Cyclic Stress-strain Behavior Research Articles

Cyclic stress–strain behavior of additively manufactured gamma prime strengthened superalloy at elevated temperatures

The γ́-precipitation hardened nickel-based superalloy IN939 manufactured by laser powder bed fusion (L-PBF) was subjected to cyclic loading to determine the cyclic stress–strain curve by short-cut procedure. The effect of building on loading direction/orientation was investigated. 〈001〉 crystallographic texture along the building direction was observed. The cyclic stress–strain curves were measured at 800 °C and 900 °C and the differences in cyclic plasticity were revealed. The specimens prepared by L-PBF with a building direction parallel to the loading axis exhibited the highest cumulative plastic deformation at both temperatures, while L-PBF with a building direction perpendicular to the loading axis was the lowest. Elastic moduli were determined and the differences were attributed to the crystallographic texture. In addition, conventionally cast IN939 was investigated as the reference material. Minor microstructural changes due to cyclic straining were inspected by transmission electron microscopy.

Application of Instrumented Indentation Procedure in Assessing the Low-Cycle Fatigue Properties of Selected Heat-Treated Steels.

The paper presents an analysis of the low-cycle fatigue (LCF) properties of C45, X20Cr13, and 34CrNiMo6 steels subjected to various heat treatment processes. Strain-controlled LCF tests were carried out with a total cyclic strain amplitude equal to 0.5, 1 and 1.5%. Fatigue life, cyclic stress-strain behavior and hardness were analyzed. Qualitative and quantitative relationships between material LCF properties resulting from the heat treatment processes, were related to the indentation force P*, which was derived experimentally by applying an instrumented indentation procedure with the use of the Vickers indenter. The proposed parameter P* and its changes ΔP* seem to be promising for the identification of the structural stress parameter σ* that is necessary for deriving values of the fatigue strength coefficients σf' corresponding to different tempering temperatures. The common feature of all steels analyzed in this paper is that the elastic parts of the strain-life characteristics remain parallel after being subjected to different tempering temperatures.

An experimental investigation on undrained cyclic behaviour of a saturated intact loess

There are growing evidence indicating that earthquakes occur more frequently in the Chinese Loess Plateau, which can possibly cause saturated intact loess liquefaction, leading to geological disasters. However, the cyclic behaviour of saturated intact loess is still much less investigated. In the presented work, typical intact loess was collected to carry out a comprehensive experimental investigation, including both undrained monotonic and cyclic triaxial shear tests with different confining stresses and cyclic stress. The results indicate that the intact loess shows an overall clay-like cyclic behaviour. It shows a strain softening behaviour under undrained monotonic shearing, while under undrained cyclic shearing, a well-defined failure pattern of plastic strain accumulation is observed, and an axial strain of 3 % is determined as the failure criterion. Although different excessive pore water pressure generation patterns and failure criteria are found under monotonic and cyclic conditions, a quantitative relationship is established between the monotonic and cyclic stress-strain behaviour based on the unique relationship found between axial strain and the defined allowable stress. Additional micro-structure observations and analyses further reveal the differences in loess structure destruction caused by different loading conditions. This study helps to further understand the cyclic behaviour and failure mechanism of intact loess, and to provide a useful reference for the evaluation and prevention of possible soil liquefaction failure in loess areas.

Low cycle fatigue behaviour of engineering metallic materials: Review on cyclic deformation micro-mechanism

The micro-mechanism of low cycle fatigue deformation behaviour has been summarised, utilising the recent advances in the state-of-the-art facility for the characterisation of deformation microstructure, and micro-texture. Besides, recent development in the approach of numerical simulation of cyclic stress-strain behaviour of polycrystalline metallic materials at multi-scale has been discussed. It has been carried out by reviewing, and re-interpreting the evidences from the investigations carried out over the last few decades on several engineering metallic materials having critical applications in various industries. The understanding of the existing material behaviour will help us in the better characterisation of the low cycle fatigue deformation microstructure of the new generation metallic materials having complex microstructure.

