### Abstract

An empirical formula for the stress concentration factor is developed for an unequal-sized cavity pair in an arbitrary orientation. Three-dimensional finite element linear elastic analyses are performed to evaluate the stress concentration factors for different sizes, orientations, and separations of cavities. A suitable mathematical function is chosen to fit the numerical results of the finite element analyses. An application is given for evaluating the maximum stress concentration factor, which governs fatigue crack initiation in aluminum die cast test pieces from an engine block. From the X-ray CT image, the location and geometry of the gas pores are evaluated so as to develop the proposed empirical formula for this actual multi-pore system simplified to a dual spherical pore system. A proof of the formula is shown by comparison with voxel finite element analysis. The proposed empirical formula can be satisfactorily used as a scientific guideline for selecting a casting method for car engine blocks from a fatigue crack initiation perspective.

Original language | English |
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Pages (from-to) | 5707-5723 |

Number of pages | 17 |

Journal | Applied Mathematical Modelling |

Volume | 39 |

Issue number | 18 |

DOIs | |

Publication status | Published - 2015 Sep 15 |

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### Keywords

- Curve fitting
- Die cast aluminum
- Dual cavity
- Finite element method
- Porosity
- Stress concentration

### ASJC Scopus subject areas

- Applied Mathematics
- Modelling and Simulation

### Cite this

*Applied Mathematical Modelling*,

*39*(18), 5707-5723. https://doi.org/10.1016/j.apm.2015.01.032