A thermo-mechanically-coupled large-deformation theory for amorphous polymers in a temperature range which spans their glass transition

Abstract

Amorphous thermoplastic polymers are important engineering materials; however, their nonlinear, strongly temperature-and rate-dependent elastic-viscoplastic behavior is still not very well understood, and is modeled by existing constitutive theories with varying degrees of success. There is no generally agreed upon theory to model the large-deformation, thermo-mechanically-coupled, elastic-viscoplastic response of these materials in a temperature range which spans their glass transition temperature. Such a theory is crucial for the development of a numerical capability for the simulation and design of important polymer processing operations, and also for predicting the relationship between processing methods and the subsequent mechanical properties of polymeric products. In this paper we extend our recently published theory , IJP 25, 1474-1494Ames et al., 2009, IJP 25, 1495-1539 to fill this need.We have conducted large strain compression experiments on three representative amorphous polymeric materials -a cyclo-olefin polymer (Zeonex-690R), polycarbonate (PC), and poly(methyl methacrylate) (PMMA) -in a temperature range from room temperature to approximately 50C above the glass transition temperature, ϑ g , of each material, in a strain-rate range of ≈ 10 −4 to 10 −1 s −1 , and compressive true strains exceeding 100%. We have specialized our constitutive theory to capture the major features of the thermomechanical response of the three materials studied experimentally.We have numerically implemented our thermo-mechanically-coupled constitutive theory by writing a usermaterial subroutine for a widely-used finite element program. In order to validate the predictive capabilities of our theory and its numerical implementation, we have performed the following validation experiments: (i) a plane-strain forging of PC at a temperature below ϑ g , and another at a temperature above ϑ g ; (ii) blowforming of thin-walled semi-spherical shapes of PC above ϑ g ; and (iii) microscale hot-embossing of channels in Zeonex and PMMA above ϑ g . By comparing the results from this suite of validation experiments of some key features, such as the experimentally-measured deformed shapes and the load-displacement curves, against corresponding results from numerical simulations, we show that our theory is capable of reasonably accurately reproducing the experimental results obtained in the validation experiments.

Effect of microstructure on anomalous strain-rate-dependent behaviour of bacterial cellulose hydrogel

“…Most traditional viscoelastic materials are characterised by strain-rate hardening with a positive ; still, in some special cases, strain-rate softening was documented. As an example, Srivastava et al [23] found that amorphous polymer Zeonex-690R exhibited strain-rate softening at large deformations at high strain rate (0.3 s -1 ), suggesting the effect of adiabatic heating (thermal softening). In the work of Canadinc et al [28], negative strain-rate-sensitivity of Hadfield steel polycrystals was determined mainly due to dynamic strain aging (Portevin-Le Chatelier effect).…”

“…The effect of temperature and strain rate on material's performances is widely studied, both theoretically and experimentally, owing to thermal softening and viscous properties, respectively [19] . A typical behaviour of thermal-softening and strain-rate-dependent hardening is well documented [20,21,22], with strain-rate softening of amorphous polymers at large deformations and high strain rates reported, as a result of quasi-adiabatic heating leading to thermal softening [23]. Some studies were focused on strain-rate behaviour of BC hydrogels; as an example, out-of-plane compressive response of BC hydrogel at various strain rates was studied by Lopez-Sanchez et al [24], showing the effect of water motion in the process of compression.…”

Multi-mechanism modeling of amorphous polymers

“…The identification procedure is performed similarily to that described above for each temperature. (Zaïri et al, 2005b) 5 Finite element analysis of plane forging of PC In this section, FE simulations of plane-strain forging experiments at 25 • C, under isothermal conditions, were performed on PC specimens as in the work of (Srivastava et al, 2010). A circular cross-section specimen having a diameter of 12.7mm is forged to "cruciform" specimen.…”

“…Various models were developed and tested to simulate these responses. Rheological models extended to three-dimensional case under finite strain assumption have been proposed, for instance, by (Alcoutlabi and MartinezVega, 2003;Anand and Ames, 2006;Dupaix and Boyce, 2007;Ames et al, 2009;Anand et al, 2009;Srivastava et al, 2010;Shim and Mohr, 2011;Fleischhauer et al, 2012;Helbig and Seelig, 2012). Some of them were devoted to phenomenological modeling (Zaïri et al, 2005b;Cheng and Ghosh, 2013) or developed within a thermodynamics framework (Drozdov, 1999;Miehe et al, 2009;Bouvard et al, 2013).…”

“…A detailed identification procedure of the material parameters is shown in section 3. In section 5, a FE (finite element) simulations of plane-strain forging experiments at 25 • C, under isothermal conditions, were performed on PC specimens as in the work of (Srivastava et al, 2010). In that section, the material parameters are first identified using the stressstrain curves.…”