Toughness Optimization of SBR Elastomers – Use of Fracture Mechanics Methods for Characterization

Elastomer materials are used in a wide application range and subjected to different loading from which failure of the material results. Because this failure is caused by initiation and propagation of cracks, the application of fracture mechanics methods for the assessment of the material is obvious. A short summary of the methods of technical fracture mechanics including possibilities of determination of crack resistance curves is given. Vulcanizates on the basis of SBR 1500 with various sulfur and carbon black contents were investigated. For describing the crack initiation and crack propagation behavior, several fracture mechanics examination methods were applied. Tear‐analyzer results were used to assess the crack propagation behavior under fatigue‐like loading conditions. Furthermore, for the characterization of the crack resistance of the materials under impact‐like loading conditions, instrumented tensile‐impact tests were performed. To obtain information about the initiation and propagation of a stable crack, quasi‐static fracture mechanics tests were applied. The results of the several tests are discussed in dependence on sulfur and carbon black contents. We found a non‐monotonous behavior of the toughness as a function of carbon black loading. An explanation is given in connection with a percolation‐like transition in filler morphology on larger length scales.

Schematic crack propagation curve for characterizing the fatigue behavior of the vulcanizates recorded in a TFA test.     

Time‐ and Temperature‐Dependent Fracture Mechanics of Polymers: General Aspects at Monotonic Quasi‐Static and Impact Loading Conditions

Well‐defined correlations exist between the maxima in mechanical loss factor and the local maxima in temperature‐ or loading‐speed‐dependent fracture toughness. The non‐linear viscoelastic fracture processes and small‐strain deformations are characterised by the same Arrhenius‐type activation enthalpies. The local increase in toughness is linearly correlated with the relaxation strength of molecular relaxation processes. Stable crack propagation can be understood as a three‐phase process resulting in steady‐state stable crack growth. The normalised steady‐state crack‐tip‐opening displacement is independent of matrix material, temperature and loading speed.

     

Fracture Behaviour of Styrene/Butadiene Block Copolymers having Different Molecular Architecture

The crack toughness behaviour of styrene/butadiene block copolymers of triblock and star architectures was investigated using instrumented Charpy impact testing. In order to evaluate adequately the toughness behaviour of the investigated materials, different concepts of elastic‐plastic mechanics (J‐integral and crack‐tip opening displacement, CTOD concepts) were used. Although the lamellar block copolymers showed a remarkably enhanced ductility in the tensile test than the neat block copolymer having hexagonal PB cylinders in PS matrix, no pronounced difference in crack toughness was found. This behaviour implies that the tensile strain cannot be regarded as the only parameter defining the toughness value. A brittle/tough transition was observed in a lamellar star block copolymer on blending with a linear thermoplastic elastomeric SBS triblock copolymer.

SEM micrograph showing the details of the stable crack propagation region in a binary block copolymer blend.     

New Insights into Fatigue Crack Growth in Graphene‐Filled Natural Rubber Composites by Microfocus Hard‐X‐Ray Beamline Radiation

Natural rubber (NR) composites containing graphene (GE) are prepared by ultrasound‐assisted latex mixing and in situ reduction. The fatigue crack propagation of the composite is examined. It is observed that GE has an opposite effect on crack growth resistance of NR, i.e., at lower fatigue strains, the inclusion of GE accelerates the crack growth, whereas at higher strains, the crack growth is retarded. It is suggested that the reason for this behavior is a competition between strain‐induced crystallization and cavitation at crack tip. Through microfocus hard‐X‐ray diffraction beamline with high spatial resolution, fatigue crack resistance is correlated to strain‐induced crystallization and new insights into the mechanism of fatigue crack growth are obtained.

     

Rheological interpretation of heat generation associated with fatigue of polycarbonate

Temperature change was measured of polycarbonate under monotonically increasing tensile and pulsating tensile loads. In the former case, the specimen temperature began to rise when an appreciable amount of viscoelastic strain was noticed on the stress—strain diagram. The rise, θ_v, could be formulated as a function of the viscoelastic strain, εv: In fatigue tests, the average temperature began to rise immediately after the decrease due to the thermoelastic effect. The amount of the heat generation, σ, was nearly constant for each cycle throughout the fatigue process and has a relation to the fatigue life, N_f, (α? a)·N_f = constant, where a is another adjustable constant. From a rheological aspect of dissipation energy, the equation is transformed to a relation between the viscoelastic strain and the fatigue life as εV^1/2 · N_f = constant, which is similar to the one for metals given by Manson and Coffin.⁶ The temperature rise in the fatigue was also related to the viscoelastic strain. The relation is of the same form as for static tension but less by a factor of one order.     

