journal article·2025-05Open access

Modelling the Bauschinger effect in copper during preliminary load cycles

Alvaro Martinez-Pechero, Eralp Demir, Chris Hardie, Yevhen Zayachuk, Anna Widdowson, Edmund Tarleton

Acta Materialia· Volume 289

Abstract

This research utilizes established cyclic deformation models to simulate the Bauschinger effect observed in copper monocrystal cantilever experiments during the initial bending and straightening phases. Crystal plasticity finite element simulations employing Armstrong-Frederick , Orowan-Sleeswyk , and various other backstress models have drawbacks to reproduce the experimental force–displacement curves accurately since they are not able to reproduce the isotropic hardening measured during cantilever straightening. However, the Armstrong-Frederick model combined with Voce-type hardening and a newly proposed modified Orowan-Sleeswyk model has proven to be effective. In this work, we propose a modified Orowan-Sleeswyk model, based on recent studies, where not all the geometrically necessary dislocations (GND) recombine during the straightening phase, but instead reorient to achieve a net zero-strain gradient with ongoing hardening during load reversal.
Source: openalex_inverted_index · Quality: baseline

Research context

OpenAlex topics: Microstructure and mechanical properties · Microstructure and Mechanical Properties of Steels · Metallurgy and Material Forming

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

References (60)

