Abstract
A direct numerical simulation of the cyclic response of a 250-grain polycrystalline aggregate over more than 1000 cycles is presented, being one of the few available simulations including a significant number of cycles. It provides unique results on the evolution of the accumulated plastic strain and ratcheting phenomena inside the grains. Even though the average stress–strain response stabilizes after 500 cycles, unlimited ratcheting is observed at some locations close to grain boundaries and triple junctions. A clear surface effect of the ratcheting behavior is evidenced based on an appropriate combination of Dirichlet, Neumann, and periodic boundary conditions. The magnitude of the ratcheting indicator is found to be significantly higher at the free surface than in the middle section of the aggregate. Both single- and polycrystalline samples of pure tantalum are tested at room temperature for identification of the parameters in the crystal plasticity model. Special attention is dedicated to modeling the static strain aging effects observed in this material.
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References
F. Barbe, S. Forest, and G. Cailletaud, Int. J. Plastic. 17, 537 (2001).
A. Hor, N. Saintier, C. Robert, T. Palin-Luc, and F. Morel, Int. J. Fatigue 67, 151 (2014).
D.L. McDowell, Mater. Sci. Eng. A 468, 4 (2007).
H. Proudhon, J. Li, F. Wang, A. Roos, V. Chiaruttini, and S. Forest, Int. J. Fatigue 82, 238 (2016).
S. Basseville, G. Cailletaud, T. Ghidossi, Y. Guilhem, E. Lacoste, H. Proudhon, L. Signor, and P. Villechaise, Mater. Sci. Eng. A 696, 122 (2017).
F. Šiška, S. Forest, P. Gumbsch, and D. Weygand, Modell. Simul. Mater. Sci. Eng. 15, S217 (2007).
H. Lim, H.J. Bong, S.R. Chen, T.M. Rodgers, C.C. Battaile, and J.M.D. Lane, JOM 68, 1427 (2016).
H. Lim, R. Dingreville, L.A. Deibler, T.E. Buchheit, and C.C. Battaile, Comput. Mater. Sci. 117, 437 (2016).
D. Colas, E. Finot, S. Forest, S. Flouriot, M. Mazière, and T. Paris, Mater. Sci. Eng. A 615, 283 (2014).
W. Wasserbach, Work-Hardening and Dislocation Behaviour of Tantalum and Tantalum Alloys (Metals and Materials Society, The Minerals, 1996).
M.N. Norlain, Comportement mécanique du tantale, texture et recristallisation. PhD thesis, unpublished (1999).
C. Kerisit, Analyse de recristallisation statique du tantale déformé à froid pour une modélisation en champ moyen. PhD thesis, Ecole Nationale Supérieure de Mines de Paris (2012).
F. Buy, Etude expérimentale et modélisation du comportement plastique du tantale. Prise en compte de la vitesse de déformation et de l’histoire de chargement. PhD thesis, Université de Metz (1996).
S. Frénois, Modélisation polycristalline du comportement mécanique du tantale. Application à la mise en forme par hydroformage. PhD thesis, Centrale Paris (2001).
Y. Guilhem, S. Basseville, F. Curtit, J.M. Stephan, and G. Cailletaud, Comput. Mater. Sci. 70, 150 (2013).
J. Cheng, A. Shahba, and S. Ghosh, Comput. Mech. 57, 733 (2016).
F. El Houdaigui, S. Forest, A.-F. Gourgues, and D. Jeulin, On the size of the representative volume element for isotropic elastic polycrystalline copper, in IUTAM Symposium on Mechanical Behavior and Micro-Mechanics of Nanostructured Materials, ed. by Q.S. Zheng, Y. Bai, Y.G. Wei (Springer, Beijing, China, 2007), pp. 171–180.
F. Barbe, R. Quey, A. Musienko, and G. Cailletaud, Mech. Res. Commun. 36, 762 (2009).
A. Zeghadi, F. Nguyen, S. Forest, A.-F. Gourgues, and O. Bouaziz, Philos. Mag. 87, 1401 (2007).
A. Zeghadi, S. Forest, A.-F. Gourgues, and O. Bouaziz, Philos. Mag. 87, 1425 (2007).
K.S. Zhang, J.W. Ju, Y.L. Bai, and W. Brocks, Mech. Mater. 85, 16 (2015).
M. Bouchedjra, T. Kanit, C. Boulemia, A. Amrouche, and M. El Amine Belouchrani, Eur. J. Mech. A Solids 72, 1 (2018).
T. Kanit, S. Forest, I. Galliet, V. Mounoury, and D. Jeulin, Int. J. Solids Struct. 40, 3647 (2003).
C. Gerard, Mesures de champs et identification de modèles de plasticité cristalline. PhD thesis, Université Paris 13 (2008).
