Do Reuss and Voigt bounds really bound in high-pressure rheology experiments?

Journal of Physics Condensed Matter

Volumn 18, Issue 25, 2006, Pages

  Chen, Jiuhua ^a   Li, Li ^a   Yu, Tony ^a   Long, Hongbo ^a   Weidner, Donald ^a   Wang, Liping ^a   Vaughan, Michael ^a  

^a STONY BROOK UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DEFORMATION; ELASTICITY; HIGH PRESSURE EFFECTS; RHEOLOGY; X RAY DIFFRACTION ANALYSIS;

LATTICE STRAINS; MULTI-ELEMENT SOLID STATE DETECTOR; PRESSURE RHEOLOGY;

POLYCRYSTALLINE MATERIALS;

EID: 33745115327     PISSN: 09538984     EISSN: 1361648X     Source Type: Journal    
DOI: 10.1016/j.nuclcard.2006.06.034     Document Type: Article

References (46)

1. Berveiller M and Zaoui A 1981 A simplified self-consistent scheme for the plasticity of two-phase metals Res. Mech. Lett. 1 119-24
2. Chen J H, Li L, Weidner D and Vaughan M 2004 Deformation experiments using synchrotron x-rays: in situ stress and strain measurements at high pressure and temperature Phys. Earth Planet. Inter. 143/144 347-56
3. Clausen B 1997 Characterization of polycrystal deformation by numerical modelling and neutron diffraction measurements Riso National Laboratory Risø-R-985(EN) (Materials Research Department. Roskilde, Denmark) p 85
4. Clausen B and Lorentzen T 1997 A self-consistent model for polycrystal deformation, description and implementation Riso National Laboratory Risø-R-970(EN) (Roskilde, Denmark) p 42
5. Copley S M and Pask J A 1965a Deformation of polycrystalline MgO at elevated temperatures J. Am. Ceram. Soc. 48 636-41
6. Copley S M and Pask J A 1965b Plastic deformation of MgO single crystals up to 1600 °C J. Am. Ceram. Soc. 48 139-46
7. Foitzik A, Skrotzki W and Haasen P 1989 Correlation between microstructure, dislocation dissociation and plastic anisotropy in ionic crystals Mater. Sci. Eng. A 113 399-407
8. Funamori N, Yagi T and Uchida T 1994 Deviatoric stress measurement under uniaxial compression by a powder x-ray diffraction method J. Appl. Phys. 75 4327-31
9. Gilormini P and Bréchet Y 1999 Mechanical properties of heterogeneous media: Which material for which model? Which model for which material? Modelling Simul. Mater. Sci. Eng. 7 805-16 (doi:10.1088/0965-0393/7/5/ 312)
10. 4 Phys. Chem. Minerals 16 186-98
11. Hearmon R F S 1956 The elastic constants of anisotropic materials-II Adv. Phys. 5 323-82
12. Hill R 1965 Continuum micro-mechanics of elastoplastic polycrystals J. Mech. Phys. Solids 13 89-101
13. Karato S and Wu P 1993 Rheology of the upper mantle-a synthesis Science 260 771-8
14. Kavner A 2003 Elasticity and strength of hydrous ringwoodite at high pressure Earth Planet. Sci. Lett. 214 645-54
15. Kavner A and Duffy T S 2001 Strength and elasticity of ringwoodite at upper mantle pressures Geophys. Res. Lett. 28 2691-4
16. Lebensohn R A and Tome C N 1993 A self-consistent anisotropic approach for the simulation of plastic deformation and texture development of polycrystals: Application to zirconium alloys Acta Metall. Mater. 41 2611-24
17. Li L, Weidner D, Raterron P, Chen J H and Vaughan M 2004 Stress measurements of deforming olivine at high pressure Phys. Earth Planet. Inter. 143/144 357-67
18. Mao H-k, Shu J, Shen G, Hemley R J, Li B and Singh A K 1998 Elasticity and rheology of iron above 220 GPa and the nature of the earth's inner core Nature 296 741-3
19. Meade C and Jeanloz R 1988 Yield strength of MgO to 40 GPa J. Geophys. Res. B 93 3261-9
20. Merkel S, Wenk H R, Shu J, Shen G, Gillet P, Mao H-k and Hemley R J 2002 Deformation of polycrystalline MgO at pressures of the lower mantle J. Geophys. Res. 107 2271 (doi:10.1029/2001JB000920)
