Deformation approach to the evaluation of the period of initiation and growth of fatigue macrocracks

We performed experimental investigation of the opening displacements of the contours of stress concentrators (notches and cracks) for various amplitudes of cyclic loading. On the basis of experimental results, we propose a new deformation parameter _t which is a function of the notch (crack) tip opening displacement , namely, _t /(+d*), where is the radius of the tip of the notch andd* is the characteristic size of the prefracture zone. It is shown that this parameter uniquely determines the number of cyclesN _l to the initiation of a fatigue macrocrack independently of the geometry of the specimens and stress concentrators in elastic and elastoplastic materials, i.e., the dependence of _t onN ₁ is a characteristic of the material. It is experimentally demonstrated that this dependence enables one to quantitatively describe the process of fatigue fracture both in the stage of initiation of macrocracks and their propagation.Karpenko Physicomechanical Institute, Ukrainian Academy of Sciences, L'viv. Translated from Fiziko-Khimicheskaya Mekhanika Materialov, Vol. 31, No. 5, pp. 7–21, September – October, 1995.     

Experimental determination of the stress-crack opening relation in fibre cementitious composites with a crack-tip singularity

A J-based-fracture-testing method is presented for determining the bridging-stress-crackopening-displacement (-) relationship in fibre-reinforced composites where the crack-tip toughness is not negligible. The J-based technique originally proposed for concrete has been well-established for cementitious composites where the fracture process is primarily dominated by the formation of a fracture-process zone and the contribution of the crack-tip toughness is negligibly small. In this study, the J-based technique is further extended to cover materials for which the crack-tip stress singularity coexists with the fracture-process zone. This extended version of the J-based technique explicitly accounts for the crack-tip singularity while considering the fracture-process zone. This newly derived testing technique has been applied to a high-strength-mortar (HSM) reinforced with carbon and steel fibres where the fibrebridging toughness can be of the same order of magnitude as the crack-tip toughness. The validity of the - relationships deduced has been examined by comparing with results obtained from direct uniaxial tension tests. It is suggested that the J-based-fracture-testing technique can provide reasonable - relationships and fracture parameters in a fibrereinforced HSM.     

Transformation-induced plasticity in two-phase (α+γ) Fe-Cr-Ni alloys

The relationship between the fracture elongation and the value of martensite per unit tensile strain has been studied for the two-phase ( + ) Fe-Cr-Ni alloys containing 10%, 35% and 52% 7. The elongation has a peak in the elongation-test temperature curve. The peak elongation is dependent upon both the delay of necking and a suitable value of martensite per unit tensile strain.     

Influence of threshold parameters on cleavage fracture predictions using the Weibull stress model

This study explores applications of three-parameter Weibull stress models to predict cleavage fracture behavior in ferritic structural steels tested in the transition region. The work emphasizes the role of the threshold parameters (_th and _{w – min}) in cleavage fracture predictions of a surface crack specimen loaded predominantly in tension for an A515-70 pressure vessel steel. A recently proposed procedure based upon a toughness scaling methodology using a modified Weibull stress (^* _w) extends the calibration scheme for the Weibull modulus, m, to include the threshold parameters. The methodology is applied to calibrate the Weibull stress parameter for the tested material and then to predict the toughness distribution for the surface crack specimen. While the functional relationship between ^* _w and m suggests a strong effect of the threshold stress, _th, on the calibrated m-parameter, the results show a remarkably weak dependence of fracture predictions on _th as does the dependence of fracture predictions on _w–min for this specimen.     

The age hardening effect in Ti-6 Al-4 V due to ω and α precipitation in the β grains

The structure at room temperature of a quenched TA6V titanium alloy has been investigated. This structure is + or + according to the treatment temperature; it is always metastable. During ageing the grains decomposed by the reaction + + +; this decomposition was accompanied by a large increase of the 0.2% yield stress. No structural modification was observed in. The and phase of TA6V were separately investigated in the form of single-phase alloys. The hardness of was insensitive to ageing, while was considerably hardened by and; we deduced that the strengthening of the minor phase during ageing is mainly responsible for the hardening of TA6V.     

