Browsing by Author "Angel, Y. C."
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Item A method to determine the ballistic limits of shielded plates subjected to hypervelocity impact(1992) Whitney, James Pliny, III; Angel, Y. C.Ballistic limit curves are determined by using experimental and theoretical results for the permanent deformation of a plate subjected to an impact load. The experiments have been performed on shielded plates of various thicknesses and materials at the Hypervelocity Impact Research Laboratory of NASA JSC. Comparison of the theoretical and experimental deformations allows one to determine the dynamic yield strength of the plate material. It is assumed that the shields can be replaced by a single equivalent shield, and that the debris cloud produced by the impact expands according to the theory of Swift. A strain criterion is imposed and ballistic limit equations describing the critical projectile radius and the critical backwall thickness are derived. The corresponding curves are plotted for the case of the most damaging impact conditions. Comparison is made with empirical limit curves that are available in the literature.Item Average antiplane motion in an elastic solid containing a layer of randomly distributed cracks(1996) Koba, Yuri K.; Angel, Y. C.The propagation of antiplane waves in an elastic solid containing a random distribution of cracks that are parallel to each other, and oriented at an arbitrary angle relative to the direction of the incident wave, is considered. The approach, which is new, is based on the system of integral equations that describes the motion of a solid containing N cracks. When the cracks are randomly distributed inside a rectangular box, the average wave motion at any point in the cracked solid is obtained. Next, the length of the box is increased to infinity. By taking the limit of the preceding result, keeping the crack density constant, the wave motion corresponding to a cracked layer is obtained. In particular, the wave motion reflected by the layer is evaluated in terms of frequency, crack density, layer thickness, and crack orientation. There is also a transmitted wave motion that propagates into the solid on the other side of the layer. Reflection and transmission coefficients are plotted versus frequency, crack density, layer thickness, and crack orientation. Inside the layer, for small values of the crack density and of the layer thickness, it is shown that the attenuation and the speed of the wave motion reduce to those obtained by assuming the existence of a complex-valued wave number.Item Dynamic plastic deformation of a free ring subjected to a point load(1997) Fuentes, Arturo Alejandro; Angel, Y. C.The permanent deformation of a rigid perfectly-plastic unsupported thin ring subjected to a concentrated time-dependent force acting along a diameter is calculated. The analysis is developed for a force pulse of arbitrary shape, and numerical results are obtained for the special case of a triangular force pulse. It is shown that, for sufficiently large values of the applied force, four plastic hinges develop along the ring. Two of the hinges are fixed, and the other two move along the ring as the force varies with time. The motion of the hinges is governed by a system of coupled nonlinear ordinary differential equations that are solved numerically. The parameters that describe the final plastic deformation of the ring are evaluated and shown graphically. Previous studies of this problem provided a numerical solution for the case of a rectangular pulse only.Item Energy release rate in a cracked elastic-plastic solid(1993) McMahon, James Joseph; Angel, Y. C.To predict the growth of a crack in a body, Griffith introduced, for linear elastic materials, the concept of the energy release rate. According to this concept, crack growth occurs when the work done on a body by the applied surface tractions minus the increase in the strain energy of the body is equal to the energy required to break the material bonds in front of the crack. This approach has been widely accepted as a criterion for crack growth. For elastic-plastic materials, the concept of the energy release rate is not as well established. In this thesis, a general criterion for crack growth in elastic-plastic materials is proposed. A general constitutive theory is used, and a new work postulate, which imposes a finite limit on the amount of work that can be recovered from an elastic-plastic body, is proposed. For a certain class of elastic-plastic materials, this finite limit is directly related to a potential function. Next, an elastic-plastic body containing an edge crack is considered, and an energy balance at the crack tip is derived. This energy balance states that quantities defined at the crack tip are equal to the sum of the rate of work of the applied surface tractions, the rate of recoverable work defined inside the body, and a term that is a measure of the rate of work dissipated by plastic deformations. Finally, an interpretation of each term in the energy balance is given, and the proposed criterion for crack growth is discussed. This new criterion takes into account the dissipative nature of plastic deformations.Item Hypervelocity impact on strain-rate sensitive shielded plates(1993) Smith, James Pope; Angel, Y. C.A ballistic limit equation for hypervelocity impact on thin plates is derived analytically. This equation applies to cases of impulsive impact on a plate that is protected by a multi-shock shield, and is valid in the range of velocity above 6 km/s. Experimental tests were conducted at the NASA Johnson Space Center on square aluminum plates. Comparing the center deflections of these plates with the theoretical deflections of a rigid-plastic