Cyclic Stress-strain Behavior Research Articles

Cyclic Behaviour of Lateral Ties Confined Polyolefin Fibre Reinforced Concrete under Repeated Axial Compression

Although various models exist for envelope curves of concrete confined by transverse reinforcement, only a few simple models represent the hysteretic behavior of the confined concrete; therefore, development of stress–strain model of unloading and reloading paths for confined concrete is needed. In this paper, an experimental and numerical investigation for describing the cyclic stress–strain behavior of lateral ties confined and polyolefin fibre reinforced concrete (CPFRC) prisms under repeated axial compressive loading is presented. The study focuses on the effect of repeated unloading and reloading cycles on confined concrete prisms. The combined effect of spacing of lateral ties and volume fraction of polyolefin fibres was studied both experimentally and numerically from the point of deformability characteristics of concrete under repeated loading as loading, unloading and reloading.The envelope curve is derived from the results of uniaxial, monotonic, compression loading tests specimens. It explicitly accounts for the effects of lateral tie spacing of 145mm spacing and 75mm spacing and polyolefin fibres of volume fractions 0.7% and 1.2% on concrete prisms of size 150 ×150 ×300 mm were investigated. The behaviour is implemented in the finite element program in ANSYS software, with a view to analyzing CPFRC prisms under repeated loading. This analysis accounts for energy dissipation through hysteretic behavior, stiffness degradation as damage progresses, and degree of confinement. It was observed from hysteretic behavior that for increased polyolefin fibres volume fractions the degradation of strength and stiffness reduces significantly.

Mean Strain Effect on the Cyclic Stress-Strain Behavior of Steel Structure Materials Q235

The low cycle fatigue (LCF) behavior of Q235 steel under mean strain control has been investigated. A serious of the strain controlled cyclic loading experiments with several combinations of strain amplitudes and mean strains have been performed. Significant cyclic hardening and mean stress relaxation were observed in all cases. Fractography by scanning electron microscopy (SEM) was used to determine the LCF failure mechanisms and fatigue crack propagation modes of the Q235 steel.

Deformation mechanisms in a TiNi shape memory alloy during cyclic loading

The deformation mechanisms governing the cyclic stress-strain behaviour of a TiNi shape memory alloy were investigated in this work. To understand the development of these mechanisms during cyclic loading, three low-cycle fatigue tests were performed and stopped at different stages. The first test was stopped after the first cycle; the second one was stopped after 40 cycles, corresponding to the beginning of the stabilisation of the cyclic strain-stress behaviour; and the last one was carried out to failure (3324 cycles). Submitted to fatigue loading, the response of the TiNi shape memory alloy presents a classical pseudoelastic response. Two deformation mechanisms, identified by TEM observations, are highlighted, the first one by twins and the second by dislocation slip and its interaction with precipitates. These two mechanisms evolve without competition during cyclic loading. The nanomechanical properties of the alloy were also examined, and the evolution of the microhardness or indentation modulus was monitored.

Low-Cycle Fatigue Behavior of Die-Cast Mg Alloys AZ91 and AM60

The influence of microstructure and artificial aging response (T6) on the low-cycle fatigue behavior of super vacuum die-cast (SVDC) AZ91 and AM60 has been investigated. Fatigue lifetimes were determined from the total strain-controlled fatigue tests for strain amplitudes of 0.2 pct, 0.4 pct, 0.6 pct, 0.8 pct, and 1.0 pct under fully reversed loading at a frequency of 5 Hz. Cyclic stress–strain behavior was determined using an incremental step test (IST) and compared with the more traditional constant amplitude test. Two locations in a prototype casting were investigated to examine the role of microstructure and porosity on fatigue behavior. At all total strain amplitudes microstructure refinement had a negligible impact on fatigue life because of significant levels of porosity. AM60 showed an improvement in fatigue life at higher strain amplitudes when compared with AZ91 because of higher ductility. T6 heat treatment had no impact on fatigue life. Cyclic stress–strain behavior obtained via the incremental step test varied from constant amplitude test results due to load history effects. The constant amplitude test is believed to be the more accurate test method. In general, larger initiation pores led to shorter fatigue life. The fatigue life of AZ91 was more sensitive to initiation pore size and pore location than AM60 at the lowest tested strain amplitude of 0.2 pct. Fatigue crack paths did not favor any specific phase, interdentritic structure or eutectic structure. A multistage fatigue (MSF) model showed good correlation to the experimental strain-life results. The MSF model reinforced the dominant role of inclusion (pore) size on the scatter in fatigue life.