Y. Guilhem, S. Basseville, F. Curtit, J.M. Stephan, and G. Cailletaud, Int. J. Fatigue 32, 1748 (2010).
J. Besson, G. Cailletaud, J.-L. Chaboche, S. Forest, and M. Blétry, Non-Linear Mechanics of Materials. Solid Mechanics and Its Applications, vol. 167 (Springer, Berlin, 2009).
L. Méric and G. Cailletaud, J. Eng. Mater. Technol. 113, 171 (1991).
V. Eyraud, M.H. Nadal, and C. Gondard, Ultrasonics 38, 438 (2000).
T. Hoc, J. Crépin, L. Gélébart, and A. Zaoui, Acta Mater. 51, 5477 (2003).
H. Lim, J.D. Carroll, C.C. Battaile, T.E. Buchheit, B.L. Boyce, and C.R. Weinberger, Int. J. Plast. 60, 1 (2015).
F. Kroupa, Plastic deformation of BCC metals with special reference to slip geometry (Ecole d’été de Pont-à-Mousson, Nancy, 1967).
V. Vitek, Cryst. Lattice Defects 5, 1 (1974).
C. Hennessey, G.M. Castelluccio, and D.L. McDowell, Mater. Sci. Eng. A 687, 241 (2017).
P. McCormick, Acta Metall. 36, 3061 (1998).
S. Zhang, P. McCormick, and Y. Estrin, Acta Mater. 49, 1087 (2000).
S. Graff, S. Forest, J.L. Strudel, C. Prioul, P. Pilvin, and J.L. Bechade, Mater. Sci. Eng. A 387–389, 181 (2004).
M. Marchenko, M. Mazière, S. Forest, and J.L. Strudel, Int. J. Plast. 85, 1 (2016).
S. Ren, M. Mazière, S. Forest, T. F. Morgeneyer, and G. Rousselier, C. R. Méc. 345:908, (2017).
Z-set package. Non-Linear Material & Structure Analysis Suite. www.zset-software.com (2013).
H. Lim, J.D. Carroll, C.C. Battaile, B.L. Boyce, and C.R. Weinberger, Int. J. Mech. Sci. 92, 98 (2015).
A. Marais, M. Mazière, S. Forest, A. Parrot, and P. Le Delliou, Philos. Mag. 92, 3589 (2012).
H.D. Wang, C. Berdin, M. Mazière, S. Forest, C. Prioul, A. Parrot, and P. Le-Delliou, Scr. Mater. 64, 430 (2011).
L. Allais, M. Bornert, T. Bretheau, D. Caldemaison, Acta Metall. Mater. 42, 3865 (1994).
S. Suresh, Fatigue of Materials (Cambridge University Press, Cambridge, 1998).
A.F. Bower and K.L. Johnson, J. Mech. Phys. Solids 37, 471 (1989).
D.L. McDowell, Int. J. Plast. 11, 397 (1995).
M. Zhang, R.W. Neu, and D.L. McDowell, Int. J. Fatigue 31, 1397 (2009).
M. Abdel-Karim and N. Ohno, Int. J. Plast. 16, 225 (2000).
S. Bari and T. Hassan, Int. J. Plast. 16, 381 (2000).
J.L. Chaboche and J. Lemaitre, Mécanique des matériaux solides. Éd. 3. Dunod (2008).
S. Sinha and S. Ghosh, Int. J. Fatigue 28, 1690 (2006).
L. Priester, Grain Boundaries: From Theory to Engineering. Springer Series in Materials Science, vol. 172, 1st ed. (Springer, Berlin, 2013).
J. Tong, L.G. Zhao, and B. Lin, Int. J. Fatigue 46, 49 (2013).
D. Colas, Approche multi-échelle du vieillissement et du comportement mécanique cyclique dans le tantale (PhD, Mines ParisTech, 2013).
S. Manchiraju, M. Asai, and S. Ghosh, J. Strain Anal. Eng. Des. 42, 183 (2007).
H. Lim, H.J. Bong, S.R. Chen, T.M. Rodgers, C.C. Battaile, and J.M.D. Lane, Mater. Sci. Eng. A 730, 50 (2018).
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Colas, D., Finot, E., Flouriot, S. et al. Local Ratcheting Phenomena in the Cyclic Behavior of Polycrystalline Tantalum. JOM 71, 2586–2599 (2019). https://doi.org/10.1007/s11837-019-03539-z
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DOI: https://doi.org/10.1007/s11837-019-03539-z