Ramberg-Osgood Research Articles

Full-Range Moment–Curvature Relationships for Beams Made of Low-Hardening Aluminium Alloys

Aluminium alloys are characterised by a rounded stress–strain relationship, with no sharply defined yield point. For example, aluminium alloy grades 6061-T6, 6082-T6, and 7075-T6 exhibit low-hardening response, which is close to linear elastic-linear plastic hardening characteristics. Commonly, the behaviour of aluminium alloys is described by Ramberg–Osgood (RO) one-dimensional constitutive relationship in the format of strain in terms of stress. In the case of low-hardening response, an alternative Richard–Abbott (RA) relationship of stress as a function of strain can be used. Both relations are analytically irreversible, but the RA is more appropriate for use in slender beams theory. In the present study, we use the latter function to derive moment as an explicit function of curvature for the sectional relation of beams. Since the obtained relation is expressed via special functions, we also propose its close approximation, which is more useful for practical purposes. It is uncomplicated and reasonably accurate compared to available models. The predictive capabilities of the new moment–curvature models developed in this article are verified with experimental results available in the literature for beams tested under four-point and three-point bending. In the case of four-point beams, predictions show very good agreement with experiments, while for three-point bending of beams, higher discrepancies are observed.

Damage Evolution Mechanism of Railway Wagon Bogie Adapter 1035 Steel and Damage Parameter Calibration Based on Gursone-Tvergaarde-Needleman Model.

As a critical component of a train, the railway wagon bogie adapter has higher quality requirements. During the forging process, external loads can induce voids, cracks, and other defects in the forging, thereby reducing its service life. Hence, studying the damage behavior of the forging material, specifically AISI 1035 steel, becomes crucial. This study involved obtaining stress-strain curves for AISI 1035 steel through uniaxial tensile tests at temperatures of 900 °C, 1000 °C, and 1100 °C, with strain rates of 0.1 s-1, 1 s-1, and 10 s-1. Subsequently, SEM was used to observe samples at various deformation stages. The damage parameters, q1, q2 and q3 in the GTN model "a computational model used to analyze and simulate material damage which can effectively capture the damage behavior of materials under different loading conditions" were then calibrated using the Ramberg-Osgood model and stress-strain curve fitting. Image Pro Plus software v11.1 quantified the sample porosity as f0, fn, fc and fF. A finite element model was established to simulate the tensile behavior of the AISI 1035 steel samples. By comparing the damage parameters of f0, fn, fc and fF obtained by the finite element method and experimental method, the validity of the damage parameters obtained by the finite element inverse method could be verified.

Measurement of Interlaminar Shear Properties of Pultruded CFRP Composites Based on Modified DNS Specimens

A double-notch shear (DNS) test was modified for a measurement of interlaminar shear properties of pultruded carbon-fibre-reinforced polymer (CFRP) composites under moderate through-thickness compressive stresses, which were applied by torqued bolts. A range of failure criteria were presented to compare with experimental results. An attempt was made to predict the shear stress-strain relationship in the combined stresses with through-thickness compressive and shear stresses. Results indicate that the modified 2DNS specimen makes the shear surface of the specimen more uniform and reduces the peel stress at the notch tip. The 2DNS fixture made it easier to study the influence of composite interlaminar shear strength and shear stress-strain relationship under moderate through-thickness compression. The initial shear stiffness was not affected by moderate through-thickness compressive stresses. Moderate through-thickness compressive stresses on pultruded CFRP materials can increase interlaminar shear strength and ductility. Of all the failure criteria, the Mohr-Coulomb criterion was preferred to predict the enhancement of the shear strength under moderate through-thickness compression. Based on the Mohr-Coulomb criterion and the inverse solution of Ramberg-Osgood model, a unified equation was proposed and can effectively characterise the interlaminar shear stress-strain relationship under moderate through-thickness compression.

