Strain-controlled Cyclic Tests Research Articles

A crystal plasticity study of cyclic constitutive behaviour, crack-tip deformation and crack-growth path for a polycrystalline nickel-based superalloy

Crystal plasticity has been applied to model the cyclic constitutive behaviour of a polycrystalline nickel-based superalloy at elevated temperature using finite element analyses. A representative volume element, consisting of randomly oriented grains, was considered for the finite element analyses under periodic boundary constraints. Strain-controlled cyclic test data at 650 °C were used to determine the model parameters from a fitting process, where three loading rates were considered. Model simulations are in good agreement with the experimental results for stress–strain loops, cyclic hardening behaviour and stress relaxation behaviour. Stress and strain distributions within the representative volume element are of heterogeneous nature due to the orientation mismatch between neighbouring grains. Stress concentrations tend to occur within “hard” grains while strain concentrations tend to locate within “soft” grains, depending on the orientation of grains with respect to the loading direction. The model was further applied to study the near-tip deformation of a transgranular crack in a compact tension specimen using a submodelling technique. Grain microstructure is shown to have an influence on the von Mises stress distribution near the crack tip, and the gain texture heterogeneity disturbs the well-known butterfly shape obtained from the viscoplasticity analysis at continuum level. The stress–strain response near the crack tip, as well as the accumulated shear deformation along slip system, is influenced by the orientation of the grain at the crack tip, which might dictate the subsequent crack growth through grains. Individual slip systems near the crack tip tend to have different amounts of accumulated shear deformation, which was utilised as a criterion to predict the crack growth path.

Numerical modeling of stress–strain behavior of sand under cyclic loading

Analysis of soil response to cyclic loading is a complex problem due to the participation of a large number of loading conditions and physical properties. In this study, a promising variant of genetic programming (GP), namely multi expression programming (MEP) is utilized to model stress–strain behavior of sands subjected to large amplitude regular cyclic loading. Generalized MEP-based formulations are derived to simulate hysteresis strain–stress curves. To construct the hysteresis curves, functional relationships are obtained between maximum shear stress at different loading cycles and several influencing parameters. New constitutive correlations are further developed for the assessment of damping ratio and shear modulus. The proposed correlations are established based on several drained strain-controlled cyclic torsional simple shear tests performed on samples of Toyoura sand. The correlations take into account the effects of initial effective confining pressure, initial relative density, initial anisotropic stress state, strain amplitude, and shear history. A subsequent parametric study is carried out and the obtained trends are confirmed with the experimental study results. For more validity verification, the MEP-based correlations are applied to simulate the stress–strain curves of a part of the laboratory results beyond the training data domain. The proposed models are effectively capable of capturing the complex hysteresis behavior of sandy soils under cyclic loading conditions. The derived correlations are particularly valuable for providing an analysis tool accessible to practicing engineers.

Crystal plasticity modeling of cyclic deformation for a polycrystalline nickel-based superalloy at high temperature

Cyclic deformation at elevated temperature has been modeled for a polycrystalline nickel-based superalloy using the crystal-plasticity constitutive formulations. Finite element analyses were carried out for a representative volume element (RVE), consisting of randomly oriented grains and subjected to periodic boundary constraints. Model parameters were determined by fitting the strain-controlled cyclic test data at 650 °C for three different loading rates. Simulated results are in good agreement with the experimental data for both stress–strain loops and cyclic hardening behavior. The model was utilized to predict the stress relaxation behavior during the hold periods at the maximum and minimum strain levels, and the prediction compares well with the experimental results. Localized stress and strain concentrations were observed due to the heterogeneous nature of grain microstructure and the mismatch of the mechanical properties of individual grains.

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.

Pore Pressure Generation of Silty Sands due to Induced Cyclic Shear Strains

It is well established that the main mechanism for the occurrence of liquefaction under seismic loading conditions is the generation of excess pore water pressure. Most previous research efforts have focused on clean sands, yet sand deposits with fines are more commonly found in nature. Previous laboratory liquefaction studies on the effect of fines on liquefaction susceptibility have not yet reached a consensus. This research presents an investigation on the effect of fines content on excess pore water pressure generation in sands and silty sands. Multiple series of strain-controlled cyclic direct simple shear tests were performed to directly measure the excess pore water pressure generation of sands and silty sands at different strain levels. The soil specimens were tested under three different categories: (1) at a constant relative density; (2) at a constant sand skeleton void ratio; and (3) at a constant overall void ratio. The findings from this study were used to develop insight into the behavior of silty sands under undrained cyclic loading conditions. In general, beneficial effects of the fines were observed in the form of a decrease in excess pore water pressure and an increase in the threshold strain. However, pore water pressure appears to increase when enough fines are present to create a sand skeleton void ratio greater than the maximum void ratio of the clean sand.

