Use of equivalent body forces for acoustic emission from a crack in a plate

A method to determine acoustic emission of surface waves from a crack near the free edge of a plate, is presented, in terms of the function f(t), which defines the time dependence of the crack opening process, the crack opening volume per unit thickness of the plate, and the elastic constants of the plate. The determination of the time-varying displacement is based on the use of equivalent body forces, which are shown to be two double forces. The acoustic emission of the crack, or the equivalent radiation from the double forces, has been obtained by a novel use of the elastodynamic reciprocity theorem. It is of interest that the normal surface-wave displacement at a position x₀ of the free edge comes out as depending on df/dt evaluated at x₀ for t > x₀/c_R, where c_R is the velocity of surface waves on the free edge.     

Effect of spanwise-varying local forcing on turbulent separated flow over a backward-facing step

An experimental study was made of turbulent separated flows over a backward-facing step. A local forcing was given to the separated flow by means of a sinusoidally oscillating jet issuing from a thin slit near the separation line. To produce a spanwise-varying local forcing at the separation edge, a banded thin tape covered the slit. Effects of the spanwise-varying local forcings on the separated flow were scrutinized by altering the spatially banded blocking width (w) and the open slit distance (g). An optimal value of w/g was sought, which led to the minimum reattachment length (x _R ). The effect of spanwise-varying local forcing on x _R was found to be slight compared to the case of two-dimensional forcing (w=0). The experiment was made at Re _H =33000 and A ₀=0.018 by changing the forcing frequency (0?St _H ?1.0).     

Interaction between an Inclined Shock and Boundary and High-Entropy Layers on a Flat Plate

The flow structure and heat exchange in the zone of interference between an inclined shock and the surface of a flat plate are investigated experimentally and theoretically as functions of many parameters, the interference being studied in both the presence and the absence of bluntness of the leading edge. The experiments were carried out at Mach numbers M = 6, 8, and 10 and the Reynolds numbers Re _L , calculated using the plate length L = 120 mm and the free-stream parameters, varied over the range from 0.24 ? 10⁶ to 1.31 ? 10⁶. The bluntness radius of the leading edge of the plate, the intensity of the impinging shock, and its location with respect to the leading edge were varied. The numerical simulation was carried out by solving the complete two-dimensional Navier-Stokes equations and averaged Reynolds equations using the q-ω turbulence model. The laminar boundary layer became turbulent inside the separation zone induced by the shock. It is shown that the plate bluntness significantly reduces the heat exchange intensity in the interference zone, this effect intensifying with increase in the Mach number.     

A moving-load controlled-displacement fracture-toughness testing machine

In conventional fracture-toughness testing, the line of application of the loads remains fixed with respect to specimen geometry. In this testing machine, the load moves with the advancing crack front, and displacement is used as the controlled variable to propagate and arrest a crack. The energy-release rate at the onset of crack propagation and, hence, the plane-strain fracture toughnessK _Ic can be measured directly without compliance calibration or stress-intensity evaluation. The specimen is in the form of a flat plat 25 by 50 cm which is simple to machine and provides about 30 values ofK _Ic. The versatility of the machine is demonstrated by making a statistical analysis ofK _Ic for 7075-T6 Al by showing the effect of plate thickness on the fracture toughnessK _c using a tapered specimen, and by evaluatingK _c in 7075 Al as a function of aging temperature in a thermal-gradient-treated specimen.     

