Stress Relaxation in Gold WireO. L. Anderson and P. Andreatch Citation: Journal of Applied Physics 26, 1518 (1955); doi: 10.1063/1.1721943 View online: http://dx.doi.org/10.1063/1.1721943 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/26/12?ver=pdfcov Published by the AIP Publishing Articles you may be interested in A simple approach to the formation of ultranarrow metal wires J. Appl. Phys. 103, 054312 (2008); 10.1063/1.2890381 Optical observations of plasma formation and wire core expansion of Au, Ag, and Cu wires with 0–1kA per wire Phys. Plasmas 11, 1145 (2004); 10.1063/1.1644582 Mesoscale x-ray diffraction measurement of stress relaxation associated with buckling in compressedthin films Appl. Phys. Lett. 83, 51 (2003); 10.1063/1.1591081 Principles for the design and operation of a molecular wire transistor J. Appl. Phys. 88, 5280 (2000); 10.1063/1.1315627 Electron heating effects in diffusive metal wires Appl. Phys. Lett. 71, 773 (1997); 10.1063/1.119641

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JOURNAL OF APPLIED PHYSICS VOLUME 26. NUMBER 12 DECEMBER, 1955

Letters to the Editor Guide to the Successful Propulsion of a Solid

Object by an Explosive Charge JOHN S. RINEHART

Astrophysical ObsenJatory, Smithsonian Institution. Cambridge 38, Massachusetts

(Received September 7, 1955)

I N a recent paper von Valkenburg and Hendricksl describe a scheme for propelling a small missile at high velocity from

an explosive charge. The scheme is a specific application of a general principle that seems not to have been described heretofore. The purpose of this note is to bring the principle to the attention of those concerned with the development and use of metal­explosive systems.

Consider a solid object of arbitrary shape with the exception that one surface of the body, the surface against which the accelerating force acts, is assumed to be flat and oriented normal to the direction of the force. If the body is to remain intact after acceleration, all parts of it must be accelerated to the same velocity v. Generally, the force F. that acts at a particular point on the body will vary rapidly with time.2 The value of F. may, and frequently will, vary markedly from point to point on the surface. The impulse f. that acts on an increment of area dS of the surface will be given by

f.= J;'" F.(t)dt.

The velocity imparted to that mass m. which lies below the elemental area dS will be given by

v.=f./m •.

If the body is to hold together, the following relationship,

.fo'" F.(t)dt constant

must be satisfied for every point on the surface. Consider specifically the case of a cylindrically symmetrical

object that is propelled off of the end of a stick of explosive. A qualitative plot of f. versus radial distance from the axis, deduced from considerations discussed previously by the author 2 is shown in Fig. 1. It is to be expected, therefore, that the pell~t used by

AXIS •

RADIAL DISTANCE

EDGE

"

FIG. 1. Graph showing qualitative variation of impulse I. delivered to a point on the end of a right circular cylinder of explosive.

van Valkenburg would hold together. It is significant that the shape of the identation made in a block of steeP is almost a mirror image of the shape of the pellet.

The greatest difficulty in applying this principle to a specific case will arise from lack of knowledge of f F .dt. Fortunately, the qualitative behavior of this quantity can frequently be surmised from a simple examination of the geometry of the metal-explosive system under consideration.

(I~Ni.E. van Valkenburg and C. D. Hendricks, Jr., J. Appl. Phys. 26, 776

• J. S. Rinehart and J. Pearson, Behavior of Metals Under Impulsi"" Loads, (A~erican Society for Metals, Cleveland, Ohio, 1954). Chap. 5.

3 J. S. Rmehart, J. Appl. Phys. 22,1178 (1951).

Stress Relaxation in Gold Wire O. L. ANDERSON AND P. ANDREATCH

Bell Telephone Laboratories, Inc., Murray Hill, New Jersey (Received July 23, 1955)

T HE stress relaxation in gold wire has been measured using the technique developed by Mallina,t and subsequently

used in determining the stress relaxation in copper and alumi­num.2.3 This technique (see Fig. 1)* consists of wrapping the wire under a prescribed tension around a rectangular metal terminal, so as to produce a twist in the terminal, and measuring the angle of twist as a function of time.

In the experiments reported here, a terminal of nickel brass alloy, commonly known as nickel silver, measuring 0.062 by 0.016 by 4 in. long was wrapped with 120 turns of 0.020 in. gold wire (purity 99.97%) tensioned with a two pound weight (6300 psi). This tension produced an angle of twist of about 26° which was read by means of a pointer attached to the terminal. A fixture holding four of these terminals was placed in an oven, whose temperature was controlled to ±2°C, for a period of 16 months. The angle of twist was read periodically through a glass window in the oven. Measurements were conducted at 70°C, 100°C, and 150°C, and also in an atmosphere-controlled room whose tem­perature is 25°C±0.5°C, and whose relative humidity is 40%. The accuracy of the twist readings is ±2%. In a period of 16 months, after being unwrapped, the creep in the terminals was found to be about 2°. The data, as presented here, are corrected for this creep.

