Stress-controlled Cycle Research Articles

Analyses of the model parameters of kinematic-isotropic hardening rule using genetic algorithm approach for predicting cyclic-plasticity of metallic structural materials

Modeling of engineering components under cyclic loading is complex because cyclic-plastic phenomena like the Bauschinger effect, ratcheting, shakedown, and mean stress relaxation are to be considered in the constitutive modeling. This has led to several investigations on modeling the cyclic-plastic behaviour of materials under stress-controlled and strain-controlled testing; but amongst these, Chaboche's isotropic-kinematic hardening (CIKH) model is quite popular and a frequently used one. A new methodology has been recently proposed by some of the present authors to use genetic algorithm towards optimization of the parameters of CIKH modeling with a demonstration of its applicability for a few materials. This investigation aims to elucidate that this approach is applicable to both cyclically stable materials as well as cyclic softening or hardening materials using several examples on structural materials. The considered metallic materials include several aluminum (like AA7075-T6 alloy), iron (like CS-1026and Sa333 C-Mn steel), titanium (like TA16 alloy), zirconium (like Zr-4 alloy)-base alloys or superalloys (like INCONEL718). The merit of the analysis of cyclic plastic deformation behaviour of materials with the current approach is inherent in its achieving higher accuracy of fitting to the experimental data with a single set of material parameters under both strain- and stress-controlled cycling. This has been established with a comparative analysis of the accuracy of fitting by the present approach with the ones available from the existing reports. The parameters obtained using the approach for the different materials are compared to get insights into the mechanism of plastic deformation.

A revised Chaboche model from multiscale approach to predict the cyclic behavior of type 316 stainless steel at room temperature

In this work, we propose a revised Chaboche model based on a crystal plasticity multiscale approach. From our experiments, 316L steel exhibits two plasticity characteristics at room temperature during the cyclic loading: varied plastic modulus in strain-controlled cycling and continuous growing ratcheting strain in stress-controlled cycling. These characteristics cannot be predicted by using the classic Chaboche model. To modify this model, we used a crystal plasticity multiscale approach to see the microstructure effect on these characteristics. The result shows that the viscous effect, which is ignored in the classic model, plays an important role in stress-controlled cycling. With the multiscale simulation results, we revise the Chaboche model in two folds: a static recovery item is included in the kinematic hardening rule to consider the influence of viscosity on ratcheting; the dynamic recovery term is varied with the accumulated plastic strain for the change of plastic modulus during the strain-controlled cycling. With the revised model, we show that the strain- and stress-controlled cyclic behaviors from experiments can be well predicted. Also, the application of the revised model in integrated structural analysis is discussed.

Creep-fatigue interaction and damage behavior in 9-12%Cr steel under stress-controlled cycling at elevated temperature: Effects of holding time and loading rate

Considering that most creep-fatigue tests were conducted under strain-controlled mode in previous works, creep-fatigue behavior of 9–12%Cr steel under stress-controlled cycling at elevated temperature was investigated in this work. Particular attention was paid to the effects of holding time and loading rate on the deformation and damage behavior. Results indicated that a remarkable creep ratcheting is generally observed in the creep-fatigue tests with the stress ratio of −1. Ratcheting strain and creep damage progress faster as the holding time becomes larger or the loading rate becomes smaller, resulting in the decrease of the number of cycles to creep-fatigue failure.

