Elsevier

Mechanics of Materials

Volume 137, October 2019, 103126
Mechanics of Materials

Effect of grain boundary sliding on fracture toughness of ceramic/graphene composites

https://doi.org/10.1016/j.mechmat.2019.103126Get rights and content

Highlights

  • We study grain boundary (GB) sliding near crack tips in ceramic/graphene composites.

  • GB sliding near crack tips can induce cracking in neighboring GBs.

  • GB sliding can reduce fracture toughness of ceramic/graphene composites.

  • The effect is significant for small grain sizes and not too small graphene platelets.

Abstract

A model is suggested describing the effect of grain boundary (GB) sliding on the fracture toughness of ceramic/graphene composites. Within the model, GB sliding near the tip of a large mode I crack initiates the formation of a new nano- or microcrack at an adjacent GB. The new crack merges with the pre-existent one, thus providing crack propagation. For the situation where the suggested crack growth mechanism restricts the fracture toughness of ceramic/graphene composites, we calculated the dependence of the fracture toughness on grain size and lateral dimensions of graphene platelets. The calculations demonstrated that GB-sliding-assisted crack growth reduces fracture toughness, and the effect is strongest for the case where grain size is small and the lateral graphene platelet dimensions are close to the sizes of GBs. The results of the calculations agree with the experimental data on the fracture toughness of alumina/graphene composites.

Introduction

Last years, ceramic/graphene composites attracted much attention due to their excellent mechanical properties and high electrical conductivity (see reviews Porwal et al., 2013a, Centeno et al., 2013, Nieto et al., 2017, Miranzo et al., 2017, Ovid'ko, 2015, Glukharev and Konakov, 2018) and original articles (Fan et al., 2010, Walker et al., 2011, Tapaszto et al., 2011, Wang et al., 2011, Kvetkova et al., 2012, Liu et al., 2012a, Liu et al., 2013, Liu et al., 2017, Liu et al., 2018, Nieto et al., 2013, Porwal et al., 2013b, Fan et al., 2014, Lee et al., 2014, Ramirez et al., 2014, Ramirez et al., 2015, Shin and Hong, 2014, Bódis et al., 2015, Mukherjee et al., 2017, Huang et al., 2018, López-Pernía et al., 2018, Obradović and Kern, 2018, Shin et al., 2018, Yin et al., 2018, Zou et al., 2018). The remarkable mechanical properties of such composites (high fracture toughness and bending strength) are related to the extraordinary properties of graphene (Miranzo et al., 2017). In particular, small volume fractions of platelets of multilayer graphene or reduced graphene oxide (RGO), which tend to be located along the grain boundaries of the ceramic matrix, can significantly increase the fracture toughness of ceramics, see, e.g., reviews (Porwal et al., 2013a, Centeno et al., 2013, Nieto et al., 2017, Miranzo et al., 2017, Ovid'ko, 2015, Glukharev and Konakov, 2018). An increase in the fracture toughness of such ceramic/graphene composites is attributed to crack bridging by graphene inclusions, the pull-out of graphene inclusions from the matrix, crack deflection and branching (Walker et al., 2011, Tapaszto et al., 2011, Wang et al., 2011, Kvetkova et al., 2012, Liu et al., 2012aa; Nieto et al., 2013, Porwal et al., 2013b), as well as to the presence of graphene wrinkles and out-of-plane compression of graphene platelets (Miranzo et al., 2017).

In addition to the experimental studies (He et al., 2014, Fan et al., 2010, Walker et al., 2011, Tapaszto et al., 2011, Wang et al., 2011, Kvetkova et al., 2012, Liu et al., 2012a, Liu et al., 2013, Liu et al., 2017, Liu et al., 2018, Nieto et al., 2013, Porwal et al., 2013b, Fan et al., 2014, Lee et al., 2014, Ramirez et al., 2014, Ramirez et al., 2015, Shin and Hong, 2014, Bódis et al., 2015, Mukherjee et al., 2017, Huang et al., 2018, López-Pernía et al., 2018, Obradović and Kern, 2018, Shin et al., 2018, Yin et al., 2018, Zou et al., 2018), the effects of graphene platelet pullout (Zhang et al., 2014, Ramirez and Osendi, 2014, Bobylev and Sheinerman, 2018) and crack deflection (Ovid'ko and Sheinerman, 2015) on fracture toughness of ceramic/graphene or polymer/graphene composites have also been addressed in several theoretical studies. These studies (Zhang et al., 2014, Ramirez and Osendi, 2014, Bobylev and Sheinerman, 2018, Ovid'ko and Sheinerman, 2015) demonstrated that both graphene platelet pullout and crack deflection can increase fracture toughness of ceramics by several tens percent, even for a small volume fraction of graphene. They also showed that for a specified volume fraction of graphene, longer graphene platelets should induce higher toughening associated with more difficult graphene platelet pullout (Bobylev and Sheinerman, 2018).

At the same time, in contrast to the latter result, recently, Porwal et al. (2016) observed a decrease in the fracture toughness of alumina/graphene composites with increasing the lateral graphene platelet dimensions. This effect was attributed to the onset of grain boundary (GB) sliding in the composites where the length of graphene platelets was close to the GB length. However, no explanation was given for the connection between the activation of GB sliding and the observed drop in the fracture toughness of the composites. To fill this gap, in the present study we suggest a model describing crack propagation assisted by GB sliding in ceramic/graphene composites.

Section snippets

Grain boundary sliding assisted crack growth in deformed ceramic/graphene composites. Model

Consider a ceramic/graphene composite in the form of a polycrystalline ceramic matrix and platelets that consist of several atomic layers of graphene or RGO (Fig. 1a). We assume that graphene platelets can be located both in GBs and in grain interiors. Let the examined specimen be under uniaxial uniform tension.

Following the observations (Porwal et al., 2016), suppose that cracks in the composite tend to propagate over GBs. Consider the situation where a flat mode I crack, whose length is much

Critical stress intensity factor for grain boundary sliding assisted crack growth in a ceramic/graphene composite

Now estimate the critical stress intensity factor for GB-sliding-assisted crack growth in a ceramic/graphene composite. To do so, examine a fragment of the composite containing a crack terminated at junction A (Fig. 2). For simplicity, we focus on the simplified case where GB AB contains only one graphene platelet whose cross section in the plane of GB AB represents a rectangle with the length p1 and width p2 (not shown in Fig. 2). For definiteness, assume that the center of the platelet

Results and discussion

To test the model, we put dGB=d/3, where d is the grain size, and calculate KIC for three α-alumina/graphene composites examined in Porwal et al. (2016) with the following values of geometric parameters: d=1.58μm, p1=1070 nm, p2=545 nm for the first specimen; d=1.38μm, p1=373 nm, p2=198 nm for the second specimen; and d=1.23μm, p1=193 nm, p2=109 nm for the third specimen. Since for the first specimen, p1 is slightly larger than dGB, while our model considers the situation where p1 ≤ dGB, we put

Conclusions

Thus, we have suggested a model describing GB-sliding-assisted crack growth in ceramic/graphene composites. Within the model, high stress concentrations near the tips of GB cracks stopped at triple junctions of GBs induce local GB sliding, which, in turn, results in the formation of new cracks in adjacent GBs. The main pre-existent cracks merge with the new ones, thus providing crack propagation. For the case where the formation and growth of new cracks near the tips of the main cracks assisted

Acknowledgement

The authors acknowledge the support of the Russian Science Foundation (grant 18-19-00255).

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