Abstract
The influence of grain size distribution on ductile intergranular crack growth resistance is investigated using full-field microstructure-based finite element calculations and a simpler model based on discrete unit events and graph search. The finite element calculations are carried out for a plane strain slice with planar grains subjected to mode I small-scale yielding conditions. The finite element formulation accounts for finite deformations, and the constitutive relation models the loss of stress carrying capacity due to progressive void nucleation, growth, and coalescence. The discrete unit events are characterized by a set of finite element calculations for crack growth at a single-grain boundary junction. A directed graph of the connectivity of grain boundary junctions and the distances between them is used to create a directed graph in J-resistance space. For a specified grain boundary distribution, this enables crack growth resistance curves to be calculated for all possible crack paths. Crack growth resistance curves are calculated based on various path choice criteria and compared with the results of full-field finite element calculations of the initial boundary value problem. The effect of unimodal and bimodal grain size distributions on intergranular crack growth is considered. It is found that a significant increase in crack growth resistance is obtained if the difference in grain sizes in the bimodal grain size distribution is sufficiently large.
References
1.
Cohen
, Y.
, Devauchelle
, O.
, Seybold
, H. F.
, Robert
, S. Y.
, Szymczak
, P.
, and Rothman
, D. H.
, 2015
, “Path Selection in the Growth of Rivers
,” Proc. Natl. Acad. Sci. U. S. A.
, 112
(46
), pp. 14132
–14137
. 10.1073/pnas.14138831122.
Osovski
, S.
, Srivastava
, A.
, Williams
, J. C.
, and Needleman
, A.
, 2015
, “Grain Boundary Crack Growth in Metastable Titanium β Alloys
,” Acta. Mater.
, 82
(1
), pp. 167
–178
. 10.1016/j.actamat.2014.08.0623.
Srivastava
, A.
, Osovski
, S.
, and Needleman
, A.
, 2017
, “Engineering the Crack Path by Controlling the Microstructure
,” J. Mech. Phys. Solids.
, 100
(1
), pp. 1
–20
. 10.1016/j.jmps.2016.12.0064.
Osovski
, S.
, Needleman
, A.
, and Srivastava
, A.
, 2019
, “Intergranular Fracture Prediction and Microstructure Design
,” Int. J. Fract.
, 216
(2
), pp. 135
–148
. 10.1007/s10704-019-00347-z5.
Lynch
, S. P.
, 1991
, “Fracture of 8090 Al-Li Plate I. Short Transverse Fracture Toughness
,” Mater. Sci. Eng.: A
, 136
, pp. 25
–43
. 10.1016/0921-5093(91)90439-T6.
Lüjtering
, G.
, and Williams
, J. C.
, 2007
, Titanium (Engineering Materials and Processes)
, 2nd ed., Springer Verlag
, Berlin
.7.
Uthaisangsuk
, V.
, Prahl
, U.
, and Bleck
, W.
, 2009
, “Characterisation of Formability Behaviour of Multiphase Steels by Micromechanical Modelling
,” Int. J. Fract.
, 157
(1–2
), pp. 55
–69
. 10.1007/s10704-009-9329-48.
Gerbig
, D.
, Srivastava
, A.
, Osovski
, S.
, Hector
, L. G.
, and Bower
, A.
, 2018
, “Analysis and Design of Dual-Phase Steel Microstructure for Enhanced Ductile Fracture Resistance
,” Int. J. Fract.
, 209
(1–2
), pp. 3
–26
. 10.1007/s10704-017-0235-x9.
Kikuchi
, S.
, Nakamura
, Y.
, Ueno
, A.
, and Ameyama
, K.
, 2015
, “Low Temperature Nitriding of Commercially Pure Titanium With Harmonic Structure
,” Mater. Trans.
, 56
(11
), pp. 1807
–1813
.10.
Ota
, M.
, Vajpai
, S. K.
, Imao
, R.
, Kurokawa
, K.
, and Ameyama
, K.
, 2015
, “Application of High Pressure Gas Jet Mill Process to Fabricate High Performance Harmonic Structure Designed Pure Titanium
,” Mater. Trans.
, 56
(1
), pp. 154
–159
.11.
Fan
, G. J.
, Choo
, H.
, Liaw
, P. K.
, and Lavernia
, E. J.
, 2006
, “Plastic Deformation and Fracture of Ultrafine-Grained AlMg Alloys With a Bimodal Grain Size Distribution
,” Acta Mater.
, 54
(7
), pp. 1759
–1766
. 10.1016/j.actamat.2005.11.04412.
Kim
, H. D.
, Han
, B. D.
, Park
, D. S.
, Lee
, B. T.
, and Becher
, P. F.
, 2002
, “Novel Two-Step Sintering Process to Obtain a Bimodal Microstructure in Silicon Nitride
,” J. Am. Ceram. Soc.
, 85
(1
), pp. 245
–252
. 10.1111/j.1151-2916.2002.tb00073.x13.
Fang
, Y.
, Yu
, F.
, and White
, K. W.
, 2000
, “Bimodal Microstructure in Silicon Nitride-Barium Aluminum Silicate Ceramic-Matrix Composites by Pressureless Sintering
,” J. Am. Ceram. Soc.
, 83
(7
), pp. 1828
–1830
. 10.1111/j.1151-2916.2000.tb01475.x14.
Becher
, P. F.