Über eine Verallgemeinerung des Korrekturfaktors K=(Prb/Prw)P,der den Einfluß temperaturabhängiger Stoffwerte auf den konvektiven Wärmeübergang berücksichtigt

The correction factorK, defined byk=(Nu _bH 3.66)/ (Nu _bo 3.66), is applicable only for the purely convective part of heat transfer in tubes. The value 3.66 is the contribution of molecular transport. A widely accepted correlation for the correction factor isK=(Pr_b/Pr_w)^p withp=0.11 for heating and cooling with laminar and turbulent fluid flow. This correlation is not in agreement with theory of similarity. Based on a few restrictive assumptions the author proves, that the exponentp is not a constant but is a function of the following dimensionless parameters: L/D;Pe; ?_Pr andRe. Without the introduction of restrictive assumptions the correction factor is at least a function of 11 dimensionless parameters for some important technical applications. Basically it is conceivable to solve the appropriate differential equations for the considered heat transfer conditions by rather complex numerical methods only for laminar flow.     

Anomalies associated with energy release parameters for cracks in piezoelectric materials

For a central crack in a piezoelectric plate, the mode-I stress intensity factor (K_I), electric displacement intensity factor (K_D), energy release rates (G, G_M) and energy density factor (S) are obtained from the finite element results. For the impermeable crack, the numerical results of K_I and K_D are coupled; this error is contrary to the uncoupled analytical solutions. The error has little effect on the total energy release rate G and energy density factor S, but in some cases, large errors in the mechanical energy release rate G_M are observed. G is global while SED is local. Also G is negative which defies physics where energy cannot be created while crack attempts to extend as implied by G. Computations should be made for the J-integral and also show that J becomes negative. What this shows is that the global fracture energy criterion is not suitable to address the local release of energy because it includes the overall energy which are irrelevant to fracture initiation being a local behavior. In addition, the case study shows that the energy density theory is the better fracture criterion for the piezoelectric material. According to the results of S, it retards the crack growth when the external electric field and piezoelectric poling are on opposite directions. This conclusion agrees with analytical and experimental evidence in the past references.     

Experimental study of pitching and plunging airfoils at low Reynolds numbers

Measurements of the unsteady flow structure and force time history of pitching and plunging SD7003 and flat plate airfoils at low Reynolds numbers are presented. The airfoils were pitched and plunged in the effective angle of attack range of 2.4°–13.6° (shallow-stall kinematics) and ?6° to 22° (deep-stall kinematics). The shallow-stall kinematics results for the SD7003 airfoil show attached flow and laminar-to-turbulent transition at low effective angle of attack during the down stroke motion, while the flat plate model exhibits leading edge separation. Strong Re-number effects were found for the SD7003 airfoil which produced approximately 25 % increase in the peak lift coefficient at Re = 10,000 compared to higher Re flows. The flat plate airfoil showed reduced Re effects due to leading edge separation at the sharper leading edge, and the measured peak lift coefficient was higher than that predicted by unsteady potential flow theory. The deep-stall kinematics resulted in leading edge separation that led to formation of a large leading edge vortex (LEV) and a small trailing edge vortex (TEV) for both airfoils. The measured peak lift coefficient was significantly higher (~50 %) than that for the shallow-stall kinematics. The effect of airfoil shape on lift force was greater than the Re effect. Turbulence statistics were measured as a function of phase using ensemble averages. The results show anisotropic turbulence for the LEV and isotropic turbulence for the TEV. Comparison of unsteady potential flow theory with the experimental data showed better agreement by using the quasi-steady approximation, or setting C(k) = 1 in Theodorsen theory, for leading edge–separated flows.     

Stress distributions in a semi-infinite plate due to a pin determined by interferometric method

The stress distributions in a semi-infinite plate due to a loaded pin of the same material as the plate are systematically investigated by an interferometric method which has been developed by the authors. For the experiments, a finite plate of diallylphthalate with a circular hole is used. It is supported at one side and loaded in the direction normal to the opposing straight edge by a pin which just fits the hole. The ratio of the distancee between the hole center and the straight edge to the diameterd of the hole is varied in steps from 4.0 to 1.0. At each step, the distributions of principal stresses σ₁ and σ₂ along the hole edge, line of symmetry and straight edge, which have not been fully investigated especially whene/d is small, are obtained separately from the isopachic and isochromatic fringes of the interfero-stress patterns. The relations between the maximum values of these stresses and the shape factore/d are determined.     

