### 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 |
---|---|

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 |

### Fingerprint

### 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

**Empirical formulation of stress concentration factor around an arbitrary-sized spherical dual-cavity system and its application to aluminum die castings.** / Bidhar, S.; Kuwazuru, O.; Shiihara, Y.; Utsunomiya, Takao; Hangai, Y.; Nomura, M.; Watanabe, I.; Yoshikawa, N.

Research output: Contribution to journal › Article

*Applied Mathematical Modelling*, vol. 39, no. 18, pp. 5707-5723. https://doi.org/10.1016/j.apm.2015.01.032

}

TY - JOUR

T1 - Empirical formulation of stress concentration factor around an arbitrary-sized spherical dual-cavity system and its application to aluminum die castings

AU - Bidhar, S.

AU - Kuwazuru, O.

AU - Shiihara, Y.

AU - Utsunomiya, Takao

AU - Hangai, Y.

AU - Nomura, M.

AU - Watanabe, I.

AU - Yoshikawa, N.

PY - 2015/9/15

Y1 - 2015/9/15

N2 - 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.

AB - 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.

KW - Curve fitting

KW - Die cast aluminum

KW - Dual cavity

KW - Finite element method

KW - Porosity

KW - Stress concentration

UR - http://www.scopus.com/inward/record.url?scp=84938554153&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84938554153&partnerID=8YFLogxK

U2 - 10.1016/j.apm.2015.01.032

DO - 10.1016/j.apm.2015.01.032

M3 - Article

AN - SCOPUS:84938554153

VL - 39

SP - 5707

EP - 5723

JO - Applied Mathematical Modelling

JF - Applied Mathematical Modelling

SN - 0307-904X

IS - 18

ER -