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.     

Low velocity surface fracture patterns and energies in poly(methyl methacrylate)

Steady-state fracture techniques were used to investigate the surface fracture patterns and surface fracture energies of poly(methyl methacrylate) at low velocities (10 cm/sec to 10^?5 cm/sec). Several anomalies were discovered: (1) Small surface cracks, running parallel to the crack front, which were initiated by imperfections; (2) a “zero velocity” transition from the normal surface fracture patterns to a “laminar” pattern; and (3) a subsequent transition from the laminar pattern to a “turbulent” pattern. The velocities at which these anomalous fracture patterns occurred were of the order of 10^?4 to 10^?6 cm/sec. The corresponding surface fracture energies were as low as 10⁵ erg/cm².     

Very slow crack growth during osmosis in epoxy and in polyester resins

It has been demonstrated that osmotic pressure filled cracks in both epoxy and polyester resins are elastic cracks. Use of classical formulas for elastic cracks has enabled estimates to be made of the time dependence of Young's modulus for both resins. Use of linear elastic fracture mechanics formulas has enabled stress intensity factors to be determined from measurements of crack profiles. Radical crack growth rates are small, in the range 10^?12–10^?9 ms^?1 for hot water tests, and remain constant over a wider range of stress intensity factor, from 0.3 to 0.8 MPa.m^1/2. To a first approximation, constant radial growth rate is compatible with a diffusion controlled mechanism. However, analysis of the data indicates an activation energy of ～50 kcal. Some evidence is presented for concluding that, in polyesters at least, the true nature of crack propagation can be by way of slip/stick.     

Fracture toughness of poly(butylene terephthalate)

The overall fracture toughness of poly(butylene terephthalate) as well as plane stress and plane strain contributions have been measured as a function of rate from 5 × 10^?2 to 5 × 10³ in/min. A pronounced sample thickness dependence in K_c is observed over this range. Poly(butylene terephthalate) appears to exhibit excellent resistance to low speed crack propagation with internal voiding providing an effective crack blunting mechanism.     

The extensional flow of poly(methyl methacrylate) and high-impact polystyrene at thermoforming temperatures

The work described in the present paper was performed to establish stress–strain–time relationships at plastic sheet thermoforming temperatures. The relationships are correlated with sheet-forming “formability”. Specimens of poly(methyl methacrylate) at 165°C and high-impact polystyrene at 122°C were extended to large strains at constant cross-head velocities. Initial strain rates were between 4.2 × 10^?3/sec and 1.6 × 10^?1/sec. It was found that the flow stress σ was related to the true strain ε and the elapsed time t by a relation σ = Kt^m′εⁿ, where K is a constant and n and m′ are indices. The value of n for both materials was approximately one. The value of m′ was ?0.052 and ?0.33 for poly(methyl methacrylate) and high-impact polystyrene, respectively. Tests were also performed in which the cross-head velocity was increased in steps. It was found that the flow stress in these tests followed the same relationship as in the constant cross-head velocity tests.     

DEPOSITION OF SALINE DROPLETS IN A MODEL OF THE HUMAN BRONCHIAL TREE

Deposition velocities were experimentally determined for aerosols of saline droplets moving in a physical model of the human airways consisting of the first two generations of bifurcations. The aerosols were generated from aqueous solutions containing 0.9 and 1.35% NaCl (by weight) by a Collison nebulizer. The size distributions of the saline droplets were approximately lognormal, with a geometric standard deviation of 1.7. The mass median diameters were 1.04 and 1.23 jim for 0.9 and 1.35% saline droplets. The constant flow rale through the trachea was 255 cm³/scc and the relative humidity of the stream was 99.7% at 22°C, The first bifurcation consisting of the trachea and the two main bronchi, was placed horizontally, while the two second bifurcations were placed in planes normal to the first bifurcation. Because the saline droplets were not monodispersed, larger droplets tended to deposit on the lower edges of the main bronchi. The average deposition velocities on the lower edge were 1.4 ×10^?2cm/sec for 1.35% saline droplets and 1.0 × 10^?2 cm/sec for 0.9% saline droplets. The average deposition velocity on the inner edges of the main bronchi was 3.25 × 10^?3 cm/sec. for both 0.9 and 1.35% saline droplets. These results show that the deposition is nonuniform and that the degree of nonuniformity depends to a great extent on the droplet size. These factors should be taken into consideration in aerosol therapy.     

