Monotonic Stress-strain Curves Research Articles

Low-cycle fatigue behavior and microstructure evolution of ODS steel pipes at high temperatures

Oxide-dispersion-strengthened (ODS) steels are candidate materials for application in advanced nuclear reactors. In this study, the low-cycle fatigue performances of 13Cr-ODS ferritic steel pipes were investigated at 600, 700, and 800 °C. Cyclic softening was observed at high strain amplitudes with an increase in the number of fatigue cycles. However, cyclic hardening appeared first, and then cyclic softening occurred at a low strain amplitude with the increase in the number of fatigue cycles. By comparing the cyclic stress–strain curves and the monotonic stress–strain curves, it was found that cyclic softening occurred regardless of the strain amplitude. The Coffin–Manson and Basquin equations were used to predict the fatigue of the pipes. Microstructure analysis indicated that cyclic softening was induced by the dynamic recovery and recrystallization, which reduced the number of low-angle grain boundaries in the deformed grains by promoting dislocation annihilation and reorganization. A complex multi-layer core–shell structure with a large size (∼500 nm) was observed.

Hysteretic behavior and cyclic constitutive model of corroded low-alloy steel in a corrosive environment

To quantitatively analyze the mechanical properties of corroded low-alloy steel under monotonic and cyclic loading, a cyclic constitutive model was established. Accelerated corrosion, monotonic tensile testing, and cyclic loading testing of 28 groups of Q345B steel specimens were conducted to examine how corrosion affected the monotonic tensile and hysteresis characteristics of the specimens, and the combined hardening parameters based on the Chaboche model were calibrated and confirmed based on the test findings. The results showed that corrosion clearly affected the monotonic stress-strain curve of steel and that most mechanical indices deteriorated linearly with respect to the corrosion rate. The combination of corrosion and cyclic cumulative damage exacerbated the degradation of the deformation capacity of the steel and affected its energy consumption capacity and cyclic hardening. The constitutive model of corroded steel calibrated on the basis of cyclic loading test data could effectively simulate the hysteresis performance of corroded Q345B steel under cyclic loading.

Mechanical Properties of Dahurian Larch Wood under Cyclic Loading: Experiments and Constitutive Model

This article presents a study on the mechanical properties and constitutive model of Dahurian larch wood under parallel-to-grain (ParG) and perpendicular-to-grain (PerG) cyclic loading. A total of twenty-four dog-bone specimens were designed and prepared. Failure modes, stress–strain curves, elastic moduli under monotonic loading, and unloading/reloading moduli under cyclic loading were analyzed. Results indicated that the tensile and compressive envelope curves of wood under cyclic loading are similar to the monotonic stress–strain curves. The unloading and reverse reloading stiffness of wood are significantly degraded in both material directions. Furthermore, a constitutive model that is capable of considering the degradation of cyclic compression unloading stiffness and the change in reverse compression (tension) stiffness after tension (compression) unloading was proposed. A comprehensive comparison with test results was conducted, and they are in good agreement. Thus, the correctness of the proposed constitutive model is verified.

Cyclic compressive behavior of hook-end steel and macro-polypropylene hybrid fiber reinforced recycled aggregate concrete

One widely accepted strategy is to add fiber into recycled aggregate concrete (RAC) to improve compressive strength. Few existing investigations have focused on the cyclic compressive behavior of hybrid fiber reinforced recycled aggregate concrete (HFRRAC). A total of eighteen groups of prismatic specimens with different fiber combinations and recycled coarse aggregate (RCA) replacement rates were conducted under cyclic compression to investigate the mechanical properties of hooked-end steel and macro-polypropylene hybrid fiber reinforced recycled aggregate concrete. Results indicate that specimens under cyclic loading fail similarly to those subjected to monotonic loading. The envelope curve of the cyclic stress-strain curve for HFRRAC closely resembles the corresponding monotonic stress-strain curve. RCA replacement rates and fiber combinations do not significantly affect plastic strain and stress deterioration. Fibers added to specimens mitigate stiffness degradation and improve hysteretic energy dissipation. The proposed constitutive equations can be used to describe the cyclic compressive behavior of HFRRAC. The fibers improve the density and structure of mortar and aggregate-paste interfaces from the microstructure morphologies. The fracture mechanisms of HFRRAC were also studied using mesoscale numerical models under uniaxial compression loading. The cohesive zone model is suitable for simulating the compressive behavior of HFRRAC. Numerical specimens fail in mixed fracture modes, primarily mode II fractures.

