Coupled Effects Of Strain Research Articles

Statistical Analysis of the Dynamic Performance of Reinforcement Steel at Elevated Temperatures: The Case of Johnson-Cook Model

Description of mechanical properties of reinforcement steel by means of mathematical models known as constitutive laws is considered. The attention is focussed on the Johnson-Cook (JC) model developed to express the stress-strain relation by considering the coupled effect of strain and strain rate hardening as well as thermal softening of steel. The JC model is analysed due to its prevailing role in the practice of constitutive relation of properties of reinforcement steels. The key element of this study is a new look at the JC model from the statistical viewpoint. The JC model is subjected to examination by confronting its deterministic nature with statistical variability of experimental data that can be acquired from stress-strain records. It is stated that to now this variability has been largely ignored. The current practice of fitting the JC model to individual and non-repetitive stress-strain records is analysed. It is suggested how to address the problem of the model fitting in the case where stress-strain data is obtained by repetitive measurements. A procedure for processing small-size statistical samples extracted from this data is proposed. The essential idea of this procedure is to fit components of the JC model to limits of one-sided confidence intervals calculated by means of the statistical technique known as bootstrap resampling.

Dynamic constitutive relationship of CuCrZr alloy based on Johnson-Cook model

Abstract CuCrZr alloy has been acknowledged as one of the most promising candidate materials for the heat sink of plasma facing components in nuclear fusion devices with its excellent thermal conductivity and specific mechanical strength. For the safety concern, it is vital to provide appropriate safety assessment on these mechanical structures with CuCrZr alloy, such as divertor and blanket, under high strain rate loading conditions like displacement events, disruption, and so on. In this work, the dynamic compressive behavior of the CuCrZr alloy over wide range of strain rates and temperatures was investigated using the split Hopkinson pressure bar technique. Based on the experiment results, a constitutive equation is built by using Johnson-Cook model to describe the dynamical property of CuCrZr alloy. However, the results indicated that the influences of the strain, strain rate and temperature on the dynamic behavior are not independent. Therefore, a modified Johnson-Cook model was further developed to take the coupled effects of strain, strain rate and temperature into account. Compared with the original Johnson-Cook model, the modified Johnson-Cook model calculated results show good agreement with the experimental data.

Modification of constitutive model and evolution of activation energy on 2219 aluminum alloy during warm deformation process

Abstract To investigate the flow behavior of 2219 Al alloy during warm deformation, the thermal compression test was conducted in the temperature range of 483−573 K and the strain rate range of 0.001−5 s−1 on a Gleeble−3500 thermomechanical simulation unit. The true stress−true strain curves obtained showed that the flow stress increased with the decrease in temperature and/or the increase in strain rate and the softening mechanism primarily proceeded via dynamic recovery. The modification on the conventional Arrhenius-type constitutive model approach was made, the material variables and activation energy were determined to be dependent on the deformation parameters. The modified flow stresses were found to be in close agreement with the experimental values. Furthermore, the activation energy obtained under different deformation conditions showed that it decreased with the rise in temperature and/or strain rate, and was also affected by the coupled effect of strain and strain rate.

Temperature dependent negative to positive strain rate sensitivity and compression behavior for 2024-T351 aluminum alloy

Uniaxial compression tests in quasi-static and dynamic loading conditions were conducted to study the compression mechanical response of 2024-T351 aluminum alloy (AA2024-T351) at strain rates of 10−4s−1-9400s−1 with temperatures of 20°C–270 °C. Strain rate sensitivity (SRS) changes from negative to positive values with increases in the strain rate. The minimum flow stress at temperature dependent transient strain rate was selected as the basic stress to calculate flow stresses at other strain rates. Yield strength decreases linearly with increases in the temperature. Work hardening rates decrease nonlinearly with increases in the strain, and evident thermal softening was observed from stress–strain curves. A new constitutive model was developed by considering the coupled effect of strain, strain rate and temperature to characterize the temperature dependent SRS. The average absolute relative errors of the calculated and experimental stresses were 6.008%, 5.439%, 5.767%, 5.237%, and 3.695% for the JC model, KHL model, ERK model, KL model and the developed model, respectively. A comparison of the aforementioned models indicates that the predicted flow stresses of developed model agree better with the measured results than those of other models over a wide range of temperatures and strain rates.

