Deformation of PC/ABS alloys at elevated temperatures and high strain rates

The objective of this paper is to experimentally study the deformation behavior of the alloys of polycarbonate (PC) and acrylonitrile–butadiene–styrene (ABS) at elevated temperatures and high strain rates. Four kinds of PC/ABS alloys with the ratio of PC to ABS being 80:20, 60:40, 50:50 and 40:60 and three different strain rates 8.0 × 10² s⁻¹, 2.7 × 10³ s⁻¹ and 1.0 × 10⁴ s⁻¹ are considered. The Split Hopkinson Pressure Bar (SHPB) experiments are carried out at 293 K and 343 K, respectively. The curves of engineering stress and engineering strain and true stress and true strain are obtained for the PC/ABS alloys at different temperatures and different strain rates, respectively. The effects of temperature, strain rate and the fraction of ABS on the deformation behavior of PC/ABS alloys are discussed in details, and then a temperature and strain rate-dependent phenomenological constitutive model for PC/ABS alloys is developed.     

A comparative study on modified Johnson Cook,modified Zerilli–Armstrong and Arrhenius-type constitutive models to predict the hot deformation behavior in 28CrMnMoV steel

The true stress-strain data from isothermal hot compression tests on Gleeble-3500 thermo mechanical simulator, in a wide range of temperatures (1173–1473 K) and strain rates (0.01–10 s⁻¹), were employed to establish the constitutive equations based on modified Johnson Cook, modified Zerilli–Armstrong, and strain-compensated Arrhenius-type models respectively to predict the high-temperature flow stress of 28CrMnMoV steel. Furthermore, a comparative study has been made on the capability of the three models to represent the elevated temperature flow behavior of this steel. Suitability of the three models were evaluated by comparing the accuracy of prediction of deformation behavior, correlation coefficient, average absolute relative error (AARE) and relative errors of prediction, the number of material constants, and the time needed to evaluate these constants. The results showed that the predicted values by the modified Johnson Cook and Zerilli–Armstrong models could agree well with the experimental values except under the strain rate of 0.01 s⁻¹. However, the strain-compensated Arrhenius-type model could track the deformation behavior more accurately throughout the entire temperature and strain rate range.     

金属和合金高温变形过程本构模型的研究进展

本构模型是预测金属和合金高温变形行为的重要途径,在不同金属和合金选择合适的变形工艺参数、预防缺陷等方面起着至关重要的作用。在近年对金属和合金高温变形过程的研究中,常通过不同工艺参数下的各类高温变形试验来获取建立本构模型的原始数据,并将所获本构模型导入Deform、Ansys等模拟软件相应模块,以预测材料在锻造等过程中应力、应变速率、温度的分布规律,进而优化实际加工参数、避免缺陷的产生,同时减少耗材及资源浪费。鉴于本构模型在优化加工参数、预防缺陷等方面的重要作用,对金属和合金本构模型的建立、选择等方面的研究较多,选择何种试验方法来获取建立材料本构模型的试验数据、运用何种数学或物理方法来建立材料的本构模型、选择何种本构模型进行预测、各类本构模型的优缺点及修正方法等都是金属和合金高温变形过程本构模型的研究重点。在近些年的研究中,常运用热压缩、热拉伸、热扭转、分离式霍布金森压杆等高温变形试验方法来获取材料不同高温变形工艺参数下的原始数据,进而建立其本构模型。常用的本构模型大致可分为唯象型、物理基型及基于人工神经网络型。各类模型分别具有不同的适用性及优缺点,而缺点最终主要体现在部分工艺参数下的拟合偏差较大,针对该现象,各国学者不断对模型进行完善、修正,其中,除了模型本身的原因外,引起偏差的原因还包括没有考虑摩擦及变形热等宏观问题的影响。目前,常用的典型唯象型本构模型包括Arrhenius型本构模型、Johnson-Cook模型等,物理基模型如Zerilli-Armstrong型等,而基于人工神经网络模型则主要是利用输入层、隐含层及输出层进行预测,各类模型在数据处理的复杂性、物理意义等方面各有优缺点。文章从金属和合金高温变形过程获取本构模型原始数据的试验方法、本构模型的种类及修正、模型的应用等方面综述了本构模型的研究及发展,分析并总结了不同本构模型的优缺点,指出了模型预测过程中个别参数下预测值与试验值偏差较大的现象及其修正方法,并展望了金属和合金高温变形过程本构模型未来的研究方向。     

