Roles of grain boundaries in improving fracture toughness of ultrafine-grained metals

T. Shimokawa, M. Tanaka, K. Kinoshita, and K. Higashida

Phys. Rev. B 83, 214113 – Published 30 June 2011

Abstract

In order to improve the fracture toughness in ultrafine-grained metals, we investigate the interactions among crack tips, dislocations, and grain boundaries in aluminum bicrystal models containing a crack and $〈 112 〉$ tilt grain boundaries using molecular dynamics simulations. The results of previous computer simulations showed that grain refinement makes materials brittle if grain boundaries behave as obstacles to dislocation movement. However, it is actually well known that grain refinement increases fracture toughness of materials. Thus, the role of grain boundaries as dislocation sources should be essential to elucidate fracture phenomena in ultrafine-grained metals. A proposed mechanism to express the improved fracture toughness in ultrafine-grained metals is the disclination shielding effect on the crack tip mechanical field. Disclination shielding can be activated when two conditions are present. First, a transition of dislocation sources from crack tips to grain boundaries must occur. Second, the transformation of grain-boundary structure into a neighboring energetically stable boundary must occur as dislocations are emitted from the grain boundary. The disclination shielding effect becomes more pronounced as antishielding dislocations are continuously emitted from the grain boundary without dislocation emissions from crack tips, and then ultrafine-grained metals can sustain large plastic deformation without fracture with the drastic increase of the mobile dislocation density. Consequently, it can be expected that the disclination shielding effect can improve the fracture toughness in ultrafine-grained metals.

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Received 13 December 2010

DOI:https://doi.org/10.1103/PhysRevB.83.214113

Authors & Affiliations

T. Shimokawa¹, M. Tanaka², K. Kinoshita³, and K. Higashida²

¹School of Mechanical Engineering, College of Science and Engineering, Kanazawa University, Kakuma-machi, Kanazawa, Ishikawa 920-1192, Japan
²Department of Materials Science and Engineering, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka 819-0395, Japan
³Division of Mechanical Science and Engineering, Graduate School of Natural Science and Technology, Kanazawa University, Kakuma-machi, Kanazawa, Ishikawa 920-1192, Japan

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Vol. 83, Iss. 21 — 1 June 2011

