组构数值模拟的原理及其在地学中的应用
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摘要
组构是指由岩石塑性变形导致多晶体的结晶学优势取向现象。组构的存在会增加岩石的各向异性,进而可能影响到岩石的后续变形。岩石组构包含了变形类型、运动学、变形环境、流变学特征等信息,因而成为显微构造学的重要内容。组构数值模拟是近年来得到重视的一种组构研究方法,它以晶体塑性理论为基础,利用计算机技术定量地模拟多晶岩石中组构的形成和演化。在晶体塑性理论中,晶体的塑性变形是由滑移系的剪切滑动导致的,由单晶塑性本构关系表征。多晶均匀化模型包括Sachs模型、Taylor模型、自洽模型和有限元模型,它们从不同角度描述了由单晶变形组成的多晶体变形。极图、反极图和取向分布函数被用来显示多晶体中各晶粒的空间取向。目前组构数值模拟在地学中的应用主要体现在各种单相和多相岩石的组构形成、重结晶作用下的组构形成、组构对地幔和地核地震波波速各向异性的影响等方面。
Texture is referred to as the crystallographic lattice preferred orientation (CPO) produced in polycrystalline rock by plastic deformation. The presence of texture would enhance the anisotropy of rock, and most likely influence subsequent deformation, if it happens. A single goal of microstructural analysis is to determine from the texture observed in rock deformation type, kinematics, environment, rheology, and so on. Based on the crystal plasticity theory, numerical modeling is efficient and powerful in calculating the formation and evolution of texture in polycrystalline rocks. Plastic deformation is therein accomplished by an infinite number of slips occurring in the slip systems of each individual crystal. The averaging scheme, such as the Sachs model, the Taylor model, the self-consistent model, and the finite element model, accounts for the response of crystal aggregate to the plastic deformation of each crystal in it. CPO is expressed either graphically in pole figure or inverse pole figure, or quantitatively using the orientation distribution functions. Numerical modeling of textures has been applied to geosciences for decades, for example, in the development of monophase and polyphase rock textures and of textures formed due to dynamic recrystallization, and in the influence of textures in the seismic anisotropy of the upper mantle and the inner core.
Texture is referred to as the crystallographic lattice preferred orientation (CPO) produced in polycrystalline rock by plastic deformation. The presence of texture would enhance the anisotropy of rock, and most likely influence subsequent deformation, if it happens. A single goal of microstructural analysis is to determine from the texture observed in rock deformation type, kinematics, environment, rheology, and so on. Based on the crystal plasticity theory, numerical modeling is efficient and powerful in calculating the formation and evolution of texture in polycrystalline rocks. Plastic deformation is therein accomplished by an infinite number of slips occurring in the slip systems of each individual crystal. The averaging scheme, such as the Sachs model, the Taylor model, the self-consistent model, and the finite element model, accounts for the response of crystal aggregate to the plastic deformation of each crystal in it. CPO is expressed either graphically in pole figure or inverse pole figure, or quantitatively using the orientation distribution functions. Numerical modeling of textures has been applied to geosciences for decades, for example, in the development of monophase and polyphase rock textures and of textures formed due to dynamic recrystallization, and in the influence of textures in the seismic anisotropy of the upper mantle and the inner core.
引文
陈运平,赵崇斌,林舸.2008.深部岩石力学性质及其在大陆构造变形过程研究中的作用.大地构造与成矿学,32(3):276-284.
嵇少丞,钟大赉,许志琴,夏斌.2008.流变学:构造地质学和地球动力学的支柱学科.大地构造与成矿学,32(3):257-264.
梁志德,徐家祯,王福.1986.组构材料的三维取向分析术.沈阳:东北工学院出版社:1-45.
毛卫民,张新明.1995.晶体材料组构定量分析.北京:冶金工业出版社:1-25.
孙圣思,嵇少丞.2011.大洋板块俯冲带地震波各向异性及剪切波分裂的成因机制.大地构造与成矿学,35(4):628-647.
王自强,段祝平.1995.塑性细观力学.北京:科学出版社:90-150.
夏浩然,刘俊来.2011.石英结晶学优选与应用.地质通报,30(1):58-70.
杨平.2007.电子背散射衍射技术及其应用.北京:冶金工业出版社:36-60.
庄茁.2002.连续体和结构的非线性有限元.北京:清华大学出版社:70-82.
