DOCSLIB.ORG

Dislocation and Diffusion Creep of Synthetic Anorthite Aggregates

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Dislocation and Diffusion Creep of Synthetic Anorthite Aggregates JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 105, NO. Bll, PAGES 26,017-26,036, NOVEMBER 10, 2000 Dislocation and diffusion creep of synthetic anorthite aggregates E. Rybacki and G. Dresen GeoForschungsZentrumPotsdam, Potsdam, Germany Abstract. Syntheticfine-grained anorthite aggregates were deformedat 300 MPa confining pressurein a Paterson-typegas deformation apparatus. Creep tests were performedat temperatures rangingfrom 1140 to 1480K, stressesfrom 30 to 600 MPa, and strain rates between 2x 10 '6 and lx10-3 s 'l. Weprepared samples with water total contents of 0.004 wt % (dry)and 0.07 wt % (wet), respectively.The wet (dry) materialcontained <0.7 (0.2) vol % glass,associated with fluid inclusionsor containedat triplejunctions. The arithmeticmean grain size of the specimensvaried between2.7 _+0.1 lamfor the dry materialand 3.4 _+0.2 lamfor wet samples.Two differentcreep regimeswere identified for dry andwet anorthiteaggregates. The datacould be fitted to a power law. At stresses> 120 MPa we founda stressexponent of n = 3 irrespectiveof the water content, indicatingdislocation creep. However, the activation energy of wetsamples is356 _+ 9 kJmol 'l, substantiallylower than for dry specimens with 648 + 20kJ mo1-1. The preexponential factor is log A = 2.6(12.7) MPa -n s -• forwet (dry) samples. Microstructural observations suggest that grain boundarymigration recrystallization is importantin accommodatingdislocation creep. In the low- stressregime we observeda stressexponent of n = 1, suggestingdiffusion creep. The activation energiesfor dry and wet samples are 467 + 16and 170 + 6 kJmol '•, respectively.Log A is 12.1 MPa-n pm m s -1 for the dry material and 1.7 MPa -" pm m s '1 for wet anorthite. The data show that the strengthsof anorthiteaggregates decrease with increasingwater content in both the dislocationand diffusioncreep regimes. A comparisonof the creepdata of syntheticplagioclase from this study with publisheddata for feldspar,olivine, andquartz indicates a linearrelationship between activationenergy and log A similarto the suggestedcompensation law for diffusionin silicates. 1. Introduction and inferred deformationmechanisms exist for experimentally and naturallydeformed feldspathic and quartzo-feldspathicrocks Geological field studiesand laboratoryinvestigations of the and are discussedin a seminalreview by Tullis [1990]. mechanicalproperties of rockssuggest a rheologicalstratification The high-temperatureplastic strength of rockscan be reduced of the continentallithosphere [e.g., Brace and Kohlstedt, 1980; considerablyby the presenceof water-relatedspecies [Kohlstedt Kohlstedt et al., 1995] with a weak lower crustal layer et al., 1995]. Tullis and Yund [1980, 1991] and Tullis et al. sandwichedbetween stronger middle crust and upper mantle [1996] showed in their experimentsthat the presenceof water [e.g., Ranalii, 1987]. Independently, Meissner and Strehlau reducesthe strengthof feldsparand may causea changeof the [1982] and Chen and Molnar [1983] suggestedthat reduced dominant deformation mechanism. Dimanov et al. [1999] seismic activity of the lower crust indicateslow ductile flow demonstratedthat the strengthand activationenergy for grain strengthrelative to the uppercrust. However, mechanical data and boundary diffusion-controlledcreep of pure fine-grained flow law parameterson the rheologyof rockstypical for the lower anorthiteaggregates is reducedat atmosphericpressure when crust, i.e., gabbros,metabasites, etc., are still scarce[Caristan, tracesof water (0.05-0.1 wt %) are present.Likewise, the stressat 1982; Sheltonand Tullis, 1981; Kirby, 1983; Carter and Tsenn, the transitionfrom diffusion to dislocationcreep of feldsparis 1987; Mackwell et al., 1998]. The amount of stresstransfer and lower with trace amountsof water present. partitioningof strain betweencrustal layers and the mantle has In this studywe investigatedislocation and diffusioncreep of given rise to much controversy[e.g., Kirby, 1985; Ord and anorthiteaggregates at elevatedconfining pressures. We present Hobbs, 1989]. constitutiveflow laws for syntheticanorthite aggregates