Threshold Fracture Energy Research Articles

Performance Assessment of Bioasphalt Mixtures Containing Guayule Resin as an Innovative Biobased Asphalt Alternative

Guayule resin was investigated through mixture to assess its role in the field performance. For performance comparisons, conventional asphalt, neat guayule, asphalt–rubber–guayule, and guayule–rubber binders were implied. Field-simulated lab mixtures were made to investigate the major distresses. Modified Lottman, rut, semicircular bending, and disk-shaped compact tension tests were used to assess stripping, rutting, fatigue, and thermal cracking resistances. Stripping and rutting susceptibilities were also assessed by Hamburg wheel-tracking test. The outcomes disclosed that when the modified Lottman test was used, guayule containing a 7% air content was more susceptible to stripping than that containing a 3.5% air content, resulting in tensile strength ratios of 40% and 71%, respectively. All investigated mixtures did not reach out the stripping inflection point under the Hamburg wheel-tracking criteria. Asphalt offered the worst Hamburg rut depth, which was 3.2 mm after 20,000 passes. Guayule-based mixtures perfectly resisted rutting as proven by the rut test. Guayule offered the worst rut depth of 6.3 mm, indicating a great rutting resistance. The guayule-based mixture had a high fracture toughness at intermediate temperatures. Guayule and guayule–rubber mixtures offered a critical strain energy release rate of 0.65–0.69 kJ/m2 compared to 0.46 kJ/m2 for asphalt. They, however, tended to possess low thermal fracture resistance (less than the threshold fracture energy, 400 J/m2). Conversely, a blend of 62.5% asphalt, 12.5% rubber, and 25% guayule offered 591 J/m2 at its performance grade low temperature (−16°C) and 409 J/m2 at −22°C compared to 429 J/m2 for asphalt at the later temperature, which represented the performance-grade low temperature of asphalt.

On the relationship between cutting and tearing in soft elastic solids.

Unique observations of cutting energy in silicone elastomers motivate a picture of soft fracture that qualitatively and quantitatively links far-field tearing with push cutting for the first time. For blades of decreasing tip radii, the cutting energy decreases until it reaches a plateau that suggests a threshold for failure. A super-molecular damage zone, necessary for new surface creation, is defined using the tip radius at the onset of this threshold. Modifying the classic Lake-Thomas theory, in which failure occurs within a molecular plane, to this super-molecular zone provides order-of-magnitude agreement with the cutting energy threshold. Together, the threshold fracture energy and damage length scale define criteria for failure that, when implemented in finite element simulation, quantitatively reproduce the increase in cutting energy with increasing blade radius outside of the plateau. The rate of increase depends on the constitutive response of the material, with more neo-Hookean solids requiring a larger failure force per incremental increase in blade radius as observed experimentally. This combination of a geometry-independent failure threshold (from the cutting energy plateau) and a need to account for the role of material deformability in the stress concentration found at the crack tip (from the rate of cutting energy increase with blade radius) align with the discovery of a new dimensionless group. This new parameter proportionally maps cutting energy to the energy required to tear a sample under far-field loading conditions by using ultimate properties obtained in uniaxial tension.

A phase-field model of frictional shear fracture in geologic materials

Geologic shear fractures such as faults and slip surfaces involve marked friction along the discontinuities as they are subjected to significant confining pressures. This friction plays a critical role in the growth of these shear fractures, as revealed by the fracture mechanics theory of Palmer and Rice decades ago. In this paper, we develop a novel phase-field model of shear fracture in pressure-sensitive geomaterials, honoring the role of friction in the fracture propagation mechanism. Building on a recently proposed phase-field method for frictional interfaces, we formulate a set of governing equations for different contact conditions (or lack thereof) in which frictional energy dissipation emerges in the crack driving force during slip. We then derive the degradation function and the threshold fracture energy of the phase-field model such that the stress–strain behavior is insensitive to the length parameter for phase-field regularization. This derivation procedure extends a methodology used in recent phase-field models of cohesive tensile fracture to shear fracture in frictional materials in which peak and residual strengths coexist and evolve by confining pressure. The resulting phase-field formulation is demonstrably consistent with the theory of Palmer and Rice. Numerical examples showcase that the proposed phase-field model is a physically sound and numerically efficient method for simulating shear fracture processes in geologic materials, such as faulting and slip surface growth.

