Phase Field Theory and Analysis of Pressure-Shear Induced Amorphization and Failure in Boron Carbide Ceramic

D. Clayton John; D. Clayton John

doi:10.3934/matersci.2014.3.143

AIMS Materials Science

2014, Volume 1, Issue 3: 143-158. doi: 10.3934/matersci.2014.3.143

Previous Article Next Article

Research article

Phase Field Theory and Analysis of Pressure-Shear Induced Amorphization and Failure in Boron Carbide Ceramic

D. Clayton John ^,

Impact Physics Branch, US Army Research Laboratory, Aberdeen MD 21005-5066, USA

Received: 10 April 2014 Accepted: 11 June 2014 Published: 08 July 2014

A nonlinear continuum phase field theory is developed to describe amorphization of crystalline elastic solids under shear and/or pressure loading. An order parameter describes the local degree of crystallinity. Elastic coefficients can depend on the order parameter, inelastic volume change may accompany the transition from crystal to amorphous phase, and transitional regions parallel to bands of amorphous material are penalized by interfacial surface energy. Analytical and simple numerical solutions are obtained for an idealized isotropic version of the general theory, for an element of material subjected to compressive and/or shear loading. Solutions compare favorably with experimental evidence and atomic simulations of amorphization in boron carbide, demonstrating the tendency for structural collapse and strength loss with increasing shear deformation and superposed pressure.
- ceramics,
- phase transformations,
- amorphization,
- boron carbide,
- phase field,
- elasticity
Citation: D. Clayton John. Phase Field Theory and Analysis of Pressure-Shear Induced Amorphization and Failure in Boron Carbide Ceramic[J]. AIMS Materials Science, 2014, 1(3): 143-158. doi: 10.3934/matersci.2014.3.143

Related Papers:

Abstract

A nonlinear continuum phase field theory is developed to describe amorphization of crystalline elastic solids under shear and/or pressure loading. An order parameter describes the local degree of crystallinity. Elastic coefficients can depend on the order parameter, inelastic volume change may accompany the transition from crystal to amorphous phase, and transitional regions parallel to bands of amorphous material are penalized by interfacial surface energy. Analytical and simple numerical solutions are obtained for an idealized isotropic version of the general theory, for an element of material subjected to compressive and/or shear loading. Solutions compare favorably with experimental evidence and atomic simulations of amorphization in boron carbide, demonstrating the tendency for structural collapse and strength loss with increasing shear deformation and superposed pressure.