Thermo-mechanical fatigue testing and simulation using a viscoplasticity model for a P91 steel

An experimental programme of cyclic thermo-mechanical testing for a P91 power plant steel, under isothermal, and in-phase and out-of-phase thermo-mechanical, temperature-strain cycle conditions, has been implemented. Using the experimental data, an optimisation procedure has been developed for the accurate determination of the material constants under isothermal conditions, in which the Chaboche model is employed to describe material responses. The material was found to exhibit cyclic softening throughout the full life cycles, which is believed to be related to the evolution of microstructure and the propagation of micro-cracks. The model developed shows good predictive capability of cyclic stress–strain behaviour and cyclic softening.

Effect of Postweld Heat Treatment on the Microstructure and Cyclic Deformation Behavior of Laser-Welded NiTi-Shape Memory Wires

NiTi wires of 0.5 mm diameter were laser welded using a CW 100-W fiber laser in an argon shielding environment with or without postweld heat-treatment (PWHT). The microstructure and the phases present were studied by scanning-electron microscopy (SEM), transmission-electron microscopy (TEM), and X-ray diffractometry (XRD). The phase transformation behavior and the cyclic stress–strain behavior of the NiTi weldments were studied using differential scanning calorimetry (DSC) and cyclic tensile testing. TEM and XRD analyses reveal the presence of Ni4Ti3 particles after PWHT at or above 623 K (350 °C). In the cyclic tensile test, PWHT at 623 K (350 °C) improves the cyclic deformation behavior of the weldment by reducing the accumulated residual strain, whereas PWHT at 723 K (450 °C) provides no benefit to the cyclic deformation behavior. Welding also reduces the tensile strength and fracture elongation of NiTi wires, but the deterioration could be alleviated by PWHT.

Adapting a multi-component model to cyclic stress–strain behaviour under thermomechanical fatigue conditions

The cyclic stress–strain behaviour of metals and alloys in cyclic saturation can reasonably be described by means of simple multi-component models. In this study, this model concept was applied to thermomechanical fatigue loading. Two metallic engineering materials, which were found to be oppositional with respect to cyclic plastic deformation, were dealt with. One material is an austenitic stainless steel of type AISI304L which can be considered as an example for a rather ductile alloy. The second alloy is a third-generation near-gamma TiAl alloy which is characterized by a very pronounced ductile-to-brittle transition (DBT) within the temperature range of TMF cycling. The experimental observations regarding isothermal and non-isothermal stress–strain behaviour and the correlation to the underlying microstructural processes were used to further develop the TMF multi-composite model in order to accurately predict the TMF stress–strain response by taking the alloy-specific features into account.

Single-element simulations of partial-drainage effects under monotonic and cyclic loading

Liquefaction-induced seepage and pore-water pressure redistribution can locally change a sands' void ratio, such that in-situ strength and deformation behavior following an earthquake depend on the coupled diffusion process and not only on pre-earthquake soil properties. The effects of partial drainage on the monotonic, cyclic, and post-cyclic behavior of liquefied sand are explored at the element scale in this study, using the constitutive model PM4Sand [1] and the finite-difference code FLAC [2]. The ability of a critical state-based constitutive model to approximate partially drained loading responses is evaluated by comparing single-element simulations to available lab data and trends. The calibrated model is then used to examine the potential effects of partial drainage on the cyclic stress–strain behavior and accumulation of shear strains for dense-of-critical sand. The importance of liquefaction-induced seepage and void redistribution to the in-situ strength and deformation behavior of liquefied sands is discussed in view of the results of these partially drained laboratory element tests and simulations.

Micromechanical modelling of the cyclic stress–strain behaviour of nickel polycrystals

A crystalline elastoplasticity model is proposed to describe the cyclic behaviour of face-centred cubic crystals. It is based on many experimental observations correlating the observed dislocation structures with the orientations of corresponding crystals. The model distinguishes between two families of crystals. The first family gathers crystals for which the tension–compression loading axis is located in the centre of the standard stereographic triangle. These crystals, in which bundle and/or slip band dislocation structures are usually observed, are subjected to single slip deformation. The second family gathers crystals in which labyrinths or wall dislocation structures develop. These crystals are subjected to multiple slip deformation. Crystalline plasticity parameters are adjusted using only the single crystal cyclic stress strain curves measured for one orientation of each of the two families. The relevance of the model is evaluated through finite elements calculations of the uniaxial cyclic deformation of texture-free nickel polycrystals at room temperature. The macroscopic predictions are in reasonable agreement with experimental data concerning both the cyclic stress–strain curve and the hysteresis loops provided either large grain sizes or intermediate to high plastic strains are considered. By construction, the modelling is unable to predict grain size effect observed at low plastic strain. The distributions of the mean grain plastic strains become narrower as the macroscopic plastic strain amplitude increases, which appears consistent with the large scattering in high-cycle fatigue lifetimes usually observed. On the contrary, the distributions of mean grain axial stresses get broader, in agreement with neutron and X-ray diffraction measurement values published in the literature. The influence of the material parameters is then discussed. Finally, the cumulative probability curves of the number of cycles to fatigue microcrack nucleation are deduced and discussed with respect to scattering mentioned previously.

