skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Assessment of surface and bulk-dominated methodologies to measure critical resolved shear stresses in hexagonal materials

Abstract

Crystallographic slip in hexagonal metals involves a number of geometrically distinct slip families characterized by their slip direction and slip plane (basal, prismatic, and pyramidal). Owing to the low symmetry of hexagonal lattices, each of these slip families only have a few symmetrically equivalent slip systems (family members). Furthermore, different slip families become active at different resolved shear stress, i.e., they have different critical resolved shear stress values (CRSS). The plastic anisotropy of hexagonal materials makes the numerical prediction of their plastic behavior challenging and depends critically on the knowledge of CRSS values. The present contribution assesses the reliability of three proposed methods (with additional variations) to quantify CRSS values of the different hexagonal slip families. Those methods (a to c) rely on: (a) the statistics of observed surface slip traces in a (slightly) deformed polycrystal; (b) an iterative adjustment of CRSS values until a simulated single crystal indentation matches the corresponding experiment in terms of load–displacement response and residual surface topography of the indent; (c) in-situ high-energy X-ray diffraction to measure the evolution of resolved stress (from lattice strains) in grains for which single-family slip is probable based upon specific lattice reorientation conditions. Virtual experiments are performed on syntheticmore » microstructures such that the (extracted) CRSS values resulting from simulating the different methodologies can be rigorously compared against the (target) CRSS values that are installed in the phenomenological constitutive material description used in the simulations. The resulting CRSS values of methods (a) exhibit a strong dependence on, and deterioration with, decreasing level of slip trace observability, which is an uncertain quantity in experimental measurements. For the inverse indentation method (b), the predicted CRSS values are within 8 % of their reference CRSS values for the two investigated cases. The high-energy X-ray diffraction method (c) most reliably determines CRSS values for basal and prism slip, but lacks a strict grain selection criterion to assess pyramidal slip.« less

Authors:
 [1];  [1]; ORCiD logo [1];  [1]; ORCiD logo [1]
  1. Michigan State Univ., East Lansing, MI (United States)
Publication Date:
Research Org.:
Michigan State Univ., East Lansing, MI (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES). Materials Sciences & Engineering Division; National Science Foundation (NSF); USDOE
OSTI Identifier:
1595226
Alternate Identifier(s):
OSTI ID: 1770940; OSTI ID: 1780086
Grant/Contract Number:  
SC0001525; DMR-1507489; DMR-1411102
Resource Type:
Accepted Manuscript
Journal Name:
Acta Materialia
Additional Journal Information:
Journal Volume: 184; Journal Issue: C; Journal ID: ISSN 1359-6454
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
36 MATERIALS SCIENCE; Virtual experiments; Surface slip trace; Nanoindentation; High-energy X-ray diffraction microscopy

Citation Formats

Chakraborty, Aritra, Zhang, Chen, Balachandran, Shanoob, Bieler, Thomas R., and Eisenlohr, Philip. Assessment of surface and bulk-dominated methodologies to measure critical resolved shear stresses in hexagonal materials. United States: N. p., 2019. Web. https://doi.org/10.1016/j.actamat.2019.11.023.
Chakraborty, Aritra, Zhang, Chen, Balachandran, Shanoob, Bieler, Thomas R., & Eisenlohr, Philip. Assessment of surface and bulk-dominated methodologies to measure critical resolved shear stresses in hexagonal materials. United States. https://doi.org/10.1016/j.actamat.2019.11.023
Chakraborty, Aritra, Zhang, Chen, Balachandran, Shanoob, Bieler, Thomas R., and Eisenlohr, Philip. Tue . "Assessment of surface and bulk-dominated methodologies to measure critical resolved shear stresses in hexagonal materials". United States. https://doi.org/10.1016/j.actamat.2019.11.023. https://www.osti.gov/servlets/purl/1595226.
@article{osti_1595226,
title = {Assessment of surface and bulk-dominated methodologies to measure critical resolved shear stresses in hexagonal materials},
author = {Chakraborty, Aritra and Zhang, Chen and Balachandran, Shanoob and Bieler, Thomas R. and Eisenlohr, Philip},
abstractNote = {Crystallographic slip in hexagonal metals involves a number of geometrically distinct slip families characterized by their slip direction and slip plane (basal, prismatic, and pyramidal). Owing to the low symmetry of hexagonal lattices, each of these slip families only have a few symmetrically equivalent slip systems (family members). Furthermore, different slip families become active at different resolved shear stress, i.e., they have different critical resolved shear stress values (CRSS). The plastic anisotropy of hexagonal materials makes the numerical prediction of their plastic behavior challenging and depends critically on the knowledge of CRSS values. The present contribution assesses the reliability of three proposed methods (with additional variations) to quantify CRSS values of the different hexagonal slip families. Those methods (a to c) rely on: (a) the statistics of observed surface slip traces in a (slightly) deformed polycrystal; (b) an iterative adjustment of CRSS values until a simulated single crystal indentation matches the corresponding experiment in terms of load–displacement response and residual surface topography of the indent; (c) in-situ high-energy X-ray diffraction to measure the evolution of resolved stress (from lattice strains) in grains for which single-family slip is probable based upon specific lattice reorientation conditions. Virtual experiments are performed on synthetic microstructures such that the (extracted) CRSS values resulting from simulating the different methodologies can be rigorously compared against the (target) CRSS values that are installed in the phenomenological constitutive material description used in the simulations. The resulting CRSS values of methods (a) exhibit a strong dependence on, and deterioration with, decreasing level of slip trace observability, which is an uncertain quantity in experimental measurements. For the inverse indentation method (b), the predicted CRSS values are within 8 % of their reference CRSS values for the two investigated cases. The high-energy X-ray diffraction method (c) most reliably determines CRSS values for basal and prism slip, but lacks a strict grain selection criterion to assess pyramidal slip.},
doi = {10.1016/j.actamat.2019.11.023},
journal = {Acta Materialia},
number = C,
volume = 184,
place = {United States},
year = {2019},
month = {11}
}

