Two stochastic mean-field polycrystal plasticity methods

Michael R. Tonks, John F. Bingert, Curt A. Bronkhorst, Eric N. Harstad, Daniel A. Tortorelli

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

In this work, we develop two mean-field polycrystal plasticity models in which the crystal velocity gradients Lc are approximated stochastically. Through comprehensive CPFEM analyses of an idealized tantalum polycrystal, we verify that the Lc tend to follow a normal distribution and surmise that this is due to the crystal interactions. We draw on these results to develop the stochastic Taylor model (STM) and the stochastic no-constraints model (SNCM), which differ in the manner in which the crystal strain rates Dc = frac(1, 2) (Lc + Lc T) are prescribed. Calibration and validation of the models are performed using data from tantalum compression experiments. Both models predict the compression textures more accurately than the fully constrained model (FCM), and the SNCM predicts them more accurately than the STM. The STM is extremely computationally efficient, only slightly more expensive than the FCM, while the SNCM is three times more computationally expensive than the STM.

Original languageEnglish (US)
Pages (from-to)1230-1253
Number of pages24
JournalJournal of the Mechanics and Physics of Solids
Volume57
Issue number8
DOIs
StatePublished - Aug 1 2009

Fingerprint

Polycrystals
polycrystals
plastic properties
Plasticity
Tantalum
tantalum
Crystals
crystals
Normal distribution
normal density functions
strain rate
Strain rate
textures
Textures
Calibration

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering

Cite this

Tonks, M. R., Bingert, J. F., Bronkhorst, C. A., Harstad, E. N., & Tortorelli, D. A. (2009). Two stochastic mean-field polycrystal plasticity methods. Journal of the Mechanics and Physics of Solids, 57(8), 1230-1253. https://doi.org/10.1016/j.jmps.2009.04.013
Tonks, Michael R. ; Bingert, John F. ; Bronkhorst, Curt A. ; Harstad, Eric N. ; Tortorelli, Daniel A. / Two stochastic mean-field polycrystal plasticity methods. In: Journal of the Mechanics and Physics of Solids. 2009 ; Vol. 57, No. 8. pp. 1230-1253.
@article{9fe60dee4a774bd39d7870322be01064,
title = "Two stochastic mean-field polycrystal plasticity methods",
abstract = "In this work, we develop two mean-field polycrystal plasticity models in which the crystal velocity gradients Lc are approximated stochastically. Through comprehensive CPFEM analyses of an idealized tantalum polycrystal, we verify that the Lc tend to follow a normal distribution and surmise that this is due to the crystal interactions. We draw on these results to develop the stochastic Taylor model (STM) and the stochastic no-constraints model (SNCM), which differ in the manner in which the crystal strain rates Dc = frac(1, 2) (Lc + Lc T) are prescribed. Calibration and validation of the models are performed using data from tantalum compression experiments. Both models predict the compression textures more accurately than the fully constrained model (FCM), and the SNCM predicts them more accurately than the STM. The STM is extremely computationally efficient, only slightly more expensive than the FCM, while the SNCM is three times more computationally expensive than the STM.",
author = "Tonks, {Michael R.} and Bingert, {John F.} and Bronkhorst, {Curt A.} and Harstad, {Eric N.} and Tortorelli, {Daniel A.}",
year = "2009",
month = "8",
day = "1",
doi = "10.1016/j.jmps.2009.04.013",
language = "English (US)",
volume = "57",
pages = "1230--1253",
journal = "Journal of the Mechanics and Physics of Solids",
issn = "0022-5096",
publisher = "Elsevier Limited",
number = "8",

}

Tonks, MR, Bingert, JF, Bronkhorst, CA, Harstad, EN & Tortorelli, DA 2009, 'Two stochastic mean-field polycrystal plasticity methods', Journal of the Mechanics and Physics of Solids, vol. 57, no. 8, pp. 1230-1253. https://doi.org/10.1016/j.jmps.2009.04.013

Two stochastic mean-field polycrystal plasticity methods. / Tonks, Michael R.; Bingert, John F.; Bronkhorst, Curt A.; Harstad, Eric N.; Tortorelli, Daniel A.

In: Journal of the Mechanics and Physics of Solids, Vol. 57, No. 8, 01.08.2009, p. 1230-1253.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Two stochastic mean-field polycrystal plasticity methods

AU - Tonks, Michael R.

AU - Bingert, John F.

AU - Bronkhorst, Curt A.

AU - Harstad, Eric N.

AU - Tortorelli, Daniel A.

PY - 2009/8/1

Y1 - 2009/8/1

N2 - In this work, we develop two mean-field polycrystal plasticity models in which the crystal velocity gradients Lc are approximated stochastically. Through comprehensive CPFEM analyses of an idealized tantalum polycrystal, we verify that the Lc tend to follow a normal distribution and surmise that this is due to the crystal interactions. We draw on these results to develop the stochastic Taylor model (STM) and the stochastic no-constraints model (SNCM), which differ in the manner in which the crystal strain rates Dc = frac(1, 2) (Lc + Lc T) are prescribed. Calibration and validation of the models are performed using data from tantalum compression experiments. Both models predict the compression textures more accurately than the fully constrained model (FCM), and the SNCM predicts them more accurately than the STM. The STM is extremely computationally efficient, only slightly more expensive than the FCM, while the SNCM is three times more computationally expensive than the STM.

AB - In this work, we develop two mean-field polycrystal plasticity models in which the crystal velocity gradients Lc are approximated stochastically. Through comprehensive CPFEM analyses of an idealized tantalum polycrystal, we verify that the Lc tend to follow a normal distribution and surmise that this is due to the crystal interactions. We draw on these results to develop the stochastic Taylor model (STM) and the stochastic no-constraints model (SNCM), which differ in the manner in which the crystal strain rates Dc = frac(1, 2) (Lc + Lc T) are prescribed. Calibration and validation of the models are performed using data from tantalum compression experiments. Both models predict the compression textures more accurately than the fully constrained model (FCM), and the SNCM predicts them more accurately than the STM. The STM is extremely computationally efficient, only slightly more expensive than the FCM, while the SNCM is three times more computationally expensive than the STM.

UR - http://www.scopus.com/inward/record.url?scp=67649479260&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=67649479260&partnerID=8YFLogxK

U2 - 10.1016/j.jmps.2009.04.013

DO - 10.1016/j.jmps.2009.04.013

M3 - Article

AN - SCOPUS:67649479260

VL - 57

SP - 1230

EP - 1253

JO - Journal of the Mechanics and Physics of Solids

JF - Journal of the Mechanics and Physics of Solids

SN - 0022-5096

IS - 8

ER -

Tonks MR, Bingert JF, Bronkhorst CA, Harstad EN, Tortorelli DA. Two stochastic mean-field polycrystal plasticity methods. Journal of the Mechanics and Physics of Solids. 2009 Aug 1;57(8):1230-1253. https://doi.org/10.1016/j.jmps.2009.04.013