Fracture instability of reinforced panel with cracks emanating from hole

Initiation of failure by yielding and/or fracture depends on the magnitude of the distortion and dilatation of material elements. According to the strain energy density theory (SED), failure is assumed to initiate at the site of the local maximum of maxima [(dW/dV)^max_max]_L by yielding and the maximum of minima [(dW/dV)^max_min]_L by fracture. The fracture is assumed to start from point L where [(dW/dV)^max_min]_L appears and tends toward G where the global maximum of dW/dV minima appears, denoted by [(dW/dV)^max_min]_G. The distance l between L and G along the anticipated crack trajectory is an indication of failure instability of the system by fracture. If l is sufficiently large and [(dW/dV)^max_min]_L exceeds the threshold, fracture initiation could lead to global failure. The local and global failure instability of a composite structural component is studied by application of the strain energy density theory. The depicted configuration is that of a panel with a circular hole reinforced by two side strips made of different material. The case of two symmetric cracks emanating from the hole and normal to the applied uniaxial tensile stress is also analyzed. Results are displayed graphically to illustrate the geometry and dissimilar material properties influence the fracture instability behavior of the two examples.     

Effects of aspect ratio on the drag of a wall-mounted finite-length cylinder in subcritical and critical regimes

The effect of cylinder aspect ratio (??H/d, where H is the cylinder height or length, and d is the cylinder diameter) on the drag of a wall-mounted finite-length circular cylinder in both subcritical and critical regimes is experimentally investigated. Two cases are considered: a smooth cylinder submerged in a turbulent boundary layer and a roughened cylinder immersed in a laminar uniform flow. In the former case, the Reynolds number Re _d (??U _?? d/??, with U _?? being the free-stream velocity and ?? the fluid viscosity) was varied from 2.61?×?10⁴ to 2.87?×?10⁵, and two values of H/d (2.65 and 5) were examined; in the latter case, Re _d ?=?1.24?×?10⁴?C1.73?×?10⁵ and H/d?=?3, 5 and 7. In the subcritical regime, both the drag coefficient C _D and the Strouhal number St are smaller than their counterparts for a two-dimensional cylinder and reduce monotonously with decreasing H/d. The presence of a turbulent boundary layer causes an early transition from the subcritical to critical regime and considerably enlarges the Re _d range of the critical regime. No laminar separation bubble occurs on the finite-length cylinder immersed in the turbulent boundary layer, and consequently, the discontinuity is not observed in the C _D?CRe _d and St?CRe _d curves. In the roughened cylinder case, the Re _d range of the critical regime grows gradually with decreasing H/d, while the C _D crisis becomes less obvious. In both cases, H/d has a negligible effect on the critical value of Re _d at which transition occurs from the subcritical to critical regime.     

Numerical simulation of the flow around a porous covering square cylinder in a channel via lattice Boltzmann method

In this paper, a detailed investigation on the flow past a porous covering cylinder is presented through the lattice Boltzmann method. The Brinkman‐Forchheimer‐extended Darcy model is adopted for the entire flow field with the solid, fluid, and porous medium. The effects of several parameters, such as porous layer thickness, Darcy number, porosity, and Reynolds number on flow field are discussed. Compared with the case of a solid cylinder, the present work shows that the porous layer may play an important role on the flow, the lift and drag force exerted on the cylinder. The numerical results indicate that the maximal drag coefficient C_d and maximal amplitude of lift coefficient C_l exist at certain Darcy number which is in the range of 10^?6–10^?2. Copyright © 2010 John Wiley & Sons, Ltd.     

