Ultrasonic velocity measurements have been made to obtain the dynamic elastic stiffnesses necessary to determine fully the elastic properties of a unidirectional glass-reinforced epoxy-fiber composite. In units of 106 psi, these stiffnesses are C11=6.01, C22=C33=2.58, C12=C13=0.70, C23=1.42, and C44=0.49, where the subscript 1 refers to the fiber direction. Since more velocities were measured than were necessary to obtain the five constants required by the symmetry of this composite, the extra measurements were used to check on the experimental method. Analysis shows the ultrasonic technique to be satisfactory for measurement of the elastic stiffnesses of a fiber composite. The experimental results are compared with the elastic constants predicted for this composite from expressions based upon several theoretical models. Good agreement is obtained when the theoretical calculations are made using the dynamic (as opposed to the static) modulus of the epoxy matrix.
A simple method is shown for calculating the relaxation time spectrum which controls the rate at which a process following simple first-order kinetics takes place. The method involves unfolding a Fredholm equation of the first kind using least-squares and then using a modified nonlinear regression rather than a linear least-squares technique, thereby avoiding the highly oscillatory solutions which tend to occur with the latter with reduced mesh spacing or an increased number of bins. The validity and accuracy of the method for analyzing experimental data to reproduce various known input spectra are assessed and found to be excellent for data with no experimental error. For data with simulated experimental error with standard deviations up to σ=0.05 the method provides acceptable approximate solutions even though no exact solution is expected. Increasing the magnitude of the experimental error for a single lognormal input spectrum appears to have an increasing but nonsystematic effect upon the uncertainty of the approximate solution. Effects due to increasing the number of bins in the interval over which the spectrum is calculated are assessed and shown not to appreciably change the results, even for up to 60 bins. The methods is shown to be applicable to a wide variety of input spectra including single and double lognormal and box distributions. Importantly, in each of the cases studied the approximate solution appeared both to be unique and to converge toward the known input spectrum. Based upon this validation it is concluded that this method has applicability to a wide range of problems in which simple exponential decay is occurring with a spectrum of time constants. It may also be useful for problems with different kernals than that for first order kinetics; however, careful validation will be required.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.