Constitutive modeling of strain-induced crystallization in filled rubbers

Abstract

Strain-induced crystallization is a unique crystallization process taking place solely in polymers subjected to large deformations. It plays a major role for reinforcement and improvement of mechanical properties of polymers with a high regularity of the molecular structure. In this paper, we develop a micromechanical model for the strain-induced crystallization in filled rubbers. Accordingly, the strain-induced crystallization is considered as a process triggered by fully stretched and continued by semistretched polymer chains. The model extends the previously proposed network evolution model [Dargazany and Itskov, Int. J. Solids Struct. 46, 2967 (2009)] and can thus, in addition to the stress upturn and evolution of crystallinity, take into account several inelastic features of filled rubbers, such as the Mullins effect, permanent set, and induced anisotropy. Finally, the accuracy of the model is verified against different set of experimental data both with respect to the stress-strain and crystallization-strain relations. The model exhibits good agreement with the experimental results, which, besides its relative simplicity, makes it a good option for finite-element implementations.

Effects of incremental depth and tool rotation on failure modes and microstructural properties in Single Point Incremental Forming of polymers

“…14c and d) might be due to strain-induced crystallization (SIC) that is observed in solid polymers (Dargazany et al, 2014). In strain-induced crystallization, the crystal morphology maybe fringed-micelle, folded-chain, extended-chain, or a combination of these and further investigations are needed to elucidate the polymer-chain orientations.…”

Coupled thermomechanical model for strain‐induced crystallization in polymers

“…1) show that the stress response builds a hysteresis which indicates that the process has a dissipative character. Most of the models focusing on the mechanical modeling of polymers use the Langevin expression for the free energy as a basis [2,3]. At the stretch of 600% the crystallinity degree reaches 15% (Fig.…”

Phase field modelling of strain induced crystal growth in an elastic matrix

“…3,5,6 Since the discovery of SIC in NR by Katz in 1925, 7,8 many experimental 1,2,[9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26] and theoretical [27][28][29][30][31][32] studies have been made in order to understand it. Experimentally, several techniques have been used with NR, synthetic rubber, and NR carbon-filled, such as birefringence, 12,13 infrared absorption, 14,15 differential scanning calorimetry (DSC), 16 and X-ray diffraction.…”

“…17,25,26 At the same time, numerous theoretical attempts to describe and understand the SIC have been proposed in the literature. [27][28][29][30][31][32] Two approaches are currently widely used in the field: crystalline morphology models [38][39][40] and more global thermodynamic 28,41,42 or kinetic models. We can mention Avrami's model for semi-crystalline polymer 43,44 or the kinetic folded chain model 39,[45][46][47] that provides only global information on the crystallinity.…”

“…41,42,[48][49][50][51] Assuming that the network chains are in thermodynamic equilibrium and using a mean statistical mechanical treatment of the deformation, he could show that crystallites can form spontaneously under traction, and that the formation of the crystal phase leads to stress relaxation in the system. Although more recent constitutive equations 31,52 and phenomenological models 53 have been proposed to highlight the impact of the crystallization on the mechanical behavior of cross-linked NR, the Flory model is still widely used because it gives a physical understanding of the SIC. However, this model is purely static and does not provide information on the shape of the crystallites or on the microstructure.…”