Fatigue crack growth resistance of ECAPed ultrafine-grained copper

Engineering Fracture Mechanics 77 (2010) 1001–1011

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Fatigue crack growth resistance of ECAPed ultrafine-grained copper Luca Collini * Department of Industrial Engineering, University of Parma, Viale G.P. Usberti 181/A, 43100 Parma, Italy

a r t i c l e

i n f o

Article history: Received 9 October 2009 Received in revised form 2 January 2010 Accepted 10 February 2010 Available online 14 February 2010 Keywords: Fatigue crack propagation Ultrafine-grained copper Threshold crack growth Branching mechanism

a b s t r a c t This work presents the experimental results of fatigue crack growth resistance of ultrafinegrained (UFG) copper. The UFG copper has a commercial purity level (99.90%) and an average grain size of 300 nm obtained by a 8-passes route Bc ECAP process. The fatigue propagation tests are conducted in air, at load ratios R = Kmin/Kmax varying from 0.1 to 0.7, on small Disk Shaped CT specimens. Both stage I and stage II regime of growth rate are explored. Results are partially in contrast with the few experimental data available in the technical literature, that are by the way about high purity UFG copper. In fact, the present material shows a relatively high fatigue crack resistance with respect to the unprocessed coarse-grained alloy, especially at high values of applied stress intensity factor DK. At higher R-ratio a smaller threshold intensity factor is found, together with a lower stage II fatigue crack growth rate. The explanation of such crack growth retardation is based on a diffuse branching mechanism observed especially at higher average DK. Ó 2010 Elsevier Ltd. All rights reserved.

1. Introduction Micro- and nano-structured metals are becoming promising for engineering applications due to the recent progress in technology and systems, that permits to obtain relatively large massive volumes of material at low cost. The advantages of micro-structured metals are connected to the improvement of their mechanical strength, that can be also 3–4-fold the conventional alloys, without a dramatic loss of ductility [1]. This strength improvement can be achieved with one of the available hardening methods: the refinement of the grains and sub-grains structure by imposing a severe plastic deformation (SPD) [2–4]. The key concept of the hardening process in a metal, i.e. of the increasing of the local plastic deformation energy, is to increase the energy necessary to cause a dislocation movement inside a single grain (pile-up mechanism), and from a grain to another crossing a grain boundary. In fact, higher the stress needed to invoke the dislocations movement, higher the yield strength of the metal. This is why the dislocation hardening produced by the grain refinement brings to a considerable enhancement of static and fatigue strength, and of hardness of metals [5–9]. One of the SPD processes developed to strongly reduce the grain size of metals and alloys is the Equal Channel Angular Pressing (ECAP). Its working principle is the imposition of a severe shear stress to the cross sections of a specimen by its extrusion throughout a specific die with an angular channel. The specimen used in this process can have rectangular or round shape, with dimensions up to 20–25 mm in diameter and 100–120 mm in length. Generally, the process of extrusion is repeated several times with a precise rotation of the billet around its longitudinal axis between each passage, in order to homogenize the microstructure and push down the grain refinement scale. With the ECAP method, grain size up till 100 nm in a porosity-free structure can be obtained [10,11]. The effect of grain size on cyclic plasticity and fatigue life of metals has been in focus of many investigations on steel, copper, nickel, titanium and magnesium based alloys. In general, two major conclusions based on these studies can be * Tel.: +39 0521 905892; fax: +39 0521 905705. E-mail address: [email protected] 0013-7944/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.engfracmech.2010.02.011

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L. Collini / Engineering Fracture Mechanics 77 (2010) 1001–1011

