Weibull Effective Volumes, Surfaces, and Strength Scaling for Cylindrical Flexure Specimens Having Bi-Modularity

Abstract

The objective of this present work was to predict the strength distribution of bi-modular cylindrical ceramic specimen from that of another based on Weibull statistical theory. In order to do so, initially, semi-analytical expression for effective volume and effective surface for the cylindrical bar loaded in flexure were derived. In addition, strength scaling ratio from one flexural loading configuration to another with various Weibull modulus was made available. Elaborate experimentation and numerical simulations was carried out to verify the analytical model. Generally, strength scaling for specimen size is dependent on whether the flaws are volume or surface distributed; however, in this study, it was observed that the ratio of strengths from any two configurations, such as three-point flexural to four-point, is independent of whether the flaws are volume or surface distributed when the cross-sectional sizes are the same.

Determining the interlaminar tensile strength of a SiCf/SiC ceramic matrix composite through diametrical compression testing

“…Secondly, while the Φ9 mm disk geometry means that it is possible for a whole unit cell to be with a specimen the exact location of crossovers and where these points are relative to the in-plane stress, σ x , is unknown. It is recognised that the modest increase seen in k between the two disk geometries could be attributed to the volume effect of Weibull analysis [31]. The characteristic strength, σ θ, ILT , is established as 53.6 MPa for the Φ4.5 mm specimens and 37.5 MPa for the Φ9 mm specimens.…”

Bond‐based peridynamics model of 3‐point bend tests of ceramic‐composite interfaces

“…There could be multiple reasons for such behavior, one of which could be the lack of variability in the fracture strength of the zirconia in the models used for the benchmark simulations. Indeed, it is well known that the size of the sintered material will affect the stochasticity of fracture, 55,70 with surface and volume scaling coefficients to be incorporated when using Weibull statistics for describing the distribution of the material's fracture stress. The model adopted until now, however, assumes a homogeneous behavior of the materials involved, there-fore only the geometric effect of the layers involved should play a role in determining the failure loads observed.…”

“…This would leave the bottom layer in a more relaxed state, and favoring the failure of the interface first until a weak spot in the porcelain would favor the propagation of a secondary crack from the interface inside the material. It must be pointed out, however, that for a correct model representing the stochasticity of fracture in the material, a two-parameter Weibull distribution applied to the bonds directly may not be sufficient in reproducing the correct behavior of the materials involved, as multiple authors showed, 55,70 However, the simple approach adopted for this analysis is sufficient to highlight the necessity of a careful selection of the stochastic model to reproduce experimental results through peridynamics.…”

Thermoelastic fracture behavior of bimodular functionally graded skin-stiffener composite panel with embedded inter-laminar delamination

“…The fundamental difference between the tension and compression behavior of certain grades of manufactured graphite has been observed, when individual specimen is stressed alternately in tension and compression. 1 Though most materials exhibit some form of different stress strain behavior during tension and compression close to the origin of stress vs. strain plots, they are ignored by the researchers for computational simplicity of solving stress dependent elasticity problems. This imposes a high constraint on the reliability of high-risk structures, which nevertheless depends too much on an assumed factor of safety against catastrophic failure.…”