Fatigue crack growth in polymers. I. Effect of frequency and temperature

The effects of frequency, from 0.1–100 Hz, and temperature, ?60°C to +21°C, on fatigue crack propagation in poly (methyl methacrylate) and polycarbonate were investigated. A cyclic crack propagation law proposed by Arad-Radon-Culver, namely where λ is (K_max²-K_min²) and K_max and K_min are the respective values of maximum and minimum stress intensity factor, was applied to describe a relationship between crack growth and cyclic life. Cyclic tests performed in tension between zero load and K_max showed a linear relationship between the crack lengths and the number of cycles for all temperatures and frequencies tested. It was found that, in general, the cyclic crack growth decreased with decreasing temperature and increasing frequency. However, important exceptions to this rule have been noted.     

Fracture toughness of acrylic resins: Viscoelastic effects and deformation mechanisms

The time dependence of fracture toughness of two different acrylic resins, one plain and one toughened, intended to be used as continuous fiber composite matrices was studied. By performing fracture tests following the fracture mechanics approach, the energy release rate, G_Ic, was determined at different temperatures and displacement rates and by applying the time‐temperature superposition it was possible to obtain G_Ic as a function of crack speed, , over a wide range of speeds. The trends obtained for the two resins were different. For the plain resin it could be well described by J. G. Williams' viscoelastic fracture theory while for the toughened resin, the trend obtained was attributed to a change in the damage mechanism occurring at the crack tip during fracture. From measurements of the process zone size it was deduced that the damage mechanism at the crack tip for the plain resin was the same irrespective of time and temperature, for the toughened resin instead, different mechanisms seem to take place. This hypothesis was supported by results of volume strain measurements in tensile tests at different temperature and strain rates. POLYM. ENG. SCI., 58:369–376, 2018. © 2017 Society of Plastics Engineers     

Layered Silicate‐Induced Enhancement of Fracture Toughness of Epoxy Molding Compounds over a Wide Temperature Range

Summary: The fracture toughness of EMC was dramatically increased over a wide temperature range by the addition of a very low volume fraction of layered silicates to EMC filled with micro‐silica particles. Layered silicate‐EMC nanocomposites containing intercalated and the exfoliated silicates were fabricated by using o‐cresol and biphenyl type epoxy resins, respectively. It was found that exfoliated silicates were more effective than intercalated silicates at toughening EMC at temperatures above T_g of the epoxy resin. Enhanced fracture toughness of EMC over a wide temperature range, from ambient to 230 °C has been attributed to the presence of layered silicates, which induces macroscopic crack deflection and severe plastic deformation in front of the crack tip.

     

Hybrid effects on mechanical properties of polyoxymethylene

The present study investigated fracture and various mechanical properties of polyoxymethylene (POM) hybrids in tension and in flexure. The hybrids examined consisted of short glass fibers (GF) and spherical glass beads (GB). Comparisons are made between experimentally observed values and predictions based on the rule-of-hybrid mixtures for hybrid strength, modulus, impact strength, fracture toughness, and strain energy release rates. Results indicated that tensile strength, flexural modulus, and fracture toughness of POM/GB/GF hybrid composites can be estimated from the following rule-of-hybrid mixtures where P_POM/GB and P_POM/GF are the measured properties of the POM/GB and POM/GF composites, and χ_POM/GB and χ_POM/GF are the hybrid ratio (by volume) of the glass bead and that of glass fiber, respectively. In view of this, none of the aforementioned properties show any signs of a hybrid effect. Flexural strengths, impact strengths, and strain energy release rate all showed the existence of a negative hybrid effect where negative deviation from the rule-of-mixtures behavior was observed. The latter was closer to the estimation based on the inverse rule-of mixtures.     

