Flow stress and ductility of AA7075-T6 aluminum alloy at low deformation temperatures

The present investigation has been conducted in order to develop a rational approach able to describe the changes in flow stress of AA7075-T6 aluminum alloy with deformation temperature and strain rate, when this material is deformed at temperatures in the range of 123-298 K at strain rates in the range of 4 × 10⁻⁴ to 5 × 10⁻² s⁻¹. The constitutive formulation that has been advanced to accomplish these objectives represents a simplified form of the mechanical threshold stress (flow stress at 0 K) model developed at Los Alamos National Laboratory (Los Alamos, New Mexico, USA). Thus, it is assumed that the current flow stress of the material arises from both athermal and thermal barriers to dislocation motion. In the present case, the effect of three thermal barriers has been considered: solid solution, precipitation hardening and work-hardening. The first two effects do not evolve during plastic deformation, whereas the last one is considered as an evolutionary component of the flow stress. Such an evolution is described by means of the hardening law earlier advanced by Estrin and Mecking (1984) [20]. The law is implemented in differential form and is integrated numerically in order to update the changes in strain rate that occur during tensile tests carried out both at constant and variable crosshead speed. The extrapolation of the hardening components from 0 K to finite temperatures is accomplished by means of the model earlier advanced by Kocks (1976) [19]. The results illustrate that the constitutive formulation developed in this way is able to describe quite accurately both the flow stress and work-hardening rate of the material, as well as temperature and strain rate history effects that are present when deformation conditions change in the course of plastic deformation. The evaluation of the ductility of the alloy indicates that the changes in this property are mainly determined by deformation temperature rather by strain rate. When deformation temperature decreases from 298 to 123 K, ductility also decreases from ∼35 to 24%. However, despite these relatively small variations, significant changes in the fracture morphology could be observed on the fracture surfaces of the examined specimens, with the predominance of a mixed ductile-brittle mechanism at lower temperatures.     

Fatigue and ratcheting assessment of AISI H11 at 500°C using constitutive theory coupled with damage rule

Hot extrusion is one of the most commonly used manufacturing methods for metal plastic deformation, and the consumption of extrusion tooling is considerably high due to its fatigue damage under cyclic serving condition. Hot‐work tool steel AISI H11 is one of these typical materials employed in extrusion tooling. This work is dedicated to calculating the stress/strain state of AISI H11 and predicting its lifetime at high temperature 500°C by building a unified constitutive model coupled with Lemaitre's damage law. Tensile tests and strain/stress reversed cycling tests have been conducted at 500°C to investigate mechanical properties and damage evolution. A unified constitutive model with Armstrong‐Fredrick/Ohno‐Wang kinematic hardening rule and a new proposed isotropic hardening rule is built; Lemaitre's damage law is employed as well. Parameters are determined based on tests and are temperature dependent. Finite element simulation of the deformation behaviour and fatigue lifetime is implemented into commercial software ABAQUS Standard v6.14‐2 with user material subroutine to validate the proposed method. The comparison shows good agreement with experimental results, and this part of work is essential and crucial to subsequent structure analysis.     

Stress-strain properties of structural steel at strain rates of up to 105 per second at sub-zero,room and high temperatures

A testing technique and method of processing the displacement-time data have been developed following which the stress-strain characteristics of structural steel at strain rates between 10³ to 10⁵ per second over a strain of about 50% and at different temperatures have been determined. The steel under present test condition within this strain rate range showed a strong strain rate sensitivity. The material inertia and temperature rise during high speed deformation were found to have mutually cancelling effect on the deduced flow stress. In determining the results, appropriate friction correction was also made and the results presented in this paper are all converted to those under frictionless condition. Finally, a constitutive equation has been proposed for the steel incorporating the effects of work-hardening and strain rate sensitivity of the material.     

