Physics of Shock and Impact: Materials and shock response

521 Pages·2018·124.527 MB·English

by  Dennis Grady

Physics of Shock and Impact,
Volume 2
Materials and shock response

Physics of Shock and Impact,
Volume 2
Materials and shock response
Dennis Grady
Applied Research Associates, Albuquerque, New Mexico
IOP Publishing, Bristol, UK
ªIOPPublishingLtd2017
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ISBN 978-0-7503-1257-8(ebook)
ISBN 978-0-7503-1258-5(print)
ISBN 978-0-7503-1259-2(mobi)
DOI 10.1088/978-0-7503-1257-8
Version:20171201
IOPExpandingPhysics
ISSN2053-2563(online)
ISSN2054-7315(print)
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fromtheBritishLibrary.
PublishedbyIOPPublishing,whollyownedbyTheInstituteofPhysics,London
IOPPublishing,TempleCircus,TempleWay,Bristol,BS16HG,UK
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Contents
Preface xi
Introduction xii
Author biography xvi
6 Shock compression of ceramics with microstructure 6-1
6.1 Introduction 6-1
6.2 Classic mixture theory of shock compression 6-4
6.2.1 Shock compressibility of silicon carbide and silicon mixture 6-4
ceramics
6.2.2 Shock compression of metal–ceramic composites 6-9
6.3 Shock compression of materials with microstructure strength 6-12
6.3.1 Objectives of the dynamic mixture model 6-14
6.3.2 Strength and EOS decomposition 6-15
6.3.3 Elastic and pressure-equilibrated mixture compressibility 6-15
6.3.4 Component compressibility relations 6-18
6.3.5 Mixture compressibility 6-19
6.3.6 Evolution of the compaction parameter 6-20
6.4 Elasticity and strength of ceramics with microstructure 6-22
6.4.1 Elasticity and microstructure 6-22
6.4.2 The Steinberg–Hugoniot elastic limit 6-23
6.5 Application to ceramics with microstructure 6-25
6.5.1 Commercial alumina ceramics 6-25
6.5.2 Boron carbide ceramics and shock-induced phase 6-28
transformation
6.5.3 Silicon carbide ceramic with microstructure 6-41
6.5.4 Tungsten carbide ceramic and composition effects 6-50
6.6 Shock strength in silicon carbide and titanium diboride 6-55
6.6.1 Silicon carbide ceramics 6-56
6.6.2 Titanium diboride ceramics 6-58
6.6.3 Microstructure features of the shock strength 6-60
6.6.4 Failure deformation mechanisms in shock compression 6-63
6.7 Strength and failure models 6-65
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PhysicsofShockandImpact,Volume2
6.7.1 Observations of failure wave phenomena 6-65
6.7.2 A meso-kinetic model of delayed failure 6-67
6.8 Assessment of experimental data and modeling of ceramics with 6-80
microstructure
References 6-83
7 Dynamic compaction of crushable solids 7-1
7.1 Introduction 7-2
7.2 Spherical symmetry shock compaction of porous media 7-3
7.2.1 Shock propagation solution 7-3
7.2.2 Flow and pressure field solution 7-5
7.2.3 Attenuation properties in spherical shocks 7-6
7.3 Kompaneets shocks in porous media with other symmetries 7-7
7.3.1 Attenuation properties in other geometries 7-8
7.3.2 Thermo-mechanics of shock compaction 7-9
7.3.3 The crush model in distended media 7-11
7.4 Compaction in planar geometries 7-12
7.4.1 Variable compaction mass 7-13
7.4.2 Plate impact solutions 7-14
7.4.3 Constitutive compaction relations 7-15
7.4.4 Application of the incompressible-crush model to plate 7-18
impact on porous media
7.4.5 Non-dimensional solutions 7-20
7.4.6 Power-law properties of the limiting solution 7-22
7.4.7 P-lambda compaction 7-24
7.4.8 Non-dimensional solution for p-lambda compaction 7-26
7.4.9 Explosive compaction of porous media 7-26
7.5 Compaction resistance in non-planar geometries 7-31
7.5.1 Kompaneets spherical geometry with compaction resistance 7-31
7.5.2 Compaction of a metal tube with porous media 7-33
7.6 Physics-based compaction models 7-37
7.6.1 Carroll and Holt porous compaction model 7-37
7.6.2 Continuum compaction models with microstructure 7-43
7.6.3 The p-lambda porous compaction model 7-51
7.7 Compaction with elastic recovery 7-55
7.7.1 Governing equations 7-56
7.7.2 Boundary and initial conditions 7-57
7.7.3 Elastic solution 7-57
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PhysicsofShockandImpact,Volume2
7.7.4 Application of the boundary conditions 7-58
7.7.5 Rigid and elastic comparisons 7-59
7.7.6 Further elastic-compaction solutions 7-61
7.8 Dissipation and heating in shock compaction 7-61
7.8.1 Shock equation of state for distended solids 7-62
7.8.2 Temperature and shock compaction 7-70
7.9 Dynamic compaction and dissipation in distended solids 7-73
7.9.1 Compaction of the distended ductile solid 7-74
7.9.2 Compaction of the distended brittle solid 7-77
7.9.3 Dynamic compaction in crushable mixtures 7-86
References 7-96
8 The nature of structured shock waves 8-1
8.1 Introduction 8-2
