Distinctive Characteristics of Internal Fracture in Tough Double Network Hydrogels Revealed by Various Modes of Stretching

Strain hardening in biaxially stretched elastomers undergoing strain-induced crystallization

We reveal strain hardening due to strain-induced crystallization (SIC) in both cross-linked natural rubber (NR) and its synthetic analogue (IR) under planar extension, a type of biaxial stretching where the rubber is stretched in one direction while maintaining the dimension in the other direction unchanged. Utilizing a bespoke biaxial tensile tester, planar extension tests were conducted on geometrically designed and optimally shaped sheet specimens to achieve a uniform and highly strained field. Evident strain hardening due to SIC was observed in both stretching (x) and constrained (y) directions when the stretch (λx) exceeded a critical value λx,c. The λx,c value aligned with the onset stretch of SIC in planar extension, as determined by wide-angle X-ray scattering measurements. Interestingly, the nominal stress ratio between the constrained (σy) and stretching (σx) axes as a function of λx exhibited a distinct minimum near λx,c. This minimum signifies that the increment of σx induced by an increase in λx surpasses that of σy before strain hardening (λx < λx,c), while the relationship is reversed in the strain hardening region (λx > λx,c). The λx,c value in planar extension (4.7 for IR and 4.5 for NR) was slightly lower than that in uniaxial extension (5.7 for IR and 5.2 for NR). This difference in λx,c values can be explained by considering a single mechanical work required for strain hardening, owing to the relatively small dissimilarities between the two stretching modes. This investigation contributes significantly to the understanding of SIC phenomena in biaxial stretching, and provides valuable insights for predicting the mechanical response of SIC rubber under various deformation conditions.

Inverse mechanical-swelling coupling of a highly deformed double-network gel

Mechanical behaviors of a polymer gel are coupled with its swelling behavior. It has been known that typical hydrogels display extension-induced swelling and drying-induced stiffening, called normal mechanical-swelling coupling. In this study, we experimentally found that highly extended double-network (DN) hydrogels exhibit abnormal inverse mechanical-swelling coupling such as extension-induced deswelling and drying-induced softening. We established theoretical hyperelastic and swelling models that reproduced all the complicated mechanical and swelling trends of the highly deformed DN hydrogels. From these theoretical analyses, it is considered that the inverse mechanical-swelling coupling of a DN gel is derived from the extreme nonlinear elasticity of its first network at its ultimate deformation state. These findings contribute toward the understanding of the mechanics of rubber-like materials up to their ultimate deformation and fracture limit.

Toughness of Network Materials: Structural Parameters Controlling Damage Accumulation

Many materials have a network of fibers as their main structural component and are referred to as network materials. Their strength and toughness are important in both engineering and biology. In this work we consider stochastic model fiber networks without pre-existing cracks and study their rupture mechanism. These materials soften as the crosslinks or fibers fail and exhibit either brittle failure immediately after the peak stress, or a more gradual, ductile rupture in the post peak regime. We observe that ductile failure takes place at constant energy release rate defined in the absence of pre-existing cracks as the strain derivative of the specific energy released. The network parameters controlling the energy release rate are identified and discussed in relation to the Lake-Thomas theory which applies to crack growth situations. We also observe a ductile to brittle failure transition as the network becomes more affine and relate the embrittlement to the reduction of mechanical heterogeneity of the network. Further, we confirm previous reports that the network strength scales linearly with the bond strength and with the crosslink density. The present results extend the Lake-Thomas theory to networks without pre-existing cracks which fail by the gradual accumulation of distributed damage and contribute to the development of a physical picture of failure in stochastic network materials.

