Ramberg-Osgood Research Articles

A General Temperature-Dependent Stress-Strain Constitutive Model for Polymer-Bonded Composite Materials.

This study develops a general temperature-dependent stress–strain constitutive model for polymer-bonded composite materials, allowing for the prediction of deformation behaviors under tension and compression in the testing temperature range. Laboratory testing of the material specimens in uniaxial tension and compression at multiple temperatures ranging from −40 C to 75 C is performed. The testing data reveal that the stress–strain response can be divided into two general regimes, namely, a short elastic part followed by the plastic part; therefore, the Ramberg–Osgood relationship is proposed to build the stress–strain constitutive model at a single temperature. By correlating the model parameters with the corresponding temperature using a response surface, a general temperature-dependent stress–strain constitutive model is established. The effectiveness and accuracy of the proposed model are validated using several independent sets of testing data and third-party data. The performance of the proposed model is compared with an existing reference model. The validation and comparison results show that the proposed model has a lower number of parameters and yields smaller relative errors. The proposed constitutive model is further implemented as a user material routine in a finite element package. A simple structural example using the developed user material is presented and its accuracy is verified.

Improvement of the Inverse Finite Element Analysis Approach for Tensile and Toughness Predictions by Means of Small Punch Technique

Abstract This paper focuses on the inverse finite element analysis (FEA) to calculate the small punch technique (SPT) tests and the prediction of the tensile and fracture toughness behavior. For the description of the SPT tests via FEA, the hardening rule of Ramberg–Osgood (RO) and the damage model of Gursson–Tvergaard–Needleman (GTN) were used. The inverse FEA optimization process cannot provide a unique solution for the 12 parameters included in the material model. This results from a dependency between some parameters, which leads to the same solution in the optimization. Hence, a novel description of the dependent parameters was developed and implemented within the optimization process. Therefore, an enhanced inverse FEA approach was proposed, which provides a fast converging solution for determination of the material model parameters. Within this study, the forged turbine shaft material EN: 27NiCrMoV15-6 was investigated. For comparison purpose, SPT tests as well as tensile tests and fracture toughness tests were carried out. In the case of the tensile properties, the test and simulation show coincidence in the curve and the characteristic values. For the toughness behavior, the characteristic value of the test was met by the simulation.

Experimental Study on Mechanical Properties of Q690 High Strength Steel in Marine Corrosive Environment

In order to study the mechanical property degradation rule of Q690 high-strength steel in the ocean wave splash area, the rusted specimen is obtained by indoor damp heat surrounding soaking environment corrosion test. The scanning electron microscopy, uniaxial tensile and cyclic loading tests of corroded steel are performed. This paper analyzes the steel from elastic modulus, yield strength, ductility and law of hysteresis degradation under different corrosion cycles and establishes the constitutive model of HSS. The results show that the appearance of HSS is obviously affected by the corrosion cycle. With the increase of the corrosion cycle, reddish-brown flaky corrosion products are formed on the surface of the steel and there are obvious corrosion pits. After 100 days of corrosion, the corrosion rate of steel reached 7.21%; the elastic modulus and yield strength under uniaxial tension load decreased by 10.2% and 4.9%. Under the effect of cyclic reciprocating load, the hysteretic energy is reduced by 15.3%; at the same time, the test curve is fitted by the secondary plastic flow model and the Ramberg–Osgood model and it is found that the shape parameter S1 and the cyclic strengthening coefficient K' are reduced by 20.1% and 10.2%, While the shape parameter S2 and the cycle strengthening index n' have no obvious changes.