Research on the Vibration Fatigue Characteristics of Ancient Building Wood Materials

In this study, we selected ancient building timber as the research object. A series of static load tests were conducted to analyze the different performances of timber under tensile and compressive loads. After that, vibration fatigue tests on ancient timber samples were carried out under different upper limit stress ratios. Finally, a dynamic constitutive model of ancient timber was established based on the Ramberg–Osgood model. The static load test results show that the tensile strength was approximately 80% of the compressive strength. Meanwhile, the samples that failed under compressive pressure had obvious residual strength, and their failure strains were also much larger than those under tensile stress. In the vibration fatigue tests, the stress–strain curves were analyzed and the results showed that the curves displayed a trend moving to sparse from dense during the loading process. Meanwhile, the curves moved right with the increase in the upper limit stress ratios. The relationship between axial strain and the number of cycles appeared to be characterized by a three-stage form, i.e., damage occurrence, damage expansion, and damage penetration, and this relationship was formulated by a nonlinear function model. Finally, a dynamic constitutive model with high accuracy in describing the vibration fatigue characteristics of ancient timber was established by converting constant parameters to the variable parameters of the Ramberg–Osgood model.

Integrating parametric HFGMC and isogeometric RZT[formula omitted] for multiscale damage modeling of composite structures: A numerical and experimental study

In this research effort, a novel multiscale analysis scheme is proposed for damage modeling of composite laminates, sandwich structures, and stiffened plates relying on capabilities of the parametric HFGMC and isogeometric RZT{3,2} formulations. The Ramberg Osgood (RO) model is incorporated into the micromechanics model to reflect polymer matrix material nonlinearities on the overall homogenized composite behavior. Carbon fibers are assumed to behave in a linear transversely isotropic manner. The higher order RZT{3,2} theory employed at the macro level facilitates efficient applicability of the model to thick composite laminates and soft core sandwiches. On the other hand, it generates all three-dimensional stress components and thus ensures dimensional consistency between micro and macro levels. Numerical discretization and prediction of RZT{3,2} kinematic variables are enabled by performing NURBS based isogeometric analysis (IGA) thereby enhancing modeling efficacy to a significant degree. Soft core plasticity and failure in the composite are evaluated at the macro level through the RO model and Hashin criteria, respectively. Applicability of the method is presented for thin and thick flat composite and sandwich laminates; and further extended to stiffened plates via developing a multipatch formulation. A comprehensive validation of our analysis is conducted by comparing the results with established benchmarks from the literature, experimental data, and three-dimensional finite element method (3D-FEM) simulations. Initially, a moderately thick, simply supported square laminate under transverse loading is examined, a common verification benchmark. Then, results from standard mechanical tests, including tensile, shear, and four-point bending tests on thin laminates, followed by experiments on moderately thick sandwich structures subjected to four-point bending, are presented. Finally, the analysis is extended to a stiffened plate under uniform pressure, demonstrating the method’s accuracy and applicability across diverse structural configurations.

EVALUATION OF THE BEHAVIOR OF WELDED STRUCTURES UNDER LOW-CYCLE FATIGUE LOADING

Welded structures are exposed to constant variable loads during their exploitation in real conditions. A variable load affects the integrity and life of a welded structure; therefore, it is of practical importance to understand fatigue behavior, especially the behavior of welded structures under the impact of low-cycle fatigue. The effect of low-cycle fatigue is very prevalent in structures and an assessment of cyclic loading of a material entails modifications of its properties and characteristics related to the dependence of stress and strain. Since the stress-strain response during low-cycle fatigue is in the form of a hysteresis loop, this paper presents the application of one of the two most common relations for testing resistance to low-cycle fatigue, the Ramberg-Osgood relation, which is used to evaluate the behavior of a material, in this case a high-strength low-alloy steel welded joint.

