Stress-controlled Cyclic Tests Research Articles

A constitutive model for uniaxial/multiaxial ratcheting behavior of a duplex stainless steel

In the framework of rate-independent plasticity theory, a constitutive model capable of simulating the uniaxial strain cycling and the uniaxial/multiaxial ratcheting responses of a super duplex stainless steel (S32750) which has cyclic hardening characteristics under strain-controlled cyclic loading is derived. In the developed constitutive model, the steady cyclic flow was reflected by the nonlinear evolution of the proposed kinematic hardening rule based on the Chaboche model and the Burlet and Cailletaud model; the cyclic hardening was modeled by the evolution of isotropic hardening; the strain memory effect was also considered through the asymptotic value of the isotropic hardening variable. Verification of the proposed constitutive model was achieved by simulating the uniaxial/multiaxial strain- and stress-controlled cyclic loading tests and comparing the predicted results with the experimental measurements.

Experimental studies on the uniaxial ratchetting of polycarbonate polymer at different temperatures

A series of uniaxial stress-controlled cyclic tests were carried out at different temperatures to investigate the uniaxial ratchetting of polycarbonate (PC) and its time-dependent behavior. The cyclic tests were conducted with a constant peak stress, various valley stresses and at four prescribed temperatures (i.e., 0, 30, 60 and 90°C). The effects of applied valley stress and ambient temperature on the uniaxial ratchetting of the PC are discussed. From the experimental observations, it is concluded that the ratchetting of the PC depends greatly on the test temperature; both the ratchetting strain and ratchetting strain rate increase with increase of test temperature. The effect of different valley stresses on the ratchetting is also dependent on the test temperatures, and fatigue rupture occurs in the load cases with negative valley stresses and at higher temperatures.

Analysis of uniaxial ratcheting behavior and cyclic mean stress relaxation of a duplex stainless steel

The growing presence of a non-conventional stainless steel like a super duplex grade S32750 requires clarification of the structural responses to cyclic loading. This study attempted to characterize the uniaxial ratcheting behavior and the cyclic mean stress relaxation of S32750 super duplex stainless steel which had cyclic hardening characteristics under strain-controlled cyclic loading. A constitutive model capable of simulating the uniaxial ratcheting response and the mean stress relaxation was developed in the framework of rate-independent plasticity theory. Verification of the proposed constitutive model was achieved by simulating uniaxial strain- and stress-controlled cyclic loading tests including cyclic mean stress relaxation and comparing the predicted results with the experimental measurements. The influences of mean stress level, stress amplitude and loading history on the uniaxial ratcheting behavior as well as the effects of mean strain and strain amplitude on the mean stress relaxation was further examined through the verified constitutive model.

The effect of the embrittlement on the fatigue limit and crack propagation in a duplex stainless steel during high cycle fatigue

In order to evaluate the effects that the “475° embrittlement” produces on the fatigue life during high-cycle fatigue, stress-controlled cyclic loading tests were conducted on a standard duplex stainless steel in two different heat treatment conditions (homogenized and embrittled). Transmission (TEM) and scanning electron microscopy (SEM) in combination with automated electron back-scattered diffraction (EBSD) techniques were carried out to analyze the surface damage as well as the initiation and propagation of fatigue cracks. These studies have revealed that the fatigue limit of the embrittled samples is substantially larger than that of the conventional samples at 107 cycles in the homogenized condition. Finally, an existing numerical short-crack propagation model was adapted using the stereological values obtained by EBSD to reproduce the propagation of microstructural fatigue cracks in the homogenized and embrittled conditions.

Nonlinear viscoelastic contribution to the cyclic accommodation of high density polyethylene in tension: Experiments and modeling

Viscous polymers tackle the prediction of the accommodated cycle from which fatigue criterion parameters should be computed, within a formalism adapted to structure calculation. This work focuses on viscoelasticity, shown to be predominant in the high cycle fatigue stress range. Stress-controlled cyclic, recovery and creep tensile tests in polyethylene at room temperature allow characterizing the frequency and the stress ratio effect on the ratcheting strain and the loop parameters. An isothermal nonlinear viscoelastic model is derived for small strains in a Thermodynamics of Irreversible Processes framework. Nonlinearity arises from the description of the relaxed state towards which viscous internal variables evolve. Both the short (loop) and long (1000cycles) time scales are captured, with a ratcheting strain globally underestimated but features of the accommodated loop satisfyingly predicted.