that are Feldspars,pyroxenes, and amphibolesare the most abundant dry or containtrace amounts of water. minerals constituting the deep continental crust. For monomineralicrocks composedof feldspar or pyroxenesome recentstudies of syntheticaggregates exist that yield constitutive 2. Starting Material and Experimental Methods equationsfor diffusioncreep [Lavie, 1998; Dimanov et al., 1998, 2.1. SpecimenFabrication 1999]. Bystricky[1998], Mackwell et al. [1998], and Xiao [1999] investigatedmixtures of clinopyroxeneor quartzwith feldsparat Anorthiteaggregates were fabricated from crushed CaA12Si2Oa various volume fractions. Detailed studies of the microstructure glass(Schott Glaswerke). The chemicalcomposition of the glass from fluorescentX-ray analysisis An9a.9Or0.2Ab0.9(normalized to 8 O) with majorimpurities of TiO2 (0.1 wt %), MgO (0.07 wt %), Copyright2000 by the AmericanGeophysical Union. Fe203(0.01 wt %), and H20 (•0.05 wt %). Papernumber 2000JB900223. The particlesize of the glasspowder was <60 pm. The powder 0148-0227/00/2000JB900223509.00 waspredried at 1073 K in air for 60 hoursand kept at 393 K for 26,017 26,018 RYBACKI AND DRESEN: CREEP OF ANORTHITE AGGREGATES severaldays before cold pressinginto steeljackets with 0.5 mm • I i I i I I I I I i • wet undeformed ......... wall thickness.A vacuumdye was usedto reducepressure to 1.5 kPa. To cold pressthe samples,an axial stressof 300 MPa was wetdeformed .........../,•\ _ applied.The diameterof the jackets was 15 mm and the length .............wetundeformed (78K) ...........-'" // \\ was 30 mm. Using a gas pycnometer(Micromeritics Accy Pyc / 1330), the porosity of the green bodies was determinedto be •30%. To fabricate "dry" specimens,we heat treatedthe cold- pressedpellets at 1073 K to 1173 K for more than 120 hours prior to hot pressing."Wet" sampleswere hot isostaticallypressed without the initial heat treatment.A Paterson-typegas apparatus was used to hot pressand annealboth wet and dry samplesin three stepsat a pressureof 300 MPa. First, sampleswere further densiftedabove the glasstransition temperature at 1173 K for 1 hour. Furtherannealing was performedat 1323 K for 2 hours,i.e., o ' I ' I ' I ' I ' I ' slightlyabove the nucleation temperature of 1297 K for•northite 2600 2800 3000 3200 3400 3600 3800 [Dresen et al., 1996]. Finally, the annealingtemperature was -1 wavenumber, cm increasedto 1473 K for 2 hoursto promotegrain growth. Heating andcooling rates were 20 and10 K min-•, respectively.After Figure 1. RepresentativeFTIR absorbancespectra of dry andwet sampleswere retrieved from the vessel, the iron jacket was anorthite aggregatessamples in the mid-IR range (3 I.tm dissolved in acid (50/50 vol % HC1/HNO3). For mechanical wavelength).Using the maximum peak heights near 3600 cm ~•, testing,the sampleswere precisionground to obtain cylindrical the calculatedwater contentof the wet sample(An10) is 9800 specimensof 10 mm diameter and 20 mm length. In this ppm H/Si before deformation(corresponding to 635 ppm H20 procedurethe initial samplesurface possibly contaminated by the (wt)) and 8400 ppm H/Si (545 ppm H20 (wt)) afterdeformation. acid was removed, and the samplediameter was reducedby 4 The dry undeformedsample (An28) contains•500 ppm H/Si (33 mm. The porosityof the samplesis lessthan •1%, as determined ppm H20 (wt)). An additionalpeak at a wavenumberof •3200 by Archimedes'method in water. cm-• wasfound in undeformedwet sample(An15, 10,400 ppm H/Si) when measuredat cryogenictemperature. The smallsharp 2.2. Water Content peaksat 2850and 2930 cm -• resultfrom resin used in sample preparation. A Fourier-transformedinfrared spectrometer(FTIR, Bruker IFS-66v) equippedwith a microscopewas used to measurethe water content of samples before and after deformation.The spectra were recorded at 293 K from >128 scans between feldsparscan contain up to severalthousand parts per million wavenumbers2500 to 4000 crn-• (resolutionof 2 crn-•).We H/Si [Kronenberg et al., 1986; Behrens, 1994; Beran, 1987; performedat least five separatemeasurements per sample.Since Hofmeisterand Rossman,1985]. the spotsize of the microscopeis roughly20 timeslarger than the 2.3. Microstructures averageanorthite grain size, our measurementsrefer to the total water contentof the samples.To quantitativelyestimate the water Figure 2a is an optical