The benefit from an adequate finite element simulation of the cold hole expansion process

The article presents outcomes from finite element and X-ray diffraction analyses of the cold hole expansion process fulfilled by means of solid mandrel gradually passing through the hole. Regardless of the manner of accomplishing – split sleeve; split mandrel; with a mating tapered split sleeve; spherical mandrelling – an axial gradient of the residual stresses is obtained due to the interaction between the layers caused by an axial force flow which passes through the mandrel, the workpiece and the support to forma closed circuit. To predict the fatigue life it is necessary to know the residual stresses on the entrance and the exit faces immediately to the hole periphery which are considered to be potential crack initiation sites. It has been proved that there are two key moments in the building of an adequate finite element model. The first is modeling of a realistic contact mandrel-workpiece with or without mediator and workpiece-support. The second is a suitable constitutive model of the workpiece material. Six hardening models of low-carbon steel obtained on the basis of a symmetric strain-controlled experiment and half-cycle test data from unidirectional tension experiment have been used consecutively in the finite element model of the process. On the basis of a comparison with experimental results obtained by means of an X-ray diffraction technique it has been established that the nonlinear kinematic hardening model obtained by a strain-controlled cyclic test to achieve a stabilized cycle secures finite element results close to the experimental ones. The chosen finite element model has been compared with simplified ones following the residual circumferential normal stress criterion and its advantages have been proved.

Modelling of hardening behaviour of cold expanded holes in medium-carbon steel

Cold expansion is a well-known approach for the enhancement of the fatigue life of fastener holes in structural components by introducing residual compressive circumferential stresses around them. In this work, the hardening of a medium-carbon structural steel is studied experimentally and numerically from the point of view of the material behaviour during the cold expansion process of holes in structural steel components. Six material hardening models obtained on the basis of symmetric strain-controlled experiments and half-cycle test data from unidirectional tension experiments have been used in a two-dimensional axisymmetric finite element model of the process. Parallel with this an x-ray diffraction analysis of the residual stresses at the entrance and exit faces of the structural component has been carried out to prove the finite element result’s authenticity. It is established that the nonlinear kinematic hardening model obtained by a strain-controlled cyclic test to achieve a stabilized cycle for this steel secures finite element results close to the experimental ones. The constitutive hardening model obtained can be applied to a corresponding finite element model for stress analysis of steel structural component with cold expanded holes, subjected to an external load.

A Cyclic Stress-Strain Constitutive Model for Polycrystalline Magnesium Alloy and its Application

The stress-strain behavior of cast magnesium alloy (AM60) was investigated by strain-controlled cyclic testing carried out on MTS. In order to describe the cyclic stress and strain properties of AM60 by means of the energy storing characteristics of microstructure during irreversible deformation, a plastic constitutive model with no yielding surface was developed for single crystal by adopting a spring-dashpot mechanical system. Plastic dashpots reflecting the material transient response were introduced to describe the plasticity of slip systems. By utilizing the KBW self-consistent theory, a polycrystalline plastic constitutive model for Magnesium alloy was formed. The numerical analysis in the corresponding algorithm is greatly simplified as no process of searching for the activation of the slip systems and slip directions is required. The cyclic stress-strain behavior, based on this model, is discussed. The simulation results show good agreement with the experimental data for AM60.

Damage evolution in a filled epoxy resin

A method is proposed for studying damage evolution in a filled epoxy resin submitted to low-cycle fatigue loading. Transmission electron microscopy analysis was performed, which indicates a damage mechanism that corresponds well to the decreasing slope of the stress–strain hysteresis observed in strain-controlled fatigue experiments. Also, the suggested damage model appears to be suitable for the simulation of strain-controlled cyclic tests and fits the damage evolution of the filled epoxy resin fairly well.

Experimental damage mechanics of microelectronic solder joints under fatigue loading

Fatigue damage is a progressive process of material degradation. The objective of this study is to experimentally qualify the damage mechanism in solder joints in electronic packaging under thermal fatigue loading. Another objective of this paper is to show that damage mechanism under thermal cycling and mechanical cycling are very different. Elastic modulus degradation under thermal cycling, which is considered as a physically detectable quantity of material degradation, was measured by Nano-indenter. It was compared with tendency of inelastic strain accumulation of solder joints in Ball Grid Array package under thermal cycling, which was measured by Moiré interferometry. Fatigue damage evolution in solder joints with traditional load-drop criterion was also investigated by shear strain hysteresis loops from strain-controlled cyclic shear testing of thin layer solder joints. Load-drop behavior was compared with elastic modulus degradation of solder joints under thermal cycling. Following conventional Coffin–Manson approach, S– N curve was obtained from isothermal fatigue testing with load-drop criterion. Coffin–Manson curves obtained from strain-controlled mechanical tests were used to predict fatigue life of solder joints. In this paper it is shown that this approach underestimates the fatigue life by an order of magnitude. Results obtained in this project indicate that thermal fatigue and isothermal mechanical fatigue are completely different damage mechanism for microstructurally evolving materials.

