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Title: Cyclic hardening in copper described in terms of combined monotonic and cyclic stress-strain curves

Abstract

Hardening of polycrystalline copper subjected to tension-compression loading cycles in the plastic region is discussed with reference to changes in flow stress determined from equations describing dislocation glide. It is suggested that hardening is as a result of the accumulation of strain on a monotonic stress-strain curve. On initial loading, the behavior is monotonic. On stress reversal, a characteristic cyclic stress-strain curve is followed until the stress reaches a value in reverse loading corresponding to the maximum attained during the preceding half cycle. Thereafter, the monotonic path is followed until strain reversal occurs at completion of the half cycle. Repetition of the process results in cyclic hardening. Steady state cyclic behavior is reached when a stress associated with the monotonic stress-strain curve is reached which is equal to the stress associated with the cyclic stress-strain curve corresponding to the imposed strain amplitude.

Authors:
 [1]
  1. (Univ. of the Witwatersrand, Johannesburg (South Africa). School of Mechanical Engineering)
Publication Date:
OSTI Identifier:
6549453
Resource Type:
Journal Article
Resource Relation:
Journal Name: Acta Metallurgica et Materialia; (United States); Journal Volume: 43:1
Country of Publication:
United States
Language:
English
Subject:
36 MATERIALS SCIENCE; COPPER; HARDENING; DISLOCATIONS; FLOW STRESS; MATHEMATICAL MODELS; METALLURGICAL EFFECTS; MICROSTRUCTURE; CRYSTAL DEFECTS; CRYSTAL STRUCTURE; ELEMENTS; LINE DEFECTS; METALS; STRESSES; TRANSITION ELEMENTS; 360103* - Metals & Alloys- Mechanical Properties

Citation Formats

Chandler, H.D.. Cyclic hardening in copper described in terms of combined monotonic and cyclic stress-strain curves. United States: N. p., 1995. Web. doi:10.1016/0956-7151(95)90262-7.
Chandler, H.D.. Cyclic hardening in copper described in terms of combined monotonic and cyclic stress-strain curves. United States. doi:10.1016/0956-7151(95)90262-7.
Chandler, H.D.. 1995. "Cyclic hardening in copper described in terms of combined monotonic and cyclic stress-strain curves". United States. doi:10.1016/0956-7151(95)90262-7.
@article{osti_6549453,
title = {Cyclic hardening in copper described in terms of combined monotonic and cyclic stress-strain curves},
author = {Chandler, H.D.},
abstractNote = {Hardening of polycrystalline copper subjected to tension-compression loading cycles in the plastic region is discussed with reference to changes in flow stress determined from equations describing dislocation glide. It is suggested that hardening is as a result of the accumulation of strain on a monotonic stress-strain curve. On initial loading, the behavior is monotonic. On stress reversal, a characteristic cyclic stress-strain curve is followed until the stress reaches a value in reverse loading corresponding to the maximum attained during the preceding half cycle. Thereafter, the monotonic path is followed until strain reversal occurs at completion of the half cycle. Repetition of the process results in cyclic hardening. Steady state cyclic behavior is reached when a stress associated with the monotonic stress-strain curve is reached which is equal to the stress associated with the cyclic stress-strain curve corresponding to the imposed strain amplitude.},
doi = {10.1016/0956-7151(95)90262-7},
journal = {Acta Metallurgica et Materialia; (United States)},
number = ,
volume = 43:1,
place = {United States},
year = 1995,
month = 1
}
  • Polycrystals of pure copper were cyclically deformed, at room temperature under symmetric tension-compression fatigue at constant total strain amplitude control with an approximate constant plastic strain rate of 10[sup [minus]4]. The relationship between the saturation stress amplitude and strain amplitude over a range of plastic strain from 2 [times] 10[sup [minus]7] to 10[sup [minus]2] reveals three regions of cyclic hardening. A quasi-plateau, where the stresses show a slow constant increase, was observed in the intermediate region extending in the plastic strain range [gamma][sub pl], of 1.5 [times] 10[sup [minus]5] to 7.5 [times] 10[sup [minus]4]. In this region, persistent slip bandsmore » (PSBs) which consist of ladder' structures, similar to the case of single crystals, were found in the bulk of the fatigued polycrystals. The fatigue limit was found to be [Delta][sigma][sub s]/2 = 73 MPa which corresponds to the plastic strain [Delta][epsilon][sub pl]/2 = 1.5 [times] 10[sup [minus]5] where PSBs do not form. 62 refs., 6 figs., 1 tab.« less
  • The cyclic stress-strain response and corresponding fatigue dislocation structures of a [{bar 3}45]/[{bar 1}17] copper bicrystal were investigated over a shear strain amplitude range from 0.28 {times} 10{sup {minus}3} to 6.45 {times} 10{sup {minus}3}. Similar to copper polycrystals, this bicrystal was found to show very high saturation stresses and no obvious plateau but a bulge in the cyclic stress strain (CSS) curve. The dislocation structures in the fatigued bicrystal were also found to be similar to usually observed in cyclically deformed copper polycrystals and multiple slip copper single crystals. However, the dislocation structures in the two component crystals were differentmore » from each other. At low strain amplitudes, the prevailing dislocation structure in the [{bar 3}45] component crystal is loop patches, while the typical dislocation structure in the [{bar 1}17] component crystal consists of labyrinth-like loop patches and less orderly persistent slip band (PSB) ladder structures. With increasing strain amplitude above 0.89 {times} 10{sup {minus}3}, cell structures and labyrinth structures were found in the [{bar 3}45] component and in the [{bar 1}17] component, respectively. The labyrinth structure was found to contain (001) and (210) walls perpendicular to each other. It was also found that the grain boundary (GB) acted as an obstacle to the motion of dislocations. The dislocation-free zones, which were reported beside the GBs in fatigued copper polycrystals, were not observed in the present fatigued bicrystal. The formation of labyrinth structure was believed to be caused by the interaction of dislocations with two orthogonally oriented Burgers vectors. The occurrence of multiple slip in the two components due to the constraint of GB is interpreted to cause the observed fatigue deformation behavior and dislocation structures.« less
  • Cyclic deformation behavior and surface deformation features of [011] multiple-slip-oriented single crystals were investigated at constant plastic shear stain amplitude ({gamma}{sub pl}) in the range of 1.1 {times} 10{sup {minus}4}--7.2 {times} 10{sup {minus}3} at room temperature in air. It was revealed that the cyclic deformation characteristic of [011] copper single crystal is quite different from that of [001] and [{bar 1}11] multiple-slip-oriented copper single crystals. The cyclic stress-strain (CSS) curve of the [011] crystal exhibits a clear plateau region over the range of plastic strain amplitude investigated. Surface observations indicated that the primary persistent slip bands (PSBs) already occur undermore » a lower strain amplitude of 1.1 {times} 10{sup {minus}4}, but the operation of secondary slip was strongly suppressed by the corresponding dislocation interactions even at high strain amplitudes. This slip characteristic was suggested to be associated with the occurrence of the plateau region. When {gamma}{sub pl} {ge} 2.5 {times} 10{sup {minus}3}, two types of deformation bands (DBI and DBII) formed on the specimen surface and their habit planes are perpendicular to each other strictly. An analysis based on the classical crystallographic deformation geometry was proposed to interpret the existence of an irreversible rotation of crystal in single crystal subjected to symmetrical push-pull loading. This phenomenon is assumed to be an essential reason for the formation of DBI and DBII. When {gamma}{sub pl} {ge} 5.0 {times} 10{sup {minus}3}, another type of deformation band (DBII) was observed on the specimen surface and its habit plane is exactly (001) for the formation of DBIII, giving rise to the cyclic softening in the cyclically deformed [011] copper single crystals at high strain amplitudes ({gamma}{sub pl} {ge} 5.0 {times} 10{sup {minus}3}).« less
  • The subject program on substructure evolution initially focused on strain localization produced by fatigue cycling and especially how such localization affects the cyclic response of polycrystalline pure metal. The latter stages have dealt with strain localization in the heavy monotonic deformation of alloys, which eventually produces forms of localized deformation that include coarse slip bands (CSB's), which are aligned to slip planes and macroscopic shear bands (MSB's), which are not aligned to slip planes. These forms of strain localization are important in that they limit the usable ductility of the material in forming processes.