We study the relation between a threshold-force based model at the microscopic scale and mode I fracture at the macroscopic scale in a system of discrete interacting springs. Specifically, we idealize the contact between two surfaces as that between a rigid surface and a collection of springs with long-range interaction and a constant tensile threshold force. We show that a particular scaling similar to that of crack-tip stress in Linear Elastic Fracture Mechanics leads to a macroscopic limit behavior. The model also reproduces the scaling behaviors of the JKR model of adhesive contact. We determine how the threshold force depends on the fracture energy and elastic properties of the material. The model can be used to study rough-surface adhesion.
Tough adhesive hydrogels find broad applications in engineering and medicine. Such hydrogels feature high resistance against both cohesion and adhesion failure. The superior fracture properties may, however, deteriorate when the hydrogels swell upon exposure of water. The underlying correlation between the polymer fraction and fracture properties of tough adhesive hydrogels remains largely unexplored. Here we study how the cohesion and adhesion energies of a tough adhesive hydrogel evolve with the swelling process. The results reveal a similar scaling law of the two quantities on the polymer f…
Adhesion between a viscoelastic material and a solid surface
在本文中，我们提出了一个定性的耗散过程中的粘弹性聚合物和固体表面之间的界面破坏的分析。我们重新评估“粘弹性喇叭”模型[P. - G. de Gennes，C. R. Acad. Sci. Paris，307，1949（1988）]，并且表明，对于交联聚合物，由于断裂尖端附近的局部过程，界面韧性G（V）从相对低的值G_0开始，并且上升到最大值$G_0 (μ_{\infty}/μ_0)$（其中$μ_0$和$μ_{\infty}$分别代表材料在低应变频率和高应变频率下的弹性模量）。这种增强的断裂能是由于远场粘性耗散的散装材料，并开始剥离率V远低于以前认为的。对于一个聚合物熔体，粘附能预计规模为1/V。在本文的第二部分中，我们比较了我们的一些理论预测与实验结果之间的粘弹性粘附聚二甲基硅氧烷聚合物熔体和玻璃表面。特别是，预期的依赖性的断裂能与分离率的实验数据证实，和观察到的变化，在裂纹轮廓的宽度与我们的简单模型是很好的协议。
As recently suggested in an interestring and stimulating paper by Menga, Carbone & Dini (MCD), applying fracture mechanics energy concepts for the case of a sliding adhesive contact, imposing also the shear stress is constant at the interface and equal to a material constant (as it seems in experiments), leads to a increase of contact area which instead is never observed. We add that the rigorous MCD theory also predict a size effect and hence a distortion of the JKR curve during sliding which is also not observed in experiments. Finally, a simpler example with the pure mode I contact case, le…
The wear volume is known to keep increasing during frictional processes, and Archard notably proposed a model to describe the probability of wear particle formation upon asperity collision in a two-body contact configuration. While this model is largely adopted in the investigations of wear, the presence of wear debris trapped between the surfaces changes the system into a three-body contact configuration already since the early stages of the process. In such a configuration, a significant amount of wear is produced at the interface between the trapped debris and the sliding bodies. Here, rely…
Recently, tribologists have shown increasing interest in rate-dependent phenomena occurring in viscoelastic fractures. However, in some cases, conflicting results are obtained despite the use of similar theoretical models. For this reason, we try to shed light on the effects that long and short-range adhesion has on the pull-off force in the contact of viscoelastic media by exploiting a recently developed numerical model. We find that, in the limit of long-range adhesion, the unloading velocity has little effect on the pull-off force, which is close to the value predicted by Bradley for rigid …
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.…
This paper gives a theoretical analysis for the fundamental problem of anisotropy induced by shear forces onan adhesive contact, discussing the experimental data of the companion Letter. We present a fracture mechanicsmodel where two phenomenological mode-mixity functions are introduced to describe the weak couplingbetween modes I and II or I and III, which changes the effective toughness of the interface. The mode-mixityfunctions have been interpolated using the data of a single experiment and then used to predict the behavior of thewhole set of experimental observations. The model extends an…
In earlier papers (Leblond et.al., 2011, 2019), we presented linear stability analyses of the coplanar propagation of a crack loaded in mixed-mode I+III, based on a "double'' propagation criterion combining Griffith (1920)'s energetic condition and Goldstein and Salganik (1974)'s principle of local symmetry. The difference between the two papers was that in the more recent one, the local value of the critical energy-release-rate was no longer considered as a constant, but heuristically allowed to depend upon the ratio of the local mode III to mode I stress intensity factors. This led to a much…
Mixed mode (I+III) loading induces segmented crack front échelon structures connected by steps. We study this instability in a highly deformable, strain-hardening material. We find that échelons develop beyond a finite, size-independent mode mixity threshold, markedly growing with energy release rate. They appear via nucleation of localized helical front distortions, and their emergence is the continuation of the mode I cross-hatching instability of gels and rubbers, shifted by the biasing effect of shear. This result, at odds with the direct bifurcation predicted by linear elastic fracture me…
The emerging applications of hydrogels in devices and machines require these soft materials to maintain robustness under cyclic mechanical loads. Whereas hydrogels have been made tough to resist fracture under a single cycle of mechanical load, these toughened gels still suffer from fatigue fracture under multiple cycles of loads. The reported fatigue threshold (i.e., the minimal fracture energy at which crack propagation occurs under cyclic loads) for synthetic hydrogels is on the order of 1-100 J/m2, which is primarily associated with the energy required to fracture a single layer of polymer…