Effect of confinement level, aspect ratio and concrete strength on the cyclic stress–strain behavior of FRP-confined concrete prisms

Behavior of rectangular concrete columns confined with FRP composites depends on several parameters, including unconfined concrete strength, confinement level, aspect ratio of cross-section (defined as the depth/width of the cross-section), and the sharpness of the section corners. For modeling the cyclic stress–strain behavior of FRP-confined rectangular concrete columns, effect of column parameters on the cyclic behavior of these columns should be examined properly. In this paper, effects of unconfined concrete strength, confinement level and the aspect ratio of cross-section are studied. The test database includes 10 prisms from recent study of authors and 18 prisms from a new experiment. Results of tests show that some aspects of cyclic behavior of FRP-confined concrete prisms such as envelope curve and stress deterioration are unaffected by the considered parameters. Results also indicate that the plastic strain decreases as the unconfined concrete strength increases, but it is independent of the aspect ratio and the confinement level. While the reloading path in all specimens was almost linear, the unloading path was highly nonlinear and was affected by unconfined concrete strength.

Experimental and Numerical Investigations on Softening Behavior of POM Under Cyclic Strain-Controlled Loading

In this paper, cyclic stress-strain behavior of POM was studied. Fatigue tests were carried out under symmetric uniaxial strain-controlled mode. In this case of loading conditions the material exhibited cyclic softening and with the increase of strain amplitude the total number of cycles to failure reduced dramatically. Additional fatigue tests were further performed under non-symmetrical uniaxial cyclic loading where specimens exhibited relaxation behavior and mean stress reached a zero value in continuous cycles. Experimental tests were performed using an INSTRON 8802 servo-hydraulic machine and the results obtained from the experiments were compared with numerical results. The numerical analysis was carried out by ABAQUS software using the following advanced plasticity models based on Von Mises criterion: isotropic hardening, linear kinematic hardening, and non-linear isotropic/kinematic hardening.

Cyclic stress-strain behavior of shape memory polymer based syntactic foam programmed by 2-D stress condition

Cyclic stress-strain responses of a shape memory polymer based syntactic foam and pure SMP were investigated after a two dimensional (2-D) programming process. Three types of cyclic loading patterns were used: multiple compression-tension cycles at 5% maximum strain, one compression-tension cycle at 40% maximum strain, and one coupled thermo-mechanical cycle at 40% maximum strain. The results indicate that the foams initially harden after the first cycle and then soften in subsequent cyclic loadings, while the pure SMP shows a monotonous softening. The hysteresis loops tend to shrink and approach asymptotically to a steady state before fatigue failure for both the foam and the pure SMP. The programmed foam and the programmed pure SMP are less sensitive to their strain histories, and dissipate more energy as compared with the non-programmed counterparts, showing better fatigue properties at the same strain level. Also, the programmed foam exhibits better mechanical properties under one cyclic thermo-mechanical loading, possessing a good adaptability to ambient temperature changing. Furthermore, the programmed foam demonstrates an increase in yield strength during compression and a decrease in residual tensile stress during tension. These particularly facilitate the programmed foam to be used as a self-healing sealant in expansion joints.

Cyclic stress–strain behavior and low cycle fatigue life of cast A356 alloys

The cyclic stress–strain behavior and the low cycle fatigue life of electrolytic A356 alloys with different Ti contents were investigated, and the corresponding properties of melting A356 alloys were also considered as a comparison. All alloys exhibited the cyclic hardening behavior, and raising Ti could increase the cyclic hardening ability. The fatigue life was mainly controlled not by the Ti-addition method but by the Ti content. Interestingly, the low yield stress and high plastic strain energy consumed during the cyclic deformation, the alloys with 0.10% Ti possessed the longer fatigue life compared to those alloys with 0.14% Ti.

