Elsevier

Acta Materialia

Volume 60, Issue 19, November 2012, Pages 6657-6672
Acta Materialia

Quasi-four-dimensional analysis of dislocation interactions with grain boundaries in 304 stainless steel

https://doi.org/10.1016/j.actamat.2012.08.036Get rights and content

Abstract

The application of diffraction contrast electron tomography to dynamic experiments involving dislocation interactions with grain boundaries is demonstrated for the first time. Two applications are shown: the first is concerned with post-mortem analysis of dislocation interactions with grain boundaries and illustrates the usefulness of the tomography technique for defect analysis; the second is in conjunction with in situ straining experiments in which the dynamics of dislocation interactions with grain boundaries are observed directly and the resulting structure visualized three-dimensionally. The in situ straining experiments were conducted at room and elevated temperatures to determine the influence, if any, of thermal processes on the slip transfer mechanism. It was found that increasing the temperature lowers the barrier for dislocation absorption and emission from the boundary and increases the complexity of the interactions, but does not change the fundamental mechanisms governing slip transmission. Previous experimentally determined criteria for slip transmission across boundaries were extended to interactions involving partial dislocations, where it was found that the reaction continues to be governed predominately by reduction of the Burgers vector of the residual grain boundary dislocation left after slip transfer.

Introduction

Manipulating grain and interphase boundaries, in terms of the type and distribution as well as the density, has important practical applications in terms of improving the mechanical strength [1], [2], corrosion resistance [3], [4], susceptibility to hydrogen embrittlement [5], [6] and tolerance to damage by energetic particle bombardment [7], [8], [9], [10]. Although the phenomena are well documented at the macroscale, there remains much to be understood about unit processes at the atomistic scale and the mesoscale. In terms of slip transmission through grain boundaries or interfaces, our understanding is incomplete in that there remain questions as to how grain and interphase boundaries generate and emit dislocations; how they act as sinks for dislocations; and how these processes depend on the grain boundary type or the orientation relationship, the character of the dislocations, and the local and global stress conditions. Consequently, in modeling and predicting the macroscale response, the factors determining damage initiation sites remain unidentified. For example, twin boundaries have been described as being transparent to dislocation transmission, serving as weak or strong barriers to slip transfer, and being effective or ineffective sites for generation of new dislocations [11], [12].

To predict the transmission of slip involving perfect dislocations through grain boundaries in face-centered cubic (fcc) crystal structures at room temperature, the emission of dislocations instigated from a dislocation system impinging on the grain boundary is governed by the following three criteria [13], [14], [15]:

  • Criterion 1. The angle between the line of intersection between the slip planes of the incoming and outgoing slip systems and the grain boundary should be minimized.

  • Criterion 2. The magnitude of the Burgers vector of the residual dislocation left in the grain boundary after emission of a dislocation from it should be minimized.

  • Criterion 3. The resolved shear stress acting on the emitted slip system should be maximized.

Criterion 1 was found to be inconsequential except in the case of direct transmission of screw dislocations through a twin boundary. For that particular case, the angle between the slip plane intersections in the grain boundary had to be zero. Criteria 2 and 3 were found to be competitive, with criterion 2 generally being the more important. For example, the dislocation system initially activated by the grain boundary may be the one experiencing the maximum resolved shear stress as expressed by criterion 3, but it will cease operation after emission of a few dislocations if it generates a residual dislocation with a large Burgers vector in the grain boundary, i.e. it does not satisfy criterion 2. Under this scenario, additional slip systems will be activated to minimize the magnitude of the strain energy increase and this may result in the initial system being deactivated. In contrast, it was found that, provided a shear stress acted on a slip system, that system could operate. These observations suggested that criterion 2 dominates the selection of the emission system. Although the initial studies emphasized fcc systems, others have shown the criteria to be applicable to other systems and interfaces [16], [17], [18], [19]. However, criterion 2 was not always found to dominate [17], [20], [21]. The previous studies emphasized interactions at ambient temperature involving perfect dislocations, whereas this paper is concerned with the interaction of perfect and partial dislocations with grain boundaries at ambient and elevated temperatures.