Asaro R J and Needleman A.1985.Texture development andstrain hardening in rate dependent polycrystals.Acta Met-all,33(6):923-953.
Beaudoia A J,Dawson P R,Mathur K K and Kock U F.1995.A hybrid finite element formulation for polycrystal plasticitywith consideration of macrostructural and microstructurallinking.International Journal of Plasticity,11(5):501-521.
Bishop J F W and Hill R.1951.A theory of the plastic distor-tion of a polycrystalline aggregate under combined stresses.Philosophical Magazine,42(19):414-427.
Bons P D and Brok B D.2000.Crystallographic preferred orien-tation development by dissolution-precipitation creep.Jour-nal of Structural Geology,22(11):1713-1722.
Bunge H J.1965.Zur darstellung allgemeiner texturen.Zeitschrift für Metallkunde,56(6):872–874.
Canoval G R,Wenk H R and Molinari A.1992.Deformationmodelling of multi-phase polycrystals:Case of a quartz-mi-ca aggregate.Acta Metallurgica et Materialia,40(7):1519-1530.
Castelnau O,Blackman D K,Lebensohn R A and Castaneda PP.2008.Micromechanical modeling of the viscoplastic be-havior of olivine.Journal of Geophysical Research,113(B9):35-46.
Castelnau O,Canova G R.,Lebensohn R A and Duval P.1996a.Modelling viscoplastic behavior of anisotropic poly-crystalline ice with a self-consistent approach.Acta Materi-alia,44(11):4823-4834.
Castelnau O,Duval P,Lebensohn R A and Canova G R.1996b.Viscoplastic modelling of texture development inpolycrystalline ice with a self-consistent approach:Compar-ison with bound estimates.Journal of Geophysical Re-search,101(B6):851-868.
Chastel Y B,Dawson P R,Wenk H R and Bennett K.1993.Anisotropic convection with implications for the upper man-tle.Journal of Geophysical Research,98(B10):757-771.
Dawson P R.2002.Modeling deformation of polycrystallinerocks.Reviews in Mineralogy and Geochemistry,51(1):331-351.
Dawson P R and Wenk H R.2000.Texturing of the upper man-tle during convection.Philosophical Magazine A,80(3):573-598.
Havner K S.1992.Finite plastic deformation of crystalline sol-ids.New York:Cambridge University Press:34-38.
Hess H H.1964.Seismic anisotropy of the uppermost mantleunder oceans.Nature,203:629-631.
Kaminskiéand Ribe N M.2001.A kinematic model for recrys-tallization and texture development in olivine polycrystals.Earth and Planetary Science Letters,189(3):253-267.
Kern H and Wenk H R.1983.Calcite texture development inexperimentally induced ductile shear zones.Contributionsto Mineralogy and Petrology,83(3):231-236.
Khan M A.1962.Anisotropy of magnetic susceptibility of someigneous and metamorphic rocks.Journal of Geophysical Re-search,67(7):2873-2885.
Kocks U F,Tome C N and Wenk H R.1998.Texture and Ani-sotropy:Preferred Orientations in Polycrystals and theirEffect on Materials Properties.New York:Cambridge Uni-versity Press:1-35.
Lebensohn R A,Dawson P R,Kernc H M and Wenk H R.2003.Heterogeneous deformation and texture developmentin halite polycrystals:Comparison of different modeling ap-proachesand experimental data.Tectonophysics,370(1):287-311.
Lebensohn R A,Montagnat M,Mansuy P,Duval P,Meysonni-er J and Philip A.2009.Modeling viscoplastic behaviorand heterogeneous intracrystalline deformation of columnarice polycrystals.Acta Materialia,57(5):1405-1415.
Lebensohn R A and Toms C N.1994.A self-consistent visco-plastic model:prediction of rolling textures of anisotropicpolycrystals.Materials Science and Engineering,175(1):71-82.
Lebensohn R A,Wenk H R and Toms C N.1998.Modellingdeformation and recrystallization textures in calcite.ActaMaterialia,46(8):2683-2693.
Leiss B,Ullemeyer K and Weber K.2000.Introduction to thespecial issue:Textures and physical properties of rock.Journal of Structural Geology,22(11):1527-1529.
Lister G S and Hobs B E.1980.The simulation of fabric devel-opment during plastic deformation and its application to qu-artzite:The influence of deformation history.Journal ofStructural Geology,2(3):355-370.
Lister G S and Paterson M S.1979.The simulation of fabric de-velopment during plastic deformation and its application toquartzite:Fabric transitions.Journal of Structural Geology,1(2):99-115.
