fatigue (LCF) life of the nickel-based superalloy GH4169 at elevated temperature (650 °C). The gauge section of the specimen was chosen as the thermodynamic system for modeling entropy generation within the framework of the Chaboche viscoplasticity constitutive theory. Furthermore, an explicitly numerical integration algorithm was compiled to calculate the cyclic stress-strain responses and thermodynamic entropy generation for establishing the framework for fatigue life assessment. A thermodynamic entropy-based life prediction model is proposed with a damage parameter based on entropy generation considering the influence of loading ratio. Fatigue lives for GH4169 at 650 °C under various loading conditions were estimated utilizing the proposed model, and the results showed good consistency with the experimental results. Finally, compared to the existing classical models, such as Manson-Coffin, Ostergren, Walker strain, and SWT, the thermodynamic entropy-based life prediction model provided significantly better life prediction results.

A combined cyclic viscoplasticity and entropy generation approach for modelling fatigue crack growth behavior of a nickel-based superalloy at high temperature

This paper developed an entropy-based approach to estimate the fatigue crack growth (FCG) behavior of GH4169 at high temperature. Firstly, systematic FCG experiments of GH4169 at 650 °C were conducted to obtain the experimental data. Then, a finite element analysis combined with Chaboche viscoplasticity and node release technology was developed to obtain cyclic stress–strain responses and entropy generation fields. Based on thermodynamic analysis, numerous discrete material elements as sub-systems were divided along the crack growth direction in simplified representative 2D middle section. Fracture process zone (FPZ) was defined equal to the size of discrete material elements (ρ) which can be determined by distribution of normal stress perpendicular to the crack plane. Subsequently, an effective cyclic entropy generation related to ρ was defined as the crack driving force. Effective cumulative entropy generation was calculated when crack increment was ρ and the results indicated that effective cumulative entropy generation float within a certain range. The average of all effective cumulative entropy generation values was defined as crack growth entropy. Finally, an entropy-based FCG rate model was established to estimate the FCG behavior of GH4169, and a good correlation between experimental results and model predictions are achieved for all the high temperature FCG tests.

Validating cyclic plasticity material model for three materials subjected to asynchronous axial-torsion conditions

In the present work, a cyclic plasticity model based on Ohno-Wang kinematic hardening rule and Tanaka non-proportionality parameter, is proposed to simulate the cyclic stress strain response of three materials. The proposed model has been validated with respect to reported test results on two grades of steel (SA 333 Gr. 6 and E355) and one grade of austenitic stainless steel (X5CrNi18-10) under asynchronous axial-torsion loading conditions with a wide range of frequency ratios. The proposed model resulted in a comparable assessment of axial and shear stress–strain response with respect to the test loops for all three materials.

Cyclic plastic response of rotary swaged Fe-14Cr-10Al-4Y2O3 ODS alloy at 1000–1200 °C

This study is dedicated to the investigation of the cyclic stress-strain response of a newly developed ferritic steel reinforced with a high-volume fraction of oxide nanoparticles. The mechanically alloyed powder was consolidated by hot rotary swaging into cylindrical rods with diameters of 15 mm and 12 mm. Subsequently, the rods were annealed at 1200 °C for 4 h to achieve a fully recrystallized coarse-grained microstructure optimal for high-temperature applications. The cyclic tests were carried out in controlled deformation mode in a symmetrical push-pull cycle with triangular waveform at 1000 °C and 1200 °C in air. The Fe-14Cr-10Al-4Y2O3 ODS steel exhibits extraordinary cyclic strength of up to 140 MPa at temperature of 1200 °C. The results show that rotary swaging to a smaller diameter does not affect the resulting stress-strain response. The coarsening of the Y2O3 nanoparticles occurs only very slowly even at 1200 °C. In areas with significant plastic deformation, a slight rotation of the coarse grains from the ideal [111] direction and partial dynamic recrystallization was observed.

