MATERIALS HIENGE& ENGIEERING ELSEVIER Materials Science and Engineering A 481-482(2008)404-408 www.elsevier.com/locate/msea Defect modelling of martensitic interfaces in plate martensite Institute of Materials Science and Technology, School of Mechanical Engineering, South China University of Technology guangzhou 510640, China Department of Engineering, University of Liverpool. Brownlow Hill, Liverpool, 169 3BX, UK Received 17 May 2006: received in revised form 13 December 2006: accepted 22 December 2006 A physical model of martensitic transformations describing the structure of the parent-martensite interface and the transformation mechanism is presented. This approach is used here to model martensitic transformations in lath and plate martensite. The habit plane comprises coherent (1 1 1)y/(o l I)a terraces where the coherency strains are accommodated by a network of near screw dislocations, originating in the martensite phase, and disconnections(transformation dislocations), also in near screw orientation. The lateral motions of the disconnections effecting the transformation shear; moreover, the transformation process is explicitly shown to be diffusionless Experimental observations from the literature of the dislocation and disconnection arrays, habit plane and orientation relationship are in good agreement with the model 2007 Elsevier B V. All rights reserved Keywords: Disconnection; Interfacial defects; Interface structure; Martensite crystallography 1. ntroduction formations in lath and plate martensite. The principles of the TM are set out in the next section, and subsequently applied The phenomenological theory of martensite crystallography to ferrous alloys. Finally, experimental observations of transfor- (PTMC) was developed more than 50 years ago [1, 2] and is the mations in ferrous systems previously reported in the literature cornerstone of our present understanding of martensitic crys- are compared with the present modelling tallography. This theory is a quantitative algorithm for finding the invariant habit plane of a shape-transformation 3, 4], and embodies the kinematic compatibility criterion for interfaces 2. Topological model of martensitic interfaces between two semi-infinite continua having no long-range dis- placement fields [5]. while a considerable body of experimental A fundamental step in the TM of a transformation is to observations is consistent with the PTMc 3-5], other data are tify a candidate interface between the phases that exhibits at variance with its predictions, for example see Ref. [6]for a coherency; this is referred to as a terrace plane. Feasible terrace review of ferrous alloys. An alternative approach has been devel- planes in stiff engineering materials are expected to have rela- oped recently in terms of interfacial defects [7, 8]and is refered tively modest coherency strains. Once a terrace plane has been to here as the"topological model"(TM). The TM is a descrip-(b, 0)and glissile disconnections(b, h)that can arise therein tion of the structure of the parent-martensite interface and the line-defects therein; the transformation proceeds by movement can be determined using the theory of interfacial defects [13] of transformation dislocations, or disconnections [9]as they are The coherency strains arising at a terrace plane must be relieved known, across the interface. This defect motion produces the by arrays of interfacial defects. An array of appropriately ori transformation shear and can be shown explicitly to be diffu- ented and spaced glissile disconnections can be one of these sets, ionless [10]. To date, the TM has been applied successfully to and synchronous motion of this set can thereby provide the dual transformations in TiMo alloy [7], ZrO2[11] and PuGa[l2]: the function of effecting the transformation and partially relieving objective of the present work is to report progress with trans- the coherency strain. The second set of defects necessary for complete misfit relief need not be glissile; however, these will intersect the disconnection array, and these intersections must Corresponding author. Tel: +86 20 2223 6396: fax: +86 20 8711 2762. not impede the glissile motion of the former. In other word E-mailaddress:maxiao@@scut.edu.cn(X.Ma) the intersections must themselves be glissile[14, 15 ]: it has been 0921-5093/S-see front matter O 2007 Elsevier B v. All rights reserved doi:10.1016/msea.2006.2.196Materials Science and Engineering A 481–482 (2008) 404–408 Defect modelling of martensitic interfaces in plate martensite X. Ma a,∗, R.C. Pond b a Institute of Materials Science and Technology, School of Mechanical Engineering, South China University of Technology, Guangzhou 510640, China b Department of Engineering, University of Liverpool, Brownlow Hill, Liverpool, L69 3BX, UK Received 17 May 2006; received in revised form 13 December 2006; accepted 22 December 2006 Abstract A physical model of martensitic transformations describing the structure of the parent–martensite interface and the transformation mechanism is presented. This approach is used here to model martensitic transformations in lath and plate martensite. The habit plane comprises coherent (1 1 1)//(0 1 1) terraces where the coherency strains are accommodated by a network of near screw dislocations, originating in the martensite phase, and disconnections (transformation dislocations), also in near screw orientation. The lateral motions of the disconnections effecting the transformation shear; moreover, the transformation process is explicitly shown to be diffusionless. Experimental observations from the literature of the dislocation and disconnection arrays, habit plane and orientation relationship are in good agreement with the model. © 2007 Elsevier B.V. All rights reserved. Keywords: Disconnection; Interfacial defects; Interface structure; Martensite crystallography 1. Introduction The phenomenological theory of martensite crystallography (PTMC) was developed more than 50 years ago [1,2] and is the cornerstone of our present understanding of martensitic crys￾tallography. This theory is a quantitative algorithm for finding the invariant habit plane of a shape-transformation [3,4], and embodies the kinematic compatibility criterion for interfaces between two semi-infinite continua having no long-range dis￾placement fields[5]. While a considerable body of experimental observations is consistent with the PTMC [3–5], other data are at variance with its predictions, for example see Ref. [6] for a review of ferrous alloys. An alternative approach has been devel￾oped recently in terms of interfacial defects [7,8] and is refered to here as the “topological model” (TM). The TM is a descrip￾tion of the structure of the parent–martensite interface and the line-defects therein; the transformation proceeds by movement of transformation dislocations, or disconnections [9] as they are known, across the interface. This defect motion produces the transformation shear and can be shown explicitly to be diffu￾sionless [10]. To date, the TM has been applied successfully to transformations in TiMo alloy [7], ZrO2 [11] and PuGa [12]; the objective of the present work is to report progress with trans- ∗ Corresponding author. Tel.: +86 20 2223 6396; fax: +86 20 8711 2762. E-mail address: maxiao@scut.edu.cn (X. Ma). formations in lath and plate martensite. The principles of the TM are set out in the next section, and subsequently applied to ferrous alloys. Finally, experimental observations of transfor￾mations in ferrous systems previously reported in the literature are compared with the present modelling. 2. Topological model of martensitic interfaces A fundamental step in the TM of a transformation is to identify a candidate interface between the phases that exhibits coherency; this is referred to as a terrace plane. Feasible terrace planes in stiff engineering materials are expected to have rela￾tively modest coherency strains. Once a terrace plane has been identified, the set of lattice invariant deformation (LID) defects (b, 0) and glissile disconnections (b, h) that can arise therein can be determined using the theory of interfacial defects [13]. The coherency strains arising at a terrace plane must be relieved by arrays of interfacial defects. An array of appropriately ori￾ented and spaced glissile disconnections can be one of these sets, and synchronous motion of this set can thereby provide the dual function of effecting the transformation and partially relieving the coherency strain. The second set of defects necessary for complete misfit relief need not be glissile; however, these will intersect the disconnection array, and these intersections must not impede the glissile motion of the former. In other words, the intersections must themselves be glissile [14,15]; it has been 0921-5093/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2006.12.196