drawn: (i) the fatigue limit of pure f.c.c. metals with relatively high stacking fault energy and wavy slip behavior is not affected by the grain size; (ii) the fatigue strength of materials exhibiting planar slip, increases with decreasing grain size and follows the Hall–Petch relationship in the same way as the yield stress in conventional polycrystalline metals [11]. Up to now, a relatively high number of studies have been conducted on static and fatigue resistance of metals with ultrafine-grained structure (UFG). In particular, the studies concerning with the UFG copper has shown some aspects that it’s worth here to summarize: (i) UFG copper exhibits higher fatigue strength than the coarse-grained (CG) counterpart when the cycling is stress-controlled [12], while the behavior is reversed for strain-controlled test [13]; (ii) fatigue strength strongly depends on the chemical purity of the alloy; in particular, a low purity copper alloy shows higher fatigue resistance in all fatigue range [14]; and (iii) the level of purity affects the fatigue behavior especially at low stress amplitudes, i.e. in the high cycle fatigue region [15]. From the point of view of the fatigue mechanism, it has been observed that while for the polycrystalline CG copper with grain size ranging from 10 lm to 2000 lm, the failure is dominated by the fatigue resistance of the grains with no influence of the grain boundaries [16], the fracture mechanism of the UFG copper is dominated by the voids created by grain-boundary sliding, which leaves wedges at the points of triple junction [17]. Whilst a certain number of studies have been conducted on static and fatigue properties of UFG copper, and of UFG metals in general, since now very few data on fatigue crack growth (FCG) resistance are available. This is mainly due to the difficulty to obtain sufficient volumes of ECAPed material to be machined in standard specimens. However, the knowledge of FCG behavior is useful for most of the engineering applications, and is necessary for a comprehensive understanding of the fatigue properties. On the author knowledge, only two works by Vinogradov [11] and Cavaliere [18] report experimental fatigue crack propagation curves of UFG copper. In these works it is demonstrated that UFG materials exhibit the same crack propagation behavior as those for polycrystals, i.e. a threshold regime, an intermediate stable growth regime, described by the well-known Paris–Erdogan law, and an instable regime at high crack growth rates. It has been also found that the growth rate of a defect in the threshold regime is higher in UFG alloys than those of the polycrystalline reference material [11,18–20]. This behavior has been ascribed to the absence of any tightening mechanism, e.g. roughness of the crack path, in the UFG state due to the ultrafine-grained microstructure. Indeed, in UFG microstructures the crack path usually appears straight and smooth, providing faster growth rates under limited crack tip plasticity. Prevalence of intergranular fracture mode during FCG was experimentally observed, explaining the nearly straight crack path in a uniform UFG structure [19]. Direct in situ observation of the initiation and growth of a small, semi-elliptical crack in a UFG copper structure, has shown a transition of the propagation mechanism after about 0.1 mm of crack length: from intergranular and straight, the crack path becomes tortuous with a decrease in the FCG rate when the cyclic plastic zone ahead of the crack tip interests quite a large number of grains [21]. However, at the moment more understanding is necessary about the FCG resistance of ultrafine-grained structures; open questions are the role of the reverse plastic zone at the crack tip, the shear bands formation mechanism, and their interaction with the specific, small-scale grains structure. The aim of this paper, which is characterized essentially by a phenomenologic approach, is to present and briefly discuss the fatigue crack growth resistance of a copper alloy in the UFG state and with a commercial purity level. The results are juxtaposed with data from the technical literature referred to CG and UFG copper with different purity. A preliminary discussion of the propagation mechanism is also conducted with the support of a SEM analysis. 2. Material and experimental The material used for this study is a copper alloy subjected to a 8-passes ECAP process throughout route Bc, i.e. where the sample is rotated in the same sense by 90° between each pass. The copper has been processed in the laboratory of Prof. R.Z.

Fig. 1. TEM micrograph of grains structure of the present UFG copper.

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L. Collini / Engineering Fracture Mechanics 77 (2010) 1001–1011 Table 1 Maximum content of impurities (wt.%) of the present UFG copper. Bi

Sb

As

Fe

Ni

Pb

Sn

S

O

Zn

Ag

Cu

0.001

0.002

0.002

0.005

0.002

0.005

0.002

0.004

0.05

0.004

0.003

Balance

Table 2 Mechanical properties of CG and present UFG polycrystalline copper. Copper

dG (lm)

ry (MPa)

ru (MPa)

A (%)

rf (108 cycles) (MPa)

CG [14] UFG [12]