The aerodynamics of a cylinder submerged in the wake of another

Flow-induced fluctuating lift (C_Lf) and drag (C_Df) forces and Strouhal numbers (St) of a cylinder submerged in the wake of another cylinder are investigated experimentally for Reynolds number (Re)=9.7×10³–6.5×10⁴. The spacing ratio L^⁎ (=L/D) between the cylinders is varied from 1.1 to 4.5, where L is the spacing between the cylinders and D is the cylinder diameter. The results show that C_Lf, C_Df and St are highly sensitive to Re due to change in the inherent nature of the flow structure. How the flow structure is dependent on Re and L^⁎ is presented in a flow structure map. Zdravkovich and Pridden (1977) observed a ‘kink’ in time-mean drag distribution at L^⁎≈2.5 for Re>3.1×10⁴, but not for Re≤3.1×10⁴. The physics is provided here behind the presence and absence of the ‘kink’ that was left unexplained since then.     

Isoparametric shear spring element applied to crack patching and instability

In this work the isoparametric shear spring element is applied to the stress and energy analysis of a center-crack panel reinforced by a rectangular patch. In this model, only transverse shears are assumed to prevail in the adhesive layer. The stresses and crack-tip stress intensity factors are obtained for reinforcement on both sides and one side of the panel, and are found to be in agreement with those obtained by previous authors using the triangular shear spring element.Crack stability that tends to vary with patch thickness is determined from the local and global maximum of the minimum strain energy density function denoted, respectively, as [(dW/dV)_min^max]_L at point L and [(dW/dV)_min^max]_G at point G. The distance l between L and G gives the prospective path of subcritical crack growth and its magnitude provides a measure of the degree of crack stability. A patched panel with small l tends to be more stable than that with large l. By increasing the patch thickness beyond a certain value, l can be contained within the patch such that failure, if initiated, will be highly localized. Such a behavior is exhibited. Numerical results are provided to support the foregoing conclusion.     

On the interaction between two fixed spherical particles

The variation of the drag (C_D) and lift coefficients (C_L) of two fixed solid spherical particles placed at different positions relative each other is studied. Simulations are carried out for particle Reynolds numbers of 50, 100 and 200 and the particle position is defined by the angle between the line connecting the centers of the particles and the free-stream direction (α) and the separation distance (d₀) between the particles. The flow around the particles is simulated using two different methods; the Lattice Boltzmann Method (LBM), using two different computational codes, and a conventional finite difference approach, where the Volume of Solid Method (VOS) is used to represent the particles. Comparisons with available numerical and experimental data show that both methods can be used to accurately resolve the flow field around particles and calculate the forces the particles are subjected to. Independent of the Reynolds number, the largest change in drag, as compared to the single particle case, occurs for particles placed in tandem formation. Compared to a single particle, the drag reduction for the secondary particle in tandem arrangement is as high as 60%, 70% and 80% for Re = 50, 100 and 200, respectively. The development of the recirculation zone is found to have a significant influence on the drag force. Depending on the flow situation in-between the particles for various particle arrangements, attraction and repulsion forces are detected due to low and high pressure regions, respectively. The results show that the inter-particle forces are not negligible even under very dilute conditions.     

Characterization of material inhomogeneity by stationary values of strain energy density

The strain energy density theory is applied to analyze the fracture instability of a mechanical system whose behavior is governed by the interaction of geometry, load and material inhomogeneity. This is accomplished by obtaining the location of the global and local relative minima of the strain energy density function dW/dV denoted, respectively, by [(dW/dV)_min]_g and [(dW/dV)_min]_¢l. The former refers to a fixed global coordinate system for the entire solid while the latter corresponds to local coordinate systems referred to each material point. An unique length parameter “ℓ” representing the distance between [(dW/dV)_min^max]_g and [(dW/dV)_min^max]_ℓ can thus be found and serves as a measure of the degree of system instability tending toward failure by fracture.Numerical results are obtained and displayed graphically for the case of a solid containing an inclusion of dissimilar material. The changes that take place in material inhomogeneity, loading type and physical dimensions of the solid and inclusion are reflected through ℓ. The method suggests the compatibility of ℓ for each member of a multi-component structure in order to avoid premature failure of a single member.     

