Hollow glass microsphere composites: preparation and properties Citation for published version (APA): Verweij, H., With, de, G., & Veeneman, D. (1985). Hollow glass microsphere composites: preparation and properties. Journal of Materials Science, 20(3), 1069-1078. https://doi.org/10.1007/BF00585751 DOI: 10.1007/BF00585751 Document status and date: Published: 01/01/1985 Document Version: Publisher’s PDF, also known as Version of Record (includes final page, issue and volume numbers) Please check the document version of this publication: • A submitted manuscript is the version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website. • The final author version and the galley proof are versions of the publication after peer review. • The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publication General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal. If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license above, please follow below link for the End User Agreement: www.tue.nl/taverne Take down policy If you believe that this document breaches copyright please contact us at: [email protected] providing details and we will investigate your claim. Download date: 02. Oct. 2021 JOURNAL OF MATERIALS SCIENCE 20 (1985) 1069-1078 Hollow glass microsphere composites: preparation and properties H. VERWEIJ, G. DE WITH, D. VEENEMAN Philips Research Laboratories, P.O. Box 80000, 5600 JA Eindhoven, The Nether~ands Composites consisting of bonded hollow glass m icrospheres are promising for construc- tions in which materials are needed that combine a high Young's modulus with a low density. The elastic,properties of ideally bonded hollow glass microsphere composites are predicted theoretically. Heat-treated castings of quartz glass microspheres approach the theoretical Young's modulus from below. The best result achieved was a Young's modulus of about 1 GPa with a strength of about 0.8 MPa at a density of about 180 kg m -3 . This was obtained with a casting of quartz glass microspheres, bonded with mono-aluminium phosphate. Composites made by pressing of appropriate microsphere/ binder mixtures, followed by heating, had a density that was lower than for castings but had a Young's modulus far below the theoretical value. 1. Introduction 2. Theory The present investigations were initiated by a In microsphere composites two kinds of porosity request for new construction materials with a low may be present: an intergranular porosity P1 and density and a high Yotmg's modulus. The require- an intragranular porosity P2. The total porosity is ments for the density pointed towards highly given by: porous materials. These materials can be subdivided P = PI+P2. (1) into simple foams and more complex composites such as hollow glass microsphere composites. A reasonable estimate for the intergranular Organic materials generally have a Young's porosity, P1, given random sphere packing is P1 "~ modulus that is an order of magnitude below that 0.4. This estimate is based on both experimental of inorganic materials, which makes them less and theoretical data; see for example [2]. suitable for the applications in mind. A well The intragranular porosity, P2, can be estimated known inorganic foam is the so-called foam glass from the average relative density of a thin-walled [1 ] with a Young's modulus of typically 1 GPa at a single hollow sphere, Ps, given by; density of 130kgm -a. This material has a large 4rr 3/[ 4rr 3} average bubble size of up to 2 mm and must be Ps = ~[ R3-(R-d) ] --~R ~3d/R (2) machined to make complex shapes. This may be a disadvantage for mass production applications. where R is the (outer) radius of the sphere and d is Microsphere composites of complex shape can be the wall thickness. The single sphere porosity, Ps, prepared by casting or pressing microsphere/binder is given by: mixtures followed by heat treatment. This can be accomplished with relatively cheap techniques. e~ = 1 -- 3a/R. (3) The present paper reports on the theory of elas- In a microsphere composite only a fraction f= tic properties of hollow microsphere composites (1 --P~) is occupied by spheres so that the intra- and on the preparation and mechanical properties granular porosity, P2, becomes: of some specific hollow glass microsphere compo sites. P2 = fPs = (1 --Px) (1--3d/R). (4) 0022-2461/85 $03.00 + .12 1985 Chapman and Hall Ltd. 1069 The Young's modulus, E, of a porous material e/e0 = exp (- ble,) {1 - exp [- b2(1 --Ps)]} can be estimated using various models. The discussion of this subject as given below is necess- = exp(-blP1){l--exp [-b~ (1-P)]}(I-P1)] arily brief. An extensive review of the micro- structure dependence of mechanical properties can (8) be found in [3]. using Equations 1,4, 6 and 7. A simple expression for E, based on load- Expression 8 satisfies the boundary condition bearing section arguments for a cubic pore sym- for P = 1. Disadvantages of the model behind metrically positioned inside a cube of solid expressions 6, 7 and 8 are that it is semi-analytical material, reads: and that some parameters have to be estimated. These problems can be avoided by using a model --- (1 (5) E/Eo --P2/3)/(1 _p2/3 + p), for calculating elastic properties without approxi- where Eo is the Young's modulus of the cube mations. One of the most sophisticated models for material. Expression 5 satisfies the boundary quasi-homogeneous, isotropic materials is the conditions E = Eo for P = 0 and E = 0 for P = 1 three-phase model [5, 6]. This model uses two but generally leads to values for E that are too concentric spheres of materials 1 and 2 with high. respective radii b and a, embedded in an infinite Another well-known expression, based on load- matrix of unknown effective properties. The bearing section arguments for a packing of solid radii are chosen such that (a/b)3 equals the volume spheres, is given by: fraction of material 2. An expression for the bulk modulus K and the shear modulus G is derived on = exp (- (6) E/Eo blP), the assumption that the infinite matrix possesses where b x is a characteristic exponent that depends the same average conditions of stress and strain on the way the spheres are stacked. For a simple and that all continuity conditions at the interfaces cubic packing with a coordination number of 6, are fulfilled. the value of bl is about 6. In that case the It can be proved that the solution for K is also dependence of E on P is reasonably described for the solution for a material consisting of a composite 0<~P<0.5. sphere as mentioned above, surrounded by other In a random sphere stacking a coordination composite spheres that completely fill the entire number of 6 is also present [2]. This means that a space. This is probably true for G as well, but has value of 6 for b 1 could also be used for random- not been proved. In our case material 2 is the pore stacked microsphere composites, but it should be phase. The Young's modulus, E, can be calculated noted that Expression 6 is strictly valid only for from K and G in the usual way. The full intergranular porosity. Expression 6 does not hold expression~ for K and especially G are rather for high porosities, but Rice [3, 4] has shown that lengthy, but have been described several times in a complementary relationship can be used based the literature so that we omit them here. An on a model with spherical pores in a solid matrix: interesting feature of the three-phase model is that it also yields correct estimates for E if the 1 -- exp [-- b2(1 -- P)], (7) E/Eo= pores are not spherical as long as the material where b2 is again a characteristic exponent with a remains (quasi) isotropic [6]. value of about 0.5 for a simple cubic pore distri- Hollow glass microspheres can be obtained with bution. The validity range for Equation 7 is 0.5 ~< different compositions and in various sizes. As an P~<I. example vitreous silica glass microspheres are Following Rice [4] one may combine the based on a bulk material with a relatively high models of Expression 6 and 7 to obtain an Young's modulus of 73 GPa [7] and a low density expression for hollow sphere composites. In that of 2200kgm -3 [8]. The estimated Young's case the E value of a material with intergranular modulus and density for a number of vitreous porosity P1 is predicted by Expression 6 with P = silica microsphere composites, based on the P1 while Eo in this expression is calculated from various expressions discussed, are given in Table I.