Post-fire constitutive model on explosively welded stainless-clad bimetallic steel after cold-forming process

This study conducted an experiment on corner stainless-clad bimetallic steel (SBS) specimens to clarify the coupling effects of the cold-forming process and fire exposure on the monotonic mechanical properties of SBS, where different exposure temperatures and cooling methods were considered. The SBS produced through the explosive welding method was used to obtain cold-formed specimens. After the cold-forming process and fire exposure, no obvious cracking was observed in the stainless-steel cladding and metallurgical bonding layer. Based on the tensile coupon test results, the yield plateau in the stress–strain curve of the virgin SBS specimen disappeared because of the cold-forming process. The effects of the exposure temperature and cooling method on the stress–strain curves of the corner SBS specimen were clarified. The variation trends of the key mechanical parameters were discussed. Predictive equations were proposed for the key mechanical parameters of corner SBS specimen after fire exposure. Two constitutive models were suggested for the corner SBS stress–strain curves with and without the yield plateau, which could be used in the numerical and theoretical investigations on the post-fire-resistant performance of cold-formed SBS components. Comparing the experimental and predicted results indicated that the residual monotonic stress–strain curves of the corner SBS could be accurately described using the proposed constitutive models.

Nonlinear time-dependent mechanical behavior of mammalian collagen fibrils.

The viscoelastic mechanical behavior of collagenous tissues has been studied extensively at the macroscale, yet a thorough quantitative understanding of the time-dependent mechanics of the basic building blocks of tissues, the collagen fibrils, is still missing. In order to address this knowledge gap, stress relaxation and creep tests at various stress (5-35 MPa) and strain (5-20%) levels were performed with individual collagen fibrils (average diameter of fully hydrated fibrils: 253±21 nm) in phosphate buffered saline (PBS). The experimental results showed that the time-dependent mechanical behavior of fully hydrated individual collagen fibrils reconstituted from Type I calf skin collagen, is described by strain-dependent stress relaxation and stress-dependent creep functions in both the heel-toe and the linear regimes of deformation in monotonic stress-strain curves. The adaptive quasilinear viscoelastic (QLV) model, originally developed to capture the nonlinear viscoelastic response of collagenous tissues, provided a very good description of the nonlinear stress relaxation and creep behavior of the collagen fibrils. On the other hand, the nonlinear superposition (NSP) model fitted well the creep but not the stress relaxation data. The time constants and rates extracted from the adaptive QLV and the NSP models, respectively, pointed to a faster rate for stress relaxation than creep. This nonlinear viscoelastic behavior of individual collagen fibrils agrees with prior studies of macroscale collagenous tissues, thus demonstrating consistent time-dependent behavior across length scales and tissue hierarchies. STATEMENT OF SIGNIFICANCE: Pure stress relaxation and creep experiments were conducted for the first time with fully hydrated individual collagen fibrils. It is shown that collagen nanofibrils have a nonlinear time-dependent behavior which agrees with prior studies on macroscale collagenous tissues, thus demonstrating consistent time-dependent behavior across length scales and tissue hierarchies. This new insight into the non-linear viscoelastic behavior of the building blocks of mammalian collagenous tissues may serve as the foundation for improved macroscale tissue models that capture the mechanical behavior across length scales.

Residual monotonic mechanical properties of bimetallic steel bar with fatigue damage

