High temperature friction characterization for viscoelastic glass contacting a mold

Journal of Non-Crystalline Solids 385 (2014) 100–110

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High temperature friction characterization for viscoelastic glass contacting a mold Balajee Ananthasayanam a, Dhananjay Joshi a, Matthew Stairiker b, Matthew Tardiff b, Kathleen C. Richardson c,1, Paul F. Joseph a,⁎ a b c

Department of Mechanical Engineering, Clemson University, Clemson, SC, USA Edmund Optics, Pennsburg, PA 18073, USA Department of Materials Science and Engineering, COMSET, Clemson University, Clemson, SC, USA

a r t i c l e

i n f o

Article history: Received 9 September 2013 Received in revised form 3 November 2013 Available online 25 November 2013 Keywords: Friction; Ring compression test; Precision lens molding; Viscoelastic; Parallel plate viscometry

a b s t r a c t Computational simulations of glass forming processes when interface slip occurs require a precise characterization of friction since friction, like viscosity, affects how much load is required to deform glass at a given rate. Friction therefore affects the processing time in the case of a load controlled process such as precision glass molding (PGM) and complicates the determination of viscosity when using parallel plate viscometry (PPV). In this combined experimental and computational study the ring compression test, where a “washer” shaped glass specimen is compressed between two flat molds at high temperature, is conducted and simulated. This test is very similar to PGM and PPV, making it ideal to quantify friction for these processes. The Coulomb friction model is used due to observed glass slipping behavior and the relatively low values of shear stress encountered in these processes. For glass at high temperature where viscosity is in the range of about 107–1011 Pa · s, it is demonstrated that the outcome of the test has a very weak dependence on material properties, which is significant since the stress and structural relaxation properties of glass within the transition temperature region are temperature dependent and difficult to obtain. The presented friction calibration curves are therefore material independent when the proposed processing procedure is followed. Sensitivity analysis is performed with respect to various factors, such as rate of deformation, magnitude of loading, temperature non-uniformity and contact of the inner and outer cylindrical surfaces with the mold surfaces, providing the experimentalist with guidelines to conduct valid tests. Using this friction characterization method, the viscosity range for PPV can be increased by accurately correcting for interface slip. © 2013 Elsevier B.V. All rights reserved.

1. Introduction Friction at the glass/mold interface is an important factor in processes such as precision glass molding (PGM) due to the following reasons: a) final size and shape of the lens and the residual stress state of the molded component are affected [1,2], b) when friction is high, the pressing force or molding duration must be increased, which affects mold life and processing time [1,2], c) wear of the mold surface (coated or uncoated) is affected by high friction, which decreases its life and affects the surface quality of the lens [3,4]. Ananthasayanam et al. [2] made use of computational mechanics and sensitivity analysis to show that the effect of friction on the shape of a molded lens can be as much as 8 microns, which is significant ⁎ Corresponding author. Tel.: +1 864 656 0545; fax: +1 864 656 4435. E-mail address: [email protected] (P.F. Joseph). 1 Currently at the College of Optics and Photonics, University of Central Florida, Orlando, FL 32816, USA. 0022-3093/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jnoncrysol.2013.11.007

when compared to the one-half micron accuracy required in precision lens design. The success of the computational approach, which is the most cost effective technique to achieve optical precision of the lens surfaces through logical re-tooling of the mold, therefore depends on accurate characterizations of behaviors such as friction. Following Ananthasayanam et al. [1], other important behaviors include the strain and temperature history dependent thermo-mechanical behavior of glass and the interface heat transfer behavior. Unfortunately, as with many of the required input parameters required to model PGM, there is a lack of friction data in the literature. While extreme cases sometimes apply, such as complete sticking of the glass to the molds at very high temperature [5,6] and frictionless contact [7], in the temperature range of precision lens molding, the actual case is believed to be between these two extremes, and hence a model and data are required to quantify slipping behavior. Parallel plate viscometry (PPV) at viscosity above the recommended range of 104–108 Pa · s (ASTM standard (2012)) is yet another application where frictional slip is important. As shown by Joshi et al. [8], PPV can be extended to higher viscosity if friction can be quantified and is taken into account.

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Several techniques to measure friction in forming processes under different operating conditions are presented in the literature [9–13] including those with applications to glass [14,15,17]. Mossaddegh and Ziegert [14] applied the double sided shear test for the direct measurement of the force required to push a mold contacting glass at a prescribed rate. Their study was motivated by PGM and was performed in a modified lens molding machine. Assuming full slip between the mold surfaces and the glass, the coefficient of friction between N-BK7 glass and a coated WC mold was determined to be in the range of 0.6– 0.7. In the study by Ananthasayanam [17] the ring compression test was used to determine a much lower coefficient of friction between L-BAL35 glass and a WC mold with a diamond like carbon (DLC) coating. The advantage of this test is the extreme sensitivity of the deformation of the inner radius of a ring-shaped specimen to the level of friction. The cylinder compression test [16] has also been used to characterize the friction coefficient by making use of the bulged shape of the cylinder, which is sensitive to interface friction. Compared to the ring compression test, this test has the advantage of simpler specimen geometry, but lacks the special feature of a quantity that is easy to measure and is very sensitive to friction. While the profile of the bulged shape can be used to estimate the friction coefficient, it is not with the same resolution as with the RCT. Of all the methods, the ring compression test [18–22] is believed to be the most relevant to PGM, especially for coefficients of friction less than about 0.3 which are most desirable for this process to reduce wear of the expensive coatings on the mold surfaces. In this test a “washer” shaped specimen is compressed between two flat dies at high temperature and the change of internal diameter, which is very sensitive to friction, is measured as a function of the change in height. Friction calibration curves quantify this response and allow a direct conversion from experimental data to a friction parameter as long as the curves are applicable to the material behavior of the specimen. A precision lens molding machine and the precision lens molding process are ideally suited to performing this test, since the pressing of a glass ring is almost identical to the pressing of a lens [1]. The same applies even more precisely to the use of a parallel plate viscometer where a glass cylinder is pressed between flat molds. A schematic of the different outcomes of the ring compression test (RCT) for different interface conditions is shown in Fig. 1. If the friction at the interface is very low, material flow is directed radially outward. As a result, both the internal and the external diameter increase. For the opposite case of high friction, the inner diameter decreases while the outer diameter increases. If the friction is between these two extremes, typically around μ = 0.1, the inner diameter may increase or decrease, depending on the level of axial deformation.

