Research Papers

The Compressive Response of Idealized Cermetlike Materials

[+] Author and Article Information
Eral Bele

Department of Engineering,
University of Cambridge,
Trumpington Street,
Cambridge CP2 1PZ, UK
e-mail: eral.bele@eng.cam.ac.uk

Vikram S. Deshpande

Department of Engineering,
University of Cambridge,
Trumpington Street,
Cambridge CP2 1PZ, UK
e-mail: vsd@eng.cam.ac.uk

Readers are referred to [38] for a detailed discussion on the random packing of spheres, including maps that specify the particle size distributions and volume fractions required in order to achieve a specified overall volume fraction of particles.

In the FE calculations the inclusions were assumed to be rigid and the stress field within these inclusions is therefore indeterminate (but of course expected to satisfy equilibrium). In order to illustrate the high pressures within the inclusions a few calculations were performed with elastic inclusions of Young's modulus 102EM and Poisson's ratio 0.4. The results of those calculations are plotted in Figs. 10(b)10(d).

We note that while Eq. (6) from the Suquet [45] analysis gives an upper bound with respect to the linear comparison composite it does not necessarily give an upper bound to the strength of the real composite.

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received January 21, 2015; final manuscript received February 9, 2015; published online February 26, 2015. Editor: Yonggang Huang.

J. Appl. Mech 82(4), 041009 (Apr 01, 2015) (11 pages) Paper No: JAM-15-1037; doi: 10.1115/1.4029782 History: Received January 21, 2015; Revised February 09, 2015; Online February 26, 2015

Metals reinforced with a high volume fraction of hard particles, e.g., cermets, have properties that are more akin to those of granular media than conventional composites. Here, the mechanical properties and deformation mechanisms of this class of materials are investigated through the fabrication and testing of idealized cermets, comprising steel spheres in a Sn/Pb solder matrix. These materials have a similar contrast in the properties of constituent phases compared to commercial cermets; however, the simpler microstructure allows an easier interpretation of their properties. A combination of X-ray tomography and multiaxial strain measurements revealed that deformation at large strains occurs by the development of shear bands similar to granular media, with the material dilating under hydrostatic pressure within these shear bands. Predictions of finite element models with a random arrangement of inclusions were in excellent agreement with the experimental results of idealized cermets. These calculations showed that at large inclusion volume fractions, composites with a random arrangement of inclusions are significantly stronger compared to their periodic counterparts, due to the development of a network of force chains through the percolated particles.

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Grahic Jump Location
Fig. 6

X-ray tomographic sections showing a longitudinal midsection scan of the (a) undeformed monodisperse (Vf = 55%) idealized cermet and (b) the corresponding scan of the same specimen compressed to an effective strain ɛE = 5%

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Fig. 5

The data of Fig. 4(b) is replotted using axes of the von Mises effective ɛE and volumetric strain ɛV (the volume fractions Vf of the idealized cermet are indicated for each curve). The analogous data for WC/Co cermets from Ref. [4] is also included.

Grahic Jump Location
Fig. 4

(a) The measured compressive axial stress σa versus axial strain ɛa curves both the mono- and bi-disperse idealized cermet specimens and (b) the corresponding axial strain ɛa versus radial strain ɛr measurements. In (a) and (b), the corresponding measurements of the as-cast Sn/Pb solder matrix material are also included. The (Vf = 0.75) case is the bidispersed idealized specimen while the other two volume fractions are for monodisperse cermets.

Grahic Jump Location
Fig. 3

X-ray tomographic sections showing longitudinal midsection scans and three diametrical scans at heights zi as indicated of the undeformed (a) monodisperse (Vf = 55%) and (b) bidisperse (Vf = 72%) idealized cermets. The longitudinal midsection scan of the bidisperse specimen only shows a 25 mm high central section of the specimen of height 40 mm.

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Fig. 2

Photographs of the as-manufactured cylindrical specimens of the (a) monodisperse and (b) bidisperse idealized cermets

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Fig. 1

(a) Optical micrograph of a WC/Co cermet showing the distribution of ceramic particle shapes and sizes (reproduced with permission from Luyckx, S., 2008, “The Hardness of Tungsten Carbide-Cobalt Hardmetal,” Handbook of Ceramic Hard Materials, R. Riedel, ed., Wiley, Weinheim, Germany, pp. 946–964). (b) Ratio of the yield strength σY of WC/Co and WC/Ni cermets to the yield strength σYM of the metal matrix as function of ceramic particle volume fraction Vf. The data is reproduced from Refs. [4] and [7-10] as indicated in the legend.

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Fig. 7

Summary of the normalized 0.2% offset yield strength, σY/σYM, measurements of the idealized cermets as a function of the inclusion volume fraction Vf. FE predictions using the 2D periodic and random models as well as the 3D periodic model are included.

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Fig. 8

Sketches of the arrangement of the monosize inclusions used in the FE models. (a) 2D periodic close-packed hexagonal arrangements of disks, (b) 3D FCC arrangement of spheres with the unit cell analyzed also marked, and (c) a representative 2D random arrangement of disks. The coordinate system used in the FE analyses is also indicated in each case.

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Fig. 9

FE predictions of compressive response of the 2D arrangements of (a) periodically and (b) randomly arranged disks for selected values of the volume fraction Vf. In (a) predictions are shown for both uniaxial compression in the x1 and x2 directions while in (b) results are shown for only compression in the x2 direction for three realizations of the RVE for each value of Vf.

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Fig. 10

(a) FE prediction of the -σ¯22/σ¯YM versus -ɛ¯22 responses of the 2D periodic and random Vf = 0.8 composite. Predictions for three RVE realizations are shown for the random case. Distributions of the of the normalized pressure p/σYM within a central portion of the RVEs at an applied strain ɛ¯22 = 0.025% are shown for (b) the periodic composite as well as (c) RVE R1 and (d) RVE R3 of the random composite.

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Fig. 11

A comparison between predictions of the normalized (a) Young's modulus E/EM and (b) yield strength σY/σYM as a function of the inclusion volume fraction Vf. Predictions are included for the 2D FE models (periodic and random monosized inclusions) and the analytical models of Eqs. (3)–(6).

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Fig. 12

FE predictions of the normalized (a) Young's modulus E/EM and (b) yield strength σY/σYM of the random 2D composites as a function of the number of particles N in the RVE. The error bars indicate the variation between the different realizations of the RVEs and results are shown for three selected values of the particle volume fraction Vf. The case included in the main body of the paper for each volume fraction is highlighted.



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