Lister G S,Paterson M S and Hobs B E.1978.The simulationof fabric development during plastic deformation and its ap-plication to quartzite:The model.Tectonophysics,45(2):107-158.
Mendelson K S and Cohen M H.1982.The effect of grain ani-sotropy on the electrical properties of sedimentary rocks.Geophysics,47(2):257-269.
Mika D P and Dawson P R.1999.Polycrystal plasticity modeling of intracrystalline boundary textures.Acta Materiali,47(4):1355-1369.
Molinari A,Ahzi S and Kouddane R.1997.On the self-consist-ent modeling of elastic-plastic behavior of polycrystals.Me-chanics of Materials,26(1):43-62.
Molinari A,Canova G R and Ahzi S.1987.A self consistentapproach of the large deformation polycrystal viscoplastici-ty.Acta Metallurgica,35(12):2983-2994.
Nemat-Nasser S,Ni L and Okinaka T.1998.A constitutivemodel for fcc crystals with application to polycrystalline OF-HC copper.Mechanics of Materials,30(4):325-341.
Nemat-Nasser S and Okinaka T.1996.A new computational ap-proach to crystal plasticity:Fcc single crystal.Mechanics of Materials,24(1):43-57.
Owens W H and Bamford D.1976.Magnetic seismic and otheranisotropic properties of rock fabrics.Philosophical Trans-actions of the Royal Society,283(1312):55-68.
Roe R.1965.Description of crystalline orientation of polycrys-talline materials.General solution to pole figure inversion.Journal of Applied Physics,36(15):2024–2031.
Romanowicz B,Li X D and Durek J C.1996.Anisotropy in theinner core:Could it be due to low-order convection.Sci-ence,274(5289):963-966.
Sachs G.1928.Zur ableitung einer fliessbedingung.Zeich-schrift der Verein deutscher Ingenieur,72(734):152-168.
Sarma G B and Dawson P R.1996.Texture predictions using apolycrystal plasticity model incorporating neighbor interac-tions.International Journal of Plasticity,12(8):1023-1054.
Schmid E.1924.Yield point of crystals,critical shear stresslaw//Proceedings of the First International Congress forApplied Mechanics,Delft.
Signorelli J,Loge R,Bolmaro R and Tommasi A.2010.Model-ling deformation and recrystallization shear textures in oli-vine.Mecánica Computacional,6:2883-2899.
Song X.1996.Anisotropy in central part of inner core.Journalof Geophysical Research,101(D7):89-97.
Taylor G I.1938.Plastic strain in metals.Journal of the Insti-tute of Metals,62(307):307–324.
Tommasi A.1998.Forward modeling of the development ofseismic anisotropy in the upper mantle.Earth and Planeta-ry Science Letters,160(1):1-13.
Tommasi A,Mainprice D,Canova G and Chastel Y.2000.Vis-coplastic self-consistent and equilibrium-based modeling ofolivine lattice preferred orientations:Implications for theupper mantle seismic anisotropy.Journal of GeophysicalResearch,105(B4):7893-7908.
Tommasi A,Tikoff B and Vauchez A.1999.Upper mantle tec-tonics:Three-dimensional deformation,olivine crystallo-graphic fabrics and seismic properties.Earth and PlanetaryScience Letters,168(1):173-186.
Tromp J.2001.Inner Core Anisotropy and Rotation.Geophysi-cal monograph,29:47-69.
Wenk H R.1986.Plastic anisotropy and texture development incalcite polycrystals.Journal of Geophysical Research,91(B3):3861-3869.
Wenk H R.1989.Viscoplastic modeling of texture developmentin quartzite.Journal of Geophysical Research,94(B12):895-906.
Wenk H R.1999.A voyage through the deformed Earth withthe self-consistent model.Modelling and Simulation in Ma-terials Science and Engineering,7:699-722.
Wenk H R,Armann M,Burlini L,Kunze K and Bortolotti M.2009.Large strain shearing of halite:Experimental andtheoretical evidence for dynamic texture changes.Earthand Planetary Science Letters,280(4):205-210.
Wenk H R,Baumgardner J R and Lebensohn R.2000b.A con-vection model to explain anisotropy of the inner core.Jour-nal of Geophysical Research,105(B3):5663-5677.
Wenk H R,Bennett K,Molinari A and Mecking H.1991.Modelling plastic deformation of peridotite with the self-con-sistent theory.Journal of Geophysical Research,96(B5):8337-8349.
