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Case Western Reserve University, Cleveland, Ohio 44106, USA *e-mail: [email protected] 1. Russo, C. et al. Nature 405, 531–532 (2000). 2. Näslund, J. et al. Proc. Natl Acad. Sci. USA 91, 8378–8382 (1994). 3. Vassar, R. et al. Science 286, 735–741 (1999). 4. Ancolio, K. et al. Proc. Natl Acad. Sci. USA 96, 4119–4124 (1999). 5. Crook, R. et al. Nature Med. 4, 452–455 (1998). 6. Russo, C. et al. Neurobiol. Dis. 8, 173–180 (2001). 7. Chen, F. et al. J. Biol. Chem. 275, 36794–36802 (2000). Nanoindentation Simulation of defect nucleation in a crystal N anoindentation is the penetration of a surface to nanometre depths using an indenting device. It can be simulated using the Bragg bubble-raft model 1 , in which a close-packed array of soap bubbles corresponds to the equilibrium positions of atoms in a crystalline solid. Here we show that homogeneous defect nucleation occurs within a crystal when its surface roughness is comparable to the radius of the indenter tip, and that the depth of the nucleation site below the surface is proportional to the half-width of the contact. Our results may explain the unusually high local stress required for defect nucleation in nano- indented face-centred cubic crystals. Nanoindentation of face-centred cubic metals causes a load-versus-displacement response that is separated into regions of elastic deformation and discrete displace- ment bursts 2–4 (Fig. 1a). The first dis- placement burst generally occurs when maximum shear stress generated under the indenter is of the order of the theor- etical shear strength 2,3 . This high local stress seems to cause homogeneous nucle- ation of dislocations beneath the surface, producing a displacement burst 3 . To confirm these observations, we used the bubble raft as a model for nanoscale atomic contact, in which the bubble posi- tions represent the equilibrium positions of atoms 1 and allow visualization of deforma- tion, dislocations, adhesion and fracture 5–7 . We prepared the bubble raft as described 1,6,7 . Indentation along the <121> direction of the raft proceeded orthogonally to the <110> closed-packed direction in the {111} plane. We flattened the raft’s contact edge by removing extraneous bubbles with a soldering iron. A completed raft, comprising more than 10 4 bubbles, measures about 250 mm2250 mm, and simulates semi-infinite boundary conditions. Each bubble was 1 mm in diam- eter, representing an atom of diameter 0.3 nm. All other relevant dimensions in the model are converted to atomic dimensions by using this conversion scale. We indented a single-crystal bubble raft, which was initially defect-free, in the plane of the raft along the <121> direction by using indenters of simulated tip radii 8 and 28 nm. The indenter, which was construct- ed of aluminium plate, was positioned in the plane of the raft and slightly below the surface of the solution. We applied the load by controlled increase in displacement using a screw-driven mechanism (Fig. 1b). The in-plane shear stress beneath the indenter was maximal at a ratio of depth, z, to contact half-width, a, of 0.78 (Fig. 1c), as predicted by two-dimensional hertzian indentation theory 8 . Figure 1c, d shows dislocation nucle- ation under atomically flat surfaces for two different indenter radii. In both cases, a dis- location nucleated beneath the indented surface along the loading axis at a depth of 0.78a; this location was determined by direct observation of z and a. The disloca- tion then split in two: one dislocation glided into the crystal and the other ran to the surface, creating a slip step. Burgers circuits confirmed the dislocations as edge- type, with Burgers vector, b, in the <110> direction. Dislocations nucleated at a con- stant depth of 0.78a; nucleation occurred farther below the surface as the indenter radius increased. Our observations provide a valid assess- ment of stress distribution down to simu- lated atomic dimensions. This suggests that our approach could correctly describe elas- tic stress in actual nanoindentation, which is consistent with the elastic response seen before the first displacement burst during nanoindentation of face-centred cubic metals (Fig. 1a) 2,3 . Indentation of an atomically ‘rough’ surface initiates plasticity at the contact sur- face (Fig. 1e). Figure 1f shows nucleation inside the crystal, caused by indentation of a surface ledge of width comparable to the indenter radius. This trend supports the idea that roughness induces plasticity dur- ing nanoindentation of metals — that is, surface roughness (in the form of asperities and ledges) is expected to cause dislocation nucleation near the surface of the crystal if the width of the ledge is substantially small- er than the tip radius. If the width of the ledge is greater than the tip radius, available sites for heterogeneous nucleation are suffi- ciently distant from the point of maximum stress beneath the indenter to sustain dis- location nucleation within the crystal. For typical nanoindentation with an indenter tip of radius 50 nm, surface asper- ities larger than 50 nm should show a simi- lar indentation response to that for an atomically flat surface. As crystalline speci- mens are routinely polished to a roughness of 50 nm or more, this explains why the first displacement burst shown in Fig. 1 corresponds to stresses that approach the theoretical shear strength. Andrew Gouldstone*, Krystyn J. Van Vliet, Subra Suresh Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA e-mail: [email protected] *Present address: Physiology Program, Harvard School of Public Health, Boston, Massachusetts 02215, USA 1. Bragg, W. L. & Nye, J. F. Proc. R. Soc. Lond. A 190, 474–481 (1947). 