Physically based models for the plastic behavior of crystalline, metallic materials are discussed. However, deformation by twinning and phase transformations as well as the evolution of texture are omitted.
Two austenitic stainless steels, with low and medium stacking fault energies (SFE), 20 mJ/m2 and 30 mJ/m2 respectively, have been studied by conventional tensile tests and in situ tensile tests in a FEG-SEM equipped for EBSD. High angle boundaries (HAB) and low angle boundaries (LAB) with misorientations >= 10o and >= 2o respectively have been determined, and size distributions for the LABs have been derived by linear intercepts. It was found that the size distributions could be described by bimodal lognormal functions. For the steel with highest SFE plastic deformation took place by dislocation slip only while the steel with low SFE deformed by slip and twinning. Using a model for slip based on the evolution of the dislocation density with the generation of dislocations inversely proportional to the mean free distance of slip and recovery of dislocations proportional to the dislocation density the stress strain-curves were analyzed and the results compared with the measured quantities. The mean free distance of slip as evaluated from the stress-strain curve for the steel with the highest SFE correlates very well with the mean size of the LABs intercept. The rate of recovery also gave an expected stress dependence. The stress needed to start deformation twinning was based on the assumption that Shockley partials become completely separated in the slip plane. The thus calculated values for the twinning stress showed an excellent agreement with the observed start of twinning as given by EBSD evaluation of twin boundaries (TB). For the alloy with low SFE both surface grains (in situ test) and bulk grains (from interrupted conventional tests) were studied. The stress needed for slip and twinning of surface grains was, as expected, in the order of 0.5-0.6 times the applied stress.
Metal working processes encompass a wide range of strain, strain rates and temperatures. Strains range from less than 0.01 (for example in skin-pass rolling of interstitial free steel) up to around 1 (cold rolling of strip, extrusion, etc.). Typical strain rates and temperatures are given in Table 11.1 (which is partly an extract from Frost and Ashby (1982). For plastic forming processes the most important characteristics of the material are: the ability to distribute strains; the deformation resistance; and the resulting properties of the formed part. The ability to distribute strains is mainly governed by the work hardening and strain-rate sensitivity. It is also affected by the strain path. The purpose of this paper is to outline the, in our view, most essential material properties for metal working processes and the microstructural reasons for them. We recognise that the presence and development of crystallographic texture is quite an important part but our purpose is not to give an extensive description of this, only to point out some consequences. For further reading we recommend a book by Kocks, Tomé and Wenk (1998). Another aspect that is only briefly covered is the influence of stress states and changes in strain paths during processing or between consecutive process steps.
A number of physically based models are combined in order to predict microstructure development during hot deformation. The models treat average values for the generation and recovery of vacancies and dislocations, recrystallization and grain growth and the dissolution and precipitation of second phase particles. The models are applied to a number of laboratory experiments made on 304 austenitic stainless steel and the model parameters are adjusted from those used for low alloyed steel mainly in order to obtain the right kinetics for the influence of solute drag on climb of dislocations and on grain growth. The thermodynamic data are obtained using Thermo-Calc© to create solubility products for the possible secondary phases. One case of wire rolling has been analyzed mainly concerning the evolution of recrystallization and grain size. The time, temperature and strain history has been derived using process information. The models are shown to give a fair description of the microstructure development during hot working of the studied austenitic stainless steel. © (2013) Trans Tech Publications, Switzerland.
A physically based model for predicting microstructural evolution has been developed. The model is based on a physical description of dislocation density evolution, where the generation and recovery of dislocations determine the flow stress and also the driving force for recrystallization. In the model, abnormally growing subgrains are assumed to be the nuclei of recrystallized grains and recrystallization starts when the subgrains reach a critical size and configuration. To verify that the model is able to describe dynamic, static and metadynamic recrystallization of C-Mn steels, hot compression tests combined with relaxation were performed at various temperatures, strains and strain rates. The model showed reasonable agreement with the experimental data for the compression tests performed at temperatures ranging from 850?C to 1200?C and strain rates ranging from 0.1 to 10 s-1. Also, the calculations of the stress relaxation tests show good agreement with experimental data. A validation of the model was done by calculating a multi-step test where good agreement with both flow-stress values and grain sizes was obtained. The main purpose of the model is to be able to predict the microstructural evolution during hot rolling and this investigation presents very promising results.
