effect of grain size - Science Direct

Available online at www.sciencedirect.com

Procedia Engineering 10 (2011) 863–868

ICM11

Damage mechanism related to localization of plastic deformation of WaspaloyTM: effect of grain size H.S. HOa*, M. RISBETa, X. FEAUGASb, G. MOULINa a

Laboratoire Roberval, Université de Technologie de Compiègne, Centre de Recherches de Royallieu, BP 20529 –60200 Compiegne cedex, France b Université La Rochelle, Laboratoire LEMMA, Bâtiment Marie Curie, Avenue Michel Crépeau, 17042 La Rochelle, France

Abstract This paper focuses on the effect of grain size on the damage mechanism of WaspaloyTM related to the localization of plastic deformation by fatigue. Such effect is examined from nano- to meso-scale by investigating the cyclic behavior of damaged specimens related to the irreversibility of plastic strain. The evolution of the average extrusion height as a function of number of cycles could be divided into three parts, which could be related to the internal stresses evolution. Damage occurrence is observed only when a saturation state, which depends on grain size is observed in terms of stress and height of extrusion.

© 2011 Published by Elsevier Ltd. Open access under CC BY-NC-ND license. Selection and peer-review under responsibility of ICM11 Keywords: Irreversibility; Nickel based superalloy; Grain size; Low cycle fatigue; Cyclic deformation behavior

1. Introduction Fatigue damage in precipitation-hardened materials is generally related to the surface phenomenon. Under low cycle fatigue loading, the presence of shearable precipitates by dislocations results in the localization of plastic deformation on the shear bands (SBs). The extrusions observed on the material surface are the consequence of the irreversible motion of dislocations in the SBs [1-5; 8-16]. Thus the topographical details along extrusions must be considered to define a crack initiation criterion. The detailed form of the profiles depends on temperature and material. Slip band emergences are generally formed by ribbon-like extrusions with a wavy character. The evolution of the height all along the extrusion shows a lesser variation (lower than 10 %) in austenitic stainless steel [2]. However, quite different results are observed in an under-aged alloy (WaspaloyTM), where the variation of emerging height along extrusion can equal to 250 % [14, 15]. This wavy characteristic enables an analysis of extrusion height by using atomic force microscopy (AFM) [1-4; 12-16]. As slip bands are the origin of fatigue crack nucleation in precipitation-hardened materials, the extrusion heights are computed by using a statistical approach in order to define fatigue crack nucleation criterion [3; 4; 1416]. In the previous works [3; 4; 14-16], it has been shown that cracks may nucleate when extrusions reach a critical

* Corresponding author. Tel.: +33-344-234-527; fax: +33-344-234-689. E-mail address: [email protected].

1877-7058 © 2011 Published by Elsevier Ltd. Open access under CC BY-NC-ND license. Selection and peer-review under responsibility of ICM11 doi:10.1016/j.proeng.2011.04.142

864

H.S. HO et al. / Procedia Engineering 10 (2011) 863–868

height of 50nm, but it is not a sufficient condition to cause damages. Risbet et al. [3] mentioned that the crystallographic Schmid factor does not affect the crack nucleation site. However, a compilation of recent measurements of plastic strain irreversibility obtained with atomic force microscopy (AFM) suggests that the fatigue crack initiation depends on grain size. In present work, we focus the analysis on the influence of grain sizes on the damaged mechanism of under-aged WaspaloyTM having one precipitate state. Fatigue tests are carried out until crack initiation state. Observation analyses of fatigued specimens are performed with scanning electron microscopy, SEM and AFM. 2. Material and Experimental Procedure

2.1. Material The material under investigation is an under-aged (shearable precipitates by dislocations) Nickel based superalloy, WaspaloyTM with the chemical compositions in wt %: 1.80 Al; 3.33 Ti; 12.64 Co; 19.45 Cr; 7.31 Mo; balance Ni. This face-centered cubic (fcc) polycrystal is characterized by strengthening spherical precipitates, Ȗ’ (Ni3Al). No crystallography texture is observed on the as-received state. The grain size and the precipitate size of the as-received state are D = 67 m and d = 45 nm. 2.2. Experimental Procedure