101

The RCT has been used to quantify interfacial slipping behavior between mold and workpiece for a variety of materials, ranging from metals [18,19,21] to softer materials such as plasticine [20]. The two primary slip models used in ring compression studies are the Coulomb friction model when the normal stress is low and the friction factor model when the normal stress is high. This latter model recognizes that there is an upper limit of shear stress that the interface can support, which is independent of the normal stress [18]. For the case of metals, which have received the most attention in the literature, it was shown by Hayhurst and Chan [22] that in some cases a combination of these models should be used, while for others one of the models is sufficient. For plasticine, which is a relatively soft material like glass at high temperature, Sofuoglu and Rasty [20] use only the Coulomb friction model. While the RCT is a convenient and reliable choice for friction evaluation for some applications, from the point of view of metal extrusion and forging processes this test is unreliable since the material is not subjected to realistic conditions [23,24,11]. Compared to these metal forming operations, the RCT has very low new surface generation, very low contact pressures and material flow conditions that are not nearly as severe. For example, Bay [25] has shown that in cold forging processes, contact pressures can reach 2500 MPa and surface enlargement can be as high as 3000%. Therefore, in such processes the RCT can provide only an estimate of the friction coefficient. The study by Wang et al. [13] presents a review of friction tests that are more appropriate for extrusion processes. Fortunately the limitations of the RCT test to metal extrusion and forging processes do not apply to the use of the RCT to PGM and PPV, where realistic interface conditions are simulated very well. In PGM the workpiece does not undergo significant shape changes or creation of surface area as in metal forming, since it is already prepared as a “preform” close in shape to the aspherical shape to be achieved through the molding process. As a result, even for high friction, the stresses at the preform/mold interface are very low compared to those in extrusion and metal forming applications. The RCT, which is relatively easy to conduct at high temperature, is therefore believed to be ideal for estimating friction behavior for the lens molding process. In the current study the RCT was applied to glass, which has complex, typically unknown, viscoelastic and structural relaxation behavior in the transition temperature range [1,2]. The Coulomb friction model was used since the interface shear stresses and the sliding speeds are relatively low. The goal of this study was to characterize friction behavior accurately between glass and mold surface within the molding temperature range and to quantify the effects of material properties and loading rate on the friction calibration curves. This study makes use of the computational model proposed and computationally validated for

(a). Before deformation After deformation

(b). Low friction case

(c). Medium friction case

(d). High friction case Fig. 1. Outcomes of the RCT for different interfacial conditions for the same mold/material pair.

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precision lens molding in [1] and validated using experimental data in [2] for both a bi-convex lens and a steep meniscus lens. Lens profile deviation [1], which is typically in the range of 10–20 microns for a lens with a diameter of 10 mm, was used in the validations. The current study applies the sensitivity approach used in [2] to changes in the inner radius of the ring in the RCT, which are typically two orders of magnitude larger than lens profile deviation. As such, several factors that were important to deviation in [2] may not be important in the RCT. 2. Experiments A Toshiba lens molding machine (GMP series) was used to conduct the RCTs. Special flat molds were created using the same Diamondlike carbon (DLC) coating that is applied to the actual molds used for lenses. The DLC coating, which is about 50 μm thick, decreases friction at the interface, prevents chemical reaction between glass and molds during the molding stage and also eases the release of the lens once the molding process is complete. Several glass rings were made of the molding glass material L-BAL35 with dimensions of 19.15 mm outer diameter (OD), 9.59 mm inner diameter (ID), and 6.37 mm tall (H) such that the standard ring ratio from Male and Depierre [18] of OD: ID:H = 6:3:2 was maintained. These dimensions are used for all specimens in this study, both experimental and computational. This will be referred to as the “standard ring.” Furthermore, symmetry in the circumferential direction refers to independence with respect to the circumferential coordinate, while symmetry in the axial direction corresponds to symmetry with respect to the plane (parallel to the mold surfaces) that divides the ring into two rings of height H/2. The rings were ground on a single sided steel tool with emery and then polished with a pitch tool. The central hole was cored out after polishing with a diamond core drill. The concentricity of the hole was on the order of a 100 μm and parallelism of the flat surfaces was better than 1 arcmin. Each ring was used in only one experiment to obtain one data point. The rings were pressed in a vacuum using the identical processing conditions as in the glass lens molding operation, which are defined in the study by Ananthasayanam et al. [1]. A vacuum was used as there was concern that trapped air in the hole would affect the results. As an alternative to a vacuum, a small hole could have been drilled in the molds. A summary of duration times for all the stages of the process is presented in Table 1. Newly made and coated molds were used for a set of nine RCTs, referred to as Data Set #1, followed by eight tests in Data Set #2. The rings in Data Set #1 were soaked for only 200 s which was not enough to achieve temperature uniformity in the axial direction. During the heating and soaking periods a 2.62 mm gap is maintained, which caused the top surface of the ring to be cooler than the bottom surface at the start of pressing. This temperature non-uniformity was revealed

Table 1 Recommended duration times for the stages of the RCT used for Data Set #2 and the simulations unless noted otherwise. Specimen dimensions are always OD = 19.15 mm, ID = 9.59 mm inner diameter, and H = 6.37 mm. Stage

Description

Duration (sec)

Heating

Heat sample from room temperature to molding temperature. Glass sample rests on lower mold with a gap of 2.62 mm from the upper mold. Molding temperature was maintained to achieve uniform temperature distribution within sample. The gap was maintained during this stage. Force Control: A pressing force of 1500 N was applied to the specimen until the desired center thickness value was achieved. Controlled slow cooling with the applied “maintenance” force reduced to 500 N. Rapid cooling back to room temperature.

210

Soaking

Main pressing

Slow cooling with a maintenance force Rapid cooling

N500

in the specimens by the profile of the inner radius in the axial direction (from top to bottom). As will be discussed in Section 4.1, this profile was slightly unsymmetric and was also inconsistent with the uniform temperature profile presented in Fig. 1b. The rings in Data Set #1, which were intended to reach 589 °C, will be used as a validation of the result determined for the rings in Data Set #2, which had an increased soaking time of 500 s. For this case six rings were pressed at a temperature of 589 °C, which resulted in about 50% or more reduction in the axial dimension. After pressing these rings, two rings were pressed at 569 °C for the same load, resulting in a height reduction of about 20%. A temperature of 589 °C was chosen as it is an ideal molding temperature for L-BAL35 type glass and a friction coefficient at this temperature was desired, while the other temperature was chosen to study the dependence of friction coefficient on temperature. Examples of two pressed rings, one at 589 °C and the other at 569 °C are shown in Fig. 2. Some rings pressed at the higher temperature were slightly elliptical in shape, such as the ring in Fig. 2. In such cases the inner radius was obtained as an average value. 3. Finite element model The numerical simulation of the RCT was done using the commercial finite element code ABAQUS [26]. A “*COUPLED-TEMPERATURE DISPLACEMENT” type of analysis was used in this simulation as the mechanical properties change significantly with temperature and the heat conduction at the interface is also affected by the changing contact surface. All the pressing and cooling stages were modeled. This model was proposed for precision lens molding in [1] and validated for lens molding using experimental data for lens profile deviation in [2]. While the RCT is very similar to lens molding, additional validation is required in the current study to address contact behavior associated with the ninety degree corners of the initial geometry of a ring or glass cylinder used in PPV that are not present in the smooth preforms used for a lens. 3.1. Model geometry The initial geometry of the model is shown in Fig. 3. An axisymmetric model (symmetry with respect to the circumferential coordinate) is used since the ring and the molds are circular and the loading can be approximated as symmetric around the central axis. Symmetry in the axial direction is not assumed due to the gap maintained during the heating and soaking stages that are described in Table 1. The ring is modeled as a linear viscoelastic material, while both the upper and lower molds are modeled as linear elastic materials. The glass ring and the molds were meshed with CAX4T elements, which are continuum axi-symmetric 4-noded elements with temperature degree of freedom. The upper and lower molds had 1284 and 1107 elements, respectively, and the glass ring was meshed with 3072 elements. It was determined that this level of meshing for the ring provided convergence for all cases when the ring had the same coefficient of friction on all surfaces. Generally speaking, the convergence of the inner radius of a ring is a straightforward computation compared to convergence of lens profile deviation in the study presented by Ananthasayanam et al. [1]. However, convergence in the current study was complicated when the coefficient of friction on the plane and cylindrical surfaces were different. A convergence study for this case, which should be avoided by proper polishing of all glass surfaces, is presented in Section 4.5. 3.2. Interface behavior

