Analytical Phase 



General. The knowledge gained from the experimental tests was 

 utilized as a basis for performing an analytical study on viewport designs. 

 In particular, analytical investigation for a spectrum of viewport parameters, 

 t/d and a ranging from 0.25 to 1 .75 and 60° to 120°, respectively, was ac- 

 complished by means of the finite element technique. 



In order to develop rational design recommendations, it is necessary 

 to define the capacity of the system, i.e., what constitutes failure. Since the 

 failure mode definition and failure criteria influence the assumptions made 

 in an analytical study, the concept of failure is discussed prior to the analy- 

 tical method of attack. 



Concept of Failure. Failure must be considered from two viewpoints: 



(1 ) the structural level and (2) the material level. First, at the structural 

 level, the investigator must define failure. In the past, structural viewport 

 failure has been taken as the complete collapse of the system, often called 

 the upper limit or ultimate strength, which is typified by large plastic flow 

 and rupture. Another definition of failure is the lower limit capacity of a 

 system which is defined as that load which causes initial plastic yielding in 

 any local region of the system. 



The authors have chosen the lower limit or "yield criterion" as the 

 definition for failure of acrylic viewports based on the following considera- 

 tions. (1 ) The functional use of a viewport is to transmit undistorted and 

 undiminished light to the viewer, however, earlier experimental results have 

 shown that this function is seriously impaired when the viewport is loaded 

 into the plastic range which results in crazing and distortion of the acrylic. 



(2) The pressure that causes yielding is much lower than the load causing 

 ultimate collapse failure, consequently, a built-in safety factor for the 

 hazardous environment is intrinsic in the lower limit design, in addition to 

 the standard safety factor used for the functional aspect. 



The second major consideration in establishing a failure criterion 

 belongs to the realm of the material itself independent of the particular 

 structure configuration and functional use. 



Since, by definition, the structure fails when local yielding occurs, 

 this dictates that a yield criterion for acrylic must be established which will 

 adequately predict yield states under combined stresses. Fortunately, much 

 research has been accomplished in this area and it has been shown that the 

 Huber-von Mises-Hencky or distortion energy theory of failure^ predicts 

 combined-stress yield-states extraordinarily well for acrylic. ^-^ However, 

 this flow law is complicated by the anisotropic response of yielding in tension 