Force coefficients and Strouhal numbers of three circular cylinders subjected to a cross-flow

In this paper, wind tunnel experiments were conducted to measure the mean force coefficients and Strouhal numbers for three circular cylinders of equal diameters in an equilateral-triangular arrangement when subjected to a cross-flow. These experiments were carried out at five subcritical Reynolds numbers ranging from 1.26 × 10⁴ to 6.08 × 10⁴. The pressure distributions on the surface of the cylinders were measured using pressure transducers. Furthermore, the hot-wire anemometer was employed to measure the vortex shedding frequencies behind each cylinder. Six spacing ratios (l/d) varying from 1.5 to 4 were investigated. It is observed that for l/d > 2, the upstream cylinder experiences a lower mean drag coefficient compared with the downstream cylinders. The minimum values of the drag coefficient for the downstream cylinders occur at l/d = 1.5 and l/d = 2, because there is no vortex shedding from the foregoing cylinders. Also, the value of the pressure coefficient behind the upstream cylinder reduces by increasing l/d. Moreover, by decreasing the value of l/d, the Strouhal number for the upstream cylinder increases. It can be concluded that the flow pattern and aerodynamic coefficients are basically dependent on l/d; in other words, decreasing l/d results in an increase in the effects of the flow interference between the cylinders.     

Tensile-shear transition in mixed mode I/III fracture

The propensity of the transition of fracture type in either brittle or ductile cracked solid under mixed-mode I and III loading conditions is investigated. A fracture criterion based on the competition of the maximum normal stress and maximum shear stress is utilized. The prediction of the fracture type is determined by comparing τ_max/σ_max at a critical distance from the crack tip to the material strength ratio τ_C/σ_C, i.e., (τ_max/σ_max)<(τ_C/σ_C) for tensile fracture and (τ_max/σ_max)>(τ_C/σ_C) for shear fracture, where σ_C (τ_C) is the fracture strength of materials in tension (shear). Mixed mode I/III fracture tests were performed using circumferentially notched cylindrical bars made of PMMA and 7050 aluminum alloy. Fracture surface morphology of the specimens reveals that: (1) for the brittle material, PMMA, only tensile type of fracture occurs, and (2) for the ductile material, 7050 aluminum alloy, either tensile or shear type of fracture occurs depending on the mode mixity. The transition (in ductile material) or non-transition (in brittle material) of the fracture type and the fracture path observed in experiments were properly predicted by the theory. Additional test data from open literature are also included to validate the proposed theory.     

Low Reynolds number airfoil aerodynamic loads determination via line integral of velocity obtained with particle image velocimetry

The small magnitude lift forces generated by both a NACA 0012 airfoil and a thin flat plate at Re?=?29,000 and 54,000 were determined through the line integral of velocity, obtained with particle image velocimetry, via the application of the Kutta–Joukowsky theorem. Surface pressure measurements of the NACA0012 airfoil were also obtained to validate the lift coefficient C _l. The bound circulation was found to be insensitive to the size and aspect ratio of the rectangular integration loop for pre-stall angles. The present C _l data were also found to agree very well with the surface pressure-determined lift coefficient for pre-stall conditions. A large variation in C _l with the loop size and aspect ratio for post-stall conditions was, however, observed. Nevertheless, the present flat-plate C _l data were also found to collectively agree with the published force-balance measurements at small angles of attack, despite the large disparity exhibited among the various published data at high angles. Finally, the ensemble-averaged wake velocity profiles were also used to compute the drag coefficient and, subsequently, the lift-to-drag ratio.     

Lift-induced drag of a cambered wing for Re ≤ 1 × 106

An investigation of the dependence of the lift-induced drag coefficient C _Di of a square-tipped, cambered wing model on Reynolds number for Re ≤ 1 × 10⁶ was conducted. Computed based on the vorticity distribution inferred from the near-field cross-flow velocity measurements of the tip vortex, different C _Di prediction schemes were used. The effect of measurement plane size and grid resolution on the C _Di calculations was also identified. The C _Di estimated by the integral method was found to increase with increasing Re and was below the C _Di = C _l²/πeAR prediction. Limits on the measurement plane size and grid resolution were determined to be at least 40% larger than the vortex outside diameter and no larger than 0.63% chord, respectively, in order to provide a good estimate of the induced drag.     

