Ramberg-Osgood Material Model Research Articles

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 oC to 550 oC. 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. The 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.

The structural strain method for fatigue evaluation of welded components: closed-form solutions

A consistent and unified analysis framework is proposed in this paper for extending the early traction-based structural stress method to low-cycle fatigue regimes in fatigue evaluation of welded structures through a novel structural strain method. Instead of local strain or notch strain, the structural strain here refers to a through-thickness strain distribution that satisfies plane-remains-plan conditions under elastic–plastic deformation conditions. This paper provides closed-form solutions to structural strain distributions corresponding to loading and unloading, structural strain range, an equivalent structural strain range, and the structural stress–strain relation by considering elastic-perfectly plastic material behavior. Both finite element method (FEA) simulations and in-house modeling tools confirm the accuracy of these closed-form analytical solutions. Although these solutions are derived based on elastic-perfectly plastic material assumption, the resulting structural strain range, as a unique fatigue damage parameter for welded components, is shown essentially the same as those obtained numerically by considering a modified Ramberg-Osgood material model under pulsating loading condition, i.e., stress ratio equals zero. Good data correlation between the equivalent structural strain range predicted results and the test results obtained for a welded steel structure under the same loading condition is achieved. Finally, the structural strain range-based parameter is proven effective in correlating a large number of both low-cycle and high-cycle fatigue test data of welded structures made of several structural materials into a narrow scatter band demonstrating the universality of the structural strain method.

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.

Verification of the Ramberg-Osgood Material Model for the Fire Design of Steel Members

Abstract In this paper, the modified Ramberg-Osgood constitutive equations for calculating the stress-strain of steel at elevated temperatures using the parameters determined based on the transient state tensile test results achieved at the Helsinki University of Technology are verified. This is done by numerically comparing the global and local buckling capacities of I-shaped steel members incorporating the modified Ramberg-Osgood model along with the material model given in the fire section of Eurocode EN1993-1-2. For this purpose, a numerical model using the ABAQUS software was developed. Then, nonlinear analyses with imperfections (GMNIA) were performed to compare the buckling capacities of the steel columns and beams of four different hot-rolled cross-sections (IPE160, IPE180, HE100B, HE500B), made of steel grade S355, at three different temperatures (400°C, 500°C, 600°C). The results showed that adopting the modified Ramberg-Osgood model can lead to the same buckling capacities resulting when using the EN1993-1-2 material model for steel temperatures of less than 400°C. However, adopting this model for 600°C overestimates the buckling capacities in most cases.

Use of the Modified Ramberg-Osgood Material Model to Predict Dynamic Modulus Master Curves of Asphalt Mixtures.

Dynamic modulus master curves are usually constructed by using sigmoid functions, but the coefficients of these functions are not independent of each other. For this reason, it is not possible to clearly identify their physical mean. Another way of describing the dynamic modulus master curves is to choose the Ramberg-Osgood (RAMBO) material model, which is also well-suited for modelling the cyclic behaviour of soils. The Ramberg-Osgood model coefficients are completely independent of each other, so the evaluation of the fitted curve is simple and straightforward. This paper deals with the application of the Ramberg-Osgood material model compared to the usual techniques for constructing a master curve, determining the accuracy in describing the material behaviour of asphalt mixtures, and seeking any surplus information that cannot be derived by traditional techniques. Because the dynamic modulus and phase angle master curves are strictly related, in the present study, the asymmetric bell-shaped frequency curve of Toranzos was used to describe the phase angle for four types of asphalt mixtures (RmB, PmB, RA, and NB). The results show that the RAMBO model is a good alternative to the sigmoid function in describing the master curve of the dynamic modulus. We successfully used the Toranzos asymmetric bell-shaped frequency curve to describe the phase angle master curve. We also found a promising relationship between the independent RAMBO model parameters and the physical properties of the investigated binders, but this requires further research.

