JOURNAL OF MATERIALS SCIENCE LETTERS 17 (1998) 1207±1209 Indentation curves and viscosity measurements on glasses G. CSEH, N. Q. CHINH, A. JUHA  SZ Department for General Physics, Lora Ând Eo È tvo È s University, Mu  zeum krt. 6-8, H-1088 Budapest, Hungary E-mail: chinh@ludens.elte.hu The high-temperature indentation test performed by a hemispherical indenter has been applied for the determination of the viscosity of glasses since the 1960s [1±3]. During the test, a hemispherical indenter with diameter d is impressed into the surface of the sample at a constant load, F , and the indentation depth, h, is recorded as a function of the elapsed time, t. The theoretical interpretation of these measurements was developed by Douglas [2], who derived the formula: h  9 Ft 32ç  d p   2=3 (1) where ç is the viscosity, which can be measured experimentally with high accuracy in the case of h  d . Recently, cylindrical indenters were also applied to determine viscosity of glasses [4]. It is well known that the viscous ¯ow of glasses can be described by the following relationship: ô  ç _ ã (2) where ô is the shear stress and _ ã is the shear strain rate. The viscosity depends strongly on the tempera- ture and generally obeys the formula: ç  ç 0 e Q kT (3) where ç 0 is constant and Q is the activation energy of the process controlling the viscous ¯ow, other symbols have the usual meaning. Instead of Equation 2 for tensile stress, ó , and strain rate, _ å, we get the formula: ç  ó 3 _ å (4) which has been used in several works to determine viscosity [4, 5]. Applying the indentation test, an important question is how the equivalent tensile stress, ó , and equivalent strain rate, _ å, can be given from other parameters characterizing the indentation measurements. So far for different shapes of indenter, these equivalent parameters have been calculated by the following formulae [4±9]: ó  c 1 p ind and _ å  c 2 _ å ind (5) where c 1 and c 2 are constants depending on the geometry of the indenter, p ind is the pressure under the indenter de®ned as the quotient of the load, F, and the projected area, A p of the contact surface: p  F A p (6) and _ å ind is given as: _ å ind  d h=d t h (7) for spherical [6], conical [6], pyramidal [7] indenter, and: _ å ind  d h=d t d (8) for the cylindrical one [8±11], where d is the diameter of the cylinder. To determine _ å ind the knowledge of the h± t relationship similar to Equation 1 is required. We have to investigate the functions describing h± t curves for different indenters. Meas- urements were carried out with a high-temperature indentation tester described in a previous paper [4]. Fig. 1a shows typical depth±time curves obtained for spherical, cylindrical, conical and pyramidal punches on lead glass. The data points are also plotted in log± log scale in Fig. 1b, from which it can be seen that the indentation depth, h, is proportional to t 1=2 , t 1=2 , t 2=3 , and t for conical, Vickers, spherical and 0261-8028 # 1998 Kluwer Academic Publishers Figure 1 Depth±time curves obtained for different punches on lead glass: (a) in normal scale; (b) in log±log scale. conical (ψ = 63°) cylindrical d cyl = 1 mm spherical d sph = 1 mm Vickers (φ = 68°) lead glass T = 478 °C h [mm] normalized time (t/ t max ) 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 (a) 1 0.1 0.01 0.1 1 spherical d sph =1mm cylindrical d cyl =1mm conical (ψ=63°) Vickers (φ=68°) lead glass T =478 °C h ~ t 0.497 h ~ t 0.503 h ~ t 0.667 h ~ t 0.992 h [mm] normalized time (t /t max ) (b) 1207