Failure initiation sites and instability of structural components with localized energy density

When the surface or interior of a solid undergoes curvature and/or material change, there results localized fluctuation of the energy density field depending on the type of loading. These fluctuations are related to changes in the distortion and dilatation of material elements that could lead to failure by yielding and/or fracture should their magnitude become sufficiently large. According to the strain energy density criterion, failure is assumed to initiate at site of local maximum of minimum strain energy density denoted by [(dW/dV)_min^max]_L and tends toward the global maximum of [(dW/dV)_min^max]_G. The distance l between these two stationary values of dW/dV at L and G provides an indication of failure instability. That is, large l corresponds to more wide spread failure while the opposite holds for small l.Specimens with three different geometries are analyzed; they consist of round shoulder, hole and edge notch. The loads are either bending or tension. As the severity of notch or hole curvature is varied, predicted failure path also altered from boundary to boundary or an interior point of the specimen. The narrowest section turns out to be most vulnerable. If the hole is filled with a material of higher modulus, it acts as a reinforcer such that failure site would be shifted away from the interface. In general, there prevails a trade off between l and [(dW/dV)_min^max]_L. The undesirable combination would be for l and [(dW/dV)_min^max]_L to increase simultaneously. Failure initiation and global instability would then likely occur in tandem. This corresponds to the bending of a specimen with round shoulders. A variety of other conditions are analyzed with results displayed graphically so that the ways with which load, geometry and material inhomogeneity affect the failure behavior of structural components with notches and holes could be better understood.     

Effects of a turbulent wall jet on heat transfer over a non-confined backward-facing step

Experimental and numerical analysis of a turbulent wall jet on the heat transfer downstream of a non-confined backward-facing step are presented. Several configurations are studied to analyse the influence of the upstream flow and the height of the step. An infrared camera and a hot wire were used to visualize a temperature map and measure the instantaneous velocity, respectively. The main objective was to visualize and compare both the fluid flow and the heat transfer, by studying the skin friction coefficient C_f and the Nusselt number Nu_d, respectively. The latter is obtained by the calculation of the heat transfer coefficient, evaluated by inverse method. Both experimental data and numerical approach provide good agreement regarding the flow structure and thermal data for measuring the position and the value of characteristics scales in the recirculation zone. A correlation between the maximum heat transfer Nu_max and the maximum Reynolds number Re_max is presented. Similarities and differences are highlighted in the paper compared to confined configurations.     

Numerical investigations into the asymmetric effects on the aerodynamic response of a pitching airfoil

The effects of asymmetric sinusoidal motion on pitching airfoil aerodynamics were studied by numerical simulations for 2-D flow around a NACA0012 airfoil at Re=1.35×10⁵. Various unsteady parameters (amplitude of oscillation, d; reduced frequency, k) were applied to investigate the effect of asymmetry parameter S on the instantaneous force coefficients and flow patterns. The results reveal that S has a noticeable effect on the aerodynamic performance, as it affects the instantaneous force coefficient, maximum lift and drag coefficient, hysteresis loops and the flow structures.     

