# Multistage Fatigue of a Cast Magnesium Subframe

## Problem Description

Being able to predict the behavior of a material or component is an extremely important factor of success when designing and optimizing new products. More so if one is able to predict that behavior without spending millions on costly experiments. The idea of multiscale modeling creates a paradigm where one can predict behavior accurately and therefore optimize the design of any component through a simulation based design.

Multiscale modeling utilizes a material model that is created by downscaling to the electronic level and back up through to the macroscale level in order to collect the variables that are needed to produce the most accurate result. Information is gathered at each scale through simulations and experiments, with the most important internal state variables being passed up to the macroscale model. The variables chosen are based on the purpose of the model. If the model was created to predict damage, then variables detrimental to damage such as the elastic modulus, high rate mechanisms, and void incubation and growth would be collected from the downscale methodology.

Multiscale modeling can be applied to many materials. Current applications include cast aluminum and magnesium alloys, as well as concrete. The process could be used to analyze damage in the form of internal state variables, as well as fatigue in the form of multistage fatigue. Multistage fatigue modeling could also be applied across all materials. This modeling could be limited by the amount of data that is available or able to be acquired.

## Multistage Fatigue Modeling Approach

Beginning an analysis by downscaling from the end goal is a strategic move done to figure out what information needs to be gathered to get to the main goal. In this paper, the main goal is to predict the fatigue life of a magnesium subframe that has been implemented into a Subaru BRZ. Predicting the fatigue life means inputting a select number of variables that define fatigue into the multistage fatigue model. These variables are collected through the downscale process. From the macroscale, the information about crack growth can be gathered at the mesoscale through experiments and finite element simulations. The variables transferred to the macro level fatigue model would include grain size and orientation, and pore size and nearest neighbor distance. The next lower scale would be at the micro level where the information about crack nucleation can be gathered. The micromechanical finite element simulations here would provide insight into the non-local plasticity parameters. The next lowest scale would be at the atomic level where the crack tip driving force can be collected. Here, coefficients such as the crack tip displacement coefficient, ΔCTD, are needed to be found through simulations using the MEAM, EAM, MD, or MS methods. The information regarding the force at which the crack travels through the material could also be helpful when running simulations regarding the nature of crack growth at the mesoscale.

## References

[1] Horstemeyer, M. (2012). Integrated Computational Materials Engineering (ICME) For Metals. Chapter 8: 340-374