Donald R. Curran

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.

Nonhydrodynamic Attenuation of Shock Waves in Aluminum

The attenuation of shock waves in 2024 aluminum has been studied experimentally by impacting aluminum flyer plates upon aluminum targets and measuring the target‐free surface velocity as a function of target thickness. The results disagree with the predictions of hydrodynamic theory, exhibiting premature attenuation. An elastic‐plastic model is proposed which adequately describes the data. In this model, Poissons ratio remains constant under compression and the tensile yield strength increases linearly with compression, attaining a value of 12 kbars at a relative volume V/V0 of 0.86.

Hugoniot Equation of State of Aluminum and Steel from Oblique Shock Measurement

A method using an explosive‐produced oblique shock in a wedge‐shaped specimen has been developed for determining the Hugoniot equation of state of solids. Simultaneous measurements of shock and free‐surface velocities along the wedge face permit calculation from a single shot of pressure and density over a pressure range exceeding 2:1. Aluminum has been studied over the range 40–180 kb, good agreement being obtained with the normal‐shock method. The data for low‐carbon steel may be qualitatively interpreted in terms of a double‐shock system, associated with the polymorphic transition from α‐ to γ‐iron proposed by Minshall and Bancroft. The present method may provide a means for measuring the pressure at which a solid undergoes a polymorphic transition under dynamic conditions. Preliminary results for antimony indicate a dynamic phase transition at 95 kb corresponding to the one observed statically at 84 kb.

Damage in steel plates from hypervelocity impact. I. Physical changes and effects of projectile material

Microscopic details of physical changes occurring in steel plates impacted at hypervelocities by spherical projectiles of several materials are studied by means of metallographic examinations of polished and etched target cross sections. A hemispherical volume of material beneath the impact site undergoes the pressure‐induced α?e polymorphic phase change. The grain structure is heavily deformed and refined, and significant hardening occurs. The boundary between transformed and untransformed material can be made visible by etching; it corresponds to about a 13‐GPa isobar. The occurrence of this phase change has a considerable effect on the stress history and on the rear‐surface fracture damage, as is shown in the following paper, Paper II. Shear banding is a dominant deformation mechanism in the crater and near‐crater regions. Furthermore, the numerous white‐etching bands of very hard untempered martensite nearly always acquire brittle cracks along their length and, hence, shear banding strongly influences...

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.