Effect of crystalline phase, orientation and temperature on the dielectric properties of poly (vinylidene fluoride) (PVDF)

The effect of crystalline phase, uniaxial drawing and temperature on the real () and imaginary () parts of the relative complex permittivity of poly (vinylidene fluoride) (PVDF) was studied in the frequency range between 10² and 10⁶ Hz. Samples containing predominantly and phases, or a mixture of these, were obtained by crystallization from a DMF solution at different temperatures. phase samples were also obtained from melt crystallization and from commercial films supplied by Bemberg Folien. Different molecular orientations were obtained by uniaxial drawing of and phase samples. The results showed that the crystalline phase exerts strong influence on the values of and , indicating that the _a relaxation process, associated with the glass transition of PVDF, is not exclsively related to the amorphous region of the polymer. An interphase region, which maintains the conformational characteristics of the crystalline regions, should influence the process decisively. The molecular orientation increased the values of for both PVDF phases and modified its dependence with temperature over the whole frequency range studied. The influence of the crystallization and molecular orientation conditions on the dc electric conductivity (_dc) were also verified. The value of _dc was slightly higher for samples crystallized from solution at the lowest temperature and decreased with draw ratio.     

In situ enhancement of toughness of SiC—TiB2 composites

A process based on liquid phase sintering and subsequent annealing for grain growth is presented to obtain the in situ enhancement of toughness of SiC–30 wt%, 50 wt%, and 70 wt% TiB2 composites. Its microstructures consist of uniformly distributed elongated -SiC grains, relatively equiaxed TiB2 grains, and yttrium aluminium garnet (YAG) as a grain boundary phase. The composites were fabricated from -SiC and TiB2 powders with the liquid forming additives of Al2O3 and Y2O3 by hot-pressing at 1850°C and subsequent annealing at 1950°C. The annealing led to the in situ growth of elongated -SiC grains, due to the phase transformation of SiC, and the coarsening of TiB2 grains. The fracture toughness of the SiC–50 wt% TiB2 composites after 6 h annealing was 7.3 MPa m1/2, approximately 60% higher than that of as-hot-pressed composites (4.5 MPa m1/2). Bridging and crack deflection by the elongated -SiC grains and coarse TiB2 grains appear to account for the increased toughness of the composites.     

Relationship between the energy supply parameters and the physicochemical l characteristics of polymer compositions during drying and thermal processing

The effect of the type of energy supply on the formation of temperature and concentration fields in the thermal processing of polymer compositions is considered.Notation T₀, T initial and current temperature of the coating - T_m temperature of the air - =(T-T_o)/(T_m-T₀) dimensionless temperature of the coating - a thermal diffusivity - A absorption power of the coating - D diffusion coefficient - thermal conductivity - c thermal capacity - density - _k convective heat transfer coefficient - i number of moles of reacting groups per unit volume of polymer - K₀ factor in front of the exponential - R gas constant - u concentration - Q thermal effect of the reaction - q_n density of the incident radiant flux - =x/ dimensionless coordinate over the thickness of the coating - Ki=Aq_n /(T_m-T₀) Kirpichev criterion characterizing the thermal effect of the reaction - Ki_p=Qi/c (T_m-T₀) analog of the Predvoditelev criterion, characterizing the rate of occurrence of a chemical excess in the system - Bu= Bouguer criterion - Lu=D/a Lykov number - Fo=a/² Fourier number - Bi= _k Biot number Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 39, No. 1, pp. 26–33, July, 1980.     

Intensity of critical opalescence of helium-4

We present measurements of the critical opalescence of helium-4. The results are analyzed by the Einstein and Ornstein-Zernike theory and the power laws. We obtain ==1.17±0.02, ==0.62±0.1,/=4.5±0.3,P _c =1706.008 mm Hg, andT _c =5,189.863 mK (T ₅₈ ). The critical behavior of helium-4 is almost the same as that of classical fluids and the influence of the quantum nature of helium-4 is not as evident as has been claimed.     