When a reinforced concrete structure experiences an earthquake and does not collapse, irreversible damage in the reinforcement is caused by the fatigue load, which affects the residual bearing capacity of the structure significantly. Stainless-clad bimetallic steel bars (BSBs) are a new type of coated reinforcement with effective resistance to corrosion. In this study, to accurately evaluate the residual bearing capacity of a concrete structure reinforced with BSBs following an earthquake, it is tested with different fatigue damage ratios. Thereafter, the monotonic stress–strain nonlinear performance, failure behaviour, and residual mechanical properties of BSBs with fatigue damage are explored. The evolution law of the mechanical properties of BSBs with fatigue damage is analysed. A monotonic stress–strain model of the BSB that considers the impact of fatigue damage is proposed. The test results indicate that the stainless-steel cladding of the BSB does not demonstrate apparent buckling following fatigue damage. Cracks are observed on both sides of the rib teeth. When the fatigue damage ratio is 0.6, a fracture occurs at the maximum crack caused by the fatigue damage. When the fatigue damage ratios are 0.2 and 0.4, fractures occur in the necking region of the upper or lower part of the specimen. Fatigue damage leads to the disappearance of the yield platform from the monotonic stress–strain curve of the BSB. The yield strength of the BSB decreases significantly owing to the fatigue damage ratio. The ultimate strength is barely affected by the fatigue damage ratio. Fatigue damage has an adverse effect on the deformation capacity of the BSB. With an increase in the fatigue strain amplitude and fatigue damage ratio, elongation following the fracture of the BSB gradually decreases. This study provides solid theoretical and experimental bases for the engineering application of BSBs, particularly in the post-earthquake evaluation of concrete structures reinforced with BSBs.

Compressive fatigue behaviors of ultra-high performance concrete containing coarse aggregate

In this work, the uniaxial compressive fatigue behaviors of ultra-high performance concrete containing coarse aggregate (UHPC-CA) were investigated, towards a better understanding of the role of CA on its fatigue responses. Upon the constant amplitude fatigue tests performed at three stress levels (i.e. S = 0.7, 0.8, and 0.9), the emphases were focused on the effects of CA content (10%, 20%, and 30%) on the failure pattern, deformation characteristics, fatigue life, failure mechanism, and damage evolution. The results showed that compared to the UHPC specimen free of CA, the crack propagation, strain development, and fatigue life of UHPC-CA specimens are largely affected by the CA incorporation, due to the introduction of weak interfacial transition zones and the interference of fiber distribution. As a result, the risk of premature fatigue failure of UHPC-CA will be generally amplified as the CA content increases. Furthermore, inspired by the experimental observation that the fatigue failure strain of UHPC-CA stably approaches the descending branch of the monotonic stress-strain curve, a modified model based on the strain development instead of highly scattered fatigue life was proposed to estimate the nonlinear evolution of the fatigue damage. The good agreements with independent test results demonstrated the applicability of the model, representing a compromise between accuracy and practicability.

Experimental investigation on the stress-strain behavior of unsaturated polyester polymer concrete subjected to monotonic and cyclic loadings

The use of polymer concrete (PC) in construction requires the development of an accurate stress-strain relationship that can accurately predict the mechanical properties of PC. Given that no constitutive equation for cyclic loading of unsaturated polyester PC (UPPC) is available in the literature, the goal of the current research has been to propose a rational analytical model for estimating the mechanical characteristics of UPPC under tensile and compressive loading. Compressive and tensile cyclic and monotonic tests were performed on specimens which had been cured for 28 days and the average monotonic stress-strain curve was obtained for the monotonic tests. The average maximum stress and strain were determined for both the compressive and tensile tests and the elastic modulus and energy absorption capacity were computed and compared with the values for normal concrete (NC) and high strength concrete (HSC) materials. Analytical models for the monotonic and skeleton curves for both tensile and compressive tests have been provided, and the proposed models were compared to experimental findings and other research results for validation. Stress-strain relationships have been proposed for the unloading and reloading paths and were compared with the cyclic test results. The ultimate stress and strain for the UPPC were three and five times higher, respectively, than for the NC in tension testing. The ultimate strain for UPPC was almost 150% greater than the final strain of HSC in compression. Under compressive loading, the UPPC absorbed to 2.33 and 5.3 times more energy, respectively, than the HSC and NC. The results showed that the skeleton curves agreed well with the monotonic curves for the compressive and tensile tests. All of the proposed models agreed well with the available experimental data and previous study results.

Behavior of cement concrete confined by fabric-reinforced geopolymer mortar under monotonic and cyclic compression

