Experimental and theoretical observations have agreed that the onset of cavitation in soft materials requires higher tensile pressure than pure water. The extra tensile pressure is required since the cavitating bubble needs to overcome the elastic energy in soft materials. In this manuscript, we have developed two models to study and quantify the extra tensile pressure. In the first approach, we proposed a strain energy based random fiber network (RFN) failure criteria in which interaction between the cavitating bubble and RFN is considered. Gelatin samples are prepared for different concentrations, and SEM images are used to study the microstructural properties of the RFN. A unit-cell model is introduced to evaluate the geometrical and mechanical properties of the RFN. The network strain energy formulation is then coupled with the bubble growth, and the critical condition is set as the fibers ultimate failure strain. We considered soft materials as homogeneous hyper-elastic Ogden material, and fracture-based failure criteria are proposed in the second approach. The critical energy release rate is considered for quantifying the extra tensile pressure. Both the models are then compared with the existing cavitation onset criteria of rubber like materials. The validation is done with the experimental results of threshold tensile pressure for different gelatin concentrations. We have found that due to the large distribution of the pore size in the network, the nucleation pressure is similar to water. Both models can moderately predict the extra tensile pressure within the intermediate range of gelatin concentrations. For low concentration, the network's non-affinity plays a significant role and must be incorporated. On the other hand, for higher concentrations, the entropic deformation dominates, and strain energy formulation is not adequate.
Nearly three decades ago, the field of mechanics was cautioned of the obscure nature of cavitation processes in soft materials [Gent, A.N., 1990. Cavitation in rubber: a cautionary tale. Rubber Chemistry and Technology, 63(3)]. Since then, the debate on the mechanisms that drive this failure process is ongoing. Using a high precision volume controlled cavity expansion procedure, this paper reveals the intimate relationship between cavitation and fracture. Combining a Griffith inspired formulation for crack propagation, and a Gent inspired formulation for cavity expansion, we show that despite …
We investigate dynamic fracture of heterogeneous materials experimentally by measuring displacement fields as a rupture propagates through a periodic array of obstacles of controlled fracture energy. Our measurements demonstrate the applicability of the classical equation of motion of cracks at a discontinuity of fracture energy: the crack speed jumps at the entrance and exit of an obstacle, as predicted by the crack-tip energy balance within the brittle fracture framework. The speed jump amplitude is governed by the fracture energy contrast and by the combination of rate-dependency of fractur…
Fracture in a disordered lattice system is studied. In our system, particles are initially arranged on the triangular lattice and each nearest-neighbor pair is connected with a randomly chosen soft or hard Hookean spring. Every spring has the common threshold of stress at which it is cut. We make an initial crack and expand the system perpendicularly to the crack. We find that the maximum stress in the stress-strain curve is larger than those in the systems with soft or hard springs only (uniform systems). Energy required to advance fracture is also larger in some disordered systems, which ind…
Entanglement of polymer chains is ubiquitous in elastomers, gels, and biological tissues. While the effects of chain entanglement on elasticity and viscoelasticity of polymer networks have been intensively studied, it remains elusive how chain entanglement affects fracture and fatigue of polymer networks. In this paper, using polyacrylamide hydrogels as a model material, we systematically compare fracture toughness and fatigue threshold of polymer networks with various levels of chain entanglement. We find that the fracture toughness and fatigue threshold of an unentangled polymer network are …
Hydrogels have the ability to undergo large deformations and yet fail like brittle materials. The development of biocompatible hydrogels with high strength and toughness is an ongoing challenge in many applications. We crosslinked bovine gelatin using glutaraldehyde (control) and methylglyoxal (MGO) and assessed changes in their fracture toughness. Swelling experiments show ~710% retention of water in MGO hydrogels as compared to ~450% in control specimens. We used FTIR to identify the presence of chemical groups that may be involved in the crosslinking of gelatin gels. Scanning electron micro…
Three dimensional calculations of ductile crack growth under mode I plane strain, small scale yielding conditions are carried out using an elastic-viscoplastic constitutive relation for a progres- sively cavitating plastic solid with two populations of void nucleating second phase particles. Full field solutions are obtained for three dimensional material microstructures characterized by ran- dom distributions of void nucleating particles. Crack growth resistance curves and fracture surface roughness statistics are calculated using standard procedures. The range of void nucleating particle vol…