micrographtaken from an ultrathin contentof the aggregatesfrom 150-Hm-thicksamples, we used (<10 Hm) sectionof the wet startingmaterial. Prismatic anorthite Beer-Lambert's law and a molar extinction coefficient of 32 grains are common with an averageaspect ratio of 2.7. Grain L(H2O)mol -• crn-• [Beran,1987]. This technique probably yields boundariesare facetted, and 120ø triple junctions are scarce. an upperlimit for the watercontent [Bell et al., 1995]. Twins with fine-spacedlamellae are abundant.A few larger Absorbancespectra for typicalwet and dry samplesare given grains show undulatory extinction. In wet samples some in Figure 1. The spectrashow a broadbandabsorbance with a spheruliteswere foundwith needle-shapedgrains up to 200 I.tm maximumnear 3600 cm-•, characteristicof molecularwater or long and arrangedin radial fashion.Spherulites were previously hydroxyl[Aines and Rossman,1984]. Specimensreferred to as observedto crystallizefrom undercooledplagioclase melt [Abeet wet contain about 11500 _+2900 ppm H/Si (0.07 _+0.02 wt % al., 1991; Kirkpatrick et al., 1979; Lofgren, 1974]. Farver and H20) on averageand
Load more

Recommended publications
  • The Viscosities of Partially Molten Materials Undergoing Diffusion Creep
    The viscosities of partially molten materials undergoing diffusion creep John F. Rudge Bullard Laboratories, Department of Earth Sciences, University of Cambridge December 10, 2018 Abstract Partially molten materials resist shearing and compaction. This resistance is described by a fourth-rank effective viscosity tensor. When the tensor is isotropic, two scalars determine the resistance: an effective shear and an effective bulk viscosity. Here, calculations are presented of the effective viscosity tensor during diffusion creep for a 2D tiling of hexagonal unit cells and a 3D tessellation of tetrakaidecahedrons (truncated octahedrons). The geometry of the melt is determined by assuming textural equilibrium. The viscosity tensor for the 2D tiling is isotropic, but that for the 3D tessellation is anisotropic. Two parameters control the effect of melt on the viscosity tensor: the porosity and the dihedral angle. Calculations for both Nabarro-Herring (volume diffusion) and Coble (surface diffusion) creep are presented. For Nabarro-Herring creep the bulk viscosity becomes singular as the porosity vanishes. This singularity is logarithmic, a weaker singularity than typically assumed in geodynamic models. The presence of a small amount of melt (0.1% porosity) causes the effective shear viscosity to approximately halve. For Coble creep, previous modelling work has argued that a very small amount of melt may lead to a substantial, factor of 5, drop in the shear viscosity. Here, a much smaller, factor of 1.4, drop is obtained for tetrakaidecahedrons. Owing to a Cauchy relation symmetry, the Coble creep bulk viscosity is a constant multiple of the shear viscosity when melt is present. 1 Introduction Dynamical models are often highly dependent on assumptions about the rheology of the material being deformed.
    [Show full text]
  • The Role of Pressure Solution Creep in the Ductility of the Earth's
    The role of pressure solution creep in the ductility of the earth’s upper crust Jean-Pierre Gratier, Dag Dysthe, Francois Renard To cite this version: Jean-Pierre Gratier, Dag Dysthe, Francois Renard. The role of pressure solution creep in the ductility of the earth’s upper crust. Advances in Geophysics, Elsevier, 2013, 54, pp.47-179. 10.1016/B978-0- 12-380940-7.00002-0. insu-00799131 HAL Id: insu-00799131 https://hal-insu.archives-ouvertes.fr/insu-00799131 Submitted on 11 Mar 2013 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. 1 The role of pressure solution creep in the ductility of the Earth’s upper crust Jean-Pierre Gratier1, Dag K. Dysthe2,3, and François Renard1,2 1Institut des Sciences de la Terre, Observatoire, CNRS, Université Joseph Fourier-Grenoble I, BP 53, 38041 Grenoble, France 2Physics of Geological Processes, University of Oslo, Norway 3Laboratoire Interdisciplinaire de Physique, BP 87, 38041 Grenoble, France The aim of this review is to characterize the role of pressure solution creep in the ductility of the Earth’s upper crust and to describe how this creep mechanism competes and interacts with other deformation mechanisms.