2.2.1. Heat Treatment, Surface Preparation and SEM Observation It is assumed here that precipitate size should not cross a threshold value of 50 nm (under-aged) in order to remain in the dislocation particle shearing deformation mode. Heat treatments are used to modify the metallurgical parameters and they are performed in a Thermolyne 4800 non-vacuum furnace on the as-received state. In order to obtain controlled microstructural dimensions, the specimens undergo through two heat treatments. The initial treatment consists in dissolving precipitates but it is also a grain-growing treatment. The heat treatments are conducted at 1100 °C for durations from four hours to seven days followed by oil quenching. The subsequent treatments are conducted from 650 °C to 750 °C from four to six hours followed by air quenching. The experimental conditions can result in three average grain sizes: 50 m, 100 m, 200 m while keeping the same average precipitate dimension of 20 nm. Concerning the surface preparations, specimens were mechanically polished up to 4000 grit SiC paper followed by chemically etched in a mixture of 2/3 hydrochloric acid and 1/3 nitric acid for a duration of 1 min 30. The surface observation was performed on a (FEG) Zeiss Sigma SEM. 2.2.2. Fatigue Experiments Low cycle fatigue tests were conducted using Instron servohydraulic machine at ambient temperature on hourglass cylindrical specimens with a gauge length of 15 mm and a gauge diameter of 6 mm. The tests were carried out until the initiation of cracks on a controlled plastic strain amplitude of İp/2 = 0.3 % with a fully reversed triangular wave form. Fatigue tests have to be interrupted in order to track the evolution of the extrusions heights with AFM and to detect the crack nucleation by SEM. The crack is considered as initiated when its length is equivalent to the dimension of a grain. According to the feature of hysteresis loops [18; 19], the cyclic stress (ıa) can be divided into two components: effective stress (ıeff) and back stress (X) which enable an investigation of the physical nature of grain size effect. The stress partition (as expressed in Eq.1) is based on the analysis proposed by Dickson et al. [20; 21]. ıeff = ½(ı-ır) + ½ ı* and X = ı- ıeff

(1)

865


where the thermal part of flow stress ı* and the reverse yield stress ır is obtained with a plastic strain offset equal to (4±2) ×10-5 . 2.2.3. Procedure to Perform AFM Measurement The surface relief was examined using Dimension 3100 Nanoscope microscopy in Tapping Mode at room temperature. A total of ten grains of a specimen were investigated for each interrupted test. The AFM topographic image of an investigated grain represents a zone of 10 ȝm x 10 ȝm showing slip bands of the grain. The methods for micrograph analysis are mentioned and detailed in [3-4]. 3. Results and Discussions

3.1. SEM Observation The microstructural features of W1 (see Table 1) are shown in Fig. 1. Slip markings are observed in each grain which corresponds to different slip systems and generally only one slip system is activated in most of the grains but sometimes two slip systems may be activated as shown in Fig. 1(a). Figure 1(b) shows features like precipitates, extrusions and microcracks initiation along slip bands while Fig. 1(c) shows microcracks initiation along grain boundaries.

(a)

(b)

(c)

Fig. 1 – (a) Activation of two slip systems in a grain, (b) microstructures features of W1 and (c) intergranular crack in W3 at crack initiation phase

Table 1 : Investigated specimens with different grain sizes

Name W1 W2 W3

D (m) 50 100 200

d (nm) 20 17 18

fv (%) 22 23 24

Ni (cycles) 800 700 650

Table 1 presents the metallurgical states of the three specimens: grain sizes D, precipitate size d and numbers of cycles leading to crack initiation Ni. The grain sizes can have effect on the cracking path, which could be intergranular or transgranular. The cracks nucleate along the slip bands in W1 and W2 specimens’. In contrast to W1 and W2, the cracks appear to be intergranular only in W3 as illustrated in Fig. 1(c). 3.2. Fatigue Tests As observed in Table 1, the number of cycles leading to crack nucleation decreases as the grain size increases. The cyclic loading behavior of each specimen is illustrated in term of stress as a function of number of cycles, as shown in Fig. 2(a). It is observed that the level of the stress decreases as the grain size increases. It is a well known

866


effect, known as the Hall-Petch mechanism, which explained the effect of grain size on both tensile and fatigue strength [7; 19]. Figure 2(b) shows the linear relationship between the yield strength, σy and saturation stress amplitude, σas as a function of D-1/2, which can be formalized with the Hall-Petch relation (Eq. 2): ı = ı0 + k/D½

(2)