Mechanical properties of 7A04-T6 high strength structural aluminium alloy at elevated temperatures and after cooling down

Recent years have witnessed an increasing use of high strength aluminium alloys in structural applications, however, the mechanical properties of this type of materials are rather susceptible to elevated temperatures. This paper presents an experimental study on the mechanical properties of 7A04-T6 high strength aluminium alloy at elevated temperatures and after cooling down. Tensile coupon tests were first carried out on the specimens at high-temperature steady state conditions and post-fire conditions for temperatures ranging from 20 to 400 °C. The effect of cooling methods (cooled by air/water) was taken into account in the post-fire tests. Key mechanical properties, including Young’s modulus, yield strength, ultimate strength and ultimate strain, as well as the stress–strain responses obtained from both tests were fully reported and the microstructures of the post-fire material were examined. It is shown that the Young’s modulus and strengths decrease dramatically when temperatures are higher than 200 °C and the strengths decrease to less than 5% of the room temperature values at 400 °C, but a large proportion (up to 90%) of them regains after cooling down. In addition, the post-fire mechanical properties of the material exposed to 400 °C was found to be higher than those exposed to 300 °C; this was further explained through the microstructure examination. The test data were then utilised to assess the accuracy of existing codified design methods and the comparisons revealed that all of them provide inaccurate and scattered predictions. Finally, design formulae for the elevated-temperature retention factors as well as the post-fire residual factors and a two-stage Ramberg–Osgood material model were proposed. The design proposal was found to provide accurate predictions for the full-range stress–strain responses of the high strength aluminium alloy at both high-temperature steady state and post-fire conditions.

Temperature and Strain Rate Effects on the Uniaxial Tensile Behaviour of ETFE Foils.

With the first use of ETFE foils in building structures in the 1980s at the Burgers’ Zoo in Arnhem, Netherlands, the implementation of ETFE foils in roof and façade systems in large-span structures has become steadily more prominent. To safely design ETFE foil structures, their mechanical behaviour has to be fundamentally understood. Until now, several research studies have been published investigating this material’s behaviour. However, the parameters influencing these plastic’s mechanical behaviour, such as the strain rate or the test temperature, have only been investigated separately but not simultaneously. In this contribution, an analytical model is presented which describes the mechanical behaviour of ETFE foils under varying test temperatures and strain rates simultaneously. The material model has been checked against experimental results achieved for materials from three different international producers and two different commonly used foil thicknesses with significant differences in their mechanical responses (so that it can be assumed that the international market is represented). In the first step, uniaxial tensile tests on strip specimens were performed to describe the nonlinear and viscoelastic temperature- and strain rate-dependent material behaviour under uniaxial tension. The achieved stress-strain curves exhibited, as expected, the two commonly so-called yield points, which can be taken as separators for three different material stages: viscoelastic, viscoelastic-plastic, and viscoplastic. In the second step, by separating the uniaxial tensile response into these three stages, two interdependent functions could be derived based on the well-known Ramberg-Osgood material model to simulate the viscoelastic and viscoelastic-plastic material behaviour of ETFE foils. For this purpose, analytical functions were developed to calculate the model parameters considering the influence of the test temperature and the test speed. It can be shown that the newly developed analytical material model fits well with the experimental results. With the use of the derived nonlinear material model, design engineers can predict the material’s mechanical behaviour considering the environmental conditions on site while maintaining independence from the material’s supplier.

Elasto-plastic fracture modelling of 3-D metallic structure using XFEM

ABSTRACT The structural integrity of metallic structures/components depends on their fracture behaviour. These materials respond non-linearly in nature under applied service conditions. Therefore, the prediction of accurate fracture parameters under elasto-plastic conditions is cumbersome. This work consists of an accurate and robust computational approach to predict elasto-plastic fracture parameters for a 3-D cracked domain. A mesh-independent novel computational method known as the Extended Finite Element Method (XFEM) is employed to predict elasto-plastic fracture parameters (J-integral). Both material and geometrical non-linearity have been incorporated into the computational approach. The Ramberg-Osgood material model has been incorporated to characterise the non-linear relationship of stress-strain. The material non-linearity is modelled by von-Mises yield criteria along with isotropic strain hardening. Elastic predictor plastic corrector algorithm is used for modelling non-linear stress-strain behaviour. The geometric non-linearity is modelled by an updated Lagrangian approach. Few numerical cases are presented to show the efficacy of the proposed computational approach. To incorporate the proposed approach, an inhouse MATLAB code has been developed. The obtained numerical results are displayed in the form of convergence study, J-integral, and deformation contours. Additionally, a component-based problem, i.e. surface crack in a spur gear, has been analysed to show the robustness of the proposed methodology.