Cyclic Stress–Strain Behavior and Model for FRP-Confined Engineered Cementitious Composite

A fiber-reinforced polymer (FRP) confined engineered cementitious composite (ECC) column as a new high-performance composite member achieves significant ductility. Understanding its cyclic behavior is necessary to guide seismic design. This paper presents an experimental study on the compressive behavior of large rupture strain (LRS) FRP and traditional glass FRP (GFRP) jacketed ECC cylinders subjected to full and partial cyclic loadings. Effects of FRP confinement level, FRP type, and loading scheme on the failure pattern, stress–strain relationship, ultimate condition, plastic strain, and stress deterioration ratio were examined. Existing equations for plastic strain and stress deterioration ratio of the envelope and internal cycles were evaluated. Based on the experimental results, new calculation formulas were derived for the plastic strain and stress deterioration ratio. A threshold involving partial unloading/reloading factors was determined to define the effective cycles. In addition, a cyclic model composed of a monotonic envelope model and an unloading/reloading model was developed for estimating the stress–strain hysteresis loops of both GFRP- and LRS FRP-confined ECC cylinders.

Estimation of Cyclic Stress-Strain Curves of Steels Based on Monotonic Properties Using Artificial Neural Networks.

This paper introduces a novel method for estimating the cyclic stress-strain curves of steels based on their monotonic properties and plastic strain amplitudes, utilizing artificial neural networks (ANNs). ANNs were trained on a substantial number of experimental data for steels, collected from relevant literature, and divided into subgroups according to alloying elements content (unalloyed, low-alloy, and high-alloy steels). Only monotonic properties that were proven to be relevant for the estimation of points on the stress-strain curve were used. The performance of the developed ANNs was assessed using an independent set of data, and the results were compared to experimental values, values obtained by existing empirical estimation methods, and by previously developed ANNs. The results showed that the new approach which combines relevant monotonic properties and plastic strain amplitudes as inputs to ANNs for cyclic stress-strain curve estimation is better than the previously used approach where ANNs estimate the parameters of the Ramberg-Osgood material model separately. This shows that a more favorable approach to the estimation of cyclic stress-strain behavior would be to directly estimate corresponding material curves using monotonic properties. Additionally, this may also reduce inaccuracies resulting from simplified representations of the actual material behavior inherent in the material model.

Cyclic stress–strain behavior of low-diameter reinforcing bars for thin concrete walls

Cyclic stress–strain behavior of low-diameter reinforcing bars for thin concrete walls

Simulation of the Cyclic Stress–Strain Behavior of the Magnesium Alloy AZ31B-F under Multiaxial Loading

Under strain control tests and cyclic loading, extruded magnesium alloys exhibit a special mechanism of plastic deformation (“twinning” and “de-twining”). As a result, magnesium alloys exhibit an asymmetric material behavior that cannot be fully characterized with the typical numerical tools used for steels or aluminum alloys. In this sense, a new phenomenological model, called hypo-strain, has been developed to correctly predict the cyclic stress–strain evolution of magnesium alloys. On this basis, this work aims to accurately describe the local cyclic elastic–plastic behavior of AZ31B-F magnesium alloy under multiaxial cyclic loading with Abaqus incremental plasticity. The phenomenological hypo-strain model was implemented in the UMAT subroutine of Abaqus/Standard to be used as a design tool for mechanical design. To evaluate this phenomenological approach, the results were correlated with the uniaxial and multiaxial proportional and non-proportional experimental tests. In addition, the estimates were also correlated with the Armstrong–Frederick nonlinear kinematic hardening model. The results show a good correlation between the experiments and the phenomenological hypo strain approach. The model and its implementation were validated in the strain range studied.