, Sun
, E. Y.
, Plucknett
, K. P.
, Alexander
, K. B.
, Hsueh
, C. H.
, Lin
, H. T.
, Waters
, S. B.
, Westmoreland
, C. G.
, Kang
, E. S.
, Hirao
, K.
, and Brito
, M. E.
, 1998
, “Microstructural Design of Silicon Nitride With Improved Fracture Toughness: I, Effects of Grain Shape and Size
,” J. Am. Ceram. Soc.
, 81
(11
), pp. 2821
–2830
. 10.1111/j.1151-2916.1998.tb02702.x15.
Kikuchi
, S.
, Hayami
, Y.
, Ishiguri
, T.
, Guennec
, B.
, Ueno
, A.
, Ota
, M.
, and Ameyama
, K.
, 2017
, “Effect of Bimodal Grain Size Distribution on Fatigue Properties of Ti-6Al-4V Alloy With Harmonic Structure Under Four-Point Bending
,” Mater. Sci. Eng. A.
, 687
, pp. 269
–275
. 10.1016/j.msea.2017.01.07616.
Saini
, J.
, Arora
, H. S.
, Grewal
, H. S.
, Perumal
, G.
, Ayyagari
, A.
, Salloom
, R.
, and Mukherjee
, S.
, 2019
, “Excellent Corrosion Resistance of Dual-Phase Bimodal Stainless Steel
,” Steel. Res. Int.
, 90
(5
), p. 1800554
. 10.1002/srin.20180055417.
Rice
, J.
, 1968
, “A Path-independant Integral and the Approximate Analysis of Strain Concentration by Notches and Cracks
,” ASME J. Appl. Mech.
, 35
(2
), pp. 379
–386
. 10.1115/1.360120618.
Belytschko
, T.
, Chiapetta
, R. L.
, and Bartel
, H. D.
, 1976
, “Efficient Large Scale Non-linear Transient Analysis by Finite Elements
,” Int. J. Numer. Methods Eng.
, 10
(3
), pp. 579
–596
. 10.1002/nme.162010030819.
Peirce
, D.
, Shih
, C. F.
, and Needleman
, A.
, 1984
, “A Tangent Modulus Method for Rate Dependent Solids
,” Comput. Struct.
, 18
(5
), pp. 875
–887
. 10.1016/0045-7949(84)90033-620.
Gurson
, A. L.
, 1975
, “Plastic Flow and Fracture Behavior of Ductile Materials Incorporating Void Nucleation, Growth and Interaction
,” Ph.D. thesis, Brown University
, Providence, RI
.21.
Tvergaard
, V.
, 1981
, “Influence of Voids on Shear Band Instabilities Under Plane Strain Conditions
,” Int. J. Fract.
, 17
(4
), pp. 389
–407
. 10.1007/BF0003619122.
Tvergaard
, V.
, 1982a
, “On Localization in Ductile Materials Containing Spherical Voids
,” Int. J. Fract.
, 18
(4
), pp. 237
–252
.23.
Tvergaard
, V.
, and Needleman
, A.
, 1984
, “Analysis of the Cup-cone Fracture in a Round Tensile Bar
,” Acta. Metall.
, 32
(1
), pp. 157
–169
. 10.1016/0001-6160(84)90213-X24.
Bowyer
, A.
, 1981
, “Computing Dirichlet Tessellations
,” Comput. Jo.
, 24
(2
), pp. 162
–166
. 10.1093/comjnl/24.2.16225.
Paris
, P. C.
, Tada
, H.
, Zahoor
, A.
, and Ernst
, H.
, 1979
, “The Theory of Instability of the Tearing Mode of Elastic-plastic Crack Growth. Elastic-Plastic Fracture
,” ASTM STP
668
, pp. 5
–36
.26.
Lee
, C. Y.
, 1961
, “An Algorithm for Path Connections and Its Applications
,” IRE Trans. Electron. Comput.
, 3
(3
), pp. 346
–365
. 10.1109/TEC.1961.521922227.
Dijkstra
, E. W.
, 1959
, “A Note on Two Problems in Connexion with Graphs
,” Numerische Mathematik
, 1
(1
), pp. 269
–271
. 10.1007/BF0138639028.
Jackson
, A. P.
, Vincent
, J. F.
, and Turner
, R. M.
, 1988
, “The Mechanical Design of Nacre
,” Proc. R. Soc. London, B.
, 234
(1277
), pp. 415
–440
. 10.1098/rspb.1988.005629.
Fratzl
, P.
, and Weinkamer
, R.
, 2007
, “Natures Hierarchical Materials
,” Prog. Mater. Sci.
, 52
(8
), pp. 1263
–1334
. 10.1016/j.pmatsci.2007.06.00130.
Chai
, H.
, Lee
, J. J. W.
, Constantino
, P. J.
, Lucas
, P. W.
, and Lawn
, B. R.
, 2009
, “Remarkable Resilience of Teeth
,” Proc. Natl. Acad. Sci. U. S. A.
, 106
(18
), pp. 7289
–7293
. 10.1073/pnas.090246610631.
Launey
, M. E.
, and Ritchie
, R. O.
, 2009
, “On the Fracture Toughness of Advanced Materials
,” Adv. Mater.
, 21
(20
), pp. 2103
–2110
. 10.1002/adma.200803322Copyright © 2019 by ASME
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