Fracture Of Elastomers Research Articles

Size-dependent fracture in elastomers: Experiments and continuum modeling

Size-dependent fracture in elastomers: Experiments and continuum modeling

Phase field modeling on fracture behaviors of elastomers considering deformation-dependent and damage-dependent material viscosity

Elastomers have attracted great research interests owing to their high compliance and large deformation capacity. However, with inevitable flaws, elastomers are susceptible to rupture, leading to reduction in stretchability and loss of functionality. Though phase field model (PFM) provides a feasible tool in fracture simulation on brittle elastic materials, numerical study on the fracture of elastomers is still at a tentative stage with challenges stemming from the extremely large deformation and the nonlinear material properties. In addition, recent experimental observations on the insensitivity of the onset of rupture to loading rates suggest another knowledge gap in revealing the role of the rate-dependent viscoelasticity in fracture. To capture such phenomenon and fill the research gap, this work will propose a finite element (FE) framework by incorporating the polymer dynamics into the PFM. For the first time, the driving force to the fracture of viscoelastic elastomers is identified and the micro-mechanism of the material viscosity is further elucidated with the consideration of polymer chain breakage. The disentanglement of polymer chains in the fracture process is considered in the model to release the constraints on polymer chain reptation from nearby chains, capturing the inherent damage-dependent as well as the deformation-dependent material viscosity. The simulation results demonstrate good agreement with existing experimental data in both loading rate sensitivity tests and geometry sensitivity tests. With the variation of loading rates, obvious differences in stress responses are observed, while the critical fracture stretches almost keep constant. This work provides a deeper understanding on the fracture mechanisms of viscoelastic materials and is expected to provide guidance for the better design and full potential applications of elastomer-based devices.

An Ogden-like formulation incorporating phase-field fracture in elastomers: from brittle to pseudo-ductile failures.

Over the past 50 years the Ogden model has been widely used in material modelling owing to its ability to match accurately the experimental data on elastomers at large strain, as well as its mathematical properties, such as polyconvexity. In this paper, these characteristics are exploited to formulate a finite-strain model that incorporates, through the phase-field approach recently proposed by Wu (Wu 2017 J. Mech. Phys. Solids 103, 72-99) for small strains, a cohesive damage mechanism which leads to the progressive degradation of the material stiffness and to failure under tension. By properly tailoring the constitutive parameters, the model is capable of encompassing a wide range of effects, from brittle to pseudo-ductile failure modes. A plane stress problem is formulated to test the model against experiments on double-network elastomers, which display a pseudo-ductile damage behaviour at large strain, and on conventional rubber compounds with brittle failure. The results show that the proposed model is applicable to fracture coalescence and propagation in a wide range of materials. This article is part of the theme issue 'The Ogden model of rubber mechanics: Fifty years of impact on nonlinear elasticity'.

The poker-chip experiments of Gent and Lindley (1959) explained

Despite being commonly credited with initiating the field of cavitation in elastomers, the famed poker-chip experiments of Gent and Lindley (1959) have yet to be fully explained. One likely reason for their elusiveness is that it had long been presumed that cavitation in elastomers was a phenomenon that could be explained solely on the basis of the elasticity of the elastomer at hand. Of late, full-field analyses and experiments carried out at high spatiotemporal resolution have impugned such a belief by indicating, instead, that cavitation in elastomers is first and foremost a fracture phenomenon. In that spirit, Kumar, Francfort, and Lopez-Pamies (2018) have introduced a comprehensive macroscopic phase-field theory for the nucleation and propagation of fracture in elastomers undergoing arbitrarily large quasistatic deformations. The purpose of this paper is to deploy this theory in order to explain in a detailed and quantitative manner the seminal poker-chip experiments of Gent and Lindley.

Sideways and stable crack propagation in a silicone elastomer

We have discovered a peculiar form of fracture that occurs in a highly stretchable silicone elastomer (Smooth-On Ecoflex 00-30). Under certain conditions, cracks propagate in a direction perpendicular to the initial precut and in the direction of the applied load. In other words, the crack deviates from the standard trajectory and instead propagates perpendicular to that trajectory. The crack arrests stably, and thus the material ahead of the crack front continues to sustain load, thereby enabling enormous stretchabilities. We call this phenomenon "sideways" and stable cracking. To explain this behavior, we first perform finite-element simulations that demonstrate a propensity for sideways cracking, even in an isotropic material. The simulations also highlight the importance of crack-tip blunting on the formation of sideways cracks. Next, we provide a hypothesis on the origin of sideways cracking that relates to microstructural anisotropy (in a nominally isotropic elastomer). To substantiate this hypothesis, we transversely prestretch samples to various extents before fracture testing, as to determine the influence of microstructural arrangement (chain alignment and strain-induced crystallization) on fracture energy. We also perform microstructural characterization that indicates that significant chain alignment and strain-induced crystallization indeed occur in this material upon stretching. We conclude by characterizing how a number of loading conditions, such as sample geometry and strain rate, affect this phenomenon. Overall, this paper provides fundamental mechanical insight into basic phenomena associated with fracture of elastomers.