Constitutive model and mechanical properties of grade 1960 steel wires under fire and post-fire conditions

The structural performance of the bridges under fire accidents has gradually become one of the hot issues in bridge safety. The fire resistance of the cables is a critical factor in the structural performance of cable-stayed bridges. The mechanical properties of 1960 high-strength steel wires at elevated temperatures were investigated in this paper. Tensile tests on steel wires were performed at various high temperatures and after cooling. The failure modes and mechanical properties of steel wires after heating and cooling were investigated in detail. The results show that mechanical properties such as yield strength and ultimate strength are continuously degraded as temperature rises at both high-temperature and after-cooling test, while elastic modulus and elongation are not changed significantly after heating–cooling process. A constitutive model was proposed based on two-segment Ramberg–Osgood model for both high temperature and cooling processes. It is shown that the proposed model well reflects the material behavior for both processes.

Experimental study of in-fire and post-fire material response of high-strength aluminium alloys

This paper presents an experimental study on the residual material properties of high-strength aluminium alloys in and after fire. A testing programme was firstly conducted on grade 7075-T6 high-strength aluminium alloy, consisting of 13 in-fire and 24 post-fire coupon tests, to derive the material stress-strain responses at and after exposure to elevated temperatures ranging from 20 °C to 550 °C. The key temperature-dependent material properties including stiffness and strengths were determined from the measured stress-strain curves and normalised by their room-temperature counterparts, resulting in a series of in-fire and post-fire retention factors. These experimentally obtained retention factors were used to analyse the effects of elevated temperatures on the residual stiffness and strengths of high-strength aluminium alloys. The design in-fire retention factors, as given in the European, American and Chinese standards, and the existing predictive models in previous studies for the post-fire retention factors, were also quantitatively and qualitatively assessed based on the test data. They were found to be inapplicable due to less accuracy; especially when used for predicting the in-fire Young's moduli, a 25 % over-prediction can be yielded, leading to unsafe design. To address the shortcoming, a series of predictive models were developed to offer accurate predictions of the in-fire and post-fire residual stiffness and strengths of high-strength aluminium alloys, with the mean test-to-prediction ratios ranging from 0.995 to 1.074 for different in-fire and post-fire material properties and the design accuracy improved by at least 15 % than existing design models. Then, a two-stage Ramberg-Osgood material model that was proposed for describing the room-temperature stress-strain curves of structural aluminium alloys was considered in this study, with its applicability to high-strength aluminium alloys assessed. The considered Ramberg-Osgood model was found to well predict the in-fire and post-fire stress–strain curves of high-strength aluminium alloys. The proposed models for retention factors and stress–strain curves can be further assessed based on more test data on other new high-strength aluminium alloy grades. Future research can focus on developing new coating technologies and optimising existing treatments to improve the fire performance of high-strength aluminium alloy structures.

Low-cycle fatigue behaviour of ribbed 1.4362 duplex stainless steel reinforcement

To investigate the fatigue behaviour of stainless steel (SS) reinforcement, monotonic tensile and cyclic fatigue loading tests on 1.4362 duplex SS bars with diameters of 12 mm, 16 mm, and 20 mm are conducted. To keep the characteristics of reinforcement used in engineering construction, the specimens remain unprocessed. Two loading schemes for cyclic tests are considered in this work: (i) constant strain-amplitude, and (ii) variable strain-amplitude. The Ramberg-Osgood model was used to fit the experimental results. The strain-based and energy-based fatigue life equations are obtained. The strain-based fatigue life equation is compared with the present fatigue life estimation equations. Moreover, the ReinforcingSteel material model in OpenSees is calibrated with the experimental data. The results show that SS bars under cyclic experience hardening followed by softening. The bar diameter does not significantly affect the fatigue life prediction. The modified fatigue life equation suggests that SS bars have better fatigue resistance than conventional steel (CS) bars. The numerical analysis indicates that the calibrated steel material model (i.e. ReinforcingSteel) can produce a good simulation of SS bars under cyclic loading. It can improve the accuracy of numerical models of concrete components reinforced by SS bars.

