Intergranular strains and plastic deformation of an austenitic stainless steel

Intergranular strains and plastic deformation of an austenitic stainless steel

Materials Science and Engineering A334 (2002) 215– 222 Intergranular strains and plastic deformation of an austenitic st...

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Materials Science and Engineering A334 (2002) 215– 222

Intergranular strains and plastic deformation of an austenitic stainless steel R. Lin Peng a,b,*, M. Ode´n a, Y.D. Wang b, S. Johansson a a

Department of Mechanical Engineering, Di6ision of Engineering Materials, Linko¨ping Uni6ersity, SE-581 83 Linko¨ping, Sweden b Studs6ik Neutron Research Laboratory, Uppsala Uni6ersity, SE-611 82 Nyko¨ping, Sweden Received 19 March 2001; received in revised form 27 August 2001

Abstract Intergranular strains due to tensile plastic deformation were investigated in a sheet material of austenitic stainless steel. The objective was to study the development of residual intergranular strains in samples unloaded from the intermediate and large plastic deformation regimes for which few theoretical and experimental studies were available. By using neutron diffraction, residual lattice strain distribution as a function of sample direction was mapped for a number of crystallographic planes. Deformation microstructures were examined by both transmission electron microscopy and the electron back scattering pattern technique. Residual intergranular strains were observed in samples deformed significantly beyond the elastic limit and the strains varied with sample directions as well as the amount of applied plastic strain. In addition, a different tendency of intergranular strain evolution was observed after large plastic deformation, which could be attributed to the change of dominant plastic deformation mode from slip to mechanical twinning. The results are discussed based on the observed deformation microstructure studies. © 2002 Elsevier Science B.V. All rights reserved. Keywords: Intergranular strains; Austenitic steel; Neutron diffraction; TEM; EBSP

1. Introduction The elastic/plastic property of single grains in a polycrystalline material is often anisotropic or related to the grain orientation. When such a material is subjected to plastic deformation, strain incompatibility between neighbouring grains having different orientation can lead to the generation of intergranular stress that varies with grain orientation and sample direction. Residual stresses due to such grain interactions can be classified as second order residual stresses. Different from macroscopic or the first order residual stresses, which are balanced over the cross-section of the material, residual intergranular stresses maintain elastic equilibrium over grain orientations. In recent years, great attention has been paid to the generation of intergranular strains and their corresponding stresses due to plastic deformation. This can * Corresponding author. Tel.: + 46-13-281161; fax: + 46-13282505. E-mail address: [email protected] (R. Lin Peng).

largely be attributed to the recent, rapid development in the field of neutron diffraction measurement of residual stress. Abnormal crystallographic plane behaviour was first reported in the late 40s and early 50s for X-ray diffraction measurements [1] and the first neutron diffraction measurement of intergranular stress was reported in the 80s [2]. Research interests in intergranular strains/stresses have grown stronger after it became clear that the use of different hkl planes for macroscopic stress measurement by neutron diffraction could lead to large discrepancy due to the existence of intergranular strains. Like macroscopic residual stress, intergranular stress may affect the performance of a material by superimposing stress on the applied stress. Thus for engineering use of a plastically deformed material, it is important to understand the cause of intergranular stress, to identify the subset(s) of grains that may accumulate significant intergranular stress, and to be able to assess the intergranular stress level. For the widely used diffraction techniques including both X-ray and neutrons, accurate macroscopic stress analysis can be ensured only when the role of intergran-

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ular stress is well appreciated. This issue is especially important for materials which are plastically anisotropic and thus may accumulate a large amount of intergranular strains during loading. Research work has previously focused on studying the orientation-dependent intergranular strain distributions in a number of materials by in-situ diffraction experiments on samples subjected to tensile loading and computer simulations using polycrystalline models such as the self-consistent scheme [3– 9]. Numerical calculation is an effective method which simulates the development of intergranular interaction and contributions of the elastic and plastic anisotropy. However, assumptions on certain materials behaviour and properties are often employed, thus model validation by experimental evidence is essential. In-situ diffraction experiments measure lattice strains of certain hkl planes under loading and provide valuable information on the evolution of intergranular strains as well as the effects of elastic anisotropy during plastic deformation. For practical reasons, the measurements are made in the principal sample axes and under low plastic strains. On the other hand, residual elastic strain measurement can be carried out conveniently along almost any sample direction on samples which are carefully prepared from unloaded samples. The obtained information will not only reveal the hkl sensitivity to intergranular strains but also provide insights into the grain interactions which lead to the development of intergranular strains. For austenitic stainless steels, which are generally characterised by highly elastic/plastic anisotropy, residual lattice strains have been studied on samples unloaded from 2% [7], 5% [9] and 8% strain [8], respectively. Knowledge of intergranular strains and their distributions as a function of sample direction in heavily, uniaxially deformed materials is still poor. For cold-rolled stainless steels, intergranular stresses were studied by experimental measurement and modelling for large area reductions [10,11]. The effect of texture was investigated on a Table 1 Chemical composition of the stainless steel in weight percent C