Numerical Simulations and Experimental Study on the Reeling Process of Submarine Pipeline by R-Lay Method

During the reeling process of the reel-lay method, the pipe will be subjected to combined loading of tension and bending. Excessive ovalization of the pipe will affect the structural performance and even lead to structural instability of the pipe. In this paper, a numerical simulation model of the pipe-reeling process is established by finite element tools. The Ramberg–Osgood material model is used to study the ovalization and bending moment of the pipe cross-section during the pipe-reeling process based on the Von Mises plasticity and nonlinear kinematic hardening rules. The results show that the ovalization and bending moment of the pipe section will change significantly during the pipe-reeling process. Subsequently, one set of 6-inch pipe-reeling experimental setups was designed to conduct a full-scale experiment. Compared with the experimental results, the feasibility of the finite element model is verified. Finally, the effects of diameter-to-thickness ratio, the material parameters of the pipe, and the pipe axial tension on the ovalization and bending moment changes are studied. Research shows that each parameter has a certain influence on the pipe of the reeling process, and the diameter-to-thickness ratio of the pipe has the most obvious effect. When the diameter-to-thickness ratio decreases, the bearing capacity for bending moments and the ability to resist ovalization of pipe are enhanced. At the same time, each parameter has a significant impact on the reeling process of the pipeline.

Fracture analysis of plastically graded material with thermo-mechanicalJ-integral

In this paper, the influence of plasticity graded property and thermal boundary conditions have been investigated on the fracture parameter, i.e. J-integral using the extended finite element method. A complete computational methodology has been presented to model elasto-plastic fracture problems with geometrical and material nonlinearities. For crack discontinuity modeling, a partition of unity enrichment concept was employed with additional mathematical functions like Heaviside and branch enrichment for crack discontinuity and stress field gradient, respectively. The modeling of the stress–strain relationship of the material is implemented using the Ramberg–Osgood material model and geometric nonlinearity is modeled using an updated Lagrangian approach. The isotropic hardening and von-Mises yield criteria are considered to check the plasticity condition. The elastic predictor–plastic corrector algorithm is employed to capture elasto-plastic stress in a cracked domain. The variation in plasticity properties for plastically graded material is modeled by exponential law. Furthermore, the nonlinear discrete equations are numerically solved using a Newton–Raphson iterative scheme. Various cracked problem geometries subjected to thermal (adiabatic and isothermal conditions) and thermo-mechanical loads are simulated for stress contours and J-integrals using the elasto-plastic fracture mechanics approach. A comparison of the results obtained using extended finite element method with literature and the finite element analysis (FEA) package shows the accuracy and effectiveness of the presented computational approach. A component-based problem, i.e. a Brazilian disc subjected to thermo-mechanical loading, has been solved to show the adaptability of this work.

Ramberg–Osgood material behavior expression and large deflections of Euler beams

Several assumptions are commonly made throughout the literature with regard to the mechanical expression of material behavior under a Ramberg–Osgood material model; specifically, the negligible effects of nonlinearity on the elastic behavior of the material. These assumptions do not reflect the complicated nonlinearity implied by the Ramberg–Osgood expression, which can lead to significant differences in the member model response from the true material behavior curve. With the proposed approach, new explicit results for Ramberg–Osgood materials are achieved without relying on these assumptions of material and model expression. The only assumptions present within the proposed model are the standard mechanical assumptions of an Euler beam. A general nonlinear moment–curvature relationship for monotone material behaviors is constructed. Large deflections of cantilever Euler beams with rectangular cross-sections under a combined loading are modeled. Numerical validation of this new method against results already given in the literature for the special cases of linear and power-law material behaviors are provided. An analysis is presented for three common material behavior relationships, with a focus on how these relationships are expressed through the deflection of members under the application of force within the model; this analysis clearly demonstrates that the sub-yield nonlinear behavior of the Ramberg–Osgood expression can be significant. The distinctions between material behavior expression demonstrated in this analysis have been long overlooked within the literature. This work addresses a gap between the modeling of Ramberg–Osgood material behaviors and the implementation of that model in mechanics.

