# Modeling the evolution of fatigue failure with peridynamics

## Keywords:

fatigue crack, peridynamics, crack propagation, crack initiation, fatigue life, fracture## Abstract

Holes and round notches are locations where fatigue cracks may arrest. Investigating the evolution of fatigue cracks after sinking into such a hole is important. Here we extend a recently proposed fatigue crack peridynamic model to treat such cases. The proposed improvements add the fatigue limit to the propagation phase. We demonstrate that the model simulates the three phases of fatigue failure (initiation, propagation, and final failure) with an example in which a fatigue crack sinks into a cutout and re-initiates from a different location along the cutout, grows, and lead to final failure of the structure. The fatigue crack path from the improved model agrees with an analysis based on strain concentrations. Convergence studies show that the peridynamic results are correct once the nonlocal size is smaller compared with the size of relevant geometrical features. We also discuss acceleration of computations on GPU-enabled hardware, obtained with minimal changes to a serial code.

## References

BRANCO, R., ANTUNES, F.V., COSTA, J.D., A review on 3D-FE adaptive remeshing techniques for crack growth modelling, Engineering Fracture Mechanics, 141, pp. 170–195, 2015.

DOLBOW, J., BELYTSCHKO, T., A finite element method for crack growth without remeshing, Int. J. Numer. Meth. Eng., 46, 1, pp. 131–150, 1999.

SINGH, I.V., MISHRA, B.K., BHATTACHARYA, S., PATIL, R.U., The numerical simulation of fatigue crack growth using extended finite element method, International Journal of Fatigue, 36, 1, pp. 109–119, 2012.

XU, Y., YUAN, H., On damage accumulations in the cyclic cohesive zone model for XFEM analysis of mixed-mode fatigue crack growth, Computational Materials Science, 46, 3, pp. 579–585, 2009.

SILLING, S.A., Reformulation of elasticity theory for discontinuities and long-range forces, Journal of the Mechanics and Physics of Solids, 48, 1, pp. 175–209, 2000.

BOBARU, F. ZHANG, G., Why do cracks branch? A peridynamic investigation of dynamic brittle fracture, International Journal of Fracture, 196, 1–2, pp. 59–98, 2015.

AGWAI, A., GUVEN, I., MADENCI, E., Predicting crack propagation with peridynamics: a comparative study, International journal of fracture, 171, 1, pp. 65–78, 2011.

HU, W., HA, Y.D., BOBARU, F., Peridynamic model for dynamic fracture in unidirectional fiberreinforced composites, Computer Methods in Applied Mechanics and Engineering, 217, pp. 247–261, 2012.

BOBARU, F., HA, Y., HU, W., Damage progression from impact in layered glass modeled with peridynamics, Open Engineering, 2, 4, pp. 551–561, 2012.

XU, J., ASKARI, A., WECKNER, O., SILLING, S., Peridynamic analysis of impact damage in composite laminates, Journal of Aerospace Engineering, 21, 3, pp. 187–194, 2008.

CHENG, Zhanqi, ZHANG, G., WANG, Y., BOBARU, F., A peridynamic model for dynamic fracture in functionally graded materials, Composite Structures, 133, pp. 529–546, 2015.

SILLING, S.A., ASKARI, A., Peridynamic model for fatigue cracking, Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States), 2014.

ZHANG, G., Le, Q., Loghin, A., Subramaniyan, A., Bobaru, F., Validation of a peridynamic model for fatigue cracking, Engineering Fracture Mechanics, 162, pp. 76–94, 2016.

SILLING, S.A., ASKARI, E., A meshfree method based on the peridynamic model of solid mechanics, Computers & Structures, 83, 17, pp. 1526–1535, 2005.

BOBARU, F., HA, Y.D., Adaptive refinement and multiscale modeling in 2D peridynamics, Journal for Multiscale Computational Engineering, 9, 6, pp. 635–659, 2011.

KLESNIL, M., LUKÁŠ, P., Fatigue of metallic materials, Vol. 71, Elsevier, 1992.

FARAHMAND, B., Fracture mechanics of metals, composites, welds, and bolted joints: application of LEFM, EPFM, and FMDM theory, Springer Science & Business Media, 2012.

NOCEDAL, J., WRIGHT, S., Numerical optimization, Springer Science & Business Media, 2006.

SHEWCHUK, J.R., An introduction to the conjugate gradient method without the agonizing pain, Carnegie-Mellon University. Department of Computer Science, 1994, www.cs.cmu.edu/ ~quake-papers/painless-conjugate-gradient.pdf

SELESON, P., Improved one-point quadrature algorithms for two-dimensional peridynamic models based on analytical calculations, Computer Methods in Applied Mechanics and Engineering, 282, pp. 184–217, 2014.

LE, Q., BOBARU, F., Surface corrections in peridynamic models in elasticity and fracture, International Journal of Solids and Structures, 2016, in review.

BOARDMAN, B., Fatigue resistance of steels, ASM International, Metals Handbook (Tenth Edition), 1, pp. 673–688, 1990.

FROST, N.E., MARSH, K.J., POOK, L.P., Metal fatigue, Courier Corporation, 1974.

MIRANDA, A.C.O., MEGGIOLARO, M.A., CASTRO, J.T.P., MARTHA, L.F., BITTENCOURT, T.N., Fatigue life and crack path predictions in generic 2D structural components, Engineering Fracture Mechanics, 70, 10, pp. 1259–1279, 2003.

## Published

## Issue

## Section

Copyright (c) 2020 The Romanian Journal of Technical Sciences. Applied Mechanics.

This work is licensed under a Creative Commons Attribution 4.0 International License.