The ratio of the stress to the initial stress is shown in Fig. 2. The points on the curve represent average values of two measurements.

The activation energy of stress relaxation is given by the following equation which is derived in reference 3.

Ba=Rln(td t2)/ [~-~J, TI T2

where tl and t2 are time values corresponding to the temperature TI and T2 at the same stress level, R is the gas constant, and Ha designates the activation energy at the stress <T. Using the solid lines in Fig. 2, the activation energy for the various stress levels is calculated and graphed in Fig. 3. Using the values of activation

(al LONGITUDINAL TENSION IN A WIRE CAUSES TERMINAL TO TWIST

(b) MODEL MADE WITH A RUBBER TERMINAL WRAPPED WITH RUBBER TUBING EMPHASIZES THE TWIST PRODUCED BY THE LONGITUDINAL TENSION IN THE TUBING

FIG. 1. Illustration of wire wrapped on terminals.

1518

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LETTERS TO THE EDITOR 1519

T:ME IN SECONDS

FIG. 2. Relaxation of stress in gold wire as a function of time and temperature.

energy in Fig. 3, the stress relaxation curve at 25°C is predicted and plotted as a dashed line in Fig. 2.

The activation energy associated with stress relaxation in gold decreases as the stress increases which is the same result

30

>-l'l cr

20 w z w z 0 10 ~ > ;:: U

0 « 0

" .... o ISOoC TO 100° C 6 100°C TO 70° C

S STRESS (IN THOUSAND PSI)

6

FIG. 3. Activation energy for stress relaxation as a function of hoop stress.

found for similar experiments with copper and aluminum de­scribed in reference 3. Furthermore, the extrapolated value of activation energy at zero stress agrees with the activation energy of gold self-diffusion (44100 cal/mole),4.5 indicating that the atomic readjustments which relieve persisting tension are similar to those involving self-diffusion.

I R. F. Mallina, Bell System Tech. J. 32, 525 (1953). 2 W. P. Mason ami T. F. Osmer, Bell System Tech. J. 32, 55i (1953). 3 W. P. Mason and O. L. Anderson, Bell System Tech. J. 33, 1093 (1954). * This figure republished from Bell System Tech. J. [3] 32, 535 (1953). 'W. A. Johnson, Trans. Am. Inst. Mining Met. Engrs. 147, 107 (1941). 5 F. Seitz, Phys. Rev. 79, 1513 (1948).

Comments on Limiting Pressure on Hydrofoils E. V. LAITONE

University of California, Berkeley. California (Received August 10, 1955)

PREVIOUSLY the writer'" had pointed out that if hydrostatic conditions are achieved on the upper surface of a thin hydro­

foil at small angles of attack as it approaches the free water surface, then there is a limiting maximum surface velocity that is

FIG. 1. Hydraulic jump on the hydrofoil (M"" =0.73, F =0.5).

produced by a hydraulic jump. That is, the supercritical flow that can occur if hydrostatic conditions are attained can be converted to sub critical flow only by means of the hydraulic jump that produces the maximum absolute water depth after the jump. This fixes the maximum local Froude number immediately up­stream of the hydraulic jump as M, = \G' =Vt!(gYI)!. This hydraulic jump always produces a doubling of the water depth (YZ/Y, = 2 ~y",,/Y,) where the maximum depth after the hydraulic jump (y,) must be only slightly less than the depth of hydrofoil trailing-edge below the original free water surface (y",,).

The writer'" pointed out two severe limitations to this theory; namely,

(1) If hydrostatic flow were not established, neither the limiting velocity nor the hydraulic jump could occur. This would be expected for thick hydrofoils or large angles of attack, or possibly for large Froude numbers based on the forward speed of the hydrofoil (V",,) and the depth of submergence since the vertical acceleration may not be negligible. Consequently, the writer' restricted the Froude number range for this theory to

M"" = V ""j (gy",,)! ~ v'J.

(2) If the hydrofoil were in a channel of finite depth, then the downstream wave disturbances could not overtake the hydrofoil in order to form a hydraulic jump whenever the Froude number based on the channel depth h became supercritical

F=V""j(gh)!>1.

Unfortunately, the experimental equipment at Berkeley did not permit testing for M "" > \G' when F < 1 in order to determine the upper range for the velocity limitation. However, recent ex­perimental and theoretical investigations by Parkin, Perry, and Wu3 have shown that at high Froude (l1I "") numbers the hydraulic jump and the accompanying velocity limitation do not occur even when F < 1. Their experimental data, all taken at subcritical channel speeds, indicate that when M "" ~ 1 the velocity limitation is applicable, but when Af"" > \G' it is definitely no longer valid.

determined by the maximum water depth recovery that can be FIG, 2. Hydraulic jump downstream of the hydrofoil (M"" =1.18, F =0.79)

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