Wenk H R,Canova G,Brechet Y and Flandin L.1997.A de-formation-based model for recrystallization of anisotropicmaterials.Acta Materialia,45(8):3283-3296.
Wenk H R,Canova G,Molinari A and Mecking H.1989.Tex-ture development in halite:Comparison of Taylor model andself-consistent theory.Acta Metallurgica,37(7):2017-2029.
Wenk H R and Christie J M.1991.Comments on the interpreta-tion of deformation textures in rocks.Journal of StructuralGeology,13(10):1091-1110.
Wenk H R and Van Houtte P.2004.Texture and Anisotropy.Reports on Progress in Physics,67:1367-1428.
Wenk H R,Matthies S R,Hemley J,Mao H K and Shu J.2000a.The plastic deformation of iron at pressures of theEarth's inner core.Nature,405:1044-1047.
Wenk H R,Takeshita T,Bechler E,Erskine B G and MatthiesS.1987.Pure shear and simple shear calcite textures:Comparison of experimental,theoretical and natural data.Journal of Structural Geology,9(5):731-745.
Zhang S Q and Karato S I.1995.Lattice preferred orientation ofolivine aggregates deformed in simple shear.Nature,375:774-777.
Zhang Y,Hobbs B E and Ord A.1994.A numerical simulationof fabric development in polycrystalline aggregates with oneslip system.Journal of Structural Geology,16(9):1297-1313.
Zhang Y and Wilson C J L.1997.Lattice rotation in polycrys-talline aggregates and single crystals with one slip system:A numerical and experimental approach.Journal of Struc-tural Geology,19(6):875-885.
嵇少丞,钟大赉,许志琴,夏斌.2008.流变学:构造地质学和地球动力学的支柱学科.大地构造与成矿学,32(3):257-264.
梁志德,徐家祯,王福.1986.组构材料的三维取向分析术.沈阳:东北工学院出版社:1-45.
毛卫民,张新明.1995.晶体材料组构定量分析.北京:冶金工业出版社:1-25.
孙圣思,嵇少丞.2011.大洋板块俯冲带地震波各向异性及剪切波分裂的成因机制.大地构造与成矿学,35(4):628-647.
王自强,段祝平.1995.塑性细观力学.北京:科学出版社:90-150.
夏浩然,刘俊来.2011.石英结晶学优选与应用.地质通报,30(1):58-70.
杨平.2007.电子背散射衍射技术及其应用.北京:冶金工业出版社:36-60.
庄茁.2002.连续体和结构的非线性有限元.北京:清华大学出版社:70-82.
Asaro R J and Needleman A.1985.Texture development andstrain hardening in rate dependent polycrystals.Acta Met-all,33(6):923-953.
Beaudoia A J,Dawson P R,Mathur K K and Kock U F.1995.A hybrid finite element formulation for polycrystal plasticitywith consideration of macrostructural and microstructurallinking.International Journal of Plasticity,11(5):501-521.
Bishop J F W and Hill R.1951.A theory of the plastic distor-tion of a polycrystalline aggregate under combined stresses.Philosophical Magazine,42(19):414-427.
Bons P D and Brok B D.2000.Crystallographic preferred orien-tation development by dissolution-precipitation creep.Jour-nal of Structural Geology,22(11):1713-1722.
Bunge H J.1965.Zur darstellung allgemeiner texturen.Zeitschrift für Metallkunde,56(6):872–874.
Canoval G R,Wenk H R and Molinari A.1992.Deformationmodelling of multi-phase polycrystals:Case of a quartz-mi-ca aggregate.Acta Metallurgica et Materialia,40(7):1519-1530.
Castelnau O,Blackman D K,Lebensohn R A and Castaneda PP.2008.Micromechanical modeling of the viscoplastic be-havior of olivine.Journal of Geophysical Research,113(B9):35-46.
Castelnau O,Canova G R.,Lebensohn R A and Duval P.1996a.Modelling viscoplastic behavior of anisotropic poly-crystalline ice with a self-consistent approach.Acta Materi-alia,44(11):4823-4834.
Castelnau O,Duval P,Lebensohn R A and Canova G R.1996b.Viscoplastic modelling of texture development inpolycrystalline ice with a self-consistent approach:Compar-ison with bound estimates.Journal of Geophysical Re-search,101(B6):851-868.
