Estimation of micro-Hall-Petch coefficients for prismatic slip system in Mg-4Al as a function of grain boundary parameters

Andani, Mohsen Taheri; Lakshmanan, Aaditya; Sundararaghavan, Veera; Allison, John; Misra, Amit

doi:10.1016/j.actamat.2021.117613

Estimation of micro-Hall-Petch coefficients for prismatic slip system in Mg-4Al as a function of grain boundary parameters

Journal Article · Fri Dec 31 04:00:00 EST 2021 · Acta Materialia

DOI:https://doi.org/10.1016/j.actamat.2021.117613· OSTI ID:1976782

Andani, Mohsen Taheri ^[1]; Lakshmanan, Aaditya ^[2]; Sundararaghavan, Veera ^[2]; Allison, John ^[2]; Misra, Amit ^[2]

University of Michigan, Ann Arbor, MI (United States); OSTI
University of Michigan, Ann Arbor, MI (United States)

Grain size strengthening, referred to as the Hall-Petch effect, is a common strategy to improve the yield strength of magnesium (Mg) alloys. Several experimental studies have reported that the Hall-Petch slope strongly depends on the texture of the alloy. This effect arises from altering grain boundaries (GBs) resistance to different slip systems to transfer across adjacent grains. The grain boundary barrier strength of certain grain boundaries to basal slip, referred to as basal micro-Hall-Petch, was investigated in the previous work. Here in this study, the micro-Hall-Petch coefficient values for the prismatic slip $$(k^{prismatic}_{μ})$$ in Mg-4Al and their correlation with the grain boundary parameters were investigated. An experimental method was developed to initiate the prismatic slip band at low-stress levels. High-resolution electron backscatter diffraction (HR-EBSD) was used to measure the residual stress tensor, from which the resolved shear stress ahead of blocked prismatic slip bands was computed for seven different grain boundaries. $$(k^{prismatic}_{μ})$$ values for each individual GB were calculated by coupling the stress profile information with a continuum dislocation pile-up model. The $$(k^{prismatic}_{μ})$$ values vary from 0.138 MPa.m^1/2 to 0.685 MPa. m^1/2 which are almost three times larger than the calculated values for the basal micro-Hall-Petch. The $$(k^{prismatic}_{μ})$$ values were correlated with the GB parameters, and a functional relationship depending on the two most effective angles, the angle between the traces of the slip planes on the GB plane ($$\phi$$) and the angle between incoming and outgoing slip directions (κ), was proposed to estimate the Hall-Petch barrier for prismatic slip system. The work provides coefficients that can be supplied as input to crystal plasticity models to couple the effect of texture and grain size effectively.

View Accepted Manuscript (DOE)

Research Organization:: University of Michigan, Ann Arbor, MI (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES). Materials Sciences & Engineering Division (MSE)

Grant/Contract Number:: SC0008637

OSTI ID:: 1976782

Alternate ID(s):: OSTI ID: 1839305

Journal Information:: Acta Materialia, Journal Name: Acta Materialia Journal Issue: C Vol. 226; ISSN 1359-6454

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

References (61)

