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Cochard T, Svetlizky I, Albertini G, Viesca RC, Rubinstein SM, Spaepen F, Yuan C, Denolle M, Song YQ, Xiao L, Weitz DA. Propagation of extended fractures by local nucleation and rapid transverse expansion of crack-front distortion. Nat Phys 2024; 20:660-665. [PMID: 38638457 PMCID: PMC11021187 DOI: 10.1038/s41567-023-02365-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 02/27/2023] [Accepted: 11/30/2023] [Indexed: 04/20/2024]
Abstract
Fractures are ubiquitous and can lead to the catastrophic material failure of materials. Although fracturing in a two-dimensional plane is well understood, all fractures are extended in and propagate through three-dimensional space. Moreover, their behaviour is complex. Here we show that the forward propagation of a fracture front occurs through an initial rupture, nucleated at some localized position, followed by a very rapid transverse expansion at velocities as high as the Rayleigh-wave speed. We study fracturing in a circular geometry that achieves an uninterrupted extended fracture front and use a fluid to control the loading conditions that determine the amplitude of the forward jump. We find that this amplitude correlates with the transverse velocity. Dynamic rupture simulations capture the observations for only a high transverse velocity. These results highlight the importance of transverse dynamics in the forward propagation of an extended fracture.
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Affiliation(s)
- T. Cochard
- National Key Laboratory of Petroleum Resources and Engineering, China University of Petroleum, Beijing, China
- School of Engineering and Applied Sciences (SEAS), Harvard University, Cambridge, MA USA
| | - I. Svetlizky
- School of Engineering and Applied Sciences (SEAS), Harvard University, Cambridge, MA USA
| | - G. Albertini
- Faculty of Engineering, University of Nottingham, Nottingham, UK
| | - R. C. Viesca
- Department of Civil and Environmental Engineering, Tufts University, Medford, MA USA
| | - S. M. Rubinstein
- The Racah Institute of Physics, The Hebrew University of Jerusalem, Jerusalem, Israel
| | - F. Spaepen
- School of Engineering and Applied Sciences (SEAS), Harvard University, Cambridge, MA USA
| | - C. Yuan
- Department of Earth and Planetary Sciences, Harvard University, Cambridge, MA USA
| | - M. Denolle
- Earth and Space Sciences, University of Washington, Seattle, WA USA
| | - Y-Q. Song
- School of Engineering and Applied Sciences (SEAS), Harvard University, Cambridge, MA USA
- Athinoula A. Martinos Center for Biomedical Imaging, Department of Radiology, Massachusetts General Hospital, Charlestown, MA USA
| | - L. Xiao
- National Key Laboratory of Petroleum Resources and Engineering, China University of Petroleum, Beijing, China
| | - D. A. Weitz
- School of Engineering and Applied Sciences (SEAS), Harvard University, Cambridge, MA USA
- Department of Physics, Harvard University, Cambridge, MA USA
- Wyss Institute for Biologically Inspired Engineering, Harvard University, Boston, MA USA
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Jensen KE, Weitz DA, Spaepen F. Local shear transformations in deformed and quiescent hard-sphere colloidal glasses. Phys Rev E Stat Nonlin Soft Matter Phys 2014; 90:042305. [PMID: 25375492 DOI: 10.1103/physreve.90.042305] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/15/2014] [Indexed: 06/04/2023]
Abstract
We perform a series of deformation experiments on a monodisperse, hard-sphere colloidal glass while simultaneously following the three-dimensional trajectories of roughly 50,000 individual particles with a confocal microscope. In each experiment, we deform the glass in pure shear at a constant strain rate [(1-5)×10(-5) s(-1)] to maximum macroscopic strains (5%-10%) and then reverse the deformation at the same rate to return to zero macroscopic strain. We also measure three-dimensional particle trajectories in an identically prepared quiescent glass in which the macroscopic strain is always zero. We find that shear transformation zones exist and are active in both sheared and quiescent colloidal glasses, revealed by a distinctive fourfold signature in spatial autocorrelations of the local shear strain. With increasing shear, the population of local shear transformations develops more quickly than in a quiescent glass and many of these transformations are irreversible. When the macroscopic strain is reversed, we observe partial elastic recovery, followed by plastic deformation of the opposite sign, required to compensate for the irreversibly transformed regions. The average diameter of the shear transformation zones in both strained and quiescent glasses is slightly more than two particle diameters.
