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Dipole heights in cyclically deformed polycrystalline AISI 316L stainless steel S. Catalao a , X. Feaugas b,∗ , Ph. Pilvin c , M.-Th. Cabrillat a b

a Laboratoire de Conception des Syst` emes Innovants (LCSI), CEA, Cadarache, France ´ Laboratoire d’Etude des Mat´eriaux en Milieux Agressifs (LEMMA), Universit´e de La Rochelle, av. Miche Crpeau, 17000 La Rochelle, France c Laboratoire G´ enie M´ecanique et Mat´eriaux (LG2M), Universit´e de Bretagne Sud-Lorient, France

Received in revised form 20 January 2005; accepted 28 March 2005

Abstract The purpose of this work is to investigate the frequency distributions of edge dipole heights in polycrystalline AISI 316L stainless steel cyclically deformed in the temperature range 300–873 K. The effects of grain orientation, temperature and plastic strain rate on dislocation microstructure are discussed in terms of the dipole annihilation distance (hmin ), the critical dipole height (hmax ), the mean dipole height h and the variance σ 2 of the frequency distributions of heights. The dipole annihilation distance (hmin ) does not depend on plastic strain rate, it increases with increasing temperature and stacking fault energy. The increase of hmin as a function of temperature can be understood in terms of the climb of edge dislocations promoted by thermal processes (formation and diffusion of vacancies). Grain orientation does not affect the dipole annihilation distance. However, the frequency distribution of heights is clearly dependent on the grain considered. The classical relation between hmax and τ µ is experimentally demonstrated in temperature range studied. © 2005 Elsevier B.V. All rights reserved. Keywords: Dipolar dislocation structures; Dipole height; Pipe diffusion

1. Introduction In a certain range of plastic strain amplitude, cyclic deformation of fcc metals leads to a localisation of plastic strain which can be recognized through a special dislocation microstructure: the so-called persistent slip bands (PSBs) surrounded by a matrix (vein and channel). For a description of microstructural mechanisms at the origin of these heterogeneous dislocation distributions and their effect on mechanical behaviour of fcc metals, knowledge of certain quantitative microstructural parameters is necessary. The main dimensional parameters generally measured: wall thickness (e) and boundary spacing (λ), have been extensively used in a composite scheme to evaluate long-range internal stresses [1–3]. However, little information has been made available regarding the evolution of the internal stress state. A measure of ∗

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0921-5093/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2005.03.094

dipole height offers a good evaluation of the rate of dislocations trapped in walls [4–6]. Edge dipoles are a characteristic feature observed in walls, channels and veins under cyclic loading. Analyses of dipole heights have been provided in metals with a medium (copper [7,8]) or high stacking fault energy (aluminium [9] and nickel [10]). However, there are remarkably few investigations in low stacking fault energy alloys [3]. The main purpose of the present contribution was to study precisely the dipole size resulting from cyclic loading in an austenitic stainless steel AISI 316L that has a low stacking fault energy (γ SFE = 25 mJ/m2 at 300 K).

2. Experimental method All experiments were performed on polycrystalline stainless steel AISI 316L with an average grain size of 53 m and a mean dislocation density below 10−10 m−2 [2,3]. The specimens and the procedures of the mechanical tests were all