Dislocation evolution in 316L stainless steel during multiaxial ratchetting deformation

Abstract Dislocation patterns and their evolutions in 316 L stainless steel during the multiaxial ratchetting deformation were observed by transmission electron microscopy (TEM). The microscopic observations indicate that the dislocation evolution presented during the multiaxial ratchetting with four kinds of multiaxial loading paths is similar to that in the uniaxial case [G. Z. Kang et al., Mater Sci Eng A 527 (2010) 5952]. That is, dislocation networks and dislocation tangles are formed quickly by the multiple-slip and cross-slip of dislocation activated by applied multiaxial stress; and then polarized patterns such as dislocation walls and elongated incipient dislocation cells are formed at the last stage of multiaxial ratchetting. The dislocation patterns evolve more quickly from the modes at low dislocation density to the ones at high density during the multiaxial ratchetting than that in the uniaxial case, and some traces of multiple-slip are observed in the multiaxial ones. The dislocation evolution during the multiaxial ratchetting deformation is summarized by comparing the observed dislocation patterns with those presented in the multiaxial strain-controlled and symmetrical stress-controlled cyclic tests. The multiaxial ratchetting of 316 L stainless steel can be microscopically and qualitatively explained by the observed evolution of dislocation patterns.

Whole-life transformation ratchetting and fatigue of super-elastic NiTi Alloy under uniaxial stress-controlled cyclic loading

► Whole-life transformation ratchetting depends on load level and mode. ► Shakedown of transformation ratchetting occurs after certain cycles. ► Dissipated energy decreases quickly during the cyclic loading. ► Transformation ratchetting shortens the fatigue life apparently. ► Fatigue life decreases greatly with the increasing dissipated energy. The whole-life transformation ratchetting and fatigue failure (including functional fatigue and structural fatigue) of super-elastic NiTi shape memory alloy were observed by uniaxial stress-controlled cyclic loading tests and at room temperature. The effects of peak stress, mean stress and stress amplitude were discussed, and then the interaction of transformation ratchetting and fatigue was then investigated. It is concluded that the whole-life transformation ratchetting of super-elastic NiTi shape memory alloy depends greatly on the stress levels and loading modes, and the dissipated energy in each cycle progressively decreases with the increasing number of cycles, which represents a functional degradation. The results also show that the structural fatigue life of the NiTi alloy presented under the stress-controlled cyclic loading is dependent on the peak stress, mean stress and stress amplitude, and the transformation ratchetting shortens the fatigue life apparently. The fatigue life decreases with the increasing dissipated energy, and a balance between dissipated energy and structural fatigue life should be reasonably considered in the design of damping devices of the NiTi alloy.

Uniaxial Ratcheting Behaviors of Metals with Different Crystal Structures or Values of Fault Energy: Macroscopic Experiments

The uniaxial ratcheting behaviors of several metals with different crystal structures or values of fault energy were observed by the stress-controlled cyclic tests at room temperature. The prescribed metals included 316L stainless steel, pure copper, pure aluminum, and ordinary 20# carbon steel. The effects of applied mean stress, stress amplitude and stress ratio on the uniaxial ratcheting were also investigated. The observations show that different crystal structures or values of fault energy result in more or less different ratcheting behaviors for the prescribed metals. The different ratcheting behaviors are partially caused by the variation of dislocation mobility.

Experimental study on uniaxial time-dependent ratcheting of a polyetherimide polymer

The uniaxial ratcheting behavior of a polyetherimide (PEI) polymer ‘TECAPEI’ was studied using stress-controlled cyclic loading at room temperature, including both cyclic tension-compression with non-zero tensile mean stress and tension-unloading tests. The experimental observations were focused on the time-dependent ratcheting of the PEI polymer revealed in cyclic tests at diverse stress rates and with different peak stress holding times. The results showed that the PEI polymer shows obvious ratcheting deformation; i.e., the ratcheting strain accumulates progressively in the tensile direction during stress-controlled cyclic tests with non-zero mean stress. The ratcheting is highly dependent on the applied mean stress and stress amplitude, and is also characterized by a strong time-dependency during the cyclic stressing at diverse stress rates and with different peak stress holding times. The time-dependent ratcheting of the PEI polymer is caused mainly by its remarkable viscosity. A comparison of the ratcheting occurring before and beyond the ultimate stress point of the PEI polymer showed that the ratcheting beyond the ultimate stress point is more significant than that occurring before that point.

