Applicability of Kocks–Mecking approach for tensile work hardening in P9 steel

Abstract

Work hardening behaviour of P9 steel in the temperature range 300–873 K has been examined in the framework of Kocks–Mecking (K–M) approach. At all temperatures, P9 steel exhibited two-stage work hardening behaviour characterised by a rapid decrease in instantaneous work hardening rate (i.e. θ?=?dσ/d?, where σ is the true stress and ? is the true plastic strain) with stress at low stresses (transient stage) followed by a gradual decrease at high stresses (stage III). Stage III work hardening of P9 steel was adequately described by K–M approach. The variations of work hardening parameters associated with K–M approach for stage III with temperature indicated three distinct temperature regimes. At all temperatures, good correlations between the respective work hardening parameters evaluated using K–M approach and from Voce equation and its derivative have been obtained for P9 steel.     

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.     

Modeling high-temperature tensile deformation behavior of AZ31B magnesium alloy considering strain effects

The hot tensile deformation behaviors of AZ31B magnesium alloy are investigated over wide ranges of forming temperature and strain rate. Considering the effects of strain on material constants, a comprehensive constitutive model is applied to describe the relationships of flow stress, strain rate and forming temperature for AZ31B magnesium alloy. The results show that: (1) The effects of forming temperature and strain rate on the flow behaviors of AZ31B magnesium alloy are significant. The true stress–true strain curves exhibit a peak stress at small strains, after which the flow stress decreases until large strain, showing an obvious dynamic softening behavior. A considerable strain hardening stage with a uniform macroscopic deformation appears under the temperatures of 523 and 573 K. The strain hardening exponent (n) increases with the increase of strain rate or the decrease of forming temperature. There are not obvious strain-hardening stages when the forming temperature is relatively high, which indicates that the dynamic recrystallization (DRX) occurs under the high forming temperature, and the balance of strain hardening and DRX softening is easy to obtain. (2) The predicted stress–strain values by the established model well agree with experimental results, which confirm that the established constitutive equation can give an accurate and precise estimate of the flow stress for AZ31B magnesium alloy.     

Tensile behaviour and strain hardening characteristics of constrained groove pressed nickel sheets

In this study commercially pure nickel sheets are severe plastically deformed at room temperature by constrained groove pressing (CGP) technique and the effect of pass number on the room temperature mechanical behaviour is investigated. Increase in strength observed after first pass is much higher than the increase observed during subsequent passes. Mechanical behaviour of constrained groove pressed sheets indicated negligible strain hardening ability during initial passes; gain in strain hardening ability is observed during latter passes resulting in enhanced ductility. The observation of shortened uniform elongation phase during tensile testing of CGP processed sheets could be linked to the lack of strain hardenability and change in deformation mechanism. Constitutive mechanical behaviour in uniform plastic deformation regime of nickel sheets in annealed condition obeys Hollomon relation whereas severely deformed sheets obey Voce relation closely. Strain hardening characteristics of groove pressed sheets analysed by Kocks–Mecking approach revealed stage-III hardening behaviour associated with high initial hardening rate when compared to annealed sheets. The influence of pass number on dislocation density evolution is assessed by Taylor’s expression. The synergistic effect of dislocation generation and recovery on the evolution of constitutive mechanical behaviour in the uniform elongation regime is described by applying single parameter based Kocks model. The kinetics of dislocation storage and dislocation annihilation in severely deformed nickel sheets during deformation corroborated with mechanical properties and dislocation density indicates the dominance of dislocation generation during earlier passes.     

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.     

A constitutive equation for hot deformation range of 304 stainless steel considering grain sizes

A general constitutive equation based on the framework of invariant theory by consideration of hot deformation key variables and also the properties of the material such as initial grain size is presented in the current work. Soundness of the considered parameters to be used in the developed formula was initially verified based on the important axioms such as objectivity, entropy principle, and thermodynamics stability. To access the prediction ability of the method, the formula was simplified for the simple hot compression test. To evaluate the simplified formula, single-hit hot compression tests were carried out at the temperature range of 900–1100 °C under true strain rate of 0.01–1 s⁻¹ on a AISI 304 stainless steel. The capability of proposed formula for reproducing the variation of flow stress with strain and the strain hardening rate with stress for the resultant flow stress data was examined. The good agreement between model predictions and actual results signified the applicability of this method as a general constitutive equation in hot deformation studies.     