Variable

300 650

The normal contact behavior was modeled as “hard” contact in ABAQUS while the tangential behavior was modeled using a penalty formulation with a Coulomb friction model. Two master-slave types of contact interaction pairs were created; one between the top surfaces of the ring and the bottom surface of the top mold and the other

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103

Fig. 2. Rings pressed to their maximum change in height at 589 °C and 569 °C are shown at the left and right, respectively.

between the bottom surfaces of the ring and the top surface of the bottom mold as shown in Fig. 3. These definitions allow the inner and outer cylindrical surfaces of the glass to come in contact with the molds, which occur for cases of high friction. Furthermore, the mold surface is the master surface and the glass surfaces are the slave surfaces. This master-slave type contact definition was used since the glass is much softer than the molds. Care was taken while meshing such that the mold elements were at least five times larger than the glass elements. This was done to avoid contact penetration because the master surface can penetrate the slave surface while the slave surface cannot penetrate the master surface. Referring to Fig. 3, two

coupling constraints are also defined; one between RPTOP and the top surface of the top mold and the other between RPBOT and the bottom surface of the bottom mold. In these constraints the vertical components of displacements of the slave surfaces were constrained to move along with their respective master reference points, while the horizontal components of displacements are free to slide. To address thermal interactions, the glass and mold surfaces exchanged heat by contact/gap conductance and radiation and the details are given in Ananthasayanam et al. [1,2]. 3.3. Material behavior of glass and molds The molds were modeled as linear elastic materials, while the glass was modeled as a linear viscoelastic material including structural relaxation to account for thermal history dependent thermal expansion and thermo-rheologically simple (TRS) behavior to account for temperature dependence of material properties. The theory and FEA implementation for structural relaxation along with the viscoelastic and TRS behaviors of glass are presented in detail by Ananthasayanam et al. [1,2] and are not repeated here. Experiments were performed using the Ohara molding glass, L-BAL35 [27], and tungsten carbide mold material [28] with a diamond like coating (DLC). The elastic and thermal properties of the molds and the glass are presented in Table 2, while the stress relaxation parameters for the viscoelastic behavior along with the TRS constants are given in Table 3. Material Set A given in Table 3 represents the full viscoelastic treatment of material behavior with a multiple term prony series for the response to shear and a single term prony series for the bulk response. Material Set B represents a simplified viscoelastic material behavior that involves a single Maxwell element in shear and an elastic bulk behavior. Material Sets A and B have the same value of

Table 2 Thermal and mechanical properties of the glass and mold materials. Property

Glass

Mold

Density, ρ (kg/m3) Young's Modulus, E (GPa)

2550 100.8, T ≤ 510 °C 10, T ≥ 560 °C 0.252 1100, T ≤ 470 °C 1730, T ≥ 570 °C 1.126

14,650 570

Poisson's Ratio, ν Specific Heat, cp (J/kg/K) Thermal Conductivity, κ (W/m/K) Thermal Expansion Coefficient, α (K−1) Glass Transition Temperature, Tg (°C) a

Fig. 3. Axisymmetric finite element model used for simulation of the RCT.

a

527

0.22 314 38 4.9 × 10−6 –

The structural relaxation behavior of glass is presented in Table 3 of Ananthasayanam et al. [1].

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Table 3 Stress relaxation functions of L-BAL35 glass used in the numerical simulations. The TRS behavior is given by TR = 569 °C, C1 = 12.41, C2 = 129 °C. Shear relaxation function

Hydrostatic relaxation function

1 ðt Þ ψ1 ðt Þ ¼ G2G 0

2 ðt Þ ψ2 ðt Þ ¼ G3K 0

Material set A (full viscoelastic material behavior) vi ¼ 1− KK∞0 0.85

τi (s) 0.38 0.48 0.88 74.4

wi 0.5794458 0.3624554 0.03 0.028

λi (s) 10

Material set B (simplified material behavior) 1.0

E K 0 ¼ 3ð1−2ν Þ

2.504

the equilibrium viscosity. The parameters presented in Tables 2 and 3 are similar to those used by Ananthasayanam et al. [1,2], while the structural relaxation parameters used in this study are identical to those of Ananthasayanam et al. [1,2] and are therefore not repeated. 4. Results In this section friction calibration curves (FCC) will be generated for glass using the Coulomb friction model with different material models and different loading. Experimental data will be used to determine the friction coefficient for a specific case in precision lens molding. Then the goal will be to identify the requirements for a universal set of FCC that can be used with reasonable accuracy for a glass with unknown material properties. Finally, through sensitivity analysis, some issues that can lead to error in the data will be quantified. 4.1. Comparison with experimental data

% Decrease in internal diameter of the ring

The FCC in Fig. 4 show how the simulation results compare with the data from the set of eight experiments in Data Set #2 performed on L-BAL35 glass rings at 569 °C and 589 °C as discussed in Section 2. The number beside each data point (solid square or solid circle) in the figure corresponds to the order number of the test, which shows that