Closed-form solution for a mode-III interfacial edge crack between two bonded dissimilar elastic strips

A closed-form solution is obtained for the problem of a mode-III interfacial edge crack between two bonded semi-infinite dissimilar elastic strips. A general out-of-plane displacement potential for the crack interacting with a screw dislocation or a line force is constructed using conformal mapping technique and existing dislocation solutions. Based on this displacement potential, the stress intensity factor (SIF, K_III) and the energy release rate (ERR, G_III) for the interfacial edge crack are obtained explicitly. It is shown that, in the limiting special cases, the obtained results coincide with the results available in the literature. The present solution can be used as the Green’s function to analyze interfacial edge cracks subjected to arbitrary anti-plane loadings. As an example, a formula is derived correcting the beam theory used in evaluation of SIF (K_III) and ERR (G_III) of bimaterials in the double cantilever beam (DCB) test configuration.     

A parametric investigation of vane pressure side cutback film cooling by dual luminophor PSP

Because of its geometry, the vane trailing edge is one of the most difficult regions to be cooled. A trailing edge cutback cooling system is one of the most effective solution for cooling the trailing edge of high-pressure gas turbine nozzle vanes. In this study, a parametric analysis of the thermal performance of a nozzle vane cascade with a pressure side cooling system including two rows of cylindrical holes and a trailing edge cutback featuring 8 rectangular slots was carried out by using dual luminophor (binary) PSP technique. Coolant to mainstream mass flow rate (MFR), density ratio (DR), main flow Mach number (Ma_2is) and turbulence intensity level (Tu₁) and the state of the approaching boundary layer were the considered parameters. Binary PSP was able to measure the coolant concentration independently from temperature, thus allowing to compute the true adiabatic film cooling effectiveness in a complex environment. MFR was shown to have a strong impact on both holes and cutback performance. The thermal protection over the cutback region was promoted by high Ma_2is and high DR values, while Tu₁ and the boundary layer state only marginally affected the thermal behavior, especially at high MFR.     

An autonomous flexible propulsor in a quiescent flow

Flapping motions of wings and fins are common in nature. Living organisms use such motions to float in a fluid or to propel themselves forward. Some entities, such as tadpoles, use distinct flexible components to generate propulsion. Here we introduce a propulsor consisting of a rigid circular head containing an energy source and a flexible fin for propulsion. The head imparts a sinusoidal torque to the leading edge of the fin and the flexible fin flaps along the leading edge. The flexible propulsor thus moves via an oscillating relative angle between the head and the leading edge of the fin. Unlike a self-propelled heaving and pitching fin, our ‘autonomous’ flexible propulsor has no prescribed motion or constraint referenced from outside coordinates. The immersed boundary method was used to model the interaction between the flexible propulsor and the surrounding fluid. A penalty method, in which the head and fin imparted a periodic torque to each other, was used to connect the head and the fin. The cruising speed and propulsive efficiency of the propulsor were explored as a function of the ratio of the head size to the fin length (D/L), the pitching amplitude (θ_p) and the pitching frequency (f). The cruising speed and the equilibrium position (g_eq) of the flexible propulsor near the ground were also examined. The optimal propulsive efficiency was achieved at the head ratio of D/L = 0.2 at θ_p = 30° and f = 0.2. The cruising speed of the flexible propulsor increased when operating near the ground. The gap distance between the propulsor and the ground was dynamically determined by the pitching motion.     

