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Odd Sture Hopperstad - One of the best experts on this subject based on the ideXlab platform.
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on the effect of Plastic Anisotropy strength and work hardening on the tensile ductility of aluminium alloys
International Journal of Solids and Structures, 2020Co-Authors: Bjorn Hakon Frodal, David Morin, Tore Borvik, Odd Sture HopperstadAbstract:Abstract The influence of Plastic Anisotropy, yield strength and work hardening on ductile failure is studied by nonlinear finite element simulations and strain localization analyses of tensile tests in different material orientations. Three aluminium alloys with different grain structures and crystallographic textures, heat-treated to three conditions giving rise to different yield strength and work-hardening behaviours, are considered. The anisotropic yield surfaces of the alloys, obtained by the crystal Plasticity finite element method, are used in the numerical simulations of ductile failure in the tensile tests. In addition, a yield surface for an isotropic material is included for comparison. These yield surfaces are combined with three stress-strain curves representative of the different heat-treatments, resulting in a range of relevant model materials with different Plastic Anisotropy, yield strength and work hardening used in the numerical investigations. Finite element simulations of tensile tests in seven in-plane directions are carried out, i.e., 0°, 15°, 30°, 45°, 60°, 75° and 90° to the reference direction, and the non-proportional loading histories are used in the subsequent strain localization analyses. Plastic Anisotropy is found to have a marked influence on the tensile ductility and to induce failure Anisotropy, i.e., a variation in the failure strain with loading direction. The shape and extension of the regions of concentrated Plastic flow in the finite element simulations vary with tensile direction for the anisotropic materials. In agreement with previous experimental evidence, the strain localization analyses predict a variation of the failure strain with tensile direction that appears to correlate with the variation of the Lankford coefficient, indicating that the failure Anisotropy is closely linked to the Plastic Anisotropy. The strain localization analyses predict a higher ductility for materials with lower yield strength and higher work hardening, as these features lead to a more distributed Plastic deformation and a stress state with a lower stress triaxiality in the neck. This redistribution of the Plastic deformation makes the tensile specimen less prone to strain localization and subsequent ductile failure. The influence of yield strength and work hardening is further found to depend on the Plastic Anisotropy.
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Work hardening and Plastic Anisotropy of naturally and artificially aged aluminium alloy AA6063
Mechanics of Materials, 2019Co-Authors: Mikhail Khadyko, Ole Runar Myhr, Odd Sture HopperstadAbstract:Abstract The Plastic Anisotropy of an extruded AA6063 alloy after different heat treatments was investigated in a previous study by Khadyko et al. (2017 ). The material was available in temper T1 (naturally aged to a substantially stable condition) and directly heat treated to the peak aged, overaged and soft annealed conditions without solution heat treatment. Tensile tests in different material directions were performed for these materials and it was found that the Plastic Anisotropy depended in a complex way on the heat treatment. In the present study, the experimental programme is extended to investigate further the influence of heat treatment on the Plastic Anisotropy. The AA6063 extruded alloy is first solution heat treated, and then either naturally aged to temper T4 or artificially aged to tempers T6 (peak aged) and T7 (over-aged). Tensile tests in three material directions are performed for these tempers and in the solution heat treated condition (temper W) to reveal the Plastic Anisotropy. The microstructure evolution of all these materials is then modelled using a nanostructure model (NaMo), which predicts the size distribution of hardening particles, the solute content, the yield strength and the work hardening. The predictions of NaMo are validated using the available data from the tensile tests and TEM observations, and used to analyse the correlation between the stress-strain behaviour and the heat treatment and microstructure of the different materials.