8.2 Steady wave profiles and the fourth-power law 8-4
8.2.1 Experimental evidence for fourth-power dependence in the 8-4
steady wave shock
8.2.2 Non-steady waves 8-6
8.3 Origin of the fourth-power law 8-8
8.3.1 Precursor attenuation in quartz 8-9
8.3.2 Steady waves in aluminum 8-10
8.3.3 Equivalence of the fourth-power relation and the 8-10
shock invariant
8.4 Dissipative action and invariance in the structured shock wave 8-12
8.4.1 Action principles and implications for the shock wave 8-12
8.4.2 Correlation dynamics and length scales 8-17
8.4.3 Langevin dynamics and the dissipative action 8-20
8.4.4 Further applications in the shock transition 8-27
8.5 Viscosity and the structuring of shock waves 8-30
8.5.1 Viscosity of steady shock waves 8-31
8.5.2 Mechanisms of shock viscosity 8-32
8.5.3 Wave scattering and shock viscosity 8-33
8.6 Structured waves in porous and composite materials 8-34
8.6.1 Structured shock waves in granular and porous solids 8-35
8.6.2 Structured shock waves in composite solids 8-41
8.7 Physics of structured shock waves 8-45
References 8-47
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PhysicsofShockandImpact,Volume2
9 Kinetics of shocks in brittle solids 9-1
9.1 Introduction 9-1
9.2 Shock compression of brittle solids 9-2
9.2.1 Nature of the shock wave 9-2
9.2.2 Experimental shock wave profiles 9-4
9.2.3 Shock- versus particle-velocity characteristics 9-7
9.2.4 Phase transformation under shock compression 9-8
9.2.5 Viscosity of brittle solids and the steady shock process 9-13
9.2.6 Hugoniot elastic limit and the shock wave elastic precursor 9-19
9.2.7 Off-Hugoniot measurements 9-22
9.3 Shock compression of dolomite rock 9-27
9.3.1 Experimental methods and materials 9-27
9.3.2 Features of the shock wave profiles 9-28
9.3.3 Ramp wave compression of dolomite rock 9-32
9.4 Rate dependence in brittle deformation and failure 9-35
9.4.1 Observations of rate dependence 9-36
9.4.2 Analysis of strain-rate-dependent deformation and failure 9-38
9.4.3 Steady elastic shock waves in dolomite rock 9-44
9.4.4 Strength at Hopkinson bar strain rates 9-48
9.4.5 Intermediate strain rates (104 s−1 to 105 s−1) 9-52
9.4.6 Strain-rate dependence in brittle materials 9-55
9.5 Testing and failure kinetics of rocks and ceramics 9-58
9.5.1 Static testing 9-59
9.5.2 Shock wave testing 9-61
9.5.3 Intermediate rate testing 9-63
9.5.4 Kinetic effects in brittle solids 9-65
References 9-78
10 The shock wave equation of state 10-1
10.1 Introduction 10-1
10.2 Equation-of-state compressibility of a solid 10-2
10.2.1 Some elementary equations of state 10-3
10.2.2 Mie–Gruneisen equation of state 10-6
10.2.3 Enthalpy-based equations of state 10-23
10.3 Universal equations of state 10-32
10.3.1 Murnaghan equation of state 10-33
10.3.2 Linear shock-velocity–particle-velocity equation of state 10-34
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PhysicsofShockandImpact,Volume2
10.3.3 Intermolecular potential equations of state 10-36
10.3.4 Finite-strain equations of state 10-42
10.3.5 Further universal equations of state 10-43
10.3.6 Linear-Z equation of state 10-49
10.3.7 Woolfolk Hugoniot equation of state and modifications 10-56
10.3.8 Assessment of universal equations of state 10-59
10.4 Temperatures under shock compression 10-60
10.4.1 Thermodynamics and temperature 10-60
10.4.2 Temperature on the isentrope 10-61
10.4.3 Temperature on the Hugoniot 10-62
10.4.4 Hugoniot temperature calculations 10-64
10.4.5 Melting on the Hugoniot 10-65
10.4.6 Plastic dissipation contribution to the shock temperature 10-67
10.4.7 The porous Hugoniot 10-68
10.4.8 Post-shock residual temperatures 10-70
10.4.9 Enthalpy equation of state and temperature on the Hugoniot 10-71
10.5 Additive mixture theory and experiment under intense shock 10-74
compression
10.5.1 Shock equation of state through additive mixture models 10-75
10.5.2 Additive mixtures modeling through Gibbs energy 10-76
10.5.3 Mixture modeling through additive Hugoniot relations 10-77
10.5.4 Additive Hugoniot mixing at the molecular level 10-86
10.5.5 Dynamic isentrope from shock compression of mixtures 10-87
References 10-101
11 Shock wave analysis and applications 11-1
11.1 Introduction 11-1
11.2 Analysis in shock wave applications 11-2
11.2.1 Wave interaction analysis 11-2
11.2.2 Distance–time plots in shock analysis 11-7
11.3 Shock equilibration in a gage plane 11-11
11.3.1 Stress wave analysis 11-11
11.3.2 Stress wave attenuation from planar defects 11-15
11.3.3 Application to multiple planar defects 11-16
11.4 Application to stress pulse attenuation in oil shale 11-19
11.4.1 Elastic scattering and stress pulse attenuation 11-20
11.4.2 Viscous attenuation of a stress pulse 11-21
ix