Elsevier

Acta Materialia

Volume 112, 15 June 2016, Pages 347-360
Acta Materialia

Full length article
Effect of low-angle grain boundaries on morphology and variant selection of grain boundary allotriomorphs and Widmanstätten side-plates

https://doi.org/10.1016/j.actamat.2016.04.033Get rights and content

Abstract

Morphology and variant selection (VS) of grain boundary (GB) allotriomorphs and Widmanstätten side-plates of α phase in an α/β titanium alloy, Ti-6Al-4V (wt%), are investigated using a three-dimensional phase field model. The structures of low-angle GBs (misorientation θm ≤ 10°) are modeled as discrete dislocation networks using Frank-Bilby theory. It is shown that α allotriomorphs and side-plates compete with each other during precipitation and the final morphology and selected α variants exhibit a strong correlation with the GB dislocation structures. While the side-plate morphology is more preferred by a symmetrical tilt GB with θm ∼ 10°, it can also be induced by a pure twist GB with θm ≤ 5°. Quantitative analysis indicates that precipitate morphology and VS are determined by the interplay among (i) elastic interaction between a nucleating α precipitate and the GB dislocation networks, (ii) growth anisotropy determined by the relative inclination of the habit plane with respect to the GB dislocations, (iii) density of nucleation sites for the same variant and coalescence during growth, and (iv) spatial confinement from simultaneously nucleated neighboring α variants of dissimilar types.

Introduction

Extended defects such as grain boundaries (GBs) and dislocations are found to have profound influences on the nucleation and growth of precipitates in a complex manner that leads to drastically different microstructures and micro-textures and, consequently, considerable variations in mechanical properties [1], [2], [3], [4]. In α/β titanium (Ti) alloys, for example, two distinctive types of α morphologies are commonly observed in β-processed alloys during cooling due to the presence of GBs, i.e., GB allotriomorphs (GBα) and Widmanstätten side-plates (WS) [5], [6], [7], [8], [9]. Upon cooling from above the β transus, GBα first nucleate and decorate the pre-existing β GBs as either continuous layers [10], [11] or a group of small near-equiaxed particles of alternating variants [12]. On the other hand, it has been reported that WS may emanate from GBα that have already nucleated at β GBs [3], [12], [13]. For example, after the GBα have occupied the GBs, WS of different orientations may nucleate and grow from the β/GBα interfaces [5], [7], [14]. In other cases [15], [16], [17], the WS may even inherit the crystallographic orientation of the GBα. However, it was also observed [8], [18] that discrete WS could grow directly from bare β GBs without the presence of GBα. Therefore, apart from the effects of GBα, the intrinsic structural characteristics of β GBs may also have a direct influence on the nucleation and growth of WS. In general, it is believed that the orientation and morphology of α precipitates at or near β GBs depend strongly on the GB structures [19], [20], [21]. Furthermore, both GBα and WS could have pronounced influences on subsequent microstructural evolution and micro-texture development of α phase in the interiors of β grains [8], [10], [16], [21].

It has been reported that the presence of continuous GBα layers at GBs has a deleterious effects on properties, especially tensile ductility [22], [23]. In contrast, discrete GBα particles of dissimilar orientation variants would lead to the subsequent formation of α colonies [23]. High density of boundaries between the Widmanstätten colonies of different orientations will shorten the effective slip length and result in tortuosity of crack path, leading to higher yield strength and high cycle fatigue strength [13], [22]. Thus, the morphologies of the GBα and WS have direct impacts on the mechanical properties of Ti-alloys. It is therefore highly desirable to understand how GB structure affects the development of GBα and WS microstructure during precipitation [10].

According to the Burgers orientation relationship (OR) between β and α, i.e., {0001}α||{110}β and 112¯0α||111β [24], twelve crystallographically equivalent orientation variants of the α phase could in principle precipitate out within one single β grain [25]. From experimental observations, however, it often appears that only a subset of the twelve variants dominates the developed microstructure [26], [27], [28], [29]. This phenomenon is known as variant selection (VS) and it has a significant effect on the mechanical properties (in particular, fatigue) of the alloy [30], [31]. Extensive studies have been carried out to investigate VS of GBα and WS due to pre-existing β GBs [8], [9], [11], [21], [32] and a set of empirical rules have been proposed based on experimental observations and some intuitive understanding of the possible mechanisms of the β to α transformation. These rules include (i) GBα tend to select a variant that makes itself appear in an orientation that maintains the Burgers OR with both adjacent β grains [3], [8], [21], [33], [34], (ii) the angle between the low-energy interfaces of GBα (i.e., their habit planes) and the GB plane (GBP) should be as small as possible [27], (iii) the growth direction of GBα should be contained in the GBP [33], [34] and (iv) GBα will stay in an orientation that gives rise to the minimum interfacial energy with the non-Burgers β grain through the “edge-to-edge” matching of the {110}β and {0002}α planes [34]. However, these empirical rules are frequently violated according to experimental observations [8], [11], suggesting that the underlying mechanisms of VS due to GBs are still not fully understood [3].