Effects of aluminum alloy constitutive models on the behavior of concrete-filled aluminum tubular stub columns under axial compression

This study aims to examine the effects of various aluminum alloy constitutive models on the behavior of concrete-filled aluminum tubular stub columns under axial compression. The bi-linear model with hardening, the Baehre model, and the Ramberg-Osgood (R-O) model, which follow the European standard (EC9) were analyzed and compared in terms of their ability to describe the stress-strain behavior of aluminum alloy tensile coupons over the full range, and their respective application scenarios were discussed. A total of 74 sets of experimental data results were collected to examine the effects of these three models on the ultimate load of concrete-filled aluminum tubular stub columns. Furthermore, a full-scale model was constructed to analyze the effect of the hardening exponent n in the R-O model on the load-displacement curves. The results show that, apart from the bi-linear model with hardening, the other two aluminum alloy constitutive models are capable of accurately predicting the stress-strain behavior of aluminum alloys throughout the full range. The accuracy of the R-O model is significantly influenced by the calculation methods of n. The Baehre model is found to be more suitable for non-heat-treated aluminum alloys. The simulated ultimate load values obtained from the three constitutive models fall within a deviation range of ±10%, indicating their suitability for practical engineering applications. Among the three models, the R-O model exhibits the highest stability, as changes in the hardening exponent n do not affect the ultimate load but have a significant effect on the load-displacement curves beyond the ultimate load.

Cyclic behavior and constitutive relations of HRB400E steel under large strain range

To study the differences in material performance between HRB400E steel and conventional strength steel, this paper performed monotonic and cyclic loading tests on HRB400E and Q355B steels under a series of loading protocols. Additionally, the self-designed fixtures were used to achieve large strain rate loading. The ductility, monotonic behavior and hysteretic characteristics of HRB400E and Q355B steels were assessed, along with the energy dissipation capacity evaluated through the energy dissipation coefficients. The cyclic skeleton curves of both steels were fitted using the Ramberg-Osgood model, with further investigation into the influence of kinematic hardening parameters on hysteretic curves. The combined hardening parameters of the Voce-Chaboche model were calibrated based on the experimental results, and the hysteretic curves were simulated under different loading protocols via ANSYS. The analysis results reveal that the energy dissipation coefficients of HRB400E steel are larger than that of Q355B steel, yet smaller than those of Q460D, LYP100, LY100, LY160, and LY225 steels. Both HRB400E and Q355B steels demonstrate significantly improved material strength under cyclic loading. Excellent agreement between simulated and experimental curves is achieved when using four pairs of kinematic hardening parameters. Additionally, the hysteretic performance of HRB400E and Q355B steels under different cyclic loading protocols can be precisely simulated by employing calibrated combined hardening parameters. Through this paper, the cyclic behavior and constitutive relations of HRB400E steel are comprehensively understood, which provides a reliable theoretical basis for engineering design and structural analysis. Furthermore, this research provides a scientific basis for material applications of HRB400E steel.

Experimental study on mechanical behaviour of friction stir welded aluminium alloy butt joints

The purpose of this paper is to understand the softening extent and stress-strain behavior of the normal-strength 6061-T6, 6013-T6, and high-strength 7075-T6 aluminium alloy butt joints using the novel friction stir welding (FSW) technique. A total of 107 monotonic tensile coupons and 33 Vickers hardness coupons were prepared from 8- or 12-mm thick welded plates using various tool rotation speed, welding transverse speed and tool configurations. The surface morphology, stress-strain curves and hardness distribution laws after welding were evaluated. The W-shaped hardness profiles were clearly observed, with the fracture location positively correlated at the lowest point of Vickers hardness near the edge of the weld toe. The strength reduction and softening extent of extruded aluminium alloys in T6 temper induced by FSW were superior to those of aluminium alloys using fusing welding process outlined in the Chinese and European standards, indicating the effectiveness and applicability of the FSW technique in the formation of components and connections for aluminium alloy structures. Additionally, the current widely used constitutive models generally yielded under-estimations on the strength under large strains. The developed three-stage Ramberg-Osgood model, using seven key input parameters, significantly improved the accuracy and consistent predictions in the full-range stress-strain curve of FSW aluminium alloys. Furthermore, the suggested model could still achieve a great balance between accuracy and practicality when using just three common available parameters with the employment of predictive expressions on other four parameters.