A damage related thermo-viscoplastic constitutive model of metallic materials under high rate deformation

Abstract

A constitutive model considering the effects of strain hardening, strain rate hardening, thermal softening and material damage softening is suggested. In order to take the effect of material damage into account, a strain softening term is added in Johnson–Cook flow stress law. The model can predict the overall deformation process of metallic materials at high strain rates and a simple way is provided to determine the coefficients of softening term.     

Constitutive modeling and prediction of hot deformation flow stress under dynamic recrystallization conditions

Simple modeling approaches based on the Hollomon equation, the Johnson–Cook equation, and the Arrhenius constitutive equation with strain-dependent material’s constants were used for modeling and prediction of flow stress for the single-peak dynamic recrystallization (DRX) flow curves of a stainless steel alloy. It was shown that the representation of a master normalized stress–normalized strain flow curve by simple constitutive analysis is successful in modeling of high temperature flow curves, in which the coupled effect of temperature and strain rate in the form of the Zener–Hollomon parameter is considered through incorporation of the peak stress and the peak strain into the formula. Moreover, the Johnson–Cook equation failed to appropriately predict the hot flow stress, which was ascribed to its inability in representation of both strain hardening and work softening stages and also to its completely uncoupled nature, i.e. dealing separately with the strain, strain rate, and temperature effects. It was also shown that the change in the microstructure of the material at a given strain for different deformation conditions during high-temperature deformation is responsible for the failure of the conventional strain compensation approach that is based on the Arrhenius equation. Subsequently, a simplified approach was proposed, in which by correct implementation of the hyperbolic sine law, significantly better consistency with the experiments were obtained. Moreover, good prediction abilities were achieved by implementation of a proposed physically-based approach for strain compensation, which accounts for the dependence of Young’s modulus and the self-diffusion coefficient on temperature and sets the theoretical values in Garofalo’s type constitutive equation based on the operating deformation mechanism. It was concluded that for flow stress modeling by the strain compensation techniques, the deformation activation energy should not be considered as a function of strain.     

Application of neural networks to predict the elevated temperature flow behavior of a low alloy steel

In order to study the workability and establish the optimum hot forming processing parameters for 42CrMo steel, the compressive deformation behavior of 42CrMo steel was investigated at the temperatures from 850 °C to 1150 °C and strain rates from 0.01 s⁻¹ to 50 s⁻¹ on Gleeble-1500 thermo-simulation machine. Based on these experimental results, an artificial neural network (ANN) model is developed to predict the constitutive flow behaviors of 42CrMo steel during hot deformation. The inputs of the neural network are deformation temperature, log strain rate and strain whereas flow stress is the output. A three layer feed forward network with 12 neurons in a single hidden layer and back propagation (BP) learning algorithm has been employed. The effect of deformation temperature, strain rate and strain on the flow behavior of 42CrMo steel has been investigated by comparing the experimental and predicted results using the developed ANN model. A very good correlation between experimental and predicted result has been obtained, and the predicted results are consistent with what is expected from fundamental theory of hot compression deformation, which indicates that the excellent capability of the developed ANN model to predict the flow stress level, the strain hardening and flow softening stages is well evidenced.     

Studies on the stress-strain relations of dual-phase steels

The correlations of the work-hardening exponent,n, with quenching temperature, martensite volume-fraction (MVF) and solute concentration in ferrite are discussed and derived for dual-phase steel. The flow stress of dual-phase steel at low strain is suggested to be expressed by the combination of the terms due to plastic deformation in ferrite and elastic deformation of martensite. Previous experimental results are compared with the behaviour suggested by this theoretical work. In addition, an expression for the work hardening exponents at moderate strains and at the onset of necking are also theoretically suggested.     