Characterisation of material and connection behaviour in sheathed cold-formed steel wall systems – Part 2: Analytical modelling

Analytical models to describe the material and connection behaviour of the key components of sheathed cold-formed steel wall systems are developed and assessed in the present paper. The experimental data generated and collected in the companion paper (Kyprianou et al. [1]) are utilised for the calibration of the developed models. The assembled experimental database comprises the results of more than 400 physical tests, featuring material tests on plasterboard and oriented strand board (OSB), screw connector tests as well such as pull-through and push-out tests. The Ramberg–Osgood model (Ramberg and Osgood [2]) was shown to accurately describe the stress–strain behaviour of both plasterboard and OSB in the longitudinal and transverse direction in both tension and compression, while the Mander model (Mander et al. [3]) was also shown to accurately capture the compression behaviour for both materials and to follow the post peak unloading response. A generalised Ramberg–Osgood curve with linear post-peak unloading was adopted for describing the pull-through load-deformation behaviour of screws in OSB and plasterboard, while a similar generalised Ramberg–Osgood formulation, but with different exponents for the initial and subsequent parts of the curve was shown to accurately capture the shear load-slip behaviour of screws in steel-to-board connections. Predictive expressions for the ultimate capacities and recommended values for the remaining model parameters are provided herein. The developed predictive models are suitable for use in numerical simulations and advanced design methods.

Residual Mechanical Properties and Constitutive Model of High-Strength Seismic Steel Bars through Different Cooling Rates.

In this study, the high-temperature test (i.e., temperature to 1000 °C) is conducted on 600 MPa seismic steel bars, and its residual mechanical properties and constitutive relations are investigated though three cooling rates, i.e., under air, furnace, and water-cooling conditions. Results show that three cooling methods have significant effects on the apparent characteristics of 600 MPa steel bars, when the heating temperature is greater than 600 °C. In addition, the ultimate and yield strength of steel bars have been significantly affected by different cooling methods, with increasing heating temperature. However, the elastic modulus is significantly not affected by temperature. Furthermore, the elongation rate after fracture and the total elongation rate at the maximum force do not change significantly, when the heating temperature is less than 650 °C. The elongation rate, after fracture, and the total elongation rate, at the maximum force, have different changes for three cooling methods. The degeneration of the stress–strain curves occurs when the heating temperature is high. The two-fold line, three-fold line, and Ramberg–Osgood models are developed based on the stress–strain curve characteristics of steel bars after cooling. The fire resistance of 600 MPa steel bars of reinforced concrete structure is analyzed, which provides a basis for post-disaster damage assessment, repair, and reinforcement of the building structure.

Estimation of Correct Long-Seam Mismatch Using FEA to Compare the Measured Strain in a Non-Destructive Testing of a Pressurant Tank

This paper discusses the design criterion of a pressurant steel tank made of HSLA 15CDV6 and proof pressure test (PPT) as a non-destructive examination. An inverse Ramberg-Osgood relation is used to represent the stress-strain curve of the material. Elasto-plastic finite element analysis (FEA) has been carried out to examine the adequacy of the design. Experimental stress analysis has been carried out from the measured strains and found maximum effective stress is at LS joint (max. measured strain location). Strain obtained from FEA is compared reasonably well with the proof pressure test (PPT) data at most of the strain gauge locations except at one long-seam (LS) joint. So, to explain the causes of difference in strains near one LS, parametric studies have been performed in a 3D FEA with varying LS mismatch to find the correct mismatch as a reverse engineering problem. It is found that a mismatch value of 0.9 mm will give the required strain at PPT, which is measured only 0.4 mm. The failure pressure estimated through nonlinear FEA/analytical expressions found to meet the design.

Mean and residual stress effects on fatigue behavior in a pre-strained corner of stainless steel sheet

There are many thin-walled corners in the components of automobiles, machines, and structures. It is essential to elucidate their fatigue properties and influence factors. Parameters for stress–strain behavior of ferritic stainless plane sheet and pre-strained sheet were obtained under tensile, bending, and cyclic bending loads using the Ramberg–Osgood model. The parameters were integrally used as the fundamental characteristics of bending fatigue behavior for obtaining the mean stress and crack initiation stress amplitude from the measured strains in the curved portion of corner specimens. Bending fatigue tests of pre-strained corner specimens were carried out, and the relationships between the crack initiation strain amplitudes and the mean strains were verified. The strain amplitude ratios of the curved inside to outside portion were analyzed. The residual stress and hardness were measured, and work hardening effect on the inside was higher than that on the outside for improving fatigue strength. The fatigue limit of the corner specimen with the radius ratio of 1.3 was 23% higher than the unworked plane sheet. The effects of mean stress and residual stress on the fatigue strength were analyzed using the fatigue limit–static stress relation equations, indicating that the Gerber parabola can be used for fatigue limit predictions in the stress ratio range of R < –0.5 and that the Goodman line can be used after the point of R = –0.5. The SWT function can be used to accurately predict the fatigue lives in various conditions of stress amplitudes combined with static stresses.

