b'were imposed on the FE model toeach of the elastic constants wasFigure 3. (a) The predicted elastic predict elastic constants, whichabout 10%. A statistical distributionconstants (symbols) of SiCf/SiCm were in good agreement with thewas also fit to MCS-generated datatubes and the reported range of experiments (shaded region). (b) The experiments as evidenced by Figurewhich is helpful in evaluating what-ifPLS values from DMM (cyan symbols 3(a). In this figure, Eq, Ey and Gqy referscenarios for the performance ofand the curve (ellipses) fit to data in to stiffnesses along hoop (q), axial (y),SiCf/SiCm tubes. each quadrant. The ellipse equation and shear modulus in q-y plane. can be used as a phenomenological In the next step, failure envelopesfailure criterion to assess the To quantify uncertainty inwere constructed in stress space byperformance of SiCf/SiCm tubeselastic constants and reduce theconsidering the proportional limit computational cost associatedstress (PLS) as a failure mode. We with complex FE analyses,used DMM to predict failure for a polynomial equations that bestgiven loading condition, knowing approximate the FE predictionsthe strength of the constituent were constructed. Initially, globalmaterials. An example failure sensitivity analysis was conductedenvelope for one combination of to determine dominant variablesstresses is shown in Figure 3(b). that influence the elastic constants.The predicted PLS is in reasonable They were identified as porosity,agreement with the experiments Youngs modulus of SiC matrix, and(green triangles). For industrial Youngs modulus of SiC fiber. Theapplications, we proposed a developed polynomial equationsphenomenological failure criterion were then used in Monte Carloby fitting ellipse equations Simulations (MCS) to quickly(regression fit) in each quadrant as generate large data of elasticthe failure criterion. The COV was constants for SiCf/SiCm tubes. Thefound to vary between 25%-48% uncertainty in elastic constantsindicating high variability in PLS.was determined by calculating the coefficient of variation (COV) from MCS-generated data. The COV in 2022|AFC ACCOMPLISHMENTS 59'