Temperature and Frequency Modified Fatigue Initiation Life of Solder Alloys Predicted by Endochronic Cyclic Damage-Coupled Viscoplasticity

ABSTRACTIn this paper, an evolution equation of cyclically internal damage in the intrinsic damage time scale after the threshold cycles N0 was extended by employing its damage parameters proposed to be dependent of frequency (v) and temperature (T) under cyclic fatigue loading. The resulting damage-coupled endochronic viscoplasticity can drive v and T modified power form equations of cyclic damage and its fatigue initiation life = N1 + N0. Under fatigue tests with T effect and N0 = 0, the power form equation of N1(T)/(Th), named as T-LCM (T modified Lee Coffin-Manson) equation for fatigue initiation life can bederived. The T modified factor (Th) depends on the T dependent material elastic modulus, the cyclicstress-strain response and the damage parameters. Theoretical predictions in the life data ofSn/3.8Ag/0.7Cu solder alloy under cyclic strain test with Tϵ [298,393] K were very well.Also under fatigue tests with v effect only, the power form equation of /v-LCM (v modified Lee-Coffin-Manson) equation for fatigue initiation life can be derived. The v modified parameter depends on the v dependent cyclic stress-strain response and the damage parameters. Theoreticalpredictions in the life data of 96.5Sn/3.5Ag solder alloy with surface cracking effect i.e. N0 ≠ 0 during cyclicstrain tests with v ϵ [0.001,1] Hz were quite well.Obviously, the values of power exponents C in the T-LCM and the v-LCM equations can not be determinedsimply by the least square method as in the Coffin-Manson empirical formulae. Also, they must bejustified by constrains imposed in the material parameters defining in the cyclic stress-strain response andthe accumulation behavior of cyclic damage.The resultant equations derived here and the Δ-LCM equation derived under Δ angle proportional cyclicstrain tests can be combined together to form a T-v-ΔLCM equation for fatigue life studies in the solderalloys using bulk specimens or BGA solider joint specimens.

Effect of twinning, slip, and inclusions on the fatigue anisotropy of extrusion-textured AZ61 magnesium alloy

In this study, experiments were conducted to quantify structure-property relations with respect to fatigue of an extruded AZ61 magnesium alloy using a MultiStage Fatigue (MSF) model. Experiments were conducted in the extruded and transverse directions under low and high cycle strain control fatigue conditions. The cyclic behavior of this alloy displayed varying degrees of twinning and slip depending on the strain amplitude as observed in the hysteresis loops of both directions. Under low cyclic conditions, asymmetrical stress strain response was observed for both orientations. However, systematic stabilization of the hysteresis occurred by half-life due to subsequent twinning and detwinning mechanisms. In addition, under high cycle fatigue, pseudo-elasticity was observed at the first and at half-life cycles. Structure-property relations were quantified by examining the fracture surfaces of the fatigued specimens using a scanning electron microscope. In terms of crack incubation, fatigue cracks were found to initiate from intermetallic particles (inclusions) that were typically larger than the mean size. Quantified sources of fatigue crack incubation, microstructurally small cracks, and cyclic stress–strain behavior were correlated to the MSF model. Based on the specific material parameters, the MSF model was able to predict the difference in the strain-life results of the AZ61 magnesium alloy in the extruded and extruded transverse directions including the scatter of the experimental results. Finally, the MSF model revealed that the inclusion size was more important in determining the fatigue life than the anisotropic effects from the texture, yield, and work hardening.

Influence of austenite stability on predicted cyclic stress-strain response of metastable austenitic steels

A modeling approach that captures the plastic strain amplitude dependence of strain induced martensite fraction evolution during low cycle fatigue (LCF) loading of metastable austenitic steels has been developed. The model is based on a modified version of the Olson-Cohen kinetic equation that retains connection to the underlying mechanisms of the transformation by relating cyclic austenite stability to monotonic stability. The kinetic model is then input into an evolving composite mechanical model that relies on a simple rule of mixtures formulation to predict cyclic stress-strain behavior, including increases in stress amplitude due to martensitic transformation. Predictions from the modeling approach compare well to fatigue data in the literature for AISI 304 stainless steel.