Elasto-Plastic Fracture Modeling for Crack Interaction with XFEM

Multiple cracks/voids have been extensively seen in structural components. The stress field gets affected due to the crack interaction, so the effect of multiple cracks should be considered in design analysis. Further, due to service load, the stress concentrations are induced at the crack tips, which is the source of failure of the component. Hence, the current work has been proposed to investigate the crack interaction phenomenon in structural components under mechanical loading conditions. A mesh-independent computational approach, namely “Extended Finite Element Method (XFEM),” has been implemented for crack discontinuities modeling. Ramberg–Osgood material model has been used for the nonlinear stress–strain relationship of material. Isotropic hardening has been used with von Mises yield criteria to decide the plasticity condition. Further, nonlinear discrete equations have been solved by the Newton–Raphson iterative scheme. Few crack interaction problems are numerically solved by the presented EPFM approach, and results are presented in the form of fracture parameters.

Application of the Ramberg-Osgood model in asphalt technology

The “Time-Temperature Superposition” known from rheology has long been a useful tool for studying the behaviour of asphalt mixture. Dynamic modulus values are measured at different temperatures and frequencies can be thoroughly studied using the master curves defined by using this principle. The master curves are usually constructed using the sigmoid functions. However, other types of functions could be used for this purpose as well. One such option is the Ramberg-Osgood material model designed to model the cyclic behaviour of soils. The present article seeks to find out how accurately the use of the Ramberg-Osgood material model can describe the material behaviour of asphalt mixtures, and if there are any new highlights compared to the commonly used master curve determination techniques.

Imperfection Insensitivity of Thin Wavy Cylindrical Shells Under Axial Compression or Bending

Abstract The presence of imperfections significantly reduces the load carrying capacity of thin cylindrical shells due to the high sensitivity of thin shells to imperfections. To nullify this unfavorable characteristic, thin cylindrical shells are designed using a conservative knockdown factor method, which was developed by NASA in the late 1960s. Almost all the design codes, explicitly or implicitly, follow this approach. Recently, a new approach has emerged to significantly reduce the sensitivity of thin cylindrical shells. In this approach, wavy cross sections are used instead of circular cross sections for creating thin cylinders. Past studies have demonstrated the effectiveness of wavy cylinders to reduce imperfection sensitivity of thin cylinders under axial compression assuming linear elastic material behavior. These studies used eigenmode imperfections which do not represent realistic imperfections found in cylinders. In this paper, using a realistic dimple-like imperfection, new insights are presented into the response of wavy cylinders under uniform axial compression and bending. Furthermore, the effectiveness of the wavy cylinders to reduce imperfection sensitivity under bending load is investigated assuming a plastic Ramberg–Osgood material model. The effect of wave parameters, e.g., the amplitude and the number of waves, is also explored. This study reveals that wavy thin cylinders are insensitive to imperfections under bending in the inelastic range of the material. It is also found that the wave parameters play a decisive role in the response of thin wavy cylinders to imperfections under bending.

FEM-Based Compression Fracture Risk Assessment in Osteoporotic Lumbar Vertebra L1

This paper presents a finite element method (FEM)-based fracture risk assessment in patient-specific osteoporotic lumbar vertebra L1. The influence of osteoporosis is defined by variation of parameters such as thickness of the cortical shell, the bone volume–total volume ratio (BV/TV), and the trabecular bone score (TBS). The mechanical behaviour of bone is defined using the Ramberg–Osgood material model. This study involves the static and nonlinear dynamic calculations of von Mises stresses and follows statistical processing of the obtained results in order to develop the patient-specific vertebra reliability. In addition, different scenarios of parameters show that the reliability of the proposed model of human vertebra highly decreases with low levels of BV/TV and is critical due to the thinner cortical bone, suggesting high trauma risk by reason of osteoporosis.

