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Measurements of thermally induced stress waves in a thin rod using birefringent coatings

Investigation aimed at developing and utilizing a technique for transient measurement of the inertial stresses induced by rapid heating of a structure

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Abstract

When an elastic body is heated rapidly, significant inertial stresses are developed if the imposed heating rates cause a substantial temperature change in times which are short relative to the mechanical response time of the body. This work describes a method for inducing and measuring the thermally induced elastic stress waves in an unrestrained thin rod. Rapid heating was accomplished electrically by discharging a low-inductance capacitor bank (0.1 μH, 2800 J) through the rod. Utilizing the frozen-stress technique, an initial fringe pattern was introduced into thin strips of a birefringent material securely bonded to each side of the rod. The longitudinal strain oscillations were measured by direct observation of the movement of the fringe patterns with a high-speed framing camera. Interpretation of these measurements required a dynamic calibration and application of a dynamic correction factor for the reinforcing effect of the coating. Oscillations with periods from 35 to 250 μsec and stress amplitudes up to 900 psi were measured and compared with the uncoupled thermoelastic theory. Good agreement was obtained, and it was concluded that this technique is suitable for transient measurements in the presence of large magnetic fields which normally restrict the use of electronic methods.

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Abbreviations

A :

cross-sectional area, in.2

a :

sonic velocity, in./sec

c :

specific heat, Btu/lb/° F

C :

capacitance, μF

E :

elastic modulus, lb/in.2

f ε :

strain-optic coefficient, in./in./fringe/in.

f σ :

stress-optic coefficient, lb/in.2/fringe/in.

h :

thickness of birefringent coating, in.

i :

current, amp

l :

half-length of “free-free” rod, in.

L :

inductance, henries

N :

fringe order

q :

heating rate, Btu/sec/in.3

R :

electrical resistance, ohms

t :

time, sec

T :

temperature, ° F

V :

voltage, v

W :

total weight of heated bar, lb

x, y, z :

rectangular Cartesian coordinates, in.

α:

coefficient of thermal expansion, in./in./° F

γ:

specific weight, lb/in.3

ε:

strain, in./in.

ν:

Poisson's ratio

ρ:

mass density, lb-sec2/in.4

σ:

stress, lb/in.2

τ:

fundamental period of longitudinal oscillation, sec

x, y, z :

x, y, z directions

O :

initial

ST :

static

Dyn :

dynamic

s :

specimen

c :

coating

m :

maximum

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Authors and Affiliations

  1. University of California, Lawrence Radiation Laboratory, Livermore, Calif.

    Arthur L. Austin (Project Engineer)

Authors
  1. Arthur L. Austin
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Austin, A.L. Measurements of thermally induced stress waves in a thin rod using birefringent coatings. Experimental Mechanics 5, 1–10 (1965). https://doi.org/10.1007/BF02320897

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  • DOI: https://doi.org/10.1007/BF02320897

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