Flow Stress Evolution Research Articles

Orthogonal Cutting Simulation of OFHC Copper Using a New Constitutive Model Considering the State of Stress and the Microstructure Effects

This work aims to develop an orthogonal cutting model for surface integrity prediction, which incorporates a new constitutive model of Oxygen Free High Conductivity (OFHC) copper. It accounts for the effects of the state of stress on the flow stress evolution up to fracture. Moreover, since surface integrity parameters are sensitive to the microstructure of the work material, this constitutive model highlights also the recrystallization effects on the flow stress. Orthogonal cutting model is validated using experimental designed cutting tests. More accurate predictions were obtained using this new constitutive model comparing to the classical Johnson-Cook model.

Unified constitutive modelling for two-phase lamellar titanium alloys at hot forming conditions

In this paper, a set of mechanism based unified viscoplastic constitutive equations have been established for two-phase titanium alloys with initial lamellar microstructure, which models the softening mechanisms of the alloys in hot forming conditions. The dislocation density, rotation and globularization of lamellar α-phase and their effects on flow behaviour can also be modelled. The values of material constants in the equation set have been calibrated, according to stress-strain curves and globularization fractions of lamellar α-phase obtained from compression tests at a range of temperatures and strain rates, using a genetic algorithm (GA) based optimisation method. Based on the determined constitutive equations, flow stress and globularization evolution of Ti-17 and TA15 alloys at different temperatures and strain rates were predicted. Good agreements between the experimental and computed results were obtained.

Constitutive analysis of tensile deformation behavior for AA1100 aluminum subjected to multi-axial incremental forging and shearing

The evolution of flow stress with imposed strain for an aluminum alloy (AA1100) processed by severe plastic deformation (SPD) has been described by utilizing three different models. The applied constitutive laws include a generalized three-dimensional dislocation density based model, a formulation based on the combination of the Estrin and Mecking model with an Avrami-type equation (EMA), and finally a relationship based upon the dimensional analysis using Pi-theorem. To verify the predicted flow stress, newly developed SPD process called multi-axial incremental forging and shearing (MAIFS) were performed from one to eight passes on the aluminum alloy workpieces. It was shown that the predictions of the EMA and Pi-theorem based models agreed well with the experimental trend of flow stress variations over a wide range of strain, and these models were able to address both hardening and softening observed at high strains. But, some modifications should be carried out on the dislocation density based model to give results with a reasonable agreement with the experimental data in the range of strain softening. The correct true stress–strain curves of each of eight passes after tensile test flow localization were firstly calculated according to a neck evolution model proposed by Segal et al. (2006). Then, a general descriptive constitutive equation for tensile flow behavior of the material after each pass of SPD process was developed based on an extension of the model originated from Pi-theorem. Furthermore, the severely deformed specimens kept fairly large total tensile elongation and for proving ductility, scanning electron microscopy observations of fracture surfaces were carried out. These observations indicated that the fracture surfaces were characterized by a dimple-like structure, which implied the existence of a ductile failure mode.

Reduced order variational multiscale enrichment method for elasto-viscoplastic problems

This manuscript presents the formulation and implementation of a novel reduced order variational multiscale enrichment (ROVME) method for elasto-viscoplastic problems. This method provides a hierarchical model order reduction technique based on the eigenstrain concept to approximate the fine scale response resolved at subdomains of interest. By eliminating the requirement of direct fine scale discretization, the computational effort associated with the variational multiscale enrichment (VME) method is significantly reduced. The model order reduction is achieved in the scale-coupled inelastic problem by automatically satisfying the microscale equilibrium state through the eigenstrain concept and coarse discretization of inelastic strain fields within the microscale domain. The inelastic material behavior is idealized with coupled Perzyna type viscoplasticity and flow stress evolution based on the Johnson–Cook model. Numerical verifications are performed to assess the capabilities of the proposed methodology, against the direct VME method with detailed fine scale resolutions. The verification results demonstrate high accuracy and computational efficiency of the reduced order VME framework for elasto-viscoplastic problems with material heterogeneity.

