A nonlinear viscoelastic constitutive model taking into account of physical aging
- PDF / 1,690,497 Bytes
- 11 Pages / 439.37 x 666.142 pts Page_size
- 53 Downloads / 224 Views
A nonlinear viscoelastic constitutive model taking into account of physical aging D. Jalocha1
Received: 28 March 2020 / Accepted: 7 October 2020 © Springer Nature B.V. 2020
Abstract Polymers exhibit viscoelastic behavior: their mechanical response depends on the loading time, or on the loading frequency. In addition, if a polymer structure has a long service life, the mechanical behavior can also depend on physical aging and chemical degradation. This paper describes a thermodynamically consistent constitutive law taking into account the viscoelastic phenomena and the physical aging. First, an original nonlinear viscoelastic law, depending on the physical aging time, is developed. Then, considering experimental values of dynamic modulus from the literature, the model parameters are identified, using a new method based on the discrete form of the spectrum of relaxation time. The obtained model is numerically implemented and compared to experimental results. Keywords Constitutive law · Nonlinear viscoelasticity · Physical aging of polymer
1 Introduction Polymers exhibit viscoelastic behavior: their mechanical response depends on the loading time, or on the loading frequency (Findley et al. 1976). In the time domain, the relaxation experiment allows the characterization of the viscoelastic behavior (Knauss et al. 2006), in the form of relaxation modulus E(t), with t being the loading time. In the frequency domain, the Dynamical Mechanical Analysis (DMA) experiment permits one to identify the viscoelastic behavior (Knauss et al. 2006), in the form of the complex modulus E ∗ (ω), with ω being the angular frequency. The complex modulus is composed of a real part, the storage modulus E (ω), and an imaginary part, the loss modulus E (ω). The experimental procedure, for both DMA and relaxation experiments, is well described in the literature (Brinson 2008; Jalocha et al. 2015b; Ozupek 1989). Classic evolutions of the relaxation modulus and the complex modulus, taken from (Jalocha et al. 2015c), are respectively presented in Fig. 1(a) and Fig. 1(b). It is recalled in Eq. (1) that the dynamic modulus of a material in
B D. Jalocha
[email protected]
1
CEA CESTA, 15 Avenue des Sablieres, 33114 Le Barp, France
Mech Time-Depend Mater
Fig. 1 Schematic evolution of (a) relaxation modulus and (b) complex modulus, (Jalocha et al. 2015c) Fig. 2 Example of physical aging effect on the storage modulus for different elapsed time at 150o C (Haidar and Vidal 1996)
the frequency domain is equal to the Fourier transform of the relaxation modulus in the time domain, and vice versa (Markovitz and Hershel 1977), E ∗ (ω) = F (E(t)).
(1)
When a polymer structure has a long service life, another physical phenomenon appears: physical aging. Depending on the considered material and the application, the physical aging can affect the viscoelastic part of the material behavior. As an example, the effect of physical aging on the storage modulus of an amorphous polymer is presented in Fig. 2, for a strain amplitude of 0.1% and for d
Data Loading...