Cyclic Stress-Strain Behavior of BGA (Sn/3.5Ag/0.75Cu) Solder Joint under Cyclically Oblique Displacement Tests and Endochronic Viscoplastic Predictions

ABSTRACTIn this paper, a methodology with workable procedures was proposed and successfully transferred the hysteresis loops of BGA solder joint specimen held by loading-directionally aligned grip system under oblique displacement controlled cyclic tests, into hysteresis loops of “representative” solder ball itself under proportional straining and constant strain rate cyclic tests. Under the elastic unloading during cyclic test, value of elastic modulus of bulk solder specimens and the linear behavior of grip system were used. Following the study of Endochronic cyclic viscoplasticity, the kernel function ρ(Z) = ρ0 exp (−KZ)/Zα was found to be independent of the oblique angle (Φ) of straining paths. However, the steady cyclic behavior of material function f(ξ) ≡ f0 in the definition of intrinsic time Z contained two functions: (1) is the effective inelastic strain amplitude, and (2) f(Φ) Φ(rad) between Φ = 0 (uniaxial) and Φ = π/2 (shear). With (ρ0, α, K) = (4MPa, 0.84, 46) and f0 = [0.24(π/2−Φ)2 − 0.018(π2−Φ) + 1.2] , the endochronic theory predicted experimental hysteresis loops of BGA Sn/3.5Ag/0.75Cu solder joint specimens and Φ = 0°, 27°, 45°, 63°, 90° quite well.Results of ρ(Z) under f0 = 1 were found under independent study based on cyclic tests of bulk specimens under constant uniaxially strain amplitude and various constant strain rates. The values of (ρ0, α, K) = (7.3MPa, 0.84, 30) with f0 = 1.0 were all independent of strain rates. Comparisons of results of both types of specimens revealed that the values of (α, K) were almost the same but (1) ρ0 was smaller for micro-size solder ball, (2) is a material function of Sn/3.5Ag/0.75Cu itself (3) f(Φ) is not a material function, rather it is a special feature to reflect the effects of detail design of solder joint specimen and its connecting methods to the substrates

Modelling of Cyclic Plasticity and Viscoplasticity of a Nimonic Alloy 75

Cyclic plasticity and viscoplasticity of a nickel-chromium alloy have been described using the Chaboche unified constitutive model. Experiments have been developed to obtain the full cyclic stress-strain and stress relaxation data at 450°C. A step-by-step method has been used to obtain the initial material parameters, while a non-linear least-square approach has been used to obtain the optimised material parameters. Satisfactory results have been obtained for the simulation of the transient and steady state cyclic stress-strain and stress relaxation behavior.

Design related aspects in advanced nuclear fission plants

Important issues to be considered for design of future reactors are: extrapolation of stress rupture data, creep–fatigue, negligible creep, damage monitoring. The paper highlights some new developments taking examples from a martensitic steel (mod 9% Cr), oxide dispersion strengthened (ODS) steels and nickel-base superalloys. Traditional approaches to extrapolation of (thermal) stress rupture data like Larson–Miller Parameter or Monkman–Grant rule seem to be valid concepts also for advanced reactors. However, a significant influence of cyclic softening on creep rates and stress rupture data can be expected as shown for grade 91. This is particularly true for creep–fatigue interactions. Based on cyclic stress–strain behaviour it is also possible to get very good life-time predictions under creep–fatigue with a strain range separation (inelastic fatigue and creep ranges) technique which could replace the currently used linear life fraction rule. Results from in-beam irradiation creep reveal no significant influence of dispersoid size. It can be assumed that irradiation creep is a matrix property. Finally it is shown that micro-sample testing of exposed material could be used as an advanced method for damage assessment in future nuclear power plants.

Cyclic stress-strain behaviour under thermomechanical fatigue conditions – Modeling by means of an enhanced multi-component model

The cyclic stress-strain behaviour of metals and alloys in cyclic saturation can reasonably be described by means of simple multi-component models, such as the model based on a parallel arrangement of elastic-perfectly plastic elements, which was originally proposed by Masing already in 1923. This model concept was applied to thermomechanical fatigue loading of two metallic engineering materials which were found to be rather oppositional with respect to cyclic plastic deformation. One material is an austenitic stainless steel of type AISI304L which shows dynamic strain aging (DSA) and serves as an example for a rather ductile alloy. A dislocation arrangement was found after TMF testing deviating characteristically from the corresponding isothermal microstructures. The second material is a third-generation near-gamma TiAl alloy which is characterized by a very pronounced ductile-to-brittle transition (DBT) within the temperature range of TMF cycling. Isothermal fatigue testing at temperatures below the DBT temperature leads to cyclic hardening, while cyclic softening was found to occur above DBT. The combined effect under TMF leads to a continuously developing mean stress. The experimental observations regarding isothermal and non-isothermal stress-strain behaviour and the correlation to the underlying microstructural processes was used to further develop the TMF multi-composite model in order to accurately predict the TMF stress-strain response by taking the alloy-specific features into account.