Crystallographic reconstruction of parent austenite grain boundaries from the martensitic microstructure in a wear resistant steel was carried out using electron backscattered diffraction (EBSD). The present study mainly aims to investigate the parent austenite grains from the martensitic structure in an as-rolled (reference) steel sample and samples obtained by quenching at different cooling rates with corresponding dilatometry. Subsequently, this study is to correlate the nearest cooling rate by the dilatometer which yields a similar orientation relationship and substructure as the reference sample. The Kurdjumov-Sachs orientation relationship was used to reconstruct the parent austenite grain boundaries from the martensite boundaries in both reference and dilatometric samples using EBSD crystallographic data. The parent austenite grain boundaries were successfully evaluated from the EBSD data and the corresponding grain sizes were measured. The parent austenite grain boundaries of the reference sample match the sample quenched at 100 °C/s (CR100). Also the martensite substructures and crystallographic textures are similar in these two samples. The results from hardness measurements show that the reference sample exhibits higher hardness than the CR100 sample due to the presence of carbides in the reference sample.
A physically based model is used to describe the microstructural evolution of Nb microalloyed steels during hot rolling. The model is based on a physical description of dislocation density evolution, where the generation and recovery of dislocations determines the flow stress and also the driving force for recrystallization. In the model, abnormally growing subgrains are assumed to be the nuclei of recrystallized grains and recrystallization starts when the subgrains reach a critical size and configuration. The model is used to predict the flow stress during rolling in SSAB Tunnplåt’s hot strip mill. The predicted flow stress in each stand was compared to the stresses calculated by a friction-hill roll-force model. Good fit is obtained between the predicted values by the microstructure model and the measured mill data, with an agreement generally within the interval ±15%.
Using a physically based model, the microstructural evolution of Nb microalloyed steels during rolling in SSAB Tunnplåt’s hot strip mill was modeled. The model describes the evolution of dislocation density, the creation and diffusion of vacancies, dynamic and static recovery through climb and glide, subgrain formation and growth, dynamic and static recrystallization and grain growth. Also, the model describes the dissolution and precipitation of particles. The impeding effect on grain growth and recrystallization due to solute drag and particles is accounted for. During hot strip rolling of Nb steels, Nb in solid solution retards recrystallization due to solute drag and at lower temperatures strain-induced precipitation of Nb(C,N) may occur which effectively retard recrystallization. The flow stress behavior during hot rolling was calculated where the mean flow stress values were calculated using both the model and measured mill data. The model showed that solute drag has an essential effect on recrystallization during hot rolling of Nb steels.
We introduce a theory-guided experimental approach to study the γ-surface of austenitic stainless steels. The γ-surface includes a series of intrinsic energy barriers (IEBs), which are connected to the unstable stacking fault (USF), the intrinsic stacking fault (ISF), the unstable twinning fault (UTF) and the extrinsic stacking fault (ESF) energies. The approach uses the relationship between the Schmid factors and the effective energy barriers for twinning and slip. The deformation modes are identified as a function of grain orientation using in situ electron backscatter diffraction measurements. The observed critical grain orientation separating the twinning and slip regimes yields the USF energy, which combined with the universal scaling law provides access to all IEBs. The measured IEBs and the critical twinning stress are verified by direct first-principles calculations. The present advance opens new opportunities for modelling the plastic deformation mechanisms in multi-component alloys.
In FCC metals a single parameter – stacking fault energy (SFE) – can help to predict the expectable way of deformation such as martensitic deformation, deformation twinning or pure dislocation glide. At low SFE one can expect the perfect dislocations to dissociate into partial dislocations, but at high SFE this separation is more restricted. The role of the magnitude of the stacking fault energy on the deformation microstructures and tensile behaviour of different austenitic steels have been investigated using uniaxial tensile testing and electron backscatter diffraction (EBSD). The SFE was determined by using quantum mechanical first-principles approach. By using plasticity models we make an attempt to explain and interpret the different strain hardening behaviour of stainless steels with different stacking fault energies.
In this study, three austenitic stainless steels with different compositions are compared in terms of their deformation behaviour. Two of the investigated steels have considerable high nitrogen content which affects their deformation behaviour. The deformation properties and microstructure of the materials were studied by tensile testing and electron backscatter diffraction. We observe that the strain hardening rate curve of the alloy with low nitrogen content shows a continuously decreasing slope, whereas those of the high‑nitrogen steels exhibit a clear plateau. Since no twinning or ε-phase formation is observed at the corresponding strain levels, we suggest that the addition of a large amount of nitrogen suppresses cross-slip and promotes dislocation planarisation. The microstructural evolution of the materials during deformation supports the above scenario. Based on the results of the ab initio calculations, the deformation behaviour of high‑nitrogen alloys cannot be explained in terms of the stacking fault energy.
