### Abstract

The formulations of self-consistent schemes for elastic-plastic deformations of polycrystals are based on the solution of an ellipsoidal inclusion embedded in an infinite matrix. Because of the non-linear nature of the problem, no exact solution is available and simplifying assumptions have to be made. Unlike the classical bounds, the self-consistent models are called for to account for the heterogeneity of deformation from grain to grain within a polycrystalline aggregate. However, because of simplifying assumptions, results from some of these models may turn out to be very close to those of the Taylor's upper bound formulations. This has been the case for elastic-plastic formulations with time-dependent plasticity (elastic-visco-plastic) in which high matrix/inclusion interactions have yielded high flow stresses and negligible deviations of the deformations from grain to grain. In an attempt to soften these interactions, new elastic-viscoplastic formulations have recently been proposed. We present a non-incremental scheme for elastic-viscoplastic deformations along with the discussion of its validity. Results from this simplified formulation are also presented with particular application to FCC metals under axisymmetric and cyclic loadings. We propose a generalization of this non-incremental formulation to include full anisotropic and elastic compressibility. We also give a rational discussion of the existing elastic-plastic self-consistent schemes for both time dependent and time independent plasticity. Based on our comparison of results from different self-consistent approaches, we discuss the validity of the incremental versus non-incremental formulations and the use of tangent versus the secant modulus in these formulations.

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

Pages (from-to) | 43-62 |

Number of pages | 20 |

Journal | Mechanics of Materials |

Volume | 26 |

Issue number | 1 |

Publication status | Published - Jul 1997 |

Externally published | Yes |

### Fingerprint

### ASJC Scopus subject areas

- Mechanics of Materials

### Cite this

*Mechanics of Materials*,

*26*(1), 43-62.

**On the self-consistent modeling of elastic-plastic behavior of polycrystals.** / Molinari, A.; Ahzi, Said; Kouddane, R.

Research output: Contribution to journal › Article

*Mechanics of Materials*, vol. 26, no. 1, pp. 43-62.

}

TY - JOUR

T1 - On the self-consistent modeling of elastic-plastic behavior of polycrystals

AU - Molinari, A.

AU - Ahzi, Said

AU - Kouddane, R.

PY - 1997/7

Y1 - 1997/7

N2 - The formulations of self-consistent schemes for elastic-plastic deformations of polycrystals are based on the solution of an ellipsoidal inclusion embedded in an infinite matrix. Because of the non-linear nature of the problem, no exact solution is available and simplifying assumptions have to be made. Unlike the classical bounds, the self-consistent models are called for to account for the heterogeneity of deformation from grain to grain within a polycrystalline aggregate. However, because of simplifying assumptions, results from some of these models may turn out to be very close to those of the Taylor's upper bound formulations. This has been the case for elastic-plastic formulations with time-dependent plasticity (elastic-visco-plastic) in which high matrix/inclusion interactions have yielded high flow stresses and negligible deviations of the deformations from grain to grain. In an attempt to soften these interactions, new elastic-viscoplastic formulations have recently been proposed. We present a non-incremental scheme for elastic-viscoplastic deformations along with the discussion of its validity. Results from this simplified formulation are also presented with particular application to FCC metals under axisymmetric and cyclic loadings. We propose a generalization of this non-incremental formulation to include full anisotropic and elastic compressibility. We also give a rational discussion of the existing elastic-plastic self-consistent schemes for both time dependent and time independent plasticity. Based on our comparison of results from different self-consistent approaches, we discuss the validity of the incremental versus non-incremental formulations and the use of tangent versus the secant modulus in these formulations.

AB - The formulations of self-consistent schemes for elastic-plastic deformations of polycrystals are based on the solution of an ellipsoidal inclusion embedded in an infinite matrix. Because of the non-linear nature of the problem, no exact solution is available and simplifying assumptions have to be made. Unlike the classical bounds, the self-consistent models are called for to account for the heterogeneity of deformation from grain to grain within a polycrystalline aggregate. However, because of simplifying assumptions, results from some of these models may turn out to be very close to those of the Taylor's upper bound formulations. This has been the case for elastic-plastic formulations with time-dependent plasticity (elastic-visco-plastic) in which high matrix/inclusion interactions have yielded high flow stresses and negligible deviations of the deformations from grain to grain. In an attempt to soften these interactions, new elastic-viscoplastic formulations have recently been proposed. We present a non-incremental scheme for elastic-viscoplastic deformations along with the discussion of its validity. Results from this simplified formulation are also presented with particular application to FCC metals under axisymmetric and cyclic loadings. We propose a generalization of this non-incremental formulation to include full anisotropic and elastic compressibility. We also give a rational discussion of the existing elastic-plastic self-consistent schemes for both time dependent and time independent plasticity. Based on our comparison of results from different self-consistent approaches, we discuss the validity of the incremental versus non-incremental formulations and the use of tangent versus the secant modulus in these formulations.

UR - http://www.scopus.com/inward/record.url?scp=0031187394&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0031187394&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0031187394

VL - 26

SP - 43

EP - 62

JO - Mechanics of Materials

JF - Mechanics of Materials

SN - 0167-6636

IS - 1

ER -