Assessment of the Impact of Shot-Peening on the Fatigue Life of a Compressor Blade Subjected to Resonance Vibrations.

This publication presents an assessment of the influence of a surface treatment such as shot-peening on the fatigue life of a compressor blade exposed to resonant vibrations. As part of the work, a geometric model of the blade was developed, and a numerical modal and fatigue analysis were performed. The fatigue analysis was based on the Manson–Coffin–Basquin and Ramberg–Osgood models. Additionally, the location of the highest equivalent stresses was established. Based on the results of the strength analysis, two points were identified where a fatigue crack may potentially occur. As part of the work, the influence of different values of residual stresses on the results of the fatigue life was determined. The obtained results were compared to the literature values of fatigue life for this blade. A secondary objective of the study was to determine the size of the grains at various points of the blade, as well as the thickness of the layer plasticized as a result of peening. The relationship between the location of the highest values of the equivalent stresses and the thickness of the plasticized layer was determined. An explanation of the effect of shot-peening on the increase in the fatigue life of the blade was proposed.

Experimental Investigation of Strain-Rate- and Temperature-Dependent Mechanical Properties of SA516Gr.70 Steel and Development of an Appropriate Material Model

The objective of this work is to develop an appropriate strain-rate- and temperature-dependent material constitutive model to simulate plastic deformation behavior of SA516Gr.70 steel in the sub-zero temperature regime (− 128 to 25 °C). For this purpose, tests have been conducted at three different strain rates covering an order of 6 in the rates, i.e., from 0.001 to 1400/s. Tests at high strain rates have been conducted using a modified split Hopkinson pressure bar test setup. The tensile tests have been designed in such a way that the strain rate remains almost constant during the test. A critical comparison of results of both tension and compression high strain-rate tests has been carried out, and the suitability of tensile experiments has been highlighted. A modified Ramberg–Osgood model, with temperature- and strain-rate-dependent parameters, has been presented. The parameters of the new model have been evaluated from a large set of experimental data. It was observed that the yield stress and ultimate tensile strength of the material increase monotonically with decreasing temperature and increasing strain rates. The ductility at fracture and extent of uniform elongation of the specimen decrease for the intermediate strain rate of 0.925 s−1, when compared to the corresponding values at quasistatic rate of loading. At very high rate of loading, ductility increases due to the increased resistance of the material to growth and coalescence of voids. From the comparison of results of model and experiment, it has been observed that the modified material model is able to predict the true stress–strain curve of the material satisfactorily in the sub-zero temperature regime over a wide range of strain rates. The nature of variation of mechanical properties with temperature and strain rate has been explained from the point of view of dislocation-based micromechanism of the plastic deformation process.

Blast loaded plates: Simplified analytical nonlinear dynamic approach

In this study, a novel simplified nonlinear dynamic method was presented to investigate the blast loaded plates. The material nonlinearity, strain rate, and various boundary conditions were included in the method together with plate geometry, scaled distance, and charge weight. The novelty of this work is that this method is easy-to-use while it covers all the important parameters affecting the blast-related dynamic responses of the isotropic plates. Equations of motion were achieved by applying the Navier solution to the dynamic governing equation of the plate. To include the material nonlinearity, the Ramberg-Osgood model, and hardening behavior were adopted. For the strain rate, the Cowper-Symonds relation was considered. Two types of boundary conditions were considered; simply supported and clamped plates. The scaled distance and charge weigh were included in the description of the blast load while the plate geometry was shown up in the stiffness and frequency of the plate. The method was validated by comparing the time history and maximum deflection of the plates obtained from the proposed method and those of the literature and finite element model through ABAQUS. Thereafter, a parametric study was carried out to examine the effects of plate aspect ratio, thickness, charge weight, and boundary conditions on the dynamic responses of the steel plates. The results showed that the plate deflection had a nonlinear relation with plate thickness, aspect ratio, and explosive charge while the clamped boundary condition resulted in a significant decrease in the maximum plate deflection.