Resolution of the threshold fracture energy paradox for solid particle erosion

Previous models of a single erosion impact, for a rigid axisymmetric indenter defined by the shape function , have shown that a critical shape parameter exists which determines the behaviour of the threshold fracture energy. However, repeated investigations into this parameter have found no physical explanation for its value. Again utilising the notion of incubation time prior to fracture, this paper attempts to provide a physical explanation of this phenomena by introducing a supersonic stage into the model. The final scheme allows for the effect of waves along the indenters contact area to be taken into account. The effect of this physical characteristic of the impact on the threshold fracture energy and critical shape parameter are investigated and discussed.

Threshold fracture energy in solid particle erosion: improved estimate for a rigid indenter impacting an elastic medium

The case of a single erosion impact is considered. The paper improves and extends the results from Argatov and Mishuris (Philos Mag 93:2485, 2013), where a lower bound for the threshold fracture energy of a rigid axisymmetric indenter was obtained based on the notion of incubation time prior to fracture. In the presented study we define an exact value for the initial energy required for fracture initiation and compare it with previous results. The incubation time based fracture criterion is utilized in order to locate the time of the initial fracture, along with the associated radial position. A brief examination of the effects of different particle parameters on the initial fracture is conducted.

Simulation of the behavior of the cutting force during ultrasonic rotary machining of materials using structure-time fracture mechanics

An analytical model is developed for the behavior of the cutting force during ultrasonic rotary polishing, and it is based on the concepts of dynamic fracture mechanics and the solution to the problem of impact surface fracture. The dependence of the threshold fracture energy obtained in the problem of erosion using a structure-time approach is used to construct the cutting force model. The dependences of the cutting force on the material feed rate and the rate of tool rotation are obtained, and the developed model is shown to be efficient to explain the effects observed in experiments.

Corrosion in low dielectric constant Si-O based thin films: Buffer concentration effects

Organosilicate glass (OSG) is often used as an interlayer dielectric (ILD) in high performance integrated circuits. OSG is a brittle material and prone to stress-corrosion cracking reminiscent of that observed in bulk glasses. Of particular concern are chemical-mechanical planarization techniques and wet cleans involving solvents commonly encountered in microelectronics fabrication where the organosilicate film is exposed to aqueous environments. Previous work has focused on the effect of pH, surfactant, and peroxide concentration on the subcritical crack growth of these films. However, little or no attention has focused on the effect of the conjugate acid/base concentration in a buffer. Accordingly, this work examines the “strength” of the buffer solution in both acidic and basic environments. The concentration of the buffer components is varied keeping the ratio of acid/base and therefore pH constant. In addition, the pH was varied by altering the acid/base ratio to ascertain any additional effect of pH. Corrosion tests were conducted with double-cantilever beam fracture mechanics specimens and fracture paths were verified with ATR-FTIR. Shifts in the threshold fracture energy, the lowest energy required for bond rupture in the given environment, GTH, were found to shift to lower values as the concentration of the base in the buffer increased. This effect was found to be much larger than the effect of the hydroxide ion concentration in unbuffered solutions. The results are rationalized in terms of the salient chemical bond breaking process occurring at the crack tip and modeled in terms of the chemical potential of the reactive species.

On the effect of the geometrical shape of a particle on threshold energy in erosion damage

The structural-temporal approach is used for analyzing the energy required for fracture. The behaviors of the threshold fracture energy in the impact of spherical and cylindrical particles against an elastic half-space are compared. It is shown that the threshold energy minimum can be attained using spherical particles. The plots of the dependence of the threshold energy on the impact duration and on the particle radius are constructed for the cases under investigation.