Two-internal variable thermodynamics modelling of severe plastic deformation: dislocation and flow stress evolutions

Two-internal variable thermodynamics model is presented to investigate the evolution of microstructure and flow stress during severe plastic deformation. Previous studies have shown that due to heterogeneous distribution of dislocations during severe plastic deformation, the use of multivariable models is needed. In this regard, a two-internal variable model is presented. In the present paper, the dislocation densities in the subgrain boundaries and interiors are considered as internal variables. The model uses general laws of thermodynamics and describes the evolution of the dislocation densities on the basis of parameters such as the self-diffusion activation energy and the stacking fault energy. The model predicts the dislocation density, subgrain size and strength. To verify the model, the achieved results are compared with the experimental data.

Analysis of flow stress and deformation mechanism under hot working of ZK60 magnesium alloy by a new strain-dependent constitutive equation

The present study investigates the variation of flow stress and microstructural evolution with strain for ZK60 magnesium alloy. A new constitutive equation was used to model the flow stress with excellent results. This constitutive analysis and the microstructural studies carried out on strained samples revealed the existence of two different regimes. At temperatures above 300°C, moderate grain growth and intragranular dislocation activity. Yet, the calculated value of the activation energy and the marked increase in the equivalent strain to fracture indicated grain boundary sliding as a dominant mechanism in this regime of strain rate and temperature, with dislocation motion playing an ancillary role. At lower temperatures, deformation was exclusively governed by dislocation motion, with the extensive occurrence of dynamic recrystallization, which started at low strains, and absence of grain growth.

Flow Curve Evolution During Cyclic Processing of Ultrafine‐Grained Aluminum Alloy by Multiaxial Forging

A model to describe the evolution of flow curves during multiaxial forging is presented. Using the Gleeble physical simulator, forging experiments are carried out on EN AW‐6082 aluminum alloy. Three forging schedules with different applied strain amplitudes are performed at room temperature, all subjected to the same level of total accumulated strain. The flow curves are calculated using the previously developed mechanical model. The resultant microstructures are investigated by TEM studies. The flow curves are monotonic. However, the flow stress drops if the direction of the deformation is changed, indicating that the flow curves are cyclic in character. The evolution of flow stress is quantified, as well as the upper and lower limiting curves and the equivalent flow curves are determined. As the applied strain per pass increases, the cyclic flow stress varies from 100 to 150 MPa, from 105 to 170 MPa, and from 115 to 200 MPa for strain amplitudes of 0.2, 0.285, and 0.4, respectively. Comparing the effect of the different strain paths on the resultant microstructure, it becomes finer and more homogeneous with increasing strain amplitude. The average grain size decreased from 1 to 0.5 μm, when the applied strain per pass was doubled.

Hot Deformation and Dynamic Recrystallization of Ti-6Al-7Nb Biomedical Alloy in Single-Phase β Region

The aim of this investigation is to evaluate the hot deformation behavior and critical conditions for onset of dynamic recrystallization in Ti-6Al-7Nb biomedical alloy. The effects of temperature and strain rate on the hot deformation behavior of Ti-6Al-7Nb alloy were studied by employing hot compression tests. The experiments were conducted at temperatures of 1050, 1100, and 1150 °C under strain rates of 0.0025, 0.025, and 0.25 s−1 up to a true strain of 0.65. The evolution of compressive flow stress during deformation of the experimental alloy in the single-phase β region was investigated. The obtained microstructures showed the occurrence of partial dynamic recrystallization along the prior grain boundaries, which was discussed relying on the continuous recrystallization process. Using the strain-hardening rate curves (dσ/de versus σ), two characteristic parameters including the critical strain for DRX initiation (e c) and the strain for peak stress (e p) were identified. The normalized critical stress and strain for initiation of DRX were, respectively, found to be 0.9 and 0.67. True stress-true strain curves have been used to construct proper constitutive equations for the experimental alloy. The obtained activation energy for hot deformation was discussed considering the dominant restoration processes. Moreover, the flow stress was modeled for different strain levels, where good agreement with the experimental alloy was found.

Variational multiscale enrichment method with mixed boundary conditions for elasto-viscoplastic problems

This manuscript presents the formulation and implementation of the variational multiscale enrichment (VME) method for the analysis of elasto-viscoplastic problems. VME is a global---local approach that allows accurate fine scale representation at small subdomains, where important physical phenomena are likely to occur. The response within far-fields is idealized using a coarse scale representation. The fine scale representation not only approximates the coarse grid residual, but also accounts for the material heterogeneity. A one-parameter family of mixed boundary conditions that range from Dirichlet to Neumann is employed to study the effect of the choice of the boundary conditions at the fine scale on accuracy. The inelastic material behavior is modeled using Perzyna type viscoplasticity coupled with flow stress evolution idealized by the Johnson---Cook model. Numerical verifications are performed to assess the performance of the proposed approach against the direct finite element simulations. The results of verification studies demonstrate that VME with proper boundary conditions accurately model the inelastic response accounting for material heterogeneity.