High temperature flow behavior and constitutive model of alloy transition layer in composite steel tube prepared by centrifugal self-propagating high-temperature synthesis (SHS)

Centrifugal self-propagation high-temperature synthesis (SHS) is a newly developed composite preparation technique by which a ceramic-alloy-carbon steel multilayer composite tube can be prepared. The hot deformation behaviors of the alloy steel layer at 800 °C–1000 °C, strain rates of 0.01 s⁻¹, 0.1 s⁻¹, 1.0 s⁻¹ and 10 s⁻¹ were studied by Gleeble-1500 thermal simulator. Rheological curve characteristics were analyzed under different thermal compression processes and a phenomenological hyperbolic sinusoidal Arrhenius constitutive equation was established to characterize the rheological mechanics of the material. The results show that the alloy steel is sensitive to temperature and strain rate, and its value of true stress decreases with the increase of temperature and strain rate. Thermal deformation process is the interaction between work hardening and dynamic softening, which is accompanied by the increase and extinction of dislocations. Under the strain rate of 10 s⁻¹, the stress-strain curve has a significant decrease when the strain exceeds 0.5. According to the observation of microstructure, this phenomenon can be attributed to the micro-crack generated by the local instability flow in the denatured zone. With the strain rate decreases, the softening mechanism of the alloy changes from dynamic recovery to dynamic recrystallization. The calculation results of the Arrhenius constitutive equation (AARE = 6.54 %, R = 0.99452) indicate that the model can predict the flow stress of the alloy accurately.     

Constitutive models for high-temperature flow behaviors of a Ni-based superalloy

The high-temperature deformation behaviors of a typical Ni-based superalloy are investigated by hot compression tests under the strain rate of 0.001–1 s⁻¹and temperature of 920–1040 °C. The experimental results show that the deformation behaviors of the studied superalloy are significantly affected by the deformation temperature, strain rate and strain. The flow stress increases with the increase of strain rate or the decrease of deformation temperature. The flow stress firstly increases with the strain to a peak value, showing the obvious work hardening behaviors. Then, the stress decreases with the further straining, indicating the dynamic flow softening behaviors. Considering the coupled effects of deformation temperature, strain rate and strain on the hot deformation behaviors of the studied Ni-based superalloy, the phenomenological constitutive models are established to describe the work hardening-dynamic recovery and dynamic softening behaviors. In the established models, the material constants are expressed as functions of the Zener–Hollomon parameter. The established constitutive models can give good correlations with the experimental results, which confirm an accurate and precise estimation of the flow stress for the studied Ni-based superalloy.     

Effect of carbon content on plastic flow behaviour of plain carbon steels at elevated temperature

Abstract

In the present study the effect of carbon composition on the hot flow behaviour of two different plain carbon steels is analysed. For this purpose the constitutive equations describing the stress–strain (σ–?) relationships at a given strain rate ? and temperature T were determined for each steel. Uniaxial hot compression tests were performed to characterise the mechanical behaviour of the alloys. It was observed that irrespective of the test conditions, the low carbon steel displayed similar flow stresses to the high carbon steel. Comparison of the characteristic parameters of the constitutive equations describing the high temperature flow behaviour of these steels, together with values reported in the literature enabled determination of the effect of carbon content on flow behaviour. It has been found that flow stresses can be rationalised as a balance between work hardening and softening processes (basically dynamic recovery). At high temperatures and small strain rates, the high carbon steel showed lower hardening rates and slower dynamic recovery kinetics than the low carbon steel. In contrast, at low temperatures and large strain rates, the high carbon steel displayed higher hardening rates and recovery rates than the low carbon steel.     

10CrNi8MoV钢的拉伸塑性应变物理本构模型

研究了10CrNi8MoV钢不同温度和应变速率下的拉伸应力-应变曲线。根据位错动力学将流变应力分解为热激活应力和非热激活应力,忽略粘拽阻力的影响。通过对塑性变形过程的分析,在Kocks热激活方程中引入位错间距演化函数,并用线性强化模型描述非热激活应力的变化,建立了10CrNi8MoV钢的物理本构模型。该模型对10CrNi8MoV钢在低应变速率和较宽的温度范围内的塑性变形行为有较好的描述结果。      

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.     

The high temperature flow behavior modeling of AZ81 magnesium alloy considering strain effects

In the field of deformation process modeling, constitutive equations are invariably used as a calculation basis to estimate the materials flow responses. Accordingly, in the present study, a constitutive analysis has been conducted on the AZ81 magnesium alloy employing experimental stress–strain data obtained from isothermal hot compression tests. These tests had been done in the temperature range of 250–450 °C under strain rates of 0.003, 0.03 and 0.3 s⁻¹. The effects of the temperature and strain rate on hot deformation behavior have been expressed in terms of an exponent-type Zener–Hollomon equation. Furthermore, the influence of strain has been included in the constitutive equation by considering its effect on different material constants. Consequently, a model to predict the high-temperature flow behavior of AZ81 magnesium alloy has been established. The true stress–true strain curves predicted by the extracted model are in good agreement with the experimental results, thereby confirming the validity of the developed constitutive relation.