### Abstract

An empirical method is developed for obtaining the stress concentration factor for a pair of equally sized spherical cavities embedded in a large continuum in three-dimensional space. For practical applications such as die-cast materials containing many pores, we construct a simple and robust closed-form equation to evaluate the stress concentration factor considering the interaction between two cavities. The stress concentration factor can be used to evaluate the effect of pores on the material strength and the probable location of pores that will initiate a fatigue crack. Three-dimensional finite element linear elastic analysis was carried out to evaluate the stress concentration factors for arbitrary locations of the two cavities. The effects of the inter-cavity distance and the orientation of the inter-cavity axis with respect to the loading direction on the stress concentration factor are numerically obtained by systematically changing each of these parameters. Two empirical equations are proposed to fit the stress concentration factor data calculated by finite element analysis after considering various boundary conditions from a mechanical standpoint, and the parameters of the empirical formula are obtained by non-linear curve fitting with regression analysis.

Original language | English |
---|---|

Pages (from-to) | 881-893 |

Number of pages | 13 |

Journal | Applied Mathematical Modelling |

Volume | 39 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2015 |

### Fingerprint

### Keywords

- Aluminum die cast
- Dual cavity
- Finite element method
- Porosity
- Stress concentration

### ASJC Scopus subject areas

- Applied Mathematics
- Modelling and Simulation

### Cite this

*Applied Mathematical Modelling*,

*39*(2), 881-893. https://doi.org/10.1016/j.apm.2014.07.005

**Practical application of empirical formulation of the stress concentration factor around equally sized dual spherical cavities to aluminum die cast.** / Bidhar, Sujit; Kuwazuru, Osamu; Shiihara, Yoshinori; Hangai, Yoshihiko; Utsunomiya, Takao; Watanabe, Ikumu; Yoshikawa, Nobuhiro.

Research output: Contribution to journal › Article

*Applied Mathematical Modelling*, vol. 39, no. 2, pp. 881-893. https://doi.org/10.1016/j.apm.2014.07.005

}

TY - JOUR

T1 - Practical application of empirical formulation of the stress concentration factor around equally sized dual spherical cavities to aluminum die cast

AU - Bidhar, Sujit

AU - Kuwazuru, Osamu

AU - Shiihara, Yoshinori

AU - Hangai, Yoshihiko

AU - Utsunomiya, Takao

AU - Watanabe, Ikumu

AU - Yoshikawa, Nobuhiro

PY - 2015

Y1 - 2015

N2 - An empirical method is developed for obtaining the stress concentration factor for a pair of equally sized spherical cavities embedded in a large continuum in three-dimensional space. For practical applications such as die-cast materials containing many pores, we construct a simple and robust closed-form equation to evaluate the stress concentration factor considering the interaction between two cavities. The stress concentration factor can be used to evaluate the effect of pores on the material strength and the probable location of pores that will initiate a fatigue crack. Three-dimensional finite element linear elastic analysis was carried out to evaluate the stress concentration factors for arbitrary locations of the two cavities. The effects of the inter-cavity distance and the orientation of the inter-cavity axis with respect to the loading direction on the stress concentration factor are numerically obtained by systematically changing each of these parameters. Two empirical equations are proposed to fit the stress concentration factor data calculated by finite element analysis after considering various boundary conditions from a mechanical standpoint, and the parameters of the empirical formula are obtained by non-linear curve fitting with regression analysis.

AB - An empirical method is developed for obtaining the stress concentration factor for a pair of equally sized spherical cavities embedded in a large continuum in three-dimensional space. For practical applications such as die-cast materials containing many pores, we construct a simple and robust closed-form equation to evaluate the stress concentration factor considering the interaction between two cavities. The stress concentration factor can be used to evaluate the effect of pores on the material strength and the probable location of pores that will initiate a fatigue crack. Three-dimensional finite element linear elastic analysis was carried out to evaluate the stress concentration factors for arbitrary locations of the two cavities. The effects of the inter-cavity distance and the orientation of the inter-cavity axis with respect to the loading direction on the stress concentration factor are numerically obtained by systematically changing each of these parameters. Two empirical equations are proposed to fit the stress concentration factor data calculated by finite element analysis after considering various boundary conditions from a mechanical standpoint, and the parameters of the empirical formula are obtained by non-linear curve fitting with regression analysis.

KW - Aluminum die cast

KW - Dual cavity

KW - Finite element method

KW - Porosity

KW - Stress concentration

UR - http://www.scopus.com/inward/record.url?scp=84922636859&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84922636859&partnerID=8YFLogxK

U2 - 10.1016/j.apm.2014.07.005

DO - 10.1016/j.apm.2014.07.005

M3 - Article

AN - SCOPUS:84922636859

VL - 39

SP - 881

EP - 893

JO - Applied Mathematical Modelling

JF - Applied Mathematical Modelling

SN - 0307-904X

IS - 2

ER -