Description of Grain Refinement by Dynamic Recrystallization Under Hot Compressions for As-Extruded 3Cr20Ni10W2 Heat-Resistant Alloy

Abstract The dynamic recrystallization (DRX) behavior of as-extruded 3Cr20Ni10W2 heat-resistant alloy was investigated by hot compressions with a fixed height reduction of 60% over a temperature range from 1,203 to 1,403 K and a strain rate range from 0.01 to 10 s−1. Results show that DRX occurs more easily at lower temperatures and higher strain rates, the stress level increases significantly with the increase of deformation temperature or the decrease of strain rate. Under such wide range of deformation conditions the flow stress evolution generally indicates two characteristics: work hardening (WH) followed by DRX, or by dynamic recovery (DRV). The variation of the average size of grains refined by DRX behavior in the alloy is characterized by linking the deformation conditions during hot compression process. At a fixed temperature, the average grain size linearly decreases with increasing strain rate in log scale. At a lower strain rate, the average grain size rapidly increases with increasing temperature, while it remains almost constant at strain rate of 10 s−1. At a higher strain rate, grain size data sets tend to be closer to the average size value, which indicates that as strain rate increases, the microstructures become more and more uniform. The effects of the temperatures and strain rates on the average grain size can be represented by Zener–Hollomon parameter, Z, and the relationships between the average grain size and Z parameter can be described as a nonlinear equation, which indicates that the average grain size decreases with increasing Z parameter. On the plot of average grain size D A $${D_A}$$ – l n Z $${\rm{ln}}\,Z$$ , the regions corresponding to DRV ( l n Z ≤ 77.9 $${\rm{ln}}\ Z\,\le \,77.9$$ ) and DRX ( l n Z > 77.9 $${\rm{ln}}\ Z\,\gt \,77.9$$ ) were clarified clearly.

Thermomechanical deformation behaviour of DH36 steel during friction stir welding by experimental validation and modelling

Friction stir welding is a solid state thermomechanical deformation process from which the plasticisation behaviour of the stirred material can be evaluated through the study of flow stress evolution. Flow stress data also supporting the development of a local microstructural numerical model have been generated. Hot compression testing of DH36 steel has been performed at a temperature range of 700–1100°C and strain rates from 10−3 to 102 s−1 to study the alloy’s thermomechanical deformation behaviour in conditions that simulate the actual friction stir welding process. It has been found that the evolution of flow stress is significantly affected by the test temperature and deformation rate. The material’s constitutive equation and constants have been calculated after analysis of these data. Preliminary numerical analysis results are in good agreement with experimental observations.

Development a dislocation density based model considering the effect of stacking fault energy: Severe plastic deformation

Considering the effect of an intrinsic material parameter, stacking fault energy (SFE), a model based on dislocation density is developed to investigate the evolutions of dislocation density, cell size and flow stress during severe plastic deformation of aluminum and nickel. In fact a model is presented considering the work hardening and different annihilation mechanisms for dislocation densities in cell interiors and cell walls. Annihilation terms are developed on the basis of SFE through the model. The calculations show that the total dislocation density, dislocation density in cell interiors, dislocation density in cell walls and flow stress are decreased with increasing SFE. To verify the model results, they are compared with the experimental data and a good agreement is observed.

