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Experimental Mechanics

, Volume 9, Issue 10, pp 441–448 | Cite as

Stress-strain data obtained at high rates using an expanding ring

Investigation indicates that dynamic symmetrical free expansion of thin rings offers a valid means for obtaining uniaxial tensile stress-strain relationships at high strain rates
  • C. R. Hoggatt
  • R. F. Recht
Article

Abstract

Dynamic uniaxial tensile stress-strain data are obtained at high strain rates by measuring the kinematics of thin-ring specimens expanding symmetrically by virtue of their own inertia. Impulsively loaded to produce high initial radial velocities, expanding rings are decelerated by the radial component of the hoop stresses. Differential equations of motion are evaluated experimentally to obtain the stress-strain (constitutive) relationships which govern the magnitude of these stresses. Techniques have been developed for producing symmetric radial expansion and measuring resulting displacements precisely as a function of time. Dynamic stress-strain relationships have been obtained for 6061-T6 aluminum, 1020 cold-drawn steel, and 6Al-4V titanium. For each of these materials, displacement-time curves are observed to be parabolic within the resolution of the measurements. Results are presented as true-stress/true-strain relationships.

Keywords

Aluminum Titanium Differential Equation Mechanical Engineer Fluid Dynamics 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Nomenclature

a

constant

b

constant

D

displacement of edge of ring

Dm

maximum displacement of edge of ring

E

Young's modulus

m

mass of ring

r

internal radius of ring

ro

initial internal radius of ring

R

external radius of ring

Ro

initial external radius of ring

\(\dot R\)

radial velocity of ring

\(\ddot R\)

radial deceleration of ring

t

time

tm

maximum time

Z

axial length of ring

Zo

initial axial length of ring

ε

true strain

\(\dot \varepsilon\)

true strain rate

ν

Poisson's ratio

ρ

mass density of ring material

σ

true stress

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Copyright information

© Society for Experimental Mechanics, Inc. 1969

Authors and Affiliations

  • C. R. Hoggatt
    • 1
  • R. F. Recht
    • 1
  1. 1.Denver Research Institute of the University of DenverDenver

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