Mechanical properties and modelling of superior high-performance steel at elevated temperatures

Steel structures have been increasingly applied in contemporary infrastructures, which always require high loading capacities and strong resistance to disasters such as earthquake actions, fire and environmental corrosion, etc. Recently a superior high-performance (SHP) steel is developed accordingly, possessing combined beneficial features of high-strength, high-ductility, corrosion-resistance and fire-resistance, which may well satisfy the structural requirements. The present study aims to investigate mechanical properties of the SHP steel at elevated temperatures and to propose its constitutive models for further usage in fire design and analyses of structural members. A comprehensive experimental programme including a series of standard tensile coupon tests at both ambient and elevated temperatures is described herein, and key mechanical properties including modulus of elasticity, yield strength, ultimate tensile stress as well as stress-strain curves of the SHP steels are obtained based on the test results. Reduction effects of elevated temperatures on their mechanical properties are quantitatively clarified, and further comparisons with prediction results in accordance with national standards as well as with independent test results reported in literature are made. It is indicated that the mechanical properties of the SHP steels differ significantly from that of conventional mild steel and fire-resistant steel. Specific prediction equations are proposed for evaluating the temperature-dependent mechanical properties of the SHP steel; furthermore, an adapted Ramberg-Osgood model is developed for describing its full range stress-strain relation. The research outcomes of the present research may serve as an essential basis for better understanding mechanical performance of the SHP steel at elevated temperatures as well as for further investigations on its structural members' behaviour; and it is helpful to promote its application in practice.

Determination of local true stress-strain response of X80 and Q235 girth-welded joints based on digital image correlation and numerical simulation

The girth-weld joint of a pipeline can be divided into three parts: base metal, heat affected zone, and weld metal. This study investigates the local mechanical properties of X80 and Q235 girth-welded joints. Microscopic observations and micro-hardness measurements were carried out, and it was observed that the metallographic structure and hardness gradients of each region were evidently different. Tensile tests of the base metal and girth-welded joint were conducted using digital image correlation (DIC) technology, and the strain distributions on the specimens and local true stress-strain curves of different regions were obtained. A parameter calculation method for the Ramberg-Osgood model considering strain was proposed. Subsequently, model parameters and mismatch coefficients were obtained and analyzed, respectively. The yield strength and hardening property of welded joints can be determined using this method, which is of great significance in calculating the strength-matching relationship of girth-welded joints. Finite element analysis based on the Gurson-Tvergaard-Needleman model was used to study the strain field and local stress-strain curves of girth-welded joints. The results obtained by the finite element analysis were in line with the results obtained by the DIC method. This demonstrates the feasibility of the simulation method and that the proposed material model is reasonably accurate in predicting the stress-strain response.

A full-range stress-strain model for metallic materials depicting non-linear strain-hardening behavior

Ramberg-Osgood (R-O) type stress-strain models are commonly employed during elasto-plastic analysis of metals. Recently, 2-stage and 3-stage R-O variant models have been proposed to replicate stress-strain behavior under large plastic deformation. The complexity of these models increases with the addition of each stage. Moreover, these models have considered deformation till necking only. In this paper, a simplistic multi-stage constitutive model is proposed to capture the strain-hardening non-linearity shown by metals including its post necking behavior. The constitutive parameters of the proposed stress-strain model can be determined using only elastic modulus and yield strength. 3-D digital image correlation was used as an experimental tool for measuring full-field strains on the specimens, which were subsequently utilized to obtain the material parameters. Our constitutive model is demonstrated with an aerospace-grade stainless steel AISI 321 wherein deformation response averaged over the gauge length (GL) and at a local necking zone are compared. The resulting averaged and local material parameters obtained from the proposed model provide interesting insights into the pre and post necking deformation behavior. Our constitutive model would be useful for characterizing highly ductile metals which may or may not depict non-linear strain hardening behavior including their post necking deformations.

