Novel features of the Mullins effect in filled elastomers revealed by stretching measurements in various geometries

Abstract

Stretching experiments with various geometries are performed using a custom-built tensile tester to reveal the intriguing features of the mechanical softening phenomena of filled elastomers in loading-unloading cycles, commonly known as the Mullins effect. The dissipated energy (D), residual strain (ε), and dissipation factor (Δ; the ratio of D to input strain energy) in the loading-unloading cycles are evaluated as a function of the maximum stretch in cyclic loading (λ) using three types of extension, i.e., uniaxial, planar, and equibiaxial extension, for silica-filled elastomers with various filler contents, and with or without a silane coupling agent. The dissipated energy D and ε increase with an increase in λ, and they depend on the type of extension when compared at the same λ: D and ε increase in the order of equibiaxial, planar, and uniaxial extension. In contrast, the values of Δ obtained for various degrees and types of extension are collapsed into a single curve when the first invariant of the deformation tensor (I) corresponding to λ is employed as a variable: Δ steeply increases with an increase in I in the small deformation regime of I < 3.2, while Δ levels off in the large deformation regime of I > 3.5. The plateau values of Δ increase with an increase in filler content. The characteristic dependence of Δ on I in each of the small and large deformation regimes is expected to reflect the destruction process of the inherent structures, including filler networks and the filler-polymer interface, and the friction between the fillers and the rubber matrix, respectively.

Probing the in-plane liquid-like behavior of liquid crystal elastomers

“…The effects of the complicated deformation around the chucks on the detected force will likely be small as the corresponding area is small relative to the area subjected to the uniform strain field. It was confirmed for conventional elastomers and gels that the corresponding effect is negligibly small in the present custom-made biaxial testers ( 38 , 43 ). These biaxial testers require the relatively large specimens (65 mm by 65 mm), and this requirement is for satisfying the condition in which the detected force is governed by the area subjected to the uniform strain field.…”

“…Each of the biaxial testers is optimized for the measurements of considerably soft gels or rigid elastomers. The details of each tester were described elsewhere ( 38 , 43 ). The two tensile forces in the orthogonal directions ( f x and f y , respectively) were measured as the functions of the stretch ratios in the x and y directions (λ x and λ y , respectively): λ i = l i / l 0 where l i and l 0 are the dimensions in the deformed and undeformed states in the i direction ( i = x , y ).…”

The Influence of Filler Size and Crosslinking Degree of Polymers on Mullins Effect in Filled NR/BR Composites

“…It should be considered that the input energy by loading ( W 0 ) increases with the increase of ε m , resulting in increased D at the same time [ 48 ]. In order to compare energy dissipation D with consideration of W 0 among the deformations under various degrees of strain, a derived parameter ‘dissipation factor’ ( Δ ) can be defined as the ratio of energy dissipation to the stored elastic energy of loading (input elastic energy): …”

Investigating the Mullins Effect and Energy Dissipation in Magnetorheological Polyurethane Elastomers

“…The area enclosed by the loading and unloading curves shown in Figure 1 provides a schematic view of the energy dissipated during one cycle [ 17 ]. Moreover, the virgin material Cauchy-stress components are determined from: in which Equation (7) has been considered.…”

“…Since the energy dissipated for each loading–unloading cycle is expected to increase with an increase in the elastic energy , the dissipation factor is introduced in an attempt to quantify the differences among the tested material samples. This dissipation factor differs from that proposed by Mai et al in [ 17 ] since in our definition, we compute the ratio of energy dissipation to the maximum strain energy density at which unloading starts, while in the definition introduced in [ 17 ], the dissipation ratio is defined as the ratio of the energy dissipation to the strain energy density of the loading curve.…”