Sensitivity of probabilistic fracture mechanics analysis to variations in statistical parameters

Probability of failure (p_f) of a structure is usually calculated for a specified set of statistical parameters (mean, standard deviation, and probability distribution) that characterize random variables. This approach may not be efficient in cases where one would like to know the effect of variations in statistical parameters on the probability of failure. A method based on generating and analyzing randomly selected statistical parameters is proposed. The method consists of generating databases of mean and coefficient of variation (COV = mean/standard deviation) values of relevant fracture mechanics variables through a random process. The method was applied to surface cracks in a flat wide plate loaded under elastic conditions. Probability of failure was calculated for each database record using the first-order reliability method (FORM). Multiple linear regression analyses of the database records were performed with p_f as dependent variable and statistical parameters as independent variables. The predicted p_f values were in very good agreement with the directly calculated p_f values for the specified variations of statistical parameters (±10%, ±15%, and ±20%), except those for fracture toughness and tensile stress, where variations should be limited to ±10% and ±15% ranges.     

Fatigue behavior of E-glass fiber reinforced phenolic composites: effect of temperature, mean stress and fiber surface treatment

Phenolic matrix is reinforced by unidirectional E-glass fibers with volume fractions of 0.30 and 0.45. Three different surface treatments are applied to the E-glass fibers. The composite specimens are tested at ambient condition and temperatures of 100°C 150° and 200°C with stress levels of R(σ_min/σ_max) equal to 0 and 0.4 for load frequencies of 1.5, 10 and 25 Hz. Data are presented in terms of S/N curves and assessed by degradation of modulus based on compliance. For a particular fiber glass surface treatment and volume fraction, the composite specimen is notched and tested at room temperature and 200°C. A fatigue strength reduction factor K_f is defined and obtained such that the results could be compared with those of the unnotched specimens. Notch effect is small if the hole diameter is equal to the specimen thickness; it would be important for larger hole sizes. Fractured surfaces are examined by the scanning electron microscope.     

Effect of transverse cracks on the mechanical properties of angle-ply composites laminates

A modified shear lag analysis, taking into account the notion of stress perturbation function, is employed to evaluate the effect of transverse cracks on the stiffness reduction in [±θ_n/90_m]_S angle-ply laminated composites. Effects of number of 90° layers and number of ±θ layers on the laminate stiffness have also been studied. The present results represent well the dependence of the degradation of mechanical properties on the fibre orientation angle of the outer layers, the number of cracked cross-ply layers and the number of uncracked outer ±θ layers in the laminate.     

Enhancement of fracture toughness of steel with defects by warm-prestressing

The technique of warm-prestressing to improve the resistance of structural steel with defects against low temperature fracture has received considerable attention. It is found that warm-prestressing can improve the fracture toughness and change the COD or δ_c, especially the crack tip plastic opening δ_p.The experimental results obtained from three-point bending tests of 42Mn2 steel specimens at −60°C and −20°C are analyzed. Experiments are also made on the bursting of pressure vessels manufactured from #20 steel. The results indicate that warm-prestressing at room temperature increased the bursting pressure at −40°C for d/t = 0.2 to 0.4, where d is the depth of surface crack and t the vessel thickness.     

Fracture toughness of CIP-HIP Beryllium at elevated temperatures

The fracture toughness of CIP-HIP Beryllium was determined using the short bar fracture toughness (K_IcSB) method. The K_IcSB value measured was 10.96 MPa√m at room temperature. This falls well within the expected range of 9 to 12 MPa√m as observed from previous fracture toughness measurements of beryllium. Toughness increased rapidly between 400°F and 500°F reaching a value of 16.7 MPa√m at 500°F.     

Fatigue and fretting fatigue of ion-nitrided 34CrNiMo6 steel

This work is concerned with the surface treatment (ion nitriding) of fretting fatigue and fatigue resistance of 34CrNiMo6. Tests are made on a servo-hydraulic machine under tension for both treated and non-treated specimens. The test parameters involve the applied displacements δ±80–±170 μm; fretting pressure σ_n=1000–1400 MPa; fatigue stress amplitude σ_a=380–680 MPa and stress ratio R=−1. The ion nitriding process improves both fatigue and fretting fatigue lives. Subsurface crack initiation from internal discontinuities was found for ion-nitrided specimens.     