Stretchy and disordered: Toward understanding fracture in soft network materials via mesoscopic computer simulations

Soft network materials exist in numerous forms ranging from polymer networks, such as elastomers, to fiber networks, such as collagen. In addition, in colloidal gels, an underlying network structure can be identified, and several metamaterials and textiles can be considered network materials as well. Many of these materials share a highly disordered microstructure and can undergo large deformations before damage becomes visible at the macroscopic level. Despite their widespread presence, we still lack a clear picture of how the network structure controls the fracture processes of these soft materials. In this Perspective, we will focus on progress and open questions concerning fracture at the mesoscopic scale, in which the network architecture is clearly resolved, but neither the material-specific atomistic features nor the macroscopic sample geometries are considered. We will describe concepts regarding the network elastic response that have been established in recent years and turn out to be pre-requisites to understand the fracture response. We will mostly consider simulation studies, where the influence of specific network features on the material mechanics can be cleanly assessed. Rather than focusing on specific systems, we will discuss future challenges that should be addressed to gain new fundamental insights that would be relevant across several examples of soft network materials.

Marked Sensitivity of Ultimate Elongation to Loading Axiality in Polyrotaxane Gels with Largely Slidable Cross Links

Polyrotaxane (PR) gels with low ring densities have figure-of-eight cross links that can slide along network strands. The slidable cross links have a unique ability to increase the network strand length between adjacent cross links in the loading direction via chain supply from the stress-free direction, thereby enhancing the ultimate elongation (λ_m) of the gels. We reveal that this enhancement of λ_m due to the slidable cross links is pronounced specifically in uniaxial stretching, while it is considerably modest in biaxial stretching. The sensitivity of λ_m to loading axiality becomes larger as the ring densities decrease. The corresponding difference in λ_m is markedly larger for the PR gels with low ring densities than that for the networks with fixed cross links. The exceptional sensitivity of λ_m to loading axiality unveils a previously unidentified aspect of the chain-supply mechanism based on slidable cross links.

Toughening hydrogels through force-triggered chemical reactions that lengthen polymer strands

[Figure: see text].

Sharing the Load: Stress Redistribution Governs Fracture of Polymer Double Networks

The stress response of polymer double networks depends not only on the properties of the constituent networks but also on the interactions arising between them. Here, we demonstrate, via coarse-grained simulations, that both their global stress response and their microscopic fracture mechanics are governed by load sharing through these internetwork interactions. By comparing our results with affine predictions, where stress redistribution is by definition homogeneous, we show that stress redistribution is highly inhomogeneous. In particular, the affine prediction overestimates the fraction of broken chains by almost an order of magnitude. Furthermore, homogeneous stress distribution predicts a single fracture process, while in our simulations, fracture of sacrificial chains takes place in two steps governed by load sharing within a network and between networks, respectively. Our results thus provide a detailed microscopic picture of how inhomogeneous stress redistribution after rupture of chains governs the fracture of polymer double networks.

Strength of stochastic fibrous materials under multiaxial loading

Many biological and engineering materials are made from fibers organized in the form of a stochastic crosslinked network, and the mechanics of the network controls the behavior of the material. In this work we investigate the strength of stochastic networks without pre-existing damage which fail due to crosslink rupture. Athermal networks ranging from approximately affine to strongly non-affine are subjected to multiaxial loading and the strength is evaluated using numerical models. It is observed that once the stress is normalized by the strength measured in uniaxial tension, the failure surface becomes approximately independent of network parameters. This extends the relation between strength and network parameters previously established in (S. Deogekar, M. R. Islam, R. C. Picu, Parameters controlling the strength of stochastic fibrous materials, Int. J. Solids Struct., 2019, 168, 194-202) to the multiaxial case. The failure surface depends on both first two invariants of the stress. Strongly non-affine networks behave somewhat different from the affine networks under loadings close to the hydrostatic and pure shear loading modes, while the difference disappears in the first quadrant of the principal stress space. The results are compared with experimental data from the literature.