Nonlinear tensile behavior of cotton fabric reinforced polypropylene composites

AbstractFrom the perspectives of elastoplasticity (nontime‐dependent) and viscoelasticity (time‐dependent), the Ramberg–Osgood relation and time‐varying viscosity Maxwell (TVM) models were used to model and analyze the stress–strain behavior of cotton fabric‐reinforced polypropylene composites (CFRLs), respectively. The Ramberg–Osgood relation could well describe the tensile behavior of CFRLs as an elastoplastic behavior, while the tensile behavior could also be described as a nonlinear viscoelasticity behavior by Maxwell model. The fitting results showed that the Maxwell model accurately described the tensile behavior of different CFRLs samples under low strain, but there was a considerable gap between the test data and model values when the strain was greater than 5%. Therefore, a time‐varying viscosity fluid damper was used instead of a Newtonian fluid damper to modify the Maxwell model, namely the TVM model. The TVM model closely described the stress–strain behavior during the entire tensile process.

Local mechanical properties of explosively welded AA2519-AA1050-Ti6Al4V layered material

The study presents the results of tests of local static and cyclic properties of an explosively welded AA2519-AA1050-Ti6Al4V layered material. In order to perform the analysis, tests were carried out with the use of microspecimens collected from 10 layers of AA2519-AA1050-Ti6Al4V material. Additionally, the determined static properties were compared with the results of an analysis based on microhardness measurement. Based on the test results, slight differences in static properties were found for particular layers of the material as well as a distinct softening of the AA2519 layer in relation to the base values. It was also found that the application of microhardness measurement for analysis of static properties can lead to their overestimation. Cyclic properties were described by the Ramberg-Osgood model. As in the case of static properties, the cyclic properties of particular layers of AA2519-AA1050-Ti6Al4V material differ insignificantly. The tests of cyclic properties showed that application for their description the Ramberg-Osgood model, based on parameters determined for whole range of plastic strains, can lead to significant errors in the modeling of a layered material. The cyclic instability of Ti6Al4V and AA2519 alloys has a significant influence on the parameters to be determined for material models of the analyzed material.

Finite element modeling of RC beams externally strengthened with iron-based shape memory alloy (Fe-SMA) strips, including analytical stress-strain curves for Fe-SMA

Research into the application of iron-based shape memory alloys (Fe-SMA) for strengthening existing structures has boosted in recent years. The shape memory effect of this material can be used to introduce prestressing forces, improving the behavior of the retrofitted structures. However, knowledge about these alloys is still limited and more research is needed. This paper proposes analytical stress-strain curves for Fe-SMA based on the modified Ramberg-Osgood models for nonlinear materials, and taking into account the differences observed according to the material’s initial state. The degree of roundedness and the level of strain hardening vary depending on the initial state, achieving in all cases a satisfactory agreement between analytical expressions and experimental curves. Moreover, these curves have been implemented into a nonlinear finite element model developed to reproduce the response of reinforced concrete beams strengthened upon shear using external Fe-SMA strips that have been previously tested by the authors. The numerical results of the finite element analysis show a very good correlation with the experimental behavior observed during the tests.

Mechanical properties of laminated bamboo under off-axis compression

To investigate the compression performance of laminated bamboo, 210 laminated bamboo specimens were tested using seven different lamination angles. Six failure types were classified. All the specimens experienced elastic stage at the beginning of the loading process and then elastic-plastic stage. At the end of the elastic-plastic stage, specimens of 15°, 30° and 45° immediately reached the ultimate bearing capacity, showing brittle failure, while other specimens entered a longer plastic stage before failure. The off-axis compression strength and the apparent elastic modulus both decreased with the increment of the angle. Two empirical formulas were proposed to predict the off-axis compression strength and apparent elastic modulus of laminated bamboo compared with several well-known failure criteria. The Poisson’s ratio in A/C planes increased with the increment of the angle while in B/D planes, it increased and peaked at 30° before decreasing. Based on Ramberg-Osgood relation, the compression and shear stress-strain curves were fitted.