N ZKLFK FKDUDFWHUL]HV WKH JUDLQ VL]H GHSHQGHQFH LV TXLWH VLPLODU IRU WHQVLRQ RU F\FOLF WHVWV DQG HTXDO 03DμP )RU WHQVLRQ ORDGLQJ WKLV YDOXH LV KLJKHU WKDQ WKH RQH REWDLQHG IRU ZDY\ VOLS IRU QLFNHO DQG IRU SODQDUVOLSIRUDXVWHQLWLFVWHHO LQVLQJOHSKDVHPHWDOVLQ>@0RUHRYHULWZDVUHSRUWHGLQ>@WKDWNVWD\V ORZHUXQGHUF\FOLFORDGLQJWKDQWKHYDOXHVREWDLQHGXQGHUWHQVLOHORDGLQJIRUQLFNHOZKLFKLVQRWWKHFDVHLQSUHVHQW ZRUN ,W ZDV VKRZQ WKDW WKH PDLQ SDUW RI JUDLQ VL]H GHSHQGHQFH RI VWUHVV LV DVVRFLDWHG ZLWK LQWHUJUDQXODU SODVWLF VWUDLQ LQFRPSDWLELOLWLHV LQ >@ 7KXV XQGHUDJHG DOOR\V H[KLELW SUREDEO\ ODUJH LQWHUQDO VWUHVVHV WKDQ VLQJOHSKDVH PHWDOV σa,MPa

1000

1200

σy , MPa

1000

W1, D = 50m 900

800 W2, D = 100m

800

600

W3, D = 200m

400 200

N,cycle

700 1

10

Nσm ax

100

1000

0 0,05

10000

σy FATIG Série1 σas

-1/2

D 0,1

(a)

-1/2

,m

0,15

(b)

Fig. 2 – (a) Fatigue stress as a function of number of cycles and (b) Hall-Petch plot

For each curve, three cyclic evolution stages can be distinguished: hardening, peak and softening. Cyclic hardening corresponds to an accumulation of dislocations within intense deformation bands through grains. Cyclic softening is principally due to the precipitates shearing by dislocations. Other reasons may also cause softening, as mentioned in [8-11]. The number of cycles corresponding to the peak value of the stress is about 20 for W1 and around 30 for W2 and W3. Concerning the specimen W1, the stress amplitude is stabilized after the softening phenomena, which is due to the presence of the twinning boundaries in small grain size [17]. σeff,MPa

X,MPa 500

450

350

W1,D=50m 350 W2,D=100m W3,D=200m 2

10 N, cycles

(a)

10

4

300 0 10

dX/dN

400

VXW1,D=50m VXW2,D=100m VXW3,D=200m

1.5

450

400

300 0 10

2

500

1 0.5

W1,D=50m W2,D=100m W3,D=200m 2

10

N, cycles

(b)

0 4

10

-0.5 0 10

1

10

2

N, cycles 10

(c)

Fig. 3 – (a) Back stress, (b) effective stress and (c) back stress rate (VX =dX/dN) as a function of number of cycles

3

10

867


The cyclic stress can be evaluated in term of internal stresses: effective stress σeff and back stress X. According to [7; 18], both internal stresses, σeff and X verify Hall-Petch relation but σeff seems to be less dependant on grain size in the contrast of X. However Fig. 3(b) seems to demonstrate the dependence of grain size on effective stress. This effect can be explained in term of shear stress. According to the shear stress formula in [22], the calculated shear stresses for W1, W2 and W3 are respectively 495 MPa, 439 MPa and 464 MPa. The differences of the value calculated for each specimen at the same order of magnitude explain well the level of the effective stresses of these three specimens. It is normal to observe this phenomenon as the precipitate size, d and the volume fraction, fv (parameters which determine the shear stress) of each specimen are not exactly the same (Table 1). As grain size has an influence on X, X is then discussed in term of back stress rate (VX = dX/dN) as a function of number of cycles as illustrated in Fig. 3(c). For these three specimens, three different stages can be identified in line with the slope. By comparing the results in Fig. 2(a) and 3(c), it is found that a fast decreasing VX in stage 1 can be related to the hardening zone while a slow decreasing VX could be associated to the peak zone and in stage 3, VX remains constant, which could be linked to the softening zone. The last state occurs above crack initiation. 3.3. AFM Experiments The irreversibility phenomena are examined by measuring the extrusion height along slip bands for each interrupted fatigue test. All experimental procedures performing AFM measurements are detailed in [3; 4]. Figure 4 shows the topographic images of three specimens of different grain sizes in the crack nucleation phase.