Fracture Energy of Epoxy Interfaces with Layers of Different Silane Coupling Agents

We investigated the fracture energy, Gc, and the threshold fracture energy, Gth, in water at 80°C of interfaces between epoxy and layers of five silane coupling agents: (3-glycidoxypropyl)trimethoxysilane (GPS), (3-aminopropyl)trimethoxysilane (APS), [3-(phenylamino)propyl]trimethoxysilane (PAPS), (3-mercaptopropyl)trimethoxysilane (MPS), and [3-(2-aminoethylamino)propyl]trimethoxysilane (AEAPS) on the native silicon oxide surface. While 10-nm-thick layers of these all had similar high Gc, APS had the best overall values of Gth, but all adhesion promoters, except for AEAPS, performed roughly similarly. The results from the XPS analysis of the silicon side of the fracture surfaces suggest that for all silane layers, the fracture occurs somewhere within that layer. When the silane coupling agents were added to the epoxy, the samples with the higher threshold fracture energies exhibited a thicker layer of the epoxy remaining on the native silicon oxide surface. Silane coupling agents that perform well as deposited layers do not necessarily perform well as additives to epoxies.

Prediction of the threshold fracture energy in impact cratering mechanics

Prediction of the threshold fracture energy in impact cratering mechanics

Study on Crosslinking of Polyethylene–Octene Elastomer with Dicumyl Peroxide

A crosslinkable metallocene polyethylene–octene elastomer (POE) containing different amounts of dicumyl peroxide (DCP) was prepared in a mixer at 110°C to remove the methanol and to ensure a uniform distribution of DCP. A crosslinking reaction of the crosslinkable mixture was carried out for 20 min in a hot press at 140°C. The properties of crosslinked products have been examined in the present study. From the results of 13C NMR, it was found that H-Link was produced on the molecular structure of POE resulting from the crosslinking reaction with DCP. The molecular weight (MW) between crosslinks of the gel was determined from Flory-Rhener theory and the result showed that MW decreased as DCP concentration was increased. According to the result of DSC and x-ray diffraction characterizations, it was found that the crystalline structure of POE was altered after crosslinking and the degree of crystallization decreased with increasing DCP content. Tensile and tear tests showed that the magnitudes of tensile strength and elongation at break, fracture energy, threshold fracture energy, and effective unstrained diameter of the tear tip all decreased when the DCP loading was increased.

Viscoelastic effects in cutting of elastomers by a sharp object

The cutting behavior of elastomers by a sharp object was investigated using various elastomers such as acrylonitrile-butadiene rubber (NBR), styrene-butadiene rubber (SBR), and natural rubber (NR). The effects of crosslinking density, cutting rate, and temperature on the cutting energy of elastomers were investigated. The cutting behavior of swollen elastomers was also investigated. It was found that the cutting energy increased as the molecular weight between crosslinks increased. It was also found that the cutting energies of various elastomers did not yield a single line. Moreover, even in the threshold condition of cutting process, the cutting energy was much higher than the threshold fracture energy. These results suggest that the cutting behavior cannot be explained by only a C-C bond rupture process, but it includes other energy dissipation processes. The curves for cutting energies obtained at different cutting rates and temperatures were well superimposed on a single master curve when they were shifted using the WLF (Williams, Landel, and Ferry) equation. Therefore, it is supposed that the cutting of elastomers by a sharp object includes viscoelastic energy dissipation process and is the viscoelastic behavior. It was also found that the variation of cutting energy over a considerable range of effective rates was smaller than that of the tear energy. It is attributed to the fact that the change of the crack tip diameter, i.e., roughening or reduction, was restricted by the diameter of razor blade.