Fig. 1. Geometry of the used tensile test samples, where „ indicates the direction of neutron diffraction measurement.

cold-rolled stainless steel axially stressed up to 1% strain [11]. It is well known that mechanical anisotropy and plastic deformation mode may change with applied strain as a result of deformation microstructure and texture development. The evolution of intergranular stress under large plastic deformation may, therefore, not follow the same trend as in the low and intermediate strain range. Based on TEM studies, Feaugas [12] showed that in stage III of plastic deformation, the formation of cell structure resulted in the gradual disappearance of the intergranular internal stress while intragranular internal stress evolved. The aim of the current work is to study the development of residual intergranular strains and the anisotropic behaviour of hkl planes commonly used for diffraction measurement of macroscopic stresses in austenitic stainless steel deformed into stage IV of plastic deformation. Neutron diffraction technique was used to map residual lattice strains for a number of crystallographic planes in samples unloaded from plastic deformation stages I– IV. In this paper, we also report on the deformation microstructures observed by transmission electron microscopy (TEM) and the texture by electron back scattering pattern (EBSP) and discuss their correlation with the observed intergranular strains.

2. Experimental details

2.1. Material and mechanical loading The material used in this study was a 3-mm thick cold-rolled austenitic stainless steel that corresponds to AISI 304 and was provided by Avesta Sheffield AB. The chemical composition of the steel is listed in Table 1. The sheet was received in solution treated condition, which was carried out by heating to 1100 °C and air-cooling. About 5% ferrite was found by neutron diffraction measurement in the centre section of the sheet, while X-ray phase analysis on the sample surface did not detect any ferrite. The grain size of the austenite was about 3 mm. Tensile specimens of 3×8 mm2 cross-section were prepared such that the loading axis was parallel to the rolling direction of the sheet, see Fig. 1. The specimens were then subjected to uniaxial tensile load at a true strain rate of about 4.5× 10 − 4 s − 1 and unloaded from different strain levels. The macroscopic stress– strain curve obtained from the tensile test is shown in Fig. 2. Four samples, A, B, C, and D, were produced by unloading from a peak plastic strain of 0.2, 7.5, 29.8, and 44.7%, respectively. As can be seen in Fig. 3 in which the work-hardening rate (d|true/dmtrue) is plotted as a logarithmic function of the true stress, |true, the samples have been produced from different plastic deformation stages (I–IV) [12].

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measures selectively a subset of grains in the gauge volume whose orientation satisfies Bragg’s law: u= 2d hkl „ sinq,

Fig. 2. Macroscopic stress –strain curve for the investigated material. Squares indicate the different load levels from which the test samples were unloaded.

Fig. 3. Strain hardening rate plotted as logarithmic function versus true stress, showing the different plastic regime characterised by changes in the slope of the curve.

The unloaded specimens were middle of the gauge section by a part of each sample was used for tion experiment and the other part examinations.

sectioned near the diamond disk. One the neutron diffracfor TEM and EBSP

2.2. Neutron diffraction measurement of residual lattice strains During neutron diffraction measurement of strain, the interplanar spacing of the investigated material is used as internal strain gauges. Elastic strains along the normal of the diffracting planes can be derived by measuring changes in the interplanar spacings. For a measurement carried out along a sample direction „, the elastic strain along this direction, m hkl „ , can be calculated by the equation below: m hkl „ =

hkl d hkl „ −d 0 , hkl d0


where d hkl is the spacing of the hkl plane that is „ perpendicular to the measured sample direction and d hkl is the reference spacing of the hkl plane. The 0 advantage of using a diffraction method is, that it


