Key issues in cyclic plastic deformation: Experimentation

Cyclic plastic deformation phenomena include the Bauschinger effect, cyclic hardening/softening, strain range effect, loading history memory, ratcheting, mean stress dependent hardening, mean stress relaxation and non-proportional hardening. In this work, different cyclic plastic deformation responses of piping materials (SA333 C-Mn steel and 304LN stainless steel) are experimentally explored. Cyclic hardening/softening is depends upon loading types (i.e. stress/strain controlled), previous loading history and strain/stress range. Pre-straining followed by LCF and mean stress relaxation shows similar kind of material response. Substantial amount of non proportional hardening is observed in SA333 C-Mn steel during 90° out of phase tension-torsion loading. During ratcheting, large amount of permanent strain is accumulated with progression of cycles. Permanent strain accumulation in a particular direction causes cross-sectional area reduction and which results uncontrollable alteration of true stress in engineering stress controlled ratcheting test. In this work, true stress control ratcheting on piping materials has been carried out in laboratory environment. Effects of stress amplitude and mean stress on the ratcheting behaviors are analyzed. A comparison has also been drawn in between the true and engineering stress controlled tests, and massive difference in ratcheting life and strain accumulation is found.     

McDowell模型改进及1070钢棘轮效应的预测

利用McDowell 模型对1070 钢比例和非比例循环加载条件下的棘轮效应进行了预测,通过对McDowell模型的修正,为McDowell 模型中的单轴参数Ai引入了与塑性应变累积相关的演化方程,改进后的McDowell 模型能精确的预测具有拉压平均应力的单轴棘轮效应,具有平均应力的拉扭比例加载,常轴向应力的扭转循环,非比例循环载荷以及多重步骤加载条件下单轴平均应力变化的棘轮效应,改进的模型对较大循环数的棘轮效应也能给予较好的描述。     

聚碳酸酯的单轴棘轮行为研究

在常温常湿下,对聚碳酸酯(PC)材料进行了一系列单轴应变循环和非对称应力循环实验。讨论了PC材料在不同加载水平、加载历史、应力率和峰值保持时间下的循环变形特征。结果表明：PC材料在应变循环过程中体现出了一定程度的循环软化特性,其响应应力幅值在应变循环中随着循环周次的增加而下降,但不是很明显;PC材料在非对称应力循环加载过程中产生明显的棘轮行为,棘轮应变随着平均应力和应力幅值的增加而增加,并且平均应力的影响大于应力幅值的影响;加载历史对于棘轮变形行为的影响较为明显,但对应变循环特性影响不大;PC材料的棘轮变形随着应力率的减小和峰值保持时间的增加而增加,体现明显的时相关性。     

碳纤维增强PEEK树脂基复合材料的单轴时相关循环特性实验研究

通过对碳纤维/PEEK复合材料(纤维体积分数30%)的单调拉伸、 应力控制循环、 应变控制循环实验, 对该材料的应力、 应变循环特性以及棘轮行为的率相关、 时相关特性进行了系统的研究。研究表明: 与PEEK树脂基体材料相比, 加入碳纤维使材料的抗蠕变性能有所提高。在应变控制循环实验中, 响应应力幅值与应变加载速率和应变加载幅值密切相关; 在应力松弛效应的影响下, 响应应力幅值随着应变峰值保持时间的增加而减小。室温下, 碳纤维/PEEK复合材料在非对称应力循环中产生明显的棘轮应变, 并且对加载应力幅值和平均应力具有明显的依赖性, 此外, 当在较低的加载速率和具有一定峰值保持时间情况下, 棘轮应变显著增强。      

Ratcheting and fatigue properties of the high-nitrogen steel X13CrMnMoN18-14-3 under cyclic loading