0

µ = 0.06

2

7

-5

8

-10

µ = 0.05

-15

Top Mold -20

3 4 5

6

Ring

µ = 0.04 1

Bottom Mold

-25

Top Mold

Experimental Data at 589oC

-30

µ = 0.03

o

Experimental Data at 569 C

Ring

Friction Calibration Curves

-35

0

10

20

after the first two specimens the results were more consistent. The material behavior for L-BAL35 glass used in the model is defined in Tables 2 and 3 (Material Set A), and Ananthasayanam et al. [1] for the structural relaxation parameters. Equilibrium viscosity values at these two temperatures are 1010.0 Pa · s and 108.33 Pa · s, respectively. The computational data was generated in an identical manner as in the experiments, i.e., the simulations model the entire process, which includes heating, soaking, pressing to the desired level of deformation and cooling to obtain each data point. Only the press time in Table 1 was varied to complete this calculation. Based on the FCC in Fig. 4, it is concluded that the friction coefficient between the L-BAL preform and the DLC coated mold in this temperature range is between 0.04 and 0.05, but closer to 0.05. The insert in the figure corresponds to an axisymmetric view of the ring at a low level of friction, which compares to Case (b) in Fig. 1. Similar values of friction coefficients associated with DLC coatings for related applications and much lower values for other applications have been reported in the literature [29,30]. The nine data points from Data Set #1 will now be used in a computational study to show the importance of measuring the ring at the centerline and the complicating effects of non-uniform temperature. The rings used in Data Set #1 had a soak time of 200 s which resulted in a non-uniform temperature in the axial direction of the ring at the start of the pressing stage. In this case the bottom of the ring was hotter, which affects the profile of the inner radius of the ring. Before presenting the FCC, the profile of the inner diameter of the ring will be studied for this case of low friction. The profile presented in Fig. 1b indicates that the centerline has the maximum inner diameter and the top and bottom of the ring, which are symmetric, have the minimum diameter. The specimens from Data Set #1 did not have this profile, although they were almost symmetric. Computational simulations of the 200 s soak time experiments provided the explanation. Actual results from computational simulations that show the contour of the deformed shape of the ring are presented in Fig. 5. These results include the entire heating and cooling process and are presented for uniform and non-uniform temperature. This figure shows how the inner diameter measured at the top or bottom of the ring compared to the measurement at the center are much different between the isothermal and non-isothermal cases. Based on a visual inspection, the profile of the inner diameter of the non-uniform temperature case in Fig. 5 was similar to that of the rings from Data Set #1. Even though the temperature was not symmetric, the deformation profile tended to be nearly symmetric, indicating that temperature nonuniformity cannot always be identified by lack of symmetry of deformation about the mid-plane of the ring. This symmetry is due to the nature of deformation in the RCT and also the fact that upon contact with the top mold, the upper surface of the ring heats relatively quickly. This heating can provide a self-correcting mechanism when there is nonuniform temperature at the start of the pressing stage if the rate of axial deformation occurs slowly compared to the rate of heat transfer. Given that the upper surface of the ring is cooler than the lower surface, in a force controlled test the press time must be increased due to the

30

40

50

60

70

% Deformation in the axial direction Fig. 4. FCC from simulations compared with experimental data for L-BAL35 glass pressed between tungsten carbide molds with a DLC coating. The heating, soaking, pressing and cooling stage durations for the Data Set #2 experiments and simulations are presented in Table 1. The number (1–8) beside each data point corresponds to the order of the test. The insert is the outline of the deformed shape from the simulations for 50% axial deformation at the higher temperature.

Bottom Mold

Top Mold Ring Bottom Mold

Fig. 5. Computational simulations of a deformed ring for a coefficient of friction of 0.05 at 50% axial deformation for uniform temperature on the left and non-uniform temperature on the right. The non-uniform results correspond to a 200 second soak time and a gap conductance parameter of h = 5000 W/m2/K. Emphasis is on the difference between centerline and top/bottom values of the inner radius for the two cases.

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4.2. Sensitivity to thermal expansion behavior (structural relaxation)

% Decrease in internal diameter of the ring

From a computational point of view it is numerically intensive to produce the FCC when each data point must experience the entire heating, soaking, pressing and cooling cycles. The extreme sensitivity of the inner radius of the ring to the level of friction sometimes allows for a simplification of the modeling process. This is demonstrated by the results in Fig. 7, which presents a study of the FCC for three levels of friction for three different thermal histories using the material behavior defined in Tables 2 and 3. The first thermal history is the actual process, the second omits the cooling stage so that the change in inner radius can be generated continuously as the ring is pressed, and the

60

% Decrease in internal diameter of the ring

presence of stiffer (cooler) material which favors this mechanism. The FCC for both the center and the minimum values of the inner diameter will next be considered. A very important point in what follows is that the gap conductance parameter, h, which quantifies how heat flows from the molds to the glass, is not known with certainty. As will be seen below, when uniform temperature is not achieved, some results are very sensitive to this parameter. Comparisons between the nine data points in Data Set #1 and three simulation results are presented in Fig. 6. The rings, which are no longer available, were (incorrectly) measured only at the minimum value of the inner diameter and not at the centerline. The three simulation results in Fig. 6, which are provided for both the centerline and the top/bottom values of the inner diameter, correspond to: 1) standard FCC for uniform temperature (solid lines), 2) non-isothermal case with 200 s soak time using a gap conductance parameter of h = 5000 W/m2/K (dashed lines) and 3) non-isothermal case with h = 280 W/m2/K (dotted lines). These results show that in addition to the importance of achieving temperature uniformity, it is essential to measure the value of the inner diameter at the centerline of the ring. It is observed that in spite of temperature non-uniformity, the FCC of the centerline provides a reasonable estimate of the correct result and this result is not too sensitive to the value of the gap conductance parameter, h. The results in Fig. 6 also show the high sensitivity of the minimum diameter to the details of the non-uniform temperature distribution indicating that the minimum diameter should not be used for these low friction cases, even though it is easier to measure. Sensitivity of the FCC to non-uniform temperature for the full range of friction coefficients is considered in Section 4.5. Finally, the comparison with results in Fig. 6 helps to validate the results from Fig. 4, which indicated that μ was slightly less than 0.05.

-10

Expt Set #1 Uniform Temperature h = 5000 W/m 2/K h = 280 W/m 2/K

-20

0

10

20

Center 30

40

50

µ = 0.15

20 0

µ = 0.04

-20 -40

µ=0 -60 -80 0

10

20

30

40

50

60

70

third also omits the heating and soaking stages. It is noted that the cooling stage also includes the unloading of the specimen. As seen from the results in Fig. 7, the sensitivity of the combination of unloading and the thermal expansion and contraction behavior on the FCC is negligible. While the effects of thermal expansion are significant for many dimensional changes, such as lens profile deviation in lens molding [2], the results in Fig. 7 show that thermal expansion for this glass type is not significant for the dimensional change of the inner radius of the ring. This is because the displacement of the inner radius due to the combination of bulging and interface slip is very large relative to the effects of unloading and structural relaxation. This is the key advantage of the RCT. Furthermore, this feature allows the test to be conducted on a more accessible parallel plate viscometer, since the sophisticated cooling capability of a lens molding machine is not necessary. This result for L-BAL35 glass can be extended to other glass types since dimensional changes due to structural relaxation are not expected to produce a significant shift in the friction curve. In order to quantify this and provide a way to check the validity of this statement for another glass type, an approximation of the change in inner diameter due to cooling alone is made. Assuming no friction, uniform temperature in the glass ring and no cooling rate dependence for thermal contraction, the change in inner diameter is given by TZ Room

α ðT ÞdT ¼ α G ðT Room −T t Þ þ

α þ α  L G ðT t −T Mold Þ; 2

ð1Þ

T Mold

-5

-15

actual process cooling omitted heating, soaking and cooling omitted

Fig. 7. FCC showing the effects of structural relaxation (thermal expansion and contraction) during the heating and cooling stages.

