Abstract
This chapter examines four topics of practical importance. It begins with an introduction to material characterization testing, covering stress relaxation, creep, constant rate, and dynamic tests. The chapter then introduces two types of analytical forms, typically used to describe mechanical constitutive property functions. One type, usually referred to as a Dirichlet-Prony series, is expressed as a finite sum of exponentials; the other form is a power law in time. This treatment is followed by a discussion of methods of inversion of material property functions given in Prony series form; both exact and approximate methods of inversion are presented. The chapter is completed with a discussion of practical ways to establish the numerical coefficients entering the analytical forms used to represent the WLF shift relation, the relaxation modulus, and the creep compliance. The use of a computer application available with the book, which was specifically developed to obtain the exact convolution inverse of function in a Prony series form, is also presented and its use is illustrated by means of some examples.
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Notes
- 1.
This condition is always met by relaxation or creep compliance functions, because a series of exponentials is complete in that it can represent any continuous function to any desired degree of accuracy, if enough terms are used in the representation.
- 2.
Typically, the time parameters are more or less arbitrarily taken at each of the several logarithmic cycles spanning the available data, such as at 10−5, 10−4,…,103, 104 min, without worrying much about their relationship to any intrinsic response times (relaxation or creep) of the material in question.
References
B.E. Read, G.D. Dean, The determination of dynamic properties of polymer composites (Wiley, London, 1978) pp. 1–12
W.G. Knauss, I. Emri, Volume change and the nonlinearly thermo-viscoelastic constitution of polymers. Polymer Eng. Sci. 27, 86–100 (1987)
R.A. Schapery, Approximate methods of transform inversion for viscoelastic stress analysis, in Proceedings of 4th U.S. national congress of Appl. Mech., 1075 (1962)
D. Gutierrez-Lemini, Exact inversion of viscoelastic property functions of exponential type, JANNAF, JSF, San Diego, CA (2005)
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Gutierrez-Lemini, D. (2014). Material Property Functions and Their Characterization. In: Engineering Viscoelasticity. Springer, Boston, MA. https://doi.org/10.1007/978-1-4614-8139-3_7
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DOI: https://doi.org/10.1007/978-1-4614-8139-3_7
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