Roland deWit

Relation between Dislocations and Disclinations

The theory of disclinations contains the equation ∂iαij +ejmnθmn=0, where α and θ are the dislocation and disclination density tensors, respectively. This expression is interpreted to mean that dislocations can end on twist disclinations. A concrete example in a hexagonal crystal is discussed to illustrate this concept. It contains a 60° wedge disclination normal to the basal plane. By basic geometrical construction it is shown how a dislocation can be made to end on a jog in the wedge disclination. This jog is a small segment of twist disclination. Several ramifications of this concept are that disclinations can act as sources and sinks of dislocations, that dislocations change their Burgers vectors as they glide around disclinations, that a dislocation which crosses a disclination remains connected to it by a dislocation, that dislocations encircling a disclination must have a node, and that the local Burgers vector is not conserved on following a dislocation around a disclination.

FRACTURE TESTING OF LARGE-SCALE THIN-SHEET ALUMINUM ALLOY.

Abstract : A series of fracture tests on large-scale, precracked, aluminum alloy panels were carried out to examine and characterize the process by which cracks propagate and link up in this material. Extended grips and test fixtures were specially designed to tension load the panel specimens in a l780-kN capacity universal testing machine. Single sheets of bare 2024-T3 aluminum alloy, approximately 4 m high, 2.3 m wide, and 1 mm thick were fabricated with simulated through cracks oriented horizontally at midheight. Using existing information, a test matrix was set up to explore regions of failure controlled by fracture mechanics, with additional tests near the boundary between plastic collapse and fracture. In addition, a variety of multiple site damage (MSD) configurations were included to distinguish between various proposed linkage mechanisms. All tests but one used antibuckling guides. Three specimens were fabricated with a single central crack, six others had multiple cracks on each side of the central crack, and one had a single crack but no antibuckling guides. The results of each fracture event were recorded on various media: film, video, computer, magnetic tape, and occasionally optical microscope. The video showed the crack tip with a load meter in the field of view, using motion picture film for one tip and super VHS video tape for the other. The computer recorded the output of the testing machine load cell, the stroke, and the twelve strain gages at 1.5-second intervals. A wideband FM magnetic tape recorder was used to record data from the same sources. The data were analyzed by two different procedures: (1) the plastic zone model based on the residual strength diagram and (2) the R-curve.

Estimate of Extrinsic Stacking‐Fault Energies from Dislocation Configurations

In this paper we use straight‐line models of observed extrinsic nodes to estimate extrinsic stacking‐fault energies. Using isotropic elasticity theory and neglecting interactions, we find simple expressions for the energy in terms of the inscribed radii of the nodes. We apply the results to observed extended nodes in a silver—8 at.% tin alloy and find a ratio of extrinsic to intrinsic stacking‐fault energy of about 3.

Uncertainty in Finite Element Modeling and Failure Analysis: A Metrology-Based Approach

In this paper, we first review the impact of the powerful finite element method (FEM) in structural engineering, and then address the shortcomings of FEM as a tool for riskbased decision making and incomplete-data-based failure analysis. To illustrate the main shortcoming of FEM, i.e., the computational results are point estimates based on “deterministic” models with equations containing mean values of material properties and prescribed loadings, we present the FEM solutions of two classical problems as reference benchmarks: (RB-101) The bending of a thin elastic cantilever beam due to a point load at its free end and (RB-301) the bending of a uniformly loaded square, thin, and elastic plate resting on a grillage consisting of 44 columns of ultimate strengths estimated from 5 tests. Using known solutions of those two classical problems in the literature, we first estimate the absolute errors of the results of four commercially available FEM codes (ABAQUS, ANSYS, LSDYNA, and MPAVE) by comparing the known with the FEM results of two specific parameters, namely, (a) the maximum displacement and (b) the peak stress in a coarse-meshed geometry. We then vary the mesh size and element type for each code to obtain grid convergence and to answer two questions on FEM and failure analysis in general: (Q-1) Given the results of two or more FEM solutions, how do we express uncertainty for each solution and the combined? (Q-2) Given a complex structure with a small number of tests on material properties, how do we simulate a failure scenario and predict time to collapse with confidence bounds? To answer the first question, we propose an easy-to-implement metrology-based approach, where each FEM simulation in a gridconvergence sequence is considered a “numerical experiment,” and a quantitative uncertainty is calculated for each sequence of grid convergence. To answer the second question, we propose a progressively weakening model based on a small number (e.g., 5) of tests on ultimate strength such that the failure of the weakest column of the grillage causes a load redistribution and collapse occurs only when the load redistribution leads to instability. This model satisfies the requirement of a metrology-based approach, where the time to failure is given a quantitative expression of uncertainty. We conclude that in today’s computing environment and with a precomputational “design of numerical experiments,” it is feasible to “quantify” uncertainty in FEM modeling and progressive failure analysis. DOI: 10.1115/1.2150843

