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Effect of microstructure on the fatigue crack growth behavior of Cu–Be–Co–Ni alloy
Journal of Alloys and Compounds 663 (2016) 784e795
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Journal of Alloys and Compounds journal homepage: http://www.elsevier.com/locate/jalcom
Effect of microstructure on the fatigue crack growth behavior of CueBeeCoeNi alloy Yanchuan Tang a, Guoming Zhu a, **, Yonglin Kang a, *, Lijuan Yue b, Xiaoliang Jiao b a b
School of Materials Science and Engineering, University of Science and Technology Beijing, Beijing 100083, China CNMC Ningxia Orient Group Co. Ltd., Shizuishan 753000, China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 17 September 2015 Received in revised form 16 November 2015 Accepted 5 December 2015 Available online 