Crack-tip damaged zones in rubber-toughened amorphous polymers: a micromechanical model

The various stages of crack propagation in rubber-toughened amorphous polymers (onset and arrest, stable and unstable growth) are governed by the rate of energy dissipation in the cracktip damaged zone; hence the relationship between the applied stress intensity factorK ₁ and the damaged zone size is of utmost importance. The size of the crack-tip damaged zone has been related toK ₁ via a parameter which is characteristic of the material in given conditions: this factor is proportional to the threshold stress for damage initiation in a triaxial stress field, and has been denoted by ^*. Theoretical values of ^* have been calculated by means of a micromechanical model involving the derivation of the stresses near the particles and the application of damage initiation criteria. The morphology, average size and volume fraction of the rubbery particles have been taken into account together with the nature of the matrix. The calculated values of ^* have been successfully compared with the experimental ones, for a wide set of high-impact polystyrenes (HIPS) and rubber-toughened poly(methyl methacrylate) (RTPMMA).Nomenclature PS; HIPS polystyrene; high-impact polystyrene - PMMA; RTPMMA poly(methyl methacrylate); rubber-toughened PMMA - MI; CS/H; CS/R particle morphologies (multiple inclusion; hard core - rubber shell; rubber core - rigid shell) - K _r;K _g bulk moduli of rubber and glassy materials - G _r;G _g shear moduli of the same materials - v _p particle volume fraction - L mean centre-to-centre distance between neighbouring particles - B; H; W standard names for the dimensions of the compact tension specimen - R _y size of the crack-tip plastic zone in a homogeneous material - h half thickness of the crack-tip damaged zone - r; polar coordinates around the crack tip (Fig. 1) - r;r _p distance from particle centre; particle radius - p normalized distance from the particle (Equation 5) - K ₁;K _1c;K _1p stress intensity factor; critical values ofK ₁ at the onset of and during crack growth - G _1c plane strain energy release rate - _y yield stress in uniaxial tension - _th macroscopic threshold stress for the onset of local damage initiation in a composite material - ^* characteristic parameter (Equation 3) - ⁰; ₁ ⁰ ; ₂ ⁰ ; ₃ ⁰ applied stress tensor and its three principal stresses - ⁰ uniaxial applied stress - ; ₁; ₂; ₃ local stress tensor and its three principal stresses - A tensor which elements are the ratios of those of over those of ⁰ (Equation 4) - v Poisson's coefficient of the matrix - g triaxiality factor of the crack-tip stress field - _e; _p Mises equivalent stress; dilatational stress (negative pressure) - I ₁;I ₂ invariants of the stress tensor - U ₁;U ₂ material parameters for argon and Hannoosh's craze initiation criterion (Equation 12)     

Electrical conductivity,thermoelectric power and dielectric constant of NiWO4

The a.c. electrical conductivity ( _ac), thermoelectric power () and dielectric constant () of antiferromagnetic NiWO₄ are presented. _ac and have been measured in the temperature range 300 to 1000 K and in the temperature range 600 to 1000 K. Conductivity data are interpreted in the light of band theory of solids. The compound obeys the exponential law of conductivity = ₀ exp (–W/kT). Activation energy has been estimated as 0.75eV. The conductivity result is summarized in the following equation =2.86 exp (–0.75 eV/kT)^–1 cm^–1 in the intrinsic region. The material is p-type below 660 K and above 950 K, and is n-type between 660 and 950 K.     

Strength of the pyroceram So115M under lengthy static loading

The article presents the results of long-time strength tests of the casting pyroceram SO115M at room temperature by the method of three-point bending. We obtained the power dependence of the time to failure _f on the applied load : _f ^–11.7.Translated from Problemy Prochnosti, No. 1, pp. 102–104, January, 1996.     

On the measurement and physical meaning of the cleavage fracture stress in steel

Elastic-plastic two-dimensional (2D) and three-dimensional (3D) finite element models (FEM) are used to analyze the stress distributions ahead of notches of four-point bending (4PB) and three-point bending (3PB) specimens with various sizes of a C-Mn steel. By accurately measuring the location of the cleavage initiation sites, the local cleavage fracture stress _f and the macroscopic cleavage fracture stress _F is accurately measured. The _f and _F measured by 2D FEM are higher than that by 3D FEM. _f values are lower than the _F, and the _f values could be predicted by _f=(0.8––1.0)_F. With increasing specimen sizes (W,B and a) and specimen widths (B) and changing loading methods (4PB and 3PB), the fracture load P _f changes considerably, but the _F and _f remain nearly constant. The stable lower boundary _F and _f values could be obtained by using notched specimens with sizes larger than the Griffiths–Owen specimen. The local cleavage fracture stress _f could be accurately used in the analysis of fracture micromechanism, and to characterize intrinsic toughness of steel. The macroscopic cleavage fracture stress _F is suggested to be a potential engineering parameter which can be used to assess fracture toughness of steel and to design engineering structure.     