Evaluation of viscoplastic parameters and its application for dynamic behaviour of plates

The evaluation of material parameters for viscoplastic Chaboche and Bodner-Partom formulations is carried out using tensile tests only. The determination of the Bodner-Partom law is quite easy. The parameter study for the Chaboche law usually requires carrying out strain-controlled cyclic tests. In this work, we propose supporting this type of experiments by numerical simulations. A set of parameters for each formulation is identified for steel, and is used to calculate the dynamic behaviour of circular plates. The results are compared with the experimental data on steel plates.

Cyclic deformation behavior of high-purity titanium single crystals: Part II. Microstructure and mechanism

Strain-controlled cyclic tests have been conducted on high-purity titanium single crystals with different orientations. The fatigue mechanisms of the titanium crystals were studied by means of a scanning electron microscope (SEM) and a transmission electron microscope (TEM). It was found that single slip lines, wavy slip lines, double slip lines, twins, and associated slip lines occurred in differently oriented single crystals. A new type of fractographic morphology, parallel traces, was observed. Dislocation patterns and cyclic twins, as well as the mechanical response, were analyzed. The dependence of the deformation mechanisms on the orientations of the single crystals is discussed.

Automated Evaluation of Material Parameters of Viscoplastic Constitutive Equations

A method will be presented that allows for a special class of viscoplastic constitutive models a fast and safe determination of the material parameters. All parameters are determined simultaneously from creep, tensile, and strain-controlled cyclic tests. It is not necessary to solve the model differential system numerically; approximations allow for almost all of these loading cases an analytical integration with sufficient precision. The procedure for the solving of the model differential equations as well as the fit procedure will be described. The computer time for the parameter evaluation lies in the range of only some minutes even for a large number of experimental data. Results of fits for the material AISI 316L at 700°C will be presented for the viscoplastic models of Robinson, Chaboche and Walker. In addition to the fits, the models are subjected to a statistical investigation which makes evident their structures with respect to the convergence behaviour of the fit procedure and the sensitivity of the models to parameter variations.

Continuum damage based constitutive equations for copper under high temperature creep and cyclic plasticity

Viscoplastic constitutive equations without damage for cast copper have been developed for cyclic mechanical and cyclic thermal loading over the temperature range 20-500 °C (nominal composition: 99.99 % Cu, 0.005 % O 2 , B.S. 10355-1037). Model predictions have been compared with experimental cyclic plasticity tests. Good agreement has been achieved. Creep and cyclic plasticity damage evolution equations have been developed. The effect of cyclic hardening on creep damage evolution has been modelled by introducing an internal variable to represent the state of material hardening. A creep cyclic plasticity interaction law has been proposed, and with the creep and cyclic plasticity damage evolution equations, has been combined with the viscoplastic constitutive equations to establish a unified material model for copper over the temperature range 20-500 °C. Predictions of lifetime and deformation history have been made for uni-axial test specimens subject to strain-controlled cyclic plasticity and ratchetting. Good agreement has been obtained with experimental results. The model has been validated for mechanical loading by predicting the response of uni-axial test specimens to strain-controlled cyclic plasticity with strain hold periods, and to combined strain-controlled cyclic plasticity tests with strain holds and ratchetting. The predictions compare well with experimental results. The model has been validated for cyclic thermal loading by predicting the response of uni-axial test specimens subjected to thermal loading cycles. Good comparisons have been achieved with experimental results.

TEM study of microstructure development during low-cycle fatigue of an overaged Al-Mg-Si alloy

The evolution of dislocation structure during room-temperature, uniaxial, low-cycle fatigue of an overaged Al-Mg-Si alloy is studied. Ageing at 450°C produces a fine dispersion of Mg2Si precipitate particles. During fully reversed strain-controlled cyclic tests, these fine particles restrict deformation to local regions and a stable dislocation substructure is developed early in fatigue life. Substructural observations of hardening and saturation by transmission electron microscopy reveal extensive dislocation band formation on Mg2Si precipitate rods. Various microstructural features such as configuration of tangled dislocations, dislocation cells, precipitate morphologies, sizes, precipitate-free zones, etc., have been examined during cyclic hardening and saturation. The results have been analysed in terms of kinematic and isotropictype microstructural mechanisms.