Journal Article:

Citation Metrics:
Cited by: 1 work
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

Creep and plasticity of hexagonal polycrystals as related to single crystal slip
journal, September 1977


A three-dimensional crystal plasticity model for duplex Ti–6Al–4V
journal, September 2007


The role of heterogeneous deformation on damage nucleation at grain boundaries in single phase metals
journal, September 2009


Simulation of slip band evolution in duplex Ti–6Al–4V
journal, February 2010


Quantitative Atomic Force Microscopy Characterization and Crystal Plasticity Finite Element Modeling of Heterogeneous Deformation in Commercial Purity Titanium
journal, December 2010

  • Yang, Y.; Wang, L.; Bieler, T. R.
  • Metallurgical and Materials Transactions A, Vol. 42, Issue 3
  • DOI: 10.1007/s11661-010-0475-0

Experimental Characterization and Crystal Plasticity Modeling of Heterogeneous Deformation in Polycrystalline α-Ti
journal, June 2010

  • Wang, L.; Barabash, R. I.; Yang, Y.
  • Metallurgical and Materials Transactions A, Vol. 42, Issue 3
  • DOI: 10.1007/s11661-010-0249-8

A crystal plasticity FE model for deformation with twin nucleation in magnesium alloys
journal, April 2015


A crystal-plasticity FEM study on effects of simplified grain representation and mesh types on mesoscopic plasticity heterogeneities
journal, September 2012


Effect of realistic 3D microstructure in crystal plasticity finite element analysis of polycrystalline Ti-5Al-2.5Sn
journal, June 2015


Crystal plasticity analysis of the deformation of a grade 2 CP-Ti oligocrystal
journal, July 2018


Methodology for estimating the critical resolved shear stress ratios of α-phase Ti using EBSD-based trace analysis
journal, December 2013


Plastic anisotropy of γ-TiAl revealed by axisymmetric indentation
journal, May 2010


Orientation informed nanoindentation of α-titanium: Indentation pileup in hexagonal metals deforming by prismatic slip
journal, December 2011

  • Zambaldi, Claudio; Yang, Yiyi; Bieler, Thomas R.
  • Journal of Materials Research, Vol. 27, Issue 1
  • DOI: 10.1557/jmr.2011.334

An inverse optimization strategy to determine single crystal mechanical behavior from polycrystal tests: Application to AZ31 Mg alloy
journal, June 2014


Modeling slip system strength evolution in Ti-7Al informed by in-situ grain stress measurements
journal, April 2017


Measuring Ti-7Al slip system strengths at elevated temperature using high-energy X-ray diffraction
journal, January 2018


Modeling bending of α-titanium with embedded polycrystal plasticity in implicit finite elements
journal, March 2013

  • Knezevic, Marko; Lebensohn, Ricardo A.; Cazacu, Oana
  • Materials Science and Engineering: A, Vol. 564
  • DOI: 10.1016/j.msea.2012.11.037

Strain hardening due to deformation twinning in α-titanium: Constitutive relations and crystal-plasticity modeling
journal, July 2005


Lattice strain evolution during tensile and compressive loading of CP Ti
journal, November 2012


Micro-cantilever testing of ⟨a⟩ prismatic slip in commercially pure Ti
journal, March 2011


Micromechanical modeling of hardening mechanisms in commercially pure α-titanium in tensile condition
journal, May 2016


Experimental and theoretical studies of intergranular strain in an alpha titanium alloy during plastic deformation
journal, September 2013


In situ monitoring of the deformation mechanisms in titanium with different oxygen contents
journal, June 2015


Effective values of critical resolved shear stress for slip in polycrystalline magnesium and other hcp metals
journal, October 2010


Elastic-Plastic Deformation at Finite Strains
journal, March 1969


An analysis of nonuniform and localized deformation in ductile single crystals
journal, June 1982


Numerically robust spectral methods for crystal plasticity simulations of heterogeneous materials
journal, March 2015


A spectral method solution to crystal elasto-viscoplasticity at finite strains
journal, July 2013


A Simplex Method for Function Minimization
journal, January 1965


Evaluation of an inverse methodology for estimating constitutive parameters in face-centered cubic materials from single crystal indentations
journal, November 2017


Factorial Sampling Plans for Preliminary Computational Experiments
journal, May 1991