Dislocation-density-related constitutive model and its applicability to cyclic deformation and damage behavior of 316LN SS at 823 K

In the present investigation, an in-depth understanding of the relationship between dislocation kinetics and cyclic plasticity, along with the description of yield asymmetry behavior during loading and unloading in nuclear grade 316LN austenitic stainless steel at 823 K, was examined by employing a constitutive framework using the evolution of physically-based internal-state variables. The formulation encompassed a set of first-order simultaneous differential equations that governed the evolution of dislocation density, mean free path of dislocations, and back stress. These variables were interdependent with the power law which described the kinetics of plastic strain rate. The evolution equations were numerically integrated, and the simulated data were fitted to the experimental data up to stabilized cycle at a temperature of 823 K and total strain amplitudes of ±0.004, ±0.006, ±0.008 and ± 0.010. The predicted cyclic stress response as a function of the cyclic number displayed the continuous cyclic hardening from the first cycle to the initiation of stabilized cycle. Further, good agreement between the predicted and experimental hysteresis loops was found at different cycle numbers. The predicted dislocation density and tensile peak values of back/effective stress increased with cyclic hardening and approached the value of saturation at the stabilized cycle. On the other hand, a rapid decrease in mean free path with cycle number was noticed. An increase in total strain amplitude resulted in a systematic increase in dislocation density, peak stress, back stress and effective stress. At the total strain amplitudes above ±0.006, the predicted higher rates of dislocation accumulation and annihilation, and the faster evolution rate of back stress towards saturation led to the development of stable dislocation substructure configurations with a clear distinction between dislocation high/low dense regions. Furthermore, the applicability of the model was extended by including an empirical relationship between the damage variable and cycle number within the power law, thereby enabling predictions of the cyclic stress-strain response beyond the stabilized cycle.

Experimental investigation of the effects of fatigue on caprock materials in H2 storage projects

Experimental investigation of the effects of fatigue on caprock materials in H2 storage projects

Cyclic elastoplasticity and XFEM based fatigue life assessment of out-of-plane gusset welded joints

Conventional design methods for high-cycle fatigue failure of engineering components often assume a linear-elastic material behaviour. The different driving forces of crack initiation and propagation fail to be considered, resulting in less accurate predictions of fatigue life. To address this issue, the present study proposes a novel method to predict the fatigue life of out-of-plane gusset welded joints based on cyclic elastoplasticity and extended finite element method (XFEM). Incorporating the welding residual stress simulated by thermal–mechanical analysis, the cyclic stress–strain response of out-of-plane gusset welded joints was assessed by Fatigue SS (FSS) constitutive model. The crack initiation life was therefore predicted by the local strain approach considering the mean stress correction. Based on the converged cyclic stress–strain response, the crack propagation behaviour and life were predicted by XFEM in combination with Virtual Crack Closure Technique (VCCT). The influence of mean stress, mixed-mode crack and residual stress on crack initiation and propagation life was also investigated. The results show that the proposed method can predict the fatigue life of out-of-plane gusset welded joints under the pure tension loading with high accuracy against experimental results.

Applicability of memory rules during cyclic stress–strain response of polymers PA6 and PA66 GF30

Polymers are rapidly emerging materials that are taking over the place in structural applications formerly reserved for metals. Structural materials require reliable load-bearing capability during the entire lifetime of products. Available simulation tools already offer constitutive models that are well applicable to metals but have not yet been approved for polymers. Typically, models with kinematic hardening incorporate Masing rule complemented by three memory rules to simulate the cyclic response of metals during variable loading. Conversely, the research presented here has been focused on polyamides as a load-bearing-capable substitute for metals in low-cycle fatigue applications. In particular, it has been studied whether natural PA6 and glass-fibre-reinforced PA66 GF30 follow the memory rules during variable amplitude loading. Incremental step tests were performed initially to determine the material parameters of the stabilised response. A high variation for the stabilised stress–strain response could reach up to 42.5% for PA6 and 24.5% for PA66 GF30 during incremental step tests. Moreover, the natural PA6 exhibited a higher degree of symmetry of the stress–strain result with less variation in stress than the reinforced PA66 GF30. Next, variable amplitude tests were performed which contained the three memory rules in the load history. The stress scatter during the variable amplitude loading in repeated tests has been observed between approximately ±15% and ±10% for natural PA6 and PA66 GF30, respectively. Finally, the Armstrong–Frederick model was used to carry out the simulations of the stress–strain response during the same variable load history. Comparison of the simulated and experimental results revealed that for both polymers, applicability of memory rules can be recognised.