Relationship between the structure and mechanical properties in ß III titanium alloy

The ageing reactions that take place during the heat-treatment of solution-treated III titanium (11.5 wt% Mo, 6 wt% Zr, 4.5 wt% Sn, balance Ti) were followed by detailed structure characterization using electron microscopy. The variations in mechanical properties with heat treatment were also followed systematically. The electron microscopy investigations indicated that the omega phase formed on quenching. The size and volume fraction of the omega phase increased on subsequent ageing,, and phases were found to co-exist at ageing temperatures between 800 and 900° F (427 and 482° C) for short ageing times. From the observations of interfacial dislocations at the/ interface and the precipitation of fine alpha near the omega particles, with a morphology that is characteristic of the prior morphology, it is suggested that the-phase forms directly from the omega phase. The observed increase in yield strength over the solution-treated condition, due to the precipitation of phase, was found to agree well with that predicted by the Orowan hardening mechanism. Since the precipitation of fine ellipsoidal-phase was found to increase the yield strength of the alloy with reasonable ductility, it is suggested that the optimum heat treatment to produce high strength with good ductility in III titanium is to age at 900° F (482° C) for 10 to 25 h.     

An instability mechanism for the sliding motion of finite depth of bulk granular materials

Summary Field observations and experimental records indicate that the primary mode of motion of many large landslides is that ofsliding rather thanflowing. Most of shear during sliding is concentrated at the base of slides, with little or no mixing taking place away from the base. This sliding motion may generate strong pressure waves at the interface between the quasi-static deforming granular mass and the grain-inertia dominated rapid granular flow, thus inducing a Kelvin-Helmholtz type instability mechanism for large landslides. The existence of a transitional zone in granular flow is essential for the generation of this type of instability waves. A model using a finite depth of elastic sliding bulk granular materials riding on a basal granular shear flow layer is estabilished to represent the sliding motion of these large volume of bulk granular materials. The balance and the stability of this sliding system are investigated under the perturbation of internal pressure waves. The generated instability waves will force favorable phase shifts between the overburden pressure and the sliding velocity, leading to a net reduction in the total power loss due to friction. The depth of sliding mass will affect the generation of this type of instability waves. Both analytical and numerical results show that smaller depth slides can induce stronger instability waves than larger depth slides do.Notation a perturbation wave amplitude - C nondimensional instability wave speed - C _i growth rate, the imaginary part ofC - C _r wave phase speed, the real part ofC - c _p compressional wave speed in elastic medium - c _s shear wave speed in elastic medium - D nondimensional depth of sliding mass - d depth of sliding mass - G shear modulus of elastic medium - H nondimensional basal depth - h depth of basal shear zone - i - K Coulomb friction coefficient - P _xx, P_yy lateral and normal pressures in granular material, respectively - P _xy shear stress in granular material - p ₀ amplitude of perturbation pressure - p _yy perturbation pressure - r nondimensional complex wave number of instability wave - S nondimensional wave number of shear wave - t time scale - U uniform sliding velocity of a landslide inx direction - u, v velocities inx direction andy direction, respectively - u ₀ granular flow velocity in the basal shear zone - V, V _c nondimensional sliding velocity and its critical velocity, respectively - W power loss to friction - internal friction angle - , Lame's potentials, and are time-independent amplitudes of and , respectively - perturbation wave surface profile - wave number of perturbation wave, _r and _i are the real and imaginary parts of - Poisson's ratio of elastic medium - wave frequency of perturbation wave - , _g density of granular material - stress component in elastic medium - Rankine's earth pressure coefficient - -K ² - Re{}, Im{} the real and imaginary parts of complex quantity inside {}, respectively - , the divergence and the curl of perturbation wave velocities, respectively - Laplacian operator - _ij Kronecker delta; _ij =1 fori=j, _ij =0 forij - ()i, ()j, ()ij tensor - ()1, ()e in sliding mass - ()2, ()b in ground     

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.     

Three-dimensional elastic stress fields ahead of blunt V-notches in finite thickness plates

