Comparison between flexural and uniaxial compression tests to measure the elastic modulus of silica aerogel Adil Hafidi Alaoui a , Thierry Woignier b , George W. Scherer c, * , Jean Phalippou b a Faculté des Sciences et Techniques de Tanger, B.P. 416, Tangiers, Morocco b Laboratoire des Verres, UMR 5587, Université Montpellier 2, Place E. Bataillon, 34095 Montpellier cedex 5, France c Princeton University, Civil and Environmental Engineering, Engineering Quad. E-319, Princeton, NJ 08544, USA article info Article history: Received 24 February 2008 Received in revised form 4 June 2008 Available online 23 July 2008 PACS: 62.20.de Keywords: Aerogels Elastic moduli abstract The Young’s moduli of a set of silica aerogels have been measured by two techniques: 3-point bending and uniaxial compression. The data found by the two methods differ strongly. The uniaxial compression test gives generally underestimated values of Young’s modulus, because of geometrical effects. The appropriate gauge lengths were estimated based on the discussion of Euler buckling and nonuniform stress distribution. The measured compressive moduli were analyzed to correct for machine compliance and possible misalignment under compression of the aerogels. Similarly, moduli obtained by 3-point bending depend on the length/thickness ratio of the sample, reaching equilibrium only for ratios above about 10. The corrected compressive moduli were comparable to those measured by 3-point bending on samples of sufficient length. Ó 2008 Elsevier B.V. All rights reserved. 1. Introduction The elastic properties of aerogels have been extensively studied, because of their importance for processing and applications of aerogels; moreover, aerogels are valuable as model materials for testing theories that relate network structure to properties. In this paper we demonstrate that experimental artifacts can produce misleading results regarding the dependence of elastic modulus on density. We show how to correct for these problems, so that the same results are obtained by different methods of measure- ment, such as uniaxial compression and 3-point bending. Gel formation has been discussed in terms of percolation theory [1–5] and cluster–cluster or monomer–cluster growth processes [6,7]. The analogy between gel formation and percolation theory is based on experimental power-law evolution of physical proper- ties, such as elastic modulus [8–10]. Another structural model based on the bending of cubic cells (proposed by Gibson and Ashby [11,12]) tries to describe the mechanical behavior of the porous open cells network and concludes that the Young’s modulus, E, is proportional to the square of the bulk density, q. To test the applicability of these models (percolation, growth process, structural model), the mechanical properties of silica alco- gels and aerogels have been studied [4,5,13–15]. The results ob- tained on different sets of aerogels (by beam bending and ultrasound velocity measurements) show that the exponent of the power-law dependence of E on q is close to 3.8 [4,5]. The same value was obtained from finite element analysis of gel structures created by computer simulations of diffusion-limited aggregation [16–18]. In one study [19], a different exponent (2.85) was found, which the authors attributed to the peculiar microstructure of their aero- gels. It must be noted that not only the kind of aerogel is different compared to the previous studies [4,5], but also the kind of test used to measure E, which was uniaxial compression. It is perfectly reasonable to imagine that the network structure will affect the exponent; however, before we can have confidence in such an interpretation, it is necessary to insure that the measurement tech- nique provides reliable results. Aerogels can be irreversibly deformed when subjected to iso- static pressure [20–22]. During the compression of the solid parts, new siloxane bonds are formed between aggregates by polycon- densation reactions of silanol bonds [22]. This new reticulation be- tween aggregates partially ‘freezes’ the network, increases the connectivity and, thus, the elastic rigidity. Therefore, it is essential that the modulus measurements be made using sufficiently small strains. It has been shown [23,24] that the uniaxial compression test is sensitive to several technical or geometrical parameters that affect the measurements. One of the most important parameters is the ratio L 0 /D [25–27] where L 0 and D are, respectively, the initial sam- ple length and diameter. The uniaxial compression test is valid if this ratio ranges between two limits [28,29], corresponding to an 0022-3093/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.jnoncrysol.2008.06.014 * Corresponding author. Tel.: +609 258 5680; fax: +609 258 1563. E-mail address: Scherer@Princeton.Edu (G.W. Scherer). Journal of Non-Crystalline Solids 354 (2008) 4556–4561 Contents lists available at ScienceDirect Journal of Non-Crystalline Solids journal homepage: www.elsevier.com/locate/jnoncrysol