Prediction Of Flow Stress Research Articles

Constitutive analysis to predict high-temperature flow stress in modified 9Cr–1Mo (P91) steel

Constitutive analysis for hot working of modified 9Cr–1Mo (P91) ferritic steel was carried out employing experimental stress–strain data from isothermal hot compression tests, in a wide range of temperatures (1123–1373 K), strains (0.1–0.5) and strain rates (10 −3–10 2 s −1). The effects of temperature and strain rate on deformation behaviour were represented by Zener–Hollomon parameter in an exponent-type equation. The influence of strain was incorporated in the constitutive equation by considering the effect of strain on different material constants. Activation energy was found to vary with strain in the range 369–391 kJ mol −1. The developed constitutive equation (considering the compensation of strain) could predict flow stress of modified 9Cr–1Mo steel over the specified hot working domain with very good correlation and generalization.

Modification of coupled model of microstructure evolution and flow stress: experimental validation

A mathematical model for prediction of flow stress and microstructure evolution during and after deformation processes was developed in the project. In the present paper, a modified model is shortly presented. The main differences between the previous and current version of the model are stressed and explained. The model consists of two almost independent parts: development of dislocations and microstructure evolution. The main changes are introduced in the calculations of the recrystallised volume. Volume applicable for nucleation is considered in another way as well. An identification of the model parameters is carried out with constrains. The paper presents results of the identification and the model validation at constant and varying deformation conditions. The results that represent grains size effect are also shown.

A new mathematical model for predicting flow stress of typical high-strength alloy steel at elevated high temperature

Abstract Numerical simulations can be truly reliable only when a proper material flow stress relationship is built because of its effective role on metal flow pattern as well as the kinetics of metallurgical transformation. Based on the hot compressive deformation behaviors of 42CrMo steel, a comprehensive constitutive model has been developed to predict stress–strain curve up to the peak stress. A new material parameter L , which is sensitive to the forming temperature and strain rate, was proposed in the developed constitutive model. Additionally, the mathematical models to predict peak stress and peak strain were established based on experimental results. The stress–strain values predicted by the developed model well agree with experimental results, which confirmed that the developed constitutive equation gives an accurate and precise estimate for the flow stress of 42CrMo steel.

Comparative study of dynamic impact properties and microstructures of weldable and unweldable aluminium–scandium (Al–Sc) alloys

The dynamic deformation behaviours of two Al–Sc alloys, one weldable and one unweldable, are investigated at strain rates ranging from 1·2 × 103 to 5·9 × 103 s–1 and temperatures of –100, 25 and 300°C respectively, using a compressive split Hopkinson pressure bar. The fracture features and microstructures of the impacted specimens are examined using scanning electron microscopy and transmission electron microscopy respectively. The stress–strain relationships indicate that for both alloys, the flow stress, work hardening rate and strain rate sensitivity increase with increasing strain rate, but decrease with increasing temperature. Moreover, the flow stress, work hardening rate and strain rate sensitivity are higher in the unweldable Al–Sc alloy than in the weldable alloy. In both alloys, the activation volume is dominated by a thermally activated mechanism and increases as the temperature increases or the strain rate decreases. Additionally, the fracture strain reduces with increasing strain rate and decreasing temperature. In describing the plastic deformation behaviour of the two Al–Sc alloys using the Zerilli–Armstrong fcc constitutive model, the error between the predicted flow stress and the measured stress is found to be <5%. The scanning electron microscopy observations reveal that the surfaces of the fractured specimens are characterised by transgranular dimpled features, which are indicative of a ductile fracture mode. The dimple like structures on the fracture surfaces of the unweldable Al–Sc alloy are shallower than those on the fracture surfaces of the weldable Al–Sc alloy, which indicates that the weldable Al–Sc alloy has a better ductility than the unweldable Al–Sc alloy. The transmission electron microscopy images show that the microstructures of the two alloys contain different types of precipitates. Specifically, the unweldable Al–Sc alloy contains both Al3Sc and Al2Cu particles, whereas the weldable Al–Sc alloy contains Al3Sc precipitates only. These particles prevent dislocation motion, and therefore prompt a significant strengthening effect. The transmission electron microscopy observations also reveal that in both alloys, the dislocation density increases with increasing strain rate, but decreases with increasing temperature. Furthermore, it is found that the dislocation density of the unweldable Al–Sc alloy is higher than that of the weldable Al–Sc alloy. In other words, the dislocation cells in the unweldable Al–Sc alloy are smaller than those in the weldable Al–Sc alloy. Thus, it is inferred that the unweldable Al–Sc alloy has a higher flow stress than the weldable Al–Sc alloy.