As an eco-friendly inorganic cementitious matrix material, a geopolymer mortar combined with short-cut fibers and fiber meshes represents a novel strengthening system, which has been proven to be effective in strengthening existing concrete structural members. However, the behavior of cement concrete cylinders confined by fabric-reinforced geopolymer mortar (FRGM) under compression is unclear. Therefore, in this work, experimental studies were performed to investigate the effects of the number of strengthening layers, matrix strength of the strengthening system, and loading path on the compressive behavior of basalt–FRGM-confined concrete. The experimental results show that two or three layers of the FRGM jacket can help substantially improve the peak stress and its corresponding axial deformation, ductility, and energy absorption ability. The envelope of the cyclic stress–strain curve is consistent with the monotonic stress–strain curve of an identical group of specimens with the same confinement. The residual plastic strain increases with repeated loading cycles, whereas the new reloading stress deteriorates. Regression models are proposed to predict the peak stress and corresponding axial strain in the basalt-FRGM-confined concrete. Finally, monotonic and hysteretic constitutive models for the FRGM-confined cement concrete are developed and compared with the experimental curves. The experimental results provide new insights into the strengthening properties of geopolymer composites and theoretical support for their application. Notably, geopolymer composites can be used in repairing aging and damaged concrete structures while ensuring a low carbon footprint.

Effect of loading protocol on the mechanical properties of 316L stainless steel

Two types of loading protocol, i.e., monotonic loading and cyclic loading, were compared to investigate the effect on the mechanical properties of 316L stainless steel. The specimen used is a dog-bone specimen in accordance with ASTM E8 and ASTM E606 standard. For cyclic loading, the multiple-step method is used to obtain the hysteresis loop of the material. A total of 13 strain amplitude conditions had been carried out, ranging from 0.05%-0.65%. The stress-strain curve shows that the cyclic stress-strain curve is higher than the monotonic stress-strain curve due to the cyclic hardening behaviour in the 316L stainless steel. The cyclic hardening behaviour increases the ultimate tensile stress of the material. However, when the material gains its strength through cyclic hardening, the ductility in the material will decrease.

Loop Algorithms for Ductility Analysis of Column Reinforced Steel with Yield Strength Above 500 MPA

There are many benefits to the use of high-strength reinforcement (above 500 MPa) in reinforced concrete buildings. The advantages of using high-strength reinforcement are reduction steel volume and dimension, reduced construction time, reduction in reinforcement congestion, as well as savings in materials and worker cost. Meanwhile, the investigation of ductility of reinforced concrete element with high-strength reinforcement to resist earthquake effects under current design procedure is needed. In the current standard, ACI 318-71, The maximum specified yield strength was restricted to 60 Ksi (413 MPa) for reinforcement in special seismic system. There were also no ASTM standard specifications for reinforcement with yield strength above 500 MPa. In the design of seismic resisting structures, the analysis of curavture ductility and flexural overstrength factor is of important consideration in order to avoid brittle failure. This paper attempts to anaylze the ductility and re-evaluate the flexural overstrength factor of reinforced concrete column. The tensile tests of steel reinforcement with yield strength above 500 MPa generates stress-strain curve. An idealisations for the monotonic stress-strain curve proposed by mander was adopted in this study. Whereas in this numerical study of confined concrete columns, the behavior of concrete cored is modeled by the stress-strain relationship of confined concrete proposed by Kappos-Konstantinidis. This stress strain model was used for the momen, curvature, ductility, and flexural overstrength factor analysis.

Monotonic and cyclic compression characteristics of CFRP confined masonry columns

The lateral confinement of masonry columns using composites have shown to improve their strength and ductility. Although, several research studies were focused on investigating the monotonic compression behaviour of confined masonry columns in the past, their cyclic compression characteristics, which are necessary for seismic and dynamic analyses, are not well investigated. Thus, an attempt has been made to experimentally characterise the confined masonry columns under monotonic and cyclic axial compression in this research. In total, 36 masonry columns were built and tested under monotonic and cyclic compression. Out of 36 columns, twelve columns were unconfined and tested under monotonic compression, while the rest of the columns were confined with Carbon Fibre Reinforced Polymer (CFRP) laminates and tested under monotonic and cyclic compression. The experimental results are presented in terms of observed failure modes, compressive strengths and stress–strain curves. Cyclic loading protocol was displayed to marginally reduce the compressive strength of CFRP confined masonry columns by 6% to 13% compared to the compressive strengths obtained through monotonic compression testing. The analytical models available to predict the monotonic stress–strain curves were used to predict the cyclic envelop stress–strain relationship of confined masonry columns. Finally, the best fit analytical model to predict the cyclic envelop compression behaviour of CFRP confined masonry columns has been proposed.