Tough combinatorial poly(urethane-isocyanurate) polymer networks and hydrogels synthesized by the trimerization of mixtures of NCO-prepolymers

The development of tough hydrogels is an essential but challenging topic in biomaterials research that has received much attention over the past years. By the combinatorial synthesis of polymer networks and hydrogels based on prepolymers with different properties, new materials with widely varying characteristics and unexpected properties may be identified. In this paper, we report on the properties of combinatorial poly(urethane-isocyanurate) (PUI) type polymer networks that were synthesized by the trimerization of mixtures of NCO-functionalized poly(ethylene glycol) (PEG), poly(propylene gylcol) (PPG), poly(ε-caprolactone) (PCL) and poly(trimethylene carbonate) (PTMC) prepolymers in solution. The resulting polymer networks showed widely varying material properties. Combinatorial PUI networks containing at least one hydrophilic PEG component showed high water uptakes of >100 wt%. The resulting hydrogels demonstrated elastic moduli of up to 10.1 MPa, ultimate tensile strengths of up to 9.8 MPa, elongation at break values of up to 624.0% and toughness values of up to 53.4 MJ m^-3. These values are exceptionally high and show that combinatorial PUI hydrogels are among the toughest hydrogels reported in the literature. Also, the simple two-step synthesis and wide range of suitable starting materials make this synthesis method more versatile and widely applicable than the existing methods for synthesizing tough hydrogels. An important finding of this work is that the presence of a hydrophobic network component significantly enhances the toughness and tensile strength of the combinatorial PUI hydrogels in the hydrated state. This enhancement is the largest when the hydrophobic network component is crystallizable in nature. In fact, the PUI hydrogels containing a crystallizable hydrophobic network component are shown to be semi-crystalline in the water-swollen state. Due to their high toughness values in the water-swollen state together with their water uptake values, elastic moduli and ultimate tensile strengths, the developed hydrogels are expected to be promising materials for biomedical coating- and adhesive applications, as well as for tissue-engineering. STATEMENT OF SIGNIFICANCE: The development of tough hydrogels is a challenging topic that has received much attention over the past years. At present, double network type hydrogels are considered state-of-the-art in the field, demonstrating toughness values of several tens of MJ m^-3. However, in terms of ease and versatility of the synthesis method, the possibilities are limited using a double network approach. In this work, we present combinatorial poly(urethane-isocyanurate) type polymer networks and hydrogels, synthesized by the trimerization of mixtures of NCO-functionalized prepolymers. The resulting hydrogels demonstrate exceptionally high toughness values of up to 53 MJ m^-3, while the synthesis method is versatile and widely applicable. This new class of hydrogels is therefore considered highly promising in the future development of load-bearing biomaterials.

Damage cross-effect and anisotropy in tough double network hydrogels revealed by biaxial stretching

Anisotropy of strain-induced internal damage in tough double network (DN) hydrogels is characterized by a sequence of two tensile experiments. Firstly, the virgin DN gels are subjected to a single biaxial loading-unloading cycle using various combinations of the two maximum strains λx,m and λy,m in the x- and y-directions (λx,m ≥ λy,m). Secondly, the rectangular subsamples, which are cut out from the unloaded specimens so that the long axis can have an angle (θ) relative to the larger pre-strain (x-)axis, are stretched uniaxially along the long axis. Directional internal damage caused by various types of pre-stretching is evaluated by comparing the loading curves of the virgin gels and the subsamples with various θ. The modulus reduction (ΔEθ) and strain-energy reduction (Dθ) are characterized as functions of λx,m, λy,m and θ. The anisotropy of damage increases with the anisotropy of imposed pre-strain field as well as λx,m, which is also observed in the anisotropic re-swelling behavior of the subsamples. The damage and the extensibility of the subsamples with θ = 0° increase with λy,m, and the damage of the subsamples with θ = 90° significantly increases with λx,m. These results reveal the presence of a pronounced damage cross-effect: a finite portion of the chain fractures in the first brittle network in one direction is caused by loading in the other orthogonal direction. This feature is in contrast to the very modest damage cross-effect in the silica reinforced elastomers, which show apparently similar stress-softening behavior but with a different origin. The strong damage cross-effect is a key feature of the internal fracture mechanism of the tough DN gels.