Understanding the fracture toughness (resistance) of glasses is a fundamental problem of prime theoretical and practical importance. Here we theoretically study its dependence on the loading rate, the age (history) of the glass and the notch radius $ρ$. Reduced-dimensionality analysis suggests that the notch fracture toughness results from a competition between the initial, age- and history-dependent, plastic relaxation timescale $τ^{pl}_0$ and an effective loading timescale $τ^{ext}(\dot{K}_I,ρ)$, where $\dot{K}_I$ is the tensile stress-intensity-factor rate. The toughness is predicted to sca…
Brittle materials fail catastrophically. In consequence of their limited flaw-tolerance, failure occurs by localized fracture and is typically a dynamic process. Recently, experiments on epithelial cell monolayers have revealed that this scenario can be significantly modified when the material susceptible to cracking is adhered to a hydrogel substrate. Thanks to the hydraulic coupling between the brittle layer and the poroelastic substrate, such a composite can develop a toughening mechanism that relies on the simultaneous growth of multiple cracks. Here, we study this remarkable behaviour by …
Soft yet tough materials are ubiquitous in nature and everyday life. The ratio between fracture toughness and intrinsic fracture energy of a soft material defines its toughness enhancement. Soft materials' toughness enhancement has been long attributed to their bulk stress-stretch hysteresis induced by dissipation mechanisms such as Mullins effect and viscoelasticity. With a combination of experiments and theory, here we show that the bulk dissipation mechanisms significantly underestimate the toughness enhancement of soft tough materials. We propose a new mechanism and scaling law to account …
Using Brownian dynamics, we simulate the fracture of polymer interfaces reinforced by diblock connector chains. We find that for short chains the interface fracture toughness depends linearly on the degree of polymerization $N$ of the connector chains, while for longer chains the dependence becomes $N^{3/2}$. Based on the geometry of initial chain configuration, we propose a scaling argument that accounts for both short and long chain limits and crossover between them.
The formation and dynamics of cavities in liquids leads to focusing of kinetic energy and emission of longitudinal stress waves during the cavity collapse. Here we report that cavitation in elastic solids may additionally emit shear waves that could affect soft tissues in human bodies/brains. During collapse of the cavity close to an air-solid boundary, the cavity moves away from the boundary and forms a directed jet flow, which confines shear stresses in a volume between the bubble and the free boundary. Elastographic and high-speed imaging resolve this process and reveal the origin of a shea…
We combine molecular dynamics simulations of deformations at the submicron scale with a continuum fracture mechanics calculation for the onset of crack propagation to predict the macroscopic fracture toughness of amorphous glassy polymers. Key ingredients in this multiscale approach are the elastic properties of polymer crazes and the stress at which craze fibrils fail through chain pullout or scission. Our results are in quantitative agreement with dimensionless ratios that describe experimental polymers and their variation with temperature, polymer length and polymer rigidity.
Here, we report measurements of detailed dynamic cohesive properties (DCPs) beyond the dynamic fracture toughness of a bicontinuously nanostructured copolymer, polyurea, under an extremely loading rate, from deep-learning analyses of a dynamic big-data-generating experiment. We first describe a new Dynamic Line-Image Shearing Interferometer (DL-ISI), which uses a streak camera to record optical fringes of displacement-gradient vs time profile along a line on sample's rear surface. This system enables us to detect crack initiation and growth processes in plate-impact experiments. Then, we prese…
We explore the Mode I fracture toughness of a polymer gel containing a semi-infinite, growing crack. First, an expression is derived for the energy release rate within the linearized, small-strain setting. This expression reveals a crack tip velocity-independent toughening that stems from the poroelastic nature of polymer gels. Then, we establish a poroelastic cohesive zone model that allows us to describe the micromechanics of fracture in gels by identifying the role of solvent pressure in promoting poroelastic toughening. We evaluate the enhancement in the effective fracture toughness throug…
In this work we investigate the Orowan hypothesis, that decreases in surface energy due to surface adsorbates lead directly to lowered fracture toughness, at an atomic/molecular level. We employ a Lennard-Jones system with a slit crack and an infiltrating fluid, nominally with gold-water properties, and explore steric effects by varying the soft radius of fluid particles and the influence of surface energy/hydrophobicity via the solid-fluid binding energy. Using previously developed methods, we employ the J-integral to quantify the sensitivity of fracture toughness to the influence of the flui…
We examine how shell geometry affects fracture. As suggested by previous results and our own phase-field simulations, shell shape dramatically affects crack evolution and the effective toughness of the shell structure. To gain insight and eventually develop new concepts for optimizing the design of thin shell structures, we derive the configurational force conjugate to crack extension for Koiter's linear thin shell theory. We identify the conservative contribution to this force through an Eshelby tensor, as well as non-conservative contributions arising from curvature.