High-nitrogen steel X13CrMnMoN18-14-3 has been used in manufacturing expanding metallic stents with 0.1 mm diameter, and such medical implant is subjected to complicated and asymmetrical cyclic loading during service. But there is no test data published for the thin wire of the material under cyclic loading. In this study, a series of tests were conducted on X13CrMnMoN18-14-3 stainless steel under uniaxial cyclic loading with mean tensile stress. The yield stress and ultimate strength were higher than that of large size specimen with diameters of 5 mm and 7 mm. The effects of stress amplitude, mean stress, loading history and stress rate on the ratcheting behavior of high-nitrogen steel were analyzed, respectively. It can be concluded that the ratcheting strain amplitude and ratcheting strain rate of X13CrMnMoN18-14-3 steel increases with increasing stress amplitude or mean stress correspondingly. At the meantime, experimental results reveal that the material exhibits a strong memory of the previous loading history, the stress cycling with higher stress amplitude or mean stress greatly restrains the ratcheting of subsequent stress cycling with lower ones. The ratcheting strain rate was very sensitive to the applied cyclic stress rate, and the accumulation of ratcheting strain under stress rate of 21.2 MPa/s is much faster than that under stress rate of 106 MPa/s. In addition, comparison of the fatigue life between bulk specimen and thin wire indicates that the size effect has significant influence on fatigue properties of the material. In the case of the test conducted under stress amplitude of 400 MPa, the fatigue life of small specimen is approximately ten times longer than that of bulk specimen under the same loading conditions.     

A plastic shakedown constitutive curve based on uniaxial ratcheting behavior of 304 stainless steel at room temperature

On the basis of the Bauschinger effect, a relationship between the elastic space defined in this study and the accumulated plastic strain is measured in uniaxial ratcheting tests of 304 stainless steel at room temperature. According to this relationship, a new model of uniaxial ratcheting is established and used to simulate uniaxial ratcheting behavior. The results of simulation agree well with the experimental results. These results demonstrate that the relationship between the elastic space and the accumulated plastic strain plays an important role in uniaxial ratcheting simulation. Furthermore, by taking into account the interaction of ratcheting and viscoplasticity, the relationships among elastic space, accumulated plastic strain and loading cases are discussed. It can be seen that, when the stress ratio R of valley stress versus peak stress is not less than zero, the accumulated plastic strain is a function of the peak stress. So, a constitutive curve is obtained to describe the stable states of plastic shakedown for 304 stainless steel material under the stress ratio R ≥ 0. It can be used to determine the accumulated plastic strain of engineering structures under cyclic loading only by an elastic–plastic analysis.     

AZ91D室温环境棘轮及其低周疲劳行为

通过AZ91D室温环境应力控制下的低周疲劳试验,对铸造镁合金棘轮及其低周疲劳行为进行了研究,讨论了室温环境下材料的应力循环特性、棘轮行为、塑性应变范围、全应变范围等疲劳参量随载荷水平和加载历史的变化规律,同时基于平均应力修正对材料的应力-寿命曲线进行了讨论。研究结果表明:AZ91D在室温环境下的应力循环呈循环硬化,材料的棘轮行为和塑性应变范围、全应变范围等疲劳参量依赖于载荷水平和加载历史,另外考虑平均应力修正后的应力-寿命曲线预测效果有明显改观。     

Steady ratcheting strains accumulation in varying temperature fatigue tests of PMMA

The evolutions of ratcheting strains of polymethyl methacrylate (PMMA) at different temperatures and stress levels were experimentally investigated. A steady ratcheting strain growth region with a constant rate was observed in all specimens, which occupied significant part of total fatigue failure life. Experimental results also showed that the steady ratcheting growth rate varied with applied temperatures and loading. In this paper, theory of thermally activated process for glassy polymers was used to describe the plastic deformations during the cycle. Based on the correlations between ratcheting strains per cycle and hysteresis loop energy, a new ratcheting strains accumulative model for polymer materials was developed, which quantificationally elucidated the effects of temperature, loading frequency, mean stress and stress amplitude on the accumulative rate of ratcheting strains. Comparing the predications from the proposed model with experimental ratcheting strain data of PMMA, it was found that the model could describe the steady ratcheting strain accumulative behaviors under arbitrary temperatures and loading conditions exactly.     