Three-dimensional stress-controlled cyclic behavior of the interface between gravel and steel

Three-dimensional (3D) stress-controlled cycling is arguably reflective for soil–structure interfaces under in-situ loading conditions. The 3D stress-controlled cyclic behavior of a gravel–steel interface and its influencing factors were explored by conducting several series of tests. Distinct tangential displacement is induced and shows a noticeable coupling effect when subjected to 3D cycling of shear stress. The stress-controlled behavior differs significantly from the displacement-controlled behavior, and presents obvious 3D features which are influenced by the shear path, shear stress amplitude, and unequal stress amplitudes. The shear path affects the magnitude and relationship pattern of the performance parameters, while the shear stress amplitude primarily impacts the magnitude. The shear stress-displacement curves exhibit elliptical and hyperbolic formations in circular and linear shear paths, respectively. The peak reversible normal displacement remains constant with cycling in two-way shear paths, but is negligible in one-way shear path. Increased shear stress amplitude results in magnified tangential displacement and migration, peak shear flexibility, irreversible and peak reversible normal displacements, and decreased non-coaxial angle. The critical shear stress amplitude is approximately 240 kPa, at which the peak shear flexibility remains constant with cycling. Induced aeolotropy of the interface occurs in the reversible normal displacement subjected to unequal stress amplitudes.

Manufacturing Technologies for Ultra-High-Vacuum–Compatible 10 MW/m2 High Heat Flux Components for Application in Fusion Devices

High heat flux components form the primary interface for thermal management of injectors in fusion devices. The requirement for such application varies from 1 to 10 MW/m2. Ultra-high-vacuum compatibility is the inherent characteristic of such components, and manufacturing processes involve the development of specific materials, process qualification of special processes like electron beam welding (EBW), and component performance validation. One such component of active thermal management in a neutral beam injector is the hypervapatron-based heat transfer element (HTE), which is designed to absorb heat flux as high as 10 MW/m2. The route to realization is through a prototype and a one-to-one model and evaluating their performance. The development route of HTEs includes several important areas. One area is development of precipitation-hardened CuCrZr material characterized for its fatigue life (more than 100 000 stress-controlled cycles); mechanical properties at ambient temperature [ultimate tensile strength (UTS) >384 MPa, elongation >13%] and at operational temperature, i.e., 350°C (UTS >263 MPa, elongation >14%); and restricted chemical composition range of Cr, Zr, Cd, and O2 to enhance the precipitation effect and weldability of the component. A second area is similar material (CuCrZr to CuCrZr) and dissimilar material (CuCrZr-Ni-SS316L) joining by an advanced technology like EBW in a controlled environment to enhance the localized high heat input over a large weld penetration depth with minimal distortion and thereby overcome the effect of thermal diffusion by typical copper during welding. A third area is validation of these weld joints with respect to international codes/standards. Successful realization of this route establishes HTEs as main baseline components of the high heat flux system or neutral beam system. Similar application areas can be identified in various fusion devices. The paper presents the implementation of this realization route of prototype HTEs including details of the assessment carried out with respect to application.

Low Cycle and Ratchetting Fatigue Behavior of High UTS/YS Ratio Reinforcing Steel Bars

Cyclic deformation behavior of high UTS/YS rebars has been studied employing both symmetric strain-controlled and asymmetric stress-controlled cycles in an attempt to understand the influence of UTS/YS ratio on fatigue life. While strain-controlled cyclic deformation did not exhibit a pronounced influence of UTS/YS ratio, a substantial life enhancement is noted for the asymmetric stress-controlled cycle. Reasons for life enhancement were found to be due to the ratchetting strain development and the associated hardening behavior. An equivalent stress-based model has been used to predict both the symmetric and asymmetric fatigue lives of rebars.

Experimental and numerical investigations on the ratcheting characteristics of cylindrical shell under cyclic axial loading

The ratcheting characteristics of cylindrical shell under cyclic axial loading are investigated. The specimens are subjected to stress-controlled cycling with non-zero mean stress, which causes the accumulation of plastic strain or ratcheting behavior in continuous cycles. Also, cylindrical shell shows softening behavior under symmetric axial strain-controlled loading and due to the localized buckling, which occurs in the compressive stress-strain curve of the shell; it has more residual plastic strain in comparison to the tensile stress-strain hysteresis curve. The numerical analysis was carried out by ABAQUS software using hardening models. The nonlinear isotropic/kinematic hardening model accurately simulates the ratcheting behavior of shell. Although hardening models are incapable of simulating the softening behavior of the shell, this model analyzes the softening behavior well. Moreover, the model calculates the residual plastic strain close to the experimental data. Experimental tests were performed using an INSTRON 8802 servo-hydraulic machine. Simulations show good agreement between numerical and experimental results. The results reveal that the rate of plastic strain accumulation increases for the first few cycles and then reduces in the subsequent cycles. This reduction is more rapid for numerical results in comparison to experiments.