More recently, dislocation dynamics, molecular dynamics computer simulations and continuum models have all been used to explore the processes of slip transmission through interfaces with the idea of developing a better understanding of the governing atomistic processes or of identifying damage initiation sites [22], [23], [24], [25], [26], [27], [28], [29], [30], [31], [32]. In general, the results of these investigations have been supportive of the three criteria, although some additional constraints have been added:

  • The step created by the residual dislocations left at the grain boundary after emission should be minimized [25], [26], [32].

  • The resolved shear stress on the grain boundary should be small [25], [26], [32].

  • The normal compressive stress on the boundary should be small [25], [26], [32].

  • The Burgers vector of the incoming dislocation should reduce the local misorientation across the boundary, i.e. the sign of the incident dislocation is important in determining the interaction with the grain boundary [27].

  • The lattice resistance to the nucleation of a partial dislocation from a coherent twin boundary should be determined by the following parameters:R=(γUS-γS)μbon the normal glide plane andR=(γUT-γS)μbon a twin plane.Here γUS is the unstable stacking-fault energy or the energy barrier to creating an intrinsic stable stacking fault from a perfect lattice, γS is the stacking-fault energy, γUT is the unstable twin energy, b is the magnitude of the Burgers vector of the dislocation and μ is the shear modulus [28].

  • The ability for a grain boundary to transmit strain, i.e. the strength of the grain boundary as a barrier to slip transfer, is correlated with the interfacial grain boundary energy, with grain boundaries with a lower static interfacial energy presenting stronger barriers to slip transmission and dislocation nucleation. Thus, Σ3 boundaries are anticipated to be strong barriers [23].

These computational studies consider perfectly characterized systems with atomic level detail available throughout the interaction. However, they are limited to interactions involving only a few dislocations of the same type, high strain rates, low temperatures and high stresses. This makes direct comparison with experiments challenging, but there have been some successes which suggest that useful comparisons can be made despite the boundary condition differences [23].

In this paper, direct observations of the interaction of both perfect and partial dislocations with grain boundaries, including twin boundaries, in austenitic 304 stainless steel at room and elevated temperatures are compared. In addition, a new three-dimensional (3-D) approach for visualizing and analyzing dislocation interactions with interfaces and for coupling it with dynamic experiments in a transmission electron microscope is presented. This approach has the benefit of recovering the information lost in the electron beam direction, a problem with all electron micrographs, allowing viewing of the interaction from optimal directions, and for rapid determination of slip planes and line directions, consistently for all dislocations involved in the interaction. The approach is more flexible than stereographic pairs, which is restricted to information recovery but from a single vantage direction only.

Electron tomograms are generally reconstructed from many images acquired over a large angular range with the same imaging condition maintained. Ideally, an image should be acquired for every degree of tilt over an angular range between 120 and 140°. In addition, the contrast should vary linearly across the images. There are numerous examples of this method being applied to studies of particles [33], [34], [35], [36], [37], but fewer on defect microstructure [34], [38], [39], [40], [41], [42], [43], [44]. The reason for the paucity of applications to defects is the challenge of retaining the same imaging conditions, diffraction vector and Bragg deviation parameter over such an angular range, and for the contrast to vary minimally over it. In this paper it will be shown that the conditions normally used to ensure a high-resolution reconstruction can be relaxed by using prior knowledge of dislocations as well as dislocation image theory to aid in the construction of a 3-D dislocation model using the tomogram as a basis. Because of this relaxation of requirements, it becomes feasible to acquire the images necessary to form a 3-D model intermittently during an in situ straining experiment in an electron microscope. The feasibility of the method is demonstrated in the case of dislocation interactions with grain boundaries, with emphasis placed on determining if the transmission criteria developed by Lee et al. [13], [15], [45] are applicable for partial as well as perfect dislocations, and if thermally activated processes change the criteria.

