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Dynamic Effects in Elastothermodynamic Damping of Hollow Particle Reinforced Metal-Matrix Composites

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Abstract

The Metal-Matrix Composites (MMCs) containing hollow spherical reinforcements are under active development for the applications such as space structures, submarine hulls etc. where weight is of critical importance. When these materials are subjected to a time varying strain field, energy is dissipated because of the thermoelastic effect (Elastothermodynamic Damping or ETD). The quasi-static ETD analysis for the MMCs containing hollow spherical particles has been reported in literature. The entropic approach, which is better suited for composite materials with perfect or imperfect interfaces, is used for the analysis. In the present work, the effect of inertia forces is carried out on ETD of hollow particle-reinforced MMCs. For given particle volume fractions (V p ), the inertia forces are found to be more significant at higher value of thermal parameter (Ω T1) (alternatively, frequency of vibration if reinforcement radius is fixed), large cavity volume fraction (V h ) and low value of the parameter B1.

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Abbreviations

a :

Reinforcement radius

b :

Matrix radius

\( B_{ 1} \) :

Non-dimensional parameter quantifying the inertia effects \( ({=}\sqrt {\tau_{T1} /\tau_{M1} } ) \)

c :

Cavity radius

C i :

Specific heats per unit volume of phase i

E i :

Moduli of elasticity of phase i

k i :

Thermal conductivity of phase i

r :

Radial coordinate

R :

Normalized radial coordinate (=r/a)

Δs :

Entropy produced per unit volume during a cycle

ΔS :

Entropy produced in the entire volume during a cycle

t :

Time

T :

Absolute temperature

\( T_{\text{o}} \) :

Equilibrium temperature \( ({=}300{\text{ K)}} \)

ΔT :

Change in temperature \( ({=}T - T_{\text{o}} ) \)

u i :

Radial displacement of phase i

U i :

Normalized radial displacement (=u i /a)

V :

Volume of composite sphere model

V h :

Cavity volume fraction

V p :

Particle volume fraction

\( V_{i}^{*} \) :

Temperature fluctuation

W :

Maximum stored elastic energy during a cycle

ΔW :

Mechanical energy dissipated during a cycle

α i :

Linear coefficients of thermal expansion of phase i

λ i :

Lame’ constant (=E i ν i /(1 + ν i )(1 − 2ν i ))

μ i :

Lame’ constant (=E i /2(1 + ν i ))

ν i :

Poisson’s ratio of phase i

ρ i :

Mass density of phase i

σ ij :

Stress components

\( \sigma_{\text{o}} \) :

Magnitude of uniform applied stress

τ Mi :

Characteristic mechanical time \( ({=}a\sqrt {\rho_{i} /(\lambda_{i} + 2\mu_{i} )} ) \)

τ Ti :

Characteristic thermal time (=a 2 C i /k i )

Ψ qs :

Specific damping capacity obtained from quasi-static solution

Ψ d :

Specific damping capacity obtained from dynamic solution

ω :

Circular frequency of vibration

Ω Mi :

Non-dimensional mechanical parameter \( ({=}\omega \, \tau_{Mi} ) \)

Ω Ti :

Non-dimensional thermal parameter \( ({=}\omega \, \tau_{Ti} ) \)

r, θ, ϕ :

Spherical co-ordinates

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Authors and Affiliations

  1. Madan Mohan Malaviya University of Technology, Gorakhpur, Uttar Pradesh, 273 001, India

    Sunil Kumar Srivastava

  2. Indian Institute of Technology Roorkee, Roorkee, Uttarakhand, 247 667, India

    Bhanu Kumar Mishra

Authors
  1. Sunil Kumar Srivastava
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  2. Bhanu Kumar Mishra
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Correspondence to Sunil Kumar Srivastava.

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Srivastava, S.K., Mishra, B.K. Dynamic Effects in Elastothermodynamic Damping of Hollow Particle Reinforced Metal-Matrix Composites. J. Inst. Eng. India Ser. C 98, 185–190 (2017). https://doi.org/10.1007/s40032-016-0253-x

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