A novel method for measuring and characterizing dynamic fracture-initiation toughness of elastic-plastic materials

The characterization and testing methods of the dynamic fracture initiation toughness of elastic-plastic materials under tensile impact are studied. By using the self-designed bar-bar tensile impact apparatus, a novel test method for studying dynamic fracture-initiation has been proposed based on the one-dimensional test principle. The curve of average loadv. s. displacement is smooth until unstable crack propagation, and the kinetic energy which does not contribute to the crack growth can be removed from total work done by external-force to the specimen. The fracture-initiation point is determined by compliance-changing rate method. The results show that these methods are feasible and effective. Through the analysis of the conversion between work and energy of a fracture specimen, the dynamicJ-integral is adopted as a characteristic parameter for elastic-plastic materials under impact loading. TheJ-integral is calculated from and curves by using the formula proposed, by Rice. TheJ-integral at fracture initiation is employed to describe the dynamic fracture-initiation toughness of elastic-plastic materials and the experimental results indicate thatJ _ID can be regarded as a material constant.     

On the operator of symmetric differentiation on a compact Riemannian manifold with boundary

We state a particular case of one of the theorems which we shall prove. Let Ω be a bounded open set in ℝ ⁿ with smooth boundary and let σ=(σ _ij )be a symmetric second-order tensor with components σ _ij εH ^k(Ω) for some (positive or negative) integer k; H ^k are Sobolev spaces on Ω. Then we have for some u _i εH ^k +1(Ω),i=1,...,n, if and only if (if k<0, the integral is in fact a duality) for any symmetric tensor (ω with components and such that ). Some applications in the theory of elasticity are also given.     

Numerical validation of the shear compression specimen. Part II: Dynamic large strain testing

Part I of this work addressed quasi-static loading of the shear compression specimen (SCS), which has been especially developed to investigate the shear dominant response of materials at various strain rates. The stress and strain states were characterized numerically. Approximations were presented to reduce the measured load,P, and displacement,d, into equivalent stress and strain . This paper addresses dynamic loading of the SCS. Several simulations were made for representative materials, whose stress-strain behavior is assumed to be rate-independent. The results show that stress wave loading induces strong oscillations in theP-d curve. However, the curve remains smooth in the gage section. The oscillations are about the quasistatic load values, so that with suitable filtering of the dynamicP-d curves, the quasi-static ones are readily recovered. Consequently, the approach that was developed for quasi-static loading of the SCS is now extended to dynamic loading situations. The average strain rate is rather constant and scales linearly with the prescribed velocity. As the plastic modulus becomes smaller, the strain rate reaches higher values. Friction at the end pieces of the specimen is also investigated, and shown to have a small overall influence on the determined mechanical characteristics. This paper thereby confirms the potential of the SCS for large strain testing of materials, using a unified approach, over a large range of strain rates in a seamless fashion.     

Theoretical mean wave resistance of precursor solition generation in two-layer flow

A new concept of pseudo mean wave resistance is introduced to find theoretical mean wave resistances of the precursor soliton generation in two-layer flow over a localized topography at near-resonance in this paper. The pseudo mean wave resistance of the precursor soliton generation of two-layer flow is determined in terms of the AfKdV equation. From the theoretical results it is shown that the theoretical mean wave resistance is equal to the pseudo mean wave resistance times 1/m ₁, wherem ₁ is the coefficient of the fKdV equation. From the regional distribution of the energy of the precursor soliton generation at the resonant points, it is shown that ratios of the theoretical mean wave resistance and regional mean energy to the total mean energy are invariant constants, i.e. : (−1/2):1:1, in which and are the mean energy of the generating regions of the precursor solitons, of the depression and of the trailing, wavetrain at the resonant points respectively, and <D> are the total energy of the system and the theoretical mean wave resistance at the resonant points. A prediction of the theoretical mean wave resistance flow over the semicircular topography is carried out in terms of the theoretical results of the present paper. The comparison shows that the theoretical mean wave resistance is in good agreement with the numerical calculation. The project supported by the Foundation of The State Education Commission “The Dynamics of Upper Ocean” and the Grants of The Physical Oceanography Laboratory of Ocean University of Qingdao     

Behaviour of the Reynolds stress on rough walls

Quadrant analysis is used to study the contributions, associated to the four quadrants of the (u,v) plane, to the production of the turbulent shear stress on rough walls. The measurements are described for a fully developed turbulent flow between two rough plates with varying the parameterλ _z(span/height ratio of roughness elements). The application of this technique indicates that the (Q ₂) events (ejections) and (Q ₄) events (sweeps) cause an intense production of the Reynolds stress —ρ as compared with the (Q ₁) and (Q ₃) quadrants. The (Q ₂) contribution to the Reynolds stress depends on the geometry factorλ _z. Variation of the parameterλ _zaffects the distributions of and forH⩽3, whereH is a particular threshold. Comparison with boundary layer flow shows that the region 0.2⩽y/h⩽0.7 is characterized by a Reynolds stress production, independent of the flow nature. The third moment of the longitudinal velocity fluctuations is found to be sensitive to the surface roughness.     

