313 



biaxial stress-strain relation in which the effect of strain hardening is 

 exactly compensated by the effect of decreasing thickness, resulting in a 

 somewhat closer fit to experimental results and a simplification of the 

 higher approximations. As stated before, it also implies ignoration of the 

 elastic domain of strain, an apparently justifiable approximation in the 

 case of ductile materials such as steel and copper in which plastic flow can 

 occur over relatively large domains of strain. In a rapid deformation 

 process going well into the plastic domain of stress, the ignoration of 

 the elastic domain is further justified by the fact that only the inertial 

 terms of the equations of motion are important /at least in Eq, (l}_7when 

 the strains are small. 



The application of von Mises condition to all parts of the plate 

 is valid only if the rate of strains keeps the same sign at each part. If 

 the rate of strain changes sign anywhere, the equations of motion are tremen- 

 dously complicated by unloading and hysteresis effects. 



The experimental stress-strain cxirves deviate, of course, rather 

 widely from the idealized one implied here. Moreover, the experimental 

 curves are found to depend upon the rate of strain; however, these effects 

 are manifested in a relatively small range of strain beyond the proportionsil 

 limit. The yield stress <T^ may be regarded as a parameter adjusted to give 

 the best agreement between the ideal and e^qaerimental curves. Hence it is 

 easy to see that the ultimate tensile strength is a better value for 0^ 

 than the stress at v^ich jrielding begins. 



The principle of the similarity of the Mohr circles of stress and 

 strain is usually assumed to hold only for stationary plastic flow. In the 