Strain Hardening Behavior in Mg–Al Alloys at Room Temperature Zhao, Chaoyue; Chen, Xianhua; Wang, Jingfeng Advanced Engineering Materials, Vol. 21, Issue 3 https://doi.org/10.1002/adem.201801062	journal	December 2018
The current trends of Mg alloys in biomedical applications—A review Riaz, Usman; Shabib, Ishraq; Haider, Waseem Journal of Biomedical Materials Research Part B: Applied Biomaterials, Vol. 107, Issue 6 https://doi.org/10.1002/jbm.b.34290	journal	December 2018
Gmsh: A 3-D finite element mesh generator with built-in pre- and post-processing facilities Geuzaine, Christophe; Remacle, Jean-François International Journal for Numerical Methods in Engineering, Vol. 79, Issue 11 https://doi.org/10.1002/nme.2579	journal	September 2009
Allgemeine Kontinuumstheorie der Versetzungen und Eigenspannungen Kröner, Ekkehart Archive for Rational Mechanics and Analysis, Vol. 4, Issue 1 https://doi.org/10.1007/BF00281393	journal	January 1959
AnIn Situ transmission electron microscope deformation study of the slip transfer mechanisms in metals Lee, T. C.; Robertson, I. M.; Birnbaum, H. K. Metallurgical Transactions A, Vol. 21, Issue 9 https://doi.org/10.1007/BF02646988	journal	September 1990
Dislocation behavior at tilt boundaries of infinite extent Marcinkowski, M. J.; Tseng, Wen Feng Metallurgical and Materials Transactions B, Vol. 1, Issue 12 https://doi.org/10.1007/BF03037870	journal	December 1970
Incorporation of Solid Solution Alloying Effects into Polycrystal Modeling of Mg Alloys Raeisinia, Babak; Agnew, Sean R.; Akhtar, Ainul Metallurgical and Materials Transactions A, Vol. 42, Issue 5 https://doi.org/10.1007/s11661-010-0527-5	journal	November 2010
Precipitation and Hardening in Magnesium Alloys Nie, Jian-Feng Metallurgical and Materials Transactions A, Vol. 43, Issue 11 https://doi.org/10.1007/s11661-012-1217-2	journal	July 2012
Magnesium alloy applications in automotive structures Easton, Mark; Beer, Aiden; Barnett, Matthew JOM, Vol. 60, Issue 11 https://doi.org/10.1007/s11837-008-0150-8	journal	November 2008
Single-crystal elastic constants of magnesium and magnesium alloys Long, T. R.; Smith, Charles S. Acta Metallurgica, Vol. 5, Issue 4 https://doi.org/10.1016/0001-6160(57)90166-9	journal	April 1957
The role of residual dislocation arrays in slip induced cavitation, migration and dynamic recrystallization at grain boundaries Lim, L. C.; Raj, R. Acta Metallurgica, Vol. 33, Issue 12 https://doi.org/10.1016/0001-6160(85)90182-8	journal	December 1985
Overview no. 42 Texture development and strain hardening in rate dependent polycrystals Asaro, R. J.; Needleman, A. Acta Metallurgica, Vol. 33, Issue 6 https://doi.org/10.1016/0001-6160(85)90188-9	journal	June 1985
Dislocation and grain boundary interactions in metals Shen, Z.; Wagoner, R. H.; Clark, W. A. T. Acta Metallurgica, Vol. 36, Issue 12 https://doi.org/10.1016/0001-6160(88)90058-2	journal	December 1988
A micromechanical theory of grain-size dependence in metal plasticity Weng, G. J. Journal of the Mechanics and Physics of Solids, Vol. 31, Issue 3 https://doi.org/10.1016/0022-5096(83)90021-2	journal	January 1983
Crystallographic texture evolution in bulk deformation processing of FCC metals Kalidindi, S. R.; Bronkhorst, C. A.; Anand, L. Journal of the Mechanics and Physics of Solids, Vol. 40, Issue 3 https://doi.org/10.1016/0022-5096(92)80003-9	journal	January 1992
Dislocation pile-up and grain boundary interactions in 304 stainless steel Shen, Z.; Wagoner, R. H.; Clark, W. A. T. Scripta Metallurgica, Vol. 20, Issue 6 https://doi.org/10.1016/0036-9748(86)90467-9	journal	June 1986
A model of crack-tip slip band blocked by grain boundary Taira, Shuji; Tanaka, Keisuke; Nakai, Yoshikazu Mechanics Research Communications, Vol. 5, Issue 6 https://doi.org/10.1016/0093-6413(78)90014-9	journal	January 1978