(a)

(b)

(c)

Fig. 4 – Topographic images taken with AFM of W1 (a), W2 (b) and W3 (c) after attaining crack initiation phase

, nm

80

Ni

60

, nm

90

W1, D=50m W2, D=100m W3, D=200m

W1, D=50m

80 50 nm

W3, D=200m

70

40

Saturation

60

20

1

2

3

50

N, cycle

0 1

10

100

W2, D=100m

1000

D, m

40 0

100

(a) Fig. 5 – Evolution of average extrusion height as a function of (a) number of cycles and (b) grain size

200

(b)

300

868


Figure 5(a) shows the evolution of as a function of number of cycles for W1, W2 and W3. It is demonstrated on these curves that three stages noted 1, 2 and 3 can be identified. This curve partitioning could be related to the one in Fig. 2(a). In Fig. 5(a), increases slightly until N = 20 in stage 1 (hardening zone in Fig. 2(a)) affirms the formation of slip bands marking. The growth of extrusion until N = 100 in stage 2 (peak zone in Fig. 2(a)) is very significant and it can be related to the intensification and multiplication of slip bands marking and the growth of extrusion height. In stage 3 (softening zone in Fig. 2(a)), extrusion height remains constant. The correlation between the curves partitioning in Fig. 5(a) related to the one in Fig. 2(a) is valid for these three specimens having different grain size. In agreement with previous work in [3-4], cracks initiate thereafter in the saturation phase. The saturation height of all investigated specimens are higher than a threshold value of 50 nm, which is in accordance with previous work [4; 16] mentioning that damage occurs only when attains this critical value. It seems that the saturation height obtained in stage 3 shows a less decreases as a function of grain size and attains saturation when D is larger than 100m as illustrated in Fig. 5(b). This situation corresponds to the occurrence of intergranular crack. 4. Conclusion The present study focuses on the effect of grain sizes of a Nickel based superalloy, WaspaloyTM on the cyclic behavior and damage occurrence related to the irreversibility of plastic strain. Heat treatments were performed to obtain three specimens having different grain sizes but same precipitate size. The effect of grain size on long-range internal stresses motivates an investigation of back stress rate, which could be divided into three stages corresponding to hardening, peak and softening zones, respectively. The evolution of the average extrusion height as a function of number of cycles could also be divided into three parts, which could be related to the previously mentioned three stages. Damage occurrence is observed only in last stage in accordance with previous work and depends on grain size. Further work is in progress in order to better understand the damage mechanism related to localization of plastic deformation of WaspaloyTM and to enlarge the existing database as well.

Reference [1] J. Man, M. Petrenec, K. Obrtlik, J. Polak, Acta Materialia 2004; 52(19); 5551-5561 [2] P. Villechaise, L. Sabatier, J.C. Girard, Materials Science and Engineering A 2002; 323(1-2); 377-385 [3] M. Risbet, X. Feaugas, C. Guillemer-Neel, M. Clavel, Materials Characterization 2008; 59(9); 1252-1257 [4] H.S. Ho, M .Risbet, X.Feaugas, G.Moulin, Procedia Engineering 2010; 2(1); 751-757 [5] J. Man, M. Valtr, A. Weidner, M. Petrenec, K. Obrtlik, J. Polak, Procedia Engineering 2010; 2(1); 1625-1633 [6] X. Feaugas, H. Haddou, Metallurgical and Materials Transactions A-Physical Metallurgy and Materials Science 2003; 34A(10); 2329-2340 [7] H. Haddou, M. Risbet, G. Marichal, X. Feaugas, Materials Science and Engineering A 2004; 379(1-2); 102-111 [8] T.S. Srivatsan, E.J. Coyne, International Journal of Fatigue 1986; 8(4); 201-208 [9] R.E. Stoltz, A.G. Pineau, Materials Science and Engineering 1978; 34; 275-284 [10] H. Mughrabi, Metallurgical and Materials Transactions B 2009; 40B; 431-453 [11] V. Gerold, D. Steiner, Scripta Metallurgia 1982; 16; 405-408 [12] J. Polak, P. Liskutin, Fatigue & Fracture of Engineering Materials & Structures 1990; 13(2); 119-133 [13] J. Polak, J. Man, K. Obrtlik, International Journal of Fatigue 2003; 25; 1027-1036 [14] M. Risbet, X. Feaugas, C.Guillemer-Neel, M.Clavel, Scripta Materialia 2003; 49(6); 533-538 [15] M. Risbet, X. Feaugas, Engineering Fracture Mechanics 2008; 75(11); 3511-3519 [16] M. Risbet, X. Feaugas, C. Guillemer-Neel, M.Clavel, Scripta Materialia 2009; 60(5); 269 – 272 [17] H. Mughrabi, International Symposium on Metallurgy and Materials Science 1983 [18] H. Haddou, X. Feaugas, Metallurgical and Materials Transactions A 2003; 34A(10); 2329-2340 [19] X. Feaugas, Acta Materialia 1999; 47(13); 3617-3632 [20] J.L. Dickson, J. Boutin, L. Handfield, Material Science and Engineering A 1984; 64; L7-L11 [21] J.L. Dickson, L. Handfield, G. L’Esperance, Material Science and Engineering A 1983; 60; L3-L7 [22] Guimier, Doctoral thesis, Université de Nancy, 1972