Lacunarity is a measure of how data fills space. It complements fractal dimension, which measures how much space is filled. This paper discusses the limitations of the standard gliding box algorithm for calculating lacunarity, which leads to a re-examination of what lacunarity is meant to describe. Two new lacunarity measures for ramified data sets are then presented that more directly measure the gaps in a ramified data set. These measures are rigorously defined. An algorithm for estimating the new lacunarity measure, using Fuzzy-C means clustering algorithm, is developed. The lacunarity estimation algorithm is used to analyze two-and three-dimensional Cantor dusts. Applications for these measures include biological modeling and target detection within ramified data sets.
This report documents results of the post-irradiation examination material property testing of the creep, control, and piggyback specimens from the irradiation creep capsule Advanced Graphite Creep (AGC)-2 are reported. This is the second of a series of six irradiation test trains planned as part of the AGC experiment to fully characterize the neutron irradiation effects and radiation creep behavior of current nuclear graphite grades. The AGC-2 capsule was irradiated in the Idaho National Laboratory Advanced Test Reactor at a nominal temperature of 600°C and to a peak dose of 5 dpa (displacements per atom). One half of the creep specimens were subjected to mechanical stresses (an applied stress of either 13.8, 17.2, or 20.7 MPa) to induce irradiation creep. All postirradiation testing and measurement results are reported with the exception of the irradiation mechanical strength testing, which is the last destructive testing stage of the irradiation testing program. Material property tests were conducted on specimens from 15 nuclear graphite grades using a similar loading configuration as the first AGC capsule (AGC-1) to provide easy comparison between the two capsules. However, AGC-2 contained an increased number of specimens (i.e., 487 total specimens irradiated) and replaced specimens of the minor grade 2020 with the newer grade 2114. The data reported include specimen dimensions for both stressed and unstressed specimens to establish the irradiation creep rates, mass and volume data necessary to derive density, elastic constants (Young's modulus, shear modulus, and Poisson's ratio) from ultrasonic time of flight velocity measurements, Young's modulus from the fundamental frequency of vibration, electrical resistivity, and thermal diffusivity and thermal expansion data from 100-500°C. No data outliers were determined after all measurements were completed.A brief statistical analysis was performed on the irradiated data and a limited comparison between pre-and post-irradiation properties is presented. A more complete evaluation of trends in the material property changes, as well as irradiation-induced creep due to irradiation, temperature, and applied load on specimens will be discussed in later AGC-2 post-irradiation examination analysis reports.
The Advanced Graphite Creep (AGC)-2 capsule is the second of six planned irradiation capsules comprising the AGC experiment test series. During the AGC experiment, graphite specimens are irradiated and stressed for comparison to irradiated unstressed and unirradiated specimens to garner the quantitative data necessary for predicting the irradiation behavior and operating performance of new nuclear-grade graphite. This testing will ascertain the in-service behavior of the graphite for pebble-bed and prismatic very high-temperature reactor designs. Similar to the first AGC (i.e., AGC-1) pre-irradiation examination report, material property tests were conducted on specimens from 16 nuclear-grade graphite types. However, AGC-2 tested an increased number of specimens (i.e., 486) compared to AGC-1 (i.e., 366) [1]. The AGC-2 capsule was irradiated in the Advanced Test Reactor at Idaho National Laboratory at approximately 600°C and to a peak dose of 5.0 displacements per atom. All of the irradiated specimen measurements for AGC-2 were conducted at Idaho National Laboratory from April 2014 to March 2015. This report describes the requirements and design of the second AGC (i.e., AGC-2) irradiation capsule. It summarizes how corrections were made to the specimen elevation due to thermal expansion, irradiation shrinkage, and creep. This correction allows a more accurate prediction of each specimen's temperature and dose. It also details how an average temperature, dose, and load is derived from the capsule thermocouple temperatures, reactor flux profile, and load cell data is summarized, along with a brief discussion about the uncertainty in these values. Tables containing specimen dose, temperature, and load are included in the appendices of this document for use in future creep analysis and material properties comparisons.
This report documents the analysis of the creep strain data from the Advanced Graphite Creep (AGC)-2 graphite creep specimens. This is the second of a series of six irradiation test trains planned as part of the AGC experiment to fully characterize the neutron irradiation effects and radiation creep behavior of current nuclear graphite grades. The AGC-2 capsule was irradiated in the Idaho National Laboratory Advanced Test Reactor at a nominal temperature of 600°C, beginning with irradiation Cycle 149A on April 12, 2011 and ending with Cycle 151B on May 5, 2012, with a total received dose range of 1.3-4.7 dpa.AGC-2 was designed to provide irradiation conditions similar to AGC-1 (i.e, the same graphite grades, a nominal irradiation temperature of 600°C, and the same applied mechanical stress levels) but was irradiated for a shorter period of time to provide material property values for the graphite samples at lower dose levels than achieved in AGC-1. Material property and dimensional strain measurements were conducted on specimens from 15 nuclear graphite grades using a similar specimen assembly configuration as the first AGC capsule (AGC-1) to provide easy comparison between the two capsules. However, AGC-2 contained an increased number of specimens (i.e., 487 total specimens irradiated) and replaced specimens of the minor grade 2020 with the newer grade 2114.Significant modifications were made to the AGC-2 irradiation capsule to improve the specimen temperature issues that were encountered with AGC-1. While the AGC-2 irradiation temperature range (399-704°C) was much narrower than AGC-1 the range is still considered less than optimal. The centrally located creep specimens (specimens under an applied mechanical stress of 13.8, 17.2, or 20.7 MPa) and control specimens (specimens with no applied stress) were irradiated over even a narrower temperature range of 541-681°C with dose levels from 2.0-4.7 dpa.The data reported include specimen dimensions and hence the dimensional strain change upon irradiation. This allowed a comparison of these data for specimen-matched pairs yielding the dimensional and volumetric creep strain. The AGC-2 creep strain analysis methodology is similar to the AGC-1 analysis and the irradiation strain results from both capsules compare well for all grades. The derived creep coefficients have been calculated for each grade and are found to compare well to literature data, despite the larger than desired spread in specimen temperatures.
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