Dynamic characterization of EPS geofoam

This paper attempts to describe the dynamic behavior of expanded polystyrene EPS geofoam, and shows the dependence of shear modulus, G, and damping ratio, λ, on shear strain, γ, density, ρ, and confining stress, σ 3, through the results of a series of resonant column and strain- and stress-controlled cyclic compression tests. Shear modulus and damping ratio versus shear strain curves were obtained and a series of equations were developed to model the dynamic behavior of EPS. From stress-controlled cyclic compression tests the effect of the number of cyclic load applications, N, on the maximum axial strain ɛ max (for a specific static deviator stress, σ e, plus the amplitude of the loading cyclic stress, σ c) and on the dynamic modulus of elasticity E dyn was evaluated as a function of the EPS density, confining stress, and the applied cyclic stress amplitude σ c.

Behavior of EPS geofoam in stress-controlled cyclic uniaxial tests

During recent years, increasing consideration has been given to the compressible inclusion function of EPS geofoam, which makes this cellular geosynthetic an ideal material for reducing the static and seismic lateral earth pressures against rigid non-yielding retaining structures. Although the behavior of EPS geofoam under monotonic loading conditions has been extensively studied using laboratory triaxial compression tests, little research has been done until present on the cyclic stress–strain behavior of this material that is essential for optimizing and improving the seismic buffer function of EPS geofoam in geotechnical earthquake engineering applications. In this context, the present paper summarizes the results of a laboratory study based on stress-controlled cyclic uniaxial tests on EPS samples with various initial (static) deviator stresses. The experimental results indicate a somewhat different dynamic response of geofoam compared to the currently published relationships obtained from strain-controlled cyclic tests. Data from stress-controlled cyclic uniaxial tests show a logarithmic decrease in the damping ratio of EPS geofoam with increasing axial strain amplitude. Furthermore, for cyclic axial strain amplitudes greater than about 0.87–1.0%, the material exhibited a visco-elasto-plastic behavior associated with the occurrence of permanent plastic strains at the end of the cyclic tests.

Constitutive model for uniaxial transformation ratchetting of super-elastic NiTi shape memory alloy at room temperature

The transformation ratchetting of super-elastic NiTi shape memory alloy was observed by the uniaxial stress-controlled cyclic tests [Kang, G.Z., Kan, Q.H., Qian, L.M., Liu, Y.J, 2009a. Ratchetting deformation of super-elastic and shape memory NiTi Alloys. Mech. Mater. 41, 139–153]. It is concluded that the NiTi alloy presents apparent ratchetting behaviour, and the ratchetting is collectively caused by the cyclic accumulation of residual induced-martensite and the transformation-induced plastic deformation (i.e., namely transformation ratchetting). Based on the experimental results, a cyclic constitutive model was constructed in the framework of generalized plasticity [Lubliner, J., Auricchio, F., 1996. Generalized plasticity and shape memory alloys. Int. J. Solids Struct. 33, 991–1003] to describe the transformation ratchetting of super-elastic NiTi alloy. The proposed model simultaneously accounts for the evolutions of residual induced-martensite and transformation-induced plastic strain during the stress-controlled cyclic loading by introducing an internal variable z c , i.e., cumulated induced-martensite volume fraction. The dependence of transformation ratchetting on the applied stress levels and the phase transformation hardening behaviour of the NiTi alloy are also considered in the developed model. The anisotropic phase transformation behaviours of the alloy presented in the tension and compression cases are described by employing a Drucker–Prager-typed transformation surface. It is shown that the simulated results of transformation ratchetting obtained by the proposed model are in good agreement with the corresponding experiments, since the typical features of transformation ratchetting are reasonably captured by the proposed model.