Based on detailed three-dimensional (3D) finite element analyses, elastic fields in front of blunt V-notches in finite thickness plates subjected to uniaxial far-end tensile stress have been investigated. By comparison with the corresponding planar V-notch fields and 3D through-thickness sharp crack fields, various aspects of the 3D fields of the blunt V-notches in finite thickness plates are revealed: (1) The plate thickness and notch angle have obvious effects on the stress concentration factor (SCF) K _t, which is higher in finite thickness plates than in the plane stress and plane strain cases. When the notch angle is smaller than 90°, the SCF is insensitive to the notch angle, but has close relation with the dimensionless plate thickness. With the notch angle increasing further, the SCF decreases and the effect of dimensionless plate thickness on it becomes weaker. (2) For any notch angle considered, the variation of the opening stress _yy normalized by its value _yy0 at the notch-root with the distance x from the root normalized by the root-radius , is insensitive to the plate thickness and coincides well with the two-dimensional (2D) planar solution. (3) The 3D distribution of the out-of-plane constraint factor T _z=_zz/(_yy+_xx) is controlled by the plate thickness (B), the notch-radius () as well as the notch angle (), but for deeper V-notches with 90°, the distribution of T _z coincides well with that of a U-notch as well as a sharp 3D through-thickness crack and an explicit empirical expression of T _z is presented. (4) The distribution of the in-plane stress ratio T _x=_yy/_xx in front of the 3D V-notch is nearly independent of the plate thickness and coincides well with the corresponding 2D solutions when the opening angle is smaller than 120°. (5) The gradient of the out-of-plane strain _zz is significant near the free surface in finite thickness plates. On the free surface, the _zz can be 3.5 times the value on the mid-plane, and the through-thickness gradient of the _zz increases with decreasing notch angle. It is of interest to note that most of the field quantities ahead of V-notches are insensitive to the notch angles when the notch angle is smaller than 90°.     

Some observations on the deformation characteristics of bulk polycrystalline zirconium hydrides

The deformation behaviour of bulk polycrystalline zirconium hydrides in the composition range ZrH_1.27 to ZrH_1.66 has been investigated by compressive loading at temperatures between room temperature and 500° C. Single-phase -zirconium hydride is brittle below 100° C. Analyses of slip traces on specimens deformed at temperatures between 100 and 250° C have shown that the glide planes are {111} types. The deformation characteristics of and ( + ) alloys at temperatures between 100 and 500° C are consistent with the hydrogen vacancies in the -phase providing significant lattice friction to the movement of dislocations in the zirconium lattice of the hydride structure. The room temperature fracture stress of ( + ) alloys increases with the volume fraction of the -phase and this can be related to the resistance offered by platelets to the propagation of cleavage cracks in the matrix. In a ( + + ) alloy the resistance to crack propagation at room temperature is further increased by the soft -zirconium phase.     

High-frequency dielectric properties of Mg-Al-Si,Ca-Al-Si and Y-Al-Si oxynitride glasses

Recently developed coaxial line techniques [1] have been used to determine, at room temperature, the values of the real () and imaginary (') parts of the dielectric constants for some Mg-Al-Si, Ca-Al-Si and Y-Al-Si oxynitride glasses over the frequency range 500 MHz to 5 GHz. The frequency dependencies of and ' are consistent with the universal law of dielectric response in that (-_t8)^(n–1) and '^(n–1) for all glass compositions; the high experimental value of the exponent (n=1.0±0.1) suggests the limiting form of lattice loss [2] situation. In this frequency range, as previously reported [3] at longer wavelengths, the addition of nitrogen increases the dielectric constant, (); in both the oxide and oxynitride glasses is also influenced by the cation, being increased with cation type in the order magnesium, yttrium, calcium as at lower frequencies.     

Effect of Grain Size on the Modulus of Elasticity and Strength of Synthetic Graphites

The effect of the grain size of the filler on the mechanical properties (compressive, bending, and tensile strength and modulus of elasticity) of synthetic graphite is analyzed using data for commercial structural graphites. As the mean particle size of the filler (_av) decreases from 3000 to 1 m, the modulus of elasticity increases, on the average, from 10 to 15 GPa, and the compressive, bending, and tensile strength increases by about one order of magnitude. The Griffith equation is used to evaluate the size of defects that initiate fracture (c _c) in different types of graphites. It is shown that the factors determining the critical defect size depend on the particle size of the filler. For _av > 150 m, c _c is comparable to _av or _max. In the range 30 < _av < 150 m, c _c is equal to or greater than _max. In graphites with _av < 30 m, c _c far exceeds _max and, presumably, corresponds to the particle size of the molding powder.     