Low-temperature synthesis,pyrolysis and crystallization of tantalum oxide gels

Tantalum oxide gels in the form of transparent monoliths and powders have been prepared from hydrolysis of tantalum pentaethoxide under controlled conditions using different mole ratios of Ta(OC₂H₅)₅C₂H₅OHH₂OHCl. Alcohol acts as the mutual solvent and HCl as the deflocculating agent. For a fixed alkoxide water HCl ratio, the time of gel formation increased with the alcohol to alkoxide molar ratio. Thermal evolution of the physical and structural changes in the gel has been monitored by differential thermal analysis, thermogravimetric analysis, X-ray diffraction, and infrared spectroscopy. On heating to 400 °C, the amorphous gel crystallized into the low-temperature orthorhombic phase -Ta₂O₅, which transformed into the high-temperature tetragonal phase -Ta₂O₅ when further heated to 1450 °C. The volume fraction of the crystalline phase increased with the firing temperature. The -Ta₂O₅ converted back into the low-temperature phase, -Ta₂O₅, on slow cooling through the transformation temperature of 1360 °C, indicating a slow but reversible transformation.     

On internal stress and activation volume in polymers

The two-site model is developed for the analysis of stress relaxation data. It is shown that the product of d In (– )/d and (- _i) is constant where is the applied stress, _i is the (deformation-induced) internal stress and = d/dt. The quantity d In ( )/d is often presented in the literature as the (experimental) activation volume, and there are many examples in which the above relationship with (- _i) holds true. This is in apparent contradiction to the arguments that lead to the association of the quantity d In (– )/d with the activation volume, since these normally start with the premise that the activation volume is independent of stress. In the modified theory presented here the source of this anomaly is apparent. Similar anomalies arise in the estimation of activation volume from creep or constant strain rate tests and these are also examined from the standpoint of the site model theory. In the derivation presented here full account is taken of the site population distribution and this is the major difference compared to most other analyses. The predicted behaviour is identical to that obtained with the standard linear solid. Consideration is also given to the orientation-dependence of stress-aided activation.     

Conventional Electronic Structure of MgB2 and ZrB2: LDA vs. de Haas-v. Alphen & ARPES Data

We compare full potential LDA band calculations of the Fermi surfaces areas and band masses of MgB₂ and ZrB₂ previously reported and new dHvA data. Discrepancies in areas in MgB₂ can be removed by a small shift of bands relative to bands. Comparison of effective masses lead to orbit averaged el-ph coupling constants =1.3 and =0.5, whereas for ZrB₂ only weak el-ph coupling with <0.3 is found. The ARPES data can be also well described by the LDA showing the presence of surface states.     

Stress relaxation in hot-drawn low density polyethylene

The tensile stress relaxation behaviour of hot-drawn low density polyethylene, (LDPE), has been investigated at room temperature at various draw ratios. The drawing was performed at 85° C. The main result was an increase in relaxation rate in the draw direction, especially at low draw ratios when compared to the relaxation behaviour of the isotropic material. This is attributed to a lowering of the internal stress. The position of the relaxation curves along the log time axis was also changed as a result of the drawing, corresponding to a shift to shorter times. The activation volume, , varied with the initial effective stress ₀ ^* according to ₀ ^* 10kT, where ₀ ^* =₀ — _i, is the difference between the applied initial stress, ₀, and the internal stress _i. This result supports earlier findings relating to similarities in the stress relaxation behaviour of different solids.     

Investigations of the copper isotope effect in oxygen-deficient YBa2Cu3O7−δ

We present data on the copper isotope effect (⁶³Cu-⁶⁵Cu), C_u =-nT_c/nm_Cu, for two isotopic pairs of oxygen-deficient YBa₂Cu₃O_7–, where varies between 0.06 and 0.52. _Cu is below 0.01 at =0.06 (fully oxygenated), it takes values between –0.14 and –0.34 in the 60 K plateau. Larger negative values of _Cu are observed away from the plateau. The dependence of _Cu is similar to that of the pressure effect dnT_c/dP.     