30 0.300 ± 0.015

95 ± 5 375 ± 4

195 ± 5 387 ± 5

41.5 18.5

77 168

Valiev at the Ufa State Aviation Technical University (Russia), starting from cylindrical samples of 20 mm in diameter and 120 mm in length. After the last ECAP pass, cylindrical samples of 16 mm in diameter and 100 mm in length were machined from the billets. The ultrafine-grained microstructure shown in the TEM micrograph of Fig. 1 was obtained: the ECAPed microstructure results fine and uniform, with grain size ranging from 100 to 800 nm and average grain size of 300 nm. Its chemical composition is indicated in Table 1; the purity level results to be 99.90%. As mentioned above, impurities in UFG copper can play a consistent effect on mechanical properties, especially on the fatigue resistance. Static and fatigue properties are reported in [12], and here summarized in Table 2 in comparison with properties of CG wrought copper alloy with grain size of 30 lm taken from Ref. [22]. Advantages of ECAP process are marked: yield strength ry is 4-fold the conventional strength, while fatigue limit rf at 108 cycles is twice. The FCG tests were conducted in laboratory on Disk Shaped CT specimens, in air and at room temperature. Specimens were machined in discs of 7 mm in thickness from the bars of 16 mm in diameter. A MTS 810 servo-hydraulic machine working at frequency of 10 Hz has been used for the test. Dimensions of the specimen and a view of the experimental set-up are showed in Fig. 2. Some practical problems emerged during the test set-up due to the small dimensions of the specimens. A Back Face Strain Measurement (BFSG) technique has been necessarily adopted to monitor the crack length with the help of a little strain gage

Fig. 2. (a) Dimensions of DSCT specimen (in mm) and detail of the strain gage and (b) experimental set-up.

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glued to the back of the specimen, as shown in Fig. 2a. In conjunction with a finite element calibration, the BFSG technique allows to calculate the mode I Stress Intensity Factor (SIF) as a function of a/W ratio, by Eq. (1):

KI ¼

Pð2 þ Wa Þ BW

1=2

ð1 

4 X

a 3=2 Þ i¼0 W

Ci

 a i W

ð1Þ

where P is the applied load, that is measured by a 3 kN load cell, B and W the characteristic specimen dimensions indicated in Fig. 2a, and Ci are constants relative to the DSCT geometry. Details of the BFSG technique are reported in [23]. The standard procedure for FCG calculation indicated in [24] is here adopted to realize K-increasing and K-decreasing (load-shedding) tests. Experimental tests are conducted at load ratio equal to 0.1, 0.3, 0.5 and 0.7. Each propagation test is repeated twice. The mode I crack propagation resistance is investigated both in the stable regime (stage II), and in the threshold regime (stage I), down to 5  107 mm/cycle propagation rate (at R = 0.1). Acquisition of each data point is automatically made every 0.1 mm of crack propagation by the FCG software. To facilitate the crack initiation and a mode I crack propagation, an initial fatigue precracking of 0.8 mm at load ratio 0.1 is conducted for all specimens, with a driving Kmax never exceeding Kmax of the following test. Treatment of data relative to the threshold FCG tests needed an elaboration, since in the experimentation the crack growth rate never reached the conventional threshold rate of 1  107 mm/cycle. Therefore, threshold stress intensity factors DKth have been estimated following the procedure of regularization indicated in [24], but adopting an exponential fitting of the experimental data. In particular, data points of the crack values ‘‘a” as a function of the applied DK, and of DK as a function of the number of fatigue cycles N, have been interpolated by exponential curves in the form:

aðNÞ ¼ a0 þ j1 ð1  ej2 N Þ

ð2Þ

DKðNÞ ¼ DK 0 þ b1 eb2 N

ð3Þ

with opportune constants j1,2 and b1,2. Deriving Eq. (2) and plotting it with respect to the DK points of Eq. (3), a regularized da/dN  DK smooth curve is obtained. Threshold DK has been extrapolated from this curve, at the growth rate of 1  107 mm/cycle. 3. Results and discussion 3.1. Stage II FCG Results of FCG tests are presented in Fig. 3a and b in the form of traditional log–log (da/dN; DK) diagrams. For the sake of clarity, only one propagation curve per R-ratio is plotted. Some other data set found in technical literature are plotted into the diagram of Fig. 3a for comparison. In particular, these are: (i) FCG curve at R = 0.25 of pure UFG copper ECAPed by 4Bc

Fig. 3. (a) Fatigue crack propagation curves at R = 0.1, 0.3, 0.5, 0.7 and (b) linear regressions of stage II crack growth rate.