Constitutive equations for hot-working of metals Anand, Lallit International Journal of Plasticity, Vol. 1, Issue 3 https://doi.org/10.1016/0749-6419(85)90004-X	journal	January 1985
Quasicrystal strengthened Mg–Zn–Y alloys by extrusion Singh, Alok; Nakamura, M.; Watanabe, M. Scripta Materialia, Vol. 49, Issue 5 https://doi.org/10.1016/S1359-6462(03)00305-1	journal	September 2003
Deformation behavior of ultrafine-grain (UFG) AZ31B Mg alloy at room temperature Yang, Q.; Ghosh, A. K. Acta Materialia, Vol. 54, Issue 19 https://doi.org/10.1016/j.actamat.2006.06.043	journal	November 2006
Simulation of slip band evolution in duplex Ti–6Al–4V Zhang, M.; Bridier, F.; Villechaise, P. Acta Materialia, Vol. 58, Issue 3 https://doi.org/10.1016/j.actamat.2009.10.025	journal	February 2010
Effect of precipitate shape on slip and twinning in magnesium alloys Robson, J. D.; Stanford, N.; Barnett, M. R. Acta Materialia, Vol. 59, Issue 5 https://doi.org/10.1016/j.actamat.2010.11.060	journal	March 2011
Effect of plate-shaped particle distributions on the deformation behaviour of magnesium alloy AZ91 in tension and compression Stanford, N.; Geng, J.; Chun, Y. B. Acta Materialia, Vol. 60, Issue 1 https://doi.org/10.1016/j.actamat.2011.10.001	journal	January 2012
A probabilistic crystal plasticity model for modeling grain shape effects based on slip geometry Sun, Shang; Sundararaghavan, Veera Acta Materialia, Vol. 60, Issue 13-14 https://doi.org/10.1016/j.actamat.2012.05.039	journal	August 2012
Stress fields and geometrically necessary dislocation density distributions near the head of a blocked slip band Benjamin Britton, T.; Wilkinson, Angus J. Acta Materialia, Vol. 60, Issue 16 https://doi.org/10.1016/j.actamat.2012.07.004	journal	September 2012
Ductility improvement of Mg alloys by solid solution: Ab initio modeling, synthesis and mechanical properties Sandlöbes, S.; Pei, Z.; Friák, M. Acta Materialia, Vol. 70 https://doi.org/10.1016/j.actamat.2014.02.011	journal	May 2014
Influence of texture on Hall–Petch relationships in an Mg alloy Wang, Yi; Choo, Hahn Acta Materialia, Vol. 81 https://doi.org/10.1016/j.actamat.2014.08.023	journal	December 2014
The mechanism for the high dependence of the Hall-Petch slope for twinning/slip on texture in Mg alloys Yu, Huihui; Li, Changzheng; Xin, Yunchang Acta Materialia, Vol. 128 https://doi.org/10.1016/j.actamat.2017.02.044	journal	April 2017
Quantitative prediction of texture effect on Hall–Petch slope for magnesium alloys Guan, Bo; Xin, Yunchang; Huang, Xiaoxu Acta Materialia, Vol. 173 https://doi.org/10.1016/j.actamat.2019.05.016	journal	July 2019
Intragranular localization induced by softening crystal plasticity: Analysis of slip and kink bands localization modes from high resolution FFT-simulations results Marano, Aldo; Gélébart, Lionel; Forest, Samuel Acta Materialia, Vol. 175 https://doi.org/10.1016/j.actamat.2019.06.010	journal	August 2019
Effect of basal precipitates on extension twinning and pyramidal slip: A micro-mechanical and electron microscopy study of a Mg–Al binary alloy Ma, Xiaolong; Jiao, Quan; Kecskes, Laszlo J. Acta Materialia, Vol. 189 https://doi.org/10.1016/j.actamat.2020.02.037	journal	May 2020
Quantitative study of the effect of grain boundary parameters on the slip system level Hall-Petch slope for basal slip system in Mg-4Al Andani, Mohsen Taheri; Lakshmanan, Aaditya; Sundararaghavan, Veera Acta Materialia, Vol. 200 https://doi.org/10.1016/j.actamat.2020.08.079	journal	November 2020
A crystal plasticity investigation of grain size-texture interaction in magnesium alloys Ravaji, Babak; Joshi, Shailendra P. Acta Materialia, Vol. 208 https://doi.org/10.1016/j.actamat.2021.116743	journal	April 2021
