Dislocation densities and intergranular stresses of plastically deformed austenitic steels

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Abstract

Heterogeneous plastic deformation behavior of <hkl> oriented individual grains-family with respect to the tensile direction in austenitic steels was studied using electron back scatter diffraction (EBSD) and neutron diffraction (ND) measurements. The kernel averaged misorientation value determined by EBSD for a plastically deformed specimen was different in grain to grain, suggesting different dislocation densities. Such insights obtained from the surface observations with EBSD were quantitatively evaluated as bulk-averaged data using ND. The convolutional multiple whole profile fitting (CMWP) for ND profiles has revealed different dislocation densities in <hkl> oriented grains-families, showing good coincidence with the EBSD results in trend.

Introduction

A polycrystalline austenitic steel is considered to be an extreme type of composite material, in which all of individual grains behave differently from each other not only in elastic but also plastic deformation. This is due to the strong anisotropy in elastic properties and <110> {111} slip systems characterized by the Schmid factor [1], [2]. Although the tensile properties of engineering steels can be macroscopically regarded to exhibit isotropic features by averaging such different behaviors of individual grains, it is important to understand how a certain grain embedded in the matrix behaves differently like single crystal's case.

This issue has been computationally studied using micromechanics approaches like the Kröner model for elastic deformation [3] and has been expanded to plastic deformation regime using elasto-plastic self-consistent (EPSC) model [2], [4], [5], crystal plasticity finite element simulation (CPFEM) [6] or more recently Fast Fourier Transforms (FFT) method which can take a large number of grains into modeling with less computational burden [7].

On the other hand, experimentally, various methods have been developed, but most of them monitor only the deformation behavior at the specimen surface where deformation undergoes nearly in a plane stress condition. For example, recent scanning electron microscopy (SEM) techniques enable us to track elastic strain distribution by the Wilkinson method using electron back scatter diffraction (EBSD) [8], [9] and distribution of dislocations by electron channeling contrast image (ECCI) [10]. The total strain distribution has been tracked with a micro-grid method [11] or digital image contrast (DIC) method [12]. However, it should always be kept in mind the deformation at the free surface is different from that in the interior of a specimen. Even in computer simulation studies, the difference in deformation at the surface and inside of a specimen has not been made clear. In order to observe a certain grain embedded in a poly-crystal material, a challenging trial has been reported using synchrotron X-ray diffraction method for a thin sample [13], but it is not easy to obtain statistically satisfactory results for engineering steels with the grain size of a few ten micrometers. It has also been expected to evaluate dislocation density precisely by an easy method. Transmission electron microscopy (TEM) observation has usually been used for this purpose, but the thin film sample preparation and high skill are required to determine the dislocation density; the determination of the foil thickness and the counting of total length of dislocation lines in a unit volume are not easy task. X-ray diffraction has frequently been used, but the obtained result is the information near the surface and strongly dependent on beam line arrangement and the analysis method [14]. Here, the Williamson-Hall (W-H) method using only Full Width at Half Maximum (FWHM) [15] has widely been employed for this purpose, although several problems are involved. For example, if one used all available diffraction peaks of a material with large elastic anisotropy like austenitic steel for the W-H analysis, the fitting error would be huge. In case of the employment of only parallel {hkl} series like 111, 222, 333, etc., the reliability of the FWHM at higher indexed planes must be poor. As is well known in case of TEM observation, a dislocation line is visible due to its local stress field and hence dependent on the Burgers vector and the direction of the incident beam, that is, scattering vector. Similarly to this, the FWHM of hkl diffraction peak is influenced by the Burgers vector, dislocation line vector, i.e., the ratio of edge and screw components, scattering vector, and elastic moduli. Then, Ungár et al. have introduced the “dislocation contrast factor” in order to take these influences into account [16] and determined dislocation density [17] by combining the modified W-H plot with the modified Warren-Averbach (W-A) method using Fourier coefficients [18]. However, the tail of diffraction peak of low indexed {hkl} cannot be fully used for the W-A analysis [14]. The FWHM is also affected by dislocation arrangement, coherently diffracting mosaic size and planar defects like stacking fault. In order to distinguish such influential factors separately, efforts have been continued, where important is to utilize whole diffraction profile into consideration. Then, a convolutional type of profile fitting starting from theoretical line broadening mechanisms has been developed by Ribarik and Ungár [19], [20], which is called Convolutional Multiple Whole Profile fitting (CMWP) method. Similar convolutional method has independently been developed by Scardi and Leoni [21]. The CMWP fitting method can evaluate the density, character (edge and screw component ratio) and arrangement of dislocation, crystallite size and frequency of planar defects. As has frequently been encountered in TEM observations, the dislocation density and configuration differ from a grain to grain depending on <hkl> with respect to the tensile direction. In case of tensile deformation, Hansen, Huang and their coworkers have reported that the dislocation arrangement, i.e., sub-structure is dependent on <hkl> of a grain with respect to the tensile direction [22], [23], [24]. The dislocation density must be different in individual grains but it is very difficult to measure quantitatively with TEM.

It is important to monitor the change in the density as well as arrangement of dislocations with tensile deformation continuously focusing on a certain grain embedded inside a bulky specimen. In this study, first, the change in distribution of dislocations was investigated on the specimen surface semi-continuously using EBSD measurement. Some features in stress and strain behaviors on the specimen surface will be obtained by this experiment. Second, the time of flight method of neutron diffraction (ND) during tensile deformation was employed. The obtained diffraction profiles were thereby analyzed using the CMWP fitting method. After the determination of the averaged, i.e., global dislocation density, the individual dislocation contrast factors were introduced to estimate the dislocation density in each <hkl> grain-family, as was done in ref. [25]. Then, it will be claimed that individual grain deforms differently from each other showing different stress-strain behavior.

Section snippets

Specimen preparation

An austenitic stainless steel, 310 (0.048C, 0.33Si, 0.80Mn, 0.024P, 0.001S, 25.1Cr and 19.8Ni (in mass%)), was made through conventional industrial process and received as hot-rolled plates. The steel plate was subjected to solution treatment at 1373 K for 0.9 ks, followed by water quenching. The solution-treated steel had a fully austenite microstructure with the grain size of approximately 33 µm, where annealing twin was counted as grain boundary. A high nitrogen bearing austenitic steel, HNS

Features of deformation behavior in <hkl> oriented grains-family observed with EBSD

As has been discussed in the previous report [9], the stresses in <hkl> oriented grains-families with respect to the tensile direction differ from each other. Using the Wilkinson method, the elastic strains were determined and it has been found that the averaged axial strain along the tensile direction in <100> oriented grains with respect to the tensile direction is larger than that in <110> [9]. This is because <100> Young modulus is much smaller than <110>, so that stress is partitioned

Conclusions

Heterogeneous deformation behavior of austenitic steels in terms of dislocation density and intergranular stresses (elastic strains) was investigated using SEM/EBSD and ND. The obtained results would be summarized as follows.

  • (1)

    A polycrystalline austenitic stainless steel is a kind of composite material consisting of differently oriented crystals showing different deformation behaviors. The elasto-plastic tensile deformation in each <hkl> oriented grains-family can be monitored by EBSD on the

Acknowledgements

The authors would like to thank Prof. Y. Adachi of NIMS (now at Nagoya University) for his help of EBSD examination and Dr. Katada of NIMS for preparation of HNS steel. The ND experiments at MLF J-PARC was performed under a user program 2014P0102 and 2016A0127.

References (38)

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Present address: JFE steel Co., 1, Kawasaki-cho, Chuoh-ku, Chiba 260-0835, Japan.

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