An experimental investigation of roll waves in high pressure two-phase inclined pipe flows

This paper examines the effects of small upward inclinations on the formation of roll waves and the properties of fully developed roll waves at high pressure conditions. A total of 984 experiments were conducted at six positive pipe inclinations θ = 0.00°, 0.10°, 0.25°, 1.00°, 2.50° and 5.00° using a 25 m long 10 cm i.d. pipe. Sulfur hexafluoride (SF₆) was used at 8 bara giving a gas density of 50 kg/m³. Two independent mechanisms for the formation of roll waves were identified; (1) interaction between 2D shallow water waves and (2) a visible long wavelength instability of the stratified layer. Viscous long wavelength linear stability analysis predicted the critical liquid flow rate and liquid height for the initiation of roll waves when roll waves were formed due to the second mechanism. A simple equation from shallow water wave theory agreed with measurements for critical liquid flow rate when roll waves were formed due to the first mechanism. Shallow water wave speed agreed with critical wave speeds at transition and nonlinear wave speeds for fully developed roll waves in certain cases. The increase in interfacial friction due to the presence of large waves was compared with models from the literature.     

Multiaxial constitutive model accounting for the strength-differential in Inconel 718

The nickel-base alloy Inconel 718 exhibits a strength-differential, that is, a different plastic flow behavior in uniaxial tension and uniaxial compression. A phenomenological viscoplastic model founded on thermodynamics has been extended for material behavior that deviates from classical metal plasticity by including all three stress invariants in the threshold function. The model can predict plastic flow in isotropic materials with or without a flow stress asymmetry as well as with or without pressure dependence. Viscoplastic material parameters have been fit to pure shear, uniaxial tension, and uniaxial compression experimental results at 650°°C. Threshold function material parameters have been fit to the strength-differential. Four classes of threshold functions have been considered and nonproportional loading of hollow tubes, such as shear strain followed by axial strain, has been used to select the most applicable class of threshold function for the multiaxial model as applied to Inconel 718 at 650 °C. These nonproportional load paths containing corners provide a rigorous test of a plasticity model, whether it is time-dependent or not. A J₂J₃ class model, where J₂ and J₃ are the second and third effective deviatoric stress invariants, was found to agree the best with the experimental results.     

Failure resistance of intermetallic matrix reinforced by wires

Composite materials with brittle matrices such as ceramics and intermetallic compounds have gained increased importance in application. Ceramics and intermetallic compounds possess unique heat-resistance at high temperatures. They are, however, vulnerable to brittle fracture. This problem can be overcome by reinforcing the intermetallic compounds with wires. NiAl-tungsten composite wire was manufactured by hot diffusion welding of alternate layers of the matrix and wires. These specimens were subjected to a three-point bending in the temperature range from 20° to 1000°C. Temperature dependence of the bending strength exhibited brittle to ductile transition behavior. At room temperature, unstable failure by bending is terminated in a stable fashion. Brittle fracture of the matrix and wire were observed. For text temperatures of 300°, 500° and 700°C, subcritical crack growth occurred where the matrix and wire showed brittle and ductile fracture, respectively. A pronounced necking of the specimen was observed as the temperature is increased. Substantial plastic deformation occurred when the test is performed at 1000°C. The critical stress intensity factor K_1c and specific work of fracture were measured and found to be two to three times larger than the intermetallic compounds without wire reinforcement.     

Observations on the theoretical and experimental foundations of thermoplasticity

The thermodynamics of materials with internal state variables has been employed to study the properties of a class of thermoplastic materials in which the evolution equation for the internal variables is given by equation k⁽ⁱ⁾ = g⁽ⁱ⁾(σ_kl, '_kl, k⁽ⁱ⁾, θ, · '_kl) where g⁽ⁱ⁾ is homogeneous of order one in · '_kl. The most general form of the Helmholtz potential consistent with the assumption of insensitivity of the elastic relations to inelastic deformation has been derived and a geometric interpretation of the Clausius-Duhem restriction has been made employing the concept of a thermodynamic reference stress. Experimental results of one of the authors have been correlated with the theory.     

Residual fracture energy of cement paste, mortar and concrete subject to high temperature

Quantifying high temperature damage is an issue that can hardly be dealt with experimentally because of the complexity of the loading control, of temperature and of moisture. The experimental investigation was carried out. The measurement of the mechanical characteristics (fracture energy, tensile strength, elastic modulus and thermal damage parameter) of five cementitious materials, cement paste, mortar, ordinary concrete and two HPC concretes were performed by three-point bending tests after heating/cooling cycles at 120, 250 and 400 °C. The tests showed that the cementitious materials behave almost identical when the fracture energy G_f is considered as a function of maximum temperature. The thermal damage due to heating from 120 to 400 °C increases the fracture energy by 50% with the reference tests at room temperature. A more tortuous crack surface is one reasonable explanation for the significant increase in G_f. It is demonstrated that the temperature exposure makes all cementitious materials tested significantly more ductile and less resistant.     