Chastel Y B,Dawson P R,Wenk H R and Bennett K.1993.Anisotropic convection with implications for the upper man-tle.Journal of Geophysical Research,98(B10):757-771.
Dawson P R.2002.Modeling deformation of polycrystallinerocks.Reviews in Mineralogy and Geochemistry,51(1):331-351.
Dawson P R and Wenk H R.2000.Texturing of the upper man-tle during convection.Philosophical Magazine A,80(3):573-598.
Havner K S.1992.Finite plastic deformation of crystalline sol-ids.New York:Cambridge University Press:34-38.
Hess H H.1964.Seismic anisotropy of the uppermost mantleunder oceans.Nature,203:629-631.
Kaminskiéand Ribe N M.2001.A kinematic model for recrys-tallization and texture development in olivine polycrystals.Earth and Planetary Science Letters,189(3):253-267.
Kern H and Wenk H R.1983.Calcite texture development inexperimentally induced ductile shear zones.Contributionsto Mineralogy and Petrology,83(3):231-236.
Khan M A.1962.Anisotropy of magnetic susceptibility of someigneous and metamorphic rocks.Journal of Geophysical Re-search,67(7):2873-2885.
Kocks U F,Tome C N and Wenk H R.1998.Texture and Ani-sotropy:Preferred Orientations in Polycrystals and theirEffect on Materials Properties.New York:Cambridge Uni-versity Press:1-35.
Lebensohn R A,Dawson P R,Kernc H M and Wenk H R.2003.Heterogeneous deformation and texture developmentin halite polycrystals:Comparison of different modeling ap-proachesand experimental data.Tectonophysics,370(1):287-311.
Lebensohn R A,Montagnat M,Mansuy P,Duval P,Meysonni-er J and Philip A.2009.Modeling viscoplastic behaviorand heterogeneous intracrystalline deformation of columnarice polycrystals.Acta Materialia,57(5):1405-1415.
Lebensohn R A and Toms C N.1994.A self-consistent visco-plastic model:prediction of rolling textures of anisotropicpolycrystals.Materials Science and Engineering,175(1):71-82.
Lebensohn R A,Wenk H R and Toms C N.1998.Modellingdeformation and recrystallization textures in calcite.ActaMaterialia,46(8):2683-2693.
Leiss B,Ullemeyer K and Weber K.2000.Introduction to thespecial issue:Textures and physical properties of rock.Journal of Structural Geology,22(11):1527-1529.
Lister G S and Hobs B E.1980.The simulation of fabric devel-opment during plastic deformation and its application to qu-artzite:The influence of deformation history.Journal ofStructural Geology,2(3):355-370.
Lister G S and Paterson M S.1979.The simulation of fabric de-velopment during plastic deformation and its application toquartzite:Fabric transitions.Journal of Structural Geology,1(2):99-115.
Lister G S,Paterson M S and Hobs B E.1978.The simulationof fabric development during plastic deformation and its ap-plication to quartzite:The model.Tectonophysics,45(2):107-158.
Mendelson K S and Cohen M H.1982.The effect of grain ani-sotropy on the electrical properties of sedimentary rocks.Geophysics,47(2):257-269.
Mika D P and Dawson P R.1999.Polycrystal plasticity modeling of intracrystalline boundary textures.Acta Materiali,47(4):1355-1369.
Molinari A,Ahzi S and Kouddane R.1997.On the self-consist-ent modeling of elastic-plastic behavior of polycrystals.Me-chanics of Materials,26(1):43-62.
Molinari A,Canova G R and Ahzi S.1987.A self consistentapproach of the large deformation polycrystal viscoplastici-ty.Acta Metallurgica,35(12):2983-2994.
Nemat-Nasser S,Ni L and Okinaka T.1998.A constitutivemodel for fcc crystals with application to polycrystalline OF-HC copper.Mechanics of Materials,30(4):325-341.
Nemat-Nasser S and Okinaka T.1996.A new computational ap-proach to crystal plasticity:Fcc single crystal.Mechanics of Materials,24(1):43-57.
Owens W H and Bamford D.1976.Magnetic seismic and otheranisotropic properties of rock fabrics.Philosophical Trans-actions of the Royal Society,283(1312):55-68.
Roe R.1965.Description of crystalline orientation of polycrys-talline materials.General solution to pole figure inversion.Journal of Applied Physics,36(15):2024–2031.
