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A single grain boundary parameter to characterize normal stress fluctuations in materials with elastic cubic grains. (English) Zbl 1480.74046

Summary: A finite element analysis of intergranular normal stresses is performed in order to identify a possible statistical correlation between the intergranular normal stresses and the corresponding grain boundary type within a polycrystalline aggregate. Elastic continuum grains of cubic lattice symmetry are assumed in the analysis. Meaningful results are obtained by analyzing the first two statistical moments of grain boundary normal stresses obtained on several grain boundary types. Among the five macroscopic parameters (5D) describing a grain boundary, the orientation of the grain boundary plane relative to the two adjacent crystal lattices (4D) is found to be the most important property influencing the normal stresses. To account for it, a single new (1D) parameter \(E_{12}\) is introduced, which combines the geometrical aspect of grain boundary with its material properties and measures the average stiffness of grain boundary neighborhood along the grain boundary normal direction. It is demonstrated that \(E_{12} \), in combination with Zener elastic anisotropy index \(A\), is able to accurately predict normal stress fluctuations on any grain boundary type in a material with cubic lattice symmetry. It is argued that largest normal stresses most likely form on grain boundaries whose normals are oriented along the stiffest direction in both adjacent grains (\( \langle 111 \rangle\) for crystals with \(A > 1\) or \(\langle 001 \rangle\) for crystals with \(A < 1\)). Moreover, it is shown that classification of grain boundaries according to their propensity to exhibit large normal stresses can be trivially reduced to the (analytical) calculation of the corresponding effective stiffness parameter \(E_{12}\). A few practical implications are discussed relevant to intergranular stress-corrosion cracking of Coincidence Site Lattice grain boundaries. For example, it is highlighted that in face-centered cubic materials the coherent \(\Sigma 3\) twin grain boundaries, which are known for their very high cracking resistance, nevertheless exhibit largest intergranular normal stresses, indicating that cracking resistance is associated with high grain boundary strength.

MSC:

74E20 Granularity
74S05 Finite element methods applied to problems in solid mechanics

Software:

MTEX; Neper
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Full Text: DOI

References:

[1] An, D.; Griffiths, T. A.; Konijnenberg, P.; Mandal, S.; Wang, Z.; Zaefferer, S., Correlating the five parameter grain boundary character distribution and the intergranular corrosion behaviour of a stainless steel using 3D orientation microscopy based on mechanical polishing serial sectioning, Acta Mater., 156, 297-309 (2018)
[2] Arafin, M.; Szpunar, J., A new understanding of intergranular stress corrosion cracking resistance of pipeline steel through grain boundary character and crystallographic texture studies, Corros. Sci., 51, 119-128 (2009)
[3] Bachmann, F.; Hielscher, R.; Schaeben, H., Texture analysis with MTEX - free and open source software toolbox, Solid State Phenom., 160, 63-68 (2010)
[4] Bower, A. F., Applied Mechanics of Solids (2010), Taylor & Francis Group
[5] Burleigh, T. D., The postulated mechanisms for stress corrosion cracking of aluminum alloys: A review of the literature 1980-1989, Corrosion, 47, 89-98 (1991)
[6] Cox, B., Environmentally Induced Cracking of Zirconium AlloysTechnical report (1970), Atomic Energy of Canada Limited
[7] Cox, B., Envrionmentally-induced cracking of zirconium alloys - a review, J. Nucl. Mater., 170, 1-23 (1990)
[8] Diard, O.; Leclercq, S.; Rousselier, G.; Cailletaud, G., Distribution of normal stress at grain boundaries in multicrystals: Application to an intergranular damamge modeling, Comput. Math. Sci., 25, 73-84 (2002)
[9] Diard, O.; Leclercq, S.; Rousselier, G.; Cailletaud, G., Evaluation of finite element based analysis of 3D multicrystalline aggregates plasticity. Application to crystal plasticity model identification and the study of strain fields near grain boundaries, Int. J. Plast., 21, 691-722 (2005) · Zbl 1112.74508
[10] El Shawish, S.; Hure, J., Intergranular normal stress distributions in untextured polycrystalline aggregates, Eur. J. Mech. / A Solids, 72, 354-373 (2018)
[11] El Shawish, S.; Vincent, P. G.; Moulinec, H.; Cizelj, L.; Gélébart, L., Full-field polycrystal plasticity simulations of neutron-irradiated austenitic stainless steel: A comparison between fe and fft-based approaches, J. Nucl. Mater., 529, Article 151927 pp. (2020)
[12] Fujii, T.; Tohgo, K.; Mori, Y.; Miura, Y.; Shimamura, Y., Crystallographic and mechanical investigation of intergranular stress corrosion crack initiation in austenitic stainless steel, Mater. Sci. Eng. A, 751, 160-170 (2019)
[13] Gertsman, V. Y.; Bruemmer, S. M., Study of grain boundary character along intergranular stress corrosion crack paths in austenitic alloys, Acta Mater., 49, 9, 1589-1598 (2001)
[14] Gonzalez, D.; Simonovski, I.; Withers, P. J.; Quinta da Fonseca, J., Modelling the effect of elastic and plastic anisotropies on stresses at grain boundaries, Int. J. Plast., 61, 49-63 (2014)
[15] Gupta, J.; Hure, J.; Tanguy, B.; Laffont, L.; Lafont, M. C.; Andrieu, E., Evaluation of stress corrosion cracking of irradiated 304 stainless steel in PWR environment using heavy ion irradiation, J. Nucl. Mater., 476, 82-92 (2016)
[16] Hure, J.; El Shawish, S.; Cizelj, L.; Tanguy, B., Intergranular stress distributions in polycrystalline aggregates of irradiated stainless steel, J. Nucl. Mater. (2016)
[17] Stress Corrosion Cracking in Light Water Reactors: Good Practices and Lessons LearnedNP-T-3.13 (2011), IAEA Nuclear Energy Series
[18] Johnson, G.; King, A.; Honnicke, M. G.; Marrow, J.; Ludwig, W., X-ray Diffraction contrast tomography: a novel technique for three-dimensional grain mapping of polycrystals. II. The combined case, J. Appl. Cryst., 41, 310-318 (2008)
[19] Johnson, D. C.; Kuhr, B.; Farkas, D.; Was, G. S., Quantitative linkage between the stress at dislocation channel – grain boundary interaction sites and irradiation assisted stress corrosion crack initiation, Acta Mater., 170, 166-175 (2019)
[20] Kanjarla, A. K.; Van Houtte, P.; Delannay, L., Assessment of plastic heterogeneity in grain interaction models using crystal plasticity finite element method, Int. J. Plast., 26, 1220-1233 (2010) · Zbl 1426.74101
[21] Kröner, E., Berechnung der elastischen konstanten des vielkristalls aus den konstanten des einskristalls, Z. Phys., 151, 504 (1958)
[22] Le Millier, M.; Calonne, O.; Crépin, J.; Duhamel, C.; Fournier, L.; Gaslain, F.; Héripré, E.; Toader, O.; Vidalenc, Y.; Was, G., Influence of strain localization on IASCC of proton irradiated 304l stainless steel in simulated PWR primary water, (16th International Conference on Environmental Degragation of Materials in Nuclear Power Systems - Water Reactors (2013))