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Affiliation(s)
- K E Jensen
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - D A Weitz
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA and School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA
| | - F Spaepen
- School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA
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Abstract
Modern confocal microscopes enable high-precision measurement in three dimensions by collecting stacks of 2D (x-y) images that can be assembled digitally into a 3D image. It is difficult, however, to ensure position accuracy, particularly along the optical (z) axis where scanning is performed by a different physical mechanism than in x-y. We describe a simple device to calibrate simultaneously the x, y, and z pixel-to-micrometer conversion factors for a confocal microscope. By taking a known 2D pattern and positioning it at a precise angle with respect to the microscope axes, we created a 3D reference standard. The device is straightforward to construct and easy to use.
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Affiliation(s)
- K E Jensen
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA.
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Park B, Spaepen F, Poate JM, Jacobson DC. The Effect of Self-Implantation on the Interdiffusion in Amorphous Si/Ge Multilayers. ACTA ACUST UNITED AC 2011. [DOI: 10.1557/proc-74-493] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/13/2022]
Abstract
AbstractArtificial amorphous Si/Ge multilayers of equiatomic average composition with a repeat length around 60 Å have been prepared by ion beam sputtering. Implantation with 29Si led to a decrease in the intensity of the X-ray diffraction peaks arising from the composition modulation, which could be used for an accurate measurement of the implantation-induced mixing distance. Subsequent annealing showed no difference between the interdiffusivity in an implanted and unimplanted sample.
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Abstract
ABSTRACTThe kinetics of rapid crystallization in metals is investigated by measuring transient optical property changes in laser irradiated gold and copper films in the picosecond and nanosecond regimes. Melt thresholds are determined by examining concentration profiles of multi-layered films before and after irradiation.
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Roorda S, Sinke W, Poate J, Jacobson D, Fuoss P, Dierker S, Dennis B, Spaepen F. Thermodynamic and Structural Properties of Mev Ion Beam Amorphized Silicon. ACTA ACUST UNITED AC 2011. [DOI: 10.1557/proc-157-683] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/13/2022]
Abstract
ABSTRACTThermodynamic and structural properties of amorphous Si (a-Si), prepared by MeV 28Si+-ion implantation are investigated by differential scanning calorimetry, Raman spectroscopy and X-ray diffraction. The influence of thermal annealing below 500 °C on a-Si is investigated with these different probes. The observed changes result from structural relaxation. Raman spectroscopy and X-ray diffraction show that structural relaxation is accompanied by changes in the average atomic structure.
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Donovan E, Spaepen F, Turnbull D, Poate J, Jacobson D. Thermodynamics and Kinetics of Crystallization of Amorphous Si and Ge Produced by Ion Implantation. ACTA ACUST UNITED AC 2011. [DOI: 10.1557/proc-27-211] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/13/2022]
Abstract
ABSTRACTAmorphous Si and Ge layers, produced by noble gas (Ar or Xe) implantation of single crystal substrates, have been crystallized in a differential scanning calorimeter (DSC). This technique allows determination of the growth velocity (which is proportional to the rate of heat evolution, ΔHac), and the total enthalpy of crystallization ΔHacAmorphous Ge was found to relax continuously to an amorphous state of lower free energy, with a total enthalpy of relaxation of 6.0 kJ.mole−1 before crystallization started. The regrowth velocity on (100) substrates,measured to be 4.2×1017 exp (−2.17eV/kT)Å/sec, is compared to other determinations. The value of ΔHac was found to be 11.66± 0.7 kJ.mole, in good agreement with ΔHac for amorphous Ge produced by other methods. For Si, ΔHac was determined to be 11.95± 0.7 kJ.mole without any evidence of heat release due to relaxation. The kinetics of crystallization measured by DSC are compared with those determined by other techniques. The effects of the implant profile on the regrowth velocity could also be observed directly in the DSC signal. The more accurate value of ΔHac allowed a more precise determination of the melting temperature of amorphous Si: Taℓ= 1420K.
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Park B, Spaepen F, Poate JM, Priolo F, Jacobson DC, Pai CS, White AE, Short KT. The Effect of Ion Implantation on the Interdiffusion in Si/Ge Amorphous Artificial Multilayers. ACTA ACUST UNITED AC 2011. [DOI: 10.1557/proc-103-173] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/13/2022]
Abstract
ABSTRACTAmorphous Si/Ge artificial multilayers have been implanted with Si and B at liquid nitrogen temperature, and partially ion mixed with Ar at different temperatures. In all cases, the square of the mixing length was found to be proportional to the dose. Annealing of Si-implanted samples showed that after relaxation the diffusivity appeared unaffected by the implantation process. Annealing of the B-implanted samples showed an enhancement of the diffusivity at the higher dose. The diffusive component of the square of the mixing length in the Ar-ion mixed samples has an Arrhenius-type temperature dependence, with an activation enthalpy of 0.22 eV.
