Appendix C 



FAILURE CRITERION APPLIED TO CONICAL 

 ACRYLIC VIEWPORTS 



A FAILURE CRITERION 



This appendix outlines the development of a rational yield-failure 

 theory utilized in the design guidelines of this report. 



In keeping with the yield-failure definition set forth in this report, 

 two entities must be completely described. First, the location and relative 

 magnitude of the maximum effective stress, a^, must be evaluated; and 

 second, the material yield strength, a^, must be determined. Unfortunately, 

 acrylic exhibits time dependency, consequently, both of the above entities 

 are functions of time, i.e., loading history. Because of the infinite variety 

 of possible loading histories, the general design procedure would be to choose 

 the most unfavorable loading history to account for all other less severe cases. 



For the special case of acrylic viewports, the most detrimental loading 

 history would be represented by a step loading raised immediately to maximum 

 operational depth and held there for the given duration. Moreover, if acrylic 

 was purely viscoelastic, the stress distribution in the viewport at time T = , 

 is identical to the distribution resulting from an elastic analysis and represents 

 the most unfavorable distribution in terms of the high magnitudes and stress 

 concentrations. As time progresses, stress relaxation occurs relieving and 

 redistributing high stress concentrations. Thus, in terms of the viscoelastic 

 behavior, the elastic solution (T = 0"*") may be conservatively used to deter- 

 mine the maximum stress concentrations and assume these magnitudes 

 constant with time rather than decreasing. Actually, the conservative assump- 

 tion of constant viewport stresses is quite accurate due to the phenomenon 

 that the elastic stresses of conical frustums are independent of Young's 

 modulus and only slightly dependent on Poisson's ratio. Hence, in view of 

 the correspondence principle, which relates elastic and viscoelastic solutions, 

 time would have very little effect on the viscoelastic stresses. In light of the 

 above, one can rationally accept the stresses resulting from an elastic 

 analysis (approximated by the finite element technique) as the governing 

 stresses throughout the loading duration, providing there is adequate 

 recovery time between loadings. 



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