Effect of grain size upon flow and fracture in a precipitation-strengthened Ti-8 wt % Al-0.25 wt % Si alloy

The interaction of grain size and precipitation strengthening has been studied in a Ti-8 wt % Al-0.25 wt %Si alloy. Grain sizes varying from 9 to 90m were produced by warm-working and annealing the alloy in the single--phase field. A uniform distribution of the coherent ₂ particles in the matrix was produced by ageing the alloy in the two-phase ( + ₂) field. The yield strength Hall-Petch slopes of the alloys with and without the ₂ precipitates were found to be nearly equal, indicating that the precipitation and grain-boundary strengthening are linearly additive. While specimens containing no precipitates exhibited a high ductility for all grain sizes, the ductility of the specimens with the ₂ particles decreased drastically with increasing grain size. TEM examination of the specimens containing the precipitates revealed a highly planar, localized slip and SEM examination of the fracture surfaces of these specimens revealed a transition in fracture behaviour from highly dimpled to mixed cleavage and intergranular with increasing grain size.     

Precipitation phenomena in the Mg-31 at% Li-1 at% Al alloy

Precipitation phenomena produced in the -phase (b c c) of the Mg-31 at% Li-1 at%Al alloy subjected to different heat treatments have been studied by sensitive single-crystal X-ray diffraction techniques. The variation of the hardness values of specimens quenched and then aged was also examined. It was confirmed that AlLi is a stable phase at room temperature for the examined Al content; AlLi precipitation is only produced for very slow cooling rates from the -field. Phase reactions for specimens quenched and then aged can be summarized as follows: ++ after ageing at room temperature; + ++ AlLi after ageing at 473 K. A considerable increase of the hardness, which attains its maximum value after about 30 h ageing at room temperature, was observed. Neither the -phase nor the AlLi-phase precipitation can account for the observed hardening process. The presence of the -metastable phase when the hardness reaches its maximum value is verified.     

Superplastic deformation in Ti-4%Al-4% Mo-2%Sn-0.5%Si (IMI550)

The superplastic deformation properties, i.e. flow scenes and stain rate sensitivities, of the commercial alloy Ti-4% Al-4% Mo-2% Sn-0.5% Si (IMI55O) have been assessed in the temperature range 805 to 915° C and for different initial microstructures. Fine grained + microstructures showed superplastic properties at temperatures above 850° C and grain coarsening, which led to increases in flow stresses and e reduction in superplastic properties, was only pronounced at the higher temperatures. In transformed microstructures the method of strain rate cycling led to a breakdown of the acicular platelets end the development of an equiaxed + microstructure. At the same time the flow stresses at low strain rates decreased and the strain rate sensitivities increased. Light and electron microscopy showed that the-phase became the continuous or matrix phase even at volume fractions below 50% (i.e. at the lower deformation temperatures) and that molybdenum segregation at the longitudinal interphase boundaries (parallel to the tensile axis) occurred. The results suggest that there is a strain distribution between the-phase and the -phase, the-phase effectively behaving as a deforming mantle around the grains.     

Deformation of a carbon-epoxy composite under hydrostatic pressure

This paper describes the behaviour of a carbon-fibre reinforced epoxy composite when deformed in compression under high hydrostatic confining pressures. The composite consisted of 36% by volume of continuous fibres of Modmur Type II embedded in Epikote 828 epoxy resin. When deformed under pressures of less than 100 MPa the composite failed by longitudinal splitting, but splitting was suppressed at higher pressures (up to 500 MPa) and failure was by kinking. The failure strength of the composite increased rapidly with increasing confining pressure, though the elastic modulus remained constant. This suggests that the pressure effects were introduced by fracture processes. Microscopical examination of the kinked structures showed that the carbon fibres in the kink bands were broken into many fairly uniform short lengths. A model for kinking in the composite is suggested which involves the buckling and fracture of the carbon fibres.List of symbols d diameter of fibre - E _f elastic modulus of fibre - E _m elastic modulus of epoxy - G _m shear modulus of epoxy - k radius of gyration of fibre section - l length of buckle in fibre - P confining pressure (= ₂ = ₃) - R radius of bent fibre - V _f volume fraction of fibres in composite - _t, _c bending strains in fibres - angle between the plane of fracture and ₁ - ₁ principal stress - ₃ confining pressure - _c strength of composite - _f strength of fibre in buckling mode - _n normal stress on a fracture plane - _m strength of epoxy matrix - shear stress - tangent slope of Mohr envelope - slope of pressure versus strength curves in Figs. 3 and 4.