Characterisation of vulcanised natural rubber behaviour by monotonic and in situ cyclic X-ray scattering tests

The effect of curing and loading conditions on the mechanical response of natural rubber are investigated by monotonic and in situ X-ray cyclic tensile tests. Tests are conducted on four samples, which differ by vulcanisation conditions. Samples are subject to two strain rates (2.7 × 10− 3 s− 1 and 16.66 × 10− 3 s− 1), and numerous imposed elongation levels range from 450 to 900%. The coupling between the strain rates and the elongation levels on the stress softening evolution resulting from strain induced crystallisation is investigated. In situ thermomechanical tensile cyclic test is performed in order to withdraw the effect of the strain induced crystallisation on the maximum stress decrease. The experimental results analysis shows that an optimum vulcanisation condition (150°C, 30 min) enhances the hardening process in the monotonic loading due to the strain induced crystallisation. However, under optimum curing conditions, cyclic loading induces a large hysteresis loss, a high stress softening and a high degree of strain induced crystallinity. The material softening sensitivity is controlled by coupled effect of strain ranges and elongation levels. This panoply of experimental measurements present a key information for material parameters identification that are useful to predict the lifetime of engineering components made of natural rubber such as racks, laminated rubber bearings and tires.

Constitutive flow stress formulation, model validation and FE cutting simulation for AA7075-T6 aluminum alloy

A consistent and reasonable description of the constitutive behavior of material under the coupled effect of strain, strain rate and temperature on the flow stress of the material is highly essential in current industrial practice to design and optimize the process parameters in manufacturing operations. In order to formulate a suitable constitutive model to predict the elevated-temperature deformation behavior in high strength aluminum alloy, AA7075-T6, isothermal uniaxial tensile tests over a practical range of deformation temperatures (300–623K) and strain rates (10−4–10−1s−1) were conducted. Two constitutive models, modified-Johnson Cook (m-JC) and modified-Zerilli–Armstrong (m-ZA) models are formulated considering the combined effects of strain, strain rate and temperature on flow stress. The prediction capability of these models is assessed in terms of statistical parameters, correlation coefficient and average absolute error between experimental and predicted flow stress data. In addition, finite element (FE) simulations have been carried out in order to validate the formulated model during orthogonal cutting processes. It was observed that both the models show a very high degree of linear dependence of fit as the value above 0.98. However, the m-ZA model can offer an accurate and precise estimate of the flow behavior for studied workmaterial over m-JC model. Further, the performance of developed model in FE cutting simulations is the most obvious for all moderate machining conditions and can provide relatively good prediction results for the AA7075-T6 machining process.

COUPLED EFFECT OF STRAIN AND MAGNETIC FIELD ON ELECTRONIC BAND STRUCTURE OF GRAPHENE

Hofstadter's fractal energy spectrum, which is also called Hofstadter butterfly, remained as one of the most interesting topics of condensed matter physics for decades. We study, in this paper, how different patterns of energy spectrum emerge when a graphene sheet is subjected to in-plane uniaxial and shear strain in the presence of transverse magnetic field. We discuss these patterns in the context of opening of the electronic energy band structure of graphene. We thus provide a unified framework for graphene under the coupled effect of strain and magnetic field. Due to such coupling, the energy bandgap opens when certain threshold of strain in the zigzag direction of graphene is crossed. The threshold strain value depends on the rationality of the parameter ϕ/ϕo, i.e., the ratio of magnetic flux through the deformed hexagonal plaquette and the quantum flux (h/e). Numerical results shows that the energy bandgap depends nonlinearly on the magnitude of strain, and that the threshold strain and energy gap decrease with decreasing magnetic field.

A Rate-Dependent Hysteresis Model for Structural Steel (SM490) Considering the Coupled Effect of Strain Rate Hardening and Temperature Rise

In steel structures, the mechanical characteristics and the hysteretic behavior during dynamic behavior is different to those during static deformation. This is due to the coupled effect of strain rate hardening and temperature rise. To predict hysteretic behavior of steel structures under dynamic/cyclic loading such as earthquake, it is therefore necessary to develop a rate-dependent hysteresis model which can accurately describe the static-dynamic mechanical characteristics considered the coupled effect of strain rate hardening and temperature rise as well as the hysteretic behavior. In this paper, to develop a rate-dependent hysteresis model of SM490(structural steel according to Korean standard), the monotonic and cyclic loading tests were performed for strain rate. Based on the test results, the rate-dependent hysteresis model of SM490 was formulated and with the material parameters used, the model was derived. The validity and the accuracy of the developed model were verified by comparing between the analyses and the experiments. The comparison results show that the rate-dependent hysteresis model of SM490 developed by the authors can accurately predict the static-dynamic hysteretic behavior of steel structures under cyclic loading.