Papers by Keyword: Weibull Statistics

Abstract: Open cell ceramic foam filters are utilized to reduce non-metallic inclusions during casting of metals and therefore to enhance the quality of cast parts. A new generation of multifunctional filters made of carbon bonded alumina (Al₂O₃-C) has been developed within the scope of the collaborative research center CRC 920 [1]. The assessment of the resistance against high thermal and mechanical loads requires a mechanical characterization of the ceramic filter material. The mechanical properties show a distinctive size dependency, that’s why the specimen dimensions should be similar to the strut size of the real filter structures. The tensile fracture behavior is investigated by means of the Small Punch Test (SPT) using miniaturized disk-shaped specimens. During the mechanical tests a load-displacement curve is measured until failure occurs and a fracture stress is calculated from the experimental results. An estimation about the failure probability by means of Weibull statistics is performed because of the large scatter of the strength of the material. Furthermore, a modified version of the SPT, the so called Ball On Three Balls Test (B3B), is applied and compared to the SPT. In a final step numerical simulations of the B3B tests are performed by means of the finite element method to identify fracture mechanical material parameters like the fracture toughness.

Abstract: The primary objective of this paper is to illustrate the effects of weak-link scaling on the tensile behaviour of fiber-reinforced composites. The proposed model takes into account the random nature of fiber strength, which is given by a two-parameter Weibull distribution function. Several hundred Monte-Carlo replications are executed to simulate the statistical strength distributions of the composites. It is shown that probabilistic tensile strength distributions and size scaling is dependent on both the stress redistribution and the fiber strength statistics.

Abstract: The fracture of mechanically loaded ceramics is a consequence of material critical defects located either within the bulk or at the surface, resulting from the processing and/or machining and handling procedures. The size and type of these defects determine the mechanical strength of the specimens, yielding a statistically variable strength and brittle fracture which limits their use for load-bearing applications. In recent years the attempt to design bio-inspired multilayer ceramics has been proposed as an alternative choice for the design of structural components with improved fracture toughness (e.g. through energy release mechanisms such as crack branching or crack deflection) and mechanical reliability (i.e. flaw tolerant materials). This approach could be extended to complex multilayer engineering components such as piezoelectric actuators or LTCCs (consisting of an interdigitated layered structure of ceramic layers and thin metal electrodes) in order to enhance their performance functionality as well as ensuring mechanical reliability. In this work the fracture mechanisms in several structural and functional multilayer components are investigated in order to understand the role of the microstructure and layered architecture (e.g. metal-ceramic or ceramic-ceramic) on their mechanical behaviour. Design guidelines based on experiments and theoretical approaches are given aiming to enhance the reliability of multilayer components.

Abstract: Particle reinforcement via the insertion of hard particles is a promising process in materials reinforcing. Particle-reinforced spheroidal graphite martensitic cast iron (SGMC), in which mixed particles of cermet and cemented carbide are dispersed, was achieved by an insertion process. A four-point bending strength test was applied to evaluate the particle composite material. An evaporative pattern process was used on the bending-test specimen to form a composite layer in the central part. Using a combination of three sizes of cermet particles and two sizes of cemented-carbide particles, the bending strength was found to increase with each small-particle combination. The Weibull coefficient m of the four-point bending strength of the particle-reinforced composite material (PRCM) ranged from 4 to 13, and m was large in the specimen with large bending strength.

Abstract: This paper presents a comparative study between 3- and 4-point bending tests applied to five Portuguese limestones. The study has been conducted on sawed limestone specimens, all showing the same surface finishing. The materials were compared for two distinct situations: i) using a 3-point flexure loading configuration in batches of materials with larger cross sectional specimen dimension (50 × 30 mm2); and ii) using a 4-point flexure loading configuration in the same batch of materials but with smaller cross sectional dimensions (30 × 25 mm2). In all situations, the materials have broken due to intrinsic volume defects. Formulae for the effective volumes and effective surfaces for rectangular beam specimens loaded in flexure were reviewed in order to analyse the strength scaling effect. The results show the applicability of the Weibull statistics to explain the differences in the results of the 3-point and 4-point bending tests, even when different cross sectional sizes are employed. Among other important remarks, in all the different limestone specimens used it was possible to confirm that the strength values determined experimentally via 3-point bending are of the same order as those estimated for the same loading configuration but via experimental data of 4-point bending tests using the Weibull strength scaling approach, even if employing a different cross-sectional dimension.

Abstract: Different sets of silica aerogels (classical aerogels, partially dense aerogels, composite aerogels) have been studied in the objective to understand the mechanical behaviour of these extremely porous solids. The mechanical behaviour of xerogels and aerogels is generally described in terms of brittle and elastic materials, like glasses or ceramics. The main difference compared to silica glass is the order of magnitude of the elastic and rupture modulus which are 104 times lower. However, if this analogy is pertinent when gels are under a tension stress (bending test) they exhibit a more complicated response when the structure is submitted to a compressive stress. The network is linearly elastic under small strains, then exhibits yield followed by densification and plastic hardening. As a consequence of the plastic shrinkage it is possible to compact and stiffen the gel at room temperature. These opposite behaviours (brittle and plastic) are surprisingly related to the same kinds of gel features: pore volume silanol content and the pore size. Both elastic modulus and plastic shrinkage depend strongly on the volume fraction of pores and on the condensation reaction between silanols. On the mechanical point of view (rupture modulus and toughness), it is shown that pores size plays likely an important role. Pores can be considered as flaws in the terms of fracture mechanics and the flaw size, calculated from rupture strength and toughness is related to the pore size distribution.

Abstract: Two available strength data sets of single-walled and multi-walled carbon nanotubes are analysed, and the effects of sample sizes on their tensile strengths are investigated. A minimum information criterion is applied to determine the optimal strength distribution. The results show that, in contrast to a two-parameter Weibull distribution, lognormal distribution seems to be a more suitable choice. A simple extrapolation of classical Weibull statistics to nanoscales may result in overestimation on the tensile strength of carbon nanotubes.