# Proposal for Multiscale Modeling of 17-4 PH and life prediction using MSF model

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## Introduction

Fatigue is the phenomenon that is making a material weaker by applying cycling loads, fatigue happens when a material is under loading and unloading. It is the damage that occurs progressively in the structure of the part or material or structure under the load. When the loads are above a certain limit, it will trigger the beginning of microscopic cracks where the stress is concentrated, that limit depends on the material or materials used. When the crack begins it will propagate slowly until it reach a given size where it will increase suddenly and dramatically, the propagation of the crack is mainly affected by the grain size of the material, bigger are the grain size easier the propagation will be for the crack, meanwhile if the grain size are small the path for the crack will be more difficult to propagate. The geometry of the part play also a major role in the fatigue life, sharp corners and holes or discontinuity in the geometry of the part will lead to concentrated stress where fatigue can initiate. The fatigue life of a material is defined by the cycles that specimen can endure before it breaks, for steel and other material there is a stress limit where the part will never fail for infinite number of cycles, it is called the infinite life and that limit is called the fatigue strength.

[4] this curve shows the greater the stress amplitude is, the fewer cycles the specimen can endure, there is a lower limit where the specimen can endure infinite cycles for this specimen it is approximately 400 Mpa.

## Fatigue for steel

The life of material is commonly determined by an S-N curve (Stress vs Number of cycles), the curve is a result from tests on specimens of the part that needs to be characterized where a regular stress is applied until failure and we record the number of cycles the specimen sustained that stress, then we repeat the same experiment with different stress value and we record the number of cycles for each one of them until failure, we get a curve that is similar as this one. [1]

## Multi-stage fatigue model (MSF)

History of MSU MSF model:[2]

-First started on a cast A356 al alloy for automotive application (1995- 2000). -Extended to aerospace aluminum alloys (7075, 7050 al) (2002-2006). -Extended to automotive cast Mg alloys (2002-present). -Recently used for several steel alloys (2005-present)

The multi-stage fatigue (MSF) model predicts the amount of fatigue cycling required to cause the appearance of a measurable crack, the crack size as a function of and loading cycles. The model incorporates microstructural features to the fatigue life predictions for incubation, microstructural small crack growth, and long crack growth stages in both high cycle and low cycle regimes.

## Methodology

In addition of this model to being the multistage of different stage of fatigue it can be used as a continuum model for multi scale modeling, many of these parameters stated above can be defined by micromechanical simulation or atomistic simulation, so basically we can get information for the material from lower length scale and input these parameters into the model which is a continuum model and then incorporate this model into a FEM and apply it on a larger geometry.

The multiscale bridges for downscaling requirements and upscaling simulation results for the multistage fatigue (MSF) model.

## Macroscale

To be able to get data on macro crack growth and fatigue life at this level this MSF model was originally constructed starting from a multiscale modeling methodology, but to investigate cracks we must first have information about crack nucleation and crack growth rate at a smaller length scale.

## Electronic scale

Before we get into atomistic scale and MEAM calibration we need to use DFT (Density field theory) to determine elastic moduli and surface energy for 17-4 PH SS and then take those result to the atomistic scale.

## Atomistic scale

Now at this length scale we can use calibration of MEAM potential (Modified Embedded Atom Method) and determine the values of microstructural small crack growth so that they can be used at a larger length scale in the MSF model.

## Conclusion

This proposal discuss and details a multiscale method for the modeling of fatigue life for 17-4 PH stainless steel where information are obtained from lower length scales to the next greater scale as mentioned in the last parts of this paper, to be finally able to use those data into our MSF (Multi Stage Fatigue) model to predict fatigue for 17-4 PH SS.

## References

[1] McDowell, D.L., Gall, K., Horstemeyer, M.F., and Fan, J., MicrostructureBased Fatigue Modeling , Engineering Fracture Mechanics, Vol. 70, pp.49-80, 2003. [2] Horstemeyer, M.F., 2012. Integrated Computational Materials Engineering (ICME) for Metals: Using Multiscale Modeling to Invigorate Engineering Design with Science. John Wiley & Sons. [3] https://www.beststainless.com/17-4-ph-stainless-steel.html [4] efunda.com Yadollahi, A., Shamsaei, N., Thompson, S.M., Elwany, A., Bian, L., 2016. Effects of building orientation and heat treatment on fatigue behavior of selective laser melted 17-4PH stainless steel.