Question

Glass Science -- Stress Relaxation : please show calculation in detail or with explanation:

1] a) Show, by calculation, how much time is required to relax 90% of the stress in a glass at the annealing point; the initial stress is 300 MPa, the temperature is 535C, the elastic modulus is 55 MPa, the shear modulus is 10 GPa and Poisson’s ratio is 0.3

b) What about at the strain point ?

c) What about at the softening point where tempering is often initiated ?

*You should understand how these kinetics play a role in annealing, tempering and glass/metal/ceramic sealing.

Answer 1

Suppose the relaxation time for a glass at some temperature near Tg is 2 hours, how many minutes will be required for 90% of the residual stress to relax

using exponential formula

σ(final)=σ(initial)exp (-t/τ_g): so   

0.10*300= 300 exp(-t/120 min)

ln(0.10)= -t/120 min;

t=(2.303)(120 min) = 276 minutes

b) Strain point:

The strain point is defined as a temperature at which a certain glass viscosity is reached. It is that point at which all movement of the glass molecules has reached a point at which no more strain can be introduced into the hot glass. It is usually about 100 degrees F or so below the annealing temperature. Like all such temperatures it represents some point in the range of such temperatures for a glass family. For example, for Effetre/Moretti glass the annealing temperature is usually listed as 968 degrees F and the strain point about 840 degrees F.

c) The softening point is the temperature at which a material softens beyond some arbitrary softness. It can be determined, for example, by the Vicat method (ASTM-D1525 or ISO 306), Heat Deflection Test (ASTM-D648) or a ring and ball method (ISO 4625 or ASTM E28-67/E28-99 or ASTM D36 or ASTM D6493 - 11).

tempering is the process that makes the glass four to five times stronger and safer than annealed or untreated glass. As a result, tempered glass is less likely to experience a thermal break. With heat-strengthened glass, the cooling process is slower, which means the compression strength is lower.