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effects of heat treatment on the Plastic Anisotropy of extruded aluminium alloy aa6063
Materials Science and Engineering A-structural Materials Properties Microstructure and Processing, 2017Co-Authors: Mikhail Khadyko, Stephane Dumoulin, Tore Borvik, Calin Daniel Marioara, Odd Sture HopperstadAbstract:Abstract The Plastic Anisotropy of aluminium alloys is known to depend not only on the crystallographic texture but also on the heat-treatment, and this effect has been studied on various alloys both experimentally and numerically. However, the 6000 series of aluminium alloys is not broadly represented in these studies. In this work, an extruded profile of the AA6063 alloy was investigated. Electron backscatter diffraction (EBSD) measurements revealed a strong cube crystallographic texture with a minor Goss component, which is typical for recrystallized aluminium alloys. The Plastic Anisotropy was studied by uniaxial tension tests in different material directions, using digital image correlation to measure the displacement field and thus to calculate the strain field. The tensile specimens were heat-treated to three different tempers: T6, T7 and O, in addition to the as-received T1 condition. Transmission electronic microscopy (TEM) was used to characterize the precipitate structure of the heat-treated material. A crystal Plasticity finite element model of the tensile test was created and calibrated using some of the experimental data. The comparison of the experimental stress-strain curves, strain ratios and flow stress ratios with their simulated counterparts revealed that the crystallographic texture is dominating the Anisotropy in all tempers. The accuracy of the CP-FEM predictions varies for different material orientations, and, in general, the simulated material exhibits a sharper Anisotropy than the real material. The effect of the heat treatment on the Anisotropy is found to be minor compared with the texture effect.
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latent hardening and Plastic Anisotropy evolution in aa6060 aluminium alloy
International Journal of Plasticity, 2016Co-Authors: Mikhail Khadyko, Stephane Dumoulin, Georges Cailletaud, Odd Sture HopperstadAbstract:The crystal Plasticity theory predicts that hardening on a particular slip system and its corresponding work-hardening rate will depend on the slip activity on both this slip system and all others. The exact form of this dependence is defined by the latent hardening description in form of the latent hardening matrix or the interaction matrix. It has been assumed that this matrix describes the relative strength of various dislocation interactions and is therefore the same for a wide range of alloys with the same lattice structure. Different methods have been used to estimate the values of the interaction matrix components: one is experimental and uses strain-path changes; another simulates the dislocations dynamics in a crystal directly at the microscale and estimates the strength of the forming locks. In this work, the influence of the interaction matrix (and thus latent hardening) on the development of Plastic Anisotropy is studied. An extruded AA6060 alloy is tested in uniaxial tension in different directions and the Anisotropy of the alloy is found to evolve considerably throughout the deformation. A crystal Plasticity model is used to simulate the experimental tests, and the use of different interaction matrices is evaluated. A noticeable influence on the predicted evolution of Plastic Anisotropy as well as on the stress–strain field and slip inside the constituent grains is found.
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description of Plastic Anisotropy in aa6063 t6 using the crystal Plasticity finite element method
Modelling and Simulation in Materials Science and Engineering, 2012Co-Authors: Stephane Dumoulin, Odd Sture Hopperstad, Olaf Engler, Oddgeir LademoAbstract:The crystal Plasticity finite element method has been used in combination with crystallographic texture data to predict the Plastic Anisotropy of the extruded aluminium alloy AA6063 in temper T6. The results are compared with experimental data from tensile tests at different angles between the tensile and extrusion directions. Inverse modelling based on the tensile test in a reference direction is used to identify the parameters of the work-hardening model at slip system level. To investigate the influence of grain interactions, various discretizations of the grains are applied in the representative volume element modelled with finite elements. In addition, alternative homogenization schemes, such as the full-constraint Taylor and viscoPlastic self-consistent methods, are used to model the behaviour of the polycrystal. It is found that the grain discretization and the homogenization scheme have only minor influence on the predicted Plastic Anisotropy. While the crystal Plasticity-based methods all give reasonable predictions of the directional variations of flow stresses and Plastic strain ratios measured experimentally, there are still significant deviations, indicating there are other sources to the Plastic Anisotropy than crystallographic texture.
Mikhail Khadyko - One of the best experts on this subject based on the ideXlab platform.