Evaluation of the true activation enthalpy of superplastic flow including a threshold stress

A new method is suggested for the evaluation of the true activation enthalpy for alloys where the strain rate of the superplastic flow varies with a power of an effective stress _e = -_o, where and _o are the applied stress and a threshold stress, respectively. Some earlier results concerning superplastic AlMgZnCu alloys containing chromium and in which a strongly temperature-dependent threshold stress can be revealed, are reanalysed. The results are in good agreement with the previous ones. It has been shown further that for the alloys investigated the true activation energy increases with increasing chromium content.     

Distribution characteristics of mechanical properties and correlation between the respective properties on S35C carbon steel

Mechanical properties of tensile strength, , upper yield stress, _SU, lower yield stress, _SL elongation, , area reduction, , Vickers hardness, H _v, and impact absorbed energy, E, were examined using 50 specimens of S35C carbon steel, which were machined from two bars supplied from the same charged and heat-treated material. Distribution characteristics of these properties are discussed, and the correlation between each pair of them is investigated from a statistical viewpoint. The main conclusions obtained are summarized as follows; distribution characteristics of _B, _SL, , , H _v and E are well approximated by a normal distribution, but those of asu are not approximated as well by this type of distribution. In the latter case, a Weibull distribution is preferable to represent the distribution pattern. No significant correlation was observed between each pair of the above mechanical properties. Consequently, individual properties have the inherent distribution characteristics independent of the other properties.     

Thermal diffusivity of inhomogeneous systems

The possibility of analyzing the nonsteady temperature fields of inhomogeneous systems using the quasi-homogeneous-body model is investigated.Notation t, t_I, t_i temperature of quasi-homogeneous body inhomogeneous system, and i-th component of system - a, , c thermal diffusivity and conductivity and volume specific heat of quasi-homogeneous body - a_{i i}, c_i same quantities for the i-th component - q heat flux - S, V system surface and volume - x, y coordinates - macrodimension of system - dimensionless temperature Fo=a/² - Bi=/ Fourier and Biot numbers - N number of plates - =h/ ratio of micro- and macrodimensions - _V, volumeaveraged and mean-square error of dimensionless-temperature determination - time - m_i i-th component concentration Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 39, No. 1, pp. 126–133, July, 1980.     

Shock response of stainless steel at high temperature

Measurements of the dynamic tensile strength of HR-2 (Cr-Ni-Mn-N) stainless steel have been carried out over the initial temperature range of 300 K–1000 K at shock stress of 8 GPa, the corresponding spall strength _f and Hugoniot elastic limit _HEL are determined from the wave profiles. In the temperature range of 300 K–806 K, _f and _HEL decrease linearly with increasing temperature T, i.e., _f = 5.63-4.32 × 10^–3T, _HEL = 2.08-1.54 × 10^–3T, but when heated to 980 K, _HEL increases from 0.84 GPa at 806 K to 0.93 GPa at 980 K and _f keeps at an almost fixed value of 2.15 GPa. The TEM analysis on recovery samples identified the existence of intermatallic compound Ni₃Al and the carbide Cr₂₃C₆ in the sample of 806 K, another intermatallic compound Ni₃Ti was found in the sample of 980 K. All these products emerge along crystal boundary. While no such products were found in the samples of 300 K and 650 K.     

Electrical conductivity of Cux(As0.4Se0.3Te0.3)100−x glasses

Results of the dc electrical conductivity () measurements (from 90 to 420 K) on 15 compositions of the Cux(As0.4 Se0.3 Te0.3)100–x glasses (x from 0 to 30) are presented. Similar to that observed [1] in the composition dependencies of the mean atomic volume (V) and the glass transition temperature (Tg) of these glasses, it is possible to delineate three regions in the composition dependence of the of these glasses. (i) For addition of Cu up to 1 at %, the register a decrease compared to that of the parent As0.4Se0.3Te0.3 glass. (ii) For Cu > 1 at %, the conduction activation energy (E) and the pre-exponential factor (C) decrease, with a concomitant increase in (at 250 K) by about six orders of magnitude. (iii) Both E and C show saturation for Cu > 23 at %. The -composition data are examined using the model developed earlier [1] to understand, the V (and Tg)-composition dependencies of these glasses.     

Fracture stress difference of notched polycarbonate between atmospheric pressure and a hydrostatic pressure

Experimental data on fracture stress of polycarbonate (PC) with and without various artificial notches have been obtained at atmospheric pressure and a high hydrostatic pressure (400 MPa). The difference in fracture stress, _F, between both pressures was directly proportional to the intensity of pressure,P, and was inversely proportional to the stress concentration factor of the notch,K _n such that _F following the form of the Kaieda-Oguchi formula, _F. By using the combined stress concentration factor,K _nc, of superposed notch and craze, and by considering the change in elastic modulus due to pressure, the experimental data agreed with the modified Kaieda-Oguchi formula. The stress concentration factor of the craze was calculated by using the Dugdale model.     