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passes with average grain size dG equal to 270 nm [18]; (ii) FCG curve at R = 0.5 of UFG copper produced by 4Bc ECAP passes and average dG = 300 nm [11]; (iii) FCG curve at R = 0.5 of UFG copper produced by 16A ECAP passes and dG = 300 nm [11]; and (iv) FCG curve at R = 0.5 of CG copper with dG = 15 lm [22]. From the analysis of obtained data the following considerations can be drawn: 1. transition from stage I to stage II test is continuous, and as for the conventional metals stage II points can be fitted by p straight lines at each R-ratio; applied DK ranges between 6 and 45 MPa m, while related FCG rates are in the range 7 3 6  10 –2  10 mm/cycle; 2. R-ratio at stage II influences the slope of the propagation curves, as showed in detail in the linear log–log (da/dN; DK) plot of Fig. 3b, and indicated in the trend of coefficient ‘‘m” of propagation law da/dN = C(DK)m, see Fig. 4a; 3. during the stage II the propagation curves do not space out but intersect each other around the growth rate of 105 mm/ cycle. When comparing these results with those found in literature [11,18], the following important aspects can be highlighted: 1. at a given applied DK range a slower crack growth rate characterizes the present UFG copper for all R-ratios; 2. the slope of the curves during the Paris regime of propagation is comparable with data from literature, i.e. a similar crack growth mechanism is found; 3. during stage II the present UFG Cu shows a higher FCG resistance than the 15 lm grain sized counterpart, as clearly shown in Fig. 3a. 3.2. Threshold FCG regime In metals and alloys the threshold FCG regime is usually achieved when crack growth rate goes below 106 mm/cycle. Since in the present tests only at R = 0.1 the crack growth rate went under 106 mm/cycle, threshold stress intensity factors

Fig. 4. (a) Paris’ law coefficients and (b) threshold SIF as a function of load ratio R.

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Table 3 Comparison of present DKth values with data from literature.

*

R

Present UFG Cu, ECAP 8Bc

UFG Cu, ECAP 4Bc [18]

UFG Cu, ECAP 4Bc [11]

UFG Cu, ECAP 16A [11]

0.1 0.3 0.5 0.7

6.3 4.4 2.0 0.8

– 2.3* – –

4.4 – – –

2.7 – – –

R = 0.25.

DKth have been estimated with the elaboration reported in Section 2. Results are summarized in Table 3 in comparison with DKth values taken from literature. The analysis of FCG curves near the threshold regime and values of extrapolated DKth generate to the following considerations: 1. R-ratio influences the threshold FCG regime: higher is R, lower is DKth, as showed in Fig. 4b; 2. threshold SIFs are higher than values found in literature for the same class of UFG copper, as indicated in Table 3 and illustrated in the trend of ‘‘C” coefficient of Fig. 4a; 3. when juxtaposed with the FCG behavior of annealed and cold worked conventional copper, the present ultrafine Cu shows higher threshold resistance for R-ratios 0.1 and 0.3, while it goes below the cold worked alloy and approaches the annealed one for high R-ratio, as plotted in Fig. 4b; this partially contrasts with other experimentations. 3.3. Discussion First of all, obtained experimental results on fatigue crack propagation resistance show two important aspects: (i) the FCG resistance of the present UFG copper is higher than that of previously tested ECAPed copper alloys, in stage II and in the threshold propagation regime too: this can be seen in the graphs of Figs. 3a and 4b and in values of Table 3; and (ii) load ratio influences the threshold stress intensity factor and the mechanism of stage II crack propagation, as highlighted in the plots of Figs. 3b, 4a and b. These two aspects will be now discussed. In order to explain the relative high crack propagation resistance of the present UFG copper in comparison with coarsegrained and other ECAPed Cu alloys, first its fatigue resistance can be taken under consideration. It has been recently shown that the fatigue strength of UFG copper with low purity is higher than that of conventional copper by a factor of 2 [12,14,15]. In particular, copper used in Ref. [12] had the same chemical composition and ECAP processing as the present material; its substantially higher fatigue resistance has been justified demonstrating the stability of the bulk microstructure during cycling, due to the stable dislocations structure and to the presence of impurities and precipitates. The grain structure within plastic zone around the cracks was shown to differ from outside of the plastic zone: the grains were found markedly elongated, but their size was shown to be preserved. Also, in comparison with the CG structure, a small grain size can potentially result in more homogeneous deformation, which can retard crack nucleation by reducing stress concentrations and ultimately raise the fatigue limit of the UFG structure. This has been demonstrated by other studies on ECAPed copper structures on low and high cycle fatigue [19,20]. Moreover, it can be considered that the interaction between a propagating crack and the grain boundaries (GBs) structure, can produce a retardation in the growth rate. Actually, in most planar slip materials, GBs provide a ‘‘topological obstacles to the slip” [25]. This phenomenon has been already noticed and theoretical models on the crack-boundaries interaction developed, with the support of experimental evidences [26,27]. In these studies, it has been shown that because of the crack-precipitate interaction at the GBs, the crack develops steps on the crack plane while bypassing the precipitates. The result is a fatigue crack retardation and deflection at a GB, that leading to an increase of the free crack surface produces a significant suppression of crack propagation rate. This topological factor can be critical in the FCG behavior of UFG metals, if one considers the huge number of GBs generated by the grain refinement process. In this study, the threshold FCG behavior is characterized by the threshold stress intensity factor DKth. In order to make a comparison with literature data, DKth values have been estimated at the FCG rate of 107 mm/cycle. They are plotted in Fig. 4b as a function of the test R-ratio and in comparison with data on CG copper from Refs. [28–31]. In partial disagreement with other experimental results, for example [11], threshold resistance of this UFG copper is comparable to that of conventional copper, but it can be definitely noticed a stronger traditional R-dependence; in fact at higher R-ratio, lower DKth are found. The dependence of DKth from R-ratio is here interpreted by the linear fit proposed by Barson [32], Eq. (4), and by the power fit proposed by Klesnil and Lucas [33], Eq. (5):

