Lynn Seaman

Dynamic failure of solids

Abstract This paper reviews recent attempts to construct a microstatistical fracture mechanics; that is, a methodology that relates the kinetics of material failure on the microstructural level to continuum mechanics. The approach is to introduce microstructural descriptions of damage into the continuum constitutive relations as internal state variables. The microstructural damage descriptions are based on dynamic and quasi-static experiments with carefully controlled load amplitudes and durations. The resulting constitutive relations describe the nucleation, growth, and coalescence of the microscopic voids and cracks, and therefore in principle describe both quasi-static and dynamic fracture on the continuum scale. The paper describes several such kinetics models in detail, shows examples of several engineering applications, and discusses the link between microstatistical fracture mechanics and continuum fracture mechanics.

Computational models for ductile and brittle fracture

Computational models of dynamic ductile and brittle fracture are developed for wave propagation in one‐ and two‐dimensional geometries. The model features have been taken mainly from detailed observations of samples partially fractured during impacts, but the functional forms are consistent with theoretical results where applicable. Basic features of the models are the nucleation and growth (hence, the acronym NAG for the models) of voids or cracks, and the stress relaxation resulting from the growing damage. The results of the calculations include number and sizes of cracks, voids, or fragments as a function of position in the material. The NAG analysis presents the nucleation law, determined from experiment, and two growth laws: both growth and nucleation are functions of stress and stress duration. Procedures for treating cracks with a range of sizes and orientation are presented with the method for computing the stress relaxation that accompanies growth of damage. Brittle fracture is essentially aniso...

Fragmentation of rock under dynamic loads

Abstract An approach is described for predicting fragment size distributions for rock under dynamic loading conditions. The approach is (1) to determine the nature and order of the physical processes occurring in the rock during loading that lead to fragment formation, (2) to treat each process computationally and (3) to insert the resulting fragmentation model into a wave propagation code which calculates the stress history in the rock caused by the dynamic load. The approach was applied to Arkansas novaculite under one-dimensional-strain impact loads. Plate slap experiments were carried out to support model development and determine values of those rock properties required for the model. A calculation was made to simulate the conditions of one of the dynamic impact experiments and compute the resulting fragment size distribution. The agreement between calculated and measured fragment size distribution illustrates that fragmentation behavior can be predicted from a few measurable rock properties.

Micromechanical model for comminution and granular flow of brittle material under high strain rate application to penetration of ceramic targets

Abstract Under sufficiently energetic attack by penetrators or explosives, brittle materials are comminuted and forced into large strain divergent flow, deforming non-elastically by sliding and ride-up of fragments, with accompanying competition between dilatancy and pore compaction. This paper describes a micromechanical model of such deformation with application to penetration of thick ceramic targets. The model was used in parametric finite element code calculations of the penetration of an eroding, long tungsten rod into a target package consisting of a thick aluminum nitride plate confined in steel. The calculations successfully exhibited the key generic features commonly observed experimentally, including the formation of a comminuted ceramic region around the eroding penetrator nose, dilatant expansion of comminuted material into the region behind the penetrator, and conical fractures radiating outward from this region into the intact material. The most important ceramic properties that govern the depth of penetration were inferred to be the friction between comminuted granules, the unconfined compressive strength of the intact material and the compaction strength of the comminuted material. However, further work is needed to define the relative importance of the properties of the comminuted and intact material.

Dynamic failure in solids

All material failure is dynamic, almost by definition. It advances by rate processes that have threshold conditions and characteristic growth kinetics.

Dynamic fracture criteria for a polycarbonate

Flat‐plate impact experiments were performed on polycarbonate specimens to produce various levels of fracture damage. Nucleation and growth functions for incipient shock damage were deduced from the observed damage and from measured and computed stress histories. These functions allow quantitative prediction of the shock damage produced by arbitrary stress histories in polycarbonate.

Lagrangian analysis for multiple stress or velocity gages in attenuating waves

Numerical techniques are presented for extending and implementing the Lagrangian analysis originated by Fowles, Williams, and Cowperthwaite. The analysis derives internal energy, specific volume, and stress and particle velocity histories from either stress or particle velocity records from a series of gages embedded in material undergoing uniaxial strain flow. The material may have an arbitrarily complex constitutive relation. The accuracy of the analysis for attenuating waves is studied by handling analytically derived stress and velocity histories. Waves with attenuation of 40–75% can be treated, depending upon the accuracy desired. The analysis is applied to waves measured in graphite, sandstone, asbestos phenolic composite, and porous alumina.

SHOCK RESPONSE OF POROUS COPPER, IRON, TUNGSTEN, AND POLYURETHANE.

For guidance in constructing a mathematical model for porous materials, impact tests were conducted with a light‐gas gun on samples of porous copper, iron, tungsten, and polyurethane foam using manganin and quartz transducer techniques. Both Hugoniot (thick flyer) and attenuation (thin flyer) experiments were conducted on the porous metal specimens, which were initially at 70% of solid density. The Hugoniot elastic limits were 1, 2.5, and 10 kbar and maximum stresses attained were 60, 50, and 140 kbar in copper, iron, and tungsten, respectively. In impacts above 20 kbar, porous iron and copper compacted to solid but tungsten was not consolidated at 140 kbar. The mathematical model was incorporated into a one‐dimensional wave propagation computer program, and stress histories were computed to compare with the transducer records. Computed peak stresses and arrival times agreed with the recorded values within 20%.

Transformation of observed crack traces on a section to true crack density for fracture calculations

A statistical procedure has been derived for transforming apparent crack orientations, lengths, and numbers that are observed on a polished section to true orientations, lengths, and numbers. The cracks are assumed to have circular cross sections, and the orientation distribution is assumed to have axial symmetry, but no form is imposed on the observed or computed orientation and length distributions. The transformation has been incorporated into a computer code which has been tested for an analytical case and has been used to transform observed crack data for Armco iron. Comparisons are made with transformations by two approximate methods to guide in detemining whether to use the complete transformation in specific applications. The transformation should also be applicable to other observed metallographic surface features, such as ellipsoidal grains, twins, inclusions, and platelets of a new material phase.

The Influence of Microstructural Features on Dynamic Fracture

Depending on the application, materials are either required to resist fracture under dynamic loads, or else to break up easily and predictably under dynamic loads. Load-carrying structures, such as nuclear reactor pressure vessels, reentry vehicles, and armored vehicles, are examples of the former case; hand grenades and other fragmenting projectiles are examples of the latter.