Show source-provided references
1. The use of copper alloy CuCrZr as a structural material for actively cooled plasma facing and in vessel components10.1016/j.fusengdes.2005.06.056 ↗
2. Material parameters of copper and CuCrZr alloy for cyclic plasticity at elevated temperatures10.1016/j.jnucmat.2007.06.005 ↗
3. The Bauschinger effect and the stresses in a strained single crystal10.1016/0956-716X(92)90407-6 ↗
4. Basis for the Bauschinger effect in copper single crystals: changes in the long-range internal stress with reverse deformation10.1007/s10853-018-03295-6 ↗
5. Importance of dislocation pile-ups on the mechanical properties and the Bauschinger effect in microcantilevers10.1557/jmr.2015.49 ↗
6. Comparative assessment of backstress models using high-energy X-ray diffraction microscopy experiments and crystal plasticity finite element simulations10.1016/j.ijplas.2020.102887 ↗
7. Dislocation wall and cell structures and long-range internal stresses in deformed metal crystals10.1016/0001-6160(83)90007-X ↗
8. The Bauschinger effect in copper10.1016/0001-6160(81)90110-3 ↗
9. E. Orowan, Internal stresses and fatigue in metals, in: Proceedings of the Symposium on Internal Stresses and Fatigue in Metals, Detroit, 1959.
10. Reversible strain in cyclic plastic deformation10.1016/0001-6160(78)90011-1 ↗
11. Long range internal stresses in single-phase crystalline materials10.1016/j.ijplas.2012.10.003 ↗
12. Bauschinger effect and latent hardening under cyclic micro-bending of Ni-base alloy 718 single crystals: Part I. Experimental analysis of single and multi slip plasticity10.1016/j.msea.2021.142027 ↗
13. Armstrong · 1966
14. On the theoretical and numerical modelling of Armstrong–Frederick kinematic hardening in the finite strain regime10.1016/j.cma.2003.09.005 ↗
15. A texture-based representative volume element crystal plasticity model for predicting Bauschinger effect during cyclic loading10.1016/j.msea.2014.04.067 ↗
16. An investigation into the robustness of a crystal plasticity finite element model
17. Bauschinger effect and latent hardening under cyclic micro-bending of Ni-base alloy 718 single crystals: Part II. Single crystal plasticity modeling with latent kinematic hardening10.1016/j.msea.2021.142030 ↗
18. Comparative assessment of backstress models using high-energy X-ray diffraction microscopy experiments and crystal plasticity finite element simulations10.1016/j.ijplas.2020.102887 ↗
19. Mechanical and microstructural single-crystal Bauschinger effects: Observation of reversible plasticity in copper during bending10.1016/j.actamat.2010.07.023 ↗
20. Irreversible evolution of dislocation pile-ups during cyclic microcantilever bending10.1016/j.matdes.2024.112682 ↗
21. Cyclic response of copper single crystal micro-beams10.1016/j.scriptamat.2010.05.014 ↗
22. Restraining geometrically-necessary dislocations to the active slip systems in a crystal plasticity-based finite element framework10.1016/j.ijplas.2024.104013 ↗
23. OXFORD-UMAT: An efficient and versatile crystal plasticity framework
24. Tarleton · 2024
25. Bunge · 2013
26. Smith · 2022
27. Constitutive analysis of elastic-plastic crystals at arbitrary strain10.1016/0022-5096(72)90017-8 ↗
28. Schmid · 2013
29. Khan · 1995
30. Ideal orientations and persistence characteristics of hexagonal close packed crystals in simple shear10.1016/j.actamat.2006.12.021 ↗
31. Huang · 1991
32. On the consequences of the adoption of the Zaremba–Jaumann objective stress rate in FEM codes10.1007/s11831-014-9130-z ↗
33. Constitutive analysis of elastic-plastic crystals at arbitrary strain10.1016/0022-5096(72)90017-8 ↗
34. The mathematics of the physical properties of crystals10.1002/j.1538-7305.1943.tb01304.x ↗
35. Spherical indentation of copper: Crystal plasticity vs experiment10.1016/j.mtla.2019.100368 ↗
36. Lengthscale-dependent, elastically anisotropic, physically-based hcp crystal plasticity: Application to cold-dwell fatigue in Ti alloys10.1016/j.ijplas.2006.10.013 ↗
37. Plastic strain in metals
38. Crystallographic aspects of geometrically-necessary and statistically-stored dislocation density10.1016/S1359-6454(99)00020-8 ↗
39. Some geometrical relations in dislocated crystals10.1016/0001-6160(53)90054-6 ↗
40. Meric · 1991
41. Chaboche · 1989
42. Kinematic hardening rules with critical state of dynamic recovery, part II: application to experiments of ratchetting behavior10.1016/0749-6419(93)90043-P ↗
43. An internal variable constitutive model for hot working of metals10.1016/0749-6419(89)90025-9 ↗
44. Crystallographic texture evolution in bulk deformation processing of FCC metals10.1016/0022-5096(92)80003-9 ↗
45. Modeling transients in the mechanical response of copper due to strain path changes10.1016/j.ijplas.2006.08.001 ↗
46. Investigation of the indentation size effect through the measurement of the geometrically necessary dislocations beneath small indents of different depths using EBSD tomography10.1016/j.actamat.2008.09.039 ↗
47. A simplex method for function minimization10.1093/comjnl/7.4.308 ↗
48. Obtaining SiC fibers–PyC interfacial properties through push-out FEM models10.1016/j.jeurceramsoc.2023.09.080 ↗
49. A quasi-2D integrated experimental–numerical approach to high-fidelity mechanical analysis of metallic microstructures10.1016/j.actamat.2023.119551 ↗
50. Microstructure versus size: mechanical properties of electroplated single crystalline cu nanopillars10.1103/PhysRevLett.104.135503 ↗
51. Dai · 1997
52. The rate-determining process in luders band growth10.1016/0036-9748(72)90125-1 ↗
53. Investigation of the indentation size effect through the measurement of the geometrically necessary dislocations beneath small indents of different depths using EBSD tomography10.1016/j.actamat.2008.09.039 ↗
54. Consistent determination of geometrically necessary dislocation density from simulations and experiments10.1016/j.ijplas.2018.05.001 ↗
55. A model of extrusions and intrusions in fatigued metals I. Point-defect production and the growth of extrusions10.1080/01418618108239541 ↗
56. A model of extrusions and intrusions in fatigued metals II. Surface roughening by random irreversible slip10.1080/01418618608242897 ↗
57. Annihilation of dislocations during tensile and cyclic deformation and limits of dislocation densities10.1080/01418617908234871 ↗
58. Cyclic slip irreversibilities and the evolution of fatigue damage10.1007/s11663-009-9240-4 ↗
59. A micromechanical model of cyclic deformation and fatigue-crack nucleation in fcc single crystals10.1016/S1359-6454(96)00368-0 ↗
60. The physics of fatigue crack initiation10.1016/j.ijfatigue.2012.10.009 ↗