Mechanics of Time-Dependent Materials

, Volume 11, Issue 3–4, pp 199–216 | Cite as

Improved relaxation time coverage in ramp-strain histories

  • W. G. Knauss
  • J. Zhao


Standard methods for deriving relaxation data from measurements invariably involve some form of ramp-type deformation history, the initial portion of which is typically not employed for modulus evaluation. In fact, the “ten-times-rule” or a variant thereof is widely used at the expense of short term data acquisition. This paper suggests a simple if (not) obvious method to extend the range of relaxation data that can be acquired from a single test at a single temperature. The method draws on new computational developments for inverting ill-conditioned systems of equations which allows the determination of relaxation parameters nearly routinely and trouble-free. We demonstrate this process for extraction of relaxation characterization from ramp strain histories through (a) numerical evaluation with a virtual test sequence, as well as through (b) data measured in the laboratory. Limitations regarding the time range over which the relaxation modulus can be extracted from laboratory measurements in terms of equipment resolution and stability are discussed. With these constraints in mind it appears feasible to extend the time range by three to four decades towards shorter times when compared with the application of the “ten-times-rule”. Similar treatments apply to the acquisition of creep compliance data.


Viscoelastic behavior Relaxation modulus Relaxation time Creep Creep compliance 


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Copyright information

© Springer Science+Business Media B.V. 2007

Authors and Affiliations

  1. 1.California Institute of TechnologyPasadenaUSA

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