Abstract
In chapter 1 an introduction to basic dislocation properties in an elastic continuum is given. Displacements, strains, stresses and energies of straight edge and screw dislocations are compiled as well as forces on dislocations, implications of dislocation motion and aspects of dislocations in real crystals. Chapter 2 details the models of dislocation self interaction for curved dislocations including the line tension model and linear elastic self interaction. The former is essential for basic understanding, whereas the latter is the basis of accurate dislocation dynamics simulations of plasticity. In chapter 3 these models are applied for 2-dimensional dislocation glide which allow to calculate the strengthening effect of second phase particles and solute atoms in a material. Finally, aspects of 3-dimensional dislocation motion are outlined in chapter 4.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Bibliography
R.J. Arsenault, S. Patu, and D.M. Esterling. Computer simulation of solid solution strengthening in fee alloys: Part i. friedel and mott limits. Met. Trans. A., 20A:1411–1418, 1989a.
R.J. Arsenault, S. Patu, and D.M. Esterling. Computer simulation of solid solution strengthening in fee alloys: Part ii. at absolute zero temperature. Met. Trans. A. 20A:1419–1428, 1989b.
D.J. Bacon. A method for describing a flexible dislocation. Phys. Stat. Sol., 23:527–538, 1967.
L.M. Brown. The self-stress of dislocations and the shape of extended nodes. Phil. Mag., 10:441–466, 1964.
L.M. Brown. A proof of lothes theorem. Phil. Mag., 15:363, 1967.
B. Devincre. Three dimensional stress field expressions for straight dislocation segments. Solid State Comm., 93:875–878, 1995.
B. Devincre and M. Condat. Model validation of a 3d simulation of dislocation dynamics: discretization and line tension effects. Acta metall. mater., 40:2629–2637, 1992.
B. Devincre, L.P. Kubin, C. Lemarchand, and R. Madec. Mesoscopic simulations of plastic deformation. Mat. Sci. Eng., 309–310:211–219, 2001.
B. Devincre, T. Hocb, and L P. Kubin. Collinear interactions of dislocations and slip systems. Mat. Sci. Eng. A, 400–401:182–185, 2005.
M.S. Duesbery, N.P. Louat, and K. Sadananda. The numerical simulation of continuum dislocations. Phil. Mag., A65:311–325, 1992.
J.D. Eshelby. The continuum theory of lattice defects. In F. Seitz and D. Turnbull, editors, Solid State Physics, page 79. Academic Press Inc., New York, Vol.3, 1956.
A.J.E. Foreman and M.J. Makin. Dislocation movement through random arrays of obstacles. Phil. Mag., 14:911–924, 1966.
A.J.E. Foreman and M.J. Makin. Dislocation movement through random arrays of obstacles. Can. J. Phys., 45:511–517, 1967.
J. Friedel. Dislocations. Pergamon Press, 1964.
N.M. Ghoniem. Computational methods for mesoscopic, inhomogeneous plastic deformation. In D. Walgraef, C. Worner, and J. Martinez-Mardones, editors, Materials Instabilities, pages 76–158. World Scientific, Singapore, 2000.
G. Gottstein. Physical Foundations of Masterials Science. Springer-Verlag, 2004.
A.G. Granato, K. Luecke, J. Schlipf, and L.J. Teutonico. Entropy factors for thermally activated unpinning of dislocations. J. Appl. Phys., 35: 2732–2745, 1964.
K. Hanson and J.W. Morris. Limiting configuration in dislocation glide through a random array of point obstacles. J. Appl. Phys., 46:983, 1975.
A. Hartmaier and P. Gumbsch. Discrete dislocation dynamics simulation of crack-tip plasticity. In D. Raabe, F. Roters, F. Barlat, and L.-Q. Chen, editors, Continuum Scale Simulation of Engineering Materials, pages 413–427. Wiley-VCH, Weinheim, 2004.
J.P. Hirth and J. Lothe. Theory of Dislocations. Krieger Publishing Company, 1992.
D. Hull and D.J. Bacon. Introduction to Dislocations. Pergamon Press, 1992.
R.D. Isaac and V. Granato. Rate theory of dislocation motion: Thermal activation and inertial effects. Phys. Rev. B., 37:9278, 1988.
K.M. Jassby and T. Vreeland. Dislocation mobility in pure copper at 4.2°k. Phys. Rev., 8B:3537–3541, 1973.
U.F. Kocks. Kinetics of solution hardening. Metall. Trans. A, 16:2109–2129, 1985.
U.F. Kocks, A.S. Argon, and M.F. Ashby. Thermodynamics and kinetics of slip. Prog. Mat. Sci., 19:1, 1975.
R. Labusch and R.B. Schwarz. Simulation of thermally activated dislocation motion in alloys. In Proc. of ICSMA 9, pages 47–69. 1992.
I.M. Lifshitz and V.V. Slyozov. The kinetics of precipitation from supersaturated solid solutions. Phys. Chem. Solids, 19:35–50, 1961.
V. Mohles. Thermisch aktivierte Versetzungshewegung in Kristallen auf der Grundlage von Simulationsrechnungen. Shaker Verlag, 1997.
V. Mohles. The critical resolved shear stress of single crystals with long-range ordered precipitates calculated by dislocation dynamics simulations. Mat. Sci. Eng. A, 365:144–150, 2004.
