Asymmetric Cyclic Loading Research Articles

Ratcheting assessment of additively manufactured SS316 alloys at elevated temperatures within the dynamic strain aging domain

The present study has evaluated the accumulation of plastic strain in additively manufactured (AM) stainless steel 316 samples undergoing asymmetric loading cycles at elevated temperature range where the dynamic strain aging (DSA) phenomenon occurred. The ratcheting response of AM steel samples were assessed through the use of the combined isotropic-kinematic hardening framework. The dynamic strain aging was introduced into the dynamic recovery term of the Ahmadzadeh-Varvani (A-V) kinematic hardening rule by an exponential function ψ(p, T). This function enabled the hardening framework to evaluate the ratcheting of AM steel samples at operating temperatures within the DSA domain. The DSA temperature range for AM SS316 samples fell between 700 K to 1140 K. Within this temperature domain, the interaction between solute atoms and dislocations led to an increase in material strength and suppressed the magnitude of ratcheting over the loading cycles. The influence of DSA on the backstress evolution and the yield surfaces translated in the deviatoric stress space and their subsequent influence on the ratcheting of samples using the A-V model were further discussed. The predicted ratcheting curves at the DSA temperature domain were found in close agreement with those of measured values.

A modified cyclic elastoplastic constitutive model considering the variational dynamic recovery term of back stress for FGH95 under asymmetrical cyclic loading

The asymmetric cyclic loading process occurs in aero-engine turbine discs. A constitutive model that accurately describes the cyclic elastoplastic behaviour of the material is important for structural design and low cycle fatigue life prediction of turbine discs. In this paper, the low cycle fatigue test of FGH95 was carried out at 620℃ under 0.5%, 0.6%, 0.7%, 0.8%, 0.9%, 1.0% and 1.1% strain amplitude with strain ratio equal to 0. The material exhibited cyclic hardening followed by cyclic softening at high strain amplitudes and cyclic softening at low strain amplitudes. The mean stress relaxation rate was similar for each strain amplitude. In addition, the evolution of effective stress and back stress was obtained through the method of internal stress division. Then, the relationship between the change in stress amplitude and the change in internal stress was discussed. The results showed that with cyclic loading, cyclic hardening/softening of FGH95 was affected by the competition mechanism of back and effective stresses. Considering that slip deformation and crystal lattice rotation coexist in plastic deformation, the dynamic recovery term of the Abdel-Karim and Ohno model was used. In order to characterize the different magnitudes of back stress change in materials at different plastic strain intervals, a dynamic recovery term coefficient was introduced to the dynamic recovery term and the critical surface of the back stress. The modified model was used to compare with experimental results. Then, it gives a good description of the material’s mean stress relaxation and strain amplitude variation and gives good agreement on the hysteresis loop.

Crack propagation kinetics under asymmetric cyclic loading for 316LN SS in high-temperature solution

Crack propagation rates (CPRs, or da/dN) of 316LN stainless steel (SS) in high-temperature solution under asymmetric cyclic loading conditions are experimentally determined, focusing primarily on the effect of load-rise time on crack propagation. The increment in crack propagation per cyclic block mainly occurs during the load-rise period. When the stress intensity factor range (ΔK) and load ratio (R) are kept similar, a faster increase in the stress intensity factor (dK/dt) during the load-rise period results in a lower average crack propagation rate (Vave-tr) during that phase. Secondary cracks and fatigue striations are observed on the fracture surface. The CPRs show a higher environmental enhancement factor (Fen) as the load-rise time increases.

