Strain softening of nano-scale fuzzy interfaces causes Mullins effect in thermoplastic polyurethane

Abstract

The strain-induced softening of thermoplastic polyurethane elastomers (TPUs), known as the Mullins effect, arises from their multi-phase structure. We used the combination of small- and wide- angle X-ray scattering (SAXS/WAXS) during in situ repeated tensile loading to elucidate the relationship between molecular architecture, nano-strain, and macro-scale mechanical properties. Insights obtained from our analysis highlight the importance of the 'fuzzy interface' between the hard and soft regions that governs the structure evolution at nanometre length scales and leads to macroscopic stiffness reduction. We propose a hierarchical Eshelby inclusion model of phase interaction mediated by the 'fuzzy interface' that accommodates the nano-strain gradient between hard and soft regions and undergoes tension-induced softening, causing the Mullins effect that becomes apparent in TPUs even at moderate tensile strains.

Figure 1

Structural evolution of 2D scattering patterns and 1-D profiles. Selected (a) SAXS patterns and (b) WAXS patterns for final loading stage (0.2–10 N); the family of equivalent 1D profiles of scattered (c) SAXS intensity with Gaussian curve fitting and (d) WAXS intensity with Gaussian curve fitting.

Figure 2

Multi-scale strains visualization. (a) Macroscopic strain evolution registered by Deben loading rig; (b) Nano-scale strain evolution interpreted from SAXS patterns along loading direction; (c) Atomic scale strain evolution derived from four diffraction peaks of WAXS patterns; (d) Crystallinity evolution obtained from WAXS patterns.

Figure 3

Softening behavior during cycles at different length scales. Macroscopic strain evolution of (a) unloading for each cycle; nano-scale strain evolution of (b) unloading for each cycle; atomic strain evolution (from peak 2) of (c) unloading for each cycle.

Figure 4

Illustrations of TPU representative volume element and the double-inclusion model. TPU is thought of as consisting of hard regions (HR) embedded within contiguous soft region (SR) matrix, with gradient transitions between HR and SR that are structurally accommodated by the “fuzzy interface” (FI). In the double-inclusion model, at level 1, the inclusions represent the combination of HR & FI, and SR serves as the matrix. At level 2, the inclusion represents only the HR, and FI serves as the matrix.

Figure 5

Schematic diagram showing softening mechanism of fuzzy interface. The overall softening process causes gradual destruction of the physical cross-links across the fuzzy interface zone, where the electron density drops steeply from the HR to SR value. This leads to a strong variation of material stiffness as a function of deformation in the fuzzy interface region (FI), whereas the stiffness values in the HR and SR remain largely unchanged.