2. Suresh, S., Nieh, T. G. & Choi, B. W. Scripta Mat. 41, 951–957 (1999). 3. Gouldstone, A., Koh, H. J., Zeng, K. Y., Giannakopoulos, A. E. & Suresh, S. Acta Mat. 48, 2277–2295 (2000). 4. Gerberich, W. W., Nelson, J. C., Lilleodden, E. T., Anderson, P. & Wyrobek, J. T. Acta Mat. 44, 3585–3598 (1996). 5. Shi, L. T. & Argon, A. S. Phil. Mag. A 19, 255–274 (1982). 6. McClintock, F. A. & O’Day, W. R. Proc. Int. Conf. Fract. 1, 75–98 (1965). 7. Georges, J. M., Meille, G., Loubet, J. L. & Tolen, A. M. Nature 320, 342–344 (1986). 8. Johnson, K. L. Contact Mechanics (Cambridge Univ. Press, Cambridge, 1985). brief communications 656 NATURE | VOL 411 | 7 JUNE 2001 | www.nature.com Figure 1 Dislocation nucleation during nanoindentation. a, Indentation load, P, plotted against depth, h, in (133) single-crystal alumi- nium, showing elastic deformation separated by displacement bursts attributed to dislocation nucleation 3 . b, Diagram of bubble-raft indentation. c, d, Initially defect-free rafts in which dislocation nucleation is induced by loading with indenters of different tip radii but at the same normalized depth, z40.78a (white circle), where a is half the width of the contact. This is the position of maximum shear stress, t rz , shown in c. Nucleation (white circle) of a dislocation dipole is seen in d: one dislocation proceeds to the surface and the other into the crystal (white arrows). e, Indentation of atomic-scale asperities, showing plasticity (white circles) at the surface. f, Indentation of surface ledges of width comparable to the indenter radius causes dislocation nucleation within the crystal (white circle). Scale bar, 10 mm (representing 3 nm in our analogy). Indentation direction Indenter Glycerine solution Bubble raft Ambient air 0.04 0.03 0.02 0.01 0 0 10 20 30 40 h (nm) P (mN) a b c d e f 0.78a z τ rz 0.78a 2a 2a © 2001 Macmillan Magazines Ltd
Transcript of document
Case Western Reserve University, Cleveland, Ohio 44106, USA*e-mail: [email protected]. Russo, C. et al. Nature 405, 531–532 (2000).
2. Näslund, J. et al. Proc. Natl Acad. Sci. USA 91,8378–8382 (1994).
3. Vassar, R. et al. Science 286, 735–741 (1999).
4. Ancolio, K. et al. Proc. Natl Acad. Sci. USA 96,4119–4124 (1999).
5. Crook, R. et al. Nature Med. 4, 452–455 (1998).
6. Russo, C. et al. Neurobiol. Dis. 8, 173–180 (2001).
7. Chen, F. et al. J. Biol. Chem. 275, 36794–36802 (2000).
Nanoindentation
Simulation of defectnucleation in a crystal
Nanoindentation is the penetration of asurface to nanometre depths using anindenting device. It can be simulated
using the Bragg bubble-raft model1, inwhich a close-packed array of soap bubblescorresponds to the equilibrium positions ofatoms in a crystalline solid. Here we showthat homogeneous defect nucleation occurswithin a crystal when its surface roughnessis comparable to the radius of the indentertip, and that the depth of the nucleation sitebelow the surface is proportional to thehalf-width of the contact. Our results mayexplain the unusually high local stressrequired for defect nucleation in nano-indented face-centred cubic crystals.
Nanoindentation of face-centred cubicmetals causes a load-versus-displacementresponse that is separated into regions ofelastic deformation and discrete displace-ment bursts2–4 (Fig. 1a). The first dis-placement burst generally occurs whenmaximum shear stress generated under the indenter is of the order of the theor-etical shear strength2,3. This high local stress seems to cause homogeneous nucle-ation of dislocations beneath the surface,
producing a displacement burst3. To confirm these observations, we used
the bubble raft as a model for nanoscaleatomic contact, in which the bubble posi-tions represent the equilibrium positions ofatoms1 and allow visualization of deforma-tion, dislocations, adhesion and fracture5–7.We prepared the bubble raft asdescribed1,6,7. Indentation along the <121>direction of the raft proceeded orthogonallyto the <110> closed-packed direction in the{111} plane. We flattened the raft’s contactedge by removing extraneous bubbles witha soldering iron.
A completed raft, comprising more than104 bubbles, measures about 250 mm2250mm, and simulates semi-infinite boundaryconditions. Each bubble was 1 mm in diam-eter, representing an atom of diameter 0.3 nm. All other relevant dimensions in themodel are converted to atomic dimensionsby using this conversion scale.