21. Molinari A, Canova G R and Ahzi S 1987 A self-consistent approach of the large deformation polycrystal viscoplasticity Acta Metall. 35 2983-94
22. Nishiyama N, Wang Y B, Uchida T, Irifune T, Rivers M L and Sutton S R 2005 Pressure and strain dependence of the strength of sintered polycrystalline Mg2SiO4 ringwoodite Geophys. Res. Lett. 32 (4)
23. Paterson M S and Weaver C W 1970 Deformation of polycrystalline MgO under pressure J. Am. Ceram. Soc. 53 463-72
24. Reuss A 1929 Berechnung der fliegrenze von mischkristallen auf grund den konstanten des einkristalls Z. Angew. Math. Mech. 9 49
25. Sachs G 1928 Zur ableitung einer fliessbedingung Z. Ver. Dtsch. Ing. 72 734-6
26. Shieh S R, Duffy T S and Shen G Y 2004 Elasticity and strength of calcium silicate perovskite at lower mantle pressures Phys. Earth Planet. Inter. 143/144 93-105
27. Singh A K 1993 The lattice strain in a specimen (cubic system) compressed nonhydrostatically in an opposed anvil device J. Appl. Phys. 73 4278-86
28. Singh A K, Balasingh C, Mao H K, Hemley R J and Shu J 1998 Analysis of lattice strains measured under nonhydrostatic pressure J. Appl. Phys. 83 7567-75
29. Sinogeikin S V and Bass J D 1999 Single-crystal elasticity of MgO at high pressure Phys. Rev. B 59 R14141-4
30. Sinogeikin S V, Bass J D and Katsura T 2003 Single-crystal elasticity of ringwoodite to high pressures and high temperatures: implications for 520 km seismic discontinuity Phys. Earth Planet. Inter. 136 41-66
31. Skrotzki W and Welch P 1983 Development of texture and microstructure in extruded ionic polycrystalline aggregates Tectonophysics 99 47-61
32. Spetzler H 1970 Equation of state of polycrystalline and single-crystal MgO to 8 kilobars and 800K J. Geophys. Res. 75 2073-87
33. 0.2)O Earth Planet. Sci. Lett. 194 229-40
34. Taylor G I 1938 Plastic strain in metals J. Inst. Met. 62 307-15
35. Tingle T N, Green H W II, Young T E and Koczynski T A 1993 Improvements to Griggs-type apparatus for mechanical testing at high pressures and temperatures Pure Appl. Geophys. 141 523-43
36. Turnock A C, Lindsley D H and Grover J E 1973 Synthesis and unit cell parameters of Ca-Mg-Fe pyroxenes Am. Mineral. 58 50-9
37. Uchida T, Funamori N and Yagi T 1996 Lattice strains in crystals under uniaxial stress field J. Appl. Phys. 80 739-46
38. Vaughan M T, Weidner D J, Wang Y B, Chen J H, Koleda C C and Getting I C 1998 T-cup: A new high-pressure apparatus for x-ray studies Rev. High Pressure Sci. Technol. 7 1520-2
39. Voigt W 1928 Lehrbuch der Kristallphysik (Berlin: Teubner)
40. Wang Y B, Durham W B, Getting I C and Weidner D J 2003 The deformation-DIA: a new apparatus for high temperature triaxial deformation to pressures up to 15 GPa Rev. Sci. Instrum. 74 3002-11
41. Weaver C W and Paterson M S 1969 Deformation of cube-oriented MgO crystals under pressure J. Am. Ceram. Soc. 52 293-302
42. Weidner D J, Li L, Davis M and Chen J H 2004 Effect of plasticity on elastic modulus measurements Geophys. Res. Lett. 31 L06621 (doi:10.1029/ 2003GL019090)
43. Weidner D J, Wang Y, Chen G, Ando J and Vaughan M T 1998 Rheology measurements at high pressure and temperature Properties of Earth and Planetary Materials at High Pressure and Temperature (Geophysical Monograph) vol 101 pp473-82
44. Wenk H-R 1999 A voyage through the deformed Earth with the self-consistent model Modelling Simul. Mater. Sci. Eng. 7 699-722
45. Wenk R 2002 Texture and anisotropy Plastic Deformation of Minerals and Rocks vol 51 ed S Karato and R Wenk (Washington, DC: Mineralogical Society of America) pp291-329
46. Yamazaki D and Karato S-i 2002 Fabric development in (Mg, Fe)O during large strain, shear deformation; implications for seismic anisotropy in earth's lower mantle Phys. Earth Planet. Inter. 131 251-67