Iterative Methods for Damage Prediction

Overview

Fiber-reinforced composites are prevalent in many industries where weight, strength, and stiffness are key drivers in material selection. Introduced roughly five decades ago, carbon fiber reinforced polymers now dominate as the material of choice for modern aircraft structures. Despite widespread adoption, much work remains to streamline design procedures given the plethora of options and the resulting analytical complexity. Substantiation of damage resistance and tolerance is of particular importance for certification of composite flight structures, and historically been difficult and expensive due to the necessity of physical testing on point designs. The recent progress with composite damage modeling offers hope to quantify these attributes earlier in the design process, reducing uncertainty and resulting in more optimal designs.

Final results and publications from this work in progress.

Contributions

• Developed scripts to translate design variables into FE simulations for damage resistance/tolerance evaluation in arbitrary FE software

• Created UQ framework for uncertainty propagation in composite damage predictions

One of the shortfalls in current composite damage modeling is the lack of consideration of the probabilistic nature of the model inputs such as material properties, geometric dimensions, and fiber orientations. To get a reliable prediction of strength from these models, it is imperative to conduct some type of uncertainty quantification or sensitivity analysis.

The most popular uncertainty quantification methods are the Monte Carlo and quasi-Monte Carlo methods. In the Monte Carlo method, a set of input parameters is randomly drawn from the probability density function of the parameters, then the model evaluated for the sample set. Thousands of samples are needed for convergence, so the method is impractical for computationally expensive models. Quasi-Monte Carlo methods reduce the number of samples needed but are still typically impractical for composite damage models. A more recent family of techniques are polynomial chaos expansions, which calculate the same statistical metrics as Monte Carlo methods, but typically with much fewer model evaluations. When the number of uncertain parameters is fairly low, polynomial chaos expansion techniques can reduce the number of model evaluations by one to three orders of magnitude.

Below are proof of concept results from this UQ framework, showing how uncertainty propagates from input parameters to the output of interest, in this case ultimate load of a panel in compression.

The desired result of any design activity is a design that meets all requirements and is hopefully optimized for one or more objectives. One approach is laminate mass optimization with damage tolerance to low velocity impact as a design constraint in the form of residual in-plane compression strength. To evaluate the performance of a laminate design, we use a discrete ply/cohesive zone damage model that has been validated with low velocity impact and compression strength after impact test data. Because the damage tolerance constraints are expensive to evaluate, a Bayesian optimization procedure is used to make the problem tractable. This class of optimization can serve to map the design space and get close to a global optimum with relatively few model evaluations. Below is an example of the design variables and constraint evaluation that can be used in this procedure.

For damage-critical aircraft components, this procedure will give designers the opportunity to arrive at a certifiable configuration prior to performing an expensive physical testing program, and will reduce the risk of full-scale test failures later in the certification process.