Study on ultra-low cycle fatigue of steel slit dampers

Steel slit dampers are typically made by cutting a number of slits in a steel plate. With the existence of the slits, the steel strips between them would yield under earthquake action and dissipate seismic energy through plastic deformation. Ultra-low cycle fatigue (ULCF) fracture of the steel strips will significantly reduce the energy dissipation capacity of the slit damper. In this research, ULCF tests were conducted on uniform, taped and hourglass-shaped steel strip (USS, TSS and HSS) specimens, which are fundamental elements of steel slit dampers. During the ULCF tests, symmetric cyclic loadings with constant amplitude were applied on the steel strip specimens. All USS, TSS and HSS specimens fractured due to ULCF but at different sections. The ULCF life and energy dissipation capacity of these specimens increase significantly in that order. Finite element (FE) analysis was carried out to simulate the ULCF tests on the steel strip specimens, based on which the ULCF fracture of these specimens was predicted with the cyclic void growth model (CVGM). The simulated hysteretic curves and the predicted ULCF lives agree well with the test results, validating the applicability of the FE model and the CVGM for the ULCF analysis of steel slit dampers. ULCF analysis was then conducted on USS, TSS and HSS specimens subjected to symmetric cyclic loadings with variable amplitudes and asymmetric cyclic loadings with constant amplitude to confirm the superior ULCF performance of the HSS specimen. Beneficial effects of additional axial compression and deviation of cyclic loadings from the damper plane on the ULCF of steel slit dampers were also investigated through numerical analysis.

The cyclic GTN model for ULCF fracture analysis of Q355 steel

The cyclic GTN (C-GTN) model, built upon the GTN model, considers the influence of cyclic loadings on the evolution of microvoids, enabling the prediction of ULCF fracture in materials. In this study, the C-GTN model was calibrated for Q355 steel based on tests on notched round bar specimens reported in the literature. Following existing four tests on single-edge notched plate (SENP) specimens subjected symmetric cyclic loadings, additional four ULCF tests were conducted on SENP specimens with asymmetric cyclic loadings. ULCF fracture was observed in these tests and ULCF lives of these SENP specimens were obtained. Mesh sensitivity was investigated for the ULCF fracture analysis of the SENP specimens with the C-GTN model. After balancing the computational accuracy and cost, the ULCF fracture analysis of the SENP specimens were conducted using finite element models with a mesh size of 0.2 mm at the notch tip. ULCF lives predicted by the C-GTN model agree very well with test results for all SENP specimens. The agreement validated the applicability of the C-GTN model for the ULCF fracture analysis of Q355 steel. The increase of the void volume fraction and the degradation of its critical value played dominant roles in the ULCF fracture of V-notched and U-notched SENP specimens respectively.

Ratcheting Response of Heat-Treated Notched 1045 Steel Samples Undergoing Asymmetric Uniaxial Loading Cycles

The present study evaluates the ratcheting response of notched cylindrical samples made of 1045 steel alloy subjected to asymmetric loading cycles using the kinematic hardening framework, coupled with Neuber’s rule. Test samples with V-shaped and semi-circular edge notches were first heat-treated under different conditions, resulting in various material hardness values at the notch root region. Local ratcheting at the notch root of samples was found to be highly dependent on the notch shape and the heat treatment conditions. HT1 samples with a lower hardness of 12 RC at the notch region possessed higher values of ratcheting, while ratcheting at the notched region for HT2 samples with 40 RC dropped to half of that in HT1 samples. The higher hardness of 50 RC at the notch edge of HT3 samples promoted the initial yield strength and the yield surface through the kinematic hardening rule with a larger translation into the deviatoric stress space as compared with samples HT1 and HT2 with 12 and 40 RC, respectively. The local ratcheting strain in sample HT1, with semi-circular notches (Kt=1.65) at a stress ratio (Smax/Sult) of 0.965, remained below 1.80% during the first hundred loading cycles. The local ratcheting decreased to 1.2% for sample HT2 and further dropped to 0.9% for sample HT3. The yield surfaces were translated consistent with the magnitude and direction of the backstress increments, as the applied loading excursion exceeded the elastic limit. Through the use of the Ahmadzadeh–Varvani (A–V) hardening rule, the predicted ratcheting values at notch roots were found to be larger in magnitudes as compared with those of experimental data, while the predicted local ratcheting through the Chaboche (CH) hardening rule fell below the experimental data. Results consistently showed that as sample hardness increased, the local ratcheting at notch roots decreased.