where u is the wavelength of neutrons and q is the diffraction angle. By using different hkl planes, strains in grains of different orientations can be separated. Another feature of neutron diffraction is that the large penetration depth of neutrons allows a large population of grains in the interior of the material to be probed and thus the result reflects the average material behaviour. Residual lattice strains of the austenite 200, 220, 311, and 222 planes were mapped as a function of sample direction, from the loading axis („= 0°) to the sheet normal („= 90°) at 15° intervals (see Fig. 1). The experiments were carried out on the dedicated stress diffractometer REST at Studsvik Neutron Research Laboratory. The nominal wavelength of the neutron beam was 1.76 A, and the size of beam slits, which defined the size of the neutron beam, was chosen to be 1.2 mm (width) by 6 mm (height). The gauge height was set parallel to the transverse direction of the sample. The 2q values for the above 4 reflections were found to be approximately 59, 88, 109, and 116°, respectively. The exact 2q values were determined by fitting a Gaussian function to each diffraction peak. A sample which was not subjected to mechanical loading was used as a stress-free reference. Scans similar to those of the deformed samples were performed. The measurements show a slight variation in the lattice spacing with sample direction for the reference sample. The maximum scatter is 9100×10 − 6 in strain for the 200 and 222 planes and 9 40× 10 − 6 in strain for the 220 and 311 planes, which are within the uncertainty of the experiment as determined from standard deviations by fitting Gaussian functions to the diffraction peaks. The stress-free reference spacing of the hkl plane used in Eq. (1) was determined by averaging the data for all „ angles from the stress-free sample.

2.3. TEM and EBSP experiments A Philip EM 400 transmission electron microscope (TEM), operated at 120 kV, was used to study the deformation microstructure of the unloaded samples. The TEM foils were prepared from 3-mm diameter discs punched from thin sections cut out of the tensile samples. The disc plane was perpendicular to the loading axis. The discs were mechanically and then electrolytically polished to electron transparency using a Struer’s device, TENUPOL-3. The EBSP studies were performed on a JEOL 6400 scanning electron microscope equipped with the Channel+ software (HKL Technology Aps, Denmark) and hardware from Jelen Technology, Norway. The exam-


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ined surfaces were taken from a plane perpendicular to the sample axis and prepared by electrolytic polishing. For texture measurement on samples A, B and C, at least six areas of 0.24×0.48 mm2, randomly chosen near the centre of the cross-section, were scanned with a step size of 10 mm. For sample D, only one area was measured. Plotting of the orientation distribution function (ODF) was performed using BEARTEX software [13,14]. The smoothing of the ODFs to obtain intensity comparable with other techniques like X-ray diffraction was done according to a procedure based on extrapolated texture index described in [15]. The poorer statistics and higher percent of zero solution in indexing contribute to a larger uncertainty for the D sample. For microorientation mapping, the scan area was reduced to 0.15 mm2 with a step-size between 0.1 and 0.5 mm.

3. Results

3.1. Residual lattice strains X-ray diffraction measurement on the surface of samples C and D detected weak diffraction peaks of martensite. The volume fraction of deformation-induced martensite is low and it will insignificantly contribute to grain interactions in the austenite phase. Therefore, neutron diffraction measurements of residual strains were carried out only on the austenitic phase. Since the plastic deformation induced a double fibre texture (Section 3.2) and high defect density (Section 3.3), the diffraction peaks obtained for certain sample directions and crystallographic orientations for the highly deformed samples were too poor to perform a reliable strain analysis. These data points are excluded from the strain plots and the discussion below. For similar reasons, uncertainties in the strain data are much larger for some directions as can be seen from the error bars shown in the strain plots.

Fig. 5. (a) – (d) Residual elastic strains in sample A – D, respectively. Legends represent the hkl planes. „ is the angle to the rolling direction (loading direction) and the normal direction is at „= 90°. Where data points are missing due to texture, dashed lines are used.

Fig. 4. Development of residual strains, along the tensile loading direction, with applied plastic strains in grains of different orientations.

The measured residual interplanar strains are plotted in Figs. 4 and 5. Each data point represents a mean strain in a subset of grains in the gauge volume that

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satisfies Bragg’s law. Each subset of grains is referred to by the hkl plane used for strain measurement. As can be seen in Fig. 4 in which strains along the loading axis are displayed, for the sample that had been loaded slightly beyond the elastic limit, the residual strains are small and comparable to the uncertainties of the measurement. Intergranular reaction became significant in the sample after 7.5% plastic deformation. The 220 plane exhibits compressive axial strain while both the 200 and 311 planes possess tensile axial strain. The strain measured in the 222 plane is close to zero. With further plastic deformation up to 29.8%, the tensile


