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Under rapid loading conditions and/or for a rapidly propagating crack, the mass density of a material affects the fields of stress and deformation. For such dynamic fracture problems plastic deformation in the immediate vicinity of a crack tip is investigated in this paper. Both stationary and propagating crack tips are considered. For a stationary crack tip, deformation theory is employed for the first phase of the loading when the fields are increasing monotonically with time. The general character of the near-tip fields is analyzed both with respect to its variation with time and with polar angle. The non-linear near-tip fields are related to the linearly elastic far-field by means of a path-independent integral. In the second part of the paper we consider rapidly propagating cracks. We discuss the near-tip fields for various models of material behavior. In particularly we briefly review some earlier work by Achenbach and Kanninen for a rapidly propagating Mode-III crack, in a material which displays strain hardening. In the last part of the paper we consider the fields near a rapidly propagating crack-tip in an elastic-perfectly plastic material for the case that inertial terms are of importance. The system of governing equations in the plastic region is presented and shown to be hyperbolic in nature. As a first approximation the steady-state case with respect to the moving crack-tip is considered and an asymptotic analysis of the near-tip field is carried out. (Author)

Some concepts available for interpreting dynamic fracture phenomena are reviewed. These include the mechanical characterization of crack edge fields, energy variations associated with crack growth, and experimental observations relevant to the points raised. More recently developed and still incomplete ideas on the influence of crack tip plasticity, material strain rate sensitivity and three dimensional effects are also outlined. Dynamic fracture is a branch of the engineering science of fracture mechanics concerned with fracture phenomena on a time scale for which inertial resistance of the material to motion is significant. The deformable body typically contains a dominant crack or other stress concentrating defect, and the phenomena of primary interest are those associated with conditions for the onset of extension of a crack or its arrest. Material inertia can have a significant effect in a variety of ways. Load transfer from the rapidly loaded boundary of a body to the region of a crack edge can occur by means of stress waves. Likewise, a rapidly running crack emits stress waves which can be geometrically reflected or scattered back to the region of the crack.

The experimental basis for the necessity of a dynamic characterization of crack run/arrest events is reviewed. Current anomalies in the use of linear elastodynamic treatments--apparent geometry and load rate dependence of the dynamic fracture toughness property--are discussed. A review of concurrent work in plastic fracture mechanics is given as a possible basis for circumventing these anomalies. (Author)

The report is divided into five chapters covering new analytical solutions for dynamic cracks in orthotropic composites. Each chapter stands alone and has been submitted, accepted or prepared for publication in a refereed journal. First, closed form solutions for uniformly loaded semi-infinite cracks in orthotropic materials are presented. Next, solutions regarding the stress intensity factor at the tip of propagating cracks in orthotropic materials are presented. In addition, closed form, dynamic Green's functions solutions are given for semi-infinite cracks in orthotropic materials. Previously, in last year's report, numerical Green's function solutions were presented for this case the first time. These newer, closed form solutions are much easier to produce and implement in more complex solutions. The problem of having a crack in transversely isotropic material rotated with respect to the crack front is also solved with some effort. The methodology used in finding all these solutions may be used in other problems including penetration mechanics. Such applications are currently being explored. Finally, experimental investigation of the application of these solutions to dynamic crack initiation in composites under impact conditions is being completed.

A dynamic fracture mechanics methodology has been implemented into the Lagrangian finite element hydrocode EPIC. The generalized energy release rate T* was assumed to be a measure of the crack driving force. This representation for the crack driving force was selected because its generality includes elastic plastic behavior and inertial effect. In addition to the introduction of the crack driving force, a nodal release algorithm to model the formation of traction free surfaces produced by a propagating crack was incorporated into EPIC. The dynamic fracture mechanics enhanced EPIC code was used in the generation phase mode to deduce be dynamic fracture toughness from measurements made during high loading rate fracture tests of AISI 4340 and AP 1410 steel specimens. The internal consistency of the approach and algorithms was demonstrated by performing application phase analyses of these fracture tests to predict the crack growth history. A second set of experiments was devised. using a different experimental arrangement and specimen geometry, to demonstrate the predictive capability of the methodology. A new dynamic test method was developed referred to as a dynamic three point bend test-in which an instrumented, precracked three-point tend specimen is dynamically loaded through a transmitter bar that is struck by a striker bar fired from a gas gun. The length and slated of the striker bar control the duration and intensity of the loading pulse. A finite element model of the experiment was developed. Numerical predictions, using the fracture toughness determined from the independent coupled pressure bar tests, are in relatively good agreement with measured crack growth and strain gage histories, thereby validating the dynamic fracture mechanics computational methodology implemented into EPIC.

A global/local analysis is applied to the problem of a panel with an edge delamination crack subject to an impulse loading to ascertain the dynamic J integral. The approach uses the spectral element method to obtain the global dynamic response and local resultants to obtain the J integral. The variation of J integral along the crack front is shown. The crack behavior is mixed mode (Mode 2 and Mode 3), but is dominated by the Mode 2 behavior.

This report summarizes the work completed in the months of June 1996 - December 1999 for the principal investigator's Young Investigator Program grant. As such, the report represents a final summary of work, organized as follows. First, in a brief summary chapter, a review of the accomplishments of the work supported from June 1996 to December 1999 is given providing an overview of the successes during that period. Next, two chapters giving details of new work during the six months since the last annual report are presented. In these results, an experimentally useful solution for the stress intensity factor history at the comer of an impacting punch is derived for isotropic and orthotropic materials. Then that solution is compared to experimental measurements of the stress intensity factor history at the comer of an impacting punch in both isotropic and anisotropic materials. Good agreement between model and experiments is seen.