A study of the fatigue behavior of fiber reinforced nylons

A phenomenological model combining a Weibull distribution function with a kinetic equation for flaw growth has been used to describe the static tensile strengths and fatigue lives of short graphite-fiber reinforced nylon 66 materials. A simple Weibull function of the form \documentclass{article}\pagestyle{empty}\begin{document}$ P\left( {\sigma _b } \right) = \exp - \left( {{{\sigma _b } \mathord{\left/ {\vphantom {{\sigma _b } {\hat \sigma }}} \right. \kern-\nulldelimiterspace} {\hat \sigma }}} \right)^{9.5} $\end{document} described the distribution of static strengths. The scale factor \documentclass{article}\pagestyle{empty}\begin{document}$ {\hat \sigma } $\end{document} varies with the annealing treatment and, in general, is a function of environmental variables. The cumulative distribution of breaking times in fatigue can be characterized by a translated three parameter Weibull function \documentclass{article}\pagestyle{empty}\begin{document}$ P\left( {t_B } \right) = \exp - \left\{ {\left. {\left( {\frac{{\sigma _{\max } }}{{\hat \sigma }}} \right)^{16} + \frac{{t_B }}{{\hat t}}} \right\}} \right.^{0.59} . $\end{document} The average time to break (which is related to the time scale factor \documentclass{article}\pagestyle{empty}\begin{document}$ {\hat t} $\end{document}), appears to be a function of the flaw growth rate. The distribution equation has been found to predict the number of half cycle failures and is thus a valid model for the proof testing of large populations. An electrical resistivity method was developed to measure flaw growth rates in prenotched cantilever beams. Experimental data fit the following equation: ln (Δa/Δn) = ?88.88 + (12.46 ± 5.68) ln (K_eff)_max. The correlation coefficient was 0.81. From curve fitting of fatigue data it appeared that flaw growth rate varied with the ninth power of flaw length (Δa/Δn) = Ma⁹. The direct measure of flaw growth rate using electrical resistance gave Δa/Δn = Ma^6.23±2.84 with 90 percent confidence. The two measurements overlap within the 90 percent confidence bands, but predictions of fatigue life using the flaw propagation data were not good. Scanning electron microscope studies showed that specimens with a short fatigue life have glassy, fibrillated fracture surfaces while specimens with a long fatigue life exhibit a high degree of ductility in portions of the fracture surface. These differences are traced to differences in the size and shape of flaws.     

Dynamic stress intensity factors during viscoelastic crack propagation at various strain rates

Dynamic stress intensity factors K_D were measured by the caustic method and crack propagation velocity ? by the velocity gauge techniques for PMMA [poly(methyl methacrylate)] during dynamic crack propagation at various strain rates \documentclass{article}\pagestyle{empty}\begin{document}$ \rm \dot \varepsilon $\end{document} . No definite applied strain rate effects on the dynamic stress intensity factor were observed for applied strain rates ranging from 8.33 × 10^?4 to 30/sec; however, the test results do show crack propagation velocity dependency in K_D ～ ? relations. The high local strain rate region may be realized at the running crack tip even under the quasi-static loading case of \documentclass{article}\pagestyle{empty}\begin{document}$ \rm \dot \varepsilon $\end{document} = 8.33 × 10^?4/sec, since all the crack propagation velocities obtained were greater than 50 m/sec even up to 450 m/sec.     

Molecular‐Weight‐Controlled Brittle‐to‐Semiductile‐to‐Ductile Transition in S‐(S/B)‐S Triblock Copolymers

Toughness enhancement of S‐(S/B)‐S triblock copolymers via a molecular‐weight‐controlled pathway is demonstrated. The post‐yield crack toughness behavior of the triblock copolymers uniquely reveal a brittle‐to‐semiductile‐to‐ductile transition with increasing while keeping the basic molecular architecture fixed. TEM and SAXS investigations indicated three distinct morphologies as a function of χ_effN as a consequence of the increase in : (i) a homogeneous structure without phase‐separation, (ii) a weakly segregated structure, and (iii) a lamellar structure. The increase in crack toughness is also reaffirmed from kinetic and strain field analysis studies concerning dynamics of crack growth in block copolymers with high PS content.