strains accumulated in the 200 and 311 planes increase and the strain in the 222 plane remains essentially zero. At this stage, the intensity of the 220 plane was too weak for further strain analysis. Orientation imaging mapping (OIM) by EBSP shows less than one percent of the grains oriented with their Ž220 direction parallel to the loading axis. Judging from the distribution for samples A and B, it is likely that these few grains are still under compression. For the sample that was subjected to 44.7% plastic strain, the residual intergranular strain in the 200 plane tends to level off while a small increase is still observed for the 311 plane. The variation of intergranular strains as a function of sample direction (Fig. 5) shows that the intergranular strains are strongest along the loading axis while essentially zero along the normal direction, with the exception for the 220 plane in sample D which displays a low compressive strain. At 7.5% deformation, difference in strain distribution is evident between different crystallographic planes. Both the 200 and 311 planes show similar variation with sample direction, with the 200 being the most strained plane. A distribution with the opposite tendency is found for the 220 plane. For the 222 plane small compressive strains developed within 15–45° of the loading axis. Increasing the plastic deformation to 29.8% increases the magnitude of the strains, but does not change the characteristics of the strain distribution for the respective diffraction planes. Further deformation to 44.7% has only a small influence on magnitudes of strain and its distributions.

3.2. Deformation texture

Fig. 6. ODF sections for ƒ2 = 0, 45 and 65° for the as received material and tensile deformed samples. (a) As received. Contour levels: 0.2 – 0.8 –1.5 – 2. Maximum intensity: 2.19. (b) Sample A. Contour levels: 0.2 – 0.8 – 1.5 –2. Maximum intensity: 2.97. (c) Sample B. Contour levels: 0.2 – 0.8 –1.5 –2–3. Maximum intensity: 3.53. (d) Sample C. Contour levels: 0.2 –0.8–1.5–2– 3–…8–9. Maximum intensity: 9.42. (e) Sample D. Contour levels: 0.2 –0.8–1.5–2–3–…9–10. Maximum intensity: 10.35.

Crystallographic orientation distribution function (ODF) was derived from orientation maps obtained by EBSP. The coordinates have been transformed so that the data can be presented in the same convention as X-ray diffraction measurement made in the rolling plane. In Fig. 6 ODF sections for ƒ2 = 0, 45 and 65° are presented for the different samples, including the as-received material. The initial texture of the material contains weak brass and cube components (Fig. 6(a)). A slight intensity increase can be observed for sample A (Fig. 6(b)) while the influence of deformation on texture is obvious in sample B (Fig. 6(c)). The brass component is now shifted towards the 111 orientation and more grains tend to line up with a Ž100 direction along the loading axis. With further plastic straining, more grains are rotated to form a duplex fibre texture of Ž111 and Ž100 (Fig. 6(d)–(e)). The intensity ratio of Ž111 to Ž100 is about 2. Such a duplex fibre texture is often observed in fcc materials subjected to axisymmetric flow and the ratio of the polar intensity varies with the stacking fault energy of the material [16].


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Fig. 7. TEM micrographs showing the microstructure for the as-received material (a) and the deformed microstructure in (b) – (e) for samples A–D, respectively.

3.3. Deformation microstructure TEM micrographs in Fig. 7 show the typical deformation microstructure observed in the respective samples, A–D. The as-received material has a microstructure with few dislocations and annealing twins that are common for the material. After a small plastic deformation, sample A shows a microstructure similar to the virgin material but with a somewhat higher dislocation density. Plastic deformation occurs by slip. At this stage, the strain-hardening rate decreases rapidly with increasing plastic strain (Fig. 3). A high defect density is observed in sample B that was loaded into stage II, during which planar slip is dominant and the logarithmic work-hardening rate remains almost constant with increasing load. The low stacking fault energy of the material also leads to the formation of extensive stacking faults. For sample C, band structures containing cells are found, indicating that multiple slip prevails during deformation and the logarithmic work-hardening rate decreases again with applied deformation (Fig. 3). Sample D was unloaded from stage IV which is the last stage before strain instability and is characterised by a constant logarithmic work-hardening rate. For deformation to such high plastic strains,

grains that favour slip could have been exhausted and mechanical twinning becomes the dominant mechanism for plastic flow.