A physically and geometrically nonlinear scaled‐boundary‐based finite element formulation for fracture in elastomers

SUMMARYThis paper is devoted to the formulation of a plane scaled boundary finite element with initially constant thickness for physically and geometrically nonlinear material behavior. Special two‐dimensional element shape functions are derived by using the analytical displacement solution of the standard scaled boundary finite element method, which is originally based on linear material behavior and small strains. These 2D shape functions can be constructed for an arbitrary number of element nodes and allow to capture singularities (e.g., at a plane crack tip) analytically, without extensive mesh refinement. Mapping these proposed 2D shape functions to the 3D case, a formulation that is compatible with standard finite elements is obtained. The resulting physically and geometrically nonlinear scaled boundary finite element formulation is implemented into the framework of the finite element method for bounded plane domains with and without geometrical singularities. The numerical realization is shown in detail. To represent the physically and geometrically nonlinear material and structural behavior of elastomer specimens, the extended tube model and the Yeoh model are used. Numerical studies on the convergence behavior and comparisons with standard Q1P0 finite elements demonstrate the correct implementation and the advantages of the developed scaled boundary finite element. Copyright © 2014 John Wiley & Sons, Ltd.

Fracture of elastomers by cavitation

Cavitation phenomenon is studied in rubber-like materials by combining experimental, theoretical and numerical approaches. Specific tests are carried out on a Styrene Butadiene Rubber to point out main characteristics of cavitation phenomenon. Hydrostatic depression is numerically modelled using finite element method. Numerical results are compared to Ball’s and Hou & Abeyaratne’s models with regard to cavity nucleation in the material. Both models well fit experimental observations suggesting that the cavitation nucleation in elastomers depends on the confinement degree of the specimen. Finally, critical hydrostatic pressure and critical global deformation are proved to govern cavitation nucleation in the studied material. Critical loadings are identified by comparing experimental and numerical load–displacement curves.

Experimental and finite element investigation of void nucleation in rubber-like materials

This work deals with fracture of elastomers by cavitation. So, tension tests were achieved on specific volumetric specimens, the shape of which should induce void nucleation in the bulk of the material. Macroscopic behaviour of this material was related to the cavitation phenomenon. It was particularly proved that the slope break of the stress–strain curves coincides with the apparition of voids. Then, all experimental tests were numerically modelled using Finite Element Method (FEM) and results were analysed. Numerical study highlighted, among others, effects of specimen shape factor and those of filler volume fraction on the nucleation and growth of cavities.

Fracture analysis of rubber‐like materials using global and local approaches: Initiation and propagation direction of a crack

AbstractIn this work, fracture of elastomers is analyzed using global and local approaches, combining experiments, analytical developments, and finite element calculations. The J‐integral is chosen as a global parameter characterizing crack initiation in such materials. Particular attention is paid to single specimen methods for measuring the fracture surface energy. More precisely, models developed in the literature are summarized and, because of the lack of accuracy of these models, an original pertinent expression of J is proposed by analogy with linear elastic fracture mechanics frameworks. However, the J‐integral is not able to predict the kinetic or the propagation direction of a crack. Thus, some local parameters are examined: principal strains, principal stresses, and the strain energy density (SED) factor. Results revealed that all these parameters represent reasonable indicators of the crack propagation direction in elastomers. Moreover, unlike maximal principal stress and SED factor, maximal principal strain seems to govern the crack initiation in this kind of materials. POLYM. ENG. SCI., 2009. © 2009 Society of Plastics Engineers