Uniaxial ratchetting of polymer and polymer matrix composites: Time-dependent experimental observations

The uniaxial time-dependent ratchetting of polyester resin and glass fiber reinforced polyester resin matrix composites was observed by the stress-controlled cyclic tension–compression with non-zero tensile mean stress and tension–tension tests at room temperature. After the ratchetting of the polyester resin had been observed by the cyclic tests with different loading conditions including some time-related factors, such as stress rate and peak stress hold, the ratchetting evolutions of the continuous and short glass fiber reinforced resin matrix composites were also investigated by the stress-controlled cyclic tests, respectively. It is concluded that: both the polyester resin and its composites present apparent ratchetting deformation, i.e., the ratchetting strain accumulates progressively in the tensile direction during the cyclic tension–compression with non-zero tensile mean stress and tension–tension tests; the ratchetting depends on the applied stress amplitude, mean stress, stress rate and peak stress hold, and the time-dependent ratchetting is obvious even for the continuous glass fiber reinforced resin matrix composites with high fiber volume fraction (such as 40% and 50%); the time-dependent ratchetting of the polyester resin and its composites mainly stems from the viscosity of the polyester resin, while the addition of glass fiber into the resin matrix improves the resistance of the composites to the ratchetting deformation and lowers the time-dependence of the ratchetting simultaneously.

Ratchetting deformation of super-elastic and shape-memory NiTi alloys

The ratchetting deformation of super-elastic NiTi alloy was first observed by uniaxial stress-controlled cyclic tests, and the dependence of ratchetting upon the applied stress and loading type was discussed. The evolutions of responded peak/valley strain, nominal elastic modulus and transformation stress, as well as dissipation energy of the alloy during the stress-controlled cyclic loading were investigated. It is shown that the super-elastic NiTi alloy presents significant “transformation ratchetting” which is mainly caused by the cyclic accumulation of remained martensite due to the incomplete reverse transformation from the stress-induced martensite to original austenite, and the transformation ratchetting and its evolution depend greatly upon the applied stress amplitude, mean stress and loading chart. For comparison, the ratchetting deformation of shape-memory NiTi alloy and its dependence upon the loading condition were also observed. It is seen that the ratchetting deformation of shape-memory NiTi alloy under the stress-controlled cyclic loading differs greatly from that of super-elastic NiTi alloy, since no reversible transformation from the austenite to the stress-induced martensite occurs in the shape-memory NiTi alloy during the stress-controlled cyclic loading at room temperature. It means that no transformation ratchetting occurs in the shape-memory NiTi alloy, and the ratchetting deformation of the alloy occurred during the asymmetrical stress-controlled cyclic loading is mainly caused by the cyclic accumulation of visco-plastic deformation of re-oriented martensite, which is similar to the ratchetting deformation of ordinary metals. For both the super-elastic and shape-memory NiTi alloys, a nearly stable stress–strain response with small dissipation energy occurs after certain cycles. Some significant conclusions are obtained, which are useful to establish a constitutive model describing the ratchetting deformation of the NiTi alloys.

Multiaxial ratchetting–fatigue interactions of annealed and tempered 42CrMo steels: Experimental observations

The multiaxial ratchetting and low-cycle fatigue failure behaviour, i.e., the multiaxial ratchetting–fatigue interactions of annealed and tempered 42CrMo steels were experimentally observed under the proportionally and non-proportionally multiaxial stress-controlled (and strain-controlled) cyclic loading tests. The multiaxial whole-life ratchetting behaviour and fatigue lives of the steels were obtained in the multiaxial stress cycling tests with different stress levels and loading paths. The effects of mean stress, stress amplitude and loading path on the multiaxial whole-life ratchetting and failure life of the steels were discussed. Some low-cycle fatigue tests were carried out under the strain-controlled cyclic loading. The experimental results show that the multiaxial whole-life ratchetting and fatigue failure behaviour of the annealed 42CrMo steel are different from those of the tempered steel due to their different cyclic softening/hardening features. Two kinds of failure modes (i.e., ductile ratchetting failure and brittle low-cycle fatigue failure) occur in the 42CrMo steels, depending on the stress level and resultant value of final ratchetting strain. The evolution of multiaxial ratchetting is greatly dependent on the proportional and non-proportional loading paths. The failure life in the multiaxial stress cycling is apparently shorter than that in the uniaxial case, and depends on the shapes of multiaxial loading paths. The fatigue damage caused by the cyclic loading accelerates the evolution of multiaxial ratchetting, especially at the end stage of cyclic loading; the multiaxial ratchetting produced in the stress cycling shortens the failure life of the steels apparently.

