Scripta Materialia, Vol. 39, Nos. 415, Pp. 533-536, 1998 1359-646298$19.00+00 PIIs1359-6462(98)00193-6 FRACTURE TOUGHNESS FROM ATOMISTIC SIMULATIONS BRITTLENESS INDUCED BY EMISSION OF SESSILE DISLOCATIONS Diana farkas Department of Materials Science and Engineering, Virginia Polytechnic Institute, Blacksburg, VA 24061 eceived in final form May 15, 1998) Introduction In recent years, considerable attention has been devoted to the understanding of the atomistic processes that are responsible for ductile-brittle behavior in solids. Brittle-ductile behavior in metals has been generally described in terms of the emission of dislocations from the crack tip. In most models, it has been assumed that a brittle failure implies that the crack propagates without the emission of disloca- tions. The materials where dislocations are emitted are generally believed to be ductile materials. This view implies a description of brittle-ductile behavior in terms of the processes occuring at the crack tip For example, Rice [1] and zhou, Carlsson and Thompson(zCt)[2I proposed two such models. Both analyses obtain material properties (Yus, Ys) for borderline materials by equating the critical mode I loading to cleave a crack tip to the corresponding value of loading to emit a dislocation from the tip In the Rice analysis [1] the critical loadings for emission and cleavage are obtained by calculating the driving force due to the crack tip stress field at the tip and the local resistance of the slip plane. If the conditions for dislocation emission occur it is assumed that these dislocations will induce ductility due to the fact that the crack is now blunted and also because of the shielding effects. Therefore dislocation emission is associated with ductile materials. whereas brittle fracture is thought to occur in cases where dislocations are not emitted. Thus, in ceramic materials dislocations are not emitted from crack tips, whereas in ductile metals dislocations are easily emitted from crack tips. Many models for the ductile to brittle transition that occurs with decreasing temperature are also based on criteria for dislocation emission /nucleation [3] On the other hand. models for the ductile to brittle transition that are based on dislocation mobil instead of dislocation nucleation have also been proposed recently [4]. Experimental investigations have shown that dislocation emission can be observed in materials with very limited ductility, such as intermetallics. For example, in NiAl in-situ observations of crack propagation by electron microscopy show dislocation emission [5] Using atomistic simulations of crack response for intermetallic materials we show that when the emitted dislocations are sessile and stay in the immediate vicinity of the crack tip the emitted dislocations can actually lead to brittle failure. We present the results of an atomistic simulation study of the simultaneous dislocation emission and crack propagation process in this class of materials. We used a molecular statics technique with embedded atom(EAM) potentials developed for NiAl [6]. The crystal structure of NiAl is the CsCI type(B2) with a lattice parameter of 0.287 nm, which is reproduced
FRACTURE TOUGHNESS FROM ATOMISTIC SIMULATIONS: BRITTLENESS INDUCED BY EMISSION OF SESSILE DISLOCATIONS Diana Farkas Department of Materials Science and Engineering, Virginia Polytechnic Institute, Blacksburg, VA 24061 (Received in final form May 15, 1998) Introduction In recent years, considerable attention has been devoted to the understanding of the atomistic processes that are responsible for ductile-brittle behavior in solids. Brittle-ductile behavior in metals has been generally described in terms of the emission of dislocations from the crack tip. In most models, it has been assumed that a brittle failure implies that the crack propagates without the emission of dislocations. The materials where dislocations are emitted are generally believed to be ductile materials. This view implies a description of brittle-ductile behavior in terms of the processes occuring at the crack tip. For example, Rice [1] and Zhou, Carlsson and Thompson (ZCT) [2] proposed two such models. Both analyses obtain material properties (gus,gs) for borderline materials by equating the critical mode I loading to cleave a crack tip to the corresponding value of loading to emit a dislocation from the tip. In the Rice analysis [1] the critical loadings for emission and cleavage are obtained by calculating the driving force due to the crack tip stress field at the tip and the local resistance of the slip plane. If the conditions for dislocation emission occur it is assumed that these dislocations will induce ductility due to the fact that the crack is now blunted and also because of the shielding effects. Therefore, dislocation emission is associated with ductile materials, whereas brittle fracture is thought to occur in cases where dislocations are not emitted. Thus, in ceramic materials dislocations are not emitted from crack tips, whereas in ductile metals dislocations are easily emitted from crack tips. Many models for the ductile to brittle transition that occurs with decreasing temperature are also based on criteria for dislocation emission /nucleation [3]. On the other hand, models for the ductile to brittle transition that are based on dislocation mobility instead