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Park B, Spaepen F, Poate JM, Priolo F, Jacobson DC. Composition- and Temperature-Dependence of Ion Mixing in Amorphous Si/Ge Artificial Multilayers. ACTA ACUST UNITED AC 2011. [DOI: 10.1557/proc-128-243] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/13/2022]
Abstract
ABSTRACTAmorphous Si/Ge artificial multilayers with a repeat length of around 60A have been partially mixed with 1.5 MeV Ar+ ions at temperatures in the range 77–673K. The change in the intensity of the first X-ray diffraction peak resulting from the composition modulation is used to determine the mixing lengths. The diffusive component of the square of the mixing length, at a given dose, is independent of the dose rate and has an Arrhenius-type temperature dependence, with activation enthalpies between 0.19 and 0.22 eV, depending on the average composition.
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Roorda S, Sinke W, Poate J, Jacobson D, Dierker S, Dennis B, Eaglesham D, Spaepen F. Changing the Structural State of Amorphous Silicon by Ion Irradiation. ACTA ACUST UNITED AC 2011. [DOI: 10.1557/proc-157-709] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/13/2022]
Abstract
ABSTRACTIon beams of keV and MeV energies have been used to bombard amorphous Si (a-Si), which had previously been annealed (‘relaxed’). Analysis by Raman spectroscopy and differential scanning calorimetry shows that when 1 out of every 20 Si atoms is displaced by a nuclear collision, the a-Si returns to its unrelaxed state and cannot be distinguished from as implanted a-Si. Moreover, the kinetics of the heat release on annealing of similarly bombarded crystalline Si (c-Si) are qualitatively identical to those of structural relaxation in a-Si. This implies that the population of ion beam induced defects in a-Si is very similar to that in c-Si. It also shows that defect annihilation is an important ingredient in the mechanism of structural relaxation of a-Si.
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Abstract
ABSTRACTA new design for a thin film microtensile tester is presented. The strain is measured directly on the free-standing thin film from the displacement of laser spots diffracted from a thin grating applied to its surface by photolithography. The diffraction grating is two-dimensional, allowing strain measurement both along and transverse to the tensile direction. In principle, both Young's modulus and Poisson's ratio of a thin film can be determined. Ag thin films with strong <111> texture were tested. The measured Young moduli agreed with those measured on bulk crystals, but the measured Poisson ratios were low, most likely due to slight transverse folding of the film that developed during the test.
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Abstract
ABSTRACTThe mechanism of ultrafast cooling (1012K sec−1) by picosecond pulsed laser irradiation is reviewed, and it is demonstrated that only partitionless transformations can occur. The glass formation range in a number of binary systems is reviewed, demonstrating that many glasses can be formed below the To-line. The formation of metastable crystalline alloys in the Fe-B, Ni-Nb, Cu-Co and Au-Co systems is reported.
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Ramsteiner IB, Weitz DA, Spaepen F. Stiffness of the crystal-liquid interface in a hard-sphere colloidal system measured from capillary fluctuations. Phys Rev E Stat Nonlin Soft Matter Phys 2010; 82:041603. [PMID: 21230283 DOI: 10.1103/physreve.82.041603] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/22/2010] [Indexed: 05/30/2023]
Abstract
Face-centered cubic single crystals of σ=1.55 μm diameter hard-sphere silica colloidal particles were prepared by sedimentation onto (100) and (110) oriented templates. The crystals had a wide interface with the overlaying liquid that was parallel to the template. The location of the interface was determined by confocal microscopic location of the particles, followed by identification of the crystalline and liquid phases by a bond-orientation order parameter. Fluctuations in the height of the interface about its average position were recorded for several hundred configurations. The interfacial stiffness γ was determined from the slope of the inverse squared Fourier components of the height profile vs the square of the wave number, according to the continuum capillary fluctuation method. The offset of the fit from the origin could quantitatively be accounted for by gravitational damping of the fluctuations. For the (100) interface, γ=(1.3±0.3)k(B)T/σ(2); for the (110) interface, γ=(1.0±0.2)k(B)T/σ(2). The interfacial stiffness of both interfaces was found to be isotropic in the plane. This is surprising for the (110), where crystallography predicts twofold symmetry. Sedimentation onto a (111) template yielded a randomly stacked hexagonal crystal with isotropic γ=0.66k(B)T/σ(2). This value, however, is less reliable than the two others due to imperfections in the crystal.