Finite element analysis and experimental study of microstructure evolution of nitrogen alloyed ultralow carbon stainless steel during hot deformation

Abstract

Hot compression experiments of a nitrogen alloyed ultralow carbon stainless steel were performed in the temperature range of 1223–1423 K, at strain rates of 0.001–1 s^?1, and with deformation amounts of 30–70% on a Gleeble-3500 thermal-simulator. Based on the results from thermo-physical simulation experiments and metallographic analyses, a physically-based constitutive model and a dynamic recrystallisation (DRX) model of the studied steel were derived, and the developed models were further embedded into a finite element method (FEM) software. The microstructure evolution of the studied steel under various hot deformation conditions was simulated by FEM, and the effects of deformation amount, strain rate and temperature on the microstructure evolution were clarified. The results obtained from the finite element analysis were verified by the experiments. The finding confirms that the thermal-mechanical FEM coupled with the developed constitutive model and DRX model can be used to accurately predict the microstructure evolution of the studied steel during hot deformation.     

Study on mechanical properties and constitutive model of 5052 aluminium alloy

The stress–strain relationship of 5052 aluminium alloy was investigated via quasi-static tensile tests and split Hopkinson pressure bar tests. The specimens were exposed to various temperatures (25–500°C) and strain rates (10^?4–0.7?×?10^4?s^?1). At strain rates ranging from 0.001 to 3000?s^?1, the material underwent significant work hardening. When the strain rate exceeded 5000?s^?1, the work hardening effect decreased and the flow stress was relatively constant. The Johnson–Cook constitutive model was modified to describe the deformation behaviour of the material subjected to high temperatures and strain rates. The accuracy of the modified model was verified through ballistic impact testing.     

Incorporation of mean stress effects into the micromechanical analysis of the high strain rate response of polymer matrix composites

The results presented here are part of an ongoing research program, to develop strain rate dependent deformation and failure models for the analysis of polymer matrix composites subject to high strain rate impact loads. A micromechanics approach is employed in this work, in which state variable constitutive equations originally developed for metals have been modified to model the deformation of the polymer matrix, and a strength of materials based micromechanics method is used to predict the effective response of the composite. In the analysis of the inelastic deformation of the polymer matrix, the definitions of the effective stress and effective inelastic strain have been modified in order to account for the effect of hydrostatic stresses, which are significant in polymers. Two representative polymers, a toughened epoxy and a brittle epoxy, are characterized through the use of data from tensile and shear tests across a variety of strain rates. Results computed by using the developed constitutive equations correlate well with data generated via experiments. The procedure used to incorporate the constitutive equations within a micromechanics method is presented, and sample calculations of the deformation response of a composite for various fiber orientations and strain rates are discussed.     

Modified Johnson-Cook description of wide temperature and strain rate measurements made on a nickel-base superalloy

In this study, uniaxial compression experiments of a Nickel-base superalloy is conducted over a wide range of temperatures (298–1073 K) and strain rates (0.1–5200/s) to obtain further understandings of the plastic flow behaviours. The temperature and strain rate effects on the plastic flow behaviour are analysed. The flow stress decreases with increasing temperature below 673 K. Within the temperature range of about 673–873 K, the flow stress varies indistinctively, and even increases slightly with increasing temperature. As the temperature further increases, the flow stress decreases again. The flow stress of the Nickel-base superalloy displays insensitive to strain rate below 800/s and an enormous increase with increasing strain rate in excess of 800/s. Then the effects of temperature and strain rate on the microstructure are discussed. The result shows that high strain rate and high temperature may make the grain boundary of Nickel-base superalloy frail. Taking into account the anomalous temperature and strain rate dependences of flow stress, modified J–C constitutive model is developed. The model is shown to be able to accurately predict the plastic flow behaviour of Nickel-base superalloy over a wide range of temperatures and strain rates.     