On a class of non-linear elastic materials

This article deals with a family of non-linear hyperelastic materials depending on a parameter varying from 0 to 1; is a masonry-like material and is linear elastic. Some properties of the function delivering the Cauchy stress corresponding to the infinitesimal strain E, are proved; in particular, it is shown that is strongly monotone for >0 and monotone for =0. Moreover, denoting by [u(·;), E(·;), T(·;)] the solution to the equilibrium problem for solids made of a material the convergence of [u(·;), E(·;), T(·;)] for going to 0 and 1, is investigated.     

High-frequency dielectric properties of BSTO ceramic prepared with hydrothermal synthesized SrTiO3 and BaTiO3 powders

BSTO dielectric ceramic was prepared from SrTi03 and BaTi03 powders synthesized by hydrothermal method, as well as from Bao.sSro.4TiO3 powder synthesized by conventional solid-state reaction. The former can be sintered at a relatively low temperature of 1120 ℃. Characterization by SEM showed that the grain shapes of both ceramics are cubical, though the grain size of the former is much smaller. Dielectric constants measured at 20℃ were shown to vary with frequency in the range from I kHz to 2 MHz and dc bias field, and further that the dielectric loss of the former to be less than 2 × 10^- 3 in the frequency range of 20 kHz to 1 MHz, much smaller than that of the latter sample. For the former, temperature dependence of dielectric constant is much flatter and there exists an extended phase transition diffusion covering a wide temperature range of Curie temperature To. The smaller grain size of the former depresses the dc bias electrical field dependence of dielectric constant. The tunability is 7% under a bias field of 0.6 kV/mm dc.     

Experimental flow study over a blunt-nosed axisymmetric body at incidence

The flowfield over a blunt-nosed cylinder was examined experimentally at a low subsonic speed for Re=1.88×10⁵ and angles of attack up to 40°. Velocity measurements were carried out (employing a seven-hole Pitot tube) as well as wall static pressure and wall shear-stress measurements. Surface flow visualization was applied using liquid crystals and a mixture of oil–TiO₂. For all the examined cases no flow asymmetries were found. For high angles of attack (20° and above) a separation “bubble” appears at the leeside of the nose area (streamwise flow separation). The basic feature of the circumferential pressure distribution at the after body area for these angles of attack is a plateau close to the suction peak and a fast recovery next to it. One streamwise vortex on each side of the symmetry plane is formed as well as a separation bubble about 90° far from this plane, where the cross-flow primary separation line is located. Each cross-flow primary separation line starts at the leeside nose area and moves towards the windward side along the cylindrical after body. The space between the two primary separation lines close to the wall is characterized by high flow fluctuations on the leeside, compared to the low fluctuations of the windward side.     

Preparation of spherical Y2SiO5 powders for thermal-spray coating

Yttrium silicate, for its high oxidation resistance, is an important candidate for protective coating for carbon-fiber-reinforced composites at temperatures above 1600 ℃. A novel method, consisting of coprecipitation, spray-drying, heat-treatment and plasma-densification, is developed to prepare Y2SiO5 powders for thermal-spraying. The composition, morphology and flowability of the synthesized Y2SiO5 powders are investigated by XRD, SEM and Hall Flowmeter, respectively. The results show that the synthesized Y2SiO5 powders are nearly spherical with high purity. The apparent density and flowability of the Y2SiO5 powders are 1.87 g/cm^3 and 37 s/50 g, respectively, which lead to a high deposition efficiency of up to 80700 for atmospheric plasma spraying.     

Influence of mean stress on the fatigue crack growth characreristics of CrlMo steel tube at elevated temperature

