582 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1953 



gies. Furthermore, the change is not Hmited to two-thirds as in the case 

 of grain boundary motion, but is much more tending toward a value 

 of 0.2 for very long times. It appears that several processes are involved 

 in addition to grain boundary motion. These are probably connected 

 with slips along slip planes which occur with a lower activation energy 

 when the stress is high. As the slip increases, strain hardening occurs 

 with a resultant increase in activation energy until the activation energy 

 of grain boundary movements is reached. For 0.3 relaxation and lower, 

 the activation energy remains constant and equal approximately to 40 

 kilocalories per mole — the self -diffusion value — as can be calculated 

 from the 150°C, 175°C and 200°C relaxation curves of Fig. 21. These 

 curves show that the activation energy varies from 12.5 kilocalories at 

 0.9 relaxation, to 40 kilocalories for long time effects. 



Similar measurements have been made on nickel silver terminals 

 which are the terminals actually used and as seen from Fig. 21 of 

 Malhna's paper, these agree quite well wdth those measured for spring 

 steel terminals. The nickel silver terminals had the dimensions 0.0148 

 inches by 0.062 inches. A twist of 46° was obtained for 100 turns of 0.020 

 inch copper wire with 2.87 pounds winding stress applied. At this angle 

 of twist, a permanent set of 19° occurred when the outside wire was un- 

 wound. If we subtract that value from the initial twist, the time-angle 

 curve is very similar to that for spring steel and indicates that no addi- 

 tional relaxation occurs in the nickel silver terminal. 



The conclusion from these experiments is that stress relaxation for the 

 value of strain used in the wrapped solderless connections follows a simi- 

 lar activation energy pattern to that followed for smaller strains except 

 that instead of a single process with a single activation energy we are 

 dealing with many separate processes having an activation energy range 

 from 12.5 kilocalories to 40 kilocalories. For each stage of the process a 

 different activation energy is effective. For example, for a ratio of re- 

 laxed stress to initial stress of 0.9 the curves of Fig. 21 indicate an activa- 

 tion energy of about 12.5 kilocalories. With this value of activation 

 energy the time required to relax this amount of stress at room tem- 

 perature of 25°C (77°F) is 2.98 X 10^ seconds or 0.0095 years as shown 

 by Fig. 22. For a ratio of relaxed to initial stress of 0.8, the activation 

 energy is 15.3 kilocalories and the time at room temperature is 0.126 

 years. Similar values can be calculated for the other relaxation ratios 

 and the complete relaxation ratio and time curves are shown by Fig. 22 

 for temperatures of 77°F and 135°F. To reach a value of 0.5 of the initial 

 hoop stress requires 2500 years at 77°F and about forty years at 135°F. 

 The circles show the measured values at 77°F carried out in a tempera- 



