### Abstract

We examine the effects of random spatial fluctuations in the yield limit on the strength of a cylindrical tube subjected to internal pressure in plane strain conditions. The analysis is conducted along the lines laid in [1], where a generalization of the method of slip-lines to random media was outlined. The basic role in this formulation is played by a Representative Volume Element (RVE) of scale δ = L/d, where L is the scale of observation while d is the size of a single grain in a polycrystalline medium. Since the microstructure is random, the yield condition of an RVE at a given δ is random and, hence, the approximating continuum is a random medium. Due to the presence of material inhomogeneities in random media, the deterministic characteristics (slip-lines) of the homogeneous medium problems are replaced by forward evolution cones representing the ranges of scatter in stochastic characteristics. Consequently, the logarithmic spirals of the deterministic problem are randomly distorted lines and extend the external radius of the plastic zone. The tube has thus to be made thicker in order to withstand the same limit internal pressure as the one made of a homogeneous material described by the average 〈k〉. The analysis may easily be extended to an arbitrary axisymmetric traction on the hole.

Original language | English (US) |
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Title of host publication | Recent Advances in Structural Mechanics - 1992 |

Publisher | Publ by ASME |

Pages | 87-92 |

Number of pages | 6 |

Volume | 248 |

ISBN (Print) | 079181131X |

State | Published - 1992 |

Externally published | Yes |

Event | Winter Annual Meeting of the American Society of Mechanical Engineers - Anaheim, CA, USA Duration: Nov 8 1992 → Nov 13 1992 |

### Other

Other | Winter Annual Meeting of the American Society of Mechanical Engineers |
---|---|

City | Anaheim, CA, USA |

Period | 11/8/92 → 11/13/92 |

### Fingerprint

### ASJC Scopus subject areas

- Industrial and Manufacturing Engineering
- Mechanical Engineering

### Cite this

*Recent Advances in Structural Mechanics - 1992*(Vol. 248, pp. 87-92). Publ by ASME.

**Limit analysis of a cylindrical tube of a random inhomogeneous plastic material under internal pressure.** / Starzewski, Martin Ostoja; Setyabudhy, R.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Recent Advances in Structural Mechanics - 1992.*vol. 248, Publ by ASME, pp. 87-92, Winter Annual Meeting of the American Society of Mechanical Engineers, Anaheim, CA, USA, 11/8/92.

}

TY - GEN

T1 - Limit analysis of a cylindrical tube of a random inhomogeneous plastic material under internal pressure

AU - Starzewski, Martin Ostoja

AU - Setyabudhy, R.

PY - 1992

Y1 - 1992

N2 - We examine the effects of random spatial fluctuations in the yield limit on the strength of a cylindrical tube subjected to internal pressure in plane strain conditions. The analysis is conducted along the lines laid in [1], where a generalization of the method of slip-lines to random media was outlined. The basic role in this formulation is played by a Representative Volume Element (RVE) of scale δ = L/d, where L is the scale of observation while d is the size of a single grain in a polycrystalline medium. Since the microstructure is random, the yield condition of an RVE at a given δ is random and, hence, the approximating continuum is a random medium. Due to the presence of material inhomogeneities in random media, the deterministic characteristics (slip-lines) of the homogeneous medium problems are replaced by forward evolution cones representing the ranges of scatter in stochastic characteristics. Consequently, the logarithmic spirals of the deterministic problem are randomly distorted lines and extend the external radius of the plastic zone. The tube has thus to be made thicker in order to withstand the same limit internal pressure as the one made of a homogeneous material described by the average 〈k〉. The analysis may easily be extended to an arbitrary axisymmetric traction on the hole.

AB - We examine the effects of random spatial fluctuations in the yield limit on the strength of a cylindrical tube subjected to internal pressure in plane strain conditions. The analysis is conducted along the lines laid in [1], where a generalization of the method of slip-lines to random media was outlined. The basic role in this formulation is played by a Representative Volume Element (RVE) of scale δ = L/d, where L is the scale of observation while d is the size of a single grain in a polycrystalline medium. Since the microstructure is random, the yield condition of an RVE at a given δ is random and, hence, the approximating continuum is a random medium. Due to the presence of material inhomogeneities in random media, the deterministic characteristics (slip-lines) of the homogeneous medium problems are replaced by forward evolution cones representing the ranges of scatter in stochastic characteristics. Consequently, the logarithmic spirals of the deterministic problem are randomly distorted lines and extend the external radius of the plastic zone. The tube has thus to be made thicker in order to withstand the same limit internal pressure as the one made of a homogeneous material described by the average 〈k〉. The analysis may easily be extended to an arbitrary axisymmetric traction on the hole.

UR - http://www.scopus.com/inward/record.url?scp=0026966734&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0026966734&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:0026966734

SN - 079181131X

VL - 248

SP - 87

EP - 92

BT - Recent Advances in Structural Mechanics - 1992

PB - Publ by ASME

ER -