Smooth and rough turbulent boundary layers at high Reynolds number

A 2-D turbulent boundary layer experiment with zero pressure gradient (ZPG) has been carried out over a rough and a smooth surface using two cross hot-wire probes. Wind tunnel speeds of 10 m/s and 20 m/s were set up in order to investigate the effects of the upstream conditions and the Reynolds number on the downstream flow. For a given set of upstream conditions, such as the wind tunnel speed, trip wire size and location, the three components of the velocity field were measured from about 14 m from the inlet of the wind tunnel to 30 m downstream. This experiment is unique because it achieves Reynolds numbers as high as R120,000, for which measurements of the mean velocity are reported. It is shown that by fixing the upstream conditions, the mean deficit profiles collapse with the freestream velocity, , but to different curves depending on the upstream conditions and surface roughness. Moreover, the effects of the upstream conditions, the Reynolds number, and roughness are completely removed from the outer flow when the mean deficit profiles are normalized by the Zagarola/Smits scaling, . Consequently, the true asymptotic profile in the turbulent boundary layer is found in ZPG flow regardless of the range of Reynolds number, surface conditions and initial conditions.     

On the analogy in slip flows—II

In the present paper two examples of (i) generalized plane Couette flow over a smooth stationary plate and (ii) flow past a smooth solid sphere have been discussed to confirm the analogy in slip flows. It has been shown that the results can directly be carried over to the flow over corresponding naturally permeable surfaces up to the order of \(\sqrt K \) (K being the permeability of the medium, which is taken to be small).     

Control of low-speed turbulent separated flow using jet vortex generators

A parametric study has been performed with jet vortex generators to determine their effectiveness in controlling flow separation associated with low-speed turbulent flow over a two-dimensional rearward-facing ramp. Results indicate that flow-separation control can be accomplished, with the level of control achieved being a function of jet speed, jet orientation (with respect to the free-stream direction), and jet location (distance from the separation region in the free-stream direction). Compared to slot blowing, jet vortex generators can provide an equivalent level of flow control over a larger spanwise region (for constant jet flow area and speed).Nomenclature C _p pressure coefficient, 2(P-P_)/V ² - C _Q total flow coefficient, Q/ v - D ₀ jet orifice diameter - Q total volumetric flow rate - R Reynolds number based on momentum thickness - u fluctuating velocity component in the free-stream (x) direction - V free-stream flow speed - VR ratio of jet speed to free-stream flow speed - x coordinate along the wall in the free-stream direction - jet inclination angle (angle between the jet axis and the wall) - jet azimuthal angle (angle between the jet axis and the free-stream direction in a horizontal plane) - boundary-layer thickness - momentum thickness - lateral distance between jet orifices A version of this paper was presented at the 12th Symposium on Turbulence, University of Missouri-Rolla, 24–26 Sept. 1990     

Development of mixed convection flow over a vertical plate due to an impulsive motion

The development of the mixed convection flow of an incompressible laminar viscous fluid over a semi-infinite vertical plate has been investigated when the fluid in the external stream is set into motion impulsively, and at the same the surface temperature is suddenly raised from its ambient temperature. The problem is formulated in such a way that at time t = 0, it reduces to Rayleigh type of equation and as time t , it tends to Blasius type of equation. The scale of time has been selected such that the traditional infinite region of integration becomes finite which significantly reduces the computational time. The nonlinear coupled singular parabolic partial differential equations governing the unsteady mixed convection flow have been solved numerically by using an implicit finite-difference scheme. The surface shear stress and the heat transfer increase or decrease with time when the buoyancy parameter is greater or less than a certain valve. There is a smooth transition from the initial steady state to the final steady state. The skin friction and heat transfer for the constant heat flux case are more than those of the constant wall temperature case. Also they increase with the buoyancy force.     

Drag measurements on V-grooved surfaces on a body of revolution in axial flow

In water flows with velocities of up to 9 m/s the friction drag of a body of revolution in axial flow was investigated for dependence on the body surface structure. This was done for different types of riblet film fixed on the surface with the riblet direction aligned with the flow. The lateral spacing between the triangular shaped riblets varied between 0.033 mm and 0.152 mm. In all cases the riblet spacing was equal to the riblet height. For comparison a smooth reference film was used.Depending on the Reynolds number and the non-dimensional riblet spacings ⁺, a turbulent drag reduction of up to 9% could be achieved with riblets in comparison with the flow over a smooth surface.In the region of transition to turbulent flow and with non-dimensional riblet spacings ofs ⁺10–15 drag reductions of up to 13% were obtained. It is therefore conjectured, that in addition to hampering the near wall momentum exchange, the riblets can delay the development of initial turbulent structures in time and space.