Physical Simulation of Hot Deformation and Microstructural Evolution for 42CrMo4 Steel Prior to Direct Quenching

Direct quenching and tempering (DQ-T) of hot rolled steel section has been widely used in steel mill for the sake of improvement of mechanical properties and energy saving. Temperature history and microstructural evolution during hot rolling plays a major role in the properties of direct quenched and tempered products. The mathematical and physical modeling of hot forming processes is becoming a very important tool for design and development of required products as well as predicting the microstructure and the properties of the components. These models were mostly used to predict austenite grain size (AGS), dynamic, meta-dynamic and static recrystallization in the rods immediately after hot rolling and prior to DQ process. The hot compression tests were carried out on 42CrMo4 steel in the temperature range of 900–1 100 °C and the strain rate range of 0. 05–1 s −1 in order to study the high temperature softening behavior of the steel. For the exact prediction of flow stress, the effective stress-effective strain curves were obtained from experiments under various conditions. On the basis of experimental results, the dynamic recrystallization fraction (DRX), AGS, hot deformation and activation energy behavior were investigated. It was found that the calculated results were in good agreement with the experimental flow stress and microstructure of the steel for different conditions of hot deformation.

Experimental analysis and constitutive modeling for the newly developed 2139-T8 alloy

Mechanical behavior of recently emerged 2139-T8 aluminum alloy, which is based on an Al–Cu–Mg–Ag system, has been characterized by uniaxial compression and tension experiments over a wide range of strain rates from 10 −4 to 10 4 s −1 and for temperatures from −60 to 300 °C. Driven by experimental results, modifications to widely used Johnson–Cook constitutive model has been proposed, and model parameters have been determined. It has been shown that modified Johnson–Cook (MJC) model satisfactorily captures rate- and temperature-dependent variations in flow stress through enhanced coupling between temperature and strain hardening as well as temperature and strain-rate sensitivity. The modified model also provides flow stress prediction over the entire range of quasi-static and dynamic regimes by a single continuous function.

The grain size dependence of flow stress in an ECAPed AZ31 Mg alloy with a constant texture

ECAPed Mg sample with a smaller grain size showed a lower yield stress compared to a unECAPed (as-extruded) sample with a large grain due to texture modification during ECAP process. An equation for the flow stress of an ECAPed alloy with a constant texture as a function of the strain and grain size was derived to quantify the effect of the grain size on the flow stress in this alloy, assuming that 2-, 3-, and 4-passed microstructures have the same texture. According to the predicted flow stress results, the strain hardening is the largest contributor to flow stress and that the solid solution hardening and grain size refinement play relatively minor roles on flow stress in ECAPed samples.

On the evolution of flow stress during constrained groove pressing of pure copper sheet

Using a mechanical model and dislocation density based model, the evolutions of dislocation density and flow stress of pure copper during constrained groove pressing (CGP) process are investigated. In this regard, the strain and strain rate are achieved from the mechanical model and then input into the dislocation model. To verify the predicted flow stress, the process of constrained groove pressing is performed on the sheets of pure copper from one to three passes. The predicted flow stresses are compared with the experimental data and a good agreement is observed. Also, it is found that during the straining of the copper sheet in CGP process, the dislocation density and strength dropping occur in lower strain than that in other severe plastic deformation processes.