Romanowicz B,Li X D and Durek J C.1996.Anisotropy in theinner core:Could it be due to low-order convection.Sci-ence,274(5289):963-966.
Sachs G.1928.Zur ableitung einer fliessbedingung.Zeich-schrift der Verein deutscher Ingenieur,72(734):152-168.
Sarma G B and Dawson P R.1996.Texture predictions using apolycrystal plasticity model incorporating neighbor interac-tions.International Journal of Plasticity,12(8):1023-1054.
Schmid E.1924.Yield point of crystals,critical shear stresslaw//Proceedings of the First International Congress forApplied Mechanics,Delft.
Signorelli J,Loge R,Bolmaro R and Tommasi A.2010.Model-ling deformation and recrystallization shear textures in oli-vine.Mecánica Computacional,6:2883-2899.
Song X.1996.Anisotropy in central part of inner core.Journalof Geophysical Research,101(D7):89-97.
Taylor G I.1938.Plastic strain in metals.Journal of the Insti-tute of Metals,62(307):307–324.
Tommasi A.1998.Forward modeling of the development ofseismic anisotropy in the upper mantle.Earth and Planeta-ry Science Letters,160(1):1-13.
Tommasi A,Mainprice D,Canova G and Chastel Y.2000.Vis-coplastic self-consistent and equilibrium-based modeling ofolivine lattice preferred orientations:Implications for theupper mantle seismic anisotropy.Journal of GeophysicalResearch,105(B4):7893-7908.
Tommasi A,Tikoff B and Vauchez A.1999.Upper mantle tec-tonics:Three-dimensional deformation,olivine crystallo-graphic fabrics and seismic properties.Earth and PlanetaryScience Letters,168(1):173-186.
Tromp J.2001.Inner Core Anisotropy and Rotation.Geophysi-cal monograph,29:47-69.
Wenk H R.1986.Plastic anisotropy and texture development incalcite polycrystals.Journal of Geophysical Research,91(B3):3861-3869.
Wenk H R.1989.Viscoplastic modeling of texture developmentin quartzite.Journal of Geophysical Research,94(B12):895-906.
Wenk H R.1999.A voyage through the deformed Earth withthe self-consistent model.Modelling and Simulation in Ma-terials Science and Engineering,7:699-722.
Wenk H R,Armann M,Burlini L,Kunze K and Bortolotti M.2009.Large strain shearing of halite:Experimental andtheoretical evidence for dynamic texture changes.Earthand Planetary Science Letters,280(4):205-210.
Wenk H R,Baumgardner J R and Lebensohn R.2000b.A con-vection model to explain anisotropy of the inner core.Jour-nal of Geophysical Research,105(B3):5663-5677.
Wenk H R,Bennett K,Molinari A and Mecking H.1991.Modelling plastic deformation of peridotite with the self-con-sistent theory.Journal of Geophysical Research,96(B5):8337-8349.
Wenk H R,Canova G,Brechet Y and Flandin L.1997.A de-formation-based model for recrystallization of anisotropicmaterials.Acta Materialia,45(8):3283-3296.
Wenk H R,Canova G,Molinari A and Mecking H.1989.Tex-ture development in halite:Comparison of Taylor model andself-consistent theory.Acta Metallurgica,37(7):2017-2029.
Wenk H R and Christie J M.1991.Comments on the interpreta-tion of deformation textures in rocks.Journal of StructuralGeology,13(10):1091-1110.
Wenk H R and Van Houtte P.2004.Texture and Anisotropy.Reports on Progress in Physics,67:1367-1428.
Wenk H R,Matthies S R,Hemley J,Mao H K and Shu J.2000a.The plastic deformation of iron at pressures of theEarth's inner core.Nature,405:1044-1047.
Wenk H R,Takeshita T,Bechler E,Erskine B G and MatthiesS.1987.Pure shear and simple shear calcite textures:Comparison of experimental,theoretical and natural data.Journal of Structural Geology,9(5):731-745.
Zhang S Q and Karato S I.1995.Lattice preferred orientation ofolivine aggregates deformed in simple shear.Nature,375:774-777.
Zhang Y,Hobbs B E and Ord A.1994.A numerical simulationof fabric development in polycrystalline aggregates with oneslip system.Journal of Structural Geology,16(9):1297-1313.
Zhang Y and Wilson C J L.1997.Lattice rotation in polycrys-talline aggregates and single crystals with one slip system:A numerical and experimental approach.Journal of Struc-tural Geology,19(6):875-885.
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