Nathanael A. Heckert

Single Fiber Tensile Properties Measured by the Kolsky Bar Using a Direct Fiber Clamping Method

The Kolsky bar test has been widely used in measuring material behavior under high strain rate conditions. In particular, polymers used in ballistic applications have been characterized by this method to investigate high strain rate behavior during ballistic impact. Research conducted by Cheng et al. (J Eng Mater Technol-Trans ASME 127(2):197–203, 2005) and Lim et al. (J Mater Sci 45(3):652–661, 2010) measured high strain rate properties of single PPTA [Poly (p-phenylene terephthalamide)] fibers and aramid co-polymer fibers by gluing the fiber directly to the Kolsky bar, which is time consuming work and can be affected by wicking of the glue into the fiber gauge length area. Kim et al. (J Mater Sci. doi: 10.1007/s10853-013-7142-y, 2013) investigated clamping effects of the glue-tab and direct gripping methods on the single PPTA fiber tensile properties under the quasi-static loading condition and applied the direct grip method for the Kolsky bar test to measure the tensile strengths at a high strain rate (Kim et al., Compos Sci Technol. doi: 10.1016/j.compscitech.2012.03.021, 2012). This study extends the measurement capability for the tensile strength, failure strain and modulus that are important parameters that influence performance of soft body armor.

Retrospective Analysis of NIST Standard Reference Material 1450, Fibrous Glass Board, for Thermal Insulation Measurements.

Thermal conductivity data acquired previously for the establishment of Standard Reference Material (SRM) 1450, Fibrous Glass Board, as well as subsequent renewals 1450a, 1450b, 1450c, and 1450d, are re-analyzed collectively and as individual data sets. Additional data sets for proto-1450 material lots are also included in the analysis. The data cover 36 years of activity by the National Institute of Standards and Technology (NIST) in developing and providing thermal insulation SRMs, specifically high-density molded fibrous-glass board, to the public. Collectively, the data sets cover two nominal thicknesses of 13 mm and 25 mm, bulk densities from 60 kg·m−3 to 180 kg·m−3, and mean temperatures from 100 K to 340 K. The analysis repetitively fits six models to the individual data sets. The most general form of the nested set of multilinear models used is given in the following equation: λ(ρ,T)=a0+a1ρ+a2T+a3T3+a4e−(T−a5a6)2where λ(ρ,T) is the predicted thermal conductivity (W·m−1·K−1), ρ is the bulk density (kg·m−3), T is the mean temperature (K) and ai (for i = 1, 2, … 6) are the regression coefficients. The least squares fit results for each model across all data sets are analyzed using both graphical and analytic techniques. The prevailing generic model for the majority of data sets is the bilinear model in ρ and T. λ(ρ,T)=a0+a1ρ+a2T One data set supports the inclusion of a cubic temperature term and two data sets with low-temperature data support the inclusion of an exponential term in T to improve the model predictions. Physical interpretations of the model function terms are described. Recommendations for future renewals of SRM 1450 are provided. An Addendum provides historical background on the origin of this SRM and the influence of the SRM on external measurement programs.

Statistical Characterizations for Tensile Properties of Co-polymer Aramid Fibers: Loading Rate Effects

High strength polymer fibers such as poly(p-phenylene terephthalamide) (PPTA), and poly(p-phenylene benzobisoxazole), (PBO) have been used for ballistic body armors. In addition to these para-oriented fibers, copolymer aramid fibers are being considered. Although mechanical properties of these fibers measured under quasi-static loading conditions are reported to be excellent, fiber tensile properties measured at comparable loading conditions for ballistic impact are rarely reported. In this study, we measure single fiber tensile properties at high rate loading conditions by clamping a fiber to the grips of a mini Kolsky bar, and investigate their statistical distributions as well as fiber morphologies.