ΔD ¼ D

Top / Bottom of Ring

40

% Deformation in the axial direction

5

0

105

60

% Deformation in the axial direction Fig. 6. Comparison of experimental data from Data set #1 with FCC from simulations for a friction coefficient of 0.05 with a short soak time. The inner diameter measured at top/ bottom and center of ring (refer to Fig. 5) are indicated in the plot for three different thermal conditions: isothermal ring and non-isothermal ring for two values of the gap conduction heat transfer parameter, h.

where the room temperature value of the coefficient of thermal expansion is assumed to be constant (αG) for T b Tt and varies linearly to that of the liquid phase value, αL, at the molding temperature, TMold. The “transition” temperature Tt is selected to represent approximately the lower limit of the actual transition region. For LBAL35 the values used in this approximation are: TRoom = 20 °C, Tt = 490 °C, TMold = 590 °C, αG = 8 × 10− 6 °C− 1 and αL = 70 × 10− 6 °C− 1. These values lead to a 0.76% reduction in the diameter which corresponds to an increase in the value of the FCC. Given the actual results using the full process (both in Fig. 7 and results to be provided later), if a different glass has a comparable approximation, it is believed that the FCC will not be appreciably affected. For most precision molding glasses, the liquid and glassy thermal expansion coefficients are not very different from L-BAL35 to affect the change in inner diameter significantly. For example, αG = 9.2 × 10−6 °C−1 and αL = 70 × 10−6 °C−1 for P-SK57. It is noted that based on the results in Fig. 7, which include all the deformation mechanisms and heating cycles,

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this approximation is an overestimate of the change. The conclusion that heating and cooling do not significantly alter the FCC is very important since it shows that the complex structural relaxation behavior of the glass does not need to be known before conducting the RCT. Furthermore, from a computational point of view, for cases when mechanical unloading does not affect the FCC results, it appears that calibration curves can be generated at isothermal conditions which would simplify the analysis. This possibility will be studied further. In addition, if a sensitivity analysis is conducted and the results are closer together than those in Fig. 7, the results will not be presented. 4.3. Sensitivity to viscoelastic material behavior (stress relaxation)

ΔD F −F M ¼ −ν P : D AE

ð2Þ

Using the values ν = 0.252, A = 2.16 × 10−4 m2, FP = 1500 N and FM = 500 N gives a percent change in the decrease of the diameter of only 0.1% for E = 1 GPa, which shows that for low friction unloading is not an issue. For high friction, however, the full process results indicate that unloading is important when the elastic modulus is low and therefore unloading should be included when approximating the full process with an isothermal process. The effect of compressibility on the FCC was also considered by comparing the elastic bulk behavior results to those for both a rigid bulk response and a single term prony series bulk response. These results were identical so it is concluded that the effect of compressibility on the FCC is also negligible. Since glass behavior is viscoelastic within the transition temperature range, it is necessary to investigate the effects of additional timedependent modes of deformation introduced by additional prony series terms in shear and bulk modulus. The results in Fig. 9 compare FCC for Material Sets A and B given in Table 3. These results show a small but negligible effect due to this more detailed material behavior at all levels of friction. Given the complexity of the material characterization required for a given glass, it is significant that simplified material behavior can be used without a loss of accuracy to characterize the friction coefficient of glass at high temperature.

% Decrease in internal diameter of the ring

When glass is in the transition temperature range the material behavior is viscoelastic, i.e., there is a transition from purely elastic behavior at low temperature to purely viscous behavior at high temperature. The transition temperature range includes the glass transition temperature, Tg and spans about 50–100 °C above and below Tg. This transition is composition-dependent and gradual, and since the molding process occurs in this temperature range, details of the material behavior in this transition region should not be neglected. All results in this section are for a constant load of 1500 N. The cases of a rate controlled test and a higher creep load are considered in the next section. The logical starting point for an investigation of the effect of mechanical behavior of glass is to quantify the effect of viscosity on the FCC, since this is the deformation mechanism at high temperature and is also the dominant deformation mechanism in the transition temperature range. First, based on press time, it is necessary to determine the range of viscosities that is practical for a load of 1500 N to reach a level of deformation of 50% for the standard ring specimen. These results are presented in Fig. 8, which shows that a press time of about an hour is required when the viscosity is between 109.5 and 1010 Pa · s. The results apply to the full range, 7 b log(η) b 11, which should easily include all practical values of viscosity since glass is unlikely to slip at a viscosity of 107 Pa · s and a creep test to 50% deformation is not practical for a viscosity of 1011 Pa · s or higher due to the long press time. The results from an isothermal study making use of Material Set B show that the FCC were independent of viscosity for the full range of friction. This was also been verified for the full process for selected cases which will be presented later. While viscosity is the most important part of the Maxwell element, the effect of the initial elastic response on the FCC was also considered using computational simulations with low (~ 1 GPa)

and high (~100 GPa) values of elastic modulus (E) at high temperatures. For this study the entire cycle of heating, soaking, pressing and cooling was simulated. The results indicate that the elastic modulus at high temperature has a negligible effect on final dimensions of the ring and the FCC remain practically unchanged. In cases where the elastic modulus is relatively high, an isothermal analysis gives good results. However, for low values of elastic modulus such as 1 GPa and high friction, it might be necessary to unload to obtain an accurate FCC. The insensitivity of unloading on the FCC for low friction can be understood by considering an approximate analysis that is analogous to the development of Eq. (1). Again the no friction case is considered and temperature is assumed to be uniform throughout the ring as it cools. The primary contribution to the change in diameter comes when the pressing force (FP) is reduced to the maintenance force (FM) at the molding temperature where the elastic modulus is its smallest value. The change in diameter for this case can be approximated by

80

µ > 0.6

Material Set A Material Set B

60 40

µ = 0.15

20 0 -20 -40 -60

µ = 0.02 0

10

20

30

40

50

60

70

% Deformation in the axial direction Fig. 8. Press times required for an axial deformation of 50% for the standard ring compression specimen and constant loads of 1500 N and 15,000 N. Both no-slip and no friction are considered for viscosity ranging from 107 to 1011 Pa · s.

Fig. 9. Comparison of simulated FCC for different relaxation behaviors. Material Set A (Table 3) corresponds to a four-term series in shear and single term series for the bulk response. Material Set B (Table 3) corresponds to a simplified viscoelastic model utilizing a single Maxwell element in shear, keeping equilibrium viscosity the same.