Briefing of CSC and its R & D Activities for Metal Forming

China Steel Corporation was founded in 1971 being the largest integrate steel mill in Taiwan. After several stages of expansion projects, its crude steel production has reached 16.5 million tons annually. CSC has made consistent efforts on its technology innovation mainly carried out by two R & D departments. One of the major tasks of its R & D activities is to establish the advanced technologies for the manufacturing better steels and aluminum alloys as well as product application technology for downstream users. This presentation will mainly brief the research activities of CSC in the field of metal forming including rolling, sheet metal forming and thermal mechanical simulations carried out at Gleeble 3800. Work rolls with continuously variable crown (CVC) were applied to produce hot-rolled strips having precise profile and flatness. Lubrication rolling technology with high speed steel rolls was developed to diminish the wearing of work rolls at hot strip mills. The campaign life of rolling cycle was greatly prolonged. Computer-aided engineering (CAE) simulation technology of sheet metal forming has been established which proved to be an effective way to deal with the sever spring back and breakage of the cold forming of high strength steel automobile parts. Hot stamping has also been developed to support the technology innovation of CSC’s downstream customers. Flow stress and microstructure evolution during hot rolling for aluminum alloys were investigated using a Gleeble 3800 simulator. Both high strength AA5182 for can end and low earing AA3104 for can body aluminum sheets have been successfully developed.

Evolution of flow stress and microstructure during isothermal compression of Waspaloy

The evolution of the flow stress and microstructure for Waspaloy was studied in the 950–1140°C temperature range under constant true strain rate conditions of 0.001–1s−1 up to a true strain of 0.83 using isothermal hot compression testing. The impact of friction at the sample/anvil interface and adiabatic heating during deformation on the flow stress evolution was also examined. Mathematical models relating the flow stress to the deformation temperature and strain rate were derived using a power–law relationship. The strain rate sensitivity and the activation energy for hot deformation of Waspaloy were found to be considerably different for deformation in the subsolvus and supersolvus temperature ranges. According to the microstructural investigations, at 950°C dynamic recovery (DRV) was the main softening mechanism. By contrast, dynamic recrystallization (DRX), partial or complete, occurred at temperatures above 950°C and resulted in flow softening.

Re-Meshing in Finite Element Simulations of Hot Working Including a Microstructural Evolution Model

Material models that couple the evolution of flow stress to the evolution of the microstructure are important for the simulation of hot working processes in which the microstructure undergoes large changes. Among the microstructural evolution mechanisms in hot working, dynamic recrystallization (DRX) plays a central role as it occurs during deformation. When the workpiece deforms, the element shape may deteriorate, which makes re-meshing necessary. At the same time, certain regions of the finite element mesh undergo DRX and a sharp interface between recrystallized and non-recrystallized portions of the workpiece develops. Elements of the old mesh that are cut by the interface contain nodes with a non-zero recrystallized volume fraction and nodes where the recrystallized volume fraction is zero. During re-meshing, when the microstructural data is transferred to the new mesh, nodes or integration points that are actually in region of the workpiece that is not yet recrystallized may be assigned a non-zero recrystallized volume fraction. As a consequence, the interface moves, which is unwanted and may produce large errors when re-meshing is frequently done. In this paper, the problem of the propagation of the DRX interface during re-meshing is treated. It is shown that the propagation occurs with standard data mapping algorithms and produces a large error at the interface. A re-meshing scheme is proposed that uses a smooth mesh-free interpolating function based on radial basis functions to interpolate the recrystallized volume fraction. The interface is the zero level set of this interpolant. Performing the mapping as a least squares fit of the interpolant allows for a substantial reduction of the mapping error and suppresses the propagation of the DRX front.

Onset of the Portevin-Le Chatelier Effect: Role of Synchronization of Dislocations

The problem of the onset of the Portevin-Le Chatelier (PLC) effect is revised by combining a study of the kinetics of the flow stress evolution upon abrupt changes in the applied strain rate and acoustic emission (AE) accompanying plastic deformation of an AlMg alloy. The kinetic measurements allow evaluating the strain-rate sensitivity of the flow stress and the time characteristics of transient processes as functions of plastic strain. Using known criteria of plastic instability, domains of instability are constructed in the (strain, strain rate) plane. A particular accent is put on the strain-rate range corresponding to the so-called “inverse” behavior. The comparison of such maps with experimental data on the critical strain testifies to the insufficiency of these criteria for explaining the onset of the PLC effect. Moreover, the slow transient kinetics contradicts observations of the fast development of stress drops. The AE measurements bear witness that the stress serrations are associated with bursts in duration of acoustic events generated by the collective motion of dislocations. The possible role of synchronization of dislocation dynamics on the onset of plastic instability is discussed.