DK th ¼ A  BR

ð4Þ

DK th ¼ Dð1  RÞc

ð5Þ p

p

with the following fitting parameters: A = 9.45 MPa m; B = 7.16 MPa m; D = 7.79 MPa proaches well describe how DKth depends on R-ratio, as shown by the plots of Fig. 4b.

p

m; c = 1.82. Both these ap-

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The analysis of the effect of R-ratio on propagation behavior in stage II is more complicated. As can be clearly seen from Figs. 3b and 4a, at a constant FCG rate, a higher R-ratio produces a slower growth rate, as if the material becomes more insensitive to a crack. This trend is not usual for polycrystalline metals, but a very similar behavior can be observed in the propagation curves of Ref. [11], in which the crack growth resistance of UFG Cu alloys with increasing ECAP passes (i.e. grain refinement) are reported: going from two CG structures with 11 and 15 lm, towards UFG structures with passes 4Bc, 12Bc, 16A and 16Bc, lower threshold but higher stage II resistances are constantly found. The same trend is noticed in the present material when R-ratio increases. In order to rationalize the influence of load ratio, a crack closure approach has been tried during the elaboration of the experimental results. The Adjusted Compliance Ratio (ACR) model proposed in [34] has been chosen. Depending on ductility, FCG rate and environmental effects, numerous causes can be responsible of an anticipated crack closure; among them, residual plasticity and roughness due to a tortuous crack path, characterize the so-called plasticity-induced crack closure (PICC) and roughness-induced crack closure (RICC), respectively. PICC and RICC are common mechanism in ductile metals; PICC is mainly related to the residual plastic deformation in the steady-state FCG regime, while at threshold closure is favored by microstructural asperities of the fracture surfaces (RICC). The ACR method is based on the hypothesis that DK effectively applied at the crack tip, DKeff, is proportional to the strain magnitude, or to the crack tip opening displacement (CTOD), defined as [35]:

CTOD ¼

ð1  m2 ÞK 2max 2ry E

ð6Þ

The effective SIF is then calculated correcting the applied SIF by a parameter (the ACR parameter) defined as follows [34]:

DK eff ¼ DK  ACR ACR ¼

ð7aÞ

Cs  Ci C0  Ci

ð7bÞ

where Cs, C0 and Ci are the specimen secant compliance, the compliance above the opening load and the compliance prior the initiation of a crack, respectively. The elaboration of experimental points by this method is depicted in Fig. 5. Two main observations can be done analyzing Fig. 5: (i) propagation curves almost overlap in stage II, and run parallel; and (ii) points below 1.5  105 mm/cycle show very poor physical sense. It can be concluded that the ACR model rationalizes the R-ratio effect in FCG stage II with discrete approximation, while it fails when applied to the threshold regime, where, as already known, the role of microstructure achieves higher importance [25]. This result is in partial accordance with FCG tests made on conventional CG copper, where

Fig. 5. Crack closure analysis by the application of the ACR model.

