D,9 • THERMAL SHOCK 



boundaries. The results given below from [i^] can also be deduced from 

 Eq. 8-2 and 8-3 for the hollow cylinder, ^ in the limit S2 — > 1. 



At any instant i > the thermal stresses have maximum values at 

 the boundaries (compression on heating) and the midplane (tension on 

 heating). Let the dimensionless stresses at the boundaries and midplane 

 be denoted by 77o(r) and ^7^(7-) respectively. As functions of r these have 

 absolute maxima, |77o|max and |77mlmax, the magnitude of which depend only 

 on the Biot number A^" = hd/k as shown in Fig. D,9. If S^ and St denote, 



1.0 



Mfe. 



00 



0.5 



10 



20 



30 



hd/k 



Fig. D,9. Maximum dimensionless stresses I?7|max in symmetrically 

 heated plane parallel slab vs. Biot number. 



respectively, the yield stress in compression and tension, the correspond- 

 ing allowed dimensionless stresses are 



^0 = 



f\t = 



^t(l - v) 



Thus, in heating the slab, the resistance to thermal shock is measured by 



* The midplane divides the slab into two regions, in each of which the thermal 

 stress distributions correspond to limiting cases of the thin hollow cylinder with 

 d = 6 — a, Q-^ 1. 



< 271 ) 



