journal article·2025-09-27Open access

Multiscale Theory of Dislocation Plasticity

Alexander R. Umantsev

Crystals· Volume 15· Issue 10

Abstract

Motion of dislocations is a common mechanism of plasticity in many materials. Dislocation-mediated deformation is essentially an inhomogeneous process, which is manifest in the formation of slip lines and complicated cell wall structures. An adequate description of these processes is an important goal of Materials Theory, which aims to describe the mechanical properties of materials and their reliability in service. This publication advances the thermodynamically consistent theory of dislocation-mediated plasticity to include the spatial gradients of the independent variables. We conducted the renormalization group scaling analysis of deformation and obtained the low-energy dislocation structures as ordinary solutions of the equilibrium equations without any arbitrary assumptions. We matched the emerging theoretical structures with the experimentally observed and made several predictions regarding possible experiments.
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Research context

OpenAlex topics: Microstructure and mechanical properties · Nonlocal and gradient elasticity in micro/nano structures · Microstructure and Mechanical Properties of Steels

SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.

Affiliations

Department of Chemistry, Physics and Materials Science, Fayetteville State University, Fayetteville, NC 28301, USA

References (46)

Show source-provided references
1. A unified phenomenological description of work hardening and creep based on one-parameter models10.1016/0001-6160(84)90202-5 ↗
2. Physics and phenomenology of strain hardening: The FCC case10.1016/S0079-6425(02)00003-8 ↗
3. Krausz, A.S., and Krausz, K. (1996). Dislocation-Density-Related Constitutive Modeling. Unified Constitutive Laws of Plastic Deformation, Academic Press, Inc.10.1016/B978-012425970-6/50006-0 ↗
4. Thermodynamic theory of dislocation-mediated plasticity10.1016/j.actamat.2010.03.009 ↗
5. Statistical thermodynamics of dislocations in solids10.1080/00018732.2023.2190730 ↗
6. A Phase-Field theory of dislocation dynamics, strain hardening and hysteresis in ductile single crystals10.1016/S0022-5096(02)00037-6 ↗
7. Dislocation Structures and the Deformation of Materials10.1103/PhysRevLett.93.265503 ↗
8. The self-force on a planar dislocation loop in an anisotropic linear-elastic medium10.1016/0022-5096(76)90001-6 ↗
9. A non-singular continuum theory of dislocations10.1016/j.jmps.2005.09.005 ↗
10. Energy of dislocation networks10.1016/j.ijengsci.2016.02.011 ↗
11. The Thermodynamics of Plastic Deformation and Generalized Entropy10.1103/RevModPhys.22.56 ↗
12. A Phenomenological Theory for Plastic Deformation of Polycrystalline Metals10.1016/0001-6160(70)90089-1 ↗
13. Sedov, L.I. (1970). Mechanics of Continuum Media, Nauka. (In Russian).
14. Landau, L.D., and Lifshitz, E.M. (1970). Theory of Elasticity, Pergamon Press. Chapter 3.
15. Bifurcation Theory of Plasticity, Damage and Failure10.1016/j.mtcomm.2021.102121 ↗
16. Thermodynamically Consistent Model of Dislocation-Mediated Plasticity
17. Kachanov, L.M. (1986). Introduction to Continuum Damage Mechanics, Martinus Nijhoff Publishers.10.1007/978-94-017-1957-5 ↗
18. Mayergoyz, I.D. (1991). Mathematical Models of Hysteresis, Springer.10.2172/6911694 ↗
19. Gurtin, M.E., Fried, E., and Anand, L. (2010). The Mechanics and Thermodynamics of Continua, Cambridge University Press.10.1017/CBO9780511762956 ↗
20. Elastic materials with couple-stresses10.1007/BF00253945 ↗
21. On first strain-gradient theories in linear elasticity10.1016/0020-7683(68)90036-X ↗
22. On the Microstructural Origin of Certain Inelastic Models10.1115/1.3225725 ↗
23. Morphogenesis in plasticity: Gradients, dislocation patterns & deformation bands-in recognition of Nasr Ghoniem’s research contributions10.1186/s41313-024-00067-5 ↗
24. A theory of strain-gradient plasticity for isotropic, plastically irrotational materials. Part I: Small deformations10.1016/j.jmps.2004.12.008 ↗
25. A Phenomenological Theory for Strain Gradient Effects in Plasticity10.1016/0022-5096(93)90072-N ↗
26. Strain Gradient Plasticity10.1016/S0065-2156(08)70388-0 ↗
27. Yuen, W.Y.D., Broadbridge, P., and Steiner, J.M. (February, January 26). From Micro- to Macroscale: Gradient Models of Plasticity. Proceedings of the International Conference on Engineering Mathematics: Research, Education and Industry Linkage, Sydney, Australia.
28. Strain gradient plasticity modelling of high-pressure torsion10.1016/j.jmps.2007.10.004 ↗
29. Dislocation Cell Formation in Metals Available to Purchase10.1063/1.1659399 ↗
30. The dislocation cell size and dislocation density in copper deformed at temperatures between 25 and 700 °C10.1016/0001-6160(72)90012-0 ↗
31. Theory of Dislocation Cell Sizes in Deformed Metals10.1016/0025-5416(82)90086-6 ↗
32. Creep and dislocation substructure10.1179/imr.1985.30.1.1 ↗
33. A Compilation and Analysis of Data for the Stress Dependence of the Subgrain Size10.1016/0025-5416(86)90265-X ↗
34. Theory of Plastic Deformation: -properties of low energy dislocation structures10.1016/0921-5093(89)90290-6 ↗
35. Evolution of F.C.C. deformation structures in polyslip10.1016/0956-7151(92)90296-Q ↗
36. Annihilation of dislocations during tensile and cyclic deformation and limits of dislocation densities10.1080/01418617908234871 ↗
37. In situ characterisation of the strain fields of intragranular slip bands in ferrite by high-resolution electron backscatter diffraction10.1016/j.actamat.2022.118284 ↗
38. Low Energy Dislocation Structures Produced by Cyclic Deformation10.1016/0025-5416(86)90281-8 ↗
39. Latent hardening in cyclic deformation of copper single crystals10.1007/BF02667593 ↗
40. Polák, J. (2023). Role of Persistent Slip Bands and Persistent Slip Markings in Fatigue Crack Initiation in Polycrystals. Crystals, 13.10.3390/cryst13020220 ↗
41. Barenblatt, G.I. (2003). Scaling, Cambridge University Press.10.1017/CBO9780511814921 ↗
42. Sedov, L.I. (1959). Similarity and Dimensional Methods in Mechanics, Academic Press.
43. Scaling Properties of Dislocation Simulations in the Similitude Regime10.1088/0965-0393/22/6/065012 ↗
44. On temperature scaling in dislocation plasticity10.1016/j.jmps.2022.105102 ↗
45. Cell structure in cold worked and creep deformed phosphorus alloyed copper10.1016/j.matchar.2014.01.007 ↗
46. Sandström, R., Hallgren, J., and Burman, G. (2025, July 12). Stress Strain Flow Curves for Cu-OFP. SKB Raport R-09-14, Swedish Nuclear Fuel and Waste Management Co. Available online: www.skb.se.