    [Show full text]
  • Grain-Sizereductionmechanisms and Rheologicalconsequences in High
    Grain-sizereductionmechanisms and rheologicalconsequences in high-temperaturegabbromylonites of Hidaka, Japan Hugues Raimbourg, Tsuyoshi Toyoshima, Yuta Harima, Gaku Kimura To cite this version: Hugues Raimbourg, Tsuyoshi Toyoshima, Yuta Harima, Gaku Kimura. Grain- sizereductionmechanisms and rheologicalconsequences in high-temperaturegabbromylonites of Hidaka, Japan. Earth and Planetary Science Letters, Elsevier, 2008, 267 (3-4), pp.637-653. 10.1016/j.epsl.2007.12.012. insu-00756068 HAL Id: insu-00756068 https://hal-insu.archives-ouvertes.fr/insu-00756068 Submitted on 22 Nov 2012 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Grain size reduction mechanisms and rheological consequences in high-temperature gabbro mylonites of Hidaka, Japan Hugues Raimbourga, Tsuyoshi Toyoshimab, Yuta Harimab, Gaku Kimuraa (a) Department of Earth and Planetary Science, Faculty of Science, University of Tokyo, Japan (b) Department of Geology, Faculty of Science, University of Niigata, Japan Corresponding Author: Hugues Raimbourg, Dpt. Earth Planet. Science, Faculty
    [Show full text]
  • Grainsize Sensitive Rheology of Orthopyroxene
    PUBLICATIONS Geophysical Research Letters RESEARCH LETTER Grain-size sensitive rheology of orthopyroxene 10.1002/2014GL060607 Rolf H.C. Bruijn1 and Philip Skemer1 Key Points: 1Department of Earth and Planetary Sciences, Washington University in St. Louis, Saint Louis, Missouri, USA • Deformation mechanism map for orthopyroxene is constructed • Diffusion creep of orthopyroxene is important over a wide range Abstract The grain-size sensitive rheology of orthopyroxene is investigated using data from rheological of conditions and microstructural studies. A deformation mechanism map is constructed assuming that orthopyroxene deforms by two independent mechanisms: dislocation creep and diffusion creep. The field boundary between these mechanisms is defined using two approaches. First, experimental data from Lawlis (1998), Correspondence to: which show a deviation from non-linear power law behavior at low stresses, are used to prescribe the location R. H. C. Bruijn, of the field boundary. Second, a new orthopyroxene grain-size piezometer is used as a microstructural [email protected] constraint to the field boundary. At constant temperature, both approaches yield sub-parallel field boundaries, separated in grain size by a factor of only 2–5. Extrapolating to lithospheric conditions, the Citation: deformation mechanism transition occurs at a grain size of ~150–500 μm, consistent with observations from Bruijn, R. H. C., and P. Skemer (2014), nature. As the transition from dislocation to diffusion creep may promote shear localization, grain-size Grain-size sensitive rheology of orthopyroxene, Geophys. Res. Lett., 41, reduction of orthopyroxene may play a prominent role in plate-boundary deformation. doi:10.1002/2014GL060607. Received 20 MAY 2014 Accepted 3 JUL 2014 1.
