Abstract
Tensile strength ft and fracture toughness KIC of ceramic are not deterministic properties or fixed values, but fluctuate within certain ranges. A nonlinear elastic fracture mechanics model was developed in this study and combined with the common normal distribution to predict ceramic’s ft and KIC with consideration of their scatters in a statistical sense. In the model, the relative characteristic crack size a*ch/G (characteristic crack size a*ch, average grain size G) was determined based on the fracture measurements on five types of ceramics with different G from 2 to 20 μm in the reference (Usami S, et al., Eng. Fract Mech. 1986, 23, 745). The combined application of the model and normal distribution has two functions: (i) probabilistic ft and KIC can be derived from seemingly randomly varied fracture tests on small ceramic specimens containing different initial defects/cracks, and (ii) with ft or KIC values (corresponding mean and standard deviation), fracture strength of heterogeneous samples with and without cracks can be predicted by considering scatter described by specified reliability. For the fine ceramics, the predicted results containing the mean and the upper and lower bounds with 96% reliability gained with the model, match very well with the experimental results (a, σN).
Highlights
One of the biggest challenges in material sensitive design is to accurately and reliably predict the fundamental mechanical properties of materials
A non-LEFM model for ceramic fracture is proposed and combined with normal distribution, which is applicable to predictions of f t, KIC and σN with consideration of their scatters
The relative characteristic crack size C (= a*ch /G) indicating the transition from f t - to KIC - controlled fracture was determined based on the five groups of fracture data on ceramics with different G from 2 to 20 μm reported in the literature and the dominant fracture mechanism of brittle materials
Summary
One of the biggest challenges in material sensitive design is to accurately and reliably predict the fundamental mechanical properties of materials. We reanalysed the fracture measurements data on four fine-grained ceramics with G from 2 to 20 μm and on two coarse-grained rocks with G = 2.5 and 10 mm, and found a semi-quantitative relation of a*ch ≥ 3G [7,10].an explicit relationship between a*ch and G is an urgency need for the fundamental knowledge of microstructure-driven material research, and for the safe design application. A non- linear elastic fracture mechanics (non-LEFM) analytical model is proposed to predict f t and KIC of ceramics as function of grain size G from common fracture measurements, and to predict fracture strength of specimens with and without small defects if f t or KIC are available. The common normal distribution was used to analyse the fracture behaviour of ceramics to consider the scatters of physical and mechanical properties
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