Influence of cavitation on blade characteristics

An experimental study of flow around a blade with a modified NACA 4418 profile was conducted in a water tunnel that also enables control of the cavitation conditions within it. Pressure, lift force, drag force and pitching moment acting on the blade were measured for different blade angles and cavitation numbers, respectively. Relationships between these parameters were elaborated and some of them are presented here in dimensionless form. The analysis of results confirmed that cavitation changes the pressure distribution significantly. As a consequence, lift force and pitching moment are reduced, and the drag force is increased. When the cavitation cloud covers one side of the blade and the flow becomes more and more vaporous, the drag force also begins to decrease. The cavity length is increased by increasing the blade angle and by decreasing thé cavitation number.List of symbols A (m²) blade area,B ·L - B (m) blade width - C _D (–) drag coefficient,F _D /(p _d ·A) - C _L (–) lift coefficient,F _L /(P _d ·A) - C _M (–) pitching moment coefficient,M/(P _d ·A ·L) - C _p (–) pressure coefficient, (p-p _r )/p _d - F (N) force - L (m) blade length - M (Nm) pitching moment - p (Pa) local pressure on blade surface - p _d (Pa) dynamic pressure, ·V ²/2 - p _r (Pa) reference wall pressure at blade nose position if there would be no blade in the tunnel - p _v (Pa) vapor pressure - p ₁ (Pa) wall pressure 350 mm in front of thé blade axis - Re (–) Reynolds number,V ·L/v - V (m/s) mean velocity of flow in the tunnel - x (m) Cartesian coordinate along thé blade profile cord - x _c (m) cavity length,x-coordinate of cavity end - (°) blade angle - v (m²/s²) kinematic viscosity - (kg/m³) fluid density - (–) cavitation number, (p _r –p _v )/p _d - (°) angle of tangent to thé blade profile contour     

Effect of heater size on ultrasonic enhancement of boiling in water and surfactant solutions

Experiments were performed to study enhancement of heat transfer from the wire of d = 50 µm and the tube of d = 1.5 mm in subcooled pool boiling by ultrasonic waves. The working fluids are clean water and Alkyl (8-16) Glucoside surfactant solutions of different concentrations and bulk temperature 30 °C. The wire resistance was translated to the temperature, using the calibration data, the temperature of the tube was measured by thermocouple. The differences between effect of ultrasonic field on boiling in water for heaters of d = 50 µm and d = 1.5 mm may be summarized as follows: for boiling on the wire of d = 50 µm in subcooled water, T_b = 30 °C, enhancement of heat transfer coefficient due to applied ultrasonic field is about 70% and 20% at heat flux q = 620 kW/m² and q = 1350 kW/m², respectively. For boiling in surfactant solutions at the same boiling conditions enhancement of heat transfer coefficient is in the range of 5–10% at heat flux q = 620 kW/m² and 10–16% at heat flux q = 1350 kW/m² depending on solution concentration. For boiling on the tube of d= 1.5 mm in subcooled water, T_b= 30 ℃, enhancement of heat transfer coefficient due to applied ultrasonic field is about 50% and 45% at heat flux q = 500 kW/m² and q = 2500 kW/m², respectively. The same values are obtained for boiling in surfactant solution of concentration C = 250 ppm. For the wire of d = 50 µm the heat transfer enhancement due to acoustic vibrations in surfactant solutions is not as strong as in water. This fact may be considered as evidence of significant role of relationship between jet flow and ultrasonic field.     

Influence of heat transfer on the aerodynamic performance of a plunging and pitching NACA0012 airfoil at low Reynolds numbers

The unsteady low Reynolds number aerodynamics phenomena around flapping wings are addressed in several investigations. Elsewhere, airfoils at higher Mach numbers and Reynolds numbers have been treated quite comprehensively in the literature. It is duly noted that the influence of heat transfer phenomena on the aerodynamic performance of flapping wings configurations is not well studied. The objective of the present study is to investigate the effect of heat transfer upon the aerodynamic performance of a pitching and plunging NACA0012 airfoil in the low Reynolds number flow regime with particular emphasis upon the airfoil's lift and drag coefficients. The compressible Navier–Stokes equations are solved using a finite volume method. To consider the variation of fluid properties with temperature, the values of dynamic viscosity and thermal diffusivity are evaluated with Sutherland's formula and the Eucken model, respectively. Instantaneous and mean lift and drag coefficients are calculated for several temperature differences between the airfoil surface and freestream within the range 0–100 K. Simulations are performed for a prescribed airfoil motion schedule and flow parameters. It is learnt that the aerodynamic performance in terms of the lift C_L and drag C_D behavior is strongly dependent upon the heat transfer rate from the airfoil to the flow field. In the plunging case, the mean value of C_D tends to increase, whereas the amplitude of C_L tends to decrease with increasing temperature difference. In the pitching case, on the other hand, the mean value and the amplitude of both C_D and C_L decrease. A spectral analysis of C_D and C_L in the pitching case shows that the amplitudes of both C_D and C_L decrease with increasing surface temperature, whereas the harmonic frequencies are not affected.     