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Images

Figure 1
(a) Schematic of the bicrystal model containing a crack of physical length $L_{c}$ . The interfaces are tilt grain boundaries with $〈 112 〉$ tilt axis and the misorientation angle $θ$ is the sum of $θ_{I}$ and $θ_{II}$ . (b) and (c) Symmetric $Σ 15$ expressed by the combination of $B$ (yellow) and $C$ (pink) structural units in model A and asymmetric $Σ 105$ grain-boundary structures expressed by the combination of $B$ structural units and steps in model B, respectively. Here light and dark gray (blue) colored atoms indicate that their nearest neighbor atomic configurations correspond to an fcc structure and other defects defined using the common neighbor analysis,[25] respectively.Reuse & Permissions
Figure 2
(a) Stress-strain curves of model A and model B containing a crack and model $A^{'}$ with $Σ 15$ boundary without a crack. Black and white circles or squares represent dislocation emissions from the left crack tip and the upper-left grain boundary, respectively. 6 and 24 dislocations and 14 and 6 dislocations are emitted from the left crack tip and the upper-left grain boundary in model A and model B, respectively. (b)–(d) Translation of the dislocation source from the crack tip to the grain boundary in model A. Atomic color represents the rotation angle from the initial state of each atom taking the fcc structure, $Δ θ$ . Black colored atoms represent defect structures. Detailed atomic structures in the white square in (d) are shown in Fig. 3.Reuse & Permissions
Figure 3
Change of grain-boundary structures from $Σ 15$ to $Σ 11$ after dislocation emissions from the $C$ structural units (pink). This atomic structure corresponds to the enlarged picture in the white box shown in Fig. 2d. Dark (red) and light gray (blue) colored atoms indicate that their nearest neighbor atomic configurations correspond to stacking fault structures and other defects, respectively. Atoms shown in other colors form an fcc structure.Reuse & Permissions
Figure 4
Relationship between the local resolved shear stress of the slip system $τ_{ck}^{L}$ at a distance of 0.4 nm from the left crack tip and the tensile stress $σ_{a}$ in model A until $ɛ_{z} = 0.025$ . The inset figure shows the distribution of resolved shear stress of $τ_{z^{I} x^{I}}$ . Solid circles represent the required stress for dislocation emissions from the left crack tip.Reuse & Permissions
Figure 5
Stress fields of $σ_{z}$ around the left crack tip in model A at 0 K. (a) Grain-boundary shielding by the nonequilibrium grain boundary containing one EGBD. (b) Equilibrium grain boundary. (c) Theoretical stress field of a Griffith-Inglis crack under an applied stress $σ_{A}$ according to linear elastic theory.Reuse & Permissions
Figure 6
Schematic representations of (a) dislocation, (b) grain boundary, and (c) disclination shielding. $K$ and $k$ represent the apparent macroscopic and the actual local stress intensity factors, respectively. $k_{dislo, i}$ , $k_{gb}$ , and $k_{discli}$ also represent the stress intensity factor due to dislocation, grain boundary, and disclination shielding, respectively.Reuse & Permissions
Figure 7
The effect of back stress due to extrinsic grain-boundary dislocations on the applied stress intensity factor $K_{e}^{j}$ required to emit the $j$ th dislocation from the crack tip as a function of changes in the distance between the crack tip and EGBDs, $r_{gb}$ . When the $j$ th dislocation is emitted from the crack tip, the number of extrinsic grain-boundary dislocations $n_{gb}$ is $j - 1$ . Solid circles represent the points at which the local $k_{e}^{j}$ reaches the critical values of Griffith level, $K_{gf}$ , namely the points where the crack propagates without dislocation emission. Thus, solid circles represent the fracture toughness $K_{IC}$ for $r_{gb}$ .Reuse & Permissions
Figure 8
Dislocation emission from a $Σ 15$ grain boundary in (a) model A and (b) model $A^{'}$ . (c) Stress-strain curves of models A and $A^{'}$ under tensile loading.Reuse & Permissions
Figure 9
(a) Resolved shear stress field $τ_{z^{II} x^{II}}$ subtracted from the average shear stress field $\overset{̲}{τ_{z^{II} x^{II}}}$ when a dislocation $D^{a}$ is ready to be emitted from the grain boundary. The grain boundary contains two lattice dislocations emitted from the left crack tip. (b) Resolved shear stress field $τ_{z^{II} x^{II}}$ by linear elastic theory around the disclination dipole containing two grain-boundary dislocations. The defect configurations correspond to the atomic model as shown in (a).Reuse & Permissions
Figure 10
Disclination shielding and its dependence on the distance between the disclination dipole, $a_{discli}$ . Distributions of $σ_{z}$ by (a) grain-boundary shielding, $k_{gb, l_{t}}$ , (b) disclination shielding, $k_{discli}$ with $a_{discli} = 3$ nm and (c) $k_{discli}$ with $a_{discli} = 6$ nm when the applied stress $σ_{a}$ equals zero. (d) The normalized disclination shielding effect $k_{discli} / k_{gb, l_{t}}$ as a function of $a_{discli}$ . The inset figure represents the grain-boundary structure by the combination of structural units $B$ and $C$ , two semi-infinite walls of grain-boundary dislocations, and disclination dipole.Reuse & Permissions
Figure 11
Normalized left crack tip stress $σ_{ck}^{L} / σ_{a}$ at a distance of 0.4 nm from the left crack tip. The values of $σ_{ck}^{L} / σ_{a}$ are also normalized by the values $σ_{ck}^{L} / σ_{a} |_{ɛ = 0.015}$ when $ɛ = 0.015$ in order to compare values between model A and model B. Solid and open marks represent dislocation emissions from the left crack tip and the upper-left grain boundary, respectively.Reuse & Permissions
Figure 12
Local stress intensity factor $k_{dislo, i}$ map for emitted dislocation $i$ from the grain boundary.Reuse & Permissions
Figure 13
Dislocation distributions around the crack tip. All dislocations are at grain boundaries. Total Burgers vectors in (a) and (b) are the same, but internal stress distributions around the crack tip are different. These pictures correspond to the states after six dislocations are emitted from grain boundary 1.Reuse & Permissions
Figure 14
Local stress intensity factors for (a) situation 1 and (b) situation 2. $k_{total} = k_{gb 1} + k_{gb 2} + k_{gb 3} + k_{gb 4} + k_{gb 5} + k_{discli}$ .Reuse & Permissions

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