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Work hardening and Plastic Anisotropy of naturally and artificially aged aluminium alloy AA6063
Mechanics of Materials, 2019Co-Authors: Mikhail Khadyko, Ole Runar Myhr, Odd Sture HopperstadAbstract:Abstract The Plastic Anisotropy of an extruded AA6063 alloy after different heat treatments was investigated in a previous study by Khadyko et al. (2017 ). The material was available in temper T1 (naturally aged to a substantially stable condition) and directly heat treated to the peak aged, overaged and soft annealed conditions without solution heat treatment. Tensile tests in different material directions were performed for these materials and it was found that the Plastic Anisotropy depended in a complex way on the heat treatment. In the present study, the experimental programme is extended to investigate further the influence of heat treatment on the Plastic Anisotropy. The AA6063 extruded alloy is first solution heat treated, and then either naturally aged to temper T4 or artificially aged to tempers T6 (peak aged) and T7 (over-aged). Tensile tests in three material directions are performed for these tempers and in the solution heat treated condition (temper W) to reveal the Plastic Anisotropy. The microstructure evolution of all these materials is then modelled using a nanostructure model (NaMo), which predicts the size distribution of hardening particles, the solute content, the yield strength and the work hardening. The predictions of NaMo are validated using the available data from the tensile tests and TEM observations, and used to analyse the correlation between the stress-strain behaviour and the heat treatment and microstructure of the different materials.
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effects of heat treatment on the Plastic Anisotropy of extruded aluminium alloy aa6063
Materials Science and Engineering A-structural Materials Properties Microstructure and Processing, 2017Co-Authors: Mikhail Khadyko, Stephane Dumoulin, Tore Borvik, Calin Daniel Marioara, Odd Sture HopperstadAbstract:Abstract The Plastic Anisotropy of aluminium alloys is known to depend not only on the crystallographic texture but also on the heat-treatment, and this effect has been studied on various alloys both experimentally and numerically. However, the 6000 series of aluminium alloys is not broadly represented in these studies. In this work, an extruded profile of the AA6063 alloy was investigated. Electron backscatter diffraction (EBSD) measurements revealed a strong cube crystallographic texture with a minor Goss component, which is typical for recrystallized aluminium alloys. The Plastic Anisotropy was studied by uniaxial tension tests in different material directions, using digital image correlation to measure the displacement field and thus to calculate the strain field. The tensile specimens were heat-treated to three different tempers: T6, T7 and O, in addition to the as-received T1 condition. Transmission electronic microscopy (TEM) was used to characterize the precipitate structure of the heat-treated material. A crystal Plasticity finite element model of the tensile test was created and calibrated using some of the experimental data. The comparison of the experimental stress-strain curves, strain ratios and flow stress ratios with their simulated counterparts revealed that the crystallographic texture is dominating the Anisotropy in all tempers. The accuracy of the CP-FEM predictions varies for different material orientations, and, in general, the simulated material exhibits a sharper Anisotropy than the real material. The effect of the heat treatment on the Anisotropy is found to be minor compared with the texture effect.
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latent hardening and Plastic Anisotropy evolution in aa6060 aluminium alloy
International Journal of Plasticity, 2016Co-Authors: Mikhail Khadyko, Stephane Dumoulin, Georges Cailletaud, Odd Sture HopperstadAbstract:The crystal Plasticity theory predicts that hardening on a particular slip system and its corresponding work-hardening rate will depend on the slip activity on both this slip system and all others. The exact form of this dependence is defined by the latent hardening description in form of the latent hardening matrix or the interaction matrix. It has been assumed that this matrix describes the relative strength of various dislocation interactions and is therefore the same for a wide range of alloys with the same lattice structure. Different methods have been used to estimate the values of the interaction matrix components: one is experimental and uses strain-path changes; another simulates the dislocations dynamics in a crystal directly at the microscale and estimates the strength of the forming locks. In this work, the influence of the interaction matrix (and thus latent hardening) on the development of Plastic Anisotropy is studied. An extruded AA6060 alloy is tested in uniaxial tension in different directions and the Anisotropy of the alloy is found to evolve considerably throughout the deformation. A crystal Plasticity model is used to simulate the experimental tests, and the use of different interaction matrices is evaluated. A noticeable influence on the predicted evolution of Plastic Anisotropy as well as on the stress–strain field and slip inside the constituent grains is found.
A.a. Benzerga - One of the best experts on this subject based on the ideXlab platform.
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Evolution of the 3D Plastic Anisotropy of HCP metals: Experiments and modeling
International Journal of Plasticity, 2019Co-Authors: B. Kondori, Jacques Besson, Yazid Madi, A.a. BenzergaAbstract:A two-surface, pressure-insensitive Plasticity model is further developed to represent the mechanical response of hexagonal close packed metals. The model describes the 3D Plastic Anisotropy of a material, the tension–compression asymmetry, and the consistent evolution upon straining of both the net Anisotropy and the asymmetry. The model may be viewed as a reduced order quasi-crystal Plasticity model whereby the two activation surfaces represent glide- and twinning-dominated flow. The two-surface formulation enables to represent independent, yet coupled, hardening laws in terms of effective Plastic strains accumulated on either generic deformation system. Application of the model to a discriminating data set assembled for a magnesium alloy thick plate illustrates the capabilities and versatility of the modeling approach.