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described in a previous work [3]. The investigated cyclic plastic strain amplitude was in a range 10−3 to 4 × 10−3 . Specimens were cyclically deformed under plastic strain control at temperatures 300, 373, 473, 573, 673, 773, 823 and 873 K with a plastic strain rate in a range 10−5 to 3 × 10−3 s−1 . The dislocation microstructures of individual grain were investigated using transmission electron microscopy (TEM). These investigations were conducted using a Jeol JEM 2011 electron microscope operating at 200 kV on specimens cut parallel and perpendicular to stress axis. Foils for TEM were thinned in a double twin-jet electropolisher using electrolytes and conditions previously described [2]. For each cyclic test condition, dipole height was determined over 50 grains for a cycle number corresponding to a saturation state (stress amplitude is quasi constant). Special care was taken to mark the TEM specimens so that the direction of the stress axis could be identified on stereographic map for each grain studied. The microstructure is composed exclusively of dipolar structures: dipoles bundles, veins, ladders and dipolar cells. Typical elements in dense regions of the dislocation substructure consist mainly of short narrow edge dipoles lying parallel to 1 1 2 (Fig. 1a) in accordance with cyclic stages II0 and III0 defined by Pedersen [11]. This is equivalent to observations on copper [7,8], aluminum [9], nickel [10] and austenitic stainless steel [3]. In the present work, the dipole height (h) was determined using classical weak-beam technique under a diffraction vector g = 2 2 0 [7–10]. The choice for the excitation error(s) is dictated by the resolution required [10]. It was later determined that conventional bright-field TEM procedure could allow an accurate determination of h when h is higher than 3 nm. Thus, conventional bright-field TEM was used to examine most of 100 dipoles in 50 grains for each test studied.

3. Results A quantitative analysis of the dipole heights has been performed for primary edge dislocation dipoles only. The frequency distributions of dipole heights are shown for different grain orientations on Fig. 1b. Grain orientation does not seem to affect the dipole annihilation distance (minimum height, hmin ). However, the frequency distribution of heights depends clearly on the grain considered. To explore the reason for this dependence, a correlation between the variance σ and the mean value h of dipole height has been performed (Fig. 2b). A value of parameters (σ 2 , h) seems to be defined for each microstructure observed with a dispersion which decreases with the increase of heterogeneity: (σ 2 , h) is less well defined for homogeneous dislocation distributions than for cell structures. Additionally, σ and h decrease when dislocations walls are well defined (wall and cell structures). In other words, an increase of the heterogeneity of dislocation distribution results in a sharpening of the frequency distribution and in a shift towards low values of h. In accordance with the Tippelt et al. results on nickel [10], only few very

narrow dipoles close to hmin are found resulting in a tail in the frequency distribution at low heights (Fig. 1b). In the following, we consider the minimum value, hmin , of dipole heights and the maximum value of these hmax , to characterize the height distribution (Fig. 2a). At 823 K, a negative sensitivity of the saturation stress amplitude has been observed as a function of strain rate in relation with dynamic strain aging (DSA) [12]. In terms of dipole heights, only hmax seems to depend on strain rate (Fig. 2a). hmax increases as a function of strain rate irrespective of the plastic strain imposed. hmin is independent of strain rate and equal to 4 nm at 823 K (Fig. 2a). The effect of temperature on hmin and hmax has been also studied (Fig. 3). As previously reported for nickel, both microstructural parameters increase with increasing temperature. The minimum dipole height increases from 1.2 nm at room temperature to 5 nm at 823 K.

4. Discussion Analytical modeling of dislocation patterning under cyclic loading considers a state equation which expresses the evolution of the density of edge dipoles ρdip as a function of plastic strain γ [4–6]. This kinetic equation depends mainly on the dipole annihilation distance (hmin ) and on the critical dipole height (hmax ). Consequently, a good knowledge of these parameters is imperative. hmax corresponds to a critical distance where elastic interactions between the two edge dislocations balance the minimum athermal stress τ µ : τµ =

µb µA = 8π(1 − ν)h h

(1)

where µ is the shear modulus, b the burgers vector and ν is the Poisson’s ratio. τ µ can be estimated using Dickson partition on hysteresis loops [13]. Consequently, τ µ /µ can be related to hmax for all the cyclic tests explored in the present work (Fig. 3a). Equation (1) is confirmed by the linear relation shown in Fig. 3 with a slope A equal to 0.018 nm, a value in agreement with that obtained using equation (1): A = 0.017 nm. The increase of hmin as a function of temperature can be understood in terms of an edge climb process promoted by a thermal process (formation and diffusion of vacancies). The attractive force between parallel edge dislocaµb2 tions with opposed Burgers vector ||dF zat || = 2π(1−ν)h dL dF climb = Evac dNvac [14] is balanced by the force of climb f dL dS [15]. Efvac is the energy of formation of vacancies and dNvac is the vacancy concentration created along the swept area dS. If we consider thermal processes of formation and migration of vacancies, dN vac can be written: dNvac = Hvac −PVat where Hvac is the energy dNat 1 − k exp − kB T µ(1+ν) of formation and migration of vacancies, P = 3π(1−ν) [14] is the hydrostatic pressure and Vat is the atomic volume. The