The effect of heat developed during high strain rate deformation on the constitutive modeling of amorphous polymers

An adiabatic constitutive model is proposed for large strain deformation of polycarbonate (PC) at high strain rates. When the strain rate is sufficiently high such that the heat generated does not have time to transfer to the surroundings, temperature of material rises. The high strain rate deformation behavior of polymers is significantly affected by temperature-dependent constants and thermal softening. Based on the isothermal model which first was introduced by Mulliken and Boyce et al. (Int. J. Solids Struct. 43:1331-1356, 2006), an adiabatic model is proposed to predict the yield and post-yield behavior of glassy polymers at high strain rates. When calculating the heat generated and the temperature changes during the step by step simulation of the deformation, temperature-dependent elastic constants are incorporated to the constitutive equations. Moreover, better prediction of softening phenomena is achieved by the new definition for softening parameters of the proposed model. The constitutive model has been implemented numerically into a commercial finite element code through a user material subroutine (VUMAT). The experimental results, obtained using a split Hopkinson pressure bar, are supported by dynamic mechanical thermal analysis (DMTA) and Decompose/Shift/Reconstruct (DSR) method. Comparison of adiabatic model predictions with experimental data demonstrates the ability of the model to capture the characteristic features of stress–strain curve of the material at very high strain rates.     

316LN不锈钢高温拉伸颈缩区塑变行为

为准确测量颈缩发生后的应力-应变行为,本文综合物理实验、有限元模拟和MLR模型的方法确定颈缩区的塑变行为,建立316LN不锈钢高温本构模型.模型中,颈缩前的真应力-真应变呈幂函数关系,颈缩发生后,较低温度时应力随着应变的增加迅速下降,而当较高温度时应力随着应变的增加而缓慢下降,真应力-真应变呈非线性关系.基于MLR模型,修正了颈缩后不同温度、不同应变速率下的真应力-真应变曲线,并将有限元模拟的颈缩区长度与实测值相对比,相对偏差为4.73%.这说明修正后的应力-应变本构模型能够准确地描述316LN的高温塑性行为.     

Development of constitutive models for dynamic strain aging regime in Austenitic stainless steel 304

The experimental stress–strain data from isothermal tensile tests over a wide range of temperatures (623–923 K at an interval of 50 K), strains (0.02–0.30 at an interval of 0.02) and strain rates (0.0001, 0.001, 0.01, 0.1 s⁻¹) were employed to determine the Dynamic Strain Aging (DSA) regime and to formulate a suitable constitutive model to predict the elevated-temperature deformation behavior in DSA regime of Austenitic Stainless Steel (ASS) 304. Four models, namely, Johnson Cook (JC) model, modified Zerilli–Armstrong (m-ZA) model, modified Arrhenius type equations (m-Arr) and Artificial Neural Networks (ANNs), were investigated. Suitability of these models was evaluated by comparing the correlation coefficient, average absolute error and its standard deviation. It was observed that JC, m-ZA and m-Arr model could not effectively predict flow stress behavior of ASS304 in DSA regime, while the predictions by ANN model are found to be in good agreement with the experimental data.     

A modified Johnson–Cook constitutive model for Mg–Gd–Y alloy extended to a wide range of temperatures

In this paper, a new phenomenological and empirically based constitutive model was proposed to change the temperature term in the original Johnson–Cook constitutive model. The new model can be used to describe or predict the stress–strain relation of the metals deformed over a wide range of temperatures even though the current temperatures were lower than the reference temperature. Based on the impact compression data obtained by split Hopkins pressure bar technique, the material constants in the new model can be experimentally determined using isothermal and adiabatic stress–strain curves at different strain rates and temperatures. Good agreement is obtained between the predicted and the experimental stress–strain curves for a hot-extruded Mg–10Gd–2Y–0.5Zr alloy at both quasi-static and dynamic loadings under a wide range of temperatures ever though the current temperatures were lower than the reference temperature.     