Effect of Empirical Constant of Ramberg-Osgood Relation on the Buckling Strength of Transformer Inner Winding

Effect of Empirical Constant of Ramberg-Osgood Relation on the Buckling Strength of Transformer Inner Winding

Mechanical properties of a novel high nitrogen and low nickel stainless steel S35657

Stainless steel exhibits excellent ductility and corrosion resistance, making it highly promising for applications in civil engineering. In order to investigate the mechanical properties of a novel stainless steel S35657, a total of 150 coupons including 125 plates and 25 rods were tested. The failure modes, stress-strain curves, and mechanical parameters of coupons were obtained. Fractographic analysis using scanning electron microscopy was also performed to investigate the failure mechanisms. It was found that all coupons exhibited ductile failure mode with elongation up to 52.08%. The nominal yield strength standard value reached 370.50 MPa, while the ultimate tensile strength standard value reached 736.07 MPa. The various existing typical constitutive models were assessed, indicating that these models provide a good fit in the elastic stage but are not applicable in the hardening stage. Based on the Ramberg-Osgood model and test results, a new constitutive model applicable to stainless steel S35657 was proposed. Moreover, a design reliability analysis was carried out using the Equivalent Normalization Method (JC method), and partial factors for resistance of stainless steel S35657 were calibrated, which were 1.05 under windless load combinations and 1.15 under windy combinations.

Experimental research on mechanical, material, and metallurgical properties of Inconel 600: Application in elevated temperature environment

Experimental research on mechanical, material, and metallurgical properties of Inconel 600: Application in elevated temperature environment

Cyclic mechanical behavior of electro-welded meshes used as structural reinforcement

In this work, the monotonic and cyclic behavior of 6, 7 and 8 mm diameter electro welded meshes manufactured in Colombia and used as reinforcement in construction is studied experimentally. The cyclic mechanical behavior of the material is modeled using the Ramberg-Osgood model, and the model parameters are adjusted based on experimental data and using linear regression. The results show that the material undergoes cyclic softening, and that the Ramberg-Osgood Ramberg -Osgood model accurately predicts the monotonic and cyclic mechanical behavior.

Strain-dependent-deformation property of Gyeongju compacted bentonite buffer material for engineered barrier system

This study aims to investigate the strain-dependent-deformation property of Gyeongju bentonite buffer material. A series of unconfined compressive tests were performed with cylindrical specimens prepared at varying dry densities (ρd = 1.58 g/cm3 to 1.74 g/cm3) using cold isostatic pressing technique. It is found that as ρd increase, the unconfined compressive strength (qu), failure strain, and elastic modulus (E) of Gyeongju compacted bentonite (GCB) increases. Normalized elastic modulus (Esec/Emax) degradation curves of GCB specimens are fitted using Ramberg-Osgood model and the elastic threshold strain (εe,th) is determined through the fitted curves. The strain-dependency of E and Poisson's ratio (v) of GCB were observed. E and v were measured constant below εe,th of 0.14 %. Then, E decreases while v increases after exceeding the strain threshold. The Esec/Emax degradation curves of GCB in this study suggests wider linear range and higher linearity than those of sedimentary clay in previous study. On top of that, the influence of ρd is observed on Esec/Emax degradation curves of GCB, showing a slight increase in εe,th with increase in ρd. Furthermore, an empirical model of qu with ρd and a correlation model between qu and E are proposed for Gyeongju bentonite buffer materials.