of dislocation nucleation have also been proposed recently [4]. Experimental investigations have shown that dislocation emission can be observed in materials with very limited ductility, such as intermetallics. For example, in NiAl in-situ observations of crack propagation by electron microscopy show dislocation emission [5]. Using atomistic simulations of crack response for intermetallic materials we show that when the emitted dislocations are sessile and stay in the immediate vicinity of the crack tip the emitted dislocations can actually lead to brittle failure. We present the results of an atomistic simulation study of the simultaneous dislocation emission and crack propagation process in this class of materials. We used a molecular statics technique with embedded atom (EAM) potentials developed for NiAl [6]. The crystal structure of NiAl is the CsCl type (B2) with a lattice parameter of 0.287 nm, which is reproduced Pergamon Scripta Materialia, Vol. 39, Nos. 4/5, pp. 533–536, 1998 Elsevier Science Ltd Copyright © 1998 Acta Metallurgica Inc. Printed in the USA. All rights reserved. 1359-6462/98 $19.00 1 .00 PII S1359-6462(98)00193-6 533
534 JOHN HIRTH SYMPOSIUM Vol. 39. Nos. 4/5 Figure 1. Emission of blunting dislocations in NiAl by the potential together with the cohesive energy and elastic constants. The compound stays ordered up to the melting point, indicating a strong tendency towards chemical ordering with a relatively high energy of the antiphase boundary(APB). As a result of this relatively large energy the dislocations of 1/2(111)type Burgers vectors imply a high energy and the deformation process occurs via the large (100)type dislocations Results from Atomistic simulations In our simulations blocks of about 100,000 atoms, we introduced a crack according to anisotropic elasticity theory and the system was allowed to relax. The boundary conditions were periodic along the crack front and fixed in all other directions. We also studied cracks that are blunted in their initial condition so that the effects of blunting are actually isolated from those of the emitted dislocations Depending on the crystallographic orientation of the crack we observed emission of(100)or 1/2(111>dislocations. For the( 100)[01 1] orientation we observed emission of (100)dislocations, which prevent crack growth. These dislocations move away from the crack tip, quickly reaching the boundaries of our simulation cell. In contrast, for the(100)[001] crack( Fig 1)we observed the emission of 1/2(111)dislocations, which stay in the vicinity of the crack tip. These dislocations are emitted in increasing numbers as the stress intensity is increased. The stress necessary to emit dislocations on the inclined (101) plane is lower than the Griffith value and dislocations are emitted. This is shown in Figure 1, at a stress of 1.96 MPa m, showing crack blunting by 5 atomic layers. Figure 2 shows the configuration of the crack tip region at a stress intensity of 3.52 MPa m, with more emitted dislocations as a result of increasing stress intensity. The crack is now more blunted. At this level the crack tip shows a configuration that is precursive to crack branching along the slip plane. Indeed,at higher stress intensities we observe crack branching and propagation along both slip planes. This occurs This process occurs in spite of the fact that the crack is now blunted ess intensity of 4.32 MPam1n2 in a brittle manner, as shown in the configuration of Figure 3 for a stre Figure 4 shows a crack at 3. 52 MPa m where four of the emitted dislocations have been removed The crack does not present the config urations in dicative of crack branching. Because of the removal of the four dislocations the ss of crack branching occurs at a higher stress, and when it occurs, it occurs along one of the slip planes first. Figure 5 shows the configuration at a stress intensity of 4.3 MPa m
by the potential together with the cohesive energy and elastic constants. The compound stays ordered up to the melting point, indicating a strong tendency towards chemical ordering with a relatively high energy of the antiphase boundary (APB). As a result of this relatively large energy the dislocations of 1/2^111& type Burgers vectors imply a high energy and the deformation process occurs via the larger ^100& type dislocations. Results from Atomistic Simulations In our simulations blocks of about 100,000 atoms, we introduced a crack according to anisotropic elasticity theory and the system was allowed to relax. The boundary conditions were periodic along the crack front and fixed in all other directions. We also studied cracks that are blunted in their initial condition so that the effects of blunting are actually isolated from those of the emitted dislocations. Depending on the crystallographic orientation of the crack we observed emission of ^100& or 1/2^111& dislocations. For the (100)[011] orientation we observed emission of ^100& dislocations, which prevent crack growth. These dislocations move away from the crack tip, quickly reaching the boundaries of our simulation cell. In contrast, for the (100)[001] crack (Fig 1) we observed the emission of 1/2^111& dislocations, which stay in the vicinity of the crack tip. These dislocations are emitted in increasing numbers as the stress intensity is increased. The stress necessary to emit dislocations on