Fracture of elastomers under static mixed mode: the strain-energy-density factor

This work deals with the fracture of rubbers under a mixed mode loading (I + II) and it is an extension of our previous papers on that subject [Aït Hocine N, Naït Abdelaziz M, Imad A (2002) Int J Fract 117:1–23; Aït Hocine N, Naït Abdelaziz M (2004) In: Sih GC, Kermanidis B, Pantelakis G (eds) 6th international conference for mesomechanics. Patras (Greece), May 31–June 4, pp 381–385]. An experimental and a numerical analysis were carried out using a Styrene Butadiene Rubber (SBR) filled with 20 and 30% of carbon black. Sheets with an initial central crack (CCT specimens) inclined with a given angle compared to the loading direction were used. The J-integral and its critical values J c (fracture surface energy) were determined by combining experimental data and finite element results. These critical values, determined at the onset of crack growth, were found to be quite constant for each elastomer tested, which suggests that J c represents a reasonable fracture criterion of such materials. Then, the strain–stress field and the strain-energy-density factor S, earlier introduced by Sih [Sih GC (1974) Int J Fract 10(3):305–321; Sih GC (1991) Mechanics of fracture initiation and propagation. Kluwer Academic Publishers, Dordrecht, 428 pp] were numerically calculated around the crack tip. According to the experimental observations, the plan of crack propagation is perpendicular to the direction of the maximum principal stretch. Moreover, as suggested by Sih in the framework of linear elastic fracture mechanics (LEFM), the minimum values S min of the factor S are reached at the points corresponding to the crack propagation direction. These results suggest that the concept of the maximum principal stretch and the one of the strain-energy-density factor can be used as indicators of the crack propagation direction.

SELF-ADHESION HYSTERESIS IN POLYDIMETHYLSILOXANE ELASTOMERS

Self-adhesion hysteresis has been investigated in crosslinked poly(dimethylsiloxane) (PDMS) lenses using the Johnson, Kendall, and Roberts technique. The experimental conditions involved relatively short contact times for which interchain penetration effects across the interface are minimal. Only lenses that had been extracted in toluene displayed self-adhesion hysteresis. The same lenses demonstrated no adhesion hysteresis when pressed against tethered polystyrene substrates, indicating that hysteresis was caused by surface interactions and not bulk viscoelastic effects. Extraction produces hysteresis by removing the free chains, which normally lubricate the interface, inhibiting the adhesion mechanism. Self-adhesion hysteresis was only observed for networks with a high molecular weight between crosslinks. More tightly crosslinked networks did not display self-adhesion hysteresis, even at extended contact times under load. By inhibiting the hydrosilylation reaction between residual vinyl and silane groups in the PDMS lenses, self-adhesion hysteresis was prevented, suggesting that the formation of chemical crosslinks across the interface caused the observed hysteresis. The molecular weight dependence of the hysteresis can be interpreted in terms of the Lake-Thomas model [1] for fracture in elastomers.

Crack blunting and the strength of soft elastic solids

When a material is so soft that the cohesive strength (or adhesive strength, in the case of interfacial fracture) exceeds the elastic modulus of the material, we show that a crack will blunt instead of propagating. Large–deformation finite–element model (FEM) simulations of crack initiation, in which the debonding processes are quantified using a cohesive zone model, are used to support this hypothesis. An approximate analytic solution, which agrees well with the FEM simulation, gives additional insight into the blunting process. The consequence of this result on the strength of soft, rubbery materials is the main topic of this paper. We propose two mechanisms by which crack growth can occur in such blunted regions. We have also performed experiments on two different elastomers to demonstrate elastic blunting. In one system, we present some details on a void growth mechanism for ultimate failure, post–blunting. Finally, we demonstrate how crack blunting can shed light on some long–standing problems in the area of adhesion and fracture of elastomers.

Fatigue and Fracture of Elastomers

Abstract The use of an energetics approach to treat various aspects of fatigue and fracture in elastomers is reviewed. Topics covered include tearing, crack growth and fatigue, tensile failure, oxidative effects, environmental cracking, cutting by sharp objects, abrasion, adhesion, friction (under circumstances where it is determined mainly by the making and breaking of contact), and cavitation. Application of the approach to service problems is also considered. Finally, physical and chemical factors affecting the crack growth characteristics—the material property linking various types of cohesive failure—are discussed.

Fracture of Elastomers by Gas Decompression

Abstract A study has been made of gas decompression failures in elastomeric seals using a fracture mechanics approach and considerations of gas permeation. An equation is proposed for the tearing energy associated with crack growth from internal gas bubbles in a finite thickness elastic media. When applied to a model experiment where an internal flaw of known size was pressurized up to failure, the equation agreed with experimental results. A series of seals were then subjected to high gas pressures (up to 69 MPa or 10,000 psi) for a range of temperatures between 20 and 230°C and the amount of crack growth was measured after decompression. The trends in crack growth were correctly accounted for when values for tearing energy and modulus were used that were appropriate for the temperature of decompression. The effect of mechanical boundary constraint was studied by varying the compression on the seal in specially designed test holders. The effect of decompression rate is also considered. The conditions under which failure will occur are created by a complex balance of the available tearing energy and the gas permeation kinetics. A fundamental problem is the unknown size of the initial flaw from which crack growth and rupture occurs. This is discussed in the light of the experimental results and it is proposed that effective surfaces of weakness form in the elastomer phase of size to provide initiation sites for crack growth.