Experimental Study on Uniaxial and Multiaxial Strain Cyclic Characteristics and Ratcheting of 316L Stainless Steel

An experimental study was carried out on the strain cyclic characteristics and ratcheting of 316L stainless steel subjected to uniaxial and multiaxial cyclic loading. The strain cyclic characteristics were researched under the strain-controlled uniaxial tension-compression and multiaxial circular paths of loading. The ratcheting tests were conducted for the stress-controlled uniaxial tension-compression and multiaxial circular, rhombic and linear paths of loading with different mean stresses, stress amplitudes and histories. The experiment results show that 316L stainless steel features the cyclic hardening, and its strain cyclic characteristics depend on the strain amplitude and its history apparently. The ratcheting of 316L stainless steel depends greatly on the Values of mean stress, stress amplitude and their histories. In the meantime, the shape of load path and its history also apparently influence the ratcheting.     

Biaxial cyclic deformation of an epoxy resin: Experiments and constitutive modeling

Biaxial (proportional and non-proportional) cyclic tests were conducted on thin-walled tubular specimens to investigate deformation behavior of an epoxy resin, Epon 826/Epi-Cure Curing Agent 9551. The focus was placed on the biaxial stress-strain response and their dependency on the load control mode, stress or strain range and loading path. Experimental results indicated that under strain-controlled equi-biaxial (proportional) cyclic loading, mean stress relaxation occurred in both axial and hoop directions, whereas under stress-controlled equi-biaxial cyclic loading, ratcheting strains accumulated in both principal directions. Under strain- or stress-controlled non-proportional cyclic loading, anisotropy in stress-strain responses was induced in both axial and hoop directions, and the axial and hoop hysteresis loops rotated in opposite directions. This was particularly evident at high stress or strain levels. The experimental results were further used to evaluate the predictive capabilities of a nonlinear viscoelastic constitutive model. Qualitative and quantitative comparison with the test data indicated a good agreement in predicting the complex stress-strain response under biaxial cyclic loading with various loading paths, applied stress or strain ranges and loading control modes.     

Experimental Study on Non—proportional Multiaxial Strain Cyclic Characteristics and Ratcheting of U71Mn Rail Steel

An experimental study was carried out on the strain cyclic characteristics and ratcheting of U71Mn rail steel subjected to non-proportional multiaxial cyclic loading.The strain cyclic characteristics were researached under the strain-controlled circular load path.The ratcheting was investigated for the stress-controlled multiaxial circular,elliptical and rhombic load paths with different mean stresses,stress amplitudes and their histories.The experiment shows that U71Mn rail steel features the cyclic non-hardening/softening, and its strain cyclic characteristics depend greatly on the strain amplitude but slightly on its history.However,the ratcheting of U71Mn rail steel depends greatly not only on the values of mean stress and stress amplitude,but also on their histories.In the meantime,the shape of load path and its history also apparently influence the ratcheting.The ratcheting changes with the different loading paths.     

Development of new cyclic plasticity model for 304LN stainless steel through simulation and experimental investigation

Cyclic plastic deformation characteristics of 304LN stainless steel material have been studied with two proposed cyclic plasticity models. Model MM-I has been proposed to improve the simulation of ratcheting phenomenon and model MM-II has the capability to simulate both cyclic hardening and softening characteristics of the material at various strain ranges. In the present paper, strain controlled simulations are performed with constant, increasing and decreasing strain amplitudes to verify the influences of loading schemes on cyclic plasticity behaviors through simulations and experiments. It is observed that the material 304LN exhibits non Masing characteristics under cyclic plastic deformation. The measured deviation from Masing is well established from the simulation as well as from experiment. Simulation result shows that the assumption of only isotropic hardening is unable to explain the hardening or softening characteristics of the material in low cycle fatigue test. The introduction of memory stress based cyclic hardening coefficient and an exponentially varying ratcheting parameter in the recall term of kinematic hardening rule, have resulted in exceptional improvement in the ratcheting simulation with the proposed model, MM-II. Plastic energy, shape and size of the hysteresis loops are additionally used to verify the nature of cyclic plasticity deformations. Ratcheting test and simulation have been performed to estimate the accumulated plastic strain with different mean and amplitude stresses. In the proposed model MM-I, a new proposition is incorporated for yield stress variation based on the memory stress of loading history along with the evolution of ratcheting parameter with an exponential function of plastic strain. These formulations lead to better realization of ratcheting rate in the transient cycles for all loading schemes. Effect of mean stress on the plastic energy is examined by the simulation model, MM-I. Finally, the micro structural investigation from transmission electronic microscopy is used to correlate the macroscopic and microscopic non Masing behavior of the material.     