Finite-element simulation of multi-axial fatigue loading in metals based on a novel experimentally-validated microplastic hysteresis-tracking method

We propose a new approach to the prediction of multiaxial fatigue with proportional and non-proportional loading based on a recently developed three-dimensional small-strain microplasticity-based constitutive theory. The core idea of the theory is to incorporate pre-full-yield microplastic deformations in a computationally efficient way. Fatigue life is then correlated to the accumulated (micro)plastic work, which is obtained from the total plastic dissipation. The constitutive parameters required are calibrated using just a monotonic stress-strain curve determined from a simple compression test experiment together with a low cycle uniaxial fatigue experiment. The resulting three-dimensional constitutive model has also been implemented into the Abaqus/Explicit finite element program through a vectorized user-material subroutine interface with a fully-implicit, unconditionally-stable and robust time integration scheme. Using the suitably-calibrated constitutive model, a series of uniaxial and multiaxial stress- and strain-based, constant-amplitude fatigue finite element simulations have been conducted to compare with the physical experiment data from the literature. It is shown that the developed theory and its finite-element implementation (which have fewer parameters than cycle counting based methods) are able to better predict the experimental fatigue life under multiaxial proportional or non-proportional loading conditions.

Design-Oriented Stress-Strain Model for FRP-Confined Lightweight Aggregate Concrete

Despite the advantages of lightweight aggregate concrete (LWAC), its brittleness in compression has limited its vast application. Jacketing by fiber-reinforced polymer (FRP) tends to be one method to overcome this negative point. The current study attempted to recognize the FRP confinement impact on the LWAC compressive monotonic behavior. Both fine and coarse aggregates were Scoria aggregate. The variables include the type and number of FRP layers; 150 × 300 mm cylindrical specimens were wrapped with 1, 2, 3, and 4 layers of glass FRP (GFRP) and carbon FRP (CFRP) strips. An investigation was performed on the monotonic stress-strain curve belonging to LWAC confined with FRP, and key points, including ultimate stress and strain on the curve, were explored. The results revealed that the key points would significantly improve by increasing FRP layers. Although the influence of GFRP confinement on enhancing the ultimate strain appears to be more considerable than the CFRP confinement, CFRP jacketing of LWAC upgrades the ultimate strength to the higher level compared to wrapping with GFRP. Based on the interpretation of experimental results, a design-oriented stress-strain model was established to predict the monotonic compressive response of Scoria-LWAC circular specimens confined with CFRP and GFRP. The validity of the model was examined. The predicted output was appropriately in line with the experimental findings.

Cyclic behaviour and modelling of stainless-clad bimetallic steels with various clad ratios

Stainless-clad (SC) bimetallic steels that are manufactured by metallurgically bonding stainless steels as cladding metal and conventional mild steels as substrate metal, are kind of advanced steel plate products. Such advanced composite steels are gaining increasingly widespread usage in a range of engineering structures and have great potential to be used extensively for large civil and building infrastructures. Unfortunately, research work on the SC bimetallic steels from material level to structural design level for the applications in structural engineering field is very limited. Therefore, the aim of this paper is to investigate the material behaviour of the SC bimetallic steels under the cyclic loading which structural steels usually could encounter in seismic scenario. A number of SC bimetallic steel coupon specimens are tested under monotonic and cyclic loadings. The experimental monotonic and cyclic stress-strain curves of the SC bimetallic steels are obtained and analysed. The effects of the clad ratio that is defined as the ratio of the thickness of cladding layer to the total thickness of SC bimetallic steel plate on the monotonic and cyclic behaviour of the SC bimetallic steels are studied. Based on the experimental observations, a cyclic constitutive model with combined hardening criterion is recommended for numerical simulation of the cyclic behaviour of the SC bimetallic steels. The parameters of the constitutive model for the SC bimetallic steels with various clad ratios are calibrated. The research outcome presented in this paper may provide essential reference for further seismic analysis of structures fabricated from the SC bimetallic steels.