    [Show full text]
  • Dislocations and Dislocation Creep
    Dislocations and dislocation creep... 1. Introduction: a) Observations of textures associated with dislocation creep b) MOVIES of dislocations in metals. 2. How do dislocations move?: single dislocations: stress, energy and motion. Orowan’s equation. Frank-Read sources, Work Hardening (Fatigue, paper clips) 3. Recovery: dislocation climb, subgrain formation 4. Recrystallization: Fabric development and grain size evolution Grain rotation (LPO development) Reduction: Mechanisms of recrystallization Growth: forces driving grain growth... ----> Localization REVISIT THE QUARTZ regimes 5. Grain Growth: static and dynamic ? Thursday: 6. Piezometers and Wattmeters Empirical Piezometers (dislocations, subgrain and grain size). Stress in the lithosphere from xenoliths (Mercier) Stress across shear zones (Kohlstedt and Weathers) The WATTMETER 1. Intro: Observations First, ALL the complexity that we want to understand ! THEN, deconstruction: simple - - - - > complex small scale (single dislocation) ----- > larger scale (behavior of ensembles) Journal of Structural Geology, Vol. 14, No. 2, pp. 145 to 159, 1992 0191-8141/92 $05.00+0.00 Printed in Great Britain (~ 1992 Pergamon Press plc Dislocation creep regimes in quartz aggregates Journal of Structural Geology, Vol. 14, No. 2, pp. 145 to 159, 1992 Dislocation creep regimes in quartz aggregate0s 191-8141/92 $05.00+0.00 147 Printed in Great GBritainREG HIRrH and JAN TULLIS (~ 1992 Pergamon Press plc 1400 Departmreengimest of Geolo gdetericalS cieminednces, Brow bn Uyn relativiversity,P reo vidence, RI 02912, U.S.A. rates of (Received 11 September 1990; accepted in revised form 30 June 1991) 1. dislocation productionDislocation creep regimes in quartz aggregates Abstract--Using opti2.ca l dislocationand TEM microsc oclimbpy we have determined that threei regimes of dislocation creep ocRcur.
    [Show full text]
  • Formation of Lithospheric Shear Zones
    Physics of the Earth and Planetary Interiors 270 (2017) 195–212 Contents lists available at ScienceDirect Physics of the Earth and Planetary Interiors journal homepage: www.elsevier.com/locate/pepi Formation of lithospheric shear zones: Effect of temperature on two-phase grain damage ⇑ Elvira Mulyukova a, , David Bercovici a a Yale University, Department of Geology and Geophysics, New Haven, CT, USA article info abstract Article history: Shear localization in the lithosphere is a characteristic feature of plate tectonic boundaries, and is evident Received 17 February 2017 in the presence of small grain mylonites. Localization and mylonitization in the ductile portion of the Received in revised form 15 June 2017 lithosphere can arise when its polymineralic material deforms by a grain-size sensitive rheology in com- Accepted 24 July 2017 bination with Zener pinning, which can impede, or possibly even reverse, grain growth and thus pro- Available online 1 August 2017 motes a self-softening feedback mechanism. However, the efficacy of this mechanism is not ubiquitous and depends on lithospheric conditions such as temperature and stress. Therefore, we explore the con- Keywords: ditions under which self-weakening takes place, and, in particular, the effect of temperature and defor- Shear zones mation state (stress or strain-rate) on these conditions. In our model, the lithosphere-like polymineralic Grain damage mechanics Mylonites material is deformed in a two-dimensional simple shear driven by constant stress or strain rate. The min- eral grains evolve to a stable size, which is obtained when the rate of coarsening by normal grain growth and the rate of grain size reduction by damage are in balance.
    [Show full text]
  • Diffusion Creep
    Diffusion Creep Poirier, Chapter 2 and 7, 1985. Gordon, 1985. Monday, Nov. 3, 2003 12.524 Mechanical properties of rocks Fick’s First Law: Driving Force ∇c z Chemical Diffusion ∇T z Thermal diffusion JD=−i ∇µ ∇V z Electrical conduction σ z Diffusion creep 12.524 Mechanical properties of rocks Types of Diffusion Mechanism Path Process Isotope Lattice Interdiffusion Self-diffusion Pipe Creep Vacancy Grain Boundary Ambipolar Interstitial Surface Ring Pore fluid 12.524 Mechanical properties of rocks Diffusion mechanisms Vacancy Diffusion Interstitial Ring Diffusion Collinear Direct Exchange Non -collinear Cyclic Exchange A B 12.524 Mechanical properties of rocks Vacancy–Assisted Diffusion From Site by Glicksman and Lupulescu, RPI, 2003 The FCC lattice geometry requires W = ( 3−1)Da = 0.73Da Images removed due to copyright considerations. For more information, see http://www.rpi.edu/~glickm/diffusion/ 12.524 Mechanical properties of rocks plan view Kinetics Equation for Vacancy Diffusion z Coefficient of Diffusivity for Self-diffusion not the same as Coefficient for Vacancy Diffusion DNDsd= vi v migration =−Nvoexp (∆∆ G vf / kT )i D v o exp − ( G vm / kT ) =−+DGGkTsd oexp (∆∆ vf vm )/ 12.524 Mechanical properties of rocks Diffusion Creep in Monatomic Solid z Basic Ideas Vacancies Supersaturated z Supersaturation of vacancies owing to stress z Diffusion results z Work done on mat’l Vacancies UndersaturatedVacancies by tractions z Energy dissipated in heat, entropy, and surface area 12.524 Mechanical properties of rocks Diffusion Creep z z Nabarro-Herring Creep Monatomic Lattice z Quasi static z Coble Creep z Vacancy Grain Boundary z Increasing length; Poisoining 12.524 Mechanical properties of rocks Critical Idea: Tension makes vacancy formation easier.