Modelling the strain induced precipitation in Nb-containing micro-alloyed steels

A physical metallurgy principle based model to predict flow stress, recovery, recrystallization and precipitation of Nb-containing micro-alloyed steels during hot rolling is developed. Precipitation kinetics is simulated by the model during hot rolling. The driving force and the equilibrium concentrations are calculated by Thermo-Calc software. The volume fraction of precipitation particles and the particle size of Nb-containing micro-alloyed steels during hot rolling are calculated with considering the effect of recovery and recrystallization on precipitation. The model is verified by the experimental results, and the volume fraction of precipitation particles and the particle sizes are predicted in different hot rolling processes.

Modeling of Size Effect on Tensile Flow Stress of Sheet Metal in Microforming

This investigation considers the size effect on the deformation behavior of simple tension in microforming and thus proposes a simple model of the tensile flow stress of sheet metal. Experimental results reveal that the measure of the flow stress can be represented as a hyperbolic function tanh(T/D), which is a function of T/D (sheet thickness/grain size). The predicted flow stress agrees very well with the published experiment. Notably, a specimen with smaller grains has lower normalized flow stress for a given T/D. Since the material properties of the macroscale specimen do not pertain to the microscale, a critical condition (T/D)c that distinguishes the macroscale from the microscale in the tensile flow stress is subsequently proposed, based on the “affected zone” model, the pile-up theory of dislocations, and the Hall–Petch relation. The distribution of the predicted (T/D)c is similar to the experimental finding that the (T/D)c decreases as the grain size increases. However, the orientation-dependent factor β is sensitive to (T/D)c. Hence, further study of the orientation-dependent factor β is necessary to obtain a more accurate (T/D)c and, thus, to evaluate and understand better the tensile flow stress of sheet metal in microforming.

Strain-dependent constitutive analysis of three wrought Mg-Al-Zn alloys.

The commonly used hyperbolic sine constitutive equation for metal forming at elevated temperatures, with no strain incorporated, is in principle applicable only to deformation in the steady state. However, the actual deformation processes applied to magnesium alloys are mostly in the non-steady state. In the present research, the results of hot uniaxial compression tests of three wrought magnesium alloys covering wide ranges of temperatures and strain rates were used for a strain-dependent constitutive analysis. A strain-dependent constitutive relationship for these alloys was established. It appeared that the apparent activation energy for deformation decreased with increasing the alloying content in these alloys. The constitutive parameters obtained were used to predict flow stresses at given strains and the results were in good agreement with experimental measurements.

Effects of strain rate and temperature on dynamic mechanical behaviour and microstructural evolution in aluminium–scandium (Al–Sc) alloy

The present study applies a compressive split Hopkinson bar to investigate the mechanical response, microstructural evolution and fracture characteristics of an aluminium–scandium (Al–Sc) alloy at temperatures ranging from − 100 to 300°C and strain rates of 1·2 × 103, 3·2×103 and 5·8 × 103 s−1. The relationship between the dynamic mechanical behaviour of the Al–Sc alloy and its microstructural characteristics is explored. The fracture features and microstructural evolution are observed using scanning and transmission electron microscopy techniques. The stress–strain relationships indicate that the flow stress, work hardening rate and strain rate sensitivity increase with increasing strain rate, but decrease with increasing temperature. Conversely, the activation volume and activation energy increase as the temperature increases or the strain rate decreases. Additionally, the fracture strain reduces with increasing strain rate and decreasing temperature. The Zerilli–Armstrong fcc constitutive model is used to describe the plastic deformation behaviour of the Al–Sc alloy, and the error between the predicted flow stress and the measured stress is found to be less than 5%. The fracture analysis results reveal that cracks initiate and propagate in the shear bands of the Al–Sc alloy specimens and are responsible for their ultimate failure. However, at room temperature, under a low strain rate of 1·2 × 103 s−1 and at a high experimental temperature of 300°C under all three tested strain rates, the specimens do not fracture, even under large strain deformations. Scanning electron microscopy observations show that the surfaces of the fractured specimens are characterised by transgranular dimpled features, which are indicative of ductile fracture. The depth and density of these dimples are significantly influenced by the strain rate and temperature. The transmission electron microscopy structural observations show the precipitation of Al3Sc particles in the matrix and at the grain boundaries. These particles suppress dislocation motion and result in a strengthening effect. The transmission electron microscopy analysis also reveals that the dislocation density increases, but the dislocation cell size decreases, with increasing strain rate for a constant level of strain. However, a higher temperature causes the dislocation density to decrease, thereby increasing the dislocation cell size.