Fractographic investigation of tensile and fatigue fracture surfaces of rubber containing inhomogeneous inclusions

Fracture of rubber begins at flaws or inclusions where local stress exceeds a critical level. Recently, a study has been undertaken to investigate the effect of inclusions on the fracture property of rubber. The inclusions studied are dirt from guayule rubber of particle size between 18 and 6000/~m. A controlled amount of dirt of definite size has been incorporated in the rubber matrix. It is worth mentioning that these dirt particles remain present even after the extraction of rubber from shrub. Fracture of guayule rubber containing different sizes and amounts of "dirt", which are basically plant tissues in nature, has been reported elsewhere [1]. Thomas [2] and Gent [3] have treated the fracture of elastomers in detail and Greensmith [4] has reported tensile and fatigue failure of natural rubber containing sand and sawdust. He observed a reduction in strength properties with the incorporation of these foreign materials. Gent et al. have investigated the tensile failure of silicone rubber containing a glass bead [5]. In the above investigations, however, the surface morphology around a flaw has not been studied. Fractography of several elastomers under different modes of failure namely tensile, tear, fatigue and abrasion has been reported before by us [6-8]. In all these studies, it has been observed that different modes of failure generate typical fracture surfaces. In this letter, the results of my observations of tensile and fatigue fracture surfaces ofelastomers containing inhomogeneous inclusions are reported. Mix formulations are as follows: natural rubber 100%; zinc oxide 6%; stearic acid 0.5%; mercaptobenzothiazole 0.5%; sulphur 3.5%; dirt 0%, 3.0%. 3% dirt has been added to the sample. Mixing and compounding have been done on an open mill. Hence, there is some breakdown of the dirt, reducing the particle size ranges from 45 to 6000/~m to 45 to 1000/~m. The small amount of dirt does not have any effect on scorch time and optimum cure time. Curing was done at 150°C at the optimum cure time. Dumbbell specimens for tensile and fatigue testing were used. Tensile testing was carried out in an Instron machine (ASTM D 412-75 method) and the fatigue experiment in a Monsanto fatigue-to-failure tester (frequency, 100 cycles min ~ ). The samples were sputter-coated with gold immediately after fracture and the fracture surfaces were examined within 24 h of test. A JEOL SMU3 scanning electron microscope was used for the study. The tensile fracture surface of guayule rubber is shown in Fig. 1. Few tear lines running from one end Figure 1 Tensile fracture surface of guayule rubber containing no external dirt: general fracture surface.

The effect of cross-linking on fracto-emission from elastomers

During the fracture of elastomers in vacuum, one frequently observes the emission of particles such as electrons, ions, neutral molecules, and photons, which we call fracto-emission. We report here measurements of electron emission and positive ion emission accompanying and following the fracture of polybutadiene (BR) and a styrene-butadiene copolymer (SBR), where the degree of cross-linking has been altered either by varying the concentration of the cross-linking agent or by exposure of the material to ultraviolet or γ-ray radiation. Our results show that over the range of cross-link densities studied, both electron and positive ion emission increase with increasing cross-link density.

Free Radicals Generated in Rubber during Fracture

Abstract EPR has been used to measure molecular phenomena during fracture of elastomers. To date, because of various technical limitations, the studies have been largely confined to identification of the polymer chain scission site during fracture at low temperature in rubbers, to studying ozone-stress-induced cracking of rubber, to development of a micro-macro Griffith-type failure criteria for this type of failure, and lastly to systematic investigation of the role of filler-matrix interaction in fracture of filled elastomers. It is hoped that the brief outline presented here will give the reader some insight into the uses and potential of the EPR methods for the study of fracture. As a final note, while we have concentrated almost totally on EPR fracture studies in rubbers, there has been fairly extensive EPR work on fracture in oriented plastic, fibers, and films. Even though some of this knowledge may be transferable, directly or indirectly, to elastomers, it has not been reviewed here, but important aspects of these studies have been reviewed elsewhere.

Flow and the activation mechanism of polymer fracture

Ideas about the fluctuation mechanism of fracture, based on a quantitative description of the dependence of the breaking stress on defect growth rate and temperature, are developed. It is shown that the relation σ=kveU/RT is a fundamental one, describing such rheological processes as viscous flow and polymer fracture. This relation describes the fracture of elastomers in cases where the change in the structure of the polymer during deformation makes it necessary to supplement the lifetime equation with three others: γ=f(T, σb); U0=f′(σb, T) and τ0=f″(σb, T).