Cyclic shearing deformation behavior of saturated clays

The apparatus for static and dynamic universal triaxial and torsional shear soil testing is employed to perform stress-controlled cyclic single-direction torsional shear tests and two-direction coupled shear tests under unconsolidated-undrained conditions. Through a series of tests on saturated clay, the effects of initial shear stress and stress reversal on the clay’s strain-stress behavior are examined, and the behavior of pore water pressure is studied. The experimental results indicate that the patterns of stress-strain relations are distinctly influenced by the initial shear stress in the cyclic single-direction shear tests. When the initial shear stress is large and no stress reversal occurs, the predominant deformation behavior is characterized by an accumulative effect. When the initial shear stress is zero and symmetrical cyclic stress occurs, the predominant deformation behavior is characterized by a cyclic effect. The pore water pressure fluctuates around the confining pressure with the increase of cycle number. It seems that the fluctuating amplitude increases with the increase of the cyclic stress. But a buildup of pore water pressure does not occur. The deformations of clay samples under the complex initial and the cyclic coupled stress conditions include the normal deviatoric deformation and horizontal shear deformation, the average deformation and cyclic deformation. A general strain failure criterion taking into account these deformations is recommended and is proved more stable and suitable compared to the strain failure criteria currently used.

Simulation of deformation and lifetime behavior of a fcc single crystal superalloy at high temperature under low-cycle fatigue loading

This work deals with the formulation of a three-dimensional crystallographic time-incremental lifetime rule for face-centered cubic (fcc) single crystals used for gas-turbine blade applications. The damage contribution rate of each slip system to the total damage is governed by the current values of the resolved shear stress and the slip rate on the corresponding slip system. The damage rule is combined with a crystallographic viscoplastic deformation model. For the nickel-base single-crystal superalloy CMSX4 at 950 °C, various strain- and stress-controlled uniaxial cyclic tests with and without hold-times can be described for different crystal orientations by one set of material parameters. For verification, simulation results for a single-crystal specimen with a notch have been compared with corresponding experimental results. The predicted lifetime is within the factor of two of the measured one.

Effects of Cyclic Loading on Internal Shear Strength of Unreinforced Geosynthetic Clay Liner

Stress-controlled static and cyclic shear tests were performed by using a direct simple shear device on samples of a geomembrane-supported geosynthetic clay liner (GCL). The dry material showed no degradation in shear strength during cyclic loading as long as the peak shear stress was less than the static shear strength of the GCL with no cyclic loading. Furthermore, cyclic loading slightly densified the dry bentonite and thus increased its shear resistance under subsequent static loading. On the other hand, the shear strength of the hydrated GCL was found to be reduced by cyclic loading. The number of cycles to cause failure decreased with increasing cyclic stress ratio (cyclic shear stress divided by undrained static shear strength); at a cyclic stress ratio of 0.67, failure occurred at 32 cycles of loading, but at a cyclic stress ratio of 0.53, failure did not occur until up to 200 cycles of loading.

Biaxial Ratcheting Under Strain or Stress-Controlled Axial Cycling With Constant Hoop Stress

Strain or stress-controlled tension-compression cyclic tests were conducted on pressurized thin-walled tubular specimens of 304 stainless steel. In strain-controlled mode ratcheting strains in hoop direction, and under stress-controlled mode ratcheting in both hoop and axial directions, were observed. To predict the observed ratcheting behavior, an additional evolution rule for the stress memory surface has been introduced in the constitutive model developed recently by the authors. Qualitative and quantitative comparisons with the test results indicate a fairly good agreement in predicting ratcheting deformations.

The effect of crack wake characteristics on fatigue crack closure. II. A non-uniform wake study: Mirzaei, M. and Provan, J. W. Theor Appl Fract Mech (Apr. 1993) 18 (3), 185–191

Multiaxial whole-life transformation ratchetting and fatigue failure of superelastic NiTi SMA micro-tubes are observed in the non-proportionally multiaxial stress-controlled cyclic tests at the human-body temperature (310 K) under five different multiaxial loading paths. The effects of the axial peak stress and stress amplitude on the transformation ratchetting and fatigue life are addressed. It is found that the super-elastic NiTi SMA micro-tubes sustain more significant path-dependent fatigue failure in the multiaxial cyclic tests with lower axial peak stress and stress amplitude, while the fatigue lives of the NiTi micro-tubes under different loading paths are gradually converged with the increasing axial peak stress and stress amplitude. Based on the experimental findings, a fatigue failure model is proposed to predict the multiaxial fatigue life of the super-elastic NiTi SMA micro-tubes by considering the initial/saturated dissipation energy and the non-proportionality of the loading paths. It is shown that the predicted multiaxial fatigue lives agree with the experimental ones fairly well.