Application of redefined J-integral range ΔJ for ultra-low cycle fatigue problems with large magnitude of elastic-plastic deformation

The redefined J-integral range ΔJ by a domain integral representation was applied to the ultra-low cycle fatigue problem of a 1 T compact tension (1TCT) specimen. The specimen was subject to large magnitude of cyclic deformation. The redefined J-integral range ΔJ is unconditionally independent of size and shape of its integral domain. The subloading surface plasticity model was adopted to appropriately reproduce the cyclic stress-strain behavior of the material. Finite element analyses on and evaluations of ΔJ were performed on the ultra-low cycle fatigue problem of a 1TCT specimen made of stainless steel SUS316. The outcomes of present study show the followings: (i) use of the redefined J-integral range ΔJ under the assumption of finite deformation theory, ductile crack propagations in ultra-low cycle fatigue problems can be characterized and (ii) deformation and load-displacement hystereses of the experiments can appropriately be reproduced by the use of the subloading surface plasticity model.

Strain-Based Fatigue Experimental Study on Ti–6Al–4V Alloy Manufactured by Electron Beam Melting

Additive manufacturing (AM) by electron beam melting (EBM) is a technique used to manufacture parts by melting powder metal layer-by-layer with an electron beam in a high vacuum, thereby generating a 3D topology. This paper studies the low-cycle fatigue of Ti–6Al–4V specimens obtained by EBM. Static tests were carried out according to ASTM E8 for a yield stress of 1023 MPa, a fracture stress of 1102 MPa, and a maximum tensile strength of 1130 MPa with a maximum true normal strain at fracture εmax = 9.0% and an elastic modulus of 120 GPa. Then, fatigue tests were conducted at a load inversion rate of R = −1. It was observed that the material exhibited plastic strain softening, which was attributed to the Bauschinger effect. These results were plotted on a strain vs. life (ε−N) curve using the Ong version of the Coffin–Manson rule and the Baumel–Seager and Meggiolaro–Castro rules. The results were compared to forged Ti–6Al–4V alloys. The cyclic stress–strain behavior was described with the Ramberg–Osgood model. Finally, the fracture surface was analyzed using scanning electron microscopy (SEM) to observe the formation of primary cracks. The fracture morphology showed a mixed surface, also known as a “quasi-cleavage”, which is characterized by dimples, cleavage facets, extensive primary cracks with broken slipping planes, and a large number of inclusions. This phenomenon caused a possible brittle behavior in the material.

Uniform fatigue damage tolerance assessment for additively manufactured and cast Al-Si alloys: An elastic-plastic fracture mechanical approach

• Influence of additively manufacturing and casting on microstructure and porosity characteristics as well as quasi-static and cyclic stress-strain behavior of Al-Si alloys. • Evaluation of Murakami-Noguchi approach and Shiozawa approach for fatigue limit and lifetime estimation, however, both approaches are not sufficient for AM Al-Si alloys. • Linking J integral (elastic-plastic fracture mechanics) including cyclic stress-strain curve by means of morrow parameter (K’, n’), defect size and position, stress amplitude and stress ratio. • New approach enables a uniform fatigue damage tolerance assessment of fatigue lifetime and limit for additively manufactured alsi10mg alloy as well as die-cast and sand-cast alsi7mg alloy. Lightweight Al-Si alloys are used in the automotive and railway industry due to their excellent strength-to-weight ratio and near-net-shape manufacturing. In additive manufacturing and casting, the near-net-shape manufacturing results in a non-homogenous solidification and cooling of the parts, leading to significant local gradient in microstructural and defect features as well as deformation behavior. In this paper, a uniform damage tolerance assessment was developed based on fracture mechanical approaches of Murakami (√area) and Shiozawa for a reliable defect-based mechanical design of fatigue-loaded structures. The linear-elastic fracture mechanical (LEFM) approaches of Murakami and Shiozawa were used to calculate defect-based lifetime curves, where the cyclic stress intensity factor (ΔK) at the failure-initiating defect (√area) was used to describe the local stress concentration conditions, called K-N curves, instead of nominal stress-based S-N curves. The LEFM-based K-N curves did not allow to describe the fatigue behavior in terms of a unified fatigue design of AM and casting material. Therefore, the cyclic stress-strain (CSS) behavior was used for a plasticity-modification of the LEFM approach by calculating the effective cyclic J integral (ΔJ eff ) to plot J-based K-N curves, called Kj-N curves. This elastic-plastic fracture mechanical (EPFM) approach allowed a uniform fatigue damage tolerance (FDT) assessment of AM and cast Al-Si alloys for the HCF regime by FDT law and fatigue limit by FDT limit. Exemplarily, the FDT limit could be used to predict synthetic Haigh diagrams for specific AM and cast batches and derive process- and service-relevant knowledge on the effect of tensile or compressive mean stress.