A phase-field model is used to capture the surfactant-driven formation of fracture patterns in particulate monolayers. The model is intended for the regime of closely-packed systems in which the mechanical response of the monolayer can be approximated as a linearly elastic solid. The model approximates the loss in tensile strength of the monolayer as the surfactant concentration increases through the evolution of a damage field. Initial-boundary value problems are constructed and spatially discretized with finite element approximations to the displacement and surfactant damage fields. A compar…
In this work the computer modeling has been used to show that longer ligands allow biological cells (e.g., blood platelets) to withstand stronger flows after their adhesion to solid walls. Mechanistic model of polymer-mediated ligand-receptor adhesion between a microparticle (cell) and a flat wall has been developed. Theoretical threshold between adherent and non-adherent regimes has been derived analytically and confirmed by simulations. These results lead to a deeper understanding of numerous biophysical processes, e.g., arterial thrombosis, and to the design of new biomimetic colloid-polyme…
In a previous paper (Leblond et al., 2011), we proposed a theoretical interpretation of the experimentally well known instability of coplanar crack propagation in mode I+III. The interpretation relied on a stability analysis based on analytical expressions of the stress intensity factors for a crack slightly perturbed both within and out of its original plane, due to Gao and Rice (1986) and Movchan et al. (1998), coupled with a double propagation criterion combining Griffith's energetic condition and principle of local symmetry. Under such assumptions instability modes were indeed evidenced fo…
Tunable mechanics and fracture resistance are hallmarks of biological tissues and highly desired in engineered materials. To elucidate the underlying mechanisms, we study a rigidly percolating double network (DN) made of a stiff and a flexible network. The DN shows remarkable tunability in mechanical response when the stiff network is just above its rigidity percolation threshold and minimal changes far from this threshold. Further, the DN can be modulated to either be extensible, breaking gradually, or stronger, breaking in a more brittle fashion by varying the flexible network's concentratio…
Adhesive [e.g. van der Waals] forces were not generally taken into account in contact mechanics until 1971, when Johnson, Kendall and Roberts (JKR) generalized Hertz' solution for an elastic sphere using an energetic argument which we now recognize to be analogous to that used in linear elastic fracture mechanics. A significant result is that the load-displacement relation exhibits instabilities in which approaching bodies `jump in' to contact, whereas separated bodies `jump out' at a tensile `pull-off force'. The JKR approach has since been widely used in other geometries, but at small length…
By performing extensive simulations with unprecedentedly large system sizes, we unveil how rigidity influences the fracture of disordered materials. We observe the largest damage in networks with connectivity close to the isostatic point and when the rupture thresholds are small. However, regardless of network and spring properties, a more brittle fracture is observed upon increasing system size. Differently from most of the fracture descriptors, the maximum stress drop, a proxy for brittleness, displays a universal non-monotonic dependence on system size. Based on this uncommon trend it is po…
We study numerically local models for the mechanical contact between two solids with rough surfaces. When the solids softly touch either through adhesion or by a small normal load $L$, contact only forms at isolated patches and fluids can pass through the interface. When the load surpasses a threshold value, $L_c$, adjacent patches coalesce at a critical constriction, i.e., near points where the interfacial separation between the undeformed surfaces forms a saddle point. This process is continuous without adhesion and the interfacial separation near percolation is fully defined by scaling fact…
Strengthening of materials and preventing abrupt fracture are really challenging jobs in the field of engineering and material science. Such problems can be resolved by using composite materials. In this work, we have studied the fracture process of a composite material in light of fiber bundle model with different elastic constants as well as different random threshold breaking strength of fibers. The critical width of the threshold distribution ($δ_c$), for which abrupt failure occurs, is studied both analytically and numerically with increasing number of components $(k)$ in the composite an…
We study the influence of thermal fluctuations on the fracture of elastic networks, via simulations of the uniaxial extension of central-force spring networks with varying rigidity, i.e. connectivity. Studying their failure response, both at the macroscopic and microscopic level, we find that an increase in temperature corresponds to a more homogeneous stress (re)distribution and induces thermally activated failure of springs. As a consequence, the material strength decreases upon increasing temperature, the damage is spread over larger lengthscales and a more ductile fracture process is obser…
The deposition of oil drops on solid substrates from mixed solutions of surfactants and cationic polymer is investigated. The used anionic surfactants are sodium laurylethersulfate (SLES) and sulfonated methyl esters (SME); the zwitterionic surfactant is cocamidopropyl betaine (CAPB). A new method, called the pressed drop method (PDM), was proposed to study the drop adhesion to substrates of different hydrophobicity. The PDM allows one to detect the presence or absence of drop adhesion at different degrees of dilution of the initial solution and, thus, to determine the threshold concentration …
At the molecular scale there are strong attractive interactions between surfaces, yet few macroscopic surfaces are sticky. Extensive simulations of contact by adhesive surfaces with roughness on nanometer to micrometer scales are used to determine how roughness reduces the area where atoms contact and thus weakens adhesion. The material properties, adhesive strength and roughness parameters are varied by orders of magnitude. In all cases the area of atomic contact rises linearly with load, and the prefactor rises linearly with adhesive strength for weak interactions. Above a threshold adhesive…