丁羟包覆层的黏超弹本构模型

为了准确地描述丁羟（HTPB）包覆层在有限变形下的拉伸力学特性,研究了HTPB包覆层的黏超弹本构模型。分别构建了含率相关函数的本构模型和并联式本构模型,前者由超弹模型与率相关项相乘得到,后者由超弹模型与含损伤因子的黏弹模型并联而成。进行了HTPB包覆层的单步松弛、多步松弛和不同速率的单轴拉伸试验,并将试验数据用于拟合模型参数。结果表明,HTPB包覆层对应变率极其敏感,且具有很大的延伸率,表现出明显的黏超弹特性;两种模型均能很好地预测HTPB包覆层较大形变范围内的拉伸力学性能,其中含率相关函数的模型的描述更加准确,其研究具有重要的军事意义。     

Applying viscoplastic constitutive models to predict ratcheting behavior of sintered nanosilver lap-shear joint

A series of displacement-controlled tests were conducted for sintered nanosilver lap-shear joints at different loading rates and temperatures. The relationship between force and displacement was studied. It was found that higher loading rate or lower temperature caused higher stress–strain response of the sintered nanosilver joint. Force-controlled cyclic tests were also performed at different mean forces, force amplitudes, dwell time at peak force, and temperatures. The mean force, the force amplitude, and the temperature played key roles in the shear ratcheting strain accumulation. The ratcheting strain rate could be enhanced with increasing the dwell time at peak force as well. A viscoplastic constitutive model based on Ohno–Wang and Armstrong–Fedrick (OW–AF) non-linear kinematic hardening rule, and Anand model were separately embedded in ABAQUS to simulate the shear and the ratcheting behavior of the sintered nanosilver joint. It was concluded that OW–AF model could predict the ratcheting behavior of the sintered nanosilver joint better than Anand model, especially at high temperatures.     

Artificial neural network and constitutive equations to predict the hot deformation behavior of modified 2.25Cr–1Mo steel

Hot compression tests of modified 2.25Cr–1Mo steel were conducted on a Gleeble-3500 thermo-mechanical simulator at the temperatures ranging from 1173 to 1473 K with the strain rate of 0.01–10 s⁻¹ and the height reduction of 60%. Based on the experimental results, an artificial neural network (ANN) model and constitutive equations were developed to predict the hot deformation behavior of modified 2.25Cr–1Mo steel. A comparative evaluation of the constitutive equations and the ANN model was carried out. It was found that the relative errors based on the ANN model varied from −4.63% to 2.23% and those were in the range from −20.48% to 12.11% by using the constitutive equations, and the average root mean square errors were 0.62 MPa and 7.66 MPa corresponding to the ANN model and constitutive equations, respectively. These results showed that the well-trained ANN model was more accurate and efficient in predicting the hot deformation behavior of modified 2.25Cr–1Mo steel than the constitutive equations.     

Constitutive analysis to predict high temperature flow stress in 20CrMo continuous casting billet

The experimental true strain–true stress data from isothermal hot compression tests on a Gleeble-1500D thermal simulation machine, across a wide range of temperatures (1173–1373 K) and strain rates (1.5 × 10⁻³–1.5 × 10⁻² s⁻¹), were employed to study the deformation behavior and develop constitutive equations of 20CrMo alloy continuous casting billet steel. The objective was to obtain the relational expression for deformation activation energy and material constants as a function of true strain and the constitutive equation for high temperature deformation of 20CrMo based on the hyperbolic sine form model. A correlation coefficient of 0.988 and an average absolute relative error between the experimental and the calculated flow stress of 8.40% have been obtained. This indicates that the constitutive equations can be used to accurately predict the flow behavior of 20CrMo alloy steel continuous casting billet during high temperature deformation.     