Section snippets

Experimental procedures

The material used in this study was 304 stainless steel. Samples were sheared to stage-specified dimensions, 3 mm disks for the double-tilt stage and 11.5 × 2.5 mm bars for the deformation stage, and ground to approximately 200 μm thick. The samples were annealed under vacuum at 1060 °C for 30 min to remove deformation and increase the grain size. Electron transparency was achieved using a twin jet polisher with a 6% perchloric acid, 39% butanol and 55% methanol electrolyte. The electron microscopy

Results

The first example illustrates dislocations interacting with a twin boundary, new dislocations being ejected from the boundary into the twinned crystal and their interaction with the other twin boundary. This sample was deformed ex situ. The overall interaction is captured in the bright-field images at two different sample tilts and diffraction vectors presented in Fig. 1; the diffraction conditions used were (A)g=(1¯11¯)in and (B)g=(2¯20)out, with the excitation error slightly positive. The

Discussion

In comparison to the slip transmission criteria proposed by Lee et al. [13], [14], [15], it was found that the magnitude of the Burgers vector of the residual grain boundary dislocation was the most important factor dictating which slip systems were activated by the grain boundary in response to the impingement of dislocations on it. No cases were found in which the resolved shear stress acting on the emitted dislocation system was insufficient for dislocations to propagate from the boundary.

Conclusions

Dislocation/grain boundary interactions were characterized using ex situ deformation and analysis in a TEM and in situ transmission electron microscopy heating and straining experiments using 304 stainless steel. The dominant dislocation slip system activated from the impingement of an incoming dislocation system, defined by the Burgers vector and slip plane of the outgoing dislocations, can be uniquely predicted by characterizing the incoming dislocation system in terms of the Burgers vector,

Acknowledgements

This work was supported by the US Department of Energy Office of Basic Energy Sciences, Division of Materials Science, under award No. DEFG-02-07ER46443. The microscopy was carried out in the Frederick Seitz Materials Research Laboratory Central Facilities, University of Illinois. I.M.R. acknowledges the National Science Foundation for support.

References (55)

  • J. Wang et al.

    Curr Opin Solid State Mater Sci

    (2011)
  • L. Tan et al.

    Corros Sci

    (2010)
  • M.L. Martin et al.

    Acta Mater

    (2012)
  • S. Bechtle et al.

    Acta Mater

    (2009)
  • K. Hattar et al.

    Scripta Mater

    (2008)
  • N. Li et al.

    J Nucl Mater

    (2009)
  • Z.X. Wu et al.

    Acta Mater

    (2009)
  • T.R. Bieler et al.

    Int J Plast

    (2009)
  • W.A.T. Clark et al.

    Scripta Metall Mater

    (1992)
  • L.M. Hsiung et al.

    Scripta Mater

    (1997)
  • L.M. Hsiung et al.

    Intermetallics

    (2004)
  • J. Gemperlová et al.

    Mater Sci Eng A

    (2002)
  • T.R. Bieler et al.

    Int J Plast

    (2009)
  • M.D. Sangid et al.

    Acta Mater

    (2011)
  • R. Kumar et al.

    Comput Mater Sci

    (2010)
  • D.V. Bachurin et al.

    Acta Mater

    (2010)
  • Z.H. Jin et al.

    Scripta Mater

    (2006)
  • A. Ma et al.

    Acta Mater

    (2006)
  • M.D. Sangid et al.

    Mater Sci Eng A

    (2012)
  • K.J. Batenburg et al.

    Ultramicroscopy

    (2009)
  • J.P. Kacher et al.

    Scripta Mater

    (2011)
  • J. Kacher et al.

    Micron

    (2012)
  • S. Mahajan et al.

    Acta Metall

    (1973)
  • T.C. Lee et al.

    Ultramicroscopy

    (1989)
  • Z.H. Jin et al.

    Acta Mater

    (2008)
  • E. Ma

    JOM

    (2006)
  • Ralston KD, Birbilis N. Corrosion...
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