A damage coupled elasto-plastic constitutive model of marine high-strength steels under low cycle fatigue loadings

To investigate the low cycle fatigue (LCF) performance and damage behaviours of marine high strength steels (HSSs), experimental analysis and constitutive modelling are carried out in this study. Basic mechanical properties are obtained by the monotonic tensile tests. Cyclic loading tests with different loading protocols are conducted to examine the cyclic stress-strain response. Based on the experimental data, the evolutions of peak stress, yield surface radius, backstress and LCF damage are discussed. The Ramberg-Osgood model and Manson-Coffin equation are fitted to characterize the cyclic stress-strain relation and LCF damage behaviours, respectively. Based on the continuum damage mechanics, a damage coupled cyclic elasto-plastic constitutive model is proposed to describe the hysteresis behaviours of marine HSSs. The model parameters are calibrated, and the model accuracy for stress-strain response and fatigue damage prediction is then verified by experimental data.

The influence of equi-biaxial and uniaxial tensile pre-strain on the low cycle fatigue performance of the AA2024-T4 aluminium alloy

In the present investigation, the low cycle fatigue performance of the aluminium alloy AA2024-T4 is examined for different tensile pre-straining histories. The equi-biaxial tensile pre-strained specimens revealed identical fatigue life to the 0% pre-strained specimens, while all the uniaxial tensile pre-strained specimens showed improved fatigue life. As-received specimens exhibit noticeable cyclic hardening at all the strain amplitude. The pre-strained specimen shows an almost stable cyclic stress–strain response for each strain amplitude. The electron backscattered diffraction examination of the without pre-strained and pre-strained specimens revealed large lattice distortion in the equi-biaxial tensile pre-strained case in comparison with the other two cases.

High-Temperature Low Cycle Fatigue of Nickel-Based Superalloy IN738LC

Polycrystalline cast nickel-based superalloy IN738LC is employed for critical parts of gas turbine components in the power industry, aircraft engines, and the marine sector. These components undergo severe degradation by low cycle fatigue caused by thermal gradients, particularly during start-up and shut-down periods. The present work reports the cyclic deformation behaviour and fatigue damage of IN738LC during high-temperature isothermal fatigue. Cylindrical specimens were cyclically deformed under strain control with constant total strain amplitude in symmetrical cycling at 800 °C and 950 °C in air. The microstructure is typical of coarse dendritic grains with carbides, eutectic, and shrinkage pores. SEM imaging revealed a γ matrix with coherent L12 γ′ precipitates with bimodal morphology. Cyclic hardening/softening curves, cyclic stress-strain response, and fatigue life diagrams were determined. An increase in testing temperature is associated with a significant decrease in stress amplitude and an increase in plastic strain amplitude. The fatigue life gradually decreases with increasing temperature. The fracture surfaces and polished sections parallel to the specimen axis were examined to study damage mechanisms in cyclic loading at high temperatures.

Cyclic deformation and dynamically induced short-range ordering in small particles reinforced Al composite

Cyclic deformation of an Al-Cu-Mg composite strengthened by small non-shareable particles was firstly investigated through strain controlled low-cycle fatigue (LCF) tests. In comparison with the reported Al-Cu-Mg composites, the in-situ TiB2/Al-Cu-Mg composite presented higher fatigue life at all the tested strain amplitudes. The composite exhibited cyclic hardening response, which was contributed by non-shareable particles, dislocations and dynamically deformation-induced short-range orderings in the Al matrix. Considering plastic strain evolution, the cyclic hardening model was established and well fitted with experimental results. When cyclic loading was controlled at higher strain amplitudes, the serrated flow occurred on stress-strain hysteresis loops and then it disappeared after the first few cycles related to the occurrence of dynamic strain aging. Onset of the stress serration on stress-strain hysteresis loop was greatly dependent on the strain amplitude rather than cumulative plastic strain. Finally, the correlative cyclic hardening model of small particles reinforced Al composite was analytically discussed based on microstructure evolution and cyclic stress-strain responses.