Validation of Multi-scale Model Describing Microstructure Evolution in Steels

Properties of deformed steels depend on various microstructure parameters such as distribution of grain size and precipitates. Strain, strain rate and temperature inhomogeneities make quantitative prediction of microstructure difficult but the Finite Element method is able to model these inhomogeneities. Different scales of phenomena occurring in deformed materials are another difficulty in modelling. Microstructure evolution can be described by more realistic methods (e.g. Cellular Automata CA, Monte Carlo), which, on the other hand, are unable to simulate larger samples. Therefore, development of the methods capable of spanning multiple scales became a current challenge. CAFE modelling, which couples FE and CA methods, is the objective of the paper. The model consists of two layers. The micro-scale layer, simulated by CA, represents microstructure evolution including nucleation and growth of the grains. Evolution of a dislocation density is described for every grain separately by solving differential equation. The FE thermal-mechanical model is used as a macro-scale part. Multistage plane strain compression tests for niobium steel are considered. Distributions of initial and final grain size are measured during the tests. The results from the CAFE model are compared to the measurements and to the predictions by a conventional model. The comparisons confirm the capability of the CAFE method to predict flow stress, recrystallized fraction and grain size distribution. Conventional approach gives a good agreement with experiments for an average grain size only.

A method to predict flow stress considering dynamic recrystallization during hot deformation

In order to establish flow stress relationship for metals and alloys in a form that can be used in numerical simulations. A method to predict flow stress considering dynamic recrystallization (DRX) during hot deformation is presented in this paper. Flow stress model is expressed by 9 independent parameters and they are obtained by least-square method. The flow stress constitutive equations of magnesium alloy AZ31B and 42CrMo steel during hot deformation were developed by the proposed method. The predicted stress–strain curves are in good agreement with experimental results, which confirmed that the developed models are accurate and the proposed method is effective to establish flow stress equations of metals and alloys during hot deformation.

Prediction of the flow stress of 6061 Al–15% SiC – MMC composites using adaptive network based fuzzy inference system

Silicon carbide reinforced aluminium composite materials are increasingly used in many engineering fields. Flow stress prediction for these materials is increasingly important. In the present work, flow stress of 1.0Mg – 0.6% Si – 0.3% Cu – 0.2% Cr rest Al with 15% SiC p during hot deformation is carried out using the conventional regression method, artificial neural network (ANN) and adaptive neuro-fuzzy inference system (ANFIS) method. The temperature at which the aluminium is compressed are 300– 500 °C with strain rates ranging from 0.00857 to 2.7 s −1 and for the strains of 0.1–0.5. Simulation studies are carried out for analysis. By comparing the performances of various modeling techniques, ANFIS modeling can effectively be employed for prediction of flow stress of 6061 Al–15% SiC composites. The convergence speed of this algorithm is higher than that of the ANN.

Analysis of high temperature deformation behavior of a high Nb containing TiAl based alloy

The effects of deformation temperature and strain rate on the hot deformation behaviors of as-cast Ti–45Al–8.5Nb–(W,B,Y) alloy were investigated. The results indicated that when deformation temperature is below 1250 °C, the flow stress decreases with the increase of deformation temperature and decrease of strain rate, once deformation temperature reaches 1250 °C, the flow stress is not sensitive to strain rate any more. A neural network model was established to predict the flow stress of this high Nb containing TiAl based alloy during hot deformation. The predicted flow stress curves are in good agreement with experimental results.