Microstructure and cyclic hardening/softening behavior of laser welded high strength steel joints under asymmetrical cyclic loading

The cyclic behavior of materials under load and its influence on the mechanical properties of materials have always been the focus of engineering research. In this study, high strength steel was successfully welded by laser welding. The microstructure of each region of the high strength steel DP590 post-welding was meticulously analyzed. Additionally, 500 cycles of low-cycle fatigue tests of laser welded high strength steel were carried out by using asymmetric stress control method. After fatigue test, tensile test shall be carried out on some samples. Under the specific combination of mean stress and stress amplitude, compare the specimens that have not been fatigue tested with those that have been fatigue tested, the change of properties of laser welded high strength steel joint under asymmetric cyclic load was analyzed. The results showed that, due to cyclic hardening, the tensile strength of the sample increased to 601 MPa and the yield strength to 325 MPa. Compared with the original sample, the tensile strength and yield strength of the sample after asymmetric cycling had increased by 8.65% and 31.3%, respectively.

Peridynamic numerical investigation of asymmetric strain-controlled fatigue behaviour using the kinetic theory of fracture

Numerical fatigue process modelling is complex and still an open task. Discontinuity caused by fatigue cracks requires special finite element techniques based on additional parameters, the selection of which has a strong effect on the simulation results. Moreover, the calculation of fatigue life according to empirical material coefficients (e.g., Paris law) does not explain the process, and coefficients should be set from experimental testing, which is not always possible. A new nonlocal continuum mechanics formulation without spatial derivative of coordinates, namely, peridynamics (PD), which was created 20 y ago, provides new opportunities for modelling discontinuities, such as fatigue cracks. The fatigue process can be better described by using the atomistic approach-based kinetic theory of fracture (KTF), which includes the process temperature, maximum and minimum stresses, and loading frequency in its differential fatigue damage equation. Standard 316L stainless steel specimens are tested, and then the KTF-PD fatigue simulation is run in this study. In-house MATLAB code, calibrated from the material S‒N curve, is used for the KTF-PD simulation. A novel KTF equation based on the cycle stress‒strain hysteresis loop is proposed and applied to predict fatigue life. The simulation results are compared with the experimental results, and good agreement is observed for both symmetric and asymmetric cyclic loading.

A Comparative Study of Ratcheting Fatigue Behavior of Modified 9Cr–1Mo Steel and Inconel 617 Alloy at Homologous Temperature of 0.42

The modified 9Cr–1Mo steel and Inconel (IN) 617 superalloy are high‐temperature alloys of prime importance in several industrial applications. Both of these are used at elevated temperature for various piping and tubing components and undergo asymmetric cyclic loading; therefore, it is highly essential to assess their resistance to accumulation of inelastic strain (ratcheting) under asymmetric stress cycling. In this study, ratcheting behavior of these alloys is compared at the homologous temperature of 0.42, under uniaxial asymmetric stress loading with positive mean stress. Deformation behavior of the tested samples is analyzed by transmission electron microscope. While there is homogeneous deformation in the modified 9Cr–1Mo steel, there is intersection of slip bands and presence of dislocation tangles in the IN 617 alloy. Fracture surface of the modified 9Cr–1Mo steel, tested under asymmetric cyclic loading, reveals typical ductile fracture resulting from tensile loading, whereas there is characteristic fatigue fracture of the IN 617 alloy.

A novel approach for corrosion fatigue life estimation under asymmetric cyclic loadings using intrinsic damage dissipation

Numerous scholars have conducted theoretical research on corrosion fatigue lifetime prediction models based on continuum damage mechanics and linear fracture mechanics. However, most of the predicted models require several material parameters, making them difficult to apply in practice. For practical application, the existing models, including the Goodman, Gerber, SWT and Walker models, are empirical or statistical and have not gained wide acceptance. Hence, an urgent need exists for an equally simple, easy-to-apply, and mechanics-based model for engineering applications. Therefore, this study proposes a corrosion fatigue stress equation associated with equivalent life based on the intrinsic damage dissipation energy. The method attached to a material parameter can be used to predict corrosion fatigue lifetime and provides a novel approach for easy application. The comparisons of experimental results and the results predicted by our proposal and the existing models were carried out, indicating that our proposal provides better correlations with experimental results than others. The proposal provides great potential for its simplicity in the evaluation of corrosion fatigue lifetime under asymmetric cyclic loadings.