B. Ananthasayanam et al. / Journal of Non-Crystalline Solids 385 (2014) 100–110

107

To further explore the effect of the details of the shear relaxation function, FCC were determined for the two different shear relaxation functions presented in Fig. 10. Once again the FCC showed almost no dependence of material property on the curves, so they were not provided. Based on the material behavior study in this sub-section, it can be concluded that the viscoelastic material properties of glass do not affect the FCC substantially. 4.4. High and low viscosity testing The results of Figs. 4–10 were obtained for a constant load of 1500 N, where the duration of the pressing stage is presented in Fig. 8 as a function of viscosity and friction level. Due to the long press times required for η ≥ 109.5 Pa · s, it is of interest to consider more convenient ways to characterize friction for such high viscosity cases. A constant rate test is considered next, using Material Set A from Table 3. The rate of deformation, which was selected to be 0.5 mm/min, corresponds to how fast the molds approach each other as the standard ring is pressed. These tests follow the process in Table 1, understanding that the pressing stage ends when the center thickness is reached. The results for the maximum force required to press a ring to 50% axial deformation are presented in Fig. 11. The inset in this figure corresponds to the force as a function of time for a viscosity of 109 Pa · s. This shows that the force increases dramatically as the deformation increases. Due to the possible development of such high forces that could damage the testing apparatus or the glass ring, a rate controlled test is not recommended at high viscosity. However, it is possible that the rate controlled test can be useful at low viscosity. As stated earlier, at a viscosity of 107 Pa · s glass behaves more like a fluid and is not expected to slip. For example, a standard procedure to determine the viscosity of glass in the range 104–108 Pa · s makes use of a parallel plate viscometer and the assumption of no slip, which is presented as an ASTM standard [31]. The experimental data at 589 °C presented in Fig. 4 corresponds to a viscosity of 108.33 Pa · s. One use of a rate controlled test could be to more carefully study the onset of slip at low viscosity. The important point for a rate controlled test is that for a reasonable range of viscosity, less than or equal to 109 Pa · s, the same FCC obtained for a creep test of 1500 N apply for this pressing rate taking into account the full process in Table 1. As shown in Fig. 8 another way to reduce the press time and not overload the specimen and/or testing apparatus is to use a higher creep load. The case of a 15,000 N load was considered, which decreases press time by more than a factor of ten compared to 1500 N. For example, for a viscosity of η = 109.5 Pa · s, the press time for zero friction and 1500 N is 1544 s, while for a load of 15,000 N it is 133 s, which corresponds to a decrease by a factor of 11.6. The corresponding press

Fig. 11. Maximum force required to reach an axial deformation of 50% for the standard ring compression specimen and a constant rate 0.5 mm/min. Both no-slip and no friction are considered for viscosity ranging from 107 to 1011 Pa · s. The inset shows how force changes as a function of time for a viscosity of 109 Pa · s.

times for no-slip are, respectively, 3313 s and 248 s, which is a factor of 13.4. Furthermore, as shown in Fig. 12, the FCC using the full process are nearly insensitive to load and Log of viscosity/ (Pa*s) in the range of 8.3–10.5. It is also observed from this figure that an isothermal approximation is reasonably close to the full process results. The isothermal results are very insensitive to load and viscosity, so one curve represents all the cases. This study was conducted for the case of high friction which is the most sensitive to changes in loading and material behavior. A more detailed study of the effect of loading and viscosity on the FCC, as well as on how the isothermal approximation compares to the full process FCC results, is presented in Table 4. This study is again for the case of high friction. This table shows two important trends which are both consequences of the extreme sensitivity of the inner radius of the cylinder to friction in the RCT. First, for the full process the FCC are basically the same for a large range of viscosity and loading. The largest variations are on the order of 3%. For cases of lower friction this variation will decrease. Second, the isothermal results are very reasonable approximations of the full process results. 4.5. Sources of experimental error In this section computational analysis is used to study the effects of three practical issues in completing a successful test. All the results in

0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1

Duffrene - multiplied by 2 Material Set A

10

-4

-2

0

10

10

2

10

log (t) 10

Fig. 10. Stress relaxation functions used in a sensitivity study on the friction calibration curves, which indicated no significant change for coefficients of friction of 0.02 and 0.6.

% Decrease in internal diameter of the ring

Shear Relaxation Function -

1

(t)

90 0.9

Isothermal Pressing

80 70

Full Process (

= 8.3 Pa·s, F = 1500 N)

Full Process (

= 9.5 Pa·s, F = 15,000 N)

Full Process (

= 10.5 Pa·s, F = 15,000 N)

60 50 40 30 20 10 0

0

10

20

30

40

50

60

% Deformation in the axial direction Fig. 12. FCC for different load and viscosity combinations using the full process presented in Table 1.

B. Ananthasayanam et al. / Journal of Non-Crystalline Solids 385 (2014) 100–110

Table 4 Comparison of percentage change in inner diameter of the ring at 35% and 50% axial deformation with the baseline case under various pressing conditions for high friction. Load

Viscosity, 10x (Pa · s)

1500 N

15,000 N

0.5 mm/min

7 8 9 10 11 8 9 10 11 7 8 9

% Decrease in inner diameter Isothermal pressing & unloading

Full process

35% height reduction

50% height reduction

35% height reduction

50% height reduction

23 23 24 23 24 22 20.5 21 21 19 23 23

52 52 52 52 52 51 49 48 48 47 51 51

23 23.5 24 23 24 22 22 21 20 17.5 22 23

50 50 49 49 50 50 48 47 47.5 47 50 51

% Decrease in internal diameter of the ring

this section are for a constant load of 1500 N. The first addresses the question of reuse of a specimen, since it is a burden to sacrifice each specimen to obtain just one data point. Assuming that the frictional characteristics of the sample's surfaces are not altered during a test, the results in Fig. 13 show that within a reasonable error tolerance, it is acceptable to reuse a specimen. To produce the multiple pressing results in this figure, the sample was put through successive cycles of heating, soaking, pressing to the indicated level of deformation and then cooling. As such, the simulation of this realistic situation is nontrivial. Each data point for the change in dimension of the ring is recorded at room temperature at the end of a cooling cycle. The next data point involves re-subjecting the ring, which now has a residual stress state, to the same complete cycle. As a second important issue, at high levels of friction the inner and outer cylindrical surfaces of the ring come in contact with molds as deformation is increased. This can be an issue if these surfaces cannot be polished to the same specifications as the flat surfaces. To study this effect standard FCC were compared to those generated when a high level of friction of μ = 1.0 was considered at the inner and outer cylindrical surfaces. As can be seen from the results in Fig. 14, which also includes a convergence study, for cases of about μ = 0.1 and higher the useable portion of the FCC is limited. The point of bifurcation of each 100 80

