Strength of AAAS Composites with Ceramic Precursor over Time

The paper deals with the approximation of the time evolution of the strengths of selected alkali-activated aluminosilicate (AAAS) composites based on ceramic precursors. Composites made of brick dust as a precursor and an alkaline activator with a silicate modulus of Ms = 0.8, 1.0, 1.2, 1.4, and 1.6 were investigated. The filler consisted of standard quartz sand in one case, and crushed brick in the other. The test specimens had nominal dimensions of 40 × 40 × 160 mm and were tested in three-point bending after 7, 28, 90, and 300 days of maturation. From each composite, 3 specimens were tested and the compressive strength was determined from the 6 specimen parts that remained after the bending tests. The obtained flexural and compressive strength values for the abovementioned 4 composite ages were approximated by the exponential function , where the coefficient a represents a horizontal asymptote to the approximation curve, i.e. the theoretical strength of the composite at time t = ∞; the exponential term of the approximation with the coefficients b and c expresses the degree of the time-dependent change of the respective compressive strength in the interval t = (0, ∞). The approximation was performed with the least squares method using genetic algorithms implemented in the Java GA package with open source code.

Some Notes on the Omega Distribution and the Pliant Probability Distribution Family

In 2020 Dombi and Jónás (Acta Polytechnica Hungarica 17:1, 2020) introduced a new four parameter probability distribution which they named the pliant probability distribution family. One of the special members of this family is the so-called omega probability distribution. This paper deals with one of the important characteristic “saturation” of these new cumulative functions to the horizontal asymptote with respect to Hausdorff metric. We obtain upper and lower estimates for the value of the Hausdorff distance. A simple dynamic software module using CAS Mathematica and Wolfram Cloud Open Access is developed. Numerical examples are given to illustrate the applicability of obtained results.

Comments on the Half Logistic Inverse Rayleigh (HLIR) cdf with “Polynomial Variable Transfer”. Some Applications

On the base of the Half Logistic – G family of distributions proposed by Cordeiro, Alizadeh and Marinho [2] some mathematical properties are investigated by Almarashi et al. [1]. We study the “saturation” to the horizontal asymptote: t=1 by the new growth function M(t) in the Hausdorff sense. Similar to our previous studies [3-6], in this article we will define and analyze in detail the new family. We will call this family the “Half-Logistic-Inverse-Rayleigh cdf with Polynomial Variable Transfer” (HLIRPVT) cdf. Section 3 shows the potentiality of proposed new model under four real data sets. Some numerical examples using CAS MATHEMATICA are given.

Scale-invariant dynamics of galaxies, MOND, dark matter, and the dwarf spheroidals

ABSTRACT The Scale-Invariant Vacuum (SIV) theory is based on Weyl’s Integrable Geometry, endowed with a gauge scalar field. The main difference between MOND and the SIV theory is that the first considers a global dilatation invariance of space and time, where the scale factor λ is a constant, while the second opens the likely possibility that λ is a function of time. The key equations of the SIV framework are used here to study the relationship between the Newtonian gravitational acceleration due to baryonic matter gbar and the observed kinematical acceleration gobs. The relationship is applied to galactic systems of the same age where the radial acceleration relation (RAR), between the gobs and gbar accelerations, can be compared with observational data. The SIV theory shows an excellent agreement with observations and with MOND for baryonic gravities gbar > 10−11.5 m s−2. Below this value, SIV still fully agrees with the observations, as well as with the horizontal asymptote of the RAR for dwarf spheroidals, while this is not the case for MOND. These results support the view that there is no need for dark matter and that the RAR and related dynamical properties of galaxies can be interpreted by a modification of gravitation.

A Nonlinear Least Squares Logistic Fit Approach to Quantifying Uncertainty in Fatigue Stress-Life Models and an Application to Plain Concrete

A large number of fatigue life models for engineering materials such as concrete and steel are simply a linear or nonlinear relationship between the cyclic stress amplitude, σa, and the log of the number of cycles to failure, Nf. In the linear case, the relationship is a power-law relation between σa and Nf, with two constants determined by a linear least squares fit algorithm. The disadvantage of this simple linear fit of fatigue test data is that it fails to predict the existence of an endurance limit, which is defined as the cyclic stress amplitude at which the number of cycles is infinity. In this paper, we introduce a nonlinear least square fit based on a 4-parameter logistic function, where the curve of the y vs. x plot will have two horizontal asymptotes, namely, y0, at the left infinity, and y1, at the right infinity with y1 < y0 to simulate a fatigue model with a decreasing y for an increasing x. In addition, we need a third parameter, k, to denote the slope of the curve as it traverses from the left horizontal asymptote to the lower right horizontal asymptote, and a fourth parameter, x0, to denote the center of the curve where it crosses a horizontal line half-way between y0 and y1. In this paper, the 4-parameter logistic function is simplified to a 3-parameter function as we apply it to model a fatigue sress-life relationship, because in a stress-log (life) plot, the left upper horizontal asymptote, y0, can be assumed as a constant equal to the static ultimate strength of the material, U0. This simplification reduces the logistic function to the following form: y = U0 − (U0 − y1) / (1 + exp(−k (x − x0)), where y = σa, and x = log(Nf). The fit algorithm allows us to quantify the uncertainty of the model and the estimation of an endurance limit, which is the parameter, y1. An application of this nonlinear modeling technique is applied to fatigue data of plain concrete in the literature with excellent results. Significance and limitations of this new fit algorithm to the interpretation of fatigue stress-life data are presented and discussed.

Experimental Study on Critical Load of Compression Column with a Rectangular Cross-Section Based on Material Mechanics

By means of resistance strain gauge and multifunctional test bench of materials mechanics, the relation curve between the axial compressive forces of the two-ends hinged column with a rectangular cross-section and total bridge strain was obtained by the resistance strain measurement method, accordingly, by the horizontal asymptote of this relation curve the critical load of compression column was obtained. The study indicates that the critical load obtained respectively by the resistance strain measurement method and Euler formula theory fits very well, and the research results verified the reliability of the experimental method.

Determination of a point sufficiently close to the asymptote in nonlinear growth functions

Growth functions with upper horizontal asymptote do not have a maximum point, but we frequently question from which point growth can be considered practically constant, that is, from which point the curve is sufficiently close to its asymptote, so that the difference can be considered non-significant. Several methods have been employed for this purpose, such as one that verifies the significance of the difference between the curve and its asymptote using a t-test, and that of Portz et al. (2000), who used segmented regression. In the present work, we used logistic growth function, which has horizontal asymptote and one inflection point, and applied a new method consisting in the mathematical determination of a point in the curve from which the growth acceleration asymptotically tends to zero. This method showed the advantage to have biological meaning besides leading to a point quite close to those obtained using the beforementioned methods.

Super Long Life Fatigue of AE42 and AM60 Magnesium Alloys

Magnesium alloys, on account of their lightweight, find useful applications in the automotive sector. During service, they experience very high number of fatigue cycles. Therefore, the understanding of their long life fatigue behavior becomes extremely important. This is possible by using ultrasonic fatigue testing, which is the only feasible way of doing it. In this study, the two such alloys viz. AE42 and AM60 has been investigated for their long life fatigue characteristics under fully reversed loading conditions, using a piezoelectric fatigue testing machine operating at a frequency of 20 kHz. The S-N data does not reach a horizontal asymptote at 107 cycles in either of the alloys. However, the alloy AM60 seems to show a fatigue limit at about at 109 cycles. The fractures examined by scanning electron microscopy (SEM) were found to be brittle in character. In very high cycle fatigue conditions, the crack was found to initiate from the specimen subsurface.