PRISMS-Plasticity: An open-source crystal plasticity finite element software Yaghoobi, Mohammadreza; Ganesan, Sriram; Sundar, Srihari Computational Materials Science, Vol. 169 https://doi.org/10.1016/j.commatsci.2019.109078	journal	November 2019
Non-ordinary state-based peridynamic simulation of elastoplastic deformation and dynamic cracking of polycrystal Gu, Xin; Zhang, Qing; Madenci, Erdogan Engineering Fracture Mechanics, Vol. 218 https://doi.org/10.1016/j.engfracmech.2019.106568	journal	September 2019
Three-dimensional crystal plasticity simulations using peridynamics theory and experimental comparison Lakshmanan, Aaditya; Luo, Jiangyi; Javaheri, Iman International Journal of Plasticity, Vol. 142 https://doi.org/10.1016/j.ijplas.2021.102991	journal	July 2021
Effect of neighboring grain orientation on strain localization in slip bands in HCP materials Ahmadikia, Behnam; Kumar, M. Arul; Beyerlein, Irene J. International Journal of Plasticity, Vol. 144 https://doi.org/10.1016/j.ijplas.2021.103026	journal	September 2021
Mean-field polycrystal plasticity modeling with grain size and shape effects for laser additive manufactured FCC metals Liu, Jian; Xiong, Wei; Behera, Amit International Journal of Solids and Structures, Vol. 112 https://doi.org/10.1016/j.ijsolstr.2017.02.024	journal	May 2017
Simulation of micro-scale shear bands using peridynamics with an adaptive dynamic relaxation method Luo, J.; Ramazani, A.; Sundararaghavan, V. International Journal of Solids and Structures, Vol. 130-131 https://doi.org/10.1016/j.ijsolstr.2017.10.019	journal	January 2018
Phenomenological crystal plasticity modeling and detailed micromechanical investigations of pure magnesium Zhang, Jing; Joshi, Shailendra P. Journal of the Mechanics and Physics of Solids, Vol. 60, Issue 5 https://doi.org/10.1016/j.jmps.2012.01.005	journal	May 2012
Hall-Petch relationship in Mg alloys: A review Yu, Huihui; Xin, Yunchang; Wang, Maoyin Journal of Materials Science & Technology, Vol. 34, Issue 2 https://doi.org/10.1016/j.jmst.2017.07.022	journal	February 2018
Grain size effects on the tensile properties and deformation mechanisms of a magnesium alloy, AZ31B, sheet Jain, A.; Duygulu, O.; Brown, D. W. Materials Science and Engineering: A, Vol. 486, Issue 1-2 https://doi.org/10.1016/j.msea.2007.09.069	journal	July 2008
Ductility enhancement of extruded magnesium via yttrium addition Wu, B. L.; Zhao, Y. H.; Du, X. H. Materials Science and Engineering: A, Vol. 527, Issue 16-17 https://doi.org/10.1016/j.msea.2010.03.054	journal	June 2010
Effect of microstructure on strength and ductility of high strength quasicrystal phase dispersed Mg–Zn–Y alloys Singh, Alok; Osawa, Yoshiaki; Somekawa, Hidetoshi Materials Science and Engineering: A, Vol. 611 https://doi.org/10.1016/j.msea.2014.05.091	journal	August 2014
Microstructure, mechanical and corrosion properties and biocompatibility of Mg–Zn–Mn alloys for biomedical application Zhang, Erlin; Yin, Dongsong; Xu, Liping Materials Science and Engineering: C, Vol. 29, Issue 3 https://doi.org/10.1016/j.msec.2008.08.024	journal	April 2009
Texture and weak grain size dependence in friction stir processed Mg–Al–Zn alloy Wang, Y. N.; Chang, C. I.; Lee, C. J. Scripta Materialia, Vol. 55, Issue 7 https://doi.org/10.1016/j.scriptamat.2006.06.005	journal	October 2006
Influence of grain size and texture on Hall–Petch relationship for a magnesium alloy Yuan, W.; Panigrahi, S. K.; Su, J. -Q. Scripta Materialia, Vol. 65, Issue 11 https://doi.org/10.1016/j.scriptamat.2011.08.028	journal	December 2011
High-resolution elastic strain measurement from electron backscatter diffraction patterns: New levels of sensitivity Wilkinson, Angus J.; Meaden, Graham; Dingley, David J. Ultramicroscopy, Vol. 106, Issue 4-5 https://doi.org/10.1016/j.ultramic.2005.10.001	journal	March 2006