Uniform fatigue damage tolerance assessment for additively manufactured and cast Al-Si alloys: size and mean stress effects

• Influence of additively manufacturing and casting on microstructure and porosity characteristics as well as quasi-static and cyclic stress-strain behavior of Al-Si alloys • Linear-elastic (LEFM: Murakami, Murakami-Schijve) and elastic-plastic fracture mechanics (EPFM: Fischer) were used for determination of stress intensity factor at failure-initiating defect and plotted in Shiozawa diagrams • LEFM and EPFM enables to consider the size effect within fatigue damage tolerance assessment • Benchmark of Woehler, Murakami, Murakami-Schijve and Fischer approaches for fatigue damage tolerance assessment regarding size effect and mean stress effect, whereby only Fischer approach enables a uniform fatigue damage tolerance assessment The near-net-shape manufacturing in additive manufactured and cast of Al-Si alloys results in a heterogeneous solidification and cooling of the parts, leading to significant gradients in microstructural and defect features as well as deformation behavior. In this paper, an elastic-plastic fracture mechanical model for uniform fatigue damage tolerance assessment of Al-Si alloys was further qualified and extended for a uniform view of different testing volumes as well as various stress ratios between R = -2…0.5 based on the fracture mechanical approaches of Murakami (√area) and Shiozawa for a reliable main crack defect-based mechanical design of fatigue-loaded structures. The linear-elastic fracture mechanical (LEFM) approaches of Murakami, Murakami-Schijve and Shiozawa were used to calculate defect-based lifetime curves, where the cyclic stress intensity factor (ΔK) at the failure-initiating defect (√area) was used to describe the local stress concentration conditions (so-called K-N curves) instead of nominal stress-based S-N curves. The LEFM-based K-N curves did not allow a unified assessment of fatigue behavior. Therefore, the cyclic stress-strain (CSS) behavior (K’, n’) was used for a plasticity-modification of the LEFM approach based on the elastic-plastic fracture mechanical (EPFM) approach of Fischer by calculating the effective cyclic J integral (ΔJ eff ) to plot J-based K-N curves, called Kj-N curves. This EPFM approach could be qualified for a uniform and reliable fatigue damage tolerance assessment of AM and sand cast Al-Si alloys for the HCF regime.

Experimental and Numerical Study of Cyclic Stress–Strain Response and Fatigue Crack Initiation Life of Mid-Carbon Steel under Constant and Multi-Step Amplitude Loading

This paper investigates the fatigue cyclic deformation behavior of mid-carbon steel. Uniaxial tensile loading tests and fatigue tests under constant and multi-step amplitude loading steps are performed to characterize the influence of loading history. The material is shown to exhibit different uniaxial ratcheting behavior depending on loading history. A smooth and gradual increase in cyclic softening is observed under smaller stress/strain conditions. Based on experimental characterization, numerical investigations are carried out to reproduce the cyclic stress–strain behavior under different variable amplitude load ranges. The nonlinear material behavior is reproduced by means of an elastoplasticity model called the Fatigue SS Model (hereafter, FSS model). The main feature of the FSS model is the ability to describe the cyclic softening behavior within a macroscopically elastic stress state. The good agreement between experimental and numerical results proves the reliability of the model to catch a realistic material response in fatigue problems. Furthermore, the present study introduces a method for the prediction of fatigue crack initiation life under variable loading conditions based on cumulative plastic work.