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fracture strains damage mechanisms and Anisotropy in a magnesium alloy across a range of stress triaxialities
Experimental Mechanics, 2014Co-Authors: Babak Kondori, A.a. BenzergaAbstract:We report on the effect of stress-state triaxiality on damage accumulation leading to fracture at ambient temperature in magnesium alloy AZ31. We find that the strain to failure is weakly sensitive to triaxiality for the conditions investigated, at variance with the behavior of most alloy systems. Using Plastic Anisotropy measurements, post-mortem fractography and transverse cross-sectioning of specimens at incipient cracking, we discuss the contributions of Plastic Anisotropy, shear failure and coalescence-controlled cracking to limiting the net effect of stress triaxiality.
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synergistic effects of Plastic Anisotropy and void coalescence on fracture mode in plane strain
Modelling and Simulation in Materials Science and Engineering, 2002Co-Authors: Jacques Besson, A.a. Benzerga, R Batisse, A PineauAbstract:The macroscopic fracture in plane strain is known to be shear-like in ductile materials. In most structural materials, fracture starts after diffuse necking, at the centre of the specimen, by micro-void coalescence giving rise afterwards to the macroscopic shear fracture mode. In this paper, the effect of coalescence on shear band development and on associated fracture mode in plane strain is analysed numerically. The calculations are performed using a recent elastic-viscoPlastic Gurson-like model that accounts for void shape evolution, coalescence and post-coalescence micromechanics along with isotropic hardening and orthotropic Plasticity for the matrix behaviour. The latter is introduced to represent the actual flow properties of hot-worked materials. No kinematic hardening or nucleation formulation is used in order to focus attention on coalescence effects and to discuss, with respect to experiments, published results based on kinematic hardening and nucleation effects. The most important finding is the synergistic effect of Plastic Anisotropy and post-coalescence yield surface curvature upon the onset of a shear band after the fracture sets in at the centre of the specimen.
Stephane Dumoulin - One of the best experts on this subject based on the ideXlab platform.
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effects of heat treatment on the Plastic Anisotropy of extruded aluminium alloy aa6063
Materials Science and Engineering A-structural Materials Properties Microstructure and Processing, 2017Co-Authors: Mikhail Khadyko, Stephane Dumoulin, Tore Borvik, Calin Daniel Marioara, Odd Sture HopperstadAbstract:Abstract The Plastic Anisotropy of aluminium alloys is known to depend not only on the crystallographic texture but also on the heat-treatment, and this effect has been studied on various alloys both experimentally and numerically. However, the 6000 series of aluminium alloys is not broadly represented in these studies. In this work, an extruded profile of the AA6063 alloy was investigated. Electron backscatter diffraction (EBSD) measurements revealed a strong cube crystallographic texture with a minor Goss component, which is typical for recrystallized aluminium alloys. The Plastic Anisotropy was studied by uniaxial tension tests in different material directions, using digital image correlation to measure the displacement field and thus to calculate the strain field. The tensile specimens were heat-treated to three different tempers: T6, T7 and O, in addition to the as-received T1 condition. Transmission electronic microscopy (TEM) was used to characterize the precipitate structure of the heat-treated material. A crystal Plasticity finite element model of the tensile test was created and calibrated using some of the experimental data. The comparison of the experimental stress-strain curves, strain ratios and flow stress ratios with their simulated counterparts revealed that the crystallographic texture is dominating the Anisotropy in all tempers. The accuracy of the CP-FEM predictions varies for different material orientations, and, in general, the simulated material exhibits a sharper Anisotropy than the real material. The effect of the heat treatment on the Anisotropy is found to be minor compared with the texture effect.
