Donald A. Shockey

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...

Failure phenomenology of confined ceramic targets and impacting rods

Abstract The mechanism by which a long rod penetrates a steel-encased ceramic block was sought by performing impact experiments at a range of velocities and examining the fracture and deformation in the recovered targets and impactors. The key processes are the crushing of a small volume of ceramic adjacent to the leading surface of the advancing penetrator, and the subsequent flow of the fine fragments lateral to and then opposite the direction of attack. The results suggest that nonconventional material properties such as the dynamic compressive failure energy and the friction, flow and abrasive properties of the finely fragmented material govern the penetration resistance of confined ceramics. This understanding of penetration mechnism can be used to guide development of specialized tests and failure models to measure pertinent material properties and to predict penetration behavior, respectively.

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.

Instability of cracks under impulse loads

A plate impact method was used to produce internal penny‐shaped cracks in polycarbonate and to study the response of these cracks to short tensile pulse loads. The observed crack instability behavior could not be explained by classical static fracture mechanics. A short‐pulse fracture mechanics was developed from static fracture mechanics concepts. The instability criterion was obtained from considerations of the early time stress intensity histories experienced by cracks struck by short‐pulse loads. This criterion, which requires that the dynamic stress intensity exceed the dynamic fracture toughness for a certain minimum time, gave results in accord with the experimental data. Short‐pulse fracture mechanics defines the conditions for which simple static expressions can be used to determine dynamic fracture toughness. The dynamic fracture toughness of polycarbonate at a stress intensification rate of 107 MN m−3/2 sec−1 was measured to be 2.2±0.2 MN m−3/2, about 60% of the quasistatic value. This result s...

The strength behavior of granulated silicon carbide at high strain rates and confining pressure

The dynamic Mohr–Coulomb behavior of silicon carbide (SiC) was inferred from symmetric pressure/shear plate‐impact experiments which entail planar impact of two SiC plates inclined at 15° to the impact direction. The transverse velocity of the free rear surface of the target plate was recorded using a laser Doppler velocimeter system, and the experiments were simulated using a postulated viscoplastic constitutive model that accounts for comminution and dilatancy. Model parameters were varied until the computed and measured velocity histories agreed. The results indicate that comminution occurred soon after loading, and thus the experiment measures the behavior of granulated material at shear strain rates of ≊105 s−1 and mean stress ranging from 1 to 9 GPa. A friction coefficient of 0.23 was obtained, which is about half the value for quasistatic compression of precomminuted ceramic reported in the literature. The simulation results were strongly affected by the values chosen for the friction coefficient a...

Short-pulse fracture mechanics

Abstract This paper summarizes the results of a multiyear research effort at SRI International aimed at extending classical static fracture-mechanics concepts to apply to cases where a load is applied as a short-duration pulse. A criterion for crack instability under short-pulse loads was deduced from considerations of Sih-Achenbach stress-intensity solutions. Impact experiments were performed on polymers and metallic alloys to observe crack-instability behavior and verify the short-pulse criteria. This new understanding of short-pulse fracture mechanics is being used to help develop procedures for high-rate fracture testing and to guide investigations of fracture incubation time.