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Research Papers

Localized Heating Near a Rigid Spherical Inclusion in a Viscoelastic Binder Material Under Compressional Plane Wave Excitation

[+] Author and Article Information
Jesus O. Mares

School of Aeronautics and Astronautics,
Maurice J. Zucrow Laboratories,
Purdue University,
West Lafayette, IN 47907

Daniel C. Woods, J. Stuart Bolton

School of Mechanical Engineering,
Ray W. Herrick Laboratories,
Purdue University,
West Lafayette, IN 47907

Caroline E. Baker

School of Mechanical Engineering,
Purdue University,
West Lafayette, IN 49707

Steven F. Son

School of Mechanical Engineering,
School of Aeronautics and Astronautics,
Maurice J. Zucrow Laboratories,
Purdue University,
West Lafayette, IN 47907

Jeffrey F. Rhoads

School of Mechanical Engineering,
Ray W. Herrick Laboratories,
Birck Nanotechnology Center,
Purdue University,
West Lafayette, IN 47907
e-mail: jfrhoads@purdue.edu

Marcial Gonzalez

School of Mechanical Engineering,
Purdue University,
West Lafayette, IN 47907

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received August 6, 2016; final manuscript received December 14, 2016; published online January 27, 2017. Assoc. Editor: Junlan Wang.

J. Appl. Mech 84(4), 041001 (Jan 27, 2017) (9 pages) Paper No: JAM-16-1391; doi: 10.1115/1.4035522 History: Received August 06, 2016; Revised December 14, 2016

High-frequency mechanical excitation has been shown to generate heat within composite energetic materials and even induce reactions in single energetic crystals embedded within an elastic binder. To further the understanding of how wave scattering effects attributable to the presence of an energetic crystal can result in concentrated heating near the inclusion, an analytical model is developed. The stress and displacement solutions associated with the scattering of compressional plane waves by a spherical obstacle (Pao and Mow, 1963, “Scattering of Plane Compressional Waves by a Spherical Obstacle,” J. Appl. Phys., 34(3), pp. 493–499) are modified to account for the viscoelastic effects of the lossy media surrounding the inclusion (Gaunaurd and Uberall, 1978, “Theory of Resonant Scattering From Spherical Cavities in Elastic and Viscoelastic Media,” J. Acoust. Soc. Am., 63(6), pp. 1699–1712). The results from this solution are then utilized to estimate the spatial heat generation due to the harmonic straining of the material, and the temperature field of the system is predicted for a given duration of time. It is shown that for certain excitation and sample configurations, the elicited thermal response near the inclusion may approach, or even exceed, the decomposition temperatures of various energetic materials. Although this prediction indicates that viscoelastic heating of the binder may initiate decomposition of the crystal even in the absence of defects such as initial voids or debonding between the crystal and binder, the thermal response resulting from this bulk heating phenomenon may be a precursor to dynamic events associated with such crystal-scale effects.