Statistical Characterization of Single PPTA Fiber Tensile Properties from High Strain Rate Tests

Single [poly (p-phenylene terephalamide)] PPTA fiber tensile strengths were measured under quasi-static and high strain rate loading conditions, and poly (methyl methacrylate) (PMMA) and rubber as gripping materials were used to investigate gripping effects for the tests. To incorporate the strength distributions of single PPTA fibers into a rate dependent stochastic strength model, it is important to estimate uncertainties of the model parameters as well as the best-fitting-distribution for the parameter estimation. We demonstrated the appropriateness of a Weibull model for the tensile strengths obtained by the quasi-static test and preliminary results for the corresponding Weibull shape parameters with approximately ±20 % parameter confidence intervals. These results will be used to characterize of the strengths obtained by the high strain rate test using the Weibull model.

Tensile Behavior of Single PPTA Fibers Measured by the Kolsky Bar Using the Direct Fiber Clamping Method

The Kolsky bar test has been widely used in measuring material behavior under high strain rate conditions. In particular, this methodology has been used to characterize the high strain rate behavior of polymer and polymer composites during ballistic impact. Chen et al. measured the tensile properties of single poly(p-phenylene terephthalamide) (PPTA) fibers at high strain rates by gluing the fiber directly to the Kolsky bar. However, the application of this technique is somewhat limited because of the time-consuming nature of the gluing procedure [1]. Due to the highly stochastic nature of fiber tensile strength, large test-sample sizes are required to analyze distributions of fiber properties such as tensile strength, modulus, and strain-to-failure. The authors have investigated the direct gripping method to facilitate high throughput single fiber tensile testing at high strain rates. As an extension of these efforts, the polymethyl methacrylate (PMMA) platens used for directly gripping the fibers are replaced here by rubber platens to assess the impact of the platen material properties on the stress transfer from the Kolsky bar to the fiber at high strain rates. In this study, the system compliance for the PMMA grips is measured under the quasi-static condition to assess the stress transfer from the grip and to correct the modulus and failure strain of the fiber. In preliminary tests using a PMMA grip, the system compliance was obtained by the 5, 10 and 60 mm gauge lengths. These data will be compared with similar data using the rubber grips to investigate the influence of the gripping material properties.

Statistical analysis of fiber gripping effects on Kolsky bar test

Preliminary data for testing fibers at high strain rates using the Kolsky bar test by Ming Cheng et al. [1] indicated minimal effect of strain rate on the tensile stress-strain behavior of PPTA [poly (p-phenylene terephathalamide)] fibers. In a different study, Lim et al. [2] reported that the tensile strengths of the copolymer aramid fibers are strain rate dependent. Usually with single fiber tests, a large sample size is needed to get statistically significant results. To date with high strain rate tests, technical issues associated with specimen preparation appear to limit the number of samples that can be tested within a reasonable time. In this study, the authors investigate the feasibility of a gripping design to establish a reliable, reproducible, and accurate Kolsky bar test methodology for single fiber tensile testing with high throughput. Preliminary results measured under a quasi-static strain rate with 5 mm and 60 mm gauge lengths showed that the PPTA fibers are gauge length dependent. This size effect must be considered in determining the true strain rate effect on fiber strength in conjunction with the gripping effect.

Statistical analysis of partial discharge phenomena. Time of occurrence distributions

This paper presents time-of-occurrence (phase) distributions of individual pulsating partial discharges (PDs) which occur in a point-dielectric gap in air for ac voltage conditions. It is determined that the pulse phase distribution is adequately modeled by a normal (Gaussian) distribution. Based on such best-fit normal distributions, estimated mean values of the phase and the standard deviations are given for the individual PD pulse distributions. For the alternating voltage case, the spread of time-of-occurrence distributions of succeeding pulses are universally broader than that of preceding pulses. PD pulse separations are non-uniform in phase. Further, if one assumes the usual sinusoidal waveform, then the voltage separation of PD pulses are also seen to be non-uniform.