Material flow stress and failure in multiscale machining titanium alloy Ti-6Al-4V

Titanium Ti-6Al-4V alloy is a typical difficult-to-machine material due to its unique physical and mechanical properties. The material properties of Ti-6Al-4V play an important role in process design and optimization. However, the dynamic mechanical behavior is poorly understood and accurate predictive models have yet to be developed. This work focuses on the dynamic mechanical behavior of machining Ti-6Al-4V beyond the range of strains, strain rates, and temperatures in conventional materials testing. The flow stress characteristics of strain hardening and thermal softening can be predicted by the Johnson–Cook model coupled with the adiabatic condition. The predicted flow stresses at small strains agree very well with those from the split Hopkinson pressure bar (SHPB) tests, while the predicted flow stresses at large strains also agree with the calculated flow stresses based on the cutting tests with a suitable depth of cut. Heat fraction and temperature parameter control the range of thermal softening and the decrease rate of flow stress. The material may exhibit super plasticity at a small depth of cut with a large radius of the cutting edge in micromachining. Strain rate is one important factor for material fracture close to the cutting edge. The failure strain increases linearly with the increase of homologous temperature, while it only increases slightly with the strain rate.

High Temperature Deformation Behavior of Ti-6Al-4V Alloy with an Equiaxed Microstructure: a Neural Networks Analysis

The hot deformation behavior of Ti−6Al−4V alloy with an equiaxed microstructure was investigated by means of Artificial Neural Networks (ANN). The flow stress data for the ANN model training was obtained from compression tests performed on a thermo-mechanical simulator over a wide range of temperature (from 700°C to 1100°C) with strain rates of 0.0001 s−1 to 100 s−1 and true strains of 0.1 to 0.6. It was found that the trained neural network could reliably predict flow stress for unseen data. Workability was evaluated by means of processing maps with respect to strain, strain rate, and temperature. Processing maps were constructed at different strains by utilizing the flow stress predicted by the model at finer intervals of strain rates and temperatures. The specimen failures at various instances were predicted and confirmed by experiments. The results establish that artificial neural networks can be effectively used for generating a more reliable processing map for industrial applications. A graphical user interface was designed for ease of use of the model.

Flow stress and microstructure evolution of semi-continuous casting AZ70 Mg-alloy during hot compression deformation

To evaluate and predict flow stress and set up hot forging process of AZ70 magnesium alloy, hot compression tests of AZ70 magnesium alloy were carried out on Gleeble 1500D thermo-mechanics tester at 300–420 °C and strain rates of 0.001–1 s −1 with different compression degrees. It is indicated that temperature and strain rate are the main factor affecting the flow stress and microstructure. Stress increases but average grain size decreases with temperature decreasing and strain rate increasing. The stress model, constituted by introducing temperature-compensated strain rate, the Zener-Hollomon parameter, has a good fitness with the proof stress value under the experimental condition. The reciprocal of grain size at true strain of 1.0 has a linear relation with natural logarithm of Z parameter, and the correlation coefficient, R=0.95, is very significant by examination. The hot deformation activation energy Q of AZ70 alloy is 166.197 kJ/mol by calculation.

Study on Flow Stress Model of a Microalloyed High Strength Steel in CSP Hot Rolling

Hot simulation tests at different deformation technology parameters were carried out for a microalloyed high strength steel produced by CSP hot rolling and the stress-strain curves during deformation were measured. Based on the experimental results and the discussions of present flow stress models, a new flow stress model incorporating interactional effect of deformation temperature, strain and strain rate on flow stress was developed in the paper. Excellent agreement between measured and predicted flow stress values is obtained for new flow stress model of a microalloyed high strength steel rolled by CSP. In addition, the comparisons of flow stress prediction errors between several models and one given in the paper reveal that the prediction accuracy of new flow stress model presented in the paper is higher than other models.