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Fig. 6. Crack tip opening displacement (CTOD) and monotonic and cyclic plastic zones ahead the crack tip calculated by Eqs. (6), (8), (9) at da/ dN = 2  107 mm/cycle and da/dN = 2  105 mm/cycle.

it has been observed that decreasing grain size the threshold DK increases, suggesting that in copper crack tip plasticity considerations are more important in determining the threshold values than crack closure effects [28]. Due to the peculiar micro-scale grain structure of UFG copper, the extension of the ‘process’ area around the crack tip where plastic deformation concentrates has been investigated. According to Irwin, the size of monotonic and cyclic plastic zones at the crack tip can be estimated by Eqs. (8) and (9) respectively:

rp ¼

 2 1 K max 3p ry

ð8Þ

 2 1 DK 3p 2ry

ð9Þ

rpc ¼

where ry is the yield stress, in this case equal to 375 MPa. Results of this elaboration are showed in Fig. 6, where rp and rpc trends are reported as a function of R-ratio, at high FCG rate (2  105 mm/cycle) and near-threshold FCG rate (2  107 mm/ cycle). The same graph depicts the CTOD as calculated by Eq. (6). Fig. 6 evidences some interesting aspects: (i) monotonic and cyclic plastic zones always are much wider than the characteristic microstructural dimension (the average grain size dG); (ii) rp and rpc trends depend on R-ratio in an opposite way: they decrease in the near-threshold regime when R increases; and (iii) the CTOD is always smaller of to rp and rpc. It other words, if the propagation of a fatigue crack is seen as the result of the accumulation of irreversible plastic deformation at the crack tip, in UFG copper this process interests one/two tenths of grains at low FCG rate, but a huge number of grains, up to some hundreds, at high FCG rate. In such conditions, one can expect a microstructure-dependent propagation mechanism only at very low FCG rates, as however already observed for this material [21]. This partially can explain the inadequateness of the ACR closure method when applied to the threshold regime. Fig. 6 shows also that at high FCG rates the cyclic plastic zone does not depend on R-ratio, or, equivalently, on the applied average SIF:

K AVG ¼

1þR DK: 1R

ð10Þ

This indicates that for increasing KAVG, the monotonic plastic zone expands, while the cyclic zone stabilizes being the microstructure able to resolve the external load. 3.4. Fractography The study of crack path and fracture surfaces is conducted to support the analysis of FCG behavior exposed above. The crack path morphology has been analyzed in terms of fracture roughness Rv, measured on SEM images of cracked specimens. Roughness, that is a quantitative measure of the crack tortuousity, has been calculated by a simple graphical method, based on the superimposition of a grid on the digital image of a specimen profile. The method, more deeply described in [36], counts the profile-grid intersections, Pi, along a chosen length, L, and then expresses Rv as:

Rv ¼

yX Pi : L i

ð11Þ

This simple technique can obviously give only a mono-dimensional estimation of roughness. Rv is calculated at different ranges of applied DK, for R-ratio equal to 0.3, 0.5 and 0.7. Results of the elaborations are presented in graphic form in Fig. 7. Crack tortuousity results higher when the driving force increases, but in practice does not depend on R-ratio. This conclusion

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Fig. 7. Roughness of crack profile as a function of applied DK and R-ratio.