    [Show full text]
  • 8. TIME DEPENDENT BEHAVIOUR: CREEP in General, the Mechanical
    8. TIME DEPENDENT BEHAVIOUR: CREEP In general, the mechanical properties and performance of materials change with increasing temperatures. Some properties and performance, such as elastic modulus and strength decrease with increasing temperature. Others, such as ductility, increase with increasing temperature. It is important to note that atomic mobility is related to diffusion which can be described using Ficks Law: æ Q ö D = D exp - (8.1) O è RT ø where D is the diffusion rate, Do is a constant, Q is the activation energy for atomic motion, R is the universal gas constant (8.314J/mole K) and T is the absolute temperature. Thus, diffusion-controlled mechanisms will have significant effect on high temperature mechanical properties and performances. For example, dislocation climb, concentration of vacancies, new slip systems, and grain boundary sliding all are diffusion-controlled and will affect the behaviour of materials at high temperatures. In addition, corrosion or oxidation mechanisms, which are diffusion-rate dependent, will have an effect on the life time of materials at high temperatures. Creep is a performance-based behaviour since it is not an intrinsic materials response. Furthermore, creepis highly dependent on environment including temperature and ambient conditions. Creep can be defined as time-dependent deformation at absolute temperatures greater than one half the absolute melting. This relative T (abs ) temperature ( ) is know as the homologous temperate. Creep is a relative Tmp (abs ) phenomenon which may occur at temperatures not normally considered "high." Several examples illustrate this point. a) Ice melts at 0°C=273 K and is known to creep at -50°C=223 K.
    [Show full text]
  • Evaluation of Diffusion Creep in Low Melting Point Materials By
    397 Evaluation of Diffusion Creep in Low Melting Point Materials by Nanoindentation Creep Test∗ Tadahiro SHIBUTANI∗∗,QiangYU∗∗ and Masaki SHIRATORI∗∗ In this study, diffusion creep in Sn-37Pb as a low melting point alloy during a nanoin- dentation creep test was examined. The creep exponent, n, from the relationship between hardness and indenter dwell time decreases as a function of time and is saturated when n = 1. From observations of the indented surface, plastic deformation due to the indenter takes place in the early stages. On the other hand, granular deformation takes place in the middle and last stages. Finite element analysis revealed that the reduction in Mises stress is faster than that of hydrostatic stress. Multiaxial stresses appear below the indenter, and axial compo- nents of stress remain after relaxation. Since the core hydrostatic stress causes a gradient in the chemical potential at grain boundaries, diffusion creep affects the behavior of indentation creep in the last stage. A transition from power-law creep to diffusion creep occurs below the indenter. Key Words: Creep, Hardness, Finite Element Method, Nanoindentation, Diffusion Creep, and Low Temperature Melting Point Alloy area(7) – (12). Displacements into the surface are measured 1. Introduction continuously under a constant load, and the creep prop- At elevated temperatures, the mechanism of creep de- erties are extracted from the evolution of the hardness on formation in metals is classified into dislocation creep and the basis of the power-law creep relationship. Indenta- diffusion creep(1). Generally, dislocation creep (power- tion creep tests are widely employed as an approximate law creep) is dominant at higher stresses and elevated tem- method, and the creep properties obtained from inden- peratures.