Measurement of residual elastic strain and lattice rotations with high resolution electron backscatter diffraction Britton, T. B.; Wilkinson, A. J. Ultramicroscopy, Vol. 111, Issue 8 https://doi.org/10.1016/j.ultramic.2011.05.007	journal	July 2011
Grain detection from 2d and 3d EBSD data—Specification of the MTEX algorithm Bachmann, Florian; Hielscher, Ralf; Schaeben, Helmut Ultramicroscopy, Vol. 111, Issue 12 https://doi.org/10.1016/j.ultramic.2011.08.002	journal	December 2011
High resolution electron backscatter diffraction measurements of elastic strain variations in the presence of larger lattice rotations Britton, T. B.; Wilkinson, A. J. Ultramicroscopy, Vol. 114 https://doi.org/10.1016/j.ultramic.2012.01.004	journal	March 2012
PRISMS-Fatigue computational framework for fatigue analysis in polycrystalline metals and alloys Yaghoobi, Mohammadreza; Stopka, Krzysztof S.; Lakshmanan, Aaditya npj Computational Materials, Vol. 7, Issue 1 https://doi.org/10.1038/s41524-021-00506-8	journal	March 2021
A quantitative study of stress fields ahead of a slip band blocked by a grain boundary in unalloyed magnesium Andani, Mohsen Taheri; Lakshmanan, Aaditya; Karamooz-Ravari, Mohammadreza Scientific Reports, Vol. 10, Issue 1 https://doi.org/10.1038/s41598-020-59684-y	journal	February 2020
The effect of grain size on fracture: Dislocation‐free zone in the front of the finite crack tip Shiue, Sham‐Tsong; Lee, Sanboh Journal of Applied Physics, Vol. 70, Issue 6 https://doi.org/10.1063/1.349319	journal	September 1991
TEM in situ deformation study of the interaction of lattice dislocations with grain boundaries in metals Lee, T. C.; Robertson, I. M.; Birnbaum, H. K. Philosophical Magazine A, Vol. 62, Issue 1 https://doi.org/10.1080/01418619008244340	journal	July 1990
The Deformation and Ageing of Mild Steel: III Discussion of Results Hall, E. O. Proceedings of the Physical Society. Section B, Vol. 64, Issue 9 https://doi.org/10.1088/0370-1301/64/9/303	journal	September 1951
Elastic Constants of Magnesium from 4.2°K to 300°K Slutsky, L. J.; Garland, C. W. Physical Review, Vol. 107, Issue 4 https://doi.org/10.1103/PhysRev.107.972	journal	August 1957
DREAM.3D: A Digital Representation Environment for the Analysis of Microstructure in 3D Groeber, Michael A.; Jackson, Michael A. Integrating Materials and Manufacturing Innovation, Vol. 3, Issue 1 https://doi.org/10.1186/2193-9772-3-5	journal	April 2014
Hall–Petch k dependencies in nanopolycrystals Armstrong, Ronald William Emerging Materials Research, Vol. 3, Issue 6 https://doi.org/10.1680/emr.14.00020	journal	December 2014
Elastic-plastic deformation at finite strains Lee, E. H. https://doi.org/10.21236/AD0678483 AD--678483	report	June 1968
60 Years of Hall-Petch: Past to Present Nano-Scale Connections Armstrong, Ronald W. MATERIALS TRANSACTIONS, Vol. 55, Issue 1 https://doi.org/10.2320/matertrans.MA201302	journal	January 2014

Figures / Tables (26)

Similar Records

Quantitative study of the effect of grain boundary parameters on the slip system level Hall-Petch slope for basal slip system in Mg-4Al

Journal Article · Sun Nov 01 00:00:00 EDT 2020 · Acta Materialia · OSTI ID:1851115

Influence of texture on Hall–Petch relationships in an Mg alloy

Journal Article · Sun Nov 30 23:00:00 EST 2014 · Acta Materialia · OSTI ID:1327045

Related Subjects

36 MATERIALS SCIENCE
42 ENGINEERING
HR-EBSD
crystal plasticity
high resolution-electron backscattering diffraction
micro-Hall–Petch coefficient
prismatic slip system

Estimation of micro-Hall-Petch coefficients for prismatic slip system in Mg-4Al as a function of grain boundary parameters

Citation Formats

References (61)

Figures / Tables (26)

Similar Records

Related Subjects