New formulation of nonlinear kinematic hardening model, Part I: A Dirac delta function approach

A new mathematical modelling framework for simulation of metal cyclic plasticity is proposed and experimental validation based on tension-compression cyclic testing of S355J2 low carbon structural steel presented over the two parts of this paper. The advantages and limitations of the stress-strain curve shape modelling given by “Armstrong and Frederick” type hardening rules are discussed and a new formulation for kinematic hardening is proposed for more accurate representation of the stress-strain dependence under cyclic loading conditions. The proposed model is shown to describe the shape of the stress-strain curve accurately under various different loading conditions. Transition effects occurring at loading reversals are incorporated through a new framework of Dirac delta functions. In addition to the yield surface, stress supersurfaces able to expand and instantly move to simulate a shift of stress-strain curves during loading reversals are determined. This also enables inclusion of the behaviour of monotonic stress-strain curves with yield plateau deformation in one mathematical model. The influence of the first stress invariant on the shape of a stress-strain curve in tension and compression directions observed in many metals is incorporated into the kinematic hardening rule. The ability of the model to accurately describe transition from elastic to elastic-plastic deformation at small offset strain yield points naturally accounts for nonlinearity of an unloading stress-strain curve after plastic pre-strain. Development of the model to include mixed cyclic hardening/softening, ratcheting and mean stress relaxation is presented in a companion paper (Part II), which includes experimental validation of the modelling framework.

A rate independent inelasticity model with smooth transition for unifying low-cycle to high-cycle fatigue life prediction

A three-dimensional rate independent inelastic constitutive model has been developed to predict the fatigue behavior of metals spanning low to high cycles, based solely on the monotonic stress strain curve and a cyclic test for a few cycles ( < 1000). The key to the development of the model is that the “microplastic response” before full yield is accounted for by a new approach to inelastic modeling while retaining a rate independent response. A numerical algorithm based on the one-dimensional version of the constitutive theory has also been implemented into a computer code to model fatigue loading under simple tension/compression i.e. uniaxial loading conditions. The material parameters in the constitutive model were calibrated through fitting the constitutive model to the monotonic stress–strain curve obtained from a simple compression test experiment. By adopting the total inelastic work dissipation (which is related to the configurational entropy created due to damage) as the failure criteria and integrating the rate of entropy generation (under isothermal conditions) over a typical stabilized hysteresis cycle (including the small scale effects due to microplasticity), a close-formed expression for stress-fatigue life prediction is also derived for zero mean stress. Finally, it is shown that the model and numerical algorithm are able to predict the experimental stress-life and strain-life (with and without mean stress) responses quite well.

Cyclic deformation behavior of a high zinc-containing cast magnesium alloy

The objective of the present study was to evaluate strain-controlled low cycle fatigue behavior of a high zinc-containing Mg-10Zn-5Al (wt.%) cast magnesium alloy in relation to the microstructure characterized via EBSD and XRD. The addition of Zn with a Zn/Al ratio of ∼2 suppressed the presence of β-Mg17Al12 phase, and the as-cast alloy consisted mainly of primary α-Mg and eutectic-like τ-Mg32(Al,Zn)49 phase in a characteristic network form. The alloy exhibited superior tensile properties compared with several commercial cast alloys. Unlike extruded magnesium alloys, the alloy exhibited almost symmetrical stress-strain hysteresis loops due to the presence of τ-Mg32(Al,Zn)49 phase and nearly random textures. Although slight cyclic softening occurred at higher strain amplitudes, cyclic stabilization basically remained. This was also reflected by the nearly overlapped cyclic and monotonic stress-strain curves. The fatigue life predicted via strain energy based approach was in good agreement with the experimental value. Fatigue crack initiated from the near-surface imperfections, and crack propagation was characterized by fatigue striation-like features along with tear ridges.

Low Cycle Fatigue Behavior of Steam Generator Tubes under Axial Loading.

Compared with the fatigue properties of the material (Inconel Alloy 690), the real fatigue lives of tubes are more meaningful in the fatigue design and assessment of steam generator (SG) tube bundles. However, it is almost impossible to get a satisfactory result by conducting fatigue tests on the tube directly. A tube with a uniform and thin wall easily fails near the clamping ends under cyclic loading due to the stress concentration. In this research, a set-up for fatigue tests of real tubes is proposed to overcome the stress concentration. With the set-up, low cycle fatigue tests were conducted in accordance with an existing fatigue design curve for Alloy 690. Strain control mode was applied with fully reversed push–pull loading under different strain amplitudes (0.15%, 0.2%, 0.3%, and 0.4%). A favourable result was obtained, and the low cycle fatigue behavior was investigated. The results showed that the fatigue life tested by the real tube was below the strain–life curve of Alloy 690 which was fitted by conventional solid specimens. A cyclic hardening behavior was found by the cyclic stress–strain curve when compared with the monotonic stress–strain curve.