     

Crack tip damage analysis in fatigue fracture of epoxy resin

The application of the crack layer theory to fatigue crack propagation (FCP) in epoxy is discussed. A crack tip damage evolution coefficient μ is introduced to assess the extent of damage as a fraction of the damage associated with critical crack propagation. The results can be expressed in the form where dl/dN is the rate of FCP, G₁ is the energy release rate whose critical value is G_1c, and β is a phenomenological constant. Although no damage was detected from microscopic analyses, μ increases fivefold during stable crack propagation. Fractal analysis of fracture surface profiles provides a quantitative measure of the roughness associated with crack advance. The fractural measure d is found to evolve in a similar fashion as μ, suggesting the applicability of d to quantify crack tip damage evolution.     

The fracture of epoxy- and elastomer-modified epoxy polymers in bulk and as adhesives

The fracture behavior of a piperidine/bisphenol A diglycidyl ether (A) resin has been determined in bulk and as an adhesive using the linear elastic fracture methods developed by Mostovoy¹. The effect of adding carboxy-terminated butadiene–acrylonitrile (CTBN) elastomer to resin A was investigated. The opening-mode fracture energy () of resin A was 120 to 150 J/m², and largely attributable to plastic deformation. Fractographic evidence was obtained for plastic flow at the crack tip during crack initiation. Propagation was unstable due to the rate dependence of the plasticity. There were no significant differences in the bulk and adhesive fracture behavior. Addition of 5–15% CTBN to resin A produced minute elastomer particles which increased to ～4000J/m² (at 15%). Further CTBN addition resulted in an elastomer–epoxy blend and a decrease in fracture energy. Fractography again indicated that crack initiation involved plastic deformation but that the elastomer had greatly increased the volume in which the deformation occurred. The adhesive fracture of the elastomer–epoxy was found to be strongly dependent on the crack-tip deformation zone size (r_yc) in that was a maximum when bond thickness was equal to 2 r_yc. At bond thicknesses less than 2 r_yc, there was a restraint on the development of the plastic zone resulting in lower values.     

Impact Modification and Fracture Mechanisms of Core–Shell Particle Reinforced Thermoplastic Protein

Mechanical properties and fracture mechanisms of Novatein thermoplastic protein and blends with core–shell particles (CSPs) have been examined. Novatein is brittle with low impact strength and energy‐to‐break. Epoxy‐modified CSPs increase notched and unnotched impact strength, tensile strain‐at‐break, and energy‐to‐break, while tensile strength and modulus decrease as CSP content increases. T_g increases slightly with increasing CSP content attributed to physical crosslinking. Changes to mechanical properties are related to the critical matrix ligament thickness and rate of loading. Novatein control samples display brittle fracture characterized by large‐scale crazing. At high CSP content a large plastic zone and a slow crack propagation zone in unnotched and tensile samples are observed suggesting increased energy absorption. Notched impact samples reach critical craze stresses easily regardless of CSP content reducing impact strength. It is concluded that the impact strength of thermoplastic protein can be modified in a similar manner to traditional thermoplastics.

     

Mechanical and fracture behavior of an artificially ultraviolet‐irradiated poly(ethylene‐carbon monoxide) copolymer

In this work, 1 wt % carbon monoxide (CO) poly(ethylene‐carbon monoxide) (ECO) copolymer sheets were artificially exposed to ultraviolet (UV) light with a power density of 3 mW/cm² for up to 130 h. A thorough mechanical characterization of the irradiated material was conducted, in which both the stress–strain data and the values of the quasistatic crack initiation and growth toughness were measured and correlated with companion uniaxial tensile tests and single‐edge‐notched fracture tests. Average values of the elastic modulus, failure strain, and failure stress were determined from the tensile tests. The full‐field optical technique of digital image correlation was used to quantify in‐plane deformation (displacements and displacement gradients) during the fracture experiments and to extract values of the crack initiation and growth fracture toughness. The elastic modulus increased monotonically with UV irradiation for the exposure times used in this investigation. In addition, for low irradiation times of less than 5 h, both the failure strain and failure stress of ECO decreased, and this caused a corresponding decrease in the crack initiation and growth toughness. However, for longer irradiation times, the failure strain remained almost invariable, whereas the failure stress increased by about 25% over that of unirradiated ECO. As a result, for longer irradiation times (>5 h), 1 wt % CO ECO became not only stiffer but also stronger and tougher, as quantified by companion fracture experiments. © 2004 Wiley Periodicals, Inc. J Appl Polym Sci 92: 139–148, 2004     