A critical review of methods for determining stress-intensity factors from isochromatic fringes

Two-parameter methods of fracture analysis for determining the stress-intensity factor from photoelastic isochromatic-fringe data were critically reviewed. The methods of Irwin, Bradley and Kobayashi, and Smith were developed in detail and differences in the three approaches were noted. Theoretical fringe loops were generated for a crack of length 2a in a semi-infinite plate with biaxial loading. These fringe loops were used to compare the three analysis methods and to determine the accuracy of each method. All three methods give a close estimate of the stress-intensity factor, with the Bradley-Kobayashi differencing procedure providing the most precise estimate ofK. However, if measurement errors become excessive (larger than 2 percent) the differencing procedure magnifies these errors and the original method proposed by Irwin is the recommended approach. The two-parameter methods can be employed to determineK to within ±5 percent, provided the angle of tilt of the isochromatic-fringe loop is 73 ≤θ _m < 139 deg. Ifθ _m is outside this range, the two-parameter methods should not be employed.     

The effect of contact stress intensity factors on fatigue crack propagation

Using the technique of Dimensional Analysis the phenomenon of crack closure is modelled using the concept of a contact stress intensity factor Kc. For constant amplitude loading, a simple expression, Kc_max = g(R) ΔK, is obtained without making idealized assumptions concerning crack tip behaviour. Further, by assuming that crack closure arises from the interaction of residual plasticity in the wake of the crack and crack tip compressive stresses, the function g(R) is shown to be constant for non-workhardening materials. This implies that any dependency of Kc_max on R must be attributed to the workhardening characteristic of the material. With Kc known, an “effective” stress intensity factor Ke may be calculated and incorporated into a crack growth law of the form da/dn = f(ΔKe). From analysis, it can be deduced that for a workhardening material, Kc_max will decrease as R increases and the effective stress intensity factor will increase. This means that the fatigue crack propagation rate will increase with R, in accordance with experimental observations.     

Photoelastic determination of mixed-mode stress-intensity factorsK I,KII andK III

On the basis of existing photoelastic methods for the determination ofK _I andK _II, this paper presents an experimental method for determiningK _III with photoelastic data, and a photoelastic method for comprehensively determiningK _I,K _II andK _III under the complex stress condition. A frozen three-dimensional photoelastic model is first used to determineK _I andK _II from the slice perpendicular to the flaw edge. Then, from that slice, a sub-slice is taken to determine the factorK _III. This method is examined by comparison with two test models.     

Mode III effects on interface delamination

For crack growth along an interface between dissimilar materials the effect of combined modes I, II and III at the crack-tip is investigated. First, in order to highlight situations where crack growth is affected by a mode III contribution, examples of material configurations are discussed where mode III has an effect. Subsequently, the focus is on crack growth along an interface between an elastic-plastic solid and an elastic substrate. The analyses are carried out for conditions of small-scale yielding, with the fracture process at the interface represented by a cohesive zone model. Due to the mismatch of elastic properties across the interface the corresponding elastic solution has an oscillating stress singularity, and this solution is applied as boundary conditions on the outer edge of the region analyzed. For several combinations of modes I, II and III crack growth resistance curves are calculated numerically in order to determine the steady-state fracture toughness. For given values of K_I and K_II the minimum fracture toughness corresponds to K_III=0 in most of the range analyzed, but there is a range where the minimum occurs for a nonzero value of K_III.     

Influence of indenter geometry on half-plane with edge crack subjected to fretting condition

An edge crack is analyzed to study fretting failure. A flat punch with rounded corners and a half-plane are regarded as an indenter and a substrate, respectively. Plane strain condition is considered. Contact shear traction in the case of partial slip is evaluated numerically. It is assumed that an initial crack is extended to the point of minimum strain energy density in the half-plane from the trailing edge of contact. Dislocation density function method is used to evaluate K_I and K_II. The variations of K_I and K_II during crack growth are examined in the case of indentation by a punch with different ratio of the flat region (l) to the punch width (L). Sih's minimum strain energy density theory [1] is also applied to predict the propagation direction of the initial crack. The direction evaluated is similar to that found in the experiment. Stress intensity factor ranges (ΔK_I and ΔK_II) are examined during cyclic shear on the contact. For the design of contacting bodies, a suggestible geometry of punch for alleviating cracking failure is studied.     