V. Mohles. Simulation of particle strengthening: Lattice mismatch strengthening. Mat. Sci. Eng. A, 319–321:201–205, 2001a.
V. Mohles. Simulation of particle strengthening: the effects of the dislocation dissociation on lattice mismatch strengthening. Mat. Sci. Eng. A, 319–321:206–210, 2001b.
V. Mohles. Computer simulations of the glide of dissociated dislocations in lattice mismatch strengthened materials. Mat. Sci. Eng. A, 324:190–195, 2002.
V. Mohles. Superposition of dispersion strengthening and size mismatch stengthening: computer simulations. Phil. Mag., 83:9–19, 2003.
V. Mohles. Simulation of dislocation glide in overaged precipitation-hardened crystals. Phil. Mag. A, 81:971–990, 2001c.
V. Mohles and B. Fruhstorfer. Computer simulations of orowan process controlled dislocation glide in particle arrangements of various randomness. Acta. Mat., 50:2503–2516, 2002.
V. Mohles and E. Nembach. The peak-and overstaged states of particle strengthened materials: computer simulations. Acta. Mat., 49:2405–2417, 2001.
V. Mohles and D. Ronnpagel. Thermal activation analysis of dislocations in obstacle fields. Comp. Mat. Sci., 7:98–102, 1996.
G. Monnet. Investigation of precipitation hardening by dislocation dynamics simulations. Phil. Mag., 86:5927–5941, 2006.
N.F. Mott and F.R.N. Nabarro. Creep and plastic flow. The Physical Society, London, 1948.
E. Nadgornyi. Dislocation dynamics and mechanical properties of crystals. Progr. Mat. Sci., 31:1, 1988.
E. Nembach. Particle Strengthening of Metals and Alloys. John Wiley, 1996.
E. Orowan. über den mechanismus des gleitvorganges. Z. Phys., 89:634, 1934.
M. Peach and J.S. Koehler. The forces exerted on dislocations and the stress fields produced by them. Phys. Rev., 80:436, 1950.
R. Peierls. The size of a dislocation. Proc. Phys. Soc, London, 52:34, 1940.
M. Polanyi. über eine art gitterstörung, die einen kristall plastisch machen könnte. Z. Phys., 89:660, 1934.
W.H. Press, S.A. Teukolsky, V.T. Vetterling, and B.P. Flannery. Numerical Recipes in C. University Press, 1992.
K.W. Schwarz. Simulation of dislocations on the mesoscopic scale, i. methods and examples. J. Appl. Phys., 85:108–119, 1999.
R.B. Schwarz and R. Labusch. Dynamic simulation of solution hardening. J. Appl. Phys., 49:5174–5187, 1978.
G.I. Taylor. Proc. R. Soc, London, A145:362, 1934.
V. Volterra. Sur lequilibre des corps elastiques multiplement connexes. Ann. Ecole Norm. Super., 24:401–517, 1907.
B. von Blanckenhagen and P. Gumbsch. Discrete dislocation dynamics simulation of thin film plastcity. In D. Raabe, F. Roters, F. Barlat, and L.-Q. Chen, editors, Continuum Scale Simulation of Engineering Materials, pages 397–412. Wiley-VCH, Weinheim, 2004.
B. von Blanckenhagen, E. Arzt, and P. Gumbsch. Discrete dislocation simulation of plastic deformation in metal thin films. Acta Metallurgica, 52: 773–784, 2004.
C. Wagner. Theorie der alterung von niederschlagen durch umlosen. Elektrochem., 65:581, 1961.
J. Weertman. Elementary Dislocation Theory. Oxford University Press, New York, 1992.
Y. Xiang and D.J. Srolovitz. Dislocation climb effects on particle bypass simulations. Phil. Mag., 86:3937–3957, 2006.
H.M. Zbib, T.D. de La Rubia, M. Rhee, and J.R Hirth. 3d dislocation dynamics: stress-strain behaviour and hardening mechanisms in fee and bec metals. J. Nucl. Mater., 276:154–165, 2000a.
H.M. Zbib, M. Rhee, and J.R Hirth. On plastic deformation and the dynamics of 3d dislocations. Int. J. Mech. Sci., 40:113–127, 2000b.
H.M. Zbib, M. Hiratani, and M. Shehadeh. Multiscale discrete dislocation dynamics plasticity. In D. Raabe, F. Roters, F. Barlat, and L.-Q. Chen, editors, Continuum Scale Simulation of Engineering Materials, pages 201–229. Wiley-VCH, Weinheim, 2004.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 CISM, Udine
About this chapter
Cite this chapter
Mohles, V. (2010). Fundamental dislocation theory and 3D dislocation mechanics. In: Pippan, R., Gumbsch, P. (eds) Multiscale Modelling of Plasticity and Fracture by Means of Dislocation Mechanics. CISM International Centre for Mechanical Sciences, vol 522. Springer, Vienna. https://doi.org/10.1007/978-3-7091-0283-1_2
Download citation
DOI: https://doi.org/10.1007/978-3-7091-0283-1_2
Publisher Name: Springer, Vienna
Print ISBN: 978-3-7091-0282-4
Online ISBN: 978-3-7091-0283-1
eBook Packages: EngineeringEngineering (R0)