the inclined (101#) plane is lower than the Griffith value and dislocations are emitted. This is shown in Figure 1, at a stress of 1.96 MPa m1/2, showing crack blunting by 5 atomic layers. Figure 2 shows the configuration of the crack tip region at a stress intensity of 3.52 MPa m1/2, with more emitted dislocations as a result of increasing stress intensity. The crack is now more blunted. At this level the crack tip shows a configuration that is precursive to crack branching along the slip plane. Indeed, at higher stress intensities we observe crack branching and propagation along both slip planes. This occurs in a brittle manner, as shown in the configuration of Figure 3 for a stress intensity of 4.32 MPa m1/2. This process occurs in spite of the fact that the crack is now blunted. Figure 4 shows a crack at 3.52 MPa m1/2 where four of the emitted dislocations have been removed. The crack does not present the configurations indicative of crack branching. Because of the removal of the four dislocations the process of crack branching occurs at a higher stress, and when it occurs, it occurs along one of the slip planes first. Figure 5 shows the configuration at a stress intensity of 4.32 MPa m1/2. Figure 1. Emission of blunting dislocations in NiAl. 534 JOHN HIRTH SYMPOSIUM Vol. 39, Nos. 4/5
Vol. 39. Nos. 4/5 JOHN HIRTH SYMPOSIUM 535 Figure 2. Further emission of blunting dislocations in NIAl Figure 3. Cleavage following emission of blunting dislocations in NiAl Figure 4. Crack in NiAl showing ductile behavior
Figure 2. Further emission of blunting dislocations in NiAl. Figure 3. Cleavage following emission of blunting dislocations in NiAl. Figure 4. Crack in NiAl showing ductile behavior. Vol. 39, Nos. 4/5 JOHN HIRTH SYMPOSIUM 535
JOHN HIRTH SYMPOSIUM Vol. 39. Nos. 475 Figure 5. Crack in NiAl with four dislocations removed, showing cleavage Diseussion These results suggest that the observed cleavage is related to the effect of the high density of dislocations in the tip region The result from the simulations can be rationalized in terms of the added stress of the emitted dislocations. The emitted dislocations add an effective mode I stress intensity which is opposite in sign to that applied and therefore the generally accepted shielding character of emitted dislocations. The emitted dislocations also add an effective mode II stress intensity, which prevents the emission of more dislocations and increases the total K value at the tip. These effects can be quantified with elasticity heory [7]. The mode Il stress intensity is generally small and only causes an embrittling effect when the dislocations are not able to move away from the crack tip and therefore the tip region presents a high density of dislocations. Our results suport models for the ductile to brittle transition that account for the effects of dislocation mobility after they are emitted from the crack tip Acknowledgments The author greatfully acknowledges helpful discussions with W.A. Curtin and R. Thompson. This work was supported by the office of Naval Research, Division of Materials Science and NSF, FAW program References 1.J.Rice,J. Solids.40,239(1992) 2. S.J. Zhou, A Carlsson, and R. Thomson, Phys. Rev. Lett. 72, 852(1994) 3. M. Khantha, D. P. Pope, and V. vitek, 73, 684(1994) 4. P Hirsch and S G. Roberts, Acta Mater. 44, 2361(1996 5. D. Caillard, C. Vaihle, and D. Farkas, Philos Mag. A(1998) 6. D. Farkas, B Mutasa, C. Vailhe, and K. Termes, Modelling Simulation Mater. Sci Eng. 3, 201(1995) 7. T C. Wang, Philos Mag. 981(1996)
Discussion These results suggest that the observed cleavage is related to the effect of the high density of dislocations in the tip region. The result from the simulations can be rationalized in terms of the added stress of the emitted dislocations. The emitted dislocations add an effective mode I stress intensity which is opposite in sign to that applied and therefore the generally accepted shielding character of emitted dislocations. The emitted dislocations also add an effective mode II stress intensity, which prevents the emission of more dislocations and increases the total K value at the tip. These effects can be quantified with elasticity theory [7]. The mode II stress intensity is generally small and only causes an embrittling effect when the dislocations are not able to move away from the crack tip and therefore the tip region presents a high density of dislocations. Our results suport models for the ductile to brittle transition that account for the effects of dislocation mobility after they are emitted from the crack tip. Acknowledgments The author greatfully acknowledges helpful discussions with W.A. Curtin and R. Thompson. This work was supported by the office of Naval Research, Division of Materials Science and NSF, FAW program. References 1. J. Rice, J. Solids. 40, 239 (1992). 2. S. J. Zhou, A. Carlsson, and R. Thomson, Phys. Rev. Lett. 72, 852 (1994). 3. M. Khantha, D. P. Pope, and V. Vitek, 73, 684 (1994). 4. P. Hirsch and S. G. Roberts, Acta Mater. 44, 2361 (1996). 5. D. Caillard, C. Vaihle, and D. Farkas, Philos. Mag. A. (1998). 6. D. Farkas, B. Mutasa, C. Vailhe´, and K. Ternes, Modelling Simulation Mater. Sci. Eng. 3, 201 (1995). 7. T. C. Wang, Philos. Mag. 981 (1996). Figure 5. Crack in NiAl with four dislocations removed, showing cleavage. 536 JOHN HIRTH SYMPOSIUM Vol. 39, Nos. 4/5