John K. Dienes

A statistical theory of fragmentation processes

The goal of the work reviewed here is a theory of material behavior accounting for the average deformation that results from the opening, shear, growth and coalescence of an ensemble of microcracks. A concomitant is the calculation of permeability from crack structure. The first part of this paper summarizes previous developments. In particular, the initial work on this problem made use of a linear Liouville equation to characterize the change in crack distribution resulting from crack growth and coalescence. Straightforward analytic solutions to this equation were possible because the mean free path of cracks was assumed constant. Though this assumption is useful for the early stages of crack growth, increasing crack size reduces the mean free path in the later stages of fragmentation. This problem is addressed in the second part of this paper. The governing (nonlinear) Liouville equation is derived therein, and it is shown that it can be reduced to an ordinary differential equation of third order involving only a single parameter, ..beta... This equation has now been solved numerically to determine the limiting value of the mean free path as a function of ..beta.., and the results are presented in graphical form. In the third part of this paper prospects for further developments are briefly discussed.

Frictional Hot-Spots and Propellant Sensitivity

When propellant cylinders are fired at low speeds against a steel plate, detonations are often observed. Since the process is not repeatable, and shock heating is not significant, it is natural to consider the possibility of detonation caused by hot spots. Several mechanisms are compared, and it is suggested that interfacial friction of closed cracks seems to be the most likely mechanism. 24 references.

Method of generalized coordinates and an application to Rayleigh–Taylor instability

The method of generalized coordinates is extended to the analysis of continuous bodies for which the degrees of freedom are independent velocity distributions in the spatial coordinates. The corresponding Lagrange equations contain generalized convective terms as well as the usual generalized forces and masses. Since the existence of a potential is not assumed, the equations of motion can be applied to media with arbitrary (possible dissipative) constitutive laws. Material deformation is characterized by the rate of strain, which is taken as the symmetric part of the velocity gradient, making the approach valid for arbitrarily large deformations. As an example, infinitesimal Rayleigh–Taylor instability is considered by analytic methods. Then, large amplitude Rayleigh–Taylor instability is represented with a single‐degree‐of‐freedom analysis that shows the development (by numerical integration) of the known spike‐and‐bubble configuration of the unstable interface. The infinitesimal stability of a plastical...

Crack behavior of ballistically impacted ceramic

A hot isostatically pressed (HIP) assembly of titanium alloy encapsulated AD995 ceramic, subjected to ballistic impact, is studied in detail. The crack behavior of ceramic confined in this way is studied in a combined experimental and computational effort. Fabrication of the HIP assembly is described. An experiment in which an assembly was impacted with a Lexan impactor at 1560 m/s is discussed, and the resulting deformation of the assembly and cracking of the ceramic are characterized. The Statistical Crack Mechanics (SCM) model for brittle materials is briefly described. The implementations of this model into the Lagrangian code PRONTO and into the Eulerian code CTH are described and used to further study the response of the ceramic during the experiment.

Modeling anisotropic damage in an encapsulated ceramic under ballistic impact

This paper presents a study of anisotropic damage and cracking in a hot isostatically pressed assembly of titanium alloy encapsulated AD-995 ceramic under ballistic impact using the statistical crack mechanics approach. Anisotropy of crack growth in the ceramic is illustrated numerically by examining the growth in crack sizes along three orientations. Comparisons with the experimental measurements of the predicted backsurface profile and the damage (cracking) in the ceramic suggest that the model predictions are consistent with the experimental data. Numerical simulation also indicates that a prestress of roughly 2kbar (200MPa) compensates for about 1% of initial porosity in the ceramic. A comparison is made to the Rajendran–Grove ceramic model in EPIC which assumes an isotropic crack distribution.

On viscosity and the inelastic nature of waves in geological media

abstract An asymptotic solution for spherical wave propagation in linear viscoelastic solids is compared with particle velocity measurements from underground explosive tests in tuff; the magnitudes of these experimental data are of the order of 5 × 10 2 cm/sec. The qualitative nature of the theoretical solution is similar to that of the measured velocity time histories. When material and kinematic parameters in the model are specified, good quantitative agreement is obtained with respect to radial attenuation of the magnitudes and radial growth of the wavelengths. Both the phenomenological character of the viscoelastic model and limitations on its applicability are discussed.

The mathematics of recirculation and the measurement of cardiac output

One approach to the measurement of cardiac output has been to inject a calibrated volume of dye and measure its concentration at a point downstream. For an open system the flow rate can be found by dividing the volume of injected dye by the integral of concentration history. For closed systems, the accuracy of this procedure is limited by the effect of recirculation. In the past, approximate methods of correcting for recirculation have been used, but it is shown in this paper that an exact solution to the mathematical problem is possible, independent of any assumptions concerning the structure of the vascular bed. Specifically, the flow rate is the largest eigenvalue of an integral equation, the term eigenvalue being used in a slightly different sense than in boundary-value problems. The theory is applied to an example in which the concentration of dye in a closed system is represented by a mathematical function. The assumed cardiac output is then accurately determined by a computer program which solves the integral equation. The same procedure can be used to determine the flow rate in any closed system from the concentration history.

On the Role of Crack Orientation in Brittle Failure

Many materials contain a large number of microcracks that can propagate under sufficiently high stress, but their stability is sensitive to crack orientation. We have explored this sensitivity using classical fracture mechanics with the added feature that interfacial friction is accounted for in the behavior of compression cracks. Our analysis shows that four types of unstable crack growth are possible for a penny‐shaped crack under a general state of stress, depending on crack orientation: opening without shear, mixed opening and shear, pure shear without friction, and shear with interfacial friction. In addition, interfacial friction prevents crack growth at all stress intensities in a certain range of compressive stress. It will be shown that these analytic results are captured by the SCRAM brittle‐failure algorithm, and that friction strongly affects the orientation of the most unstable shear crack as well as the range of unstable orientations. A second study examines the variations in material response as a function of the number of orientations represented. This is done by computing the dynamic response of an axisymmetric thick ring to internal pressure. With the traditional 9 crack orientations the fluctuation in porosity is about 28%, while with 480 orientations the fluctuation drops to just over 2%.