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References

Ying, C. F. , and Truell, R. , 1956, “ Scattering of a Plane Longitudinal Wave by a Spherical Obstacle in an Isotropically Elastic Solid,” J. Appl. Phys., 27(9), pp. 1086–1097. [CrossRef]
Pao, Y. H. , and Mow, C. C. , 1963, “ Scattering of Plane Compressional Waves by a Spherical Obstacle,” J. Appl. Phys., 34(3), pp. 493–499. [CrossRef]
Thau, S. A. , 1967, “ Radiation and Scattering From a Rigid Inclusion in an Elastic Medium,” ASME J. Appl. Mech., 34(2), pp. 509–511. [CrossRef]
Mow, C. C. , and Pao, Y. H. , 1971, “ The Diffraction of Elastic Waves and Dynamic Stress Concentrations,” United States Air Force Project, RAND Report No. R-482-PR.
Oien, M. A. , and Pao, Y. H. , 1973, “ Scattering of Compressional Waves by a Rigid Spheroidal Inclusion,” ASME J. Appl. Mech., 40(4), pp. 1073–1077. [CrossRef]
Gaunaurd, G. C. , and Uberall, H. , 1978, “ Theory of Resonant Scattering From Spherical Cavities in Elastic and Viscoelastic Media,” J. Acoust. Soc. Am., 63(6), pp. 1699–1712. [CrossRef]
Beltzer, A. , Robinson, B. , and Rudy, N. , 1979, “ The Effect of Random Compressional Waves on a Rigid Sphere Embedded in an Elastic Medium,” J. Sound Vib., 66(4), pp. 513–519. [CrossRef]
Beltzer, A. I. , 1980, “ Random Response of a Rigid Sphere Embedded in a Viscoelastic Medium and Related Problems,” ASME J. Appl. Mech., 47(3), pp. 499–503. [CrossRef]
Sessarego, J. P. , Sageloli, J. , Guillermin, R. , and Uberall, H. , 1998, “ Scattering by an Elastic Sphere Embedded in an Elastic Isotropic Medium,” J. Acoust. Soc. Am., 104(5), pp. 2836–2844. [CrossRef]
Avila-Carrera, R. , and Sanchez-Sesma, F. J. , 2006, “ Scattering and Diffraction of Elastic P-and S-Waves by a Spherical Obstacle: A Review of the Classical Solution,” Geofís. Int., 45(1), pp. 3–21.
Tauchert, T. R. , 1967, “ Heat Generation in a Viscoelastic Solid,” Acta Mech., 3(4), pp. 385–396. [CrossRef]
Brinson, H. F. , and Brinson, L. C. , 2008, Polymer Engineering Science and Viscoelasticity: An Introduction, Springer, New York.
Dinzart, F. , Molinari, A. , and Herbach, R. , 2008, “ Thermomechanical Response of a Viscoelastic Beam Under Cyclic Bending: Self-Heating and Thermal Failure,” Int. Appl. Mech., 60(1), pp. 59–85.
Dimarogonas, A. D. , and Syrimbeis, N. B. , 1992, “ Thermal Signatures of Vibrating Rectangular Plates,” J. Sound Vib., 157(3), pp. 467–476. [CrossRef]
Chervinko, O. P. , and Senchenkov, I. K. , 2002, “ The Coupled Thermomechanical State of a Notched Viscoelastic Rectangular Plate Under Harmonic Loading,” Int. Appl. Mech., 38(2), pp. 209–216. [CrossRef]
Chervinko, O. P. , 2004, “ Calculating the Critical Parameters Characterizing the Thermal Instability of a Viscoelastic Prism With a Stress Concentrator Under Harmonic Compression,” Int. Appl. Mech., 40(8), pp. 916–922. [CrossRef]
Chervinko, O. P. , Senchenkov, I. K. , and Yakimenko, N. N. , 2007, “ Vibrations and Self-Heating of a Viscoelastic Prism With a Cylindrical Inclusion,” Int. Appl. Mech., 43(6), pp. 647–653. [CrossRef]
Katunin, A. , and Fidali, M. , 2012, “ Self-Heating of Polymeric Laminated Composite Plates Under the Resonant Vibrations: Theoretical and Experimental Study,” Polym. Compos., 33(1), pp. 138–146. [CrossRef]
Woods, D. C. , Miller, J. K. , and Rhoads, J. F. , 2015, “ On the Thermomechanical Response of HTPB-Based Composite Beams Under Near-Resonant Excitation,” ASME J. Vib. Acoust., 137(5), p. 054502. [CrossRef]
Miller, J. K. , Woods, D. C. , and Rhoads, J. F. , 2014, “ Thermal and Mechanical Response of Particulate Composite Plates Under Inertial Excitation,” J. Appl. Phys., 116(24), p. 244904. [CrossRef]
Hinders, M. K. , Fang, T. M. , McNaughton Collins, M. F. , and Collins, J. J. , 1994, “ An Analytic Solution for Energy Deposition in Model Spherical Tumors Undergoing Ultrasound-Hyperthermia Treatments,” Phys. Med. Biol., 39(1), pp. 107–132. [CrossRef] [PubMed]
Bowden, F. P. , and Yoffe, A. D. , 1952, Initiation and Growth of Explosion in Liquids and Solids, Cambridge University Press, New York.