References

[1]	Gregoryanz E, Hemley R, Mao H, et al. (2000) High pressure elasticity of α-quartz: instability and ferroelastic transition.Phys Rev Lett 84: 3117-3120.
[2]	Watson G, Parker S (1995) Dynamical instabilities in α-quartz and α-berlinite: a mechanism for amorphization.Phys Rev B 52: 13306-13309.
[3]	Goel P, Mittal R, Choudhury N, et al. (2010) Lattice dynamics and Born instability in yttrium aluminum garnet, Y3Al5O12..J Phys: Condens Mat 22: 065401.
[4]	Yan X, Tang Z, Zhang L, et al. (2009) Depressurization amorphization of single-crystal boron carbide.Phys Rev Lett 102: 075505.
[5]	Born M (1940) On the stability of crystal lattices I.Math Proc Cambridge 36: 160-172.
[6]	Hill R (1975) On the elasticity and stability of perfect crystals at finite strain.Math Proc Cambridge 77: 225-240.
[7]	Morris J, Krenn C (2000) The internal stability of an elastic solid.Phil Mag A 80: 2827-2840.
[8]	Clayton J, Bliss K (2014) Analysis of intrinsic stability criteria for isotropic third-order Green elastic and compressible neo-Hookean solids.Mech Mater 68: 104-119.
[9]	Fanchini G, McCauley J, Chhowalla M (2006) Behavior of disordered boron carbide under stress.Phys Rev Lett 97: 035502.
[10]	Taylor D, Wright T, McCauley J (2011) First principles calculation of stress induced amorphization in armor ceramics. US Army Research Lab Res Rep ARL-MR-0779.Aberdeen Proving Ground, MD .
[11]	Taylor D, McCauley J, Wright T (2012) The effects of stoichiometry on the mechanical properties of icosahedral boron carbide under loading.J Phys: Condens Mat 24: 505402.
[12]	Aryal S, Rulis P, Ching W (2011) Mechanism for amorphization of boron carbide B4C under uniaxial compression.Phys Rev B 84: 184112.
[13]	Subhash G, Maiti S, Geubelle P, Ghosh D (2008) Recent advances in dynamic indentation fracture, impact damage and fragmentation of ceramics.J Am Ceram Soc 91: 2777-2791.
[14]	Chen M, McCauley J, Hemker K (2003) Shock-induced localized amorphization in boron carbide.Science 299: 1563-1566.
[15]	Grady D (2011) Adiabatic shear failure in brittle solids.Int J Impact Eng 38: 661-667.
[16]	Clayton J (2012) Towards a nonlinear elastic representation of finite compression and instability of boron carbide ceramic.Phil Mag 92: 2860-2893.
[17]	Clayton J (2013) Mesoscale modeling of dynamic compression of boron carbide polycrystals.Mech Res Commun 49: 57-64.
[18]	Koslowski M, Cuitino A, Ortiz M (2002) A phase-field theory of dislocation dynamics, strain hardening, and hysteresis in ductile single crystals.J Mech Phys Solids 50: 2597-2635.
[19]	Clayton J, Knap J (2011) A phase field model of deformation twinning: nonlinear theory and numerical simulations.Physica D 240: 841-858.
[20]	Clayton J, Knap J (2011) Phase field modeling of twinning in indentation of transparent single crystals.Model Simul Mater Sci Eng 19: 085005.
[21]	Clayton J, Knap J (2013) Phase-field analysis of fracture induced twinning in single crystals.Acta Mater 61: 5341-5353.
[22]	Kuhn C, Müller R (2012) Interpretation of parameters in phase field models for fracture.Proc Appl Math Mec 12: 161-162.
[23]	Borden M, Verhoosel C, Scott M, et al. (2012) A phase-field description of dynamic brittle fracture.Comput Method Appl Mech Eng 271: 77-95.
[24]	Voyiadjis G, Mozaffari N (2013) Nonlocal damage model using the phase field method: theory and applications.Int J Solids Structures 50: 3136-3151.
[25]	Clayton J, Knap J (2014) A geometrically nonlinear phase field theory of brittle fracture.Int J Fracture, submitted .
[26]	Clayton J (2005) Dynamic plasticity and fracture in high density polycrystals: constitutive modeling and numerical simulation.J Mech Phys Solids 53: 261-301.
[27]	Clayton J (2009) A continuum description of nonlinear elasticity, slip and twinning, with application to sapphire.Proc R Soc Lond A 465: 307-334.
[28]	Clayton J (2010) Modeling nonlinear electromechanical behavior of shocked silicon carbide.J Appl Phys 107: 013520.
[29]	Clayton J (2010) Analysis of shock compression of strong single crystals with logarithmic thermoelastic-plastic theory.Int J Eng Sci 79: 1-20.
[30]	Benallal A, Marigo J (2007) Bifurcation and stability issues in gradient theories with softening.Model Simul Mater Sci Eng 15: S283-S295.
[31]	Clayton J (2011) Nonlinear Mechanics of Crystals, Dordrecht.Springer .
[32]	Ashbee K (1971) Defects in boron carbide before and after irradiation.Acta Metall 19: 1079-1085.
[33]	Sano T, Randow C (2011) The effect of twins on the mechanical behavior of boron carbide.Metall Mater Trans A 42: 570-574.
[34]	Clayton J (2010) On anholonomic deformation, geometry, and differentiation.Math Mech Solids 17: 702-735.
[35]	Clayton J (2010) Deformation, fracture, and fragmentation in brittle geologic solids.Int J Fracture 163: 151-172.
[36]	Clayton J, McDowell D, Bammann D (2006) Modeling dislocations and disclinations with finite micropolar elastoplasticity.Int J Plasticity 22: 210-256.
[37]	Clayton J (2013) Defects in nonlinear elastic crystals: differential geometry, finite kinematics, and second-order analytical solutions.Z Angew Math Mech (ZAMM) in press .
[38]	Clayton J (2014) An alternative three-term decomposition for single crystal deformation motivated by non-linear elastic dislocation solutions.Q J Mech Appl Math 67: 127-158.
[39]	Clayton J, Bammann D, McDowell D (2005) A geometric framework for the kinematics of crystals with defects.Phil Mag 85: 3983-4010.
[40]	Clayton J (2009) A non-linear model for elastic dielectric crystals with mobile vacancies.Int J Non-Linear Mech 44: 675-688.
[41]	Clayton J (2008) A model for deformation and fragmentation in crushable brittle solids.Int J Impact Eng 35: 269-289.
[42]	Ivaneshchenko V, Shevchenko V, Turchi P (2009) First principles study of the atomic and electronic structures of crystalline and amorphous B4C.Phys Rev B 80: 235208.
[43]	Clayton J (2013) Nonlinear Eulerian thermoelasticity for anisotropic crystals.J Mech Phys Solids 61: 1983-2014.
[44]	Clayton J, McDowell D (2003) A multiscale multiplicative decomposition for elastoplasticity of polycrystals.Int J Plasticity 19: 1401-1444.
[45]	Hu S, Henager C, Chen LQ (2010) Simulations of stress-induced twinning and de-twinning: a phase field model.Acta Mater 58: 6554-6564.
[46]	Ghosh D, Subhash G, Lee C, et al. (2007) Strain-induced formation of carbon and boron clusters in boron carbide during dynamic indentation.Appl Phys Lett 91: 061910.

Reader Comments

Your name:*

Email:*
© 2014 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)