Charged defects-controlled conductivity in Ge-ln-Se glasses

The variation of the d.c. electrical conductivity, , with composition and temperature was investigated for glasses of the Ge-In-Se system. The results indicate a decrease in the activation energy for electrical conductivity, E, and an increase in on introduction of indium into Ge-Se glasses. The changes in E and with composition (selenium content in the glasses) are identical for the Ge_x In₅ Se_95–x and Ge_x In₈Se_92–x families. The results have been traced to the conduction controlled by charged defects in these chalcogenide glasses. The changes in E and have been explained by a shift in the Fermi level, being brought by the introduction of indium.     

The influence of grain size on the creep of uranium dioxide

The creep of uranium dioxide has been investigated as a function of grain size. At high stresses, when creep is controlled by dislocation movement, grain boundaries exert a strengthening effect and this strengthening is correlated with the Hall-Petch equation. The degree of strengthening diminishes with increases in temperature. At lower stresses, when creep is controlled by mass transport, grain boundaries exert a weakening effect owing to the reduction in diffusion path length as grain size is reduced. In this range behaviour is correlated with the Nabarro-Herring equation with stress replaced by an effective stress _E=–₀ where ₀ is a threshold stress for diffusional creep associated with the limitation of the ability of boundaries to emit and absorb vacancies. ₀ appears to decrease as grain size is increased.     

Notch tip stress distribution in strain hardening materials

Using the results of elastic-plastic stress analyses for notched bars, it is shown that a modified form of slip-line field solution can satisfactorily explain the variation of longitudinal stress ahead of notch tips in strain hardening materials.

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Résumé En utilisant les résultats d'analyses de contrainte élastoplastique dans le cas de barres entaillées, on montre qu'il est possible d'utiliser une forme simplifiée de solution du champ des lignes de glissement pour expliquer de façon satisfaisante la variation des contraintes longitudinales en avant d'extrémités d'entaille dans des matériaux susceptibles d'un écrouissage.

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Nomenclature _yy longitudinal tensile stress in the notch tip plastic zone - _xx transverse stress in the x-direction - _zz transverse stress in the z-direction - k yield stress in shear - ₀ yield stress in tension - ₀ ^* strain hardened yield stress (flow stress) - _{0/* c} flow stress at notch tip - _total total strain _pl plastic strain _l principal strain - _{1 c} maximum principal strain at notch tip - _1pl plastic strain in they-direction - _{1 cp1} E_{1 pl} at notch tip - _eff effective plastic strain - _{c eff eff} at notch tip - ₀ yield strainC Stress decay constant in the notch tip region - /e_pl linear strain hardening rate - n strain hardening exponent in power hardening law - 2 flank angle of notch - distance from notch tip - p notch tip radius - k _I applied stress intensity for Mode I loading - E Young's modulus - V _c crack tip opening displacement     

Some electrical characteristics of lithium and yttrium sialons

Some electrical properties of hot-pressed lithium sialons, Li _x/8Si_6–3x/4Al_5x/8O _x N_8–x havingx<5 and an yttrium sialon were measured between 291 and 775 K; the former consisted essentially of a single crystalline phase whereas the latter contained 98% glassy phase. For lithium sialons, the charging and discharging current followed al(t) t ^–nlaw withn=0.8 at room temperature. The d.c. conductivities were about 10^–13 ohm^–1 cm^–1 at 291 K and rose to 5×10^–7 ohm^–1 cm^–1 at 775 K. At high temperatures electrode polarization effects were observed in d.c. measurements. The variation of the conductivity over the frequency range 200 Hz to 9.3 GHz followed the () ⁿ law. The data also fitted the Universal dielectric law,() ^n–1 well, and approximately fitted the Kramers-Kronig relation()/()– =cot (n/2) withn decreasing from 0.95 at 291 K to 0.4 at 775 K. The temperature variations of conductivities did not fit linearly in Arrhenius plots. Very similar behaviour was observed for yttrium sialon except that no electrode polarization was observed. The results have been compared with those obtained previously for pure sialon; the most striking feature revealed being that _d.c. for lithium sialon can be at least 10³ times higher than that of pure sialon. Interpretation of the data in terms of hopping conduction suggests that very similar processes are involved in all three classes of sialon.