PSI - Issue 19

A. Halfpenny et al. / Procedia Structural Integrity 19 (2019) 150–167 Author name / Structural Integrity Procedia 00 (2019) 000–000

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4.3. Stochastic simulation A statistical uncertainty analysis was performed on 2 simulation parameters listed in Table 2.

Table 2. Parameter substitutions

Scale ±10% of max stress

Parameter

Distribution

Location

Error on FEA stress Material variability

uniform normal

1.0

50% 16.6% Error on FEA stress : accounts for FEA modelling errors and uncertainty in the input loading.

The uncertainty on stress arising from FEA modelling is mostly epistemic. It can be improved by mesh refinement and greater care in modelling the as-manufactured component. However, there is a limit to the extent of refinement possible. Limitations in the calculation method, as well as uncertainties in the input parameters, will lead to unavoidable uncertainty in the final stress result. There is also a compromise between the desirable accuracy and the complexity of the FEA model. In general, there is no benefit in performing an FEA with greater accuracy than the known input parameters. The stochastic analysis will determine whether an optimal degree of accuracy is achieved. The pressure loads applied in the reliability tests were carefully monitored and there is negligible uncertainty associated with the loading. A conservative estimate on stress uncertainty from FEA modelling is usually assumed between ±10%. In this case study, a ‘Uniform’ probability distribution is assumed because the actual stress is assumed to be anywhere within the range ±10% with equal likelihood. Material uncertainty: is an aleatoric uncertainty associated with the scatter in the material EN data. Fatigue life always includes some scatter, and at any given level of strain amplitude, the distribution of fatigue lives is assumed to be log-normal. The scatter is often expressed as a Standard Error value in the DesignLife software and is modelled using Equation (7). � = � �� � 10 �� � (2 � ) � + � � 10 �� � (2 � ) � (7) � is the expected number of cycles to failure for strain amplitude � . � � , � � , and are strain-life curve fitting parameters. � and � are the standard error values associated with the elastic and plastic portions of the curve respectively. is the desired reliability statistic expressed in terms of the number of standard deviations. is determined from a percentage reliability using Equation (8). = √2  �� (2 − 1) (8) is the desired reliability statistic in the range (0,1) and −1 R is the desired reliability statistic in the range (0,1) and �� ( ) is the inverse error function, where the error function is defined as ( ) = √ � � ∫ �� � � � . Statistical variability is modelled as a ‘ Normal ’ distribution with location 50% and scale ≈ 16 % ≈ 16.6% in this case.  Reliability simulation A Monte Carlo statistical simulation was performed over 20 iterations using nCode DesignLife and a statistical reliability study was performed using Reliasoft Weibull++. A 2-parameter Weibull model was used to fit the experimental data and a 3-parameter Weibull model used for the simulation data. A Weibull plot comparing results from the measured and simulated data is shown in Fig. 12. A comparison of the two Probability Density Functions (PDF) is given in Fig. 13. A summary of the statistical results is given in Table 3.