In our previous paper (Eur. Phys. J. E 4, 121 (2001)) we proposed a coarse-grained elastic energy for nacre, or stratified structure of hard and soft layers. We then analyzed a crack running perpendicular to the layers and suggested one possible reason for the enhanced toughness of this substance. In the present paper, we consider a crack running parallel to the layers. We propose a new term added to the previous elastic energy, which is associated with the bending of layers. We show that there are two regimes for the parallel-fracture solution of this elastic energy; near the fracture tip the…
Soft materials including elastomers and gels are pervasive in biological systems and technological applications. Whereas it is known that intrinsic fracture energies of soft materials are relatively low, how the intrinsic fracture energy cooperates with mechanical dissipation in process zone to give high fracture toughness of soft materials is not well understood. In addition, it is still challenging to predict fracture energies and crack-tip strain fields of soft tough materials. Here, we report a scaling theory that accounts for synergistic effects of intrinsic fracture energies and dissipat…
Molecular-dynamics simulations of fracture in metallic glass-like systems are observed to undergo embrittlement due to a small change in interatomic potential. This change in fracture toughness, however, is not accompanied by a corresponding change in flow stress. Theories of brittle fracture proposed by Freund and Hutchinson indicate that strain rate sensitivity is the controling physical parameter in these cases. A recent theory of viscoplasticity in this class of solids by Falk and Langer further suggests that the change in strain rate sensitivity corresponds to a change in the susceptibili…
We study experimentally the fracture mechanisms of a model cohesive granular medium consisting of glass beads held together by solidified polymer bridges. The elastic response of this material can be controlled by changing the cross-linking of the polymer phase, for example. Here we show that its fracture toughness can be tuned over an order of magnitude by adjusting the stiffness and size of the polymer bridges. We extract a well-defined fracture energy from fracture testing under a range of material preparations. This energy is found to scale linearly with the cross-sectional area of the bri…
Physically assembled gels have promising applications in many fields because of their tunable mechanical properties. Here, we report the mechanical properties as a function of polymer volume fraction ($ϕ$) for a physical gel system consists of poly(styrene)-poly(isoprene)-poly(styrene) [PS-PI-PS] in mineral oil. The PI-block molecular weight is higher than the entanglement molecular weight, which leads to the entanglement of PI-blocks at higher $ϕ$. The micellar microstructure for all gels results in a similar stress relaxation mechanism, as captured by the superposition of stress-relaxation r…
The fundamental problem of friction in the presence of macroscopic adhesion, as in soft bodies, is receiving interest from many experimentalists. Since the first fracture mechanics `purely brittle' model of Savkoor and Briggs, models have been proposed where the mixed mode toughness is interpreted with phenomenological fitting coefficients introducing weaker coupling between modes than expected by the "purely brittle" model. We compare here two such previously proposed models and introduce a third one to show that the transition to sliding is very sensitive to the form of the mixed-mode model.…
Cavitation is a common damage mechanism in soft solids. Here, we study this using a phase-separation technique in stretched, elastic solids to controllably nucleate and grow small cavities by several orders of magnitude. The ability to make stable cavities of different sizes, as well as the huge range of accessible strains, allows us to systematically study the early stages of cavity expansion. Cavities grow in a scale-free manner, accompanied by irreversible bond breakage that is distributed around the growing cavity, rather than being localized to a crack tip. Furthermore, cavities appear to…
Understanding the fracture toughness of glasses is of prime importance for science and technology. We study it here using extensive atomistic simulations in which the interaction potential, glass transition cooling rate and loading geometry are systematically varied, mimicking a broad range of experimentally accessible properties. Glasses' nonequilibrium mechanical disorder is quantified through $A_{\rm g}$, the dimensionless prefactor of the universal spectrum of nonphononic excitations, which measures the abundance of soft glassy defects that affect plastic deformability. We show that while …