µ = 0.4 1

Isothermal Press Single sample pressed and cooled

120

60 40

µ 1 = 0.1

20 0

µ = 0.04 1

-20 -40

µ 1 = 0.02

-60 -80 -100 0

10

20

30

40

50

60

70

curve corresponds to the axial deformation level when the outer cylindrical surface first comes into contact with the molds, which is independent of the level of friction on the cylindrical surface. This bifurcation point and consequently the entire FCC beyond this point are difficult to determine for some friction cases due to convergence with respect to the mesh. The convergence results in Fig. 14 are discussed below. As demonstrated in Fig. 14, the baseline mesh of 3072 elements provides converged FFCs for all constant coefficient of friction results, since the FCC results obtained using a mesh with 12,096 elements are nearly identical. However, the baseline mesh did not always provide a converged result when the coefficient of friction is different on the flat and cylindrical surfaces. For low friction (μ = 0.04) the result converges since the cylindrical surface does not contact the mold. For high friction (μ = 0.6) the results converge for the baseline mesh since there is very little difference between 0.6 and 1.0, i.e., μ = 0.6 is enough to essentially prevent slip. However, when friction is high enough to cause cylindrical surface contact, but low enough to allow significant slip, the baseline mesh did not provide a correct result. This is due to behavior at both the inner and outer radii of the ring. For the two friction cases presented, which are μ = 0.12 and 0.2, a much finer mesh has to be used to obtain a mesh independent solution. To summarize, the results in Fig. 14 show the following: 1) the cylindrical surfaces play a significant role in the RCT for coefficients of friction higher than about 0.1, 2) the FCCs are universal only if the friction behavior is the same on all the surfaces of the cylinder, and 3) when the coefficient of friction is not the same, computational convergence can be achieved but it is more difficult. Temperature non-uniformity is the third consideration, such as what occurred in the first set of experimental results described in Sections 2 and 4.1. In the discussion of Fig. 6 it was demonstrated that for low friction if a temperature variation in the axial direction exists at the start of the pressing stage, the FCC measured at the centerline had an error of about 2%. The error was small due to relatively rapid heating once the upper mold came into contact with the top of the ring. This self-correcting mechanism is dependent on the rate of heat transfer being significantly higher than the rate of axial deformation, which might not always be the case. Therefore, in order to estimate a maximum error due to non-uniform temperature at the start of the pressing stage, a numerical experiment using the procedure in Table 1 was performed in which a temperature difference of 10 °C between the upper (594 °C) and lower (584 °C) mold surfaces was imposed. This temperature difference remained unchanged throughout the pressing stage, which could correspond to inadequate soak time with a relatively high rate of axial deformation or a case where the

80

% Deformation in the axial direction

% Decrease in internal diameter of the ring

108

100 80 60 40 20 0 1

-20 -40 -60 -80

2

0

10

20

=1 30

40

50

60

70

80

% Deformation in the axial direction Fig. 13. Comparison of simulated FCC obtained using single isothermal pressing (line) to computationally generated data for a single sample that has been re-used with three cycles of heating, soaking, pressing and cooling. Material Set A from Table 3 was used for generating results.

Fig. 14. Sensitivity of FCC to a high level of friction on the inner and outer cylindrical surfaces of the ring sample. Convergence with respect to a uniform mesh is also demonstrated.

B. Ananthasayanam et al. / Journal of Non-Crystalline Solids 385 (2014) 100–110

4.6. Universal friction calibration curves

5. Discussion

% Decrease in internal diameter of the ring

Use of the RCT depends on computational mechanics to link the change in the inner diameter to the friction coefficient. As such, the computational approach must be validated, especially for glass due to its complex thermo-mechanical time-dependent material behavior. The general approach used in the current study was validated first 100

µ = 0.6

Uniform Non-uniform, center Non-uniform, minimum

µ = 0.2

60 40 20 0

= 0.04

-20 -40 -60

µ=0

-80 0

10

20

30

40

0.6 80

= 0.4 = 0.3

60

= 0.2

40

= 0.15 = 0.12

20

50

60

70

= 0.1 = 0.08 = 0.07 = 0.06 = 0.05 = 0.04

0 -20

= 0.03 -40

= 0.02

-60 -80

Based on the results presented in this study, universal FCC, which by definition are measured at the centerline of the ring, can be generated for glass at high temperature under conditions of constant load and also constant rate for relatively low viscosity. Friction is assumed to be the same on all surfaces and the glass should have reached a near constant temperature before the ring is pressed. A single term prony series in shear is sufficient to account for mechanical behavior and material compressibility need not be taken into account. Furthermore, the thermal expansion behavior of the glass need not be known since it has been shown that the entire computations can be carried out at constant temperature. For these assumptions, the final FCC are presented in Fig. 16. Friction coefficients so obtained can be used to: 1) provide a necessary input to computational simulations of processes like PPV and PGM and 2) to quantify the level of shear stresses that can lead to wear of mold surfaces in processes such as PGM.

80

100

% Decrease in internal diameter of the ring

upper and lower mold surfaces are incorrectly heated to different temperatures that remain constant. The results of this numerical experiment are presented in Fig. 15 for friction coefficients of 0, 0.04, 0.2 and 0.6. It is clear from these results that a significant temperature difference results in relatively small changes in the FCCs when measured at the centerline. Consistent with Fig. 6, the FCC at the minimum radius has a more significant error. A conclusion from the study of non-uniform temperature in Fig. 6 is that the load-controlled process considered can be self-correcting in terms of inadequate soak time. In a rate-controlled process or a loadcontrolled process at higher temperature, press time will be reduced and this self-correction mechanism is less likely. The limiting case of a short press time for temperature non-uniformity is presented in Fig. 15. As a general statement, while the recommendation is to achieve a near uniform temperature at the start of the pressing stage, as long as the diameter is measured at the centerline, as shown in Figs. 6 and 15, the error in the estimation of the friction coefficient is small.

109

= 0.01 0

10

20

30

40

50

60

= 0.0 70

80

% Deformation in the axial direction Fig. 16. Universal FCC for glass at high temperature.

with a sandwich seal solution [17] well known in the glass literature and then in another study [2] by predicting lens profile deviation in precision lens molding to within one micron of experimental measurements for two different lens types. In that study several factors were identified that caused a change in over two microns, which is significant to a lens designer. Structural relaxation of the glass was determined to be the most significant factor, which can cause changes of 10 μ or more. Since the pressing of a ring is very similar to the pressing of a lens, it is believed that this validation applies to the study of the RCT, and similarly that the friction results apply to lens molding. Finally, convergence of the computational solution for the ring geometry was demonstrated herein, which showed the importance of polishing the cylindrical surfaces of the ring, which come into contact with the molds for coefficients of friction higher than about 0.1. The RCT is useful since the displacement of the inner diameter of the ring is both large and very sensitive to changes in interface friction. This displacement is due to the complex combination of glass deformation and interface behavior that can include full slip, no-slip or partial slip. Through a significant effort to prove the universal nature of the FCCs, the computational model takes all this complexity into account to capture whether the glass surface is slipping or not slipping. This is a non-trivial point since in any process involving glass deformation at relatively high temperature, the displacement component due to glass deformation can be large making the degree of slip that contributes to the displacement response uncertain [8]. As seen from the FCC in Fig. 16, the change in the 9.59 mm inner diameter ranges from a decrease of over 7 mm for high friction to an increase of over 5 mm for low friction. Compared to the micron scale changes in lens profile deviation, the displacements of the inner diameter are three orders of magnitude larger. This difference is the primary reason the FCC are not sensitive to material behavior. While all the factors considered in this study affect the inner diameter, they do not affect it enough to be significant as long as the recommended procedures for conducting the test are followed. Interface slip and bulging dominate the change in the inner diameter of the ring and these mechanisms are not affected significantly by the material behavior of glass.