Ratcheting prediction of stainless steel 304 and 316L samples undergoing asymmetric loading cycles at elevated temperatures incorporating dynamic strain aging phenomenon

The present study intends to assess the plastic strain accumulation in austenitic stainless steel 304 and 316 L samples undergoing uniaxial loading cycles at elevated temperatures incorporating the dynamic strain aging (DSA) phenomenon. The DSA function was adapted into the dynamic recovery term of the Ahmadzadeh-Varvani (A-V) kinematic hardening rule to address the accumulated plastic strain (ratcheting strain) of steel samples at elevated temperature ranges where materials show a negative strain rate sensitivity. The range of temperature at which stainless steel samples manifested DSA event was evidenced between 573 K and 900 K. At this temperature range, the interaction of solute atoms with dislocations resulted in an elevation in materials strength. The evolution of yield strength at various temperatures was calibrated with a multi-variable function developed earlier by the Voyiadjis-Song-Rusinek (VSR) model. The higher strength due to the interaction of solute atoms and dislocations, suppressed the ratcheting magnitude and rate of steel samples at the DSA domain. Applied loads beyond the elastic limit resulted in the yield surface translation, in the deviatoric stress space, governed by the A-V hardening rule. The DSA phenomenon promoted the yield surface and the backstress evolution for stainless steel samples at the operating temperature of 673 K. The predicted ratcheting curves within the DSA domain were largely associated with the operating temperature, accumulated plastic strain, and asymmetric loading cycles.

P-Y Lateral Pile Analyses Accounting for Arbitrary Loading Directions and Calibration Uncertainty

A bounding surface plasticity p-y model accommodating pile lateral loading in arbitrary directions with respect to the pile axis is demonstrated via back-analysis of test piles. The demonstration analyses include: planar conditions, three-dimensional conditions with asymmetric cyclic loading, and Monte Carlo investigations of the influence of calibration choices. The p‑y model and its host finite element program are implemented in the MATLAB programing environment. Monte Carlo simulations investigating modelling uncertainty are accomplished efficiently when taking advantage of MATLAB’s parallel processing capability. Analysis results are compared to those observed for nine test piles at the Cowden site with diameters 0.272 m, 0.762 m and 2 m having length-to-diameter ratios between 3 and 10. The implemented p-y model is based upon and is a natural extension of the traditional API methodology. The modelling technique accurately reproduces the observed response characteristics of piles in a challenging soil profile with considerable uncertainty in its strength characteristics. It is robust, theoretically rigorous, efficient and requires the same level of effort as traditional p-y analyses. The results are easily interpreted by designers familiar with the p-y method. The characteristic responses of the p-y model under biaxial loading compare favorably to those from finite element elastic-plastic planar continuum analyses as well as small-scale physical tests on rigid piles.

Mechanism of ratcheting deformation of HSLA steel: Effects of internal stresses and dislocation density

The objective of this study is to elucidate the mechanism of ratcheting deformation of HSLA steel in relation to the evolution of internal stresses i.e. effective stress (σef) and backstress (σb) associated with the generation of dislocations during asymmetric cyclic loading. Effective and back stresses are calculated from the stress-strain hysteresis loops and dislocation density is estimated from the X-ray diffraction technique. The results exhibit an increase in the accumulation of ratcheting strain associated with a sharp reduction in fatigue life by the increment in stresses. A continuous cyclic softening until the final failure is observed for all the ratcheting tests. It is noticed that the effect of stress amplitude is more prominent than the mean stress for controlling cyclic softening, which is evidenced by the evolution of effective stress and backstress in association with dislocation density. Additionally, transmission electron microscopic images are used to correlate strain conditions and substructural patterns.