Finite element analysis of static and dynamic fracture of brittle microcracking solids was performed. The continuum constitutive modeling for rate-dependent fracture of brittle microcracking solids is discussed. The rate-type constitutive equation that is proposed takes into account the rate effect on microcracking and plastic deformation. In order to test the validity of the proposed modeling, numerical studies were conducted on a bar under uniaxial tension, a beam under pure bending, and on the phenomenon of microcracking around the tip of a macrocrack under mode-I loading. Finite element analysis of stationary and rapidly-propagating macrocracks under dynamic loading. The microcrack toughening effect is discussed, along with the influence on it of the size of the microcracked process zone and the various parameters in the microcrack density evolution equation, through the observation of the behavior of the general crack-tip energy-release parameter, the T integral. Some important aspects associated with the transformation induced plasticity in Al2O2ZrO2 are analyzed using a computer simulation based on Finite Element Method. (MM)

Finite element analysis of static and dynamic fracture of brittle microcracking solids was performed. The continuum constitutive modeling for rate-dependent fracture of brittle microcracking solids is discussed. The rate-type constitutive equation that is proposed takes into account the rate effect on microcracking and plastic deformation. In order to test the validity of the proposed modeling, numerical studies were conducted on a bar under uniaxial tension, a beam under pure bending, and on the phenomenon of microcracking around the tip of a macrocrack under mode-I loading. Finite element analysis of stationary and rapidly-propagating macrocracks under dynamic loading. The microcrack toughening effect is discussed, along with the influence on it of the size of the microcracked process zone and the various parameters in the microcrack density evolution equation, through the observation of the behavior of the general crack-tip energy-release parameter, the T integral. Some important aspects associated with the transformation induced plasticity in Al2O2ZrO2 are analyzed using a computer simulation based on Finite Element Method. (MM)

A method is developed for the optimization against buckling of structures that undergo snap buckling. Simple formulae are obtained for the dependence of J integral on the angle or edge crack in an infinite strip of fully plastic material under antiplane shear. An assessment is made on the range of validity of the dominant term in the singular field solution for stationary cracks. The mathematical problems arising in the elastic-plastic crack growth problems are highlighted.

The objective of this work is to develop a procedure by which crack tip plasticity can be taken directly into account in rapid crack propagation. To set the stage, a background description of linear elastic dynamic fracture mechanics is first given. Existing solutions for dynamic crack propagation and for quasistatic crack growth accompanied by crack tip plasticity are reviewed. It is found that existing dynamic plastic fracture solutions are essentially confined to strip yield (Dugdale model) plastic zones that are collinear with the crack. The ultimate goal of the research reported in this paper is to provide the basis of a computational procedure for plastic dynamic crack propagation in structures of engineering interest. The prerequisite for such a development is knowledge of the nature of the crack tip singularity, which can be obtained via an asymptotic analysis in which attention is focused on the very near crack tip region. Here we have considered the specific case of crack propagation in antiplane strain (Mode III). The results suggest some interesting general conclusions, and the analysis has pointed the way to the solution of the Mode I problem.

A hybrid experimental-numerical procedure was used to analyze the micro-mechanics of the mixed-mode, static and dynamic fracture of a concrete three-point bend specimen with an offset precrack. Four/two beam moire interferometry was used to record simultaneously separating horizontal and vertical displacements associated with stable/rapid growth. An elasto-static/ elasto-dynamic finite element code was execute in its propagation mode with assumed crack closure stress (CCS) versus crack opening displacement (COD) and crack shearing stress (CSS) versus crack sliding displacement (CSD) relations which were adjusted to match the computed and measured COD's and CSD's. The resultant CCS versus COD and the CSS versus CSD relations were then used to compute the dissipated energy in the FPZ. This energy dissipation rate in the FPZ accounted for about 80% of the total energy release rate throughout the dynamic fracture process. This study also showed that the strain energy released at the crack tip and the dissipated energy in the fracture process zone after crack kinking are due mainly to mode I crack tip) deformation.

The report is divided into two parts, one covering the work on orthotropic composites and the other covering the work on isotropic metals. Each part consists of two chapters which stand alone, each having been submitted, accepted or prepared for publication in a referred journal. Separate bibliographies are given for parts 1 and 2. The work on composites has succeeded in producing fundamental, dynamic Green's functions solutions for cracks in orthotropic materials. These solutions may be used in calculating the stress intensity factor history on stationary cracks subjected to dynamic loading and may be very useful in predicting crack initiation under such conditions. Currently, experimental investigation of the application of these solutions to crack initiation in composites in two different configurations is beginning. It is expected that a report on that work will be submitted next year. The work on metals has been successful in experimentally demonstrating the usefulness of the dynamic stress intensity factor in predicting shear failure in metals under impact loads. This demonstration is predicted on the assumption that small scale yielding conditions exist in the experiments. The last chapter reflects an ongoing experimental investigation into the validity of that assumption. It seems to suggest that the assumption is correct, but further, more conclusive results are sought.

Progress is reviewed with emphasis on a model of stress intensity factors in dynamic punch test. The specimen is assumed to be initially at rest and the projectile is rigid. Impact of the rigid projectile is modeled by a constant velocity condition on the impact surface. Three support geometries are considered for each specimen geometry: a free back surface, a fixed back surface, and a two dimensional punch. Analytical approximations for the stress intensity factor history are given for short times, while dynamic quarter point finite element solutions are included for longer times. The stress intensity factor is shown to increase with time due to wave reflection in the two dimensional punch and fixed back support geometries, while it decreases with time for the free back surface. The stress intensity factors in the plate specimen are also greater than those in the edge notched specimen in all tests. For applicability to manufacturing operations and increased chance of shear dominated failure, it is recommended that the two dimensional punch or fixed back surface geometries of the plate specimen be used in experimental studies.