    [Show full text]
  • Research Creep Deformation and Fracture Processes in of and OFF
    SKI Report 2005:18 Research Creep Deformation and Fracture Processes in OF and OFF Copper William H Bowyer October 2004 ISSN 1104-1374 ISRN SKI-R-05/1 8-SE SKi SKI Perspective Background and purpose of the project The integrity of the canister is an important factor for long-term safety of the repository for spent nuclear fuel. When the canister is placed in the repository hole it will be subjected to mechanical loads due to the hydrostatical pressure and the swelling pressure of the bentonite surrounding it. Copper is a soft material and will creep and lay down on the ductile iron insert due to the loads. The creep process will go on until the bentonite is fully saturated. During this time period the creep properties of the copper canister are very essential for the integrity of the copper shell. The copper material may creep but is not supposed to fracture. SKB has investigated the creep properties of the used copper material (Oxygen Free Copper with 40 - 60 ppm phosphorous, OFP material), by carrying out different research projects regarding creep. All the relevant work arising from the development programme concentrates on measurement of minimum creep rates and creep lives for Oxygen free copper (OF) and OF to which 50ppm phosphorus has been added (OFP) under conditions where test duration has not exceeded two years. This has required testing to be accelerated by using higher temperatures and/or higher stresses than would be expected in service. Extrapolation of test data over five orders of magnitude in time, coupled with reductions in temperature and stress, has been used to predict service behaviour.
    [Show full text]
  • 9. Microphysics of Mantle Rheology
    9. Microphysics of Mantle Rheology Ge 163 5/7/14 Outline • Introduction • Vacancies and crystal imperfections • Diffusion Creep • Dislocation creep • Deformation maps • Viscosity in the Deep Mantle • Visco-elastic relaxation and thickness of the lithosphere • Role of Water in influencing creep strength • Appendix A • Details of the theory of Diffusion creep Why does elastic thickness (h, Te) increases with age ? Watts [2001] Diffusion Creep Diffusion creep is the migration or diffusion of point defects through the crystal lattice. An example of a point defect is a vacancy, where an atom is missing from the normal highly regular crystal lattice. Another is an impurity, where some species (of a minor concentration) exists or is located within the regular lattice. So the diffusion of a minor species becomes: b 2 1/2 φo ⎛ φo ⎞ −2φo /kT D = 2 ⎜ ⎟ e 3π kT ⎝ m ⎠ In general, the diffusion coefficient is a function of both temeprature and pressure and is expressed in the form: ⎛ E + pV ⎞ D = D exp − a a o ⎝⎜ RT ⎠⎟ where R is the gas constant, Ea is the activation energy, and Va is the activation volume. The pVa term takes into account of the effect of pressure in reducing the number of vacanies and increasing the potential energy barrier between lattice sites. Diffusion of atoms in a crystal in the presence of differential stress can result in creep. compression Poirier [1991] 12V D ε = a σ xx RTh2 This is "Diffusion Creep" (also known as Nabarro-Herring creep) which resuslts in a linear relation between strain-rate and stress. Recall that we have previously described a "constitutive relation" for a fluid as: σ = 2ηεxx ∴ the "viscosity" for a crystalline solid is: RTh2 η = 24VaD But substituting the relation that we have already derived for the D, the Diffusion 2 RTh ⎛ Ea + pVa ⎞ η = exp⎜ ⎟ 24VaDo ⎝ RT ⎠ In Nabarro-Herring creep, the atoms and vacanies diffuse through the interior of mineral grains.
    [Show full text]
  • Rheological Properties of Minerals and Rocks
    1 Rheological properties of minerals and rocks Shun-ichiro Karato Yale University Department of Geology and Geophysics New Haven, CT 06520, USA to be published in “Physics and Chemistry of the Deep Earth” (edited by S. Karato) Wiley-Blackwell 2 SUMMARY Plastic deformation in Earth and planetary mantle occurs either by diffusion or by dislocation creep. In both mechanisms, the rate of deformation increases strongly with temperature but decreases with pressure at modest pressures. Addition of water and grain-size reduction enhance deformation. Influence of partial melting is modest for a small amount of melt. Models on the rheological structures of Earth’s mantle can be developed by including experimental results on all of these effects combined with models of temperature, water and grain-size distribution. The rheological properties in the upper mantle are controlled mostly by temperature, pressure and water content (locally by grain-size reduction). The strength of the lithosphere estimated from dry olivine rheology for homogeneous deformation is too high for plate tectonics to occur. The influence of orthopyroxene to reduce the strength is suggested. Transition from the lithosphere to the asthenosphere occurs largely by the increase in temperature but partly by the change in the water content. Rheological properties of the transition zone and the lower mantle are controlled by phase transformations. However, a transition to high-density structures does not necessarily increase the viscosity. The grain-size reduction caused by a phase transformation has a stronger effect and weakens the material substantially. The deep mantles of the Moon and Mars are inferred to have low viscosities due presumably to the high water content.
    [Show full text]