[23] Lebensohn, R. A.; Kanjarla, A. K.; Eisenlohr, P., An elasto-viscoplastic formulation based on fast fourier transforms for the prediction of micromechanical fields in polycrystalline materials, Int. J. Plast., 32-33, 59-69 (2012)
[24] Liang, D.; Hure, J.; Courcelle, A.; El Shawish, S.; Tanguy, B., A micromechanical analysis of intergranular stress corrosion cracking of an irradiated austenitic stainless steel, Acta Mater., 204, Article 116482 pp. (2021)
[25] Liu, T.; Xia, S.; Bai, Q.; Zhou, B.; Lu, Y.; Shoji, T., Evaluation of grain boundary network and improvement of intergranular cracking resistance in 316l stainless steel after grain boundary engineering, Materials, 12, 242-258 (2019)
[26] Ludwig, W.; Schmidt, S.; Lauridsen, E. M.; Poulsen, H. F., X-ray Diffraction contrast tomography: a novel technique for three-dimensional grain mapping of polycrystals. I. Direct beam case, J. Appl. Cryst., 41, 302-309 (2008)
[27] Mackenzie, J. K., Second paper on statistics associated with the random disorientation of cubes, Biometrika, 45, 229-240 (1958) · Zbl 0084.36402
[28] Nishioka, H.; Fukuya, K.; Fujii, K.; Torimaru, T., IASCC initiation in highly irradiated stainless steels under uniaxial constant load conditions, J. Nucl. Sci. Tech., 45, 1072-1077 (2008)
[29] Olmsted, D. L.; Foiles, S. M.; Holm, E. A., Survey of computed grain boundary properties in face-centered cubic materials: I. Grain boundary energy, Acta Mater., 57, 3694-3703 (2009)
[30] Panter, J.; Viguier, B.; Cloué, J. M.; Foucault, M.; Combrade, P.; Andrieu, E., Influence of oxide films on primary water stress corrosion cracking initiation of alloy 600, J. Nucl. Mater., 348, 213-221 (2006)
[31] Quey, R.; Dawson, P. R.; Barbe, F., Large-scale 3D random polycrystals for the finite element method: Generation, meshing and remeshing, Comput. Methods Appl. Mech. Engrg., 200, 1729-1745 (2011) · Zbl 1228.74093
[32] Rahimi, S.; Engelberg, D. L.; Duff, J. A.; Marrow, T. J., In situ observation of intergranular crack nucleation in a grain boundary controlled austenitic stainless steel, J. Microsc., 233, 3, 423-431 (2009)
[33] Rahimi, S.; Marrow, T. J., Effects of orientation, stress and exposure time on short intergranular stress corrosion crack behaviour in sensitised type 304 austenitic stainless steel, Fatigue Fract. Eng. Mater. Struct., 35, 359-373 (2011)
[34] Ranganathan, S. I.; Ostaja-Starzewski, M., Universal elastic anisotropy index, Phys. Rev. Lett., 101, Article 055504 pp. (2008)
[35] Shen, C. H.; Shewmon, P. G., A mechanism for hydrogen-induced intergranular stress corrosion cracking in alloy 600, Metall. Trans. A., 21A, 1261-1271 (1990)
[36] Abaqus 6.14-2 (2016)
[37] Speidel, M. O., Stress corrosion cracking of aluminum alloys, Metall. Mater. Trans. A, 6A, 631-651 (1975)
[38] Stephenson, K. J.; Was, G. S., Crack initiation behavior of neutron irradiated model and commercial stainless steels in high temperature water, J. Nucl. Mater., 444, 331-341 (2014)
[39] Stratulat, A.; Duff, J. A.; Marrow, T. J., Grain boundary structure and intergranular stress corrosion crack initiation in high temperature water of a thermally sensitised austenitic stainless steel, observed in situ, Corros. Sci., 85, 428-435 (2014)
[40] Van Rooyen, D., Review of the stress corrosion cracking of inconel 600, Corrosion, 31, 327-337 (1975)
[41] Voigt, W., Lehrbuch der Kristallphysik (1928), Teubner · JFM 54.0929.03
[42] Wang, Z. F.; Atrens, A., Initiation of stress corrosion cracking for pipeline steels in a carbonate-bicarbonate solution, Metall. Mater. Trans. A, 27A, 2686-2691 (1996)
[43] West, E. A.; Was, G. S., A model for the normal stress dependence of intergranular cracking of irradiated 316l stainless steel in supercritical water, J. Nucl. Mater., 408, 2, 142-152 (2011)
[44] MathematicaVersion 10.0 (2014)
[45] Zener, C., Elasticity and Anelasticity of Metals (1948), University of Chicago · Zbl 0032.22202
[46] Zhang, Z.; Xia, S.; Bai, Q.; Liu, T.; Li, H.; Zhou, B.; Wang, L.; Ma, W., Effects of 3D grain boundary geometrical angles and the net normal stress on intergranular stress corrosion cracking initiation in a 316 stainless steel, Mater. Sci. Eng. A, 765, Article 138277 pp. (2019)
[47] Zhang, J. M.; Zhang, Y.; Xu, K. W.; Ji, V., Young’s modulus surface and Poisson’s ratio curve for cubic metals, J. Phys. Chem. Solids, 68, 503-510 (2007)
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