totally confirms the insensitivity of the cyclic plastic zone with respect to R-ratio at a given load range as already evidenced. Furthermore, supporting the discussion about the crack closure, it can be stated from Fig. 7 that Rv is of the order of magnitude of the grain size dG only at the near-threshold regime. It means that the mechanism of fracture may be microstructure-dependent only during the threshold regime. The fractographic analysis of the surfaces has been also conducted, in order to investigate the fracture mechanism and its dependence from load ratio. Several images of the crack path on the specimen profiles and of the fracture surface have been acquired at the SEM microscope at different magnifications. Here the most significant for the discussion are presented in Figs. 8–10. Figs. 8 and 9 show the crack propagation profile at R = 0.3 and 0.7 respectively, at increasing applied DK going from left to right in the figure. Indication about the average SIF calculated by Eq. (10) are also given. Looking at the profile morphology, an increasing tortuousity and fragmentation with the average DK can be seen for both R-ratios. Figs. 8c and 9c, that correspond to the highest loads, show bifurcation, multi-cracking and branching of the main crack. Several small secondary cracks can be clearly seen in perpendicular and parallel direction with respect to the main crack path direction, even at some distance from it. A very similar mechanism has been already observed in commercial pure UFG Ti [19], in UFG Cu [37], in AA6063 aluminum alloy [38], and reviewed in [11].

Fig. 8. Stage II crack propagation profiles at constant R = 0.3 and applied[average] DK equal to: (a) 8.6[16.0] MPa p 41.0[76.1] MPa m.

p

m; (b) 11.2[20.8] MPa

Fig. 9. Stage II crack propagation profiles at constant R = 0.7 and applied[average] DK corresponding to: (a) 8.1[45.9] MPa p (c) 18.7[106.0] MPa m.

p

p

m and (c)

m; (b) 12.3[69.7] MPa

p

m and

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Fig. 10. Crack paths during the threshold regime: (a) intergranular fracture at R = 0.3 and (b) fracture surface morphology at R = 0.5.

Actually, multi-cracking indicates the poor capacity of dislocation mechanism to generate around the crack tip and in the plastic wave of the hardened structure. Microcracks generate to accommodate excessive strain in the crack vicinity for a decrease in the strain hardening capability due to the severe grain refinement. On the other hand, the branching mechanism may be directly responsible of the insensitivity toward crack propagation found at the stable FCG rate. During stage II, FCG rate diminishes when R-ratio (or KAVG) increases, see Fig. 4a, i.e. when branching becomes more evident. Indeed, it has been shown that crack deflection or multi-cracking can enhance Kmax by a factor of about 20–30% [25]. This could definitely explain the noticed FCG behavior, otherwise impossible to rationalize with crack closure arguments. Fig. 10 shows the fracture profile and the fracture surface near the threshold regime, at R = 0.3 and R = 0.5, respectively. Fracture morphology of Fig. 10a, taken when the cyclic plastic zone at the crack tip was about 5–8 times the grain size, evidences an intergranular mechanism, justifying the high value of DKth found. The SEM image of Fig. 10b shows relatively long, straight-line (secondary) microcracks, perpendicular to the direction of crack growth. Coherently with the previous observations, this indicates rather a brittle, intergranular micro-mechanism of propagation. In conclusion, it can be stated that not only the peculiar grain size distribution, but also ductility, hardening conditions and boundaries impurities have an influence on FCG behavior of UFG copper. 4. Conclusions In this work the experimental characterization of the fatigue crack growth resistance of ultrafine-grained copper is presented and discussed. The UFG copper has a commercial purity level (99.90%), and an average grain size of 300 nm obtained by 8 ECAP passes. The main conclusions can be summarized as follows: 1. the present UFG copper shows higher FCG resistance in stage II propagation, when compared with high-purity ECAPed UFG copper and with conventional copper, too; 2. in contrast with data from literature on high-purity ECAPed copper, values of DKth are comparable with those of CG copper: grain boundaries impurities may have a significant role in the threshold fracture process; 3. the increasing insensitivity toward the fatigue crack propagation shown during stage II when R-ratio increases, is index of a mechanism of apparent toughening that can be explained, at least qualitatively, considering the effect of the observed branching of crack path onto slip bands;

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4. monotonic and cyclic plastic zones at the crack tip show that: (i) a large number of grains are involved in the propagation process for most of the analyzed range, and (ii) PICC mechanism is the most probable closure mechanism, while a comparison between crack tip opening displacement and crack profile roughness indicates the possibility of a RICC mechanism only at the threshold FCG rate this is consistent with the average material grain size. Acknowledgment This work has been conducted in collaboration with the Institute of Physics of Materials (IPM) of the Academy of Science of Czech Republic, in Brno. The author wish to thank Prof. Ludvik Kunz from IPM for the material supply and his precious indications. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38]

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