A Priori Pulse Shaper Design for Constant-Strain-Rate Tests of Elastic-Brittle Materials

  • John T. Foster
  • Erik E. Nishida
Conference paper
Part of the Conference Proceedings of the Society for Experimental Mechanics Series book series (CPSEMS)


Pulse shaping techniques have been used for many years now in Kolsky bar testing of brittle materials. The use of pulse shapers allow the experimentalist to conduct high-strain-rate tests on brittle materials while ensuring that the sample will achieve a state of dynamic stress equilibrium before it fails, as well as to achieve a constant-strain-rate loading state for a large portion of the test. The process of choosing the appropriate pulse shaper system has typically been one of trail-and-error, sometimes requiring many experimental trails to achieve optimal results. Advances in analytic modeling of Kolsky bar tests now make it possible, in an a priori fashion, to design a pulse shaper system to produce a known constant-strain-rate experiment. This paper describes the approach of coupling these analytic models to an optimization technique to quickly find a pulse shaper system that will produce an experiment at a known constant-strain-rate. Experiments were conducted and the model predictions compared to resulting strain-rate histories for a G-10 material.


Pulse Shaper Maraging Steel Dynamic Stress Equilibrium Compressive Wave Speed Laminate Glass Cloth 
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This work was partially supported by Sandia National Laboratories. Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy under Contract DE-AC04-94AL85000.


  1. 1.
    Kolsky H (2003) Stress waves in solids. Dover, MineolaGoogle Scholar
  2. 2.
    Graff KF (1991) Wave motion in elastic solids. Dover, New YorkGoogle Scholar
  3. 3.
    Chen W, Song B (2010) Split hopkinson (Kolsky) bar: design, testing and applications. Springer, New YorkGoogle Scholar
  4. 4.
    Frew DJ, Forrestal MJ, Chen W (2001) A split Hopkinson pressure bar technique to determine compressive stress-strain data for rock materials. Exp Mech 41:40–46CrossRefGoogle Scholar
  5. 5.
    Kimberly J, Ramesh KT (2011) The dynamic strength of an ordinary chondrite. Meteorit Planet Sci 46(11):1653–1669CrossRefGoogle Scholar
  6. 6.
    Frew DJ, Forrestal MJ, Chen W (2002) Pulse shaping techniques for testing brittle materials with a split Hopkinson pressure bar. Exp Mech 42(1):93–106CrossRefGoogle Scholar
  7. 7.
    Frew DJ, Forrestal MJ, Chen W (2005) Pulse shaping techniques for testing elastic-plastic materials with a split Hopkinson pressure bar. Exp Mech 45(2):186–195CrossRefGoogle Scholar
  8. 8.
    Ravichandran G, Subhash G (1994) Critical appraisal of limiting strain rates for compression testing of ceramics in a split hopkinson pressure bar. J Am Ceram Soc 77(1):263–267CrossRefGoogle Scholar
  9. 9.
    Foster JT (2012) Comments on the validity of test conditions in Kolsky bar experiments of elastic-brittle materials. Exp Mech. AcceptedGoogle Scholar
  10. 10.
    Pan Y, Chen W, Song B (2005) Upper limit of constant strain rates in a split hopkinson pressure bar experiment with elastic specimens. Exp Mech 45(5):440–446CrossRefGoogle Scholar
  11. 11.
    Marquardt DW (1963) An algorithm for least-squares estimation of nonlinear parameters. J Soc Ind Appl Math 11(2):431–441MathSciNetzbMATHCrossRefGoogle Scholar
  12. 12.
    Lyness JN, Moler CB (1967) Numerical differentiation of analytic functions. SIAM J Numer Anal 4(2):202–210MathSciNetzbMATHCrossRefGoogle Scholar
  13. 13.
    Lyness JN (1968) Differentiation formulas for analytic functions. Math Comput 22(102):352–362MathSciNetzbMATHCrossRefGoogle Scholar
  14. 14.
    Squire W, Trapp G (1998) Using complex variables to estimate derivatives of real functions. SIAM Rev 40:110–112MathSciNetzbMATHCrossRefGoogle Scholar
  15. 15.
    Voorhees A, Millwater H, Bagley R (2011) Complex variable methods for shape sensitivity of finite element models. Finite Elem Anal Des 47(10):1146–1156CrossRefGoogle Scholar

Copyright information

© The Society for Experimental Mechanics, Inc. 2013

Authors and Affiliations

  1. 1.Mechanical Engineering DepartmentThe University of TexasSan AntonioUSA
  2. 2.Terminal Ballistics Technology DepartmentSandia National LaboratoriesAlbuquerqueUSA

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