Improvement of the Adhesive Fracture Toughness of Bonded Aluminum Joints Using E-Glass Fibers at Cryogenic Temperature

Fracture toughness and crack resistance of aluminum adhesive joints were measured at the cryogenic temperature of ?150°C, with respect to the orientation and volume fraction of the E-glass fibers in the epoxy adhesive. Cleavage tests on the DCB (Double Cantilever Beam) adhesive joints were performed using two different test rates of 1.67 × 10^?2 and 8.33 × 10^?4 mm/s to observe the crack propagation trends. From the experiments, it was found that the DCB joints bonded with the epoxy adhesive reinforced with E-glass fibers not only showed a stable crack propagation with a low crack propagation speed, but also higher fracture toughness and crack resistance than those of the DCB joints bonded with the unreinforced epoxy adhesive at a cryogenic temperature of ?150°C.     

Slow crack propagation in a heavily-filled particle reinforced epoxide resin

The fracture properties of two proprietary composite dental restorative materials and a model composite system were studied to determine the effects of filler concentration, exposure to water, and particle/polymer adhesion on subcritical crack propagation. Particle content ranged from 36 to 60 volume percent. The double torsion (DT) test was used to measure relationships between the stress intensity factor (K₁) and the speed of decelerating cracks or the rate of loading in dry and wet materials in air at laboratory conditions. Materials with weak particle/polymer interfaces fractured by continuous crack growth in both dry and wet conditions. In dry and wet materials with strong interfaces, continuous cracking also occurred at the low end of the range of speeds observed (10⁻⁷ to 10⁻³ m/s), but under test conditions of high crack speeds unstable (stick-slip) crack propagation was found in dry specimens and in wet model composites with 41 percent vol, filler. Water had a corrosive effect lowering K_1c for continuous crack propagation. The exponential dependence of K_1c on crack velocity, representing the viscoelastic response of the materials, was positively correlated to the filler concentration and the plasticizing effect of water. Observations on fracture surfaces indicate that low velocity cracks (<10⁻⁵ m/s) propagate through regions of high stress concentrations (interfaces, corners, pores) while at higher crack velocities failure occurs by a combination of interparticle and transparticle fracture.     

Elasticity at large deformations and high strain rates in injection molded polypropylene

The deformation behavior of isotactic polypropylene (PP) as a function of strain rate was investigated at 50°C in uniaxial tension. Injection molded dogbone specimens were tested at high strain rates, ε = 10^?1 – 10² s^?1, and the local deformation in the neck was studied using fast tensile videometry. A strong elastic recoil was observed after fracture in this strain rate range with local elastic strains as high as ?_e = 2.0 – 3.2. The recoil is very fast and takes place within 1 ms. The elastic fraction of the strain at break was found to increase with the local strain rate. The elasticity further depends on strain and temperature. The elastic deformation behavior is part of the known transition from ductile cold drawing behavior to brittle fracture that occurs with strain rate or temperature. The elasticity in PP is thought to be due to a decrease in crystallinity, resulting in a discontinuous crystalline structure comparable to that of thermoplastic elastomers.     