plate subjected to a blast load, one determines the dynamic yield strength of the plate material. The analysis is based on a theory for the expansion of the fragmented projectile and on a simple failure criterion. Curves are presented for the critical projectile radius versus the projectile velocity, and for the critical plate thickness versus the velocity. These curves are in good agreement with curves that have been generated empirically.Item Plastic deformation of beams under time-dependent transverse impact(1991) Attibele, Pradeep R.; Angel, Y. C.The permanent deformation of a rigid perfectly-plastic beam subjected to a time-dependent line load is calculated. The beam has finite length, and the load is applied transversely in the middle of the span. At the initial time, the load is zero; thereafter, it increases linearly, reaches a maximum value, and then decreases linearly to zero. For sufficiently large values of the applied load, there is a plastic hinge moving along the beam. The system of nonlinear ordinary differential equations that governs the motion of the hinge is solved numerically. After the plastic deformation has taken place, the beam appears as a bent curve that translates in the direction of the applied load. Formulas for the permanent deformation of the beam are obtained, and curves are presented to illustrate the results.Item Scattering of antiplane surface waves by an embedded crack in a layered elastic solid(1996) Ad-Doheyan, AbdRahman D.; Angel, Y. C.The scattering of an incident antiplane surface wave (Love-wave) by an embedded crack normal to the free surface in a layered half-space is investigated in this study. The crack is first assumed to be entirely contained in the surface layer, then the case in which the crack breaks through the interface is considered. The total displacement and stress fields are analyzed as the superposition of the incident fields in an uncracked half-space and the scattered fields in the cracked half-space. A general solution for the scattered displacement and stress fields in the cracked half-space is obtained by using Fourier sine and cosine transforms techniques. The mixed displacement and stress boundary value problem is reduced to a singular integral equation for the density of displacement discontinuity across the crack faces (dislocation density). The singular integral equation is approximated by a linear system of equations by using a Gaussian method. Further, the amplitudes of the reflected and transmitted displacement fields in the cracked half-space at some distance away from the crack plane are evaluated. It is shown that these displacement fields are the superposition of a finite number of Love-wave modes. In the case when the embedded crack breaks through the interface, the dislocation density function is shown to be discontinuous across the interface between the two solids, and the magnitude of the discontinuity is related to the ratio of the shear moduli. The numerical results for the reflection coefficients of the first three modes as well as for the transmitted coefficient of the first mode are presented for three different layer-embedded cracks and for four different interface-breaking cracks. These coefficients depend strongly on the position of the upper tip and the width of the crack. The results, when the upper tip is very close to the free surface, are compared with those for the surface-breaking crack configurations that are available in the literature. Good agreement is observed.Item Scattering of antiplane waves by fluid-filled cracks(1999) Mayorga-Martin, Obdulia; Angel, Y. C.Propagation of time-harmonic antiplane waves in an unbounded linearly-elastic solid containing parallel fluid-filled cracks is investigated. The viscous friction effects are represented by appropriate boundary conditions on the crack faces. The cracks are randomly distributed in a slab of finite thickness. Taking configurational averages over all crack configurations, one finds that the average motion in the solid is governed by two coupled integral equations. It is inferred from these equations that, inside the cracked region, there is a forward motion and a backward motion, which are described by a complex-valued wavenumber. Outside the cracked region, there are unattenuated reflected and transmitted wave motions, for which simple expressions are obtained. Numerical results are presented for the speed, attenuation, reflection and transmission in terms of the frequency, viscosity, crack density, angle of incidence and slab thickness.Item The use of shock physics to predict the mechanics of hypervelocity impact(2000) Smith, James Conrad Pope; Angel, Y. C.Shielding of spacecraft is a concern in the design of modern space vehicles. Due to unplanned spacecraft failures and naturally occurring planetary matter, the space environment is littered with orbital debris. This orbital debris poses a real threat to the safety of humans in space and the structural integrity and mission success of spacecraft. Debris shields mitigate the damage caused by debris impacting objects at hypervelocity. An effective shield shocks the incoming projectile, causing the projectile to break and expand. The expansion causes the projectile's momentum to be spread over a larger volume, thereby decreasing its potential to damage. A model is developed to estimate the velocity, shape, and mass distribution of debris clouds that are produced by the impact of a projectile on a bumper at hypervelocity. Models are developed for both normal and oblique impact in terms of the material and geometrical properties of the projectile and target. The model utilizes the Hugoniot shock equations to predict the states of stress and velocity in the projectile and bumper.