Re-visiting the ‘rule of mixture’ used in materials with multiple constituting phases: A technical note on morphological considerations in austenite case study

Prawoto, Yunan; Djuansjah, Joy Rizki Pangestu; Shaffiar, Norhashimah

doi:10.1016/j.commatsci.2012.08.008

Cited by 10 publications

(6 citation statements)

References 31 publications

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“…The results indicate that the volume-weighted average grain size, based on the rule of mixtures, captures the response of the material better than the average grain size as the characteristic length of the microstructure. This finding is supported by earlier investigations, where the rule of mixtures has been successfully applied to model grain boundary behaviour [50], elastic properties of multi-phase materials [51], and strength of composites [52,53].…”

Section: Discussionsupporting

confidence: 76%

Influence of grain size distribution on the Hall–Petch relationship of welded structural steel

Lehto

Remes

Saukkonen

et al. 2014

Materials Science and Engineering: A

190

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The strength of polycrystalline metals increases with a decrease in grain size according to the HallPetch relationship. However, heterogeneous microstructures deviate from this relationship depending on the distribution of grain sizes. This paper introduces a rule of mixtures based approach for determining the characteristic length of the microstructure for heterogeneous weld metal. The proposed grain size parameter, the volume-weighted average grain size, is measured experimentally for nine structural steel weld metals and two base materials. The weld metals are found to have a large variety of grain size distributions that are noticeably broader than those of the base material due to differences in phase contents. The results show that the volume-weighted average grain size is able to capture the influence of grain size distribution on the strength of welded structural steel. Based on the experimental results, a modified Hall-Petch relationship is formulated for the strength prediction of heterogeneous microstructures. The modified relationship is also found to be applicable to data from the literature.

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Section: Discussionsupporting

confidence: 76%

Influence of grain size distribution on the Hall–Petch relationship of welded structural steel

Lehto

Remes

Saukkonen

et al. 2014

Materials Science and Engineering: A

190

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“…The materials rule of mixtures states that certain properties of a composite can be estimated through the weighted mean of the components, which can describe elasticity, thermal and electrical conductivity. This estimation is described between two bounds, which represent the parallel and perpendicular effects of the specific property .…”

Section: Resultsmentioning

confidence: 78%

Determining the Dielectric Constants of Organic Photovoltaic Materials Using Impedance Spectroscopy

Hughes

Rosenthal

Ran

et al. 2018

Adv Funct Materials

109

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The photovoltaic and electrical properties of organic semiconductors are characterized by their low dielectric constant, which leads to the formation of polarons and Frenkel excitons. The low dielectric constant of organic semiconductors has been suggested to be significantly influential in geminate and bimolecular recombination losses in organic photovoltaics (OPVs). However, despite the critical attention that the dielectric constant has received in literature discussions, there has not yet been a thorough study of the dielectric constant in common organic semiconductors and how it changes when blended. In fact, there have been some inconsistent and contradictory reports on such dielectric constants, making it difficult to identify trends. Herein, at first a detailed explanation of a specific methodo logy to determine the dielectric constant in OPV materials with impedance spectroscopy is provided, including guidelines for possible experimental pitfalls. Using this methodology, the analysis for the dielectric constant of 17 common neat organic semiconductors is carried out. Furthermore, the relationship between the dielectric constant and blend morphology are studied and determined. It is found that the dielectric constant of a blend system can be very accurately predicted solely based on the dielectric con stants of the neat materials, scaled by their respective weight ratios in the blend film.

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“…The early theoretical treatments of the hybrid effect showed that calculations based on a simple rule of mixtures (ROM) contradicted the experimental results, suggesting the complexity of the ''hybridization'' [64]. Rules of mixtures are mathematical expressions that provide a homogeneous property for a heterogeneous composite in terms of the properties, quantity and arrangement of its constituents [65]. It is an operational tool that uses the weighted volume average of the component properties in isolation to obtain the magnitude of the property for the heterogeneous materials.…”

Section: Hybrid Polymer Composites and Synergy Effectmentioning

confidence: 98%

Synergy in hybrid polymer/nanocarbon composites. A review

Szeluga

Kumanek

Trzebicka

2015

Composites Part A: Applied Science and Manufacturing

297

184

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Re-visiting the ‘rule of mixture’ used in materials with multiple constituting phases: A technical note on morphological considerations in austenite case study

Cited by 10 publications

References 31 publications

Influence of grain size distribution on the Hall–Petch relationship of welded structural steel

Influence of grain size distribution on the Hall–Petch relationship of welded structural steel

Determining the Dielectric Constants of Organic Photovoltaic Materials Using Impedance Spectroscopy

Synergy in hybrid polymer/nanocarbon composites. A review

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