The following examples show how finite element simulation was combined with the probabilistic tools for reliability assessment of structures and materials.
Reliability Based Creep Life Prediction of Structures
Sest, Inc. has successfully applied probabilistic approach to assess the reliability of hot temperature components such as an Stirling Convertor heater head (see figure below). Creep and fatigue of the thin-walled heater head structure at high temperature is one of the critical single point failure of the convertor. To predict the long-term creep life of the heater head with the design reliability, firstly a creep deformation model for the head material is developed based on customer provided uniaxial creep tests at various stress and temperature. Then the creep deformation model is implemented into finite element code using user customized subroutines; secondly the developed finite element model is validated comparing the simulated creep strains with those determined from a benchmark testing of the actual heater head. Figure below compares the predicted creep strain (blue, magenta) with the measured from the test (X- and Y-laser) as shown in figure below. The developed creep deformation model was applied to predict the long-term reliability of the heater head.
Reliability-Based Fatigue Life Prediction of Structures
The following example describes application of the probabilistic approach to assess the fatigue reliability of the critical section of the National Wind Tunnel structure. Uncertainties in the aerodynamic pressures, material properties, strength, geometry, and boundary conditions (support movements) were considered in the reliability assessment. Typical life contours for the 0.9999 reliability are plotted and the sensitivities of design variables to the life reliability are quantified (see figures below). The sensitivity analysis shows that the uncertainties in the pressure loads and material strength are major factors affecting the fatigue life reliability.
Probabilistic Material Behavior Characterization
Sest, Inc. engineers developed valuable experience in probabilistic characterization of material behavior. Uncertainties associated with the variables such as manufacturing process, mechanical parameters, and geometric parameters can be simulated to quantify the scatter in the material behavior.
For example, micro/macro mechanics based computer code PCEMCAN, developed by Sest, Inc., facilitates to characterize the response of the ceramic matrix composites (CMC) probabilistically considering processing temperature, fiber volume ratio, void volume ratio, constituent properties (fiber, matrix and interface), and geometric parameters (ply thickness, interphase thickness) have been simulated to quantify the scatter in the first matrix cracking strength (FMCS) and the ultimate tensile strength of SCS-6/RBSN (SiC fiber (SCS-6) reinforced reaction-bonded silicon nitride composite) ceramic matrix composite laminate at room temperature. The code was validated comparing the analytical prediction with the experimentally observed uniaxial test data to characterize the laminate composite behavior probabilistically. Results shown on figure below show a very good agreement between the simulation and the experimental data. The predicted first matrix mean strength is 225 MPa compared to observed 221 MPa in the test. The predicted scatter range is 125-300 MPa vs experimentally observed range of 172-275 MPa.
The sensitivity analysis shows that the thermal expansion coefficient and modulus of the fiber in longitudinal direction, matrix strength, fiber volume ratio, and matrix modulus are most sensitive to the first matrix cracking strength. Similarly, the predicted mean ultimate strength is 660 MPa vs experimentally observed 690 MPa and its predicted scatter range of 345-965 MPa vs experimentally observed range of 414-970 MPa. The sensitivity analysis indicates that fiber strength in longitudinal direction and fiber volume ratio are the most sensitive to the ultimate strength. Sensitivity study also suggests that the uncertainties in the most sensitive variable should be reduced through quality control, inspection or process change in order to reduce scatter in the strengths and improve reliability.
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