Fracture energies of styrene-butadiene-styrene block copolymers (II). Strength at high temperatures

It has been found that SBS block copolymers possess excellent tear strength at room temperature. However, tear strength is virtually zero at temperatures higher than the glass transition temperature of PS phase, ca. 95C. Tear strength at high temperatures can be improved by slight crosslinking of PB chains of SBS molecules with a small amount of dicumyl peroxides (DCP). The present work describes results of measurements of strength at high temperatures carried out on the DCP-cured SBS block copolymers. Fracture energies of DCP-cured specimens were determined using both a conventional tear test and a recently developed cutting test. The effect of crosslink density on fracture energy was investigated and correlated with microstructure. It has been found that specimens crosslinked with 0.01 phr DCP still possess relatively large tear strength at room temperature, about 10 kJ/m 2 , when compared with uncrosslinked SBS specimens. Tear strength at high temperatures has been effectively enhanced to be about 100 to 1000 J/m 2 , depending on the tearing rate. Specimens crosslinked with a higher level of DCP, however, showed a pronounced reduction of tear strength at room temperature, with tear strength of SBS specimens crosslinked with 1 phr DCP about one-tenth of that of neat SBS. The threshold fracture energy of crosslinked SBS copolymers is found to be proportional to the square root of the molecular weight between chemical crosslinks in the PB phase, which is in accord with the theory of Lake and Thomas. Moreover, from the results of cutting test, it is found that the majority, about 70%, of the fracture energy of neat SBS specimens comes from the rupture of the long PB chains of SBS molecules. The rest is the contribution from the energy associated with the PB/PS interface.

Threshold fracture of lightly crosslinked networks

Threshold fracture energy, G 0 , is reported for several lightly cross-linked PDMS networks. The average length between chemical junctions, ξ c , characterized with statistical theory, is much greater than the average length between entanglement points, ξ e , for PDMS in each network. Data indicate that the dependence of G 0 on ξ c for lightly cross-linked networks is much weaker than the classic form, ξ c 1/2 . Two alternative limiting expressions for G 0 based on the role of trapped entanglements on the fracture mechanism are discussed

Threshold Fracture of Networks

AbstractWe discuss the threshold fracture energy, GO, of networks over a wide range of cross-link density. C, for networks with an average number of main chain steps, ςc, that compare favorably with the entanglement spacing, ςc, follow the 1/2 power law, Go - ς1/2. Two views of molecular fracture, one a chain-breaking mechanism and the other a suction process, produce the 1/2 power law. For lightly cross-linked networks (ςc ≫ ςe), Go appears to decrease with increasing ςc. Trapped entanglements limit the extensibility and fracture energy of these networks. Consideration of rupture of trapped entangled chains gives Go -ςc-1/2; this form agrees reasonably well with data at high ςc.

Role of entanglement couplings in threshold fracture of a rubber network

The threshold fracture energy was determined for a crosslinked poly(dimethylsiloxane) network, using the Lake Thomas theory, it is shown that the average network subchain that is extended to the breaking joint under threshold conditions is approximately 140 monomer units long. The results suggest that entangled subchains trapped by chemical junctions along elastically active strands are responsible for threshold fracture. The average length of elastically active subchains between chemical junction points is calculated using a statistical theory

Effect of Interfacial Bonding on the Self-Adhesion of SBR and Neoprene

Abstract When two elastomer layers are partially crosslinked in contact with each other, the strength of adhesion increases. This effect has now been studied for simple vulcanizates of SBR and for CR vulcanizates crosslinked with sulfur and/or oxide linkages. Under threshold conditions, e.g., at high temperatures and in the swollen state, when both viscous effects and strain-induced crystallization are virtually eliminated, the work of detachment is small and approximately proportional to the inferred degree of interlinking, rising from a few J/m2 when only Van der Waals' attractions are present, up to 40–70 J/m2 in the fully-interlinked state. No significant differences were observed between SBR and CR vulcanizates, or with different types of crosslinking of CR. The principal structural factors governing the adhesive strength under threshold conditions appear to be the number and length of the molecular strands comprising the network and crossing the interface. The threshold fracture energy is directly proportional to the density of such strands and is smaller for shorter strands, in accord with the theory of Lake and Thomas. Under normal conditions, e.g., at room temperature and in the unswollen state, CR vulcanizates were found to adhere much more strongly for a given degree of interlinking, presumably due to strain-induced crystallization. Indeed, some enhancement of strength persisted even at temperatures of 100–150°C, in the unswollen state.