Wrinkling of Tubes by Axial Cycling

Circular tubes compressed into the plastic range first buckle into axisymmetric wrinkling. Initially, the wrinkle amplitude grows with increasing load, but induces a gradual reduction in axial rigidity that eventually leads to a limit load instability and collapse. For lower D/t tubes, the two instabilities can be separated by strain levels of a few percent. Persistent stress-controlled cycling can cause accumulation of deformation by ratcheting. Here, the interaction of ratcheting and wrinkling is investigated. In particular, it is asked if compressive ratcheting can first initiate wrinkling and then grow it to amplitudes associated with collapse. Experiments on SAF2507 super-duplex steel tubes with D/t of 28.5 have shown that a geometrically intact tube cycled under stress control initially deforms uniformly due to material ratcheting. However, in the neighborhood of the critical wrinkling strain under monotonic loading, small amplitude axisymmetric wrinkles develop. This happens despite the fact that the maximum stress of the cycles can be smaller than the critical stress under monotonic loading. In other words, wrinkling appears to be strain rather than stress driven, as is conventionally understood. Once the wrinkles are formed, their amplitude grows with continued cycling, and as a critical value of amplitude is approached, wrinkling localizes, the rate of ratcheting grows exponentially, and the tube collapses. Interestingly, collapse was also found to occur when the accumulated average strain reaches the value at which the tube localizes under monotonic compression. A custom shell model with small initial axisymmetric imperfections, coupled to a cyclic plasticity model, is used to simulate these cyclic phenomena successfully.

Microstructural stability during cyclic loading of multilayer copper/copper samples with nanoscale twinning

The response to cyclic deformation has been studied for Cu/Cu multilayer material consisting of columns of closely spaced, parallel nanotwins. The fatigue life under stress-controlled cycling is greatly improved over that of coarse-grained Cu. Nanotwinning provides significant strengthening, which is unchanged by fatigue or severe compression. Observations by focused ion beam microscopy showed that the microstructure is quite stable under deformation. Localized deformation from indentation produced shear bands and apparently some loss of nanotwinned area but no decrease in hardness.

Correspondence principles for complex shear characteristics in a nonisothermal model of monoharmonic approximation for physically nonlinear materials

The Bodner–Partom nonisothermal flow model and the generalized method of harmonic linearization are used to calculate the complex shear modulus and compliance for AMg-6 aluminum alloy. The strainand stress-controlled cycles of loading in the temperature range 20–400°C are considered. The correspondence between the shear modulus and the compliance is studied. It is similar to the inverse proportionality condition in the theory of linear viscoelasticity. It is established that representing the modulus and compliance as functions of the strain amplitude is better than as functions of the stress amplitude due to the universal description of the characteristics for soft and hard cycles and high accuracy of correspondence

Cyclic creep of copper due to axial cyclic and tensile mean stresses

The behaviour of materials under axial stress-controlled cycling with tensile mean stress within the plastic region is governed by a superposition of cyclic creep and fatigue processes. Cyclic creep may dominate the damage process and cause distortional failure before the onset of fatigue cracking. The aim of this work was to investigate cyclic creep in copper under such loading conditions at room temperatures, and to derive an empirical relationship for cyclic creep in terms of imposed stress amplitude and mean stress, via a previously proposed exponential mean-stress function that accounts for the effect of mean stress on cyclic behaviour. It is found that cyclic creep behaviour at room temperatures could be described by a power-law relation similar to that of static creep at high temperatures.

