Comment on ‘‘Viscosity Measurement by Cylindrical Compression forNumerical Modeling of Precision Lens Molding Process’’ by A. Jain,

G. C. Firestone, and A. Y. Yi

Frank Richterw,z and Hans-Juergen Hoffmann

Institute of Materials Science and Technology: Vitreous Materials, University of Technology of Berlin, 10587 Berlin,Germany

A. Jain, G. C. Firestone, and A. Y. Yi determine the viscosityand ‘‘elastic parameters’’ of two optical glasses SK5 and BK7using the cylinder compression method.1 With the data deter-mined from the experiment, they numerically calculate the nec-essary deformation load as a function of time. This simulation iscompared with the actually measured data in Figs. 6(a) and (b)in their paper,1 which can be considered as a test for the relia-bility of their data. Unfortunately, the numerical data fail to fitconvincingly to the experimental data far beyond the inevitableinaccuracies or scattering of data. From our own experience, weknow that the method and the procedure applied by these au-thors should deliver a better agreement between experimentaland simulated data.

The authors determined the tensile viscosity by their evaluationusing Eq. 3. Therefore, their data on the viscosity from the cyl-inder compression experiment (‘‘curve fit’’) are about a factor of 3larger (lg10(3)50.4771) than the data supplied by the manufac-turer and their own experiment (‘‘measured’’) by applying Eq. 1(Figs. 5(a) and (b)). We recall that the factor of three is correctlyincluded in their Eq. 1, delivering the shear viscosity. Thus, fromthe experiments1 the shear viscosity resulted, which was fed intothe authors’ finite-element-code (Section V).1 Hence, the numer-ically predicted force (Fig. 6) roughly equals the measured force inthe long-time range, but the elastic parameter is clearly in error asthe numerically computed relaxation time is evidently too small.As the authors imprecisely speak of an ‘‘elastic modulus,’’ theyseem reluctant to interpret it as the Young’s modulus.

Analysis and simulation of cylinder compression experimentson silica glass (Suprasil 1, Heraeus, Germany) were the focus ofa recent Ph.D. thesis.2 Building in part upon the same referencesas the publication in question, also the numerical reconstructionof measured curves using a self-written UMAT-subroutine inABAQUS has matured by now. Both curve fitting and numericswork well using a single Maxwell element. Precise interpretationof measured data allows to quantify both the Young’s modulusand the tensile viscosity. The method was applied to digitizeddata, yielding improved versions of Figs. 6(a) and (b) shownhere as Figs. 1 and 2. The strain rate was read from Fig. 4.1 Thediscrepancy between the fitting routine output (using Eq. 31)that effectively coincides with the experimental data and anyFEM result is caused by a combination of reasons, among themthe friction. The fitting routine assumes a friction-free deforma-tion. Two simulations were run for each experiment. Wheneveran ‘‘infinite’’ friction coefficient is plugged into the simulation, aforce higher than measured is predicted. Hence, the deviation ofthis numerically computed force from the measured data andthe curve fit increases as the deformation progresses. Whereasthe simulated force with the deformation assumed to proceed

friction free is slightly lower than measured in Fig. 1, it remainssomewhat larger than measured in Fig. 2. Strictly speaking, thecurve fit and the simulation without friction should produceidentical results. However, the simulation requires the total dis-placement (taken as the constant strain rate times initial heighttimes duration of the experiment), which likely incorporatessome error because of a slightly varying strain rate (SectionIV1). The value of Poisson’s ratio is immaterial in the curve fit,but a value of 0.1 was picked arbitrarily for all simulations. Thequestion to which extent the choice of the Poisson’s ratio affectsthe stress generation in the simulation under interface friction canbe neglected in the case of uniaxial deformation. Minor devia-tions in the strain rate, an incorrect Poisson’s ratio, and the elu-sive friction accommodate any substantial difference between thenumerically predicted force and the measured one. The match in

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Journal

J. Am. Ceram. Soc., 90 [9] 3017–3018 (2007)

DOI: 10.1111/j.1551-2916.2006.01292.x

r 2006 The American Ceramic Society

Fig. 1. Digitized data from Fig. 6a1 (triangles), new curve fit2 (full line,providing the Young’s modulus E and the tensile viscosity Zt), FEM-result (using a UMAT-code2) for infinite friction (dashed curve) and forzero friction (dotted–dashed curve).

Fig. 2. Same as Fig. 1, but for Fig. 6b.1

Based in part on the Ph.D. thesis submitted by F. Richter for the degree of ‘‘Doktor derIngenieurwissenschaften’’ in materials science, University of Technology of Berlin, Germany,2006.

wAuthor to whom correspondence should be addressed. e-mail: Frank.Richter@ruhr-uni-bochum.de

zPresent address: Fraunhofer Institute for Mechanics of Materials IWM, Freiburg,Germany.

Manuscript No. 21929. Received June 23, 2006; approved August 22, 2006.

Figs. 1 and 2 is clearly superior to the one shown in the originalpublication.1 Further, identifying in Fig. 4 the experiments de-picted in Fig. 6 reveal that the strain rate varied significantly orthat the representation of the data in Fig. 6 is incomplete (fromtime equals strain divided by strain rate in case of a constantstrain rate). The deformation of 10% shown in Fig. 7 is fargreater than the one imposed in the experiments (Fig. 4).

References

1A. Jain, G. C. Firestone, and A. Y. Yi, ‘‘Viscosity Measurement by CylindricalCompression for Numerical Modeling of Precision Lens Molding Process,’’ J. Am.Ceram. Soc., 88 [9] 2409–14 (2005).

2F. Richter, ‘‘Upsetting and Viscoelasticity of Vitreous SiO2: Experiments,Interpretation and Simulation’’; PhD Thesis, Technische Universitat Berlin,Germany, 2006. Available for download at http://opus.kobv.de/tuberlin/volltexte/2006/1179/. &

3018 Journal of the American Ceramic Society—Richter and Hoffmann Vol. 90, No. 9