Abstract
Recent progress in nanotechnology enables us to utilize the elastic strain engineering, the emerging technology capable of controlling the physio-chemical properties of materials via externally-imposed elastic strains, for hard materials. Because the range of accessible properties by imposing elastic strains are set by materials' elasticity limits, it is of great importance to suppress the occurrence of any inelastic deformations and failure, and thereby the fundamental knowledge on fracture behavior at nanoscale is highly required. The conventional Weibull theory, which has been widely used for last a few decades to explain the failure statistics of brittle bulk materials, has a limitation to be directly applied to the samples of nanometer dimensions because the baseline assumption on statistical equivalence becomes intractable for small samples. In this study, we suggest an integrated equation presenting the sample size effect on fracture strength for brittle nanomaterials by further considering the confinement of the flaw size distribution. This new approach is applicable to any homogeneous brittle nanomaterials whose failure is governed by linear elastic fracture mechanics, and shows good agreement with experimental data collected from literatures. We expect that this theoretical study offers new guideline to employ brittle nanomaterials in designing and fabricating the advanced strain engineering system.
Highlights
Thermodynamic potentials and free energies of elastically-deformed solid bodies explicitly depend on the strains or stresses (Kittel and McEuen, 1996; Gilman, 2003)
Recent studies on nanomechanics revealed that both yield (Jang and Greer, 2010; Wang et al, 2013) and fracture (Suresh and Li, 2008; Jang et al, 2013) strengths of many hard nanomaterials drastically increase, up to a significant fraction of their ideal strengths, and the elasticity limits increase as well, when the sample sizes decrease down
We present some examples of actual experimental data collected from the literature that reports the uniaxial tensile strengths of brittle nano-whiskers made of ZnO (Hoffmann et al, 2007; Xu et al, 2010; He and Zhu, 2011) and single crystalline Cu (Richter et al, 2009).Two important features are noteworthy here: (i) clear demonstration of the reciprocal square-root relation between the diameter t and fracture strength and (ii) large scatter in the data. The former serves as the strong evidence for our work, and the latter indicates that the statistical fluctuation originated from the large Weibull modulus is still dominant in this regime
Summary
Thermodynamic potentials and free energies of elastically-deformed solid bodies explicitly depend on the strains or stresses (Kittel and McEuen, 1996; Gilman, 2003). The former serves as the strong evidence for our work, and the latter indicates that the statistical fluctuation originated from the large Weibull modulus is still dominant in this regime
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