Hydrogen effects on low cycle fatigue of high strength steels

Hydrogen absorption occurs during steelmaking processes and causes detriment on mechanical properties, such as plasticity, fatigue strength and tensile strength, among others. The main purpose of the present paper is to study the hydrogen effects on the low cycle fatigue behaviour of a high strength steel, resulphurised and microalloyed. Before the cyclic tests, samples are cathodically charged using a H2SO4 acid solution. In some samples, poisons are added. The flow stress evolution during cycling was studied by analysing the so called ‘back’ and ‘friction’ stresses derived from the hysteresis loops. Fatigued specimens were observed through scanning electron microscopy and transmission electron microscopy. Additionally, the metallographic technique known as ‘silver decoration’ allows evaluation of the hydrogen distribution in the structure by applying energy dispersive analysis. The higher stress levels and cyclic softening rates exhibited by hydrogen charged samples in comparison with uncharged ones are related with the friction stress behaviour. The hydrogen is found mainly associated with MnS inclusions.

A cluster-type grain interaction deformation texture model accounting for twinning-induced texture and strain-hardening evolution: Application to magnesium alloys

Twinning plays two important roles in deformation texture evolution: it reorients the twinned volume of a grain discontinuously, thus causing a texture change; and the lamellar structure of twins reduces the mean free path for dislocation slip, which effectively promotes work-hardening. To correctly predict the texture evolution of materials in which twinning plays an important role, both effects of deformation twinning must be taken into consideration. In the current work, both effects are accounted for in the cluster-type deformation texture grain interaction (GIA) model. Slip-induced strain-hardening was considered by employing a one-parameter hardening model, which calculates the flow stress evolution for each slip system. Twinning-induced strain-hardening was incorporated into the model by treating twin lamellae as ellipsoidal inclusions formed by alternating layers of twin and matrix domains. The twin–matrix interfaces provide barriers and define a directional mean free path for the propagations of subsequent slip or further twinning. The modified GIA model is called the GIA-TW-HD model. It was applied to predict the deformation behavior and texture evolution of Mg alloy AZ31 at 100°C. The predicted texture evolution as well as strain-hardening curves were compared with experimental results. Overall good agreement between simulation and experiment was obtained.

Unified modeling of flow softening and globularization for hot working of two-phase titanium alloy with a lamellar colony microstructure

In this paper, a set of physically based constitutive model coupling microstructure evolution was developed for unified prediction of flow stress and globularization evolution during hot working of two-phase titanium alloys with initial lamellar microstructure. The dislocation density variation, dynamic globularization and effect of Hall–Petch strengthening were considered in the microstructure model. The dynamic globularization was modeled by two parts: critical strain for initiation of globularization and globularization rate, both of which are function of processing conditions (temperature and strain rate); In the modeling of Hall–Petch strengthening, the dependence of Hall–Petch coefficient on processing conditions were considered and the loss of Hall–Petch strengthening with deformation process was molded. The microstructure model was implemented to a physically based constitutive model, composed of a thermally activated stress and an athermal stress, to realize the unified prediction of flow stress and globularization evolution. The material parameters were determined by calibration using the experimental flow stress and globularization fraction in isothermal compression tests through the genetic algorithm based optimization method. Based on the set of constitutive models, flow stress and globularization evolution of Ti–6Al–4V and TA15 alloys at different temperatures and strain rates were predicted. Good agreements between the experimental and computed results were obtained.

Multi-Phase-Field Simulation of Flow Stress and Microstructural Evolution during Deformation-Induced Ferrite Transformation in a Fe–C Alloy

Deformation-induced ferrite transformation (DIFT) is one of the most effective ways of refining ferrite grains in steel. In this study, we employed a multi-phase-field (MPF) model to simulate both variations in macroscopic flow stress and microstructural evolution during DIFT. Using the MPF model, two-dimensional simulations of DIFT in a Fe–C alloy were performed to investigate the effects of strain rate, austenite grain size, and dynamic recrystallization (DRX) of the ferrite phase on flow stress curve and ferrite grain size. The results demonstrated that increasing the rate of ferrite nucleation by increasing the strain rate and reducing the austenite grain size is essential to obtaining fine-grained ferrite. The results of the simulations also indicated that it is important to reduce the interfacial mobility and increase the nucleation rate of the ferrite grains subjected to DRX in order to obtain ultrafine-grained ferrite by DIFT when it is accompanied by DRX of the ferrite phase. Thus, the MPF model is an effective tool for elucidating the correlation between the variation in the flow stress and the evolution of the ferrite grains during DIFT.