Response of circular clamped plates to square-wave stress pulses

An account is given of an experimental investigation of the reeponse of clamped circular mild-steel plates of various thicknesses subjected to rectangular stress pulses over a small circular region. The stress pulses were transmitted to the plates through a 1/2-in.-diam shock bar and the strain-time responses of the plates were measured. The stress-wave interactions between the bar and the plates were measured for a number of thicknesses and the effect of the applied stress on the extent of the plastic deformation was determined. It was found that the elastic response was accurately predicted by the theory of Sneddon and the plastic response behaved according to a simple modification of this theory. The interaction between the stress pulse and plates of various thickness was theoretically predicted and found to be in excellent agreement with experimental measurements. The final plate deflections were theoretically predicted using a rigid viscoplastic theory and was in substantial agreement with the data. From this theory, the data were analyzed to determine the visco-plastic constant or relaxation time of the material. It is proposed that this testing arrangement is a suitable and convenient method for determining dynamic yield properties under biaxial-loading conditions.     

Experimental study of multiple interior impacts

In this paper, experiments involving interior impacts on soft, lead targets are described. The term “interior impact” refers to the impact of a projectile at the bottom of a predrilled hole in the target. It is known that impact of low-velocity projectiles into such soft targets results in plastic flow and cavities similar to those obtained in high-velocity impact of hard targets. Therefore, comparatively simple rifle-propelled projectile impacts on soft targets may yield useful information for high-speed hard-target impacts. Double impacts with a short-time interval, on the order of microseconds, between projectile arrivals were conducted. The leading projectile creates a plastic flow in the target which partially seals the entrance hole. The trailing projectile must first force open the passage hole before achieving additional penetration. The total penetration was measured for different time intervals between the projectiles. A method was developed to obtain double impacts at the same point. The method utilizes a duplex round, which is made up of two separate projectiles fired from the same cartridge. With this round, a series of impact experiments was conducted. It was learned that occlusion, or the close up of the hole, is negligible for nearly simultaneous projectiles (less than 10 μs between impacts), and greatest with about 80 to 100 μs between impacts. The projectile velocity was measured by the use of properly placed photodiodes.     

A note on duality in finite elasticity

The duality between stress and deformation fields for plane deformations of a compressible isotropic hyperelastic material established by J. M. Hill [1]is generalized to deformations of a homogeneous elastic material without the restrictions of isotropy and hyperelasticity. At the same time a clarification of Hill's results is achieved.     

The non-uniform transformation strain problem for an anisotropic ellipsoidal inclusion

The problem of an anisotropic ellipsoidal inclusion which undergoes a stress-free transformation strain (in the sense of J.D. Eshelby) is considered, and the following theorem is proved: If an ellipsoidal region in an infinite anisotropic linear elastic medium undergoes, in the absence of its surroundings, a stress-free transformation strain which is a polynomial of degree M in the position coordinates x_t, then the final stress and strain state in the transformed inclusion, when constrained by its surroundings, is also a polynomial of degree M in x_t.     

Strain-optic law for a certain class of birefringent composites

A strain-optic law for a certain class of birefringent fiber-reinforced composite materials is developed. The strain-optic law requires both mechanical and optical characterization of the material. Previous investigations have hypothesized the existence of three independent optical properties for the anisotropic birefringent material. The strain-optic relation developed in this study, however, requires only a single strain-optic coefficient, coupled with four independent mechanical material properties, for prediction of the optical response of a birefringent anisotropic material. Experimental results are presented which show good agreement with the developed strain-optic relation. Finally, the isoclinic parameter is investigated and preliminary evidence is presented which indicates a correspondence between principal-strain direction and optical isoclinic angle.     

A unified theory of thermoviscoplasticity of crystalline solids

A unified theory of thermoviscoplasticity of crystalline solids is presented. In particular it is shown that a thermodynamics for ‘viscoplastic’ materials can be accommodated within the framework of modern mechanics of materials with memory. The basic physical concepts are derived from the consideration of dislocation behaviour of crystalline solids. Relationships of the present approach to several of the existing theories of plasticity are examined.     

The diffractographic strain gage

A method for measuring strain using diffraction of light from a single aperture is described, and results of a comparison tensile test with an electrical-resistance strain gage are presented. The “diffractographic strain gage” is shown to have high sensitivity, linearity, accuracy and temperature compensation and the ability to operate in a variety of hostile environments. It is furthermore simple, inexpensive, and the data can be collected by eye without assistance from further instrumentation.     

Radiation from an electric dipole in the presence of a corrugated cylinder

Summary A solution is outlined for the problem of an electric dipole which is located outside and parallel to the axis of a circular cylinder fo infinite length. The corrugated surface of the cylinder is assumed to be described by an anisotropic boundary impedance which specifies the ratios of the tangential electric and magnetic fields. It is shown that, in general, the radiated field is elliptically polarized.     

Optimal solenoidal interpolation of turbulent vector fields: application to PTV and super-resolution PIV

A new approach for the interpolation of a filtered turbulence velocity field given random point samples of unfiltered turbulence velocity data is described. In this optimal interpolation method, the best possible value of the interpolated filtered field is obtained as a stochastic estimate of a conditional average, which minimizes the mean square error between the interpolated filtered velocity field and the true filtered velocity field. Besides its origins in approximation theory, the optimal interpolation method also has other advantages over more commonly used ad hoc interpolation methods (like the adaptive Gaussian window). The optimal estimate of the filtered velocity field can be guaranteed to preserve the solenoidal nature of the filtered velocity field and also the underlying correlation structure of both the filtered and the unfiltered velocity fields. The a posteriori performance of the optimal interpolation method is evaluated using data obtained from high-resolution direct numerical simulation of isotropic turbulence. Our results show that for a given sample data density, there exists an optimal choice of the characteristic width of cut-off filter that gives the least possible relative mean square error between the true filtered velocity and the interpolated filtered velocity. The width of this optimal filter and the corresponding minimum relative error appear to decrease with increase in sample data density. Errors due to the optimal interpolation method are observed to be quite low for appropriate choices of the data density and the characteristic width of the filter. The optimal interpolation method is also seen to outperform the adaptive Gaussian window, in representing the interpolated field given the data at random sample locations. The overall a posteriori performance of the optimal interpolation method was found to be quite good and hence makes a potential candidate for use in interpolation of PTV and super-resolution PIV data.     

Nonpremixed flame control with microjets

The hydrodynamic control of buoyant nonpremixed flames is investigated by injecting high-momentum fluid through a central microjet. The resulting flame characteristics are mapped for jets of different strengths. The flame height decreases linearly with an increase in the microjet Froude number as the flow changes from a buoyancy-dominated to a momentum-controlled regime. The flame luminosity is reduced by injecting stronger microjets. The jets alter the flame structure by establishing strong entrainment of the ambient air from the quiescent surroundings. The introduction of an inert species as the microjet fluid has a similar qualitative effect as air. Microjet assistance is as effective as partial premixing for reducing the flame height and luminosity.