Wide plate crack arrest testing

Abstract Five wide-plate crack arrest tests have been performed between September 1984 and December 1985 on an ASTM A533B quenched and tempered steel. These tests were done in the 26 MN Universal Testing Machine located at the National Bureau of Standards. The specimens were fractured in a thermal gradient to make the crack initiate at a preexisting notch in a cold, brittle region, and arrest in a hot, tough region. To obtain a great deal of information from these tests, each specimen was thoroughly instrumented with thermocouples, strain gages, crack-mouth-opening displacement gages, timing wires, and/or acoustic emission transducers. Fast data response was obtained from these sensors during the run-arrest events, which generally lasted for less than 10 ms. Estimates of two types of important data were obtained: (1) crack velocity as a function of time, and (2) initiation and arrest toughness. Thus, a successful data collecting system was developed for acquiring the basic data required for the prediction of the behavior of nuclear pressure vessels subjected to pressurized thermal shock.

Thermodynamic Force on a Dislocation

The thermodynamic force on a dislocation is defined as the negative gradient of the Gibbs free energy of the crystal with respect to dislocation motion. This is shown to lead to a consistent force expression which contains two terms: the Peach‐Koehler force due to the stress, and the Bardeen‐Herring force due to the vacancy concentration. The precise definition of these two terms is arbitrary, though their sum is unique. Various forms of the force expression are derived in terms of different reference vacancy concentrations, including the original forms of Weertman and Lothe and Hirth.

Field dependence of the barrier to magnetization reversal of a Stoner-Wohlfarth particle

It is well known that the energy barrier for magnetization reversal, EB, varies quadratically with the magnetic field for the Stoner-Wohlfarth model. However, the enthalpy H (switching energy) required to reverse the magnetization is the sum of EB and the work Wf done by the Neel fluctuation field. The sum of these two terms gives an enthalpy of reversal. If the fluctuation field is uniaxial and parallel to the holding field, then the enthalpy barrier for switching is linear in the holding field. The linearity is consistent with certain experimental results. If the fluctuation field is anisotropic, then for the same size field, the probability of the particle’s switching will depend upon the direction of that field. The paper discusses the holding field variation of the energy barrier for different fluctuation field directions.

Robust Engineering Design for Failure Prevention

To advance the state of the art of engineering design, we introduce a new concept on the “robustness” of a structure by measuring its ability to sustain a sudden loss of a part without causing an immediate collapse. The concept is based on the premise that most structures have built-in redundancy such that when the loss of a single part leads to a load redistribution, the “crippled” structure tends to seek a new stability configuration without immediate collapse. This property of a “robust” structure, when coupled with a continuous or periodic inspection program using nondestructive evaluation (NDE) techniques, is useful in failure prevention, because such structure is expected to display “measurable” signs of “weakening” long before the onset of catastrophic failure. To quantify this “robustness” concept, we use a large number of simulations to develop a metric to be named the “Robustness Index (RBI).” To illustrate its application, we present two examples: (1) the design of a simple square grillage in support of a water tank, and (2) a classroom model of a 3-span double-Pratt-truss bridge. The first example is a “toy” problem, which turned out to be a good vehicle to test the feasibility of the RBI concept. The second example is taken from a textbook in bridge design (Tall, L., Structural Steel Bridge , 2nd ed., page 99, Fig. 4.3(b), Ronald Press, New York NY, 1974). It is not a case study for failure analysis, but a useful classroom exercise in an engineering design course. Significance and limitations of this new approach to catastrophic failure avoidance through “robust” design, are discussed.Copyright

Wide-plate crack-arrest tests utilizing prototypical and degraded (simulated) pressure vessel steels☆

Abstract Sixteen wide-plate crack-arrest tests have been completed, ten utilizing specimens fabricated from A533B class 1 material and six fabricated from a low-upper-shelf base material. Each test utilized a single-edge notched specimen that was subjected to a linear thermal gradient along the plane of crack propagation. Test results exhibit an increase in crack-arrest toughness ( K 1a ) with temperature, with the rate of increase becoming greater as the temperature increases. When the wide-plate test results are compared with other large-specimen results, the data show a consistent trend in which the K 1a data extend above the limit provided in ASME Section XI.

Wide-Plate Crack-Arrest Testing: Evolution of Experimental Procedures

Between September 1984 and December 1985, five wide-plate crack-arrest tests on A533B quenched and tempered steel were carried out on the 26-MN tensile capacity universal testing machine at the National Bureau of Standards. Each test was different with respect to the conditions of testing, specimen configuration, and instrumentation used to monitor the dynamic response of the specimen during crack propagation and subsequent arrest. The progressive changes in test procedure discussed here represent attempts to obtain desired crack-run and crack-arrest behavior and to improve the quality of the data collected. Also, the optimization of strain gage locations and the final choice of recording instrumentation are reported in detail. Two techniques for measuring crack velocity are compared. Efforts to cause crack initiation and propagation at lower values of stress-intensity factor than were found in the first test are also discussed.