The fatigue crack growth characteristics of CrlMo steel have been investigated at 861 K over the R-ratio range 0.1–0.7 utilising a dwell time of 10 min. at maximum load. All tests were conducted under load control in a laboratory air environment. It was established that the R-ratio significantly affected the fatigue crack extension behaviour inasmuch that with increasing R-ratio, the critical ΔK level for the onset of creep fatigue interactive growth, ΔK^IG, decreased from 20 to 7 MPa√m and the threshold stress intensity, ΔK_th, decreased from 9 to about 3 MPa√m. At intermediate ΔK levels, i.e. between ΔK_th and ΔK^IG, the fatigue crack extension rates, for all R-ratio values, resided on or slightly below the CTOD line, which represents the upper bound for contrnuum controlled fatigue crack growth. Creep fatigue interactive growth was typified by crack extension rates that reside above the CTOD line with a ΔK^IG dependence; the attainment of some critical creep condition or crack linkage condition which causes the abrupt change in crack extension behaviour at ΔK^IG; and crack extension occurs almost exclusively in an intergranular manner. The R-ratio and ΔK^IG followed a linear relation. A literature review concerning the effect of temperature on the threshold fatigue crack growth characteristics of low alloy ferritic steels demonstrated powerful effects of temperature; the magnitude of these effects, however, were dependent upon the testing temperature regime and R-ratio level. The effect of R-ratio on ΔK_th was greatest at temperatures >400°C, significant at ambient temperatures and least in the temperature range 90°C to <300°C. The relationship between temperature and ΔK_th, at a given R-ratio, exhibited a through and a minimum ΔK_th value was observed in the temperature range 200–250°C. The magnitude of the temperature effects on ΔK_th decreased with increasing R-ratio. Such effects of temperature and R-ratio on ΔK_th was reasonably explained in terms of crack closure effects. Finally, the present elevated temperature fatigue crack growth data exhibited massive crack extension enhancement values when compared to ambient near-threshold fatigue crack growth data for CrlMo steel. Such large enhancement values were the combined effects of temperature (environment) and frequency.     

Flow structure of wake behind a rotationally oscillating circular cylinder

Flow around a circular cylinder oscillating rotationally with a relatively high forcing frequency has been investigated experimentally. The dominant parameters affecting this experiment are the Reynolds number (Re), oscillation amplitude (θ_A), and frequency ratio F_R=f_f/f_n, where f_f is the forcing frequency and f_n is the natural frequency of vortex shedding. Experiments were carried out under conditions of Re=4.14×10³, 0°θ_A60° and 0.0F_R2.0. Rotational oscillation of the cylinder significantly modified the flow structure in the near-wake. Depending on the frequency ratio F_R, the cylinder wake showed five different flow regimes, each with a distinct wake structure. The vortex formation length and the vortex shedding frequency were greatly changed before and after the lock-on regime where vortices shed at the same frequency as the forcing frequency. The lock-on phenomenon always occurred at F_R=1.0 and the frequency range of the lock-on regime expanded with increasing oscillation amplitude θ_A. In addition, the drag coefficient was reduced when the frequency ratio F_R was less than 1.0 (F_R<1.0) while fixing the oscillation amplitude at θ_A=30°. When the oscillation amplitude θ_A was used as a control parameter at a fixed frequency ratio F_R=1.0 (lock-on regime), the drag reduction effect was observed at all oscillation amplitudes except for the case of θ_A=30°. This type of active flow control method can be used effectively in aerodynamic applications while optimizing the forcing parameters.     

Lock-on characteristics of a cavity shear layer

This investigation focuses on defining the lock-on regions of a cavity shear layer subject to local periodic excitations. A circular cylinder of small diameter (d=4 mm), located very close to the upstream edge of cavity, is used to generate the local periodic excitations in the form of oscillatory rotation about its center with various angular amplitudes (Δθ) and frequencies (f_e). All the experiments were conducted in a recirculating water channel at three different Reynolds numbers that are based on the momentum thickness at the upstream edge of cavity (Re_θ0=152, 216 and 278). The LDV system and the laser-sheet technique are employed to perform the quantitative velocity measurements and the qualitative flow visualization, respectively. For cavity flows at three Reynolds numbers studied, the resonant lock-on is found to be the primary lock-on region within the range of frequency ratio (f_e/f₀=0.28–2.0). Here f₀ denotes the natural instability frequency of an unexcited cavity shear layer. The frequency bandwidth of resonant lock-on region does increase with increasing excitation amplitudes (Δθ). While the excitation amplitudes are smaller than 5° (Δθ5°), the resonant lock-on region, at Reynolds numbers 216 and 278, distributes asymmetrically about f_e/f₀=1.0 and biases to the high frequency (or large f_e/f₀) side. However, the sidewise expansion of resonant lock-on region is enlarged and the degree of asymmetric distribution is alleviated at large excitation amplitudes (Δθ>5°). The amount of sidewise expansion of the resonant lock-on region biased toward the high-frequency side is more significant at the lowest Reynolds number (152) than those at two higher Reynolds numbers (216 and 278). Besides, there exists a sub-harmonic lock-on region only at the lowest Reynolds number 152. The existence of a sub-harmonic lock-on region clearly reveals that the differential equation governing the self-excited oscillation within a cavity contains the quadratic nonlinear term. Further, at the lowest Reynolds number (152), the sidewise expansion of the sub-harmonic lock-on region is much narrower than that of the resonant lock-on region.