References
- Acharya, A., Bassani, J.L. and Beaudoin, A. (2003), "Geometrically necessary dislocations, hardening, and a simple gradient theory of crystal plasticity", Scripta Materialia, 48(2), 167-172. https://doi.org/10.1016/S1359-6462(02)00337-8
- Aslan, O. and Forest, S. (2011), "The micromorphic versus phase field approach to gradient plasticity and damage with application to cracking in metal single crystals", Multiscale Methods in Computational Mechanics, Springer, Netherlands.
- Bargmann, S., Ekh, M., Runesson, K. and Svendsen, B. (2010), "Modeling of polycrystals with gradient crystal plasticity: A comparison of strategies", Philosoph. Magaz., 90(10), 1263-1288. https://doi.org/10.1080/14786430903334332
- Bargmann, S., Svendsen, B. and Ekh, M. (2011), "An extended crystal plasticity model for latent hardening in polycrystals", Comput. Mech., 48(6), 631-645. https://doi.org/10.1007/s00466-011-0609-2
- Bargmann, S. and Ekh, M. (2013), "Microscopic temperature field prediction during adiabatic loading in a gradient extended crystal plasticity theory", Int. J. Solid. Struct., 50(6), 899-906. https://doi.org/10.1016/j.ijsolstr.2012.11.010
- Bayley, C., Brekelmans, W. and Geers, M. (2006), "A comparison of dislocation induced back stress formulations in strain gradient crystal plasticity", Int. J. Solid. Struct., 43(24), 7268-7286. https://doi.org/10.1016/j.ijsolstr.2006.05.011
- Bazant, Z. and Lin, F.-B. (1988), "Non-local yield limit degradation", Int. J. Numer. Meth. Eng., 26(8), 1805-1823. https://doi.org/10.1002/nme.1620260809
- Bodelot, L., Charkaluk, E., Sabatier, L. and Dufrenoy, P. (2011), "Experimental study of heterogeneities in strain and temperature fields at the microstructural level of polycrystalline metals through fully-coupled full-field measurements by digital image correlation and infrared thermography", Mech. Mater., 43(11), 654-670. https://doi.org/10.1016/j.mechmat.2011.08.006
- Borg, U. (2007), "A strain gradient crystal plasticity analysis of grain size effects in polycrystals", Eur. J. Mech. Solid., 26(2), 313-324. https://doi.org/10.1016/j.euromechsol.2006.09.006
- Cermelli, P. and Gurtin, M.E. (2001), "On the characterization of the geometrically necessary dislocations in finite plasticity", J. Mech. Phys. Solid., 49(7), 1539-1568. https://doi.org/10.1016/S0022-5096(00)00084-3
- Clayton, J. and McDowell, D. (2004), "Homogenized finite elastoplasticity and damage: theory and computations", Mech. Mater., 36(9), 799-824. https://doi.org/10.1016/j.mechmat.2003.08.001
- Dimitrijevic, B.J. and Hackl, K. (2011), "A regularization framework for damage-plasticity models via gradient enhancement of the free energy", Int. J. Numer. Meter. Biol. Eng., 27(8), 1199-1210. https://doi.org/10.1002/cnm.1350
- Dunne, F.P.E., Wilkinson, A.J. and Allen, R. (2007), "Experimental and computational studies of low cycle fatigue crack nucleation in a polycrystal", Int. J. Plast., 23(2), 273-295. https://doi.org/10.1016/j.ijplas.2006.07.001
- Ekh, M., Lillbacka, R. and Runesson, K. (2004), "A model framework for anisotropic damage coupled to crystal (visco)plasticity", Int. J. Plast., 20(12), 2143-2159. https://doi.org/10.1016/j.ijplas.2004.04.007
- Ekh, M., Grymer, M., Runesson, K. and Svedberg, T. (2007), "Gradient crystal plasticity as part of the computational modeling of polycrystals", Int. J. Numer. Meter. Eng., 72(2), 197-220. https://doi.org/10.1002/nme.2015
- Ekh, M., Bargmann, S. and Grymer, M. (2011), "Influence of grain boundary conditions on modeling of size-dependence in polycrystals", Acta Mechanica, 218(1-2), 103-113. https://doi.org/10.1007/s00707-010-0403-9
- Evers, L.P., Brekelmanns, W.A.M. and Geers, M.G.D. (2004), "Non-local crystal plasticity model with intrinsic ssd and gnd effects", J. Mech. Phys. Solid., 52(10), 2379-2401. https://doi.org/10.1016/j.jmps.2004.03.007
- Evers, L.P., Brekelmanns, W.A.M. and Geers, M.G.D. (2004a), "Scale dependent crystal plasticity framework with dislocation density and grain boundary effects", Int. J. Solid. Struct., 41(18), 5209-5230. https://doi.org/10.1016/j.ijsolstr.2004.04.021
- Fleck, N.A., Muller, G.M., Ashby, M.F. and Hutchinson, J.W. (1994), "Strain gradient plasticity: theory and experiment", Acta Metallurgica et Materialia, 42(2), 475-487. https://doi.org/10.1016/0956-7151(94)90502-9
- Fleck, N.A. and Hutchinson, J.W. (1997), "Strain gradient plasticity", Adv. Appl. Mech., 33, 295-361. https://doi.org/10.1016/S0065-2156(08)70388-0
- Gurtin, M.E. (2004), "A gradient theory of small-deformation isotropic plasticity that accounts for the Burgers vector and for dissipation due to plastic spin", J. Mech. Phys. Solid., 52(11), 2545-2568. https://doi.org/10.1016/j.jmps.2004.04.010
- Hakansson, P., Wallin, M. and Ristinmaa, M. (2008), "Prediction of stored energy in polycrystalline materials during cyclic loading", Int. J. Solid. Struct., 45(6), 1570-1586. https://doi.org/10.1016/j.ijsolstr.2007.10.009
- Heino, S. and Karlsson, B. (2001), "Cyclic deformation and fatigue behavior of 7Mo-0.5N superaustenitic stainless steel characteristics and development of the dislocation structures", Acta Materialia, 49(2), 353-363. https://doi.org/10.1016/S1359-6454(00)00200-7
- Horstemeyer, M., Ramaswamy, S. and Negrete, M. (2003), "Using a micromechanical finite element parametric study to motivate a phenomenological macroscale model for void/crack nucleation in aluminum with a hard second phase", Mech. Mater., 35(7), 675-687. https://doi.org/10.1016/S0167-6636(02)00165-5
- Hou, N., Wen, Z. and Yue, Z. (2009), "Creep behavior of single crystal superalloy specimen under temperature gradient condition", Mater. Sci. Eng., A510, 42-45.