Uniaxial ratcheting of SS304 stainless steel at high temperatures: visco-plastic constitutive model

The uniaxial ratcheting of SS304 stainless steel at high temperatures (300, 600 and 700 °C) were analyzed experimentally, and described by a cyclic constitutive visco-plasticity model. The rate dependence of the material was accounted for by introducing a viscous term. The cyclic hardening and cyclic flow behavior of the material under asymmetrical stress-controlled cycling were described by the evolution rules of kinematic hardening back stress and isotropic deforming resistance. Under the isothermal condition, temperature effect was included by terms involving temperature in the evolution equations of isotropic deforming resistance. The effect of load history on ratcheting was also considered by introducing a fading memory function of the maximum inelastic strain amplitude and isotropic deformation resistance. After the material constants were determined from the experimental data, the uniaxial ratcheting of SS304 stainless steel was numerically simulated and compared with the corresponding experimental results at high temperatures. The predicted results agree well with the experimental ones.

Uniaxial and non-proportionally multiaxial ratcheting of SS304 stainless steel at room temperature: experiments and simulations

The uniaxial and non-proportionally multiaxial ratcheting behaviors of SS304 stainless steel at room temperature were initially researched by experiment and then were theoretically described by a cyclic constitutive model in the framework of unified visco-plasticity. The effects of cyclic stress amplitude, mean stress, and their histories on the ratcheting were experimentally investigated under uniaxial and different multiaxial loading paths. The shapes of non-proportional loading paths were linear, circular, elliptical and rhombic, respectively. In the constitutive model, the rate-dependent behavior of the material was reflected by a viscous term; the cyclic flow and cyclic hardening behaviors of the material under asymmetrical stress-controlled cycling were reflected by the evolution rules of kinematic hardening back stress and isotropic deforming resistance, respectively. The effect of loading history on the ratcheting was also considered by introducing two fading memorization functions for maximum inelastic strain amplitude and isotropic deformation resistance, respectively, into the constitutive model. The effect of multiaxial loading path on the ratcheting was reflected by a non-proportional factor defined in this work. The predicting ability of the developed model was proved to be good by comparing the simulations with corresponding experiments.

Modeling of uniaxial and biaxial ratcheting behavior of 1026 Carbon steel using the simplified Viscoplasticity Theory Based on Overstress (VBO)

Hassan and Kyriakides [1], Hassan et al. [2], and Corona et al. [3] performed uniaxial and biaxial ratcheting experiments on heat-treated 1026 Carbon steel. The loading histories performed with uniaxial and tubular specimens were selected to simulate those encountered in nuclear reactor vessels. The stress-strain diagram of 1026 Carbon steel was used to determine the material constants in a simplified version of VBO. Small rate dependence was allowed. The model represents some nonlinear rate dependence, kinematic hardening and cyclically neutral behavior. The set of material constants determined only from uniaxial tests was used throughout the paper. Numerical experiments included are: (i) uniaxial stress-controlled cycling with various mean stresses, (ii) strain-controlled axial tests with tubular specimens under constant and variable internal pressure, and (iii) examination and variation of certain material constants of the VBO model that can influence ratcheting. Very good agreement with the experiments is found for the uniaxial case. However the ratchet strain accumulation during biaxial cycling is over-predicted by VBO and other constitutive models.

The stability of PSBs in Cu single crystals under stress-controlled cycling

The stability of PSBs in Cu single crystals under stress-controlled cycling

Fatigue Deformation Mechanisms of Zirconia Ceramics

Two distinct fatigue deformation mechanisms, microcracking and transformation plasticity, have been identified in 3Y‐TZP and Mg‐PSZ. Microcracking is dominant in 3Y‐TZP, while transformation plasticity is more evident in Mg‐PSZ. However, the proportion of these two mechanisms is dependent on the frequency and stress amplitude, with transformation plasticity favored at low frequency and high stress. Generally, microcracks form in the tensile half‐cycle and partly close in the compressive half‐cycle, whereas transformation from the tetragonal to the monoclinic phase, as well as the reverse transformation, can occur in both tension and compression. Under stress‐controlled cycling, although the initial hysteresis loop is highly asymmetric with respect to the stress, cyclic softening and the development of an internal stress cause it to gradually evolve to yield an essentially symmetric cyclic stress–strain curve.