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latent hardening and Plastic Anisotropy evolution in aa6060 aluminium alloy
International Journal of Plasticity, 2016Co-Authors: Mikhail Khadyko, Stephane Dumoulin, Georges Cailletaud, Odd Sture HopperstadAbstract:The crystal Plasticity theory predicts that hardening on a particular slip system and its corresponding work-hardening rate will depend on the slip activity on both this slip system and all others. The exact form of this dependence is defined by the latent hardening description in form of the latent hardening matrix or the interaction matrix. It has been assumed that this matrix describes the relative strength of various dislocation interactions and is therefore the same for a wide range of alloys with the same lattice structure. Different methods have been used to estimate the values of the interaction matrix components: one is experimental and uses strain-path changes; another simulates the dislocations dynamics in a crystal directly at the microscale and estimates the strength of the forming locks. In this work, the influence of the interaction matrix (and thus latent hardening) on the development of Plastic Anisotropy is studied. An extruded AA6060 alloy is tested in uniaxial tension in different directions and the Anisotropy of the alloy is found to evolve considerably throughout the deformation. A crystal Plasticity model is used to simulate the experimental tests, and the use of different interaction matrices is evaluated. A noticeable influence on the predicted evolution of Plastic Anisotropy as well as on the stress–strain field and slip inside the constituent grains is found.
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description of Plastic Anisotropy in aa6063 t6 using the crystal Plasticity finite element method
Modelling and Simulation in Materials Science and Engineering, 2012Co-Authors: Stephane Dumoulin, Odd Sture Hopperstad, Olaf Engler, Oddgeir LademoAbstract:The crystal Plasticity finite element method has been used in combination with crystallographic texture data to predict the Plastic Anisotropy of the extruded aluminium alloy AA6063 in temper T6. The results are compared with experimental data from tensile tests at different angles between the tensile and extrusion directions. Inverse modelling based on the tensile test in a reference direction is used to identify the parameters of the work-hardening model at slip system level. To investigate the influence of grain interactions, various discretizations of the grains are applied in the representative volume element modelled with finite elements. In addition, alternative homogenization schemes, such as the full-constraint Taylor and viscoPlastic self-consistent methods, are used to model the behaviour of the polycrystal. It is found that the grain discretization and the homogenization scheme have only minor influence on the predicted Plastic Anisotropy. While the crystal Plasticity-based methods all give reasonable predictions of the directional variations of flow stresses and Plastic strain ratios measured experimentally, there are still significant deviations, indicating there are other sources to the Plastic Anisotropy than crystallographic texture.
B K Jha - One of the best experts on this subject based on the ideXlab platform.
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processing of low carbon deep drawing steel with high Plastic Anisotropy using two stage batch annealing cycle
Journal of Materials Engineering and Performance, 2021Co-Authors: A Deva, Pratiksha Pandey, M Alam, Biraj Kumar Sahoo, Ravi B Kumar, Sandip Ghosh Chowdhury, B K JhaAbstract:Anisotropy in texture determines capacity of the steel to achieve maximum Plastic flow in the plane of the sheet and maximum resistance to flow in a direction perpendicular to the sheet. Present work has been carried out to explore the potential of maximizing Plastic Anisotropy (r(m)) value in extra deep-drawing steel. Industrial heat was made with low carbon (0.03 wt.%), low manganese (0.15 wt.%), and low sulfur (0.007 wt.%) levels. Continuously cast slabs were hot-rolled and then cold-rolled to 1 mm thickness. The cold-rolled sheets were subsequently subjected to annealing in an annealing simulator furnace adopting specially designed two-stage batch annealing cycle. In batch-annealed steel samples, grains were found to be recrystallized and had undergone grain growth preferentially along the longitudinal direction with strong gamma fiber, comparable to that of Interstitial Free steel. Excellent combination of strength and forming properties, in terms of yield strength 190 MPa, ultimate tensile strength 290 MPa, and total elongation 45%, YS/UTS: - 0.66 with very high Plastic Anisotropy (r(m)): 2.45, could be achieved. Properties achieved have been correlated with the alloy chemistry, processing path history, percentage reduction, two-stage batch annealing cycle and the resultant grain size, microstructure and texture.