- Husser, E., Lilleodden, E. and Bargmann, S. (2014), "Computational modeling of intrinsically induced strain gradients during compression of c-axis oriented magnesium single crystal", Acta Materialia, 71, 206-219. https://doi.org/10.1016/j.actamat.2014.02.017
- Kroner, E. (1960), "Allgemeine kontinuumstheorie der versetzungen und eigenspannungen", Archiv. Ration. Mech. Anal., 4(1), 273-334. https://doi.org/10.1007/BF00281393
- Kuroda, M. and Tvergaard, V. (2006), "Studies of scale dependent crystal viscoplasticity models", J. Mech. Phys. Solid., 54(9), 1789-1810. https://doi.org/10.1016/j.jmps.2006.04.002
- Kuroda, M. and Tvergaard, V. (2008), "On the formulations of higher-order strain gradient crystal plasticity models", J. Mech. Phys. Solid., 56(4), 1591-1608. https://doi.org/10.1016/j.jmps.2007.07.015
- Kuroda, M. and Tvergaard, V. (2008a), "A finite deformation theory of higher-order gradient crystal plasticity", J. Mech. Phys. Solid., 56(8), 2573-2584. https://doi.org/10.1016/j.jmps.2008.03.010
- Lammer, H. and Tsakmakis, C. (2000), "Discussion of coupled elastoplasticity and damage constitutive equations for small and finite deformations", Int. J. Plast., 16(5), 495-523. https://doi.org/10.1016/S0749-6419(99)00074-1
- Lemaȋtre, J. (1992), A Course on Damage Mechanics.
- Levkovitch, V. and Svendsen, B. (2006), "On the large-deformation-and continuum-based formulation of models for extended crystal plasticity", Int. J. Solid. Struct., 43(24), 7246-7267. https://doi.org/10.1016/j.ijsolstr.2006.05.010
- McBride, A., Bargmann, S. and Reddy, D. (2015), "A computational investigation of a model of singlecrystal gradient thermoplasticity that accounts for the stored energy of cold work and thermal annealing", Compos. Mech., 55(4), 755-769. https://doi.org/10.1007/s00466-015-1134-5
- Ohno, N. and Okumura, D. (2007), "Higher-order stress and grain size effects due to self-energy of geometrically necessary dislocations", J. Mech. Phys. Solid., 55(9), 1879-1898. https://doi.org/10.1016/j.jmps.2007.02.007
- Parisot, R., Forest, S., Pineau, A., Grillon, F., Demonet, X. and Mataigne, J.-M. (2004), "Deformation and damage mechanisms of zinc coatings on hot-dip galvanized steel sheets: Part II. Damage modes", Metal. Mater. Trans. A, 35(3), 813-823. https://doi.org/10.1007/s11661-004-0008-9
- Peerlings, R., Poh, L. and Geers, M. (2012), "An implicit gradient plasticity-damage theory for predicting size effects in hardening and softening", Eng. Fract. Mech., 95, 2-12. https://doi.org/10.1016/j.engfracmech.2011.12.016
- Rice, J. (1971), "Inelastic constitutive relations for solids: an internal-variable theory and its application to metal plasticity", J. Mech. Phys. Solid., 19(6), 433-455. https://doi.org/10.1016/0022-5096(71)90010-X
- Roters, F., Eisenlohr, P., Hantcherli, L., Tjahjanto, D., Bieler, T. and Raabe, D. (2010), "Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: Theory, experiments, applications", Acta Materialia, 58(4), 1152-1211. https://doi.org/10.1016/j.actamat.2009.10.058
- Vrech, S.M. and Etse, G. (2007), "FE approach for thermodynamically consistent gradient-dependent plasticity", Latt. Am. Appl. Res., 37(2), 127-132.
- Welschinger, F. (2011), "A variational framework for gradient-extended dissipative continua. Application to damage mechanics, fracture, and plasticity", Ph.D. thesis, University of Stuttgart, Germany.
- Yefimov, S., Groma, I. and Giessen, E. van der (2004), "A comparison of a statistical-mechanics based plasticity model with discrete dislocation plasticity calculations", J. Mech. Phys. Solid., 52(2), 279-300. https://doi.org/10.1016/S0022-5096(03)00094-2
- Yefimov, S. and Giessen, E. van der (2005), "Multiple slip in a strain-gradient plasticity model motivated by a statistical-mechanics description of dislocations", Int. J. Solid. Struct., 42(11), 3375-3394. https://doi.org/10.1016/j.ijsolstr.2004.10.025