The effect of strain rate on the stress–strain curve of oriented polymers. II. The influence of heat developed during extension

The temperature changes which take place in a yarn during extension are considered. From thermodynamical considerations and the heat-transfer coefficient it is shown that extension of the yarns studied will take place isothermally at strain rates below 0.04 sec.^?1 and adiabatically at rates above 4 sec.^?1 It is not possible to make an accurate estimate of the magnitude of the temperature rise during adiabatic extension, because of the lack of information on internal energy changes during irreversible extension, but by assuming these to be zero it is estimated that the temperature is likely to rise by 20–30°C. at strains above 10%. Results from a study of the effect of strain rate on the stress-strain curves of five different yarns show in all these materials a range of strain rate in which the stress that produces a given strain increases less rapidly with strain rate than elsewhere. For viscose and poly(ethylene terephthalate) this effect occurs in the expected range of strain rate, and its magnitude is of the correct order for it to be attributed to the temperature rise resulting from the transition from isothermal to adiabatic extension. For the other materials the transition does not seem likely to provide a complete explanation of this effect. There is no evidence that the transition significantly affects the breaking properties.     

Mechanics of crack growth in epoxide resins

Experiments have been conducted employing tapereddouble-cantilever-beam joints with different epoxide adhesives. Depending on the adhesive employed, crack propagation occurred either (a) in a continuous stable manner with crack propagation velocities in the range 10^?4 to 5 m/s and values of the adhesive fracture energy, G_Ic, being almost independent of the crack velocity, or (b) intermittently in an unstable manner when the initial crack velocity was never less than about 20 m/s and, in some instances, rose to about 450 m/s; values of G_Ic (initiation) increased rapidly with increasing velocity. It is proposed that the amount of localized plastic deformation arising from shear yielding that occurs at the crack tip prior to crack propagation is controlling. Secondly, the longterm strength of stressed, structural adhesive joints has been investigated. The fracture of these joints over eight decades of time is uniquely described by a critical plastic zone size developed at the crack tip at failure.     

Molecular response of a glassy polymer to active deformation

The behavior of a glassy polyethylene-like polymer undergoing active compressive deformation was investigated via molecular dynamics simulation. Several important features can be identified within the stress-strain response of the system. Namely, the system deforms elastically, yields, softens, and then at large strains exhibits strain hardening. Simulations reveal that the actively deforming polymer exhibits several distinct characteristics at the molecular scale. Active deformation is found to significantly increase the transition rate between different dihedral angle states as well as promote the propagation of dihedral angle flips along the chain. When deformation is stopped, the transition rates decrease and propagation of these transitions along the chain is once again hindered. Below the glass transition temperature, transitions are heterogeneously distributed within the system. However, a local density-transition rate correlation study shows that this transitional heterogeneity is not attributable to heterogeneity in the local density. Instead, the high local transition rates must be caused by stresses propagated along the chain backbone as indicated by changes in neighbor correlations with stress. The yield stress is determined as a function of strain rate between strain rates of 10⁸ s⁻¹ and 5×10¹⁰ s⁻¹. The activation volume within the context of the Eyring model is calculated to be 0.21 nm³ for this system.     

Twin structures in copper after shock and Shockless high-rate loading

The structure of copper formed after high-rate loading up to pressures of 20–80 GPa with a strain rate of 10⁵–10⁹ sec^?1 is considered. In situations with pressures above 20 GPa and strain rates above 10⁶ sec^?1, the deformation twins are grouped into packets, which are seen in an optical microscope as parallel bands of localized strains inside individual grains. The number of bands in the structure increases with increasing grain size and strain rate, with decreasing sample temperature, and with increasing period of sample loading. The characteristic time of formation of twin bands in copper is estimated as 0.3 µsec.     