Fatigue crack growth modelling by means of the strain energy density-based Huffman model considering the residual stress effect

In this research work, the modelling of the fatigue crack growth behaviour of the 6061-T651 aluminium alloy through the Huffman fatigue crack growth approach, based on the strain energy density from dislocations and considering the residual stress effects was suggested. The Huffman fatigue crack growth model is based on the cyclic stress–strain behaviour of the material as well as the local elastoplastic stresses and strains obtained for a distance ahead of the crack tip (x), where those stresses are related to the fatigue damage of a crack increment Δa, as calibrator parameter. The calculations of the elastoplastic stresses and strains are done using Neuber’s or Glinka’s approach. Two approaches supported by the Noroozi and Huffman's suggestions to consider the residual stress effects were studied and discussed. Besides, in the modelling of the fatigue crack growth behaviour, the influence of the strain energy density calculated for values of critical dislocation density driven by the highest strain amplitude specimen and the mean value of the dislocation density for the available experimental fatigue results were also considered in this investigation. A comparison between the analytical solutions based on the Neuber and Glinka rules and numerical solutions from the finite element modelling of the CT geometry was done, where a satisfactory agreement for the elastoplastic stress distributions was found. The studied critical dislocation density values do not significantly influence the fatigue crack propagation behaviour. It is also concluded that the procedure for considering the residual stress effects influences the calibration parameter, Δa, being not possible to conclude which is the better method to describe the residual stress effects.

Cyclic elasto-plasticity behavior and fatigue crack initiation lives of low carbon steels and their simulated HAZ.

Fatigue is one of the major causes of structural failure. In particular, the crack initiation and propagation are usually located in correspondence of the welded parts of a structure. Therefore, the correct evaluation and prediction of the fatigue life of welded components is a crucial aspect to avoid unexpected failure and to improve the design and durability of structural parts. The present study focuses on the cyclic stress-strain behavior in the weld heat-affected zone (HAZ), where mostly fatigue cracks are found. In order to investigate the cyclic plasticity behavior of HAZ including cyclic hardening and softening together, experimental and numerical campaigns are carried out. The experimental part of this study deals with the fatigue experiments conducted on test specimens that have undergone the same temperature history to which the heat-affected zone of a weld is exposed (hereafter, simulated HAZ) and the softening and hardening response of base metal, CGHAZ and FGHAZ are observed. Numerical investigations aim to reproduce the cyclic stress–strain behavior simulating the nonlinear material behavior utilizing an elasto-plasticity model called the Fatigue SS Model (hereafter, FSS model). The main feature of the FSS model is the ability to describe the cyclic softening behavior within a macroscopically elastic stress state. The cyclic stress-strain behavior predicted by numerical simulation showed good agreement with the experimental result. Finally, fatigue crack initiation life criteria of SM490A is proposed based on experimental result.

Qualification of uniform fatigue damage tolerance law for additively manufactured and cast Al-Si alloys

The demand on lightweight structures and materials are steadily growing in automotive and aerospace industries. Hypo-eutectic Al-Si alloys are promising candidates due to its high specific material strength and corrosion resistance. Near net shape manufacturing by additive manufacturing (AM) or castings allow a high resource efficiency. The complex geometries lead to a wide range of structural features due to process-induced variations in local cooling rate. Therefore, the relationships between structural characteristics (e.g. dendrites, grain, eutectic, porosity, lack of fusion) and fatigue behavior have to be understood to enable a lightweight and reliable design of Al-Si alloys. In this study, the effect of process and process-induced structural characteristics on stress-strain behavior (quasi-static, cyclic) and high cycle fatigue behavior were characterized. The specimens were processed by laser-based powder bed fusion (PBF-LB) and sand casting (SC) with variation in porosity and dendrite arm spacing. Hereby, the age-hardenable Al-Si alloys AlSi10Mg (AM, SC) and AlSi7Mg (SC) were investigated. AM batches were tested in as-built condition. All casting batches got a HIP densification and T6 heat treatment. The fatigue results were analyzed based on nominal stresses according to Woehler (S-N curve) and local stress intensity based on linear-elastic fracture mechanics (stress intensity factor) as well as elastic-plastic fracture mechanics (J integral). J integral based Shiozawa diagrams allowed a sufficient and uniform fatigue damage tolerance (FDT) assessment for all AM and SC alloys. Hereby, the FDT of Al-Si alloys were dominated by defects (size, position) and cyclic stress-strain behavior (yield strength, cyclic hardening).