Monotonic and cyclic constitutive behaviour of rubberised one-part alkali-activated concrete

This study presents an experimental assessment into the monotonic and cyclic compressive stress-strain rate-dependent response of rubberised one-part alkali-activated concrete. Three different volumetric crumb rubber replacement ratios of total natural aggregates (0%, 30% and 60%), and three different strain rates accounting for quasi-static, moderate seismic and severe seismic conditions are considered. The results indicate a reduction in the elastic modulus, compressive strength, and crushing energy in proportion to the rubber content regardless of the strain rate or loading condition, monotonic or cyclic. A reduction in the axial crushing strain is also obtained with the increase in rubber content within the ranges considered. The increase in strain rate leads to a proportional enhancement in elastic modulus, compressive strength, and axial crushing strain. Under cyclic conditions, the unloading and reloading branches of the stress-strain response fall within the monotonic curves. The cumulative energy dissipation from each first cyclic loop reduces with the increase in rubber content, whilst an increase in the loading rate results in a proportional increase in the cumulative energy dissipation. The unloading modulus is shown to be sensitive to the unloading strain, rubber content and strain rate, while the plastic residual strain is mainly influenced by the unloading strain. Analytical expressions to predict the reduction in elastic modulus, compressive strength, axial crushing strain, unloading modulus and plastic residual strain, with varying rubber contents and for the different strain rates considered, are proposed. Constitutive models representing the monotonic stress-strain response of rubberised alkali-activated concrete materials, as well as the unloading and reloading branches of the cyclic stress-strain response, are also given. Finally, formulations for the strain rate-dependent dynamic increase factors for the elastic modulus, compressive strength, and axial crushing strain are also provided.

Improvement of superelasticity conditions in Cu-based shape memory alloys for seismic control applications

Shape memory alloys (SMAs) are smart materials with self-centering characteristics that can be used to reduce the earthquake damage to structures. In this paper, the optimal thermal treatment to obtain the ideal mechanical properties of a CuAlBe SMA wires for seismic protection applications is discussed. For this purpose, the uniaxial cyclic and monotonic stress-strain response of a 1.4 mm-diameter wire subjected to heat treatments applied for different durations is evaluated. Wire specimens are tested in multiple environments at several strain amplitudes and loading protocols. The variation of mechanical properties over time is also addressed. Test results show that a minimum treatment time of 25 min at 750 °C (∼200 μm) is necessary for obtaining superelasticity at all ambient temperatures tested. Also, as the heat treatment time increases, the residual strain, functional fatigue, strength, energy dissipation and hysteresis degradation decrease, but the superelasticity limit and low cycle fatigue life are increased. However, a 35 min treatment (∼400 μm) causes the loops to become unstable at high temperatures and the training process is not efficient. The best conditions for seismic protection purposes are achieved with a 30 min treatment (∼300 μm), due to its maximum recoverable strain of 6.5 %, 3.6 % equivalent viscous damping, negligible residual strain and stable hysteresis under all temperatures evaluated and over time. A low-cycle fatigue model based on the Coffin - Manson relationship is also proposed.

Experimental and Numerical Study of Cyclic Stress–Strain Response and Fatigue Crack Initiation Life of Mid-Carbon Steel under Constant and Multi-Step Amplitude Loading

This paper investigates the fatigue cyclic deformation behavior of mid-carbon steel. Uniaxial tensile loading tests and fatigue tests under constant and multi-step amplitude loading steps are performed to characterize the influence of loading history. The material is shown to exhibit different uniaxial ratcheting behavior depending on loading history. A smooth and gradual increase in cyclic softening is observed under smaller stress/strain conditions. Based on experimental characterization, numerical investigations are carried out to reproduce the cyclic stress–strain behavior under different variable amplitude load ranges. The nonlinear material behavior is reproduced by means of an elastoplasticity model called the Fatigue SS Model (hereafter, FSS model). The main feature of the FSS model is the ability to describe the cyclic softening behavior within a macroscopically elastic stress state. The good agreement between experimental and numerical results proves the reliability of the model to catch a realistic material response in fatigue problems. Furthermore, the present study introduces a method for the prediction of fatigue crack initiation life under variable loading conditions based on cumulative plastic work.