Similarity solution of mixed convection over a horizontal moving plate

Investigation to the mixed convective heat and mass transfer over a horizontal plate has been carried out. By applying transformation group theory to analysis of the governing equations of continuity, momentum, energy and diffusion, we show the existence of similarity solution for the problem provided that the temperature and concentration at the wall are proportional to x ^4/(7-5n) and that the moving speed of the plate is proportional to x ^(3-n)/(7-5n), and further obtain a similarity representation of the problem. The similarity equations have been solved numerically by a fourth-order Runge–Kutta scheme. The numerical results obtained for Pr=0.72 and various values of the parameters Sc, K ₁, K ₂ and K ₃ reveals the influence of the parameters on the flow, heat and mass transfer behavior.     

Aerodynamic flow vectoring of a wake using asymmetric synthetic jet actuation

This paper reports an experimental investigation on the wake of a blunt-based, flat plate subjected to aerodynamic flow vectoring using asymmetric synthetic jet actuation. Wake vectoring was achieved using a synthetic jet placed at the model base 2.5?mm from the upper corner. The wake Reynolds number based on the plate thickness was 7,200. The synthetic jet actuation frequency was selected to be about 75?% the vortex shedding frequency of the natural wake. At this actuation frequency, the synthetic jet delivered a periodic flow with a momentum coefficient, C _??, of up to 62?%. Simultaneous measurements of the streamwise and transverse components of the velocity were performed using particle image velocimetry (PIV) in the near wake. The results suggested that for significant wake vectoring, vortex shedding must be suppressed first. Under the flow conditions cited above, C _?? values in the range of 10?C20?% were required. The wake vectoring angle seemed to asymptote to a constant value of about 30° at downstream distances, x/h, larger than 4 for C _?? values ranging between 24 and 64?%. The phase-averaged vorticity contours and the phase-averaged normal lift force showed that most of the wake vectoring is produced during the suction phase of the actuation, while the blowing phase was mostly responsible for vortex shedding suppression.     

Classification of stress-intensity factors from isochromatic-fringe patterns

The stresses in the local neighborhood of a crack tip have been used to develop a relation between the isochromatic-fringe orderN, its position parametersr and θ and the stress field expressed in terms of stress intensities,K _I ,K _II , and a far-field stress σ _ox . This relation was programmed and a plotting routine was developed to map isochromatic (σ₁ ? σ₂) fields in the neighborhood of the crack tip. The stress intensitiesK _I andK _II and the far-field stress σ _ox were varied and isochromatic fields were constructed for each combination. As bothK _II and σ _ox influence the size, shape and orientation of the isochromatics loops in a systematic manner, the pictorial representation of the isochromatic fields can be used to classify the state of stress (K _I ,K _II and σ _ox ) at the crack tip. Isochromatics which classify six different states of stress have been illustrated and methods used to determineK _I ,K _II , andσ _ox in five of the six states are given.     

Two-dimensional interaction between an incident shock and a turbulent boundary layer in the presence of an entropy layer

The results of an experimental and numerical investigation of flow and heat transfer in the region of the interaction between an incident oblique shock and turbulent boundary layers on sharp and blunt plates are presented for the Mach numbers M_∞ = 5 and 6 and the Reynolds numbers Re_∞L = 27×10⁶ and 14×10⁶. The plate bluntness and the incident shock position were varied. It is shown that the maximum Stanton number St _m in the shock incidence zone decreases with increase in the plate bluntness radius r to a certain value and then varies only slightly with further increase in r. In the case of a turbulent undisturbed boundary layer heat transfer is diminished with increase in r more slowly than in the case of a laminar undisturbed flow. In the presence of an incident shock the bluntness of the leading edge of the flat plate results in a greater decrease in the Stanton number than in the absence of the shock. With increase in the bluntness of the leading edge of the plate the separation zone first sharply lengthens and then decreases in size or remains constant.