Mader, C. L. , 1963, “ Shock and Hot Spot Initiation of Homogeneous Explosives,” Phys. Fluids, 6(3), pp. 375–381. [CrossRef]
Chaudhri, M. M. , and Field, J. E. , 1974, “ The Role of Rapidly Compressed Gas Pockets in the Initiation of Condensed Explosives,” Proc. R. Soc London A, 340(1620), pp. 113–128. [CrossRef]
Swallowe, G. M. , and Field, J. E. , 1982, “ The Ignition of a Thin Layer of Explosive by Impact; the Effect of Polymer Particles,” Proc. R. Soc. London A, 379(1777), pp. 389–408. [CrossRef]
Mares, J. O. , Miller, J. K. , Gunduz, I. E. , Rhoads, J. F. , and Son, S. F. , 2014, “ Heat Generation in an Elastic Binder System With Embedded Discrete Energetic Particles Due to High-Frequency, Periodic Mechanical Excitation,” J. Appl. Phys., 116(20), p. 204902. [CrossRef]
Chen, M. W. , You, S. , Suslick, K. S. , and Dlott, D. D. , 2014, “ Hot Spots in Energetic Materials Generated by Infrared and Ultrasound, Detected by Thermal Imaging Microscopy,” Rev. Sci. Instrum., 85(2), p. 023705. [CrossRef] [PubMed]
You, S. , Chen, M. W. , Dlott, D. D. , and Suslick, K. S. , 2015, “ Ultrasonic Hammer Produces Hot Spots in Solids,” Nat. Commun., 6(4), p. 6581. [CrossRef] [PubMed]
Miller, J. K. , Mares, J. O. , Gunduz, I. E. , Son, S. F. , and Rhoads, J. F. , 2016, “ The Impact of Crystal Morphology on the Thermal Responses of Ultrasonically-Excited Energetic Materials,” J. Appl. Phys., 119(2), p. 024903. [CrossRef]
Borcherdt, R. D. , 2009, Viscoelastic Waves in Layered Media, Cambridge University Press, New York.
Zener, C. , 1938, “ Internal Friction in Solids II: General Theory of Thermoelastic Internal Friction,” Phys. Rev., 53(1), pp. 90–99. [CrossRef]
Ting, E. C. , 1973, “ Dissipation Function of a Viscoelastic Material With Temperature-Dependent Properties,” J. Appl. Phys., 44(11), pp. 4956–4960. [CrossRef]
Bishop, J. E. , and Kinra, V. K. , 1996, “ Equivalence of the Mechanical and Entropic Descriptions of Elastothermodynamic Damping in Composite Materials,” Mech. Compos. Mater. Struct., 3(2), pp. 83–95. [CrossRef]
Lakes, R. , 1997, “ Thermoelastic Damping in Materials With a Complex Coefficient of Thermal Expansion,” J. Mech. Behav. Mater., 8(3), pp. 201–216. [CrossRef]
Incropera, F. P. , DeWitt, D. P. , Bergman, T. L. , and Lavine, A. S. , 2007, Introduction to Heat Transfer, Wiley, Hoboken, NJ.
Bradie, B. , 2006, A Friendly Introduction to Numerical Analysis, Pearson Prentice Hall, Upper Saddle River, NJ.
Dow Corning Corporation, 1986, “ Information About High Technology Materials Sylgard® 182 & 184 Silicone Elastomers,” Data Sheet No. 61-113C-01.
Dow Corning Corporation, 2014, “ Product Information, Sylgard® 184 Silicone Elastomer,” Data Sheet No. 11-3184B-01.
Gibbs, T. R. , and Popolato, A. , eds., 1980, LASL Explosive Property Data, University of California Press, Berkeley, CA.
Shepodd, T. , Behrens, R. , Anex, D. , Miller, D. , and Anderson, K. , 1997, “ Degradation Chemistry of PETN and Its Homologues,” Sandia National Laboratories, Report No. SAND–97-8684C.
Millett, J. C. F. , Whiteman, G. , Stirk, S. M. , and Bourne, N. K. , 2011, “ Shear Strength Measurements in a Shock Loaded Commercial Silastomer,” J. Appl. Phys., 44(18), p. 185403.
Garvin, K. A. , Hocking, D. C. , and Dalecki, D. , 2010, “ Controlling the Spatial Organization of Cells and Extracellular Matrix Proteins in Engineered Tissues Using Ultrasound Standing Wave Fields,” Ultrasound Med. Biol., 36(11), pp. 1919–1932. [CrossRef] [PubMed]
Pritz, T. , 1998, “ Frequency Dependences of Complex Moduli and Complex Poisson's Ratio of Real Solid Materials,” J. Sound Vib., 214(1), pp. 83–104. [CrossRef]
Pritz, T. , 2000, “ Measurement Methods of Complex Poisson's Ratio of Viscoelastic Materials,” Appl. Acoust., 60(3), pp. 279–292. [CrossRef]
Agrawal, J. P. , 2010, High Energy Materials: Propellants, Explosives, and Pyrotechnics, Wiley, Weinheim, Germany.
Mares, J. O. , Woods, D. C. , Baker, C. E. , Son, S. F. , Rhoads, J. F. , Bolton, J. S. , and Gonzalez, M. , 2016, “ Localized Heating Due to Stress Concentrations Induced in a Lossy Elastic Medium via the Scattering of Compressional Waves by a Rigid Spherical Inclusion,” ASME Paper No. IMECE2016-68219.