The stacking fault energy (SFE) is often used as a key parameter to predict and describe the mechanical behaviour of face centered cubic material. The SFE determines the width of the partial dislocation ribbon, and shows strong correlation with the leading plastic deformation modes. Based on the SFE, one can estimate the critical twinning stress of the system as well. The SFE mainly depends on the composition of the system, but temperature can also play an important role. In this work, using first principles calculations, electron backscatter diffraction and tensile tests, we show a correlation between the temperature dependent critical twinning stress and the developing microstructure in a typical austenitic stainless steel (316L) during plastic deformation. We also show that the deformation twins contribute to the strain hardening rate and gradually disappear with increasing temperature. We conclude that, for a given grain size there is a critical temperature above which the critical twinning stress cannot be reached by normal tensile deformation, and the disappearance of the deformation twinning leads to lower strain hardening rate and decreased ductility.
The microstructure evolution of a martensitic Stainless steel subjected to hot compression is simulated with a physically based model. The model is based on coupled sets of evolution equations for dislocations, vacancies, recrystallization and grain growth. The advantage of this model is that with only a few experiments, the material dependent parameters of the model can be calibrated and used for a new alloy in any deformation condition. The experimental data of this work is obtained from a series of hot compression, and subsequent stress relaxation tests performed in a Gleeble thermo-mechanical simulator. These tests are carried out at various temperatures ranging from 900 to 1200⁰C, strains up to 0.7 and strain rates of 0.01, 1 and 10 s-1. The grain growth, flow stress, and stress relaxations are simulated by finding reasonable values for model parameters. The flow stress data obtained at the strain rate of 10 s-1 were used to calibrate the model parameters and the predictions of the model for the lower strain rates were quite satisfactory. An assumption in the model is that the structure of second phase particles does not change during the short time of deformation. The results show a satisfactory agreement between the experimental data and simulated flow stress, as well as less than 5% difference for grain growth simulations and predicting the dominant softening mechanisms during stress relaxation according to the strain rates and temperatures under deformation.
The mean size and fraction of the second-phase particles in a 13% chromium steel are investigated, while no plastic deformation was applied. The results of the measurement are compared with the modelling results from a physicallybased model. The heating sequence is performed on samples using a Gleeble thermo-mechanical simulator over the temperature range of 850?1200°C. Using scanning electron microscopy (SEM) and energy dispersive spectroscopy (EDS), the size distribution and composition of the carbides were evaluated, respectively. For obtaining particle size distribution (PSD), an image-processing software was employed to analyse the SEM images. Additionally, the relation between the 2D shape factor and size of the particles is also studied at different temperatures and most of the particles turned out to have a shape factor close to two. In order to measure the carbide weight fraction, electrochemical phase isolation was employed. The Ms and fraction of the martensite phase after quenching of samples are calculated and the results were comparable with the measured hardness values at corresponding temperatures. The measured hardness of the samples is found to comply very well with the measured mean size of the precipitates. The calculated mean size of the particles from the model shows very good agreement with both hardness value and experimentally measured mean size, while the calculated volume fraction from simulation follows a slightly different trend.
The behavior of a 13% chromium steel subjected to hot deformation has been studied by performing hot compression tests in the temperature range of 850 to 1200 ⁰C and strain rates from 0.01 to 10 s-1. The uniaxial isothermal compression tests were performed on a Gleeble thermo-mechanical simulator. The best function that fits the peak stress for the material and its relation to the Zener-Hollomon parameter (Z) is illustrated. The average activation energy of this alloy for the entire test domain was reviled to be about 557 [kJ mol-1] from the calculations and the dynamic recrystallization (DRX) kinetic were studied to find the fraction DRX in the course of deformation.
A physical model for austenite recrystallization of steel concerning TMCP is developed. Dislocation density plays a key role as recrystallization driving force. The dislocation density change is a result of competition between dislocation generation and dynamic recovery. Recrystallization is described as a nucleation-growth process. An abnormal subgrain growth mechanism is introduced for nucleation. A few subgrains fulfilling abnormal growth conditions will stand out and become nuclei of recrystallization. The recrystallized grain grows to the deformed materials driven by the stored energy. Oswald ripening occurs for grains surrounded by recrystallized grains. The models were verified by laboratory simulation results for selected austenite stainless steels. It showed good agreement between predicted and experimental results.