高强钢TRB高温下热流变特性

为了准确仿真高强钢板热冲压成形过程,获得高强钢高温下的材料本构关系模型,利用Gleeble3500热模拟试验机在不同温度和应变速率下对不同厚度的高强钢B1500HS钢板进行了单向拉伸试验,获得各种工艺条件下的应力-应变曲线,并基于变形抗力数学模型,引入板材厚度参数,通过最小二乘法进行数据拟合获得高强钢TRB高温下的材料本构关系.利用试验结果对本构关系模型进行的拟合验证表明,拟合程度较好,说明建立的材料本构关系能很好地描述高强钢TRB在高温下的应力-应变关系.     

Comparisons of deformation and fracture behaviour of PC/ABS blend and ABS copolymer under dynamic shear loading

Abstract

The dynamic shear deformation and fracture characteristics of PC/ABS blend and ABS copolymer with regard to the relation between mechanical properties and strain rate, are studied experimentally using a torsional split Hopkinson bar at room temperature under strain rates ranging from 8 × 10² s^-1 to 3.4 × 10³ s^-1. Fracture phenomena are analysed by scanning electron microscopy and correlated with macroscopic behaviour. The relative properties and fracture mechanism of both polymers are also compared. Results show that strain rate enhances shear strength of both PC/ABS blend and ABS, but fracture shear strain tends to decrease with increasing strain rate. ABS exhibits better ductility and lower shear strength. For both polymers, strain rate sensitivity increases with increasing range of strain rate, while an inverse tendency occurs for activation volume. Higher strain rate sensitivity and lower activation volume are found in PC/ABS blend. PC/ABS blend fracture is dominated by mixed shearing and tearing, but ABS fracture shows only shearing. Due to the increasing deformation heat, fracture surface viscoplastic flow for both polymers increases with increasing strain rate, inducing lower flow resistance and lower fracture strain at higher stain rates. The viscoplastic flow behaviour in ABS is more active.     

Constitutive equation and model validation for a 31 vol.% B4Cp/6061Al composite during hot compression

An accurate constitutive equation is essential to understanding the flow behavior of B₄C/Al composites during the hot deformation. However, the constitutive equations developed previously in literature are generally for low strain rate deformation. In the present work, we modified the general constitutive equation and take the high strain rate correction into account. The constitutive equation for a 31 vol.% B₄Cp/6061Al composite was constructed based on the flow stresses measured during isothermal hot compression at temperatures ranging from 375 to 525 °C and strain rates from 0.01 to 10 s^?1. The experimental flow stresses were corrected by considering temperature-dependent Arrhenius factor. The modified equation was then verified by using DEFORM-3D finite element analysis to simulate the experimental hot compression process. The results show that the modified equation successfully predicts flow stress, load–displacement, and the temperature rise. This helps to optimize the hot deformation process, and to obtain desirable properties, such as reduced porosity and homogenous particle distribution in B₄C/Al composites.     

Constitutive modeling of powder metallurgy processed Al–4%Cu preforms during compression at elevated temperature

In this study, a hot deformation constitutive base analysis has been conducted on powder metallurgy (P/M) processed Al–4%Cu preforms. The main objective is to evaluate the effect of initial relative density on the hot deformation behaviour and to establish the constitutive equation which considers the effect of initial relative density during hot compression test. This has been carried out by using the true stress–true strain curve data obtained from hot compression test of P/M processed Al–4%Cu preforms with different initial relative density of 0.84, 0.87 and 0.9 for various range of temperature 300–500 °C and strain rate range of 0.1–0.4 s⁻¹. It has been found that the flow stress is notably influenced by initial relative density, temperature and strain rate. The results show that the flow stress exhibits peak value at certain strain value, and then decreases showing flow softening until the flow stress remains constant at higher strain values. A constitutive equation that predicts the flow stress in hot compression of P/M processed Al–4%Cu preforms has been developed. The predicted flow stress values are in a good agreement with the experimental results and it is confirmed that the formulated constitutive equation is accurate and reliable to predict the flow stress of Al–4%Cu preforms during hot compression at elevated temperature.