Figures

Grahic Jump Location
Fig. 1

A diagram of the rectangular and spherical coordinate systems at a rigid spherical particle of radius a in an infinite linear viscoelastic medium. An incident harmonic compressional plane wave travels in the positive z-direction in the viscoelastic medium.

Grahic Jump Location
Fig. 2

The magnitudes (in MPa) of the (a) radial stress σ̃rr and (b) shear stress σ̃rθ induced in the HMX–Sylgard® system by a 1 μm, 500 kHz compressional plane wave traveling in the positive z-direction

Grahic Jump Location
Fig. 3

The magnitudes (in MPa) of the (a) polar stress σ̃θθ and (b) azimuthal stress σ̃ϕϕ induced in the HMX–Sylgard® system by a 1 μm, 500 kHz compressional plane wave traveling in the positive z-direction

Grahic Jump Location
Fig. 4

The time-averaged volumetric heat generation q (in W/mm3) induced in the HMX–Sylgard® system by a 1 μm, 500 kHz compressional plane wave traveling in the positive z-direction

Grahic Jump Location
Fig. 5

The maximum transient temperature increase in the crystal (lower curve) and binder (upper curve) induced in the HMX–Sylgard® system by a 1 μm, 500 kHz compressional plane wave

Grahic Jump Location
Fig. 6

The temperature distribution (in  °C above ambient T0) at t = 0.5 s induced in the HMX–Sylgard® system by a 1 μm, 500 kHz compressional plane wave traveling in the positive z-direction

Grahic Jump Location
Fig. 7

The maximum crystal temperature at t = 0.5 s (blue curve) and corresponding rate of temperature increase (green curve) in the HMX–Sylgard® system as a function of incident wave: (a) amplitude and (b) frequency

Grahic Jump Location
Fig. 8

The displacement amplitude of the crystal induced in the HMX–Sylgard® system by a 1 μm compressional plane wave as a function of incident wave frequency

Grahic Jump Location
Fig. 9

A conceptual diagram representing the transient temperature rise of the crystal and the regions of applicable heating phenomena. The shaded region represents short excitation times and low temperature heating of the crystal as governed by the viscoelastic heating model presented in this work. The unshaded regions represent regimes over which additional heating mechanisms are expected to significantly impact the thermal response.

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