An investigation of the fatigue of CK45 steel in the as‐received state and after pre‐fatigue deformation

Fatigue failure, ratcheting behaviour and influence of pre‐fatigue on fatigue behaviour were investigated under uniaxial cyclic loading for CK45 steel at room temperature. The fatigue life was recorded for various stress ratios, and then, three mean stress models were considered. The Walker model showed an acceptable accuracy in comparison with Smith–Watson–Topper and Park et al. models. The ratcheting strains were measured for various loading conditions in order to evaluate the impact of mean stress, stress amplitude and stress ratio on ratcheting behaviour. The experimental results showed that the ratcheting strain increased with increasing mean stress, stress amplitude and stress ratio. In addition, the results of the post‐ratcheting‐fatigue tests showed that although the fatigue life decreased with increasing pre‐ratcheting strain (the ratcheting strain that is accumulated in pre‐fatigue), the loading condition that pre‐fatigue experiments were conducted has a significant effect on subsequent fatigue behaviour.     

Cyclic plastic deformation behavior in SA333 Gr. 6 C-Mn steel

Low cycle fatigue, ratcheting and dependence of their deformation response on previous deformation histories are investigated at room temperature laboratory environment for SA333 C-Mn steel. It is noticed that cyclic hardening/softening response of low cycle fatigue is considerably influenced by applied strain amplitude, monotonic pre-straining and high to low step loading sequences. Results indicate that ratcheting under high to low step loading has significant effect on its subsequent ratcheting response. However, ratcheting under low to high step loading has very little effect on successive ratcheting responses.     

Effect of stress parameters on ratcheting deformation stages of polycrystalline OFHC copper

Engineering stress‐controlled ratcheting tests under different sets of stress amplitudes and mean stresses show that ratcheting deformation in polycrystalline OFHC copper occurs in three different stages. A plateau region with almost no accumulation of inelastic strain follows general ratcheting deformation during initial loading cycles. With breakdown of the plateau region inelastic ratcheting deformation occurs at an increasingly rapid rate. The effect of the stress amplitude on the ratcheting process is found to be more than mean stress effect. Reconstruction of the ratcheting curves clearly separates the conditions for stress‐controlled low cycle fatigue with zero mean stress and ratcheting with tensile mean stress.     

Ratcheting assessment of materials based on the modified Armstrong–Frederick hardening rule at various uniaxial stress levels

The present study evaluates ratcheting response of materials by means of the Armstrong–Frederick (A–F) hardening rule, the modified A–F rule (Bower's model), and further modifications of the hardening rule based on new introduced coefficients. The implemented modifications on the A–F‐based hardening rule aims to address stages of ratcheting over stress cycles. The modified hardening rule predicts the ratcheting strain rate decay over stage I and the constant rate of strain accumulation during stage II. The modified hardening rule consisted of the coefficients of the hardening rule controlling stress–strain hysteresis loops generated over stress cycles during ratcheting process (Bower's modification on A–F rule) plus the coefficients controlling rates over stages of materials ratcheting deformation. Stress–strain‐dependent coefficients in the modified rule are responsible to compromise overprediction of ratcheting of A–F during stage I and the premature plastic shakedown beyond stage I induced by Bower's model. Ratcheting strain rate coefficients improved the hardening rule capability to calibrate and control the rate of ratcheting in stages I and II and enabled the modified hardening rule to predict ratcheting strain over a prolonged domain of stress cycles. The modified hardening rule was employed to assess ratcheting response of 304, 42CrMo, 316L steel and copper samples under uniaxial loading conditions. The predicted ratcheting values based on the modified hardening rule and the experimental ratcheting strains were found in good agreements.     