Characterization and Model Validation for Large Format Chopped Fiber, Foamed, Composite Structures Made from Recycled Olefin Based Polymers.

The purpose of this research is to predict the material performance of large format foamed core composite structures, such as crossties or structural timbers, using only constitutive properties. These structures are fabricated from recycled post-consumer/post-industrial waste composed of High-Density Polyethylene (HDPE) and Glass Filled Polypropylene (GFPP). A technical challenge in predicting the final part performance is the mathematical correlation between the microstructural variations and the macroscopic responses as a function of fiber aspect ratio, cell density, and constitutive properties of the polymer blend. The structures investigated have a dense and consolidated outer shell and a closed cell foamed core. The non-linear shell and the foamed core material properties are analyzed with micromechanics models, and the reference stress of the shell and core is predicted using a modified Rule of Mixtures model. The predicted properties are used as the inputs for a Finite Element Analysis (FEA) model, and the computational results are compared to experimental four-point bend test results for sixteen samples performed on a 120-kip compression stage. The results show that the mean of the characterized deflections from the four-point bend tests did not show any variations for an isotropic and transversely isotropic model using a linear analysis. This model was then extended to a non-linear analysis using the Ramberg–Osgood model to predict the full crosstie four-point bend test behavior. The FEA model results show a deviation of 2.45 kN compared to the experimental variation of 3.58 kN between the samples measured.

Local Constitutive Behavior of Undermatched Welded Joints in Pipeline Steel Using Digital Image Correlation Technology

Abstract Although the identification of local constitutive behaviors is possible based on digital image correlation (DIC), few studies have been reported that characterize the properties of the girth-welded joints of pipeline steel. The DIC technique was used to measure the strain fields of undermatched girth-welded joints of X80 pipeline steel under uniaxial tension in this paper. First, microstructure optical observations and micrometer hardness measurements were used to test the size and hardness of the subregions in the specimens. Second, the local strain data in different regions of the girth-welded joint were obtained via DIC technology, and the stress data were obtained via uniaxial tensile tests. Then, the stress–strain relationships of the weld metal (WM), base metal (BM), and subregions of the heat-affected zone (HAZ) of the girth-welded joints of pipeline steel were obtained. Finally, the constitutive parameters of the Ramberg–Osgood model in the different regions were determined by curve fitting of the strain and stress data. The local yield strength, elastic modulus, and hardening exponent of the welded joints were obtained. The yield stresses of the different subregions of the welded steel joint followed the sequence BM &amp;gt; WM &amp;gt; HAZ, which was consistent with the results of the hardness measurements. The hardening exponents of the different subregions of the welded steel joint followed the sequence HAZ &amp;gt; WM&amp;gt; BM.

Cyclic behavior and constitutive model of high strength low alloy steel plate

Cyclic loading tests with different protocols were conducted for a high strength low alloy steel. Based on the test results, the low cycle fatigue and extremely low cycle fatigue performance of the high strength steel was discussed and an appropriate constitutive model was established. The experimental results implied that the low and extremely cycle fatigue failure showed different fracture features. For low cycle fatigue, there was a strong negative linear correlation between the fatigue life and the strain amplitude in the log–log scale. However, they did not conform the linear relation when transiting to the low cycle fatigue. The steel represented obvious cyclic softening and good energy dissipation capacity. With the increase of strain amplitude, the softening degree decreased and equivalent damping ratio increased. The cyclic stress–strain curve could be descried by the Ramberg-Osgood model, and the strength coefficient and strain hardening exponent of this steel were larger than those of steel with lower strength. A combined hardening model was calibrated to describe the cyclic plasticity of the steel, and it was verified by the simulation results.