Influences of wind tunnel parameters on airfoil characteristics at high subsonic speeds

The influences of several wind tunnel parameters on airfoil characteristics are experimentally investigated in a transonic wind tunnel. Quantified as Mach number errors they show decisive effects and confirm that they have to be taken into consideration in a valuation of test results. Differences in data gained in measurements of several wind tunnels can be partly explained thereby.List of symbols C chord length - C _d drag coefficient - C ₀ d drag coefficient at zero lift - C ₁ lift coefficient - C _{1 max} lift coefficient at maximum lift - C _p pressure coefficient - D divergence - M Mach number - P ₀ stagnation pressure - Re Reynolds number - S _h suction along the horizontal walls - S _v suction along the vertical walls - X axial coordinate - X _ref position of the reference point - X _s shock position - angle of attack     

Phase behavior and effects of microstructure on viscoelastic properties of a series of polylactides and polylactide/poly(ε-caprolactone) copolymers

Dynamic viscoelastic measurements were combined with differential scanning calorimetry (DSC) and atomic force microscopy (AFM) analysis to investigate the rheology, phase structure, and morphology of poly(l-lactide) (PLLA), poly(ε-caprolactone) (PCL), poly(d,l-lactide) (PDLLA) with molar composition l-LA/d-LA?=?53:47, and poly(l-lactide-co-ε-caprolactone) (PLAcoCL) with molar composition l-LA/CL?=?67:33. After melt conformation, both copolymers PDLLA and PLAcoCL were found to be amorphous whereas PLLA and PCL presented partial crystallinity. The copolymers and PCL were considered as thermorheologically simple according to the rheological methods employed. Therefore, data from different temperatures could be overlapped by a simple horizontal shift (a _T) on elastic modulus, G′, and loss modulus, G′, versus frequency graph, generating the corresponding master curves. Moreover, these master curves showed a dependency of G″≈ω and G′≈ω ² at low frequencies, which is a characteristic of homogeneous melts. For the first time, fundamental viscoelastic parameters, such as entanglement modulus G _N ⁰ and reptation time τ _d, of a PLAcoCL copolymer were obtained and correlated to chain microstructure. PLLA, by contrast, was unexpectedly revealed as a thermorheologically complex liquid according to the failure observed in the superposition of the phase angle (δ) versus the complex modulus (G*); this result suggests that the narrow window for rheological measurements, chosen to be close to the melting point centered at 180 °C thus avoiding thermal degradation, was not sufficient to assure an homogeneous behavior of PLLA melts. The understanding of the melt rheology related to the chain microstructural aspects will help in the understanding of the complex phase structures present in medical devices.     

The free jets as boundary-layer flows induced by continuous stretching surfaces

This paper proves that the free laminar jets of the classical hydrodynamics may be identified with certain boundary-layer flows induced by continuous surfaces immersed in quiescent incompressible fluids and stretched with well-defined velocities. In this sense: (i) Schlichting's round jet of momentum flow coincides with the axisymmetric flow induced by a thin continuous wire issuing from a small orifice at x=0 and stretching along the x-axis with velocity U _w(x) = 3J˙/(8πρνx), and (ii) the Schlichting–Bickley plane jet of momentum flow J˙ coincides with the boundary-layer flow induced by an impermeable plane wall issuing from a long slit (of length l) and stretching with velocity U _w(x)= [{3J˙ ²/(32νρ² l ² x)}]^1/3.