The evolution of the deformation structure with strain has been studied using electron backscatter diffraction (EBSD). Samples from interrupted uniaxial tensile tests and from a cyclic tension/compression test were investigated. The evolution of low angle boundaries (LABs) was studied using boundary maps and by measuring the LAB density. From calculations of local misorientations, smaller orientation changes in the substructure can be illustrated. The different orientations developed with strain within a grain, due to operation of different slip systems in different parts of the grain, were studied using a misorientation profile showing substantial orientation changes after a true strain of 0.24. The texture evolution with increasing strain was followed by using inverse pole figures (IPFs). The observed substructure development in the ferritic and austenitic phases could be successfully correlated with the stress-strain curve from a tensile test. LABs were first observed in the different phases when the strain hardening rate changed in appearance indicating that cross slip started to operate as a significant dislocation recovery mechanism. The evolution of the deformation structure is concluded to occur in a similar manner in the austenitic and ferritic phases but with different texture evolution for the two phases.
Material characterization is of great importance for example to improve and further develop physically based models for predicting the microstructural evolution in steels during and after hot deformation. The aim of this study was to characterize the microstructure evolution during wire rod rolling of an austenitic stainless steel of type AISI 304L in a wire rod block, consisting of eight pairs of rolls, using electron backscatter diffraction. The investigation showed that the grain size in the center of the bar decreases during the first four passes. The grain size decrease from 6.5 Όm after the first roll pass down to 2 Όm, and only small changes was measured in the overall grain size during the last four passes. The subgrain size adopts an almost constant size of 0.9 Όm from the second until the fifth roll pass. During the first 3 passes almost no recrystallization is observed and strain accumulates. Partial recrystallization then starts and for the last 3 passes the recrystallization is almost complete and the texture is nearly random. © (2013) Trans Tech Publications, Switzerland.
Specimens from split Hopkinson pressure bar experiments, at strain rates between ~ 1000–9000 s− 1 at room temperature and 500 °C, have been studied using electron backscatter diffraction. No significant differences in the microstructures were observed at different strain rates, but were observed for different strains and temperatures. Size distribution for subgrains with boundary misorientations > 2° can be described as a bimodal lognormal area distribution. The distributions were found to change due to deformation. Part of the distribution describing the large subgrains decreased while the distribution for the small subgrains increased. This is in accordance with deformation being heterogeneous and successively spreading into the undeformed part of individual grains. The variation of the average size for the small subgrain distribution varies with strain but not with strain rate in the tested interval. The mean free distance for dislocation slip, interpreted here as the average size of the distribution of small subgrains, displays a variation with plastic strain which is in accordance with the different stages in the stress-strain curves. The rate of deformation hardening in the linear hardening range is accurately calculated using the variation of the small subgrain size with strain.
Abstract The microstructure evolution in both surface and bulk grains in a pure Fe-19Cr-12Ni alloy has been analyzed using electron backscatter diffraction after tensile testing interrupted at different strains. Surface grains were studied during in situ tensile testing performed in a scanning electron microscope, whereas bulk grains were studied after conventional tensile testing. The evolution of the deformation structure in surface and bulk grains displays a strong resemblance but the strain needed to obtain a similar deformation structure is lower in the case of surface grains. Both slip and twinning are observed to be important deformation mechanisms, whereas deformation-induced martensite formation is of minor importance. Since the stacking fault energy (SFE) is low, 17mJ/m2, dynamic recovery by cross slip of un-dissociated dislocations is unfavorable. This reduces the annihilation of dislocations which in turn leads to a significant increase of low angle boundaries with increasing strain. The low SFE also favors formation of deformation twins which reduces the slip distance, leading to a hardening similar to the Hall-Petch relation. The combination of a low ability for cross-slip and a reduced slip distance caused by twinning is concluded to be the main reason for maintaining a high strain-hardening rate up to strains close to necking.
Plastic deformation of surface grains has been observed by electron backscatter diffraction technique during in situ tensile testing of a high-nickel austenitic stainless steel. The evolution of low- and high-angle boundaries as well as the orientation changes within individual grains has been studied. The number of low-angle boundaries and their respective misorientation increases with increasing strain and some of them also evolve into high-angle boundaries leading to grain fragmentation. The annealing twin boundaries successively lose their integrity with increasing strain. The changes in individual grains are characterized by an increasing spread of orientations and by grains moving towards more stable orientations with 〈111〉 or 〈001〉 parallel to the tensile direction. No deformation twins were observed and deformation was assumed to be caused by dislocation slip only.