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Affiliation(s)
- I B Ramsteiner
- School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA
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Affiliation(s)
- J. L. Katz
- a Department of Chemical Engineering and Institute of Colloid and Surface Science , Clarkson College of Technology, Potsdam , New York , 13676 , U.S.A
| | - F. Spaepen
- b Division of Applied Sciences, Harvard University , Cambridge , Massachusetts , 02138 , U.S.A
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Ramsteiner IB, Jensen KE, Weitz DA, Spaepen F. Experimental observation of the crystallization of hard-sphere colloidal particles by sedimentation onto flat and patterned surfaces. Phys Rev E Stat Nonlin Soft Matter Phys 2009; 79:011403. [PMID: 19257031 DOI: 10.1103/physreve.79.011403] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/05/2008] [Indexed: 05/27/2023]
Abstract
We present a confocal microscopy study of 1.55 microm monodisperse silica hard spheres as they sediment and crystallize at the bottom wall of a container. If the particles sediment onto a feature less flat wall, the two bottom layers crystallize simultaneously and layerwise growth follows. If the wall is replaced by a hexagonal template, only layerwise growth occurs. Our results complement earlier numerical simulations and experiments on other colloidal systems.
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Affiliation(s)
- I B Ramsteiner
- School of Engineering and Applied Sciences, Harvard University, 9 Oxford Street, Cambridge, Massachusetts 02138, USA
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Affiliation(s)
- Tsai-Wei Wu
- a Division of Applied Sciences , Harvard University , Cambridge , Massachusetts , 02138 , U.S.A
| | - F. Spaepen
- a Division of Applied Sciences , Harvard University , Cambridge , Massachusetts , 02138 , U.S.A
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Pozdnyakova I, Hennet L, Mathiak G, Brillo J, Zanghi D, Brun JF, Brassamin S, Bytchkov A, Cristiglio V, Véron E, Matzen G, Geandier G, Thiaudière D, Moss SC, Spaepen F, Egry I, Price DL. Structural properties of molten dilute aluminium-transition metal alloys. J Phys Condens Matter 2006; 18:6469-6480. [PMID: 21690847 DOI: 10.1088/0953-8984/18/28/003] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
The short-range order in liquid binary Al-rich alloys (Al-Fe, Al-Ti) was studied by x-ray diffraction. The measurements were performed using a novel containerless technique which combines aerodynamic levitation with inductive heating. The average structure factors, S(Q), have been determined for various temperatures and compositions in the stable liquid state. From S(Q), the pair correlation functions, g(r), have been calculated. The first interatomic distance is nearly temperature-independent, whereas the first-shell coordination number decreases with increasing temperature for all the alloys investigated. For the Al-Fe alloys, room-temperature scanning electron microscropy (SEM) studies show the formation of a microstructure, namely the existence of Al(13)Fe(4) inclusions in the Al matrix.
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Affiliation(s)
- I Pozdnyakova
- Centre de Recherche sur les Matériaux à Haute Température, CNRS-CRMHT, 1d avenue de la Recherche Scientifique, 45071 Orléans cedex 2, France
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Roorda S, Sinke WC, Poate JM, Jacobson DC, Dierker S, Dennis BS, Eaglesham DJ, Spaepen F, Fuoss P. Structural relaxation and defect annihilation in pure amorphous silicon. Phys Rev B Condens Matter 1991; 44:3702-3725. [PMID: 9999999 DOI: 10.1103/physrevb.44.3702] [Citation(s) in RCA: 137] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Abstract
A historical perspective on the development of physical metallurgy is presented. Two recent advances in the control of microstructure, rapid solidification and artificial multilayers, are discussed. Rapid solidification has produced metallic glasses and metastable crystalline systems, and has led to important technological and scientific discoveries. The synthesis of artificial multilayers by direct deposition represents the ultimate control of such microstructures.
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Chason E, Greer AL, Kelton KF, Pershan PS, Sorensen LB, Spaepen F, Weiss AH. Structural relaxation of amorphous Pd82Si18: X-ray measurements, electrical-resistivity measurements, and a comparison using the Ziman theory. Phys Rev B Condens Matter 1985; 32:3399-3408. [PMID: 9937478 DOI: 10.1103/physrevb.32.3399] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/11/2023]
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