Ratcheting Simulation of Additively Manufactured Aluminum 4043 Samples through Finite Element Analysis

This study presents a finite element-based ratcheting assessment of additively manufactured aluminum 4043 samples undergoing asymmetric loading cycles. The Chaboche material model in ANSYS was utilized and the effects of mesh and element type were examined. Different element numbers were used in a thorough convergence study to obtain independent meshing structures. The coefficients of this model were defined through stress–strain hysteresis loops determined from the strain-controlled tests. The backstress evolution and the corresponding yield surface translation in the deviatoric stress space were discussed as three different mesh elements of linear brick, quadratic tetrahedron, and quadratic brick were adopted. The magnitude of backstress was affected as different element types were employed. The first-order brick elements resulted in the highest backstress increments, while the lowest backstresses were determined when quadratic brick elements were taken. Backstress increments are positioned in an intermediate level with the use of quadratic tetrahedron elements. The choice of the element type, shape, and number influenced material ratcheting response over the loading process. The use of quadratic brick elements elevated the simulated ratcheting curves. The quadratic tetrahedron and linear brick elements, however, suppressed ratcheting level as compared with those of experimental data. The closeness of the simulated ratcheting results to those of the measured values was found to be highly dependent on these finite element variables.

Research on fatigue life prediction model for 2A70-T6 aluminum alloy at different strain ratios

PurposeIn practical engineering, oil filters often work under asymmetric cyclic loading. In order to improve the prediction accuracy of fatigue life of the oil filters under asymmetric cyclic loading, the effect of strain ratio and low cycle fatigue plastic deformation on fatigue life need to be considered. This paper aims to discuss the aforementioned objective.Design/methodology/approachFirst, strain-controlled fatigue tests with strain ratios of 0, 0.5 and −1 were carried out on the oil filter material 2A70-T6 aluminum alloy, and the test data were used to obtain strain fatigue life curves at three strain ratios. Then, based on the idea of the constant life curve method, the average value of the ratio of the strain amplitude corresponding to different strain ratios under the same partial life was defined as the strain ratio factor. Finally, the elastic-plastic factor was modified by the strain ratio factor, and a new fatigue life prediction model considering the effect of strain ratio was proposed.FindingsThe proposed model was validated, respectively, by fatigue test data of 2A70-T6 aluminum alloy, 2124-T851 aluminum alloy and oil filter and the results of the proposed model were compared with the Coffin–Manson equation, Morrow model and Smith–Watson–Topper (SWT) model, showing that the proposed model had higher applicability and accuracy.Originality/valueIn this work, a strain ratio factor is established based on the idea of the constant life curve method, and the strain ratio factor is used to modify the introduced elastic-plastic factor, and then a new fatigue life prediction model considering the influence of strain ratio and low cycle fatigue plastic deformation on material fatigue damage accumulation is proposed. The results show that the prediction results of the proposed model are in good agreement with the experimental data, and the proposed model has good fatigue life prediction ability considering the influence of strain ratio and lays a foundation for the fatigue life prediction of the oil filter.

Modeling on magnetization behavior of ferromagnetic material during cyclic deformation

In this paper, a nonlinear magneto-mechanical coupling constitutive model is established to describe the magnetization behavior of ferromagnetic materials under cyclic elastoplastic deformation. The critical state is introduced into the hysteretic magneto-mechanical model. In the critical state, the magnetization rates of loading and unloading are different. A new nonlinear plastic effective magnetic field is proposed by considering the effect of pinning sites caused by cross slip dislocation to describe the magnetization behavior under asymmetric cyclic loading. The softening factor and activation condition of plastic modulus parameter are introduced based on the cyclic plastic constitutive model to describe the decrease of plastic modulus. A new magnetization model for ferromagnetic materials under cyclic plastic deformation is established by combining the magneto-mechanical coupling model with the cyclic plastic constitutive model. Compared with the experiments and existing models, it is shown that the proposed model can capture the deformation and magnetization behavior well under cyclic loading.