Influence of material nonlinearity on the buckling resistance of stainless steel shells

One of the greatest challenges in the design of shell structures made of stainless steel compared to those made of carbon steel is the meaningful consideration of the nonlinear stress-strain behaviour of stainless steels which has a significant influence on the buckling behaviour of axially compressed shells in the medium slenderness range and lead to lower buckling strengths. A detailed description of the actual material behaviour of stainless steels is given by the material model developed by Arrayago, Real and Gardner on the basis of the by Rasmussen modified two stage Ramberg-Osgood material model. One of the parameters of which the model consists is the exponent n, which describes the nonlinear behaviour just before the 0.2% proof stress. This exponent is of great importance for the buckling behaviour of axially loaded shell structures of medium slenderness. For this reason, a thorough numerical parametric study has been conducted in order to evaluate the effect of the nonlinear material behaviour described by the exponent n on the buckling resistance of austenitic, duplex, and ferritic stainless steel shells. The numerical model has been validated by experimental results of axially compressed cylindrical shells conducted in the frame of the European RFCS-research project BiogaSS.

Verification of the Ramberg-Osgood Material Model in Midas GTS NX with the Modeling of Torsional Simple Shear Tests

This study focuses on the back analysis of a geotechnical laboratory test with nonlinear finite element modeling using the Ramberg-Osgood material model. This model has been used by several authors recently for nonlinear ground response analysis and it has been implemented by Midas into their commercial finite element code Midas GTS NX 2014. The verification of the model for 1D nonlinear site response analysis can be found in the documentation of the software package. In this study, Torsional Simple Shear tests were modeled and a comprehensive study was performed to provide verification of the material model for static torsional loading and axisymmetric conditions.

Investigation of Mechanical Properties and Fracture Simulation of Solution-Treated AA 5754

In this work, mechanical properties and fracture toughness of as-received and solution-treated aluminum alloy 5754 (AA 5754) are experimentally evaluated. Solution heat treatment of the alloy is performed at 530 °C for 2 h, and then, quenching is done in water. Yield strength, ultimate tensile strength, impact toughness, hardness, fatigue life, brittle fracture toughness $$(K_{\text{Ic}} )$$ and ductile fracture toughness $$(J_{\text{Ic}} )$$ are evaluated for as-received and solution-treated alloy. Extended finite element method has been used for the simulation of tensile and fracture behavior of material. Heaviside function and asymptotic crack tip enrichment functions are used for modelling of the crack in the geometry. Ramberg-Osgood material model coupled with fracture energy is used to simulate the crack propagation. Fracture surfaces obtained from various mechanical tests are characterized by scanning electron microscopy.

Developing and evaluating a finite element model for predicting the two-posts rollover protective structure nonlinear behaviour using SAE J2194 static test

This research focuses on applying Non-linear Finite Element (FE) techniques to predict ROPS force-deflection curves under the simulated standardised static tests. The Society of Automotive Engineers (SAE) J2194 ROPS static standard test was selected for this study. According to the SAE J2194 standard, ROPS must be capable of absorbing predefined levels of energy under longitudinal (rear) and transverse (side) load tests before collapsing as well as avoiding large deformations that infringe upon the driver's clearance zone or leave the clearance zone unprotected. A nonlinear finite element approach was used to predict the response of two rear-mount two-post ROPS under simulated side and rear test conditions for Allis Chalmers 5040 and Long 460 tractors. The ROPS were designed with the Computer-based ROPS Design Program using a bolted corner bracket assembly to simplify the ROPS design process. The recommended FE model (ASTM, C3D10M, 0.01) was found to predict the ROPS performance deflection (RPD) with average error less than 10% compared to experimental test measurements. The FE model predicted the ROPS behaviour under rear loads more accurately than under side loads. The developed FE model based on measured stress-strain curves from test specimens was found to predict the ROPS behaviour more accurately than the FE models developed based on the Ramberg-Osgood material model.

Numerical simulation of elastic plastic fatigue crack growth in functionally graded material using the extended finite element method

ABSTRACTIn the present work, the extended finite element method has been used to simulate the fatigue crack growth problems in functionally graded material in the presence of holes, inclusions, and minor cracks under plastic and plane stress conditions for both edge and center cracks. Both soft and hard inclusions have been implemented in the problems. The validity of linear elastic fracture mechanics theory is limited to the brittle materials. Therefore, the elastic plastic fracture mechanics theory needs to be utilized to characterize the plastic behavior of the material. A generalized Ramberg-Osgood material model has been used for modeling purposes.