Influence of Heterogeneous Dislocation Arrangements on X-ray Diffraction Profiles Measured on Cyclically Deformed Nickel Single Crystals: Part II: Shape Changes of Diffraction Profiles During a Deformation Cycle

Michael Hecker; Ellen Thiele; Carl Holste

doi:10.3139/ijmr-1998-0037

Article

Influence of Heterogeneous Dislocation Arrangements on X-ray Diffraction Profiles Measured on Cyclically Deformed Nickel Single Crystals

Part II: Shape Changes of Diffraction Profiles During a Deformation Cycle

Michael Hecker , Ellen Thiele and Carl Holste

Published/Copyright: December 27, 2021

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From the journal International Journal of Materials Research Volume 89 Issue 3

Abstract

Nickel single crystals of different orientations were deformed cyclically into the stage of mechanical saturation and investigated by high resolution X-ray diffraction after unloading from different points of the mechanical hysteresis loop. Characteristic changes of the diffraction profile shape were found indicating a variation of long-range internal stresses within the hysteresis cycle. By an analysis of the diffraction profiles these stresses could be determined for different dislocation structures. For example, the internal stresses arising in persistent slip bands (PSBs) were estimated. From the experimental results the conclusion is drawn that macroyielding occurs not only in PSBs but also in regions with a dislocation structure typical for the [001] sample orientation, provided the strain amplitude exceeds a threshold value.

Abstract

An Nickel-Einkristallen verschiedener Orientierung, die bis ins Stadium der Sättigung der mechanischen Eigenschaften zyklisch verformt worden sind, wurden hochaufgelöste Röntgenbeugungsprofile nach Entlastung von unterschiedlichen Punkten der mechanischen Hystereseschleife gemessen. Es traten charakteristische Änderungen der Profilform auf, die auf die Änderung weitreichender innerer Spannungen im Hysteresezyklus zurückzuführen sind. Diese Spannungen konnten für verschiedene Versetzungsstrukturen, beispielsweise für persistente Gleitbänder (PSBs), mittels einer Analyse der Beugungsprofile bestimmt werden. Es wird geschlußfolgert, daß in Gebieten mit PSBs und, oberhalb einer Schwellamplitude, in Bereichen mit der für [001]-Orientierung typischen Struktur „Makrofließen“ auftritt.

Michael Hecker, Ellen Thiele, Carl Holste Institut für Physikalische Metallkunde Technische Universität Dresden Mommsenstr. 13 D-01069 Dresden, Germany

Support of this work by the DFG (contract No. Ho 1342/4-2) is gratefully acknowledged.

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Appendix

For the measuring conditions of the present investigation, the number of {311} reflections measurable on a sample surface is not sufficient to determine the full strain tensor ε_ij. Therefore, model assumptions are needed to estimate internal shear strains in a slip system. The value experimentally available is the normal strain ε_g which may be calculated from the diffraction profile parameters for a given measuring direction.

An assumption used already in [1] is that a heterogeneous plastic shear strain in an active slip system gives rise to an elastic strain which may be written in the form

(A1) ε= 0γ20γ200000

for the mean elastic strain within a mesoscopic region. If a strain tensor of such type is assumed to be produced in each of n active slip systems, the resulting elastic shear strain ε^121 can be calculated for the primary slip system from the contributions of all active slip systems according to

(A2) ε ^ 12 ( 1 ) = γ 2 ∑ i = 1 n cos b → ( 1 ) , b → ( i ) ⋅ cos n → a ( 1 ) , n → a ( i ) + cos b → ( 1 ) , n → a ( i ) ⋅ cos n → a ( 1 ) , b → ( i )

where b→i and n→ai denote the Burgers vector and the slip plane normal vector of the i-th slip system. For n> 1 it is assumed that the plastic shear strains are of equal magnitude in each slip system. For the double-slip orientation the number of active slip systems is set to n = 2, whereas for the [001] orientated crystal n = 8 slip systems are considered.

The normal strain ε_g in measuring direction can be expressed in a similar way by

(A3) εg=γ∑i=1ncosg→,b→i⋅cosg→,n→ai

(g→.. diffraction vector).

Both quantities may be related formally by an “orientation factor” K_γ:

(A4) εg=Kγε^121

For the special case of only one active slip system, K_γ results to be [1]

(A5) Kγ=2cosg→,b→1⋅cosg→,n→a1

In the framework of isotropic elasticity, it follows for the shear stress τ in the primary slip system

(A6) τ=2GεgKγ

Taking into account the definition of the asymmetry parameter ϑas and using the assumptions discussed in Section 4.1, the mean internal shear stress τPRE of the dislocation-poor regions in the primary slip system can be related to ϑas according to

(A7) τPrEγp=2G−π180°ϑasγpKγtanθ

In analogy to Eq. (A7), the breadth of the PR stress distribution is given by

(A8) Δβτ=2G−π180°ΔFWHMKγtan θ

Received: 1997-07-17

Published Online: 2021-12-27

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https://doi.org/10.3139/ijmr-1998-0037