We indented a single-crystal bubble raft,which was initially defect-free, in the planeof the raft along the <121> direction byusing indenters of simulated tip radii 8 and28 nm. The indenter, which was construct-ed of aluminium plate, was positioned inthe plane of the raft and slightly below thesurface of the solution. We applied the loadby controlled increase in displacementusing a screw-driven mechanism (Fig. 1b).The in-plane shear stress beneath theindenter was maximal at a ratio of depth, z,to contact half-width, a, of 0.78 (Fig. 1c), aspredicted by two-dimensional hertzianindentation theory8.
Figure 1c, d shows dislocation nucle-ation under atomically flat surfaces for twodifferent indenter radii. In both cases, a dis-location nucleated beneath the indentedsurface along the loading axis at a depth of0.78a; this location was determined bydirect observation of z and a. The disloca-
tion then split in two: one dislocation glided into the crystal and the other ran tothe surface, creating a slip step. Burgers circuits confirmed the dislocations as edge-type, with Burgers vector, b, in the <110> direction. Dislocations nucleated at a con-stant depth of 0.78a; nucleation occurredfarther below the surface as the indenterradius increased.
Our observations provide a valid assess-ment of stress distribution down to simu-lated atomic dimensions. This suggests thatour approach could correctly describe elas-tic stress in actual nanoindentation, whichis consistent with the elastic response seenbefore the first displacement burst duringnanoindentation of face-centred cubic metals (Fig. 1a)2,3.
Indentation of an atomically ‘rough’surface initiates plasticity at the contact sur-face (Fig. 1e). Figure 1f shows nucleationinside the crystal, caused by indentation ofa surface ledge of width comparable to theindenter radius. This trend supports theidea that roughness induces plasticity dur-ing nanoindentation of metals — that is,surface roughness (in the form of asperitiesand ledges) is expected to cause dislocationnucleation near the surface of the crystal ifthe width of the ledge is substantially small-er than the tip radius. If the width of theledge is greater than the tip radius, availablesites for heterogeneous nucleation are suffi-ciently distant from the point of maximumstress beneath the indenter to sustain dis-location nucleation within the crystal.
For typical nanoindentation with anindenter tip of radius 50 nm, surface asper-ities larger than 50 nm should show a simi-lar indentation response to that for anatomically flat surface. As crystalline speci-mens are routinely polished to a roughnessof 50 nm or more, this explains why thefirst displacement burst shown in Fig. 1corresponds to stresses that approach thetheoretical shear strength.Andrew Gouldstone*, Krystyn J. Van Vliet,Subra SureshDepartment of Materials Science and Engineering,Massachusetts Institute of Technology, Cambridge,Massachusetts 02139, USAe-mail: [email protected]*Present address: Physiology Program, Harvard School of Public Health, Boston,Massachusetts 02215, USA1. Bragg, W. L. & Nye, J. F. Proc. R. Soc. Lond. A 190,
474–481 (1947).
2. Suresh, S., Nieh, T. G. & Choi, B. W. Scripta Mat. 41, 951–957
(1999).
3. Gouldstone, A., Koh, H. J., Zeng, K. Y., Giannakopoulos, A. E.
& Suresh, S. Acta Mat. 48, 2277–2295 (2000).
4. Gerberich, W. W., Nelson, J. C., Lilleodden, E. T., Anderson, P.
& Wyrobek, J. T. Acta Mat. 44, 3585–3598 (1996).
5. Shi, L. T. & Argon, A. S. Phil. Mag. A 19, 255–274 (1982).
6. McClintock, F. A. & O’Day, W. R. Proc. Int. Conf. Fract. 1,
75–98 (1965).
7. Georges, J. M., Meille, G., Loubet, J. L. & Tolen, A. M. Nature
320, 342–344 (1986).
8. Johnson, K. L. Contact Mechanics (Cambridge Univ. Press,
Cambridge, 1985).
brief communications
656 NATURE | VOL 411 | 7 JUNE 2001 | www.nature.com
Figure 1 Dislocation nucleation during nanoindentation. a, Indentation load, P, plotted against depth, h, in (133) single-crystal alumi-
nium, showing elastic deformation separated by displacement bursts attributed to dislocation nucleation3. b, Diagram of bubble-raft
indentation. c, d, Initially defect-free rafts in which dislocation nucleation is induced by loading with indenters of different tip radii but at
the same normalized depth, z40.78a (white circle), where a is half the width of the contact. This is the position of maximum shear
stress, trz, shown in c. Nucleation (white circle) of a dislocation dipole is seen in d: one dislocation proceeds to the surface and the other
into the crystal (white arrows). e, Indentation of atomic-scale asperities, showing plasticity (white circles) at the surface. f, Indentation of
surface ledges of width comparable to the indenter radius causes dislocation nucleation within the crystal (white circle). Scale bar, 10 mm
(representing 3 nm in our analogy).
Indentation direction
Indenter
Glycerine solution
Bubble raftAmbient air
0.04
0.03
0.02
0.01
00 10 20 30 40
h (nm)
P (m
N)
a
b
c d
e f
0.78a
z
τrz 0.78a
2a2a
© 2001 Macmillan Magazines Ltd