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effect of b n ratio on Plastic Anisotropy behaviour in low carbon aluminium killed steel
Materials Science and Technology, 2008Co-Authors: A Deva, B K JhaAbstract:It is well known that dissolved nitrogen in ferrite seriously impairs the formability of hot rolled unalloyed steel. Boron being a strong nitride former, combines aggressively with dissolved nitrogen in steel, and thereby improves the forming properties. Further, atomic ratio of boron to nitrogen (B/N) plays an important role in influencing the microstructure and properties of low carbon steel. Whenever excess boron is present in solution in austenite, it segregates to the c grain boundary, thus inhibiting the transformation of austenite to ferrite, and resulting in increase in hardenability of steel. Although plenty of works have been carried out on the effect of boron on properties of hot rolled steels, limited literature is available on its effect in cold rolled formable grades particularly when carbon is in the range 0?03–0?06 wt-%. The present paper discusses the effect of B/N atomic ratio on the forming properties in general and Plastic Anisotropy ratio rm in particular, in low carbon aluminium killed batch annealed steel. The present study has been carried out on the industrially produced low carbon (0?04–0?06 wt-%) steel with varying B/N atomic ratio. The chemical composition of steels used for the present study is shown in Table 1. Steel A is the typical chemistry used for producing extra deep drawing steel. All the steels were continuously cast to 210 mm thick slabs and were hot rolled to 2?8 mm thickness. The hot rolled bands were finish rolled at 880i10uC and coiled at 620i10uC. As lower coiling temperature (,600uC) results in higher rm values in batch annealed aluminium killed steel, some coils were coiled at 540uC also. Hot rolled coils were cold reduced to 1 mm thickness. The cold rolled coils were annealed with shorter and longer annealing cycles as schematically shown in Fig. 1. Conventionally shorter annealing cycle is practiced for normal cold rolled steel whereas longer annealing cycle is used for extra deep drawing grade. Table 2 shows the mechanical properties of steels with varying B/N ratio processed under different annealing cycles. Properties of boron added steel has shown a significant improvement compared to steel without boron in terms of lower yield strength and higher elongation. In spite of being subjected to similar hot rolling conditions and annealing cycle parameters, lower YS (242 MPa), lower UTS (360 MPa) and higher elongation has been obtained in boron added steel B1 as compared to boron free steel A. It can be attributed to the reduced solute nitrogen and carbon contents in Steel. As expected, increasing the annealing time has led to lowering the strength values and increasing elongation further. As the tensile properties alone does not depict the forming behaviour of cold rolled steel completely, Plastic Anisotropy ratio r, which is a good measure of deep drawability of steel, has been assessed. A mean value rm is defined as rm5(r0z2r45zr90)/4, where subscripts refer to the angles of tensile tests to the rolling direction. Figure 2 shows the effect of B/N ratio on rm for the steels (with and without boron) annealed with longer cycle. Steel with B/N ratio of 0?8 (steel C) shows lower value of rm (1?12) as compared to rm value of 1?66 in steel with B/N ratio of 0?3 (steel B2) processed under identical conditions of hot/cold rolling and annealing. The rm value of steel A, subjected to coiling temperature of 540uC and longer annealing cycle, has also been compared to steel B3 to assess the effect of boron. rm for both the steel were found to be nearly same (Fig. 2) with value of 1?76 for steel A and value of 1?74 for steel B3. The results show that lower value of B/N ratio does not affect rm adversely. It can be explained in terms of availability of nitrogen for AlN precipitation in steel during batch annealing. Depending on the Al, B and N concentration in steel, the range of temperature at which AlN and BN precipitate coincide in general. However, Ohmari and Yamanaka have reported that BN will form first compared to AlN due to higher diffusivity of boron. In the present study also, it appears that most of nitrogen has been combined by boron before precipitation of AlN in the hot rolled stage, which in turn has resulted in lower availability of nitrogen in solution depending on B/N atomic ratio for combining with aluminium during batch annealing. It is well known that there is strong influence of aluminium nitride during batch annealing of aluminium killed steel. High rm values are produced by textures containing a high proportion of grains with (111) planes and low proportion of (100) planes parallel to the sheet surface. The aluminium nitrides lead to enhancement of the (111) texture components and a concurrent reduction of the (100) components. While developing the desirable texture, aluminium nitrides also help at the same time in formation of a pancake grain structure which results in better rm value in steel. This emphasises the Research and Development Centre for Iron and Steel, Steel authority of India Limited, Ranchi, 834002, India