A comparative assessment of the effects of laser shock peening and ultrasonic shot peening on surface integrity and ratcheting fatigue performance of HSLA steel

In this work, a comparative assessment of the effects of laser shock peening (LSP) and ultrasonic shot peening (USP) on surface integrity and ratcheting fatigue performance of ASTM A588 Grade D high strength low alloy steel was done. Surface roughness, microhardness, microstructure, residual stress, and micro-texture analyses were used to describe the unpeened and peened surfaces. Three sets of tension-compression asymmetric cyclic loading tests were carried out at room temperature on unpeened and peened specimens to evaluate the effects of the applied treatment on strain accumulation and fatigue life. The quantitative dislocation densities of selected specimens were calculated in order to examine the mechanism underlying the softening behavior of USP-treated specimens during fatigue testing. The results are presented in light of the substantial surface roughness, lower compressive residual stress, and weakening of texture intensity revealing an unexpectedly large drop in fatigue strength following USP treatment compared to the unpeened and laser-peened specimens.

Experimental and numerical investigation of ratcheting behavior in seamless carbon steel 90° elbow pipe with small dimensions under constant internal pressure and in-plane cyclic bending

The purpose of this study is to identify the effects of mean fatigue load, amplitude fatigue load, internal pressure and loading history on ratcheting behavior of seamless A234 WPB steel elbow pipe. So, in this paper the ratcheting behavior of seamless 90° elbow pipe of A234 WPB steel under constant internal pressure and in-plane cyclic bending is investigated experimentally and numerically. At first, in order to the confirm of elbow pipe material, a series of experimental tests were performed on elbow specimen, including: chemical composition analysis, metallography testing, hardness testing and uniaxial tensile testing. In the next step, the fatigue tests were performed on elbow pipe specimens at ambient temperature (25 °C) under asymmetric cyclic loading with load-control conditions. According to the experimental fatigue data, concluded that the increasing of mean load, amplitude load and internal pressure, increases the accumulation of ratcheting strain in axial direction at intrados and extrados locations, and also in hoop direction at crown location. So that the increasing of mean load or amplitude load has the greatest effect on the ratcheting strain at intrados and extrados locations. Also, it was found that the loading history affected to ratcheting behavior and premature failure of pressurized elbow pipes. Finally, the finite element simulation was carried out by ANSYS software based on the nonlinear kinematic/isotropic hardening model, and the FE simulation results were compared with experimental fatigue data and it was found that the numerical results are in good agreement with experimental fatigue data.

An energy‐based approach for uniaxial fatigue life estimation under asymmetric cyclic loading

AbstractEnergy parameter formed by multiplying the maximum strain range and the peak stress has the problem that one value may correspond to multiple fatigue damage states. For this issue, a new energy parameter suitable for tension–compression is proposed, which includes an improved strain‐energy model and a strain‐energy ratio. The improved strain‐energy model deduced by judging the volume change of the micro‐element has positive and negative function which can use to distinguish tensile and compressive deformation. The strain‐energy ratio is established to characterize the alternate tensile and compressive deformation under asymmetric cyclic loading. Then, applying fatigue test data, a modeling approach for fatigue life estimation based on the strain‐energy ratio is proposed, and three example models are also exhibited. Finally, according to the example model, the case of a cantilever beam under asymmetric cycle loading is carried out. The results illustrate the feasibility of the improved energy parameter in characterizing tension–compression state and the applicability of the strain‐energy ratio‐based model in fatigue analysis.

Accumulation of Plastic Strain at Notch Root of Steel Specimens Undergoing Asymmetric Fatigue Cycles: Analysis and Simulation

The present study evaluates the ratcheting response at notch roots of 1045 steel specimens experiencing uniaxial asymmetric fatigue cycles. Local stress and strain components at the notch root were analytically evaluated through the use of Neuber, Glinka, and Hoffman-Seeger (H-S) rules coupled with the Ahmadzadeh-Varvani (A-V) kinematic hardening model. Backstress promotion through coupled kinematic hardening model with the Hoffman-Seeger, Neuber, and Glinka rules was studied. Relaxation in local stresses on the notched samples as hysteresis loops moved forward with plastic strain accumulation during asymmetric loading cycles was observed. Local ratcheting results were simulated through FE analysis, where the Chaboche model was employed as the materials hardening rule. A consistent response of the ratcheting values was evidenced as predicted, and simulated results were compared with the measured ratcheting data.