Fatigue life and plastic deformation behavior of electrodeposited copper thin film under variable amplitude loading

As an exploratory study to investigate fatigue behavior of an elecrodeposited copper thin film under variable amplitude loading, repeated two-block loading tests were performed for various loading conditions. Plastic deformation behavior was continuously measured during the tests. Due to the load interaction effect under repeated two-block loading, fatigue life is significantly reduced. A concept is introduced to evaluate the load interaction effect and successfully utilized to predict fatigue life through simulation of the monotonic plastic strain (ratcheting strain) behavior under repeated two-block loading. Effects of load parameters of repeated two-block loading on fatigue life were also discussed.     

Ratcheting assessment of steel alloys under step-loading conditions

The present study examines the capability of a recently modified hardening rule to characterize ratcheting response of materials subjected to multi-step uniaxial stress cycles. The modified hardening rule was developed based on Armstrong–Frederick (A–F) hardening rule through implementing new ratcheting rate dependent coefficients γ₂ and δ. These coefficients were estimated by means of calibrated curves for any given stress levels defined from the uniaxial single-step ratcheting response at various cyclic stress levels. At a constant mean stress, ratcheting strain progressively increased as stress amplitude over steps of loading history increased. Similar response was also evident for step-loading with constant stress amplitude while the values of mean stress increased. For high–low histories, the trend of predicted ratcheting strain from higher to lower magnitudes found agreeable with that of experimental data. The discrepancy of the predicted and experimentally ratcheting strain values in the high–low step loading however was due to constancy in the shape and size of translating yield surface in the modified kinematic hardening rule. The modified hardening rule was employed to assess ratcheting response of SS316L, SA333, SS316L(N) and 1070 steel alloys under various step-loading conditions. Predicted ratcheting data at various stress level were found in good agreements as compared with the experimental ratcheting strains.     

Kinematic hardening rules for modeling uniaxial and multiaxial ratcheting

Ratcheting, which is the strain accumulation observed under the unsymmetrical stress controlled loading and non-proportional loadings, is modeled using the simplified viscoplasticity theory based on overstress (VBO). The influences of kinematic hardening laws on the uniaxial and multiaxial non-proportional ratcheting behavior of CS 1026 carbon steel have been investigated. The following kinematic hardening rules have been considered: the classical kinematic hardening rule, the kinematic hardening rules introduced by Armstrong–Frederick, Burlet–Cailletaud and the modified Burlet–Cailletaud. The investigated loading conditions include uniaxial stress controlled test with non-zero mean stress, and axial strain controlled cyclic test of thin-walled tubular specimen in the presence of constant pressure. Numerical results are compared with the experimental data obtained by Hassan and Kyriakides [Hassan T, Kyriakides S. Ratcheting in cyclic plasticity, part I: uniaxial behavior. Int J Plast 1992;8:91–116] and Hassan et al. [Hassan T, Corona E, Kyriakides S. Ratcheting in cyclic plasticity, part I: multiaxial behavior. Int J Plast 1992;8:117–146]. It is observed that all investigated kinematic hardening rules do not improve ratcheting behavior under multiaxial loading, but over-prediction still exists.     

Effect of axial ratcheting deformation on torsional low cycle fatigue life of lead-free solder Sn–3.5Ag

Multiaxial fatigue tests were conducted on Sn–3.5Ag solder specimens under axial/torsional loading at room temperature. It was found that the ratcheting strain increased while the fatigue life decreased with the increase of axial stress and shear strain amplitude. A power relationship of ratcheting strain rate versus fatigue life was observed. Equivalent strain approach and critical plane approaches were evaluated with fatigue life data obtained in the tests. Since those approaches excluded the consideration of the ratcheting strain and mean stress, the methods for fatigue life prediction were improper for multiaxial fatigue with ratcheting strain. Coffin model, considered the effect of ratcheting on fatigue life depending on the ratio of ratcheting strain to material ductility, brought the fatigue life predictions on non-conservative side if the ratcheting deformation was large. For this reason, a model with the maximum shear strain range and axial ratcheting strain rate was proposed as a new damage parameter. The new model could not only describe the fatigue life in torsion test, but also predicted torsional fatigue life of the lead-free solder with axial ratcheting.