Memory-Element-Based Hysteresis: Identification and Compensation of a Piezoelectric Actuator

Hysteresis phenomena can significantly deteriorate the performance when performing servo tasks with piezoelectric actuators. The aim of this brief is to model this nonlinear hysteresis effect and use this model to develop a feedforward controller that compensates for the hysteretic behavior. Exploiting the dual-pair concept, a connection is established between hysteresis models and general memory (MEM) elements examplified by the Ramberg–Osgood model. This facilitates both a straightforward identification procedure of a hysteresis model and a feedforward controller design. Both the identification procedure and the feedforward controller are implemented on a piezoelectric actuator indicating a performance improvement by a factor 3.5.

Simplified constitutive model of austenitic stainless steel at high temperatures

Based on completed experimental data and constitutive models, we proposed the simplified constitutive model of austenitic S30408 (AISI304) stainless steel at high temperatures. According to continuous trial calculation and analysis fined that the simplified constitutive model can be divided into two segments. In the first segment, the Ramberg-Osgood model (R–O model) was adopted, while the second segment was represented using a straight-line expression. Next, simplified constitutive model was obtained by nonlinear fitting using Matlab. Based on this, FEA models were created, incorporating the simplified constitutive model, refined constitutive model, and constitutive model fitted based on experimental data from other literature. Using the sequential therm-mechanical coupling analysis method, the FEA of the fire-resistant performance of three specimens including simply supported stainless steel rectangular beam, restrained rectangular stainless steel column and restrained stainless steel H-section columns, was carried out and compared. The conclusions drawn were as follows: For members at low temperatures, when the strain value is small, the deformation and force calculated using simplified constitutive model is not much different from that using the constitutive model fitted based on experimental results. For members at high temperatures, when the strain value is large, the deformation and force calculated using simplified constitutive model deviates from that using the constitutive model fitted based on experimental results, but deviation is within an acceptable range. Therefore, the simplified constitutive model demonstrates both feasibility and accuracy, making it suitable for calculating the fire resistance of specimens.

Grain-Scale Study of SAC305 Oligocrystalline Solder Joints: Anisotropic Elasto-Plastic Constitutive Properties of Single Crystals

Abstract This paper focuses on anisotropic elastic-plastic constitutive modeling of SAC (SnAgCu) solder grains because of their importance in modeling the behavior of oligocrystalline (few-grained) micron-scale solder joints that are increasingly common in heterogeneous integration. Such grain-scale anisotropic modeling approach provides more accurate assessment of the mechanical response of solder interconnects in terms of predicting different failure modes, failure sites, and variability in time-to-failure. Anisotropic plasticity is represented using Hill–Ramberg–Osgood (RO) continuum plasticity model, which utilizes Hill's anisotropic plastic potential along with a RO power-law plastic hardening flow rule. Mechanistically motivated empirical scaling factors are proposed to extrapolate the stress–strain response for different grain sizes/shapes and for different coarseness of microstructures within each grain (generated with different cooling rates). This scaling factor can therefore also capture the effects of microstructural coarsening due to isothermal aging. This goal is achieved by first conducting monotonic tensile and shear tests on monocrystalline and oligocrystalline SAC305 solder joints containing grains of various geometries and also intragranular microscale (dendritic and eutectic) structures of various coarseness. The grain structures are characterized for each tested specimen using electron backscattered diffraction (EBSD). The Hill–RO model constants and the empirical scaling factors are then estimated by matching grain-scale anisotropic elastic-plastic finite element models of each tested specimen to the measured stress–strain behavior, using an inverse-iteration process. Grain shape is seen to influence the sensitivity of the effective stress–strain curves to the applied stress state (i.e., to the orientation of the principal stress directions) relative to (i) the material principal directions and (ii) the geometric principal directions of grains with high aspect ratio. Limitations of the current results and opportunities for future improvements are discussed.