Constitutive equation of a non-simple elastic plastic material

Summary The mechanical response predicted by the constitutive equation of a non-simple elastic material is considered in relation to the total strain behaviour of an elastic-plastic solid extensively deformed in the range of plastic strain. Both loading and unloading are considered in relation to the range of total elastic-plastic strain. In the absence of appropriate experimental studies, comparison of the predictions of the proposed constitutive equation of a non-simple elastic material, when applied to the work-hardening behaviour of the material, has been restricted to a study of the characteristic stress-strain behaviour of a strain hardening material. This has centred on the correlation of stress-strain curves characteristic of the mechanical response of a material tested in simple compression, simple torsion and pure shear with the object of obtaining a universal stress-strain curve.With 1 Figure     

Constitutive modelling for high temperature behavior of 1Cr12Ni3Mo2VNbN martensitic steel

The deformation behavior of 1Cr12Ni3Mo2VNbN martensitic steel in the temperature range of 1253 and 1453 K and the strain rate range of 0.01 and 10 s⁻¹ are investigated by isothermal compression tests on a Gleeble 1500 thermal-mechanics simulator. Most of the stress-strain curves exhibit a single peak stress, after which the stress gradually decreases until a steady state stress occurs, indicating a typical dynamic recrystallization (DRX) behavior of the steel under the deformation conditions. The experimental data are employed to develop constitutive equations on the basis of the Arrhenius-type equation. In the constitutive equations, the effect of the strain on the deformation behavior is incorporated and the effects of the deformation temperature and strain rate are represented by the Zener-Holloman parameter. The flow stress predicted by the constitutive equations shows good agreement with the experimental stress, which validates the efficiency of the constitutive equations in describing the deformation behavior of the material.     

Further observations on the plastic deformation of a normalized low carbon steel

The plastic deformation of a commercial grade low carbon steel has been investigated using microhardness and grain strain measurement techniques. Two distinct modes of deformation during plastic flow in low carbon ferritic steel have been identified. The initial stage involves the propagation of the Luder's band along the gauge length of the sample by slip strain in the surface and near surface grains only, the strain accommodation in the interior of the material being attained by a predominantly grain translation mode. The second stage involves the propagation of a strain hardening front through the cross-section of the material as the macro-strain is increased through the flow stress region.     

An improved constitutive model for high-temperature flow behaviour of the Fe–Mn–Al duplex steel

The high-temperature flow curves of the Fe–Mn–Al duplex steel showed an uncommon yield-like behaviour and an abnormal dynamic recrystallisation behaviour that occurred at low temperatures rather than high temperatures. The interaction of strain partitioning and unsynchronised softening behaviour in δ-ferrite and austenite caused this peculiar flow behaviour. By discussing the stress exponent and apparent activation energy, respectively, at low and high temperatures, a modified hyperbolic sine function was developed to predict the characteristic stresses. By simplifying the material constant θ and compensating the microstructural evolution in the exponential saturation work-hardening law, an improved constitutive model was developed to predict the transient stress. The comparison between the experimental and calculated values confirmed a high prediction accuracy of this improved model.     

Construction of a constitutive model in calculations of pressure-dependent material

To make constitutive modeling of materials more approaching reality, a new theory is proposed, in which a corresponding constitutive model can be constructed and characterized experimentally via two steps, one relates to the characterization of yielding behavior of material, and the second relates to the characterization of plastic flow of material deformation. The constitutive model involves two functions, yield function and plastic potential. A relationship between two functions is suggested, therefore, a corresponding plastic potential can be easily created after we have an appropriate yield function. To consider the non-isotropic hardening feature of strength differential in the constitutive model, the concept of equivalent hardening state is introduced, and then, multi-experimental flow stresses can be addressed in the model. When pressure sensitive materials are taken as an example in discussions, the Drucker–Prager yield function is employed to express the yielding behavior of material and a differently experimental characterization of the model is created as the corresponding plastic potential to describe the feature of plastic flow of material. This simple constitutive model can reproduce three sets of experimental results; including two flow-stresses and the volumetric plastic strain. The constitutive model can also well predict stress–strain relations with different pressures loaded on the material. Study shows that the feature of plastic flow is not that sensitive to the pressure loaded on the material when the yielding stress is.