Effect of heat treatment on the ratcheting behaviour of additively manufactured and thermo-mechanically treated Ti–6Al–4V alloy

The ratcheting behaviour of the additively manufactured and thermo-mechanically treated Ti–6Al–4V alloy has been investigated. Post heat treatment microstructures of comparable mechanical strength properties have been developed from both the material. Additively manufactured Ti–6Al–4V has a heterogeneous microstructure with defects and residual stresses as compared to the homogeneous microstructure of thermo-mechanically treated Ti–6Al–4V. It has been found that the fatigue life of the as-built additively manufactured sample is less than 50% of the thermo-mechanically treated sample and the fatigue life decreases further after heat treatment. The macroscopic cyclic stress-strain behaviour could not be predicted well using the combined hardening model in the Finite Element Method for the additively manufactured alloy. This has been attributed to the heterogeneous evolution of microscopic strain investigated using the Digital image correlation (DIC) technique. The detrimental effect of heterogeneity of the microstructure on the ratcheting behaviour of the heat-treated additively manufactured alloy has been investigated using the Electron backscatter diffraction (EBSD) technique. It reveals that the presence of multi-variant needle-shaped martensite is effective in increasing the crack propagation resistance and increasing the fatigue life of the as-built additively manufactured alloy as compared to its heat-treated counterparts in which both lamellar and acicular morphology of alpha is prevalent.

Monotonic and Cyclic Stress–Strain Behavior of Uncoated and Coated Superalloy Rene®80 at Elevated Temperature

Monotonic and Cyclic Stress–Strain Behavior of Uncoated and Coated Superalloy Rene®80 at Elevated Temperature

Compound concrete-filled FRP tubular columns under cyclic axial compression

The direct use of large pieces of crushed demolition concrete (referred to as recycled concrete lumps or RCLs) for mixing with fresh concrete to create a new kind of recycled concrete (referred to as compound concrete), has obvious advantages in terms of recycling efficiency, cost-effectiveness and maximum recycling ratio compared with the recycling of concrete as aggregates. Existing research has revealed certain performance concerns with such compound concrete, including reductions in strength and durability, due to the presence of RCLs. The confinement of compound concrete with an external fiber-reinforced polymer (FRP) confining tube has recently been explored as an effective technique to improve its mechanical properties and durability. This paper presents the results of the first ever experimental study on compound concrete filled FRP tubular (CCFFT) columns aimed at the understanding and modelling of the cyclic stress–strain behavior of FRP-confined compound concrete. The effects of RCL mix ratio, FRP tube thickness, and loading scheme are examined. A monotonic stress–strain model and two cyclic stress–strain models previously developed for FRP-confined normal concrete are used to predict the test results. It is shown that the inclusion of RCLs has a marginal effect on the cyclic stress–strain behavior of FRP-confined concrete.

Mechanical behavior of FRP confined rubber concrete under monotonic and cyclic loading

This study investigated the mechanical properties of carbon fiber reinforced polymer (CFRP)-confined rubber concrete under monotonic and cyclic axial compression loading. Thirty-six concrete cylinders were cast with three rubber volume replacement ratios of fine aggregates (0%, 20%, and 30%). Twenty-four rubber concrete cylinders confined with 1 layer and 2 layers of FRP sheets were used to investigate the monotonic and cyclic stress–strain behavior. Twelve unconfined rubber concrete cylinders with different rubber volume replacement ratios Rf were used to determine the compressive strength. The test results show that the rubber volume replacement ratio Rf has an insignificant effect on the failure mode. With the increase in the rubber volume replacement ratio Rf, the compressive strength and ultimate strain of the FRP-confined rubber concrete show a decreasing trend, and the unloading and reloading stiffness of the FRP-confined rubber concrete decreases with increasing rubber content. Finally, a cyclic stress–strain model for FRP-confined rubber concrete was developed by using the test data. The evaluation results show that the proposed model can accurately predict the whole cyclic stress–strain response of FRP-confined rubber concrete.