Plastic Strain Energy in Fatigue Failure

In this paper the cyclic plastic strain energy of the A-516 Gr. 70 carbon low-alloy steel during fully reversed constant strain or stress-controlled cycles is discussed. A relationship is proposed which can be used to determine the plastic strain energy per cycle for a non-Masing material for various stress ranges during the entire life cycle. Predictions of the proposed method are in good agreement with the experimental data. The variation of the plastic strain energy per cycle and cyclic creep during the life of fully reversed stress-controlled tests is also presented. It is shown that the cyclic creep strain affects the fatigue crack initiation period and consequently the amount of the total absorbed plastic strain energy to failure.

Cyclic response and inelastic strain energy in low cycle fatigue

The cyclic response of ASTM A-516 Gr 70 carbon low alloy steel subjected to fully-reversed constant strain- or stress-controlled cycles has been determined. The cyclic stress/strain relationship of the material was obtained through a least squares fit technique. Stable hysteresis loops at half life for various strain ranges are presented. The material does not exhibit Masing-type behaviour. The total inelastic strain energy is calculated by a new method and is in good agreement with the measured values. Comparison is also made with other proposed relationships. The total strain energy dissipated at failure may be expressed as W f = KN f α

The influence of mode control, mean value and frequency of loading on the cyclic stress-strain curve

In this paper we present the cyclic stress-strain curves for low carbon steel in the range from the strain fatigue limit ϵ ap C up to the fatigue ductility, obtained both for strain-controlled cycling and for stress-controlled cycling with various mean strains ϵ m and mean stress σ m . It is shown that the stress-controlled cyclic stress-strain curves are clearly influenced by the mean stress level σ m (as σ m increases, the slope of the stress-strain curve also increases) whereas the strain-controlled cyclic stress-strain curves for various ϵ m values are identical and their shape is not influenced by the cycling frequency (up to 10 Hz). Furthermore, the stress-controlled cyclic stress-strain curve reveals a discontinuity which separates the low cycle fatigue and the high cycle fatigue ranges. However, changes in the control modes, the mean values and the cycling frequencies do not influence the strain fatigue limit ϵ apC of the material used, which is in the range 2 × 10 −5 – 5 × 10 −5.

Fatigue crack propagation in two classes of directionally solidified eutectic alloys

Fatigue crack propagation rates were measured in two classes of directionally solidified eutectic alloys under isothermal, stress-controlled cycling at temperatures of 298 to 1311 K. Alloy 73C, a cobalt-base material reinforced by fibers of Cr7C3, and γ/γ′ + δ, a nickel-base alloy reinforced by lamellae (platelets) of Ni3Cb, were grown at solidification rates of 1 and 25 cm/h to achieve significant differences in interfiber and interlamellar spacing (λ). No influence of the spacing of the reinforcing phase on crack growth rates were found for either alloy. In addition, chromium level and perfection of the microstructure had a minimal effect on propagation rates for γ/γ′ + δ. The independence of the fatigue crack growth rates on λ may be associated with the ratio of the cyclic plastic zone diameter at the crack tip to λ. In all instances, this ratio was estimated to be greater than one for the test conditions employed. At the lower temperatures, crack propagation rates in γ/γ′ + δ were up to two orders of magnitude lower than those in Alloy 73C due to crack deflection at interlamellar interfaces and grain boundaries which lowered the effective stress intensity range for opening mode cracking.