80

% Deformation in the axial direction Fig. 15. Sensitivity of FCC to a non-uniform temperature in the ring due to an imposed temperature difference of 10 °C between the upper and lower mold surfaces. Equilibrium viscosity log(ηR) = 8.33 Pa · s and the WLF equation with TR = 589 °C, C1 = 5, C2 = 149 °C were assumed for TRS behavior.

6. Conclusions The RCT is a reliable test to characterize friction behavior at a glass/ mold interface for PGM and PPV. Although this test can be unreliable for metal extrusion and cold forming applications where the contact

110

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pressures can be very high, it is ideal for these applications since: 1) the maximum contact pressure is on the order of 10–20 MPa [3], which is very low, 2) the same precision lens molding machine and processing conditions used to press a lens can be used to conduct the RCT, and 3) a parallel plate viscometer can also be used to conduct the RCT by following the same PPV procedure used to press a glass cylinder. The key point of the study is that the RCT provides a universal set of FCC for glass rings as long as the ring is at a nearly uniform temperature during pressing, friction is the same on all surfaces and the ring is pressed under conditions of constant load or at low rates. Therefore, the FCC allow for a reliable test to characterize friction at any temperature without the need for material properties. This is significant since the time dependent material behavior of glass is very difficult to characterize and there is very little material property data available in the literature. As a general statement, the RCT is best applied to cases with a coefficient of friction that is less than about 0.3, since at higher values the calibration curves become less sensitive to friction, more sensitive to factors such as differences in material behavior and loading rate, and involve the contact of the outer cylindrical surface of the ring. This range of friction coefficients is desired for reduced wear of expensive coatings in precision lens molding. The results are also important for parallel plate viscometer testing at high viscosity when slip with friction can occur. As shown by Joshi et al. [8], in such cases a correct estimate of the viscosity of glass requires knowledge of the level of friction. Acknowledgment This material is based upon work supported in part by the U.S. Army Research Laboratory and the U. S. Army Research Office under contract/ grant number ARO No. 56858-MS-DPS and by a DoD-ARO Cooperative Research Agreement, “Molding Science of IR Optics,” through Benét Labs and Edmund Optics, with subcontract to Clemson University. References [1] B. Ananthasayanam, P.F. Joseph, D. Joshi, S. Gaylord, L. Petit, V.Y. Blouin, K.C. Richardson, D.L. Cler, M. Stairiker, M. Tardiff, J. Therm. Stresses 35 (2012) 550–578.

[2] B. Ananthasayanam, P.F. Joseph, D. Joshi, S. Gaylord, L. Petit, V.Y. Blouin, K.C. Richardson, D.L. Cler, M. Stairiker, M. Tardiff, J. Therm. Stresses 35 (2012) 614–636. [3] F. Klocke, T. Bergs, K. Georgidis, H. Sarikaya, F. Wang, in: K.D. Bouzakis, F.E. Bach, B. Denkena, M. Geiger (Eds.), Coatings in Manufacturing Engineering, Laboratory of Machine Tools and Manufacturing Engineering, Greece, 2008, pp. 209–217. [4] K.J. Ma, H.H. Chien, W.H. Chuan, C.L. Chao, K.C. Hwang, Design Of Protective Coatings For Glass Lens Molding, Volume: Optics Design and Precision Manufacturing Technologies, Key Eng. Mater. 364–366 (2008) 655–661. [5] A. Jain, A.Y. Yi, J. Manuf. Sci. Eng. 128 (2006) 683–690. [6] A.Y. Yi, A. Jain, J. Am. Ceram. Soc. 88 (2005) 579–586. [7] M. Sellier, C. Breitbach, H. Loch, N. Siedow, Proc. Inst. Mech. Eng. Part B J. Eng. Manuf. 221 (2007) 25–33. [8] D. Joshi, P. Mosaddegh, J.D. Musgraves, K.C. Richardson, P.F. Joseph, J. Rheol. 57 (2013) 1367–1389. [9] J.A. Schey, Tribology in Metal working: Friction, lubrication and wear, Volume 1, ASM, Metals Park, OH, 1983. [10] F. Wang, J.G. Lenard, J. Eng. Mater. Technol. 114 (1992) 13–18. [11] T. Nakamura, N. Bay, Z.-L. Zhang, J. Tribol. - T. ASME. 119 (1997) 501–506. [12] F. Fereshteh-Saniee, I. Pillinger, P. Hartley, J. Mater. Process. Technol. 153–154 (2004) 151–156. [13] L. Wang, J. Zhou, J. Duszczyk, L. Katgerman, Tribol. Int. 56 (2012) 89–98. [14] P. Mossaddegh, J.C. Ziegert, J. Non-Cryst. Solids 357 (2011) 3221–3225. [15] M. Falipou, F. Sicloroff, C. Donnet, Glass Sci. Technol. 72 (1999) 59–66. [16] S.H. Chang, Y.M. Lee, T.S. Jung, J.J. Kang, S.K. Hong, G.H. Shin, Y.M. Heo, NUMIFORM'07, Mater. Process. Des. (2012) 1055–1060. [17] B. Ananthasayanam, Computational Modeling of Precision Molding of Aspheric Glass Optics, [Ph.D. Dissertation] Clemson University, Clemson, SC, December 2008. [18] A.T. Male, V. Depierre, ASME J. Lubr. Technol. 92 (1970) 389–397. [19] H. Sofuoglu, H. Gedikli, J. Rasty, ASME J. Eng. Mater. Technol. 123 (2001) 338–348. [20] H. Sofuoglu, H.J. Rasty, Tribol. Int. 32 (1999) 327–335. [21] T. Robinson, H. Ou, C.G. Armstrong, J. Mater. Process. Technol. 153/154 (2004) 54–59. [22] D.R. Hayhurst, M.W. Chan, Int. J. Mech. Sci. 47 (2005) 1–25. [23] E. Kropp, T. Udagawa, T. Altan, Investigation of metal flow and lubrication in isothermal precision forging of aluminum alloys, in: P.W. Lee, B.L. Ferguson (Eds.), Proc. ASM Conf. on Near Net Shape Manufacturing, Columbus, OH, November 1988, ASM International, Metals Park, OH, November 1988, p. 37. [24] A. Buschhausen, K. Wienmann, J. Lee, T. Atlan, J. Mater. Process. Technol. 33 (1992) 95–108. [25] N. Bay, J. Mater. Process. Technol. 46 (1994) 19–40. [26] ABAQUS version 6.8 User Documentation, Dassault Systems Inc., 2007 [27] Specification Sheet for L-BAL35 Glass, Ohara, Japan, www.ohara-inc.co.jp. [28] Specification Sheet for Tungsten Carbide Material, Kennametal Inc., Latrobe, PA, USA, Available at www.Kennametal.com. [29] J. Brand, R. Gadow, A. Killinger, Surf. Coat. Technol. 180–181 (2004) 213–217. [30] A. Heimberg, K.J. Wahl, I.L. Singer, A. Erdemir, Appl. Phys. Lett. 78 (2001) 2449–2451. [31] ASTM standard C1351M–96, 2012.