Post-Fire Mechanical Properties of Concrete Reinforced with Spanish Broom Fibers

In this study, we conducted an initial investigation of the post-fire mechanical properties of concrete reinforced with Spanish broom fibers. The mechanical properties were determined at room temperature, and the post-fire mechanical properties were determined at elevated temperature, so that the fire resistance of the concrete could be determined. Five mixtures were considered: three with differently treated Spanish broom fibers, a polypropylene fiber mixture, and a reference concrete mixture. The concrete and reinforced concrete samples were first dried to 100 °C, then heated to 400 °C, and left to cool to room temperature. The samples were tested immediately and 96 h after cooling. The compressive strength, weight loss, ultrasonic pulse velocity, and dynamic modulus of elasticity were determined and compared. The cross-sectional images of the concrete samples captured through an optical microscope were observed and analyzed. The changes in fiber structure were monitored by TG/DTG analysis. The results of the study indicate that even the reference concrete mixture did not have satisfactory residual properties. The reinforced concretes did not improve the residual properties of the reference concrete, but reduced the spalling and explosive failure performance under a compressive load. The concrete reinforced with Spanish broom fibers showed improved residual properties compared with concrete reinforced with polypropylene fibers.

Residual Properties in Damaged Laminated Composites through Nondestructive Testing: A Review

The development of damage tolerance strategies in the design of composite structures constitutes a major challenge for the widespread application of composite materials. Damage tolerance approaches require a proper combination of material behavior description and nondestructive techniques. In contrast to metals, strength degradation approaches, i.e., the residual strength in presence of cracks, are not straightforwardly enforceable in composites. The nonhomogeneous nature of such materials gives rise to several failure mechanisms and, therefore, the definition of an ultimate load carrying capacity is ambiguous. Nondestructive techniques are thus increasingly required, where the damage severity is quantified not only in terms of damage extension, but also in terms of material response of the damaged region. Based on different approaches, many nondestructive techniques have been proposed in the literature, which are able to provide a quantitative description of the material state. In the present paper, a review of such nondestructive techniques for laminated composites is presented. The main objective is to analyze the damage indexes related to each method and to point out their significance with respect to the residual mechanical performances, as a result of the working principle of each retained technique. A possible guide for future research on this subject is thus outlined.

Effect of Microcracks on the Tensile Properties of 3D Woven Composites

This study provides an experimental investigation on the effect of microcracks on the tensile properties of 3D woven composites. A four-step experimental procedure using the combination of micro-XCT, acoustic emission (AE) and digital image correlation (DIC) is here proposed. Typical tensile damage behaviors were characterized by the stress–strain curves, AE signal analysis and DIC full field strain measurement. Due to a typical four stages stress–strain behavior, phenomena of stiffness degradation and stiffness hardening were successively found during the tensile process. Samples with various damage levels were produced by the in situ AE monitoring. Their 3D microcrack morphologies show the crack initiation, propagation process and the damage modes. Detectable damages initiated during the stress range from 65.98% to 72.93% σs. The cracks volume fraction (CVF) shows a positive correlation relationship with the corresponding tensile load. Moreover, the CVF was used to characterize the degree of damage. The samples with various phased damages were tested again in the fourth step to obtain their residual modulus and residual strength. Detected microcracks have little influence on the residual strength, while the residual modulus witnesses a regular decrease along with the damage increase. The effect of microcracks on the tensile properties is characterized by the relationships between the gradually increased damages and the corresponding residual properties which provide a foundation for damage evaluation of 3D woven structures in service.

Computational Analysis of Quantitative Characteristics of some Residual Properties of Solvable Baumslag-Solitar Groups

Let $G_{k}$ be defined as $G_{k} = \langle a, b;\ a^{-1}ba = b^{k} \rangle$, where $k \ne 0$. It is known that, if $p$ is some prime number, then $G_{k}$ is residually a finite $p$-group if and only if $p \mid k - 1$. It is also known that, if $p$ and $q$ are primes not dividing $k - 1$, $p < q$, and $\pi = \{p,\,q\}$, then $G_{k}$ is residually a finite $\pi$-group if and only if $(k, q) = 1$, $p \mid q - 1$, and the order of $k$ in the multiplicative group of the field $\mathbb{Z}_{q}$ is a $p$\-number. This paper examines the question of the number of two-element sets of prime numbers that satisfy the conditions of the last criterion. More precisely, let $f_{k}(x)$ be the number of sets $\{p,\,q\}$ such that $p < q$, $p \nmid k - 1$, $q \nmid k - 1$, $(k, q) = 1$, $p \mid q - 1$, the order of $k$ modulo $q$ is a $p$\-number, and $p$, $q$ are chosen among the first $x$ primes. We state that, if $2 \leq |k| \leq 10000$ and $1 \leq x \leq 50000$, then, for almost all considered $k$, the function $f_{k}(x)$ can be approximated quite accurately by the function $\alpha_{k}x^{0.85}$, where the coefficient $\alpha_{k}$ is different for each $k$ and $\{\alpha_{k} \mid 2 \leq |k| \leq 10000\} \subseteq (0.28;\,0.31]$. We also investigate the dependence of the value $f_{k}(50000)$ on $k$ and propose an effective algorithm for checking a two-element set of prime numbers for compliance with the conditions of the last criterion. The results obtained may have applications in the theory of computational complexity and algebraic cryptography.