Impact energy absorption of unidirectional glass fiber-epoxy composites

The influence of resin and fiber properties on the impact behavior of composites can be assessed in a three-point drop-weight impact test by varying the length-to-thickness ratio of the specimen. The fracture initiation energy per unit deformed volume, w_i, can be described by the expression: where τ₁₁ is the tensile stress, τ₁₂ is shear stress; E₁₁ is tensile modulus; and G₁₂ is shear modulus. A unidirectional glass fiberepoxy composite was tested at impact velocities of 2.2 m/s (5 mph) and 4.5 m/s (10 mph). The energy to initiate fracture, w_i, was in the range of 2 to 3.5 MJ/m³, apparently independent of impact velocity. The total energy absorbed by the impacted composite was also found to be independent of impact rate but very sensitive to the length to thickness ratio: about 13 and 3.5 MJ/m3 at the corresponding ratios of 4.6 and 23. It was generally observed that high fracture energy is associated with extensive specimen delamination, i.e. failure in shear.     

The mechanical behavior of polyarylsulfone

A detailed study of the fracture behavior of polyarylsulfone was conducted over a temperature range of ?175 to 120°C. Both fatigue crack propagation and fracture toughness tests were run as well as forced torsion pendulum tests to characterize the dynamic properties. The polymer exhibited a broad secondary loss peak and a high glass transition temperature at ?110 and 295°C, respectively. Fracture toughness, K_IC, and fatigue crack growth resistance were found to vary similarly with temperature, minima being observed near ?50°C. Below that temperature, both a rise in toughness and in fatigue resistance is associated with the broad secondary loss peak. The slopes of the log fatigue crack velocity (da/dN) vs log stress intensity range (ΔK) curves varied from 2.6 to 13.2. Since the equation da/dN = α(ΔK)ⁿ described all of the data, the log-log slope or exponent, n = ?ln(da/dN)?ln ΔK, was considered as a stress intensity sensitivity index with respect to fatigue behavior. This index was at a maximum near ?50°C, where the minimum in toughness occurred. A kinetic model was utilized to correlate the stress intensity sensitivity index and suggested that a single thermally activated mechanism controls the low temperature mechanical behavior of polyarylsulfone.     

Slow crack growth in cellulose film

A simple photographic method for measuring the slow crack growth in transparent polymer film is described. Framing speeds up to 100 per second have been achieved. Experimental data for a cellulose film with centrally located initial cuts indicate that for 0 < t < 0.8t_b, the crack length c increases with time t according to where c₀ is the initial cut size, K a constant, and t_b the time to fracture.     

Polymer melt elongation—methods,results, and recent developments

For film blowing of polyethylene it has been shown previously that melt elongation is very powerful for polymer characterization. With two types of rheometers, simple (also called “uniaxial”) elongational tests as well as creep tests can be performed homogeneously. In simple elongation, the melts of branched polyethylene show a remarkable strain hardening. With respect to their advantages and disadvantages, these rheometers complement each other. For multiaxial elongations the various modes of deformation can be performed by means of the rotary clamp technique. With the strain rate components ordered such that \documentclass{article}\pagestyle{empty}\begin{document}$ \dot \varepsilon $\end{document}₁₁ ? \documentclass{article}\pagestyle{empty}\begin{document}$ \dot \varepsilon $\end{document}₂₂ ≥ \documentclass{article}\pagestyle{empty}\begin{document}$ \dot \varepsilon $\end{document}₃₃, the ratio m = \documentclass{article}\pagestyle{empty}\begin{document}$ \dot \varepsilon $\end{document}₂₂/\documentclass{article}\pagestyle{empty}\begin{document}$ \dot \varepsilon $\end{document}₁₁ characterizes the test mode. The Stephenson definition of the elongational viscosities makes use of the linear viscoelastic material equation and proves to be very efficient because the linear shear viscosity (t) (“stressing” viscosity) can act as the reference for the nonlinear behavior in elongation. Results are given for polyisobutylene measured not only in simple, equibiaxial, and planar elongations, but also in new test modes with a change of m during the deformation. This allows one to investigate the consequences of a deformation-induced anisotropy of the rheological behavior.