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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

Figures

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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.

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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

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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

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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

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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

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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

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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

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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

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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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