In parallel to the experimental studies, extensive theoretical modeling has also been carried out to investigate the effect of GB on precipitation. For example, the nucleation of GBα has been analyzed using the classical theory of heterogeneous nucleation [35], [36], [37], [38], [39], [40]. More recently, the influence of GBs on the morphology and VS of GBα has been studied [40] by analyzing experimental characterization results against the empirical rules mentioned earlier. These studies essentially treated GBs as continuum dividing surfaces with an excess boundary energy. In reality, however, GBs have internal discrete atomistic structures that influence the properties of GBs in a profound manner [41], [42], [43], [44], [45], [46] and, as a consequence, the nucleation and growth behavior of GB precipitates may vary significantly from GB to GB even though they may have similar boundary energy.

In this study, we investigate the effects of different types of low angle GBs on precipitation of GBα and WS using three-dimensional (3-D) phase field simulations. Low-angle (with misorientation angle θm ≤ 10°) symmetrical tilt and pure twist GBs are considered for simplicity but without losing generality. It builds upon our previous work [47], [48], [49] on the effect of individual dislocations on precipitation. By incorporating discrete dislocation structures of these GBs, whose stress fields vary significantly with the GB characteristics, diverse GBα and WS microstructures have been observed in the simulations and the morphologies of these precipitates and selected α variants exhibit a strong correlation with the GB dislocation structures. In the following sections, we first introduce the theories and methods, including the calculation of GB dislocation structures and the resulting stress field of GB dislocation networks (Section 2.1), as well as a brief introduction of the multi-phase field model that is extended from our previous work in order to consider an elastically inhomogeneous solid medium (Section 2.2). Simulation results on morphology and VS of GBα and WS are presented in Section 3 and discussed in Section 4. Major findings of the study are summarized in Section 5.

Section snippets

Dislocation networks at low-angle grain boundaries and their stress fields

Small angle and special GBs as well as semi-coherent interfaces have been modeled as discrete dislocation networks using the Frank-Bilby theory [50], [51], O-lattice theory [52], [53] or microscopic phase field microelasticity theory [54]. The dislocations are called intrinsic dislocations in the sense that they inherently describe the structure of GBs and interfaces in an otherwise homogeneous continuum medium. In the current work, we apply the Frank-Bilby theory to describe GB dislocation

Grain boundary dislocation networks

As schematically shown in Fig. 1 (a), starting with the reference state i.e., the median lattice that is essentially a perfect β crystal, the symmetrically tilted bi-crystal is obtained by first halving the (infinite) perfect crystal along the (010)β plane and rotating the two resulting grains by θm/2 and −θm/2, respectively, around an axis parallel to the [101]β direction. Since slip in b.c.c metals usually occurs in the close-packed 〈111〉β directions with the Burgers vector of dislocations

Discussion

Till now, the mechanisms of VS by GBs remain controversial, including whether the selection process is nucleation- or growth-dominated [3]. In the current study, VS at the early nucleation stage is found to be driven mainly by the elastic interaction between the nucleating coherent α variants and the anisotropic and heterogeneous stress field associated with discrete GB dislocations. However, because of their mutual interactions and their interactions with the GB dislocations during growth,

Conclusions

The effects of intrinsic grain boundary (GB) structure on morphology and variant selection (VS) during α precipitation at low-angle β GBs in Ti-6Al-4V are investigated systematically using phase field simulations. Symmetrical tilt and pure twist GBs are considered and their structures are modeled as dislocation networks. It is found that the formation of two distinctive types of α precipitates at or near a GB frequently observed in experiments, i.e., GB allotriomorphs (GBα) and Widmanstätten

Acknowledgements

This work is supported by the 973 Programs under Grants No. 2012CB619600 and No. 2014CB644003, National Nature Science Foundation of China under Grant No. 51504151 (D.Q., D.Z. and W.L) and NSF DMREF program under Grant No. DMR-1435483 (R.P.S and Y.W).

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