4. Discussion The sign of intergranular strains observed for the four hkl planes is the same as that reported in [7,8] for two austenitic stainless steels with higher alloying content than our samples, which were subjected to low and intermediate plastic deformation, respectively. Along the axial direction the 200 and 311 planes, which are elastically and plastically soft, accumulate tensile strains, while the stiffer 220 and 222 planes collect compressive strains. With a Taylor factor for axisymmetric flow via slip and a Young’s modulus lower than the bulk value, the 200 plane seems to play a dominant role in grain interactions during loading and sustains the largest residual elastic strain after unloading. The compressive strains in the 220 and 222 planes are needed to help reestablish the elastic equilibrium among grains upon unloading. In comparison with the study in [8] where the sample was subjected to 8% deformation, sample B (unloaded from 7.5% plastic strain) has a

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smaller tensile strain in the 200 plane but a larger compressive strain in the 220 plane. This difference between the two samples could be attributed largely to the possible difference in elastic/plastic anisotropy due to the different chemical compositions of the materials. The same trend of intergranular strain evolution holds for deformation up to 29.8% plastic strain. TEM examination (Fig. 7(d)) reveals that the same mechanism for plastic deformation, that is slip by dislocation movement, is dominant within this range. Hence, the intergranular strains evolve according to the plastic anisotropy described by the Taylor model despite load repartitioning from strain hardening of individual crystallographic orientation and grain rotation. The plastically soft orientations 200 and 311 further develop tensile residual lattice strains which are partially balanced by the more stiffer orientations including the 222. At large plastic strain, where the duplex Ž111 and Ž100 fibre texture forms, grain interaction between the two texture components would become more important for intergranular strain development. One would then expect that the 222 plane eventually accumulates significant, compressive, elastic strains. The reason why the strain remains low in the 222 plane could be explained to a certain extent by the high volume fraction of grains oriented in the Ž111 fibre and the high stiffness of the 222 plane. The observed large difference in strain magnitude between the 200 and 222 planes may also imply that while the 200 plane dominates over the evolution of intergranular strains, the 222 plane plays a minor role in establishing the elastic equilibrium which is maintained among all the grain orientations. A steady decrease of residual axial strain rate with increasing plastic strains is found for deformation up to 29.8% (Fig. 4). This can be attributed to the evolution of deformation microstructure, in particular the cell structure, which results in the evolution of intragranular heterogeneity and the decrease of intergranular reaction [12]. Sample D shows a different trend of intergranular strain development. An increase in the plastic strain leads to further increase of tensile strain in the 311 grains but hardly changes the intergranular strain in the 200 grains. At 44.7% of plastic strain a high density of mechanical twins was found. The Taylor analysis for axisymmetric flow by combined twinning via {111}Ž112 and slip via {111}Ž110 in the fcc structure shows that twinning has the effect of levelling the overall strength anisotropy [17]. Thus, extensive twinning evident at large plastic deformation greatly lowers the strain incompatibility due to plastic anisotropy. As grains with their Ž200 nearly parallel to the axial loading direction are more difficult to deform by mechanical twinning [17,18], the 200 orientation is now plastically stiffer. 311 remains a soft orientation and


further development of residual intergranular strains may, therefore, largely be controlled by the 311 plane. The off-axis lattice strains are mainly a result of strain incompatibility along the loading axis. The strain obtained by neutron diffraction is then the mean value over a subset of grains possessing various stress states, caused by different crystallographic orientations parallel to the loading axis. Thus, while strain variation within the subset may be large the average over the subset is often small, as is observed in Fig. 5. For fcc materials it has been found that the 200 is a problematic plane which exhibits large intergranular strains. For austenitic steel axially deformed to 8% of plastic strain, it has been argued that the 311, 220 and 222 are less sensitive to intergranular reaction [7,8] and are thus recommended for macroscopic residual stress measurement by diffraction. The current study reveals that residual axial strain in the 311 plane becomes more significant after large plastic deformation and the 220 probably also shows a substantial residual intergranular strain. Among the four investigated planes, the 222 plane is found to accumulate the least residual intergranular strains throughout the whole plastic deformation range and, therefore, might be a better choice for diffraction measurement of macroscopic stress in such materials.

5. Conclusions Significant residual lattice strains due to intergranular reaction are found in samples unloaded from intermediate to large plastic deformations. The intergranular strains are most pronounced along the loading direction and they develop linearly up to 29.8% of plastic strain. The 200 crystallographic plane sustains the largest intergranular strains while the 222 plane has the lowest intergranular strains. The 311 shows intermediate values. Increasing the plastic strain to 44.7% leads to a small increase of axial strain for 311, while 222 and 200 are hardly affected. TEM studies show that slip is the main mechanism of plastic deformation for deformation up to 29.8%. At 44.7% of strain, a different plastic deformation mode, mechanical twinning, becomes dominant. The twinning mechanism leads to a weaker strain incompatibility and somewhat different plastic anisotropy between the investigated hkl planes, which may account for the different trend of intergranular strain development.

Acknowledgements The authors would like to thank Bertil Trostell of Uppsala University for assisting with part of the neutron diffraction experiment.


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