High strain fatigue crack growth in nickel-base alloys: Marchand, N. J. and Pelloux, R. M. Res. Mech. 1989 27, (4), 285–308

In this study, the fatigue behavior of a semi-crystalline thermoplastic polyether ether ketone (PEEK) is investigated. A series of tests at ambient temperature, including uniaxial monotonic (tension and compression) at different strain rates and uniaxial fully-reversed strain-controlled cyclic tests at strain amplitudes ranging from 0.02 mm/mm to 0.04 mm/mm at various frequencies, were conducted. The frequency influence on the strain-controlled fatigue lives of unfilled PEEK specimens was found to be highly dependent on the strain level. A minimal frequency effect was observed at a lower strain amplitude of 0.02 mm/mm, whereas increasing the test frequency at higher strain amplitudes resulted in longer fatigue lives. Additionally, load-controlled cyclic tests that utilized applied loads corresponding to stress responses obtained from the strain-controlled fatigue tests were performed. The cyclic behavior under the two control modes were compared and discussed. Three types of fatigue models, including a strain-based (Coffin–Manson) model, a strain–stress-based (Smith–Watson–Topper) model, and an energy-based model, were employed to correlate the data in this study. Among the three fatigue models, the energy approach was found to better correlate the PEEK experimental data at various frequencies.

Cyclic stress-strain response of porous aluminum

A model of endochronic constitutive theory is applied to the analysis of stress-strain behavior of sintered high purity aluminum powder-based material (P/M) under uniaxial strain-controlled cyclic test conditions. Different strain amplitudes were used on specimens which during fabrication were subjected to cold isostatic pressure of 25 ksi. It was found that mean strain does not significantly affect the fatigue life. It was also discovered that Poisson's ratio at the peak tensile strain decreases gradually with the number of loading cycles, while it reaches a constant value at the peak compressive strain as the number of cycles increases. Results provide a comparison between theory and experiment for both hydrostatic and deviatoric stress-strain behavior for several cases of peak strains in the strain-controlled test. Reasonable agreement has been achieved. The changing trends of the peak volumetric strain, deviatoric stress, hydrostatic stress and Poisson's ratio versus loading cycles are also reported for each case.

Cyclic behavior and delayed softening of commercial purity titanium

Strain-controlled cyclic tests have been conducted on annealed and prestrained commercialpurity titanium. At total strain amplitudes of ±0.15 pct to ±0.725 pct, a decrease in stress response (termed “delayed softening”) occurred after approximately 300 cycles in the annealed samples. The maximum amount of delayed softening, approximately 48 MPa (7000 psi), was associated with a cyclic amplitude of -0.5 pct. A smaller amount of delayed softening was observed in specimens prestrained 8 pct. Prestraining also resulted in a general decrease in fatigue life both at the high and low strain amplitudes. Metallographic examination revealed that delayed softening was accompanied by an increase in slip activity and surface damage. In general, the extent of cyclic damage in the annealed specimens was greater than in the prestrained samples. Delayed softening is attributed to a recovery mechanism which involves the breakdown of unstable barriers to dislocation motion, thus allowing easier slip. This mechanism tends to be countered by the formation of stronger and more stable obstacles at higher cyclic strain amplitudes in the annealed material and during any prestraining. A comparison with electron microscopic work indicates that delayed softening is associated with a large reduction in the density of long, straight screw dislocations.

Liquefaction of Saturated Sand in Triaxial Torsion Shear Test

Strain-controlled cyclic torsion tests were run on a saturated sand using a triaxial torsion apparatus in which the vertical piston was designed so that its cross sectional area was equal to that of the specimen. In the first series of tests, a cyclic twist was applied while keeping the principal stress ratio constant. In these tests liquefaction did not occur and failure was associated with the development of a large amount of shear strain. In the second series of tests, a sample was consolidated anisotropically and then subjected to a cyclic twist while preventing entry of the cell water. This produced the situation in which the lateral expansion of the sample was completely confined. In these tests liquefaction did occur and the sample consolidated anisotropically was found to develop pore pressure faster than the sample consolidated isotropically. Such difference in the potentiality of pore pressure development was accounted for by the fact that the lateral stress was gradually increased during cyclic loading until the principal stress ratio became equal to unity at the onset of liquefaction. The concept of the principal stress ratio change during cyclic loading was used to account for the difference in liquefaction potential between the normal type of a cyclic triaxial test and a simple shear test.