Comparison of mechanical properties of PP/SEBS blends at intermediate and high strain rates with SiO2 nanoparticles vs. CaCO3 fillers

The present article focuses on the effect of two types of inorganic fillers (SiO₂ and CaCO₃) on the mechanical properties of PP/SEBS blend. The nominal particle diameters of SiO₂ and CaCO₃ are 7 nm and 1 μm, respectively. The studied blend ratios were PP/SEBS/SiO₂ (CaCO₃) = 75/22/3 and 73/21/6 vol %. The morphology of polymer blends was observed and the distributions of the SEBS, SiO₂, and CaCO₃ particles were analyzed by transmission electron microscopy (TEM). Tensile tests were conducted at nominal strain rates from 3 × 10^?1 to 10² s^?1. The apparent elastic modulus has the local strain‐rate dependency caused by SiO₂ nanoparticles around SEBS particles in the blend of PP/SEBS/SiO₂. The yield stress has weak dependency of morphology. The absorbed strain energy has strong dependency of the location of SiO₂ nanoparticle or CaCO₃ fillers and SEBS particle in the morphology. It is considered that such morphology, in which inorganic nanoparticles are located around SEBS particles, can prevent the brittle fracture while the increased local strain rate can enhance the apparent elastic modulus of the blend at the high strain rate. On the basis of the results of this study, the location and size of inorganic nanoparticles are the most important parameters to increase the elastic modulus without decreasing the material ductility of the blend at both low and high strain rates. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci, 2008     

Ultra-high creep resistant SiC ceramics prepared by rapid hot pressing

The high-temperature compression creep of additive-free β/α silicon carbide ceramics fabricated by rapid hot pressing (RHP) was investigated. The creep tests were accomplished in vacuum at temperature range 1500 °C–1750 °C and compressive loads of 200 MPa to 400 MPa. Under investigated condition the RHP ceramics possessed the lowest creep rate reported in the literature. The observed strain rates changed from 2.5 × 10^?9 s^?1 at 1500 °C and a lowest load of 275 MPa to 1.05 × 10^?7 s^?1 at 1750 °C and a highest load of 400 MPa. The average creep activation energy and the stress exponent remain essentially constant along the whole range of investigated parameters and were 315 ± 20 kJ?mol^?1, and 2.22 ± 0.17, respectively. The suggested creep mechanism involves GB sliding accommodated by GB diffusion and β?α SiC phase transformation.     

Temperature and rate dependent fracture in glass-filled polystyrene

The rate and temperature dependent fracture behavior of glass-filled polystyrene has been investigated over the crack speed range of 10¹³ to 1 mm/sec and in the temperature range 283 to 396°K for three environmental conditions: (i) air; (ii) water; and (iii) hot water exposure at 363°K and subsequent drying. Relationships between fracture toughness (K_c), crack speed and temperature have been obtained experimentally and analysed according to the concepts of fracture mechanics and reaction rate theories. Crack propagation in air is shown to be controlled by a β-relaxation process associated with crazing. Activation energies of 200 ～ 210 kj/mole in air and 80 ～ 120 kj/mole in water are reported. At a given temperature and crack speed, the glass-filled polystyrene is shown to display smaller crack propagation resistances in a water environment when compared with the air results. Specimens subjected to hot water exposure and then tested after drying also possess less cracking resistance. This toughness degradation phenomenon is a result of the damaging effects of the water which penetrates into the glass-filled composite.     

Strain-rate-dependent compressive and compression-shear response of an alumina ceramic

This paper assessed the microstructure and properties of CeramTec ALOTEC 98 SB alumina ceramic through microscopic characterization and mechanical experiments. The rate-dependent strength and failure response of an alumina ceramic were studied under both uniaxial compression and compression-shear loading. Under quasi-static uniaxial compression at rates of 10^?5 to 10³ s^?1, the strength had an average of 3393 ± 306 MPa, and at dynamic strain rates of 10² to 10³ s^?1, the strength ranged from 3763 to 4645 MPa. The CeramTec ALOTEC 98 SB alumina ceramic was found to have greater mechanical properties than other commercial alumina ceramics from the literature (i.e., AD-995). To monitor the strain field and the failure process of the alumina ceramic during testing, an ultra-high-speed camera coupled with digital image correlation (DIC) was used to visualize crack initiation and propagation processes, and obtain quantitative stress-strain information. A new data processing method was then proposed in this study to calculate the shear components for the compression-shear tests. Validation of the proposed method was confirmed by the shear strain obtained from the DIC analysis with the ultra-high-speed camera. Using the results obtained by the proposed model and the DIC analysis, new observations and understandings of failure mechanisms are obtained. (1) In compression-shear tests, the shear failure happens before complete failure, and shear behavior plays an important role during the failure process. (2) The equivalent peak stress (strength) of compression-shear test is smaller than the uniaxial compression one. (3) The directional cracks have weak influence on the compressive stiffness, but have a strong influence on the shear response.     

Gas combustion in narrow single channels

Combustion of propane-air mixtures flowing in quartz tubes with internal diameter greater but comparable to the critical diameter was studied experimentally. It was shown that in opposed flame propagation, the flame velocity decreased linearly to almost zero with increasing flow velocity. In the region of zero velocity, there was a transition from the regime of high velocities to a stationary regime with propagation velocities typical of the low-velocity regime (LVR) of filtration gas combustion (about 10⁻⁴ m/sec). This regime was studied and classified as the LVR-2 in view of its special properties. It was shown that a further increase in the flow velocity led to flame stabilization in the LVR-2. In various ranges of flow velocities, various types of instability of the flame front were observed.     

Sodium bisulfite-initiated polymerization of methyl methacrylate in aqueous medium in the presence of the metal oxides CuO and MnO2

Sodium bisulfite-initiated polymerization of methyl methacrylate (MMA) in water medium was carried out in the absence and in the presence of cupric oxide and manganese dioxide using various initiator concentrations at various temperatures ranging from 30° to 60°C. It seems that the metal oxide–water interface plays an important role, as it has been found that both oxides accelerate the rate of polymerization. Cupric oxide was found to be more effective than manganese dioxide. The cupric oxide was found to have nearly the same catalytic effect as the cuprous oxide, and manganese dioxide was found to be somewhat more effective than titanium dioxide. The initial rate of polymerization increased from 2.3 × 10^?5 mole/(l.sec) to 3.4 × 10^?4 mole/(l.sec) and to 6.6 × 10^?5 mole/(l.sec) when the metal oxide concentration increased from 0 to 3 g/l. in case of cupric oxide and manganese dioxide, respectively. The initial rate of polymerization increased from 3.7 × 10^?4 mole/(l.sec) to 4.2 × 10^?4 mole/(l.sec) and from 7.2 × 10^?5 to 2.2 × 10^?4 mole/(l.sec) when the temperature was raised from 30° to 60°C in the presence of cupric oxide and manganese dioxide, (9 g/l.), respectively. Both the rate of polymerization and the number-average molecular weights were found to increase with increase the monomer concentration; the rate values were higher while the number-average molecular weights were lower in case of cupric oxide than in case of manganese dioxide. For example, the rate of polymerization increased from 2 × 10^?5 mole/(l.sec) to 8.1 × 10^?5 mole/(l.sec) and from 1.9 × 10^?5 mole/(l.sec) to 6.9 × 10^?5 mole/(l.sec); and the number-average molecular weight increased from 0.7 × 10⁵ to 2.2 × 10⁵ and from 1.5 × 10⁵ to 4.9 × 10⁵ in the presence of cupric oxide and manganese dioxide (10 g/l.), respectively, when the monomer concentration was increased from 23.5 g to 94 g/1. water. The apparent energy of activation for the polymerization of methyl methacrylate in water medium between 40° and 50°C was found to be 0.8 and 4.3 kcal/mole when using cupric oxide and manganese dioxide (9 g/l.), respectively.     

Strain disturbances due to viscoelastic crack propagation

Local strain disturbances near a running crack in a viscoelastic material were investigated in PMMA. Specimens having different initiation crack tip radii and under different tensile strain rates were examined by use of a series of strain gauges placed parallel and close to the expected crack path, and by velocity gauges. The strain disturbance, which was observed ahead of the running crack front, diminished gradually owing to the viscoelastic damping. The maximum strain disturbances increased with increase in gross breaking load.