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Fig. 1. Weak-beam micrograph of a dipole bundle with g = [2 2 0] (a) and frequency distributions of dipole height for εp = 10−3 , dεp /dt = 3 × 10−3 s−1 and T = 823 K (b).

Fig. 2. Mean values of hmax and hmin as a function of strain rate (a) and the variance σ 2 as a function of the mean dipole height h (b) (T = 823 K).

Fig. 3. Correlation between hmax and µ/τ µ (a) and hmin as a function of the temperature (b).

of Hvac does not correspond to the activation energy for f +m self-diffusion (Hvac = 2.4 eV) but is of the order of the f +m energy for pipe-diffusion (0.25–0.5Hvac ) [17].

critical configuration ||dF zat || = ||dF climb || is written: hmin =

hc

−PVat 1 − k exp − Hvac kB T

µb2 hc = √ 2 2π(1 − ν)Efvac

with

(2)

where the pre-exponential factor k ≈ 1.8 and Efvac = 1.4 eV [16]. Equation (2) provides a fair account of experimental using the values hc = 1.1 nm and Hvac = 0.72 eV. The value

5. Conclusion Grain orientation does not affect the dipole annihilation distance. However, the frequency distribution of heights is clearly dependent on the grain considered. The maximum

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height dimension hmax corresponds to a critical distance where elastic interactions between the two edge dislocations balance the minimum athermal stress τ µ . The increase of annihilation distance, hmin , as a function of temperature can be understood in terms of edge climb process promoted by core diffusion of vacancies without it being necessary to take DSA into account. Acknowledgements The authors thank the Centre Commun d’Analyse, Universit´e de La Rochelle for electron microscopy facilities and the Roberval Laboratory, Universit´e de Technologie de Compi`egne for TEM and fatigue testing facilities. Financial support from Commissariat a` l’Energie Atomique is gratefully acknowledged. References [1] H. Mughrabi, Acta Metall. Mater. 31 (1983) 1367.

[2] X. Feaugas, Acta Mater. 47 (1999) 3632. [3] G. Gaudin, X. Feaugas, Mat. Sci. Eng. A A209–A310 (2001) 382. [4] K. Differt, U. Essmann, Mat. Sci. Eng. A A164 (1993) 295. [5] P. H¨ahner, Scr. Mat. 34 (1996) 435. [6] C. Gaudin, X. Feaugas, P. Pilvin, International Conference of Plasticity, Canada, June, 2003. [7] J.G. Antonopoulos, A.T. Winter, Philos. Mag. 33 (1976) 87. [8] M.E. Kassner, M.A. Wall, Mat. Sci. Eng. A A317 (2001) 28. [9] M.E. Kassner, M.A. Wall, Met. Trans. A 30A (1999) 777. [10] B. Tippelt, J. Bretschneider, P. H¨ahner, Phys. Status Solidi (a) 163 (1997) 11. [11] O.B. Pedersen, Acta Metall. 38 (7) (1990) 1221. [12] S. Catalao, X. Feaugas, Ph. Pilvin, M.-Th. Cabrillat, Colloque MECAMAT03, 2003. [13] J.L. Dickson, J. Bountin, L. Handfield, Mater. Sci. Eng. A 64 (1983) L3–L7. [14] D. Hull, D.J. Bacon, Introduction to Dislocations, Butterworth– Heinemann, 1984. [15] J. Friedel, Dislocations, Pergamon Press, 1964. [16] M.E. Glicksman, Diffusion in Solids, J. Wiley, 2000. [17] J.P. Hirth, J. Lothe, Theory of Dislocations, J. Wiley, 1982.