# Fileset
[2018-09-05-manuscript-tib2-nbb2-r20-s1.pdf](https://mdr.nims.go.jp/filesets/8a706b14-acea-4a32-8f43-594d4c67fc6e/download)
## Creator
[Dmytro Demirskyi](https://orcid.org/0000-0002-6870-6726), Ievgen Solodkyi, Toshiyuki Nishimura, [Oleg O. Vasylkiv](https://orcid.org/0000-0002-5041-6130)
## Rights
This is the peer reviewed version of the following article: Demirskyi D, Solodkyi I, Nishimura T, Vasylkiv OO. Fracture and property relationships in the double diboride ceramic composites by spark plasma sintering of TiB2 and NbB2. J Am Ceram Soc. 2019; 102: 4259–4271, which has been published in final form at https://doi.org/10.1111/jace.16276. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions. This article may not be enhanced, enriched or otherwise transformed into a derivative work, without express permission from Wiley or by statutory rights under applicable legislation. Copyright notices must not be removed, obscured or modified. The article must be linked to Wiley’s version of record on Wiley Online Library and any embedding, framing or otherwise making available the article or pages thereof by third parties from platforms, services and websites other than Wiley Online Library must be prohibited.[In Copyright](http://rightsstatements.org/vocab/InC/1.0/)
## Other metadata
[Fracture and property relationships in the double diboride ceramic composites by spark plasma sintering of TiB 2 and NbB 2](https://mdr.nims.go.jp/datasets/f37f1af0-b348-4dca-812c-840eff9ea04c)
## Fulltext
Microsoft Word - 2018-09-05-manuscript-tib2-nbb2-r20-s1.docx† Authors to whom correspondence should be addressed, Dmytro Demirskyi, demirskyi.dmytro.e2@tohoku.ac.jp /phone +81-(0)70-2010-6281/ and Oleg Vasylkiv, oleg.vasylkiv@nims.go.jp /phone +81-(0)80-4144-4747 Fracture and property relationships in the double diboride ceramic composites via spark plasma sintering of TiB2 and NbB2 D. Demirskyi (a,b)†, I. Solodkyi (a), T. Nishimura (c), and O. Vasylkiv (a)†. (a) Research Center for Functional Materials, National Institute for Materials Science, 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047, Japan (b) Tohoku University Advanced Institute for Materials Research (AIMR), 2-1-1 Katahira, Aoba-ku, Sendai, 980-8577 Japan (c) National Institute for Materials Science, 1-1 Namiki, Tsukuba, Ibaraki 305-0044, Japan Supplementary data. In this appendix, the equations used for calculating the residual stress in TiB2 and NbB2 grains, σm and σi, due to the inclusion of secondary diboride phase. According to a model presented by Taya et al. in [37] for a binary composite, stresses accumulated in matrix during cooling can be estimated as: 𝜎" = $%&'∗(*+%)(&-$)(*-./)-0&%(*+./) (1) where Em is Young’s modulus of the matrix, f is the volume fraction of inclusions and 𝛽 is given by: 𝛽 = *-./*+$.2323/ (2) Ep, 𝜈5 and 𝜈" are Young’s modulus and Poisson ratio of particle inclusions and matrix, respectively, and 𝜀∗ is the thermal expansion misfit strain given by: [𝛼5 − 𝛼"] Δ𝑇 (3) where the 𝛼5, 𝛼" are the thermal expansion coefficients of reinforcement and matrix, respectively and ∆T is the temperature at which stresses begin to accumulate, set as 1800 °C and more realistically at 1200–1400 °C [40]. 2 Change in flexural strength behaviour can be explained by changes in microstructure that occur during testing or stress state of material during the testing. In general, improvement or decrease in toughness in two-phase ceramic composites is known to be a result of mismatch in CTE [37]. Importantly, in the present study two phases TiB2 and NbB2 have similar CTE’s in the wide temperature range between 25 and 1900 °C, and more crucially bellow 1200 °C (see Figure S1.1) [28]. At room temperature widely accepted values of CTE are 5.6 and 6.3x10-6, for TiB2 and NbB2, respectively. Mind that dashed area in Fig. S1.1 indicates the zone where CTE of two phases are within the error of their estimation [28, 29]. Figure S1.1 – Coefficients of thermal expansion of TiB2 and NbB2 the temperature range of 300 K to 2400 K [28]. 3 Figure S1.2 – Evaluation of thermal stresses accumulated during cooling of TiB2–NbB2 (1:1) ceramic composite. Hence, we attempted to estimate the accumulated stresses using Taya's model [37] and available data on mechanical characteristics of TiB2 and NbB2 [28–30,39]. Such analysis using a temperature gradient of 1800 °C, showed that residual stresses on the TiB2 matrix σm (1:1 4 composite) and NbB2 inclusions σi are −255 MPa and 398 MPa, respectively. A negative value of the residual stress at matrix indicates compression, while a positive value of the residual stress at reinforcement suggests tension. In this case, where the temperature gradient is 1200 °C or 1400 °C [40], values of 115 MPa and –173 MPa can be estimated. Mind, that at higher temperatures the CTE of TiB2 is fairly larger than that of NbB2 (i.e., 9 and 8.2 x10-6, respectively), but they come to equilibrium at the range of 600–800 °K (see Fig. S1.2), thus the sign of stresses at matrix and inclusions are reversed. Importantly, the absolute value of stresses induced on the diborides have same magnitude of below 500 MPa. In the case of all compositions used in the present study, the maximum stresses associated with a temperature gradient of 1800 °C are presented in Table S1. Table S1 Evaluation of thermal residual stresses for TiB2–NbB2 ceramic composites. Composition Residual stress at matrix, σm, MPa Residual stress at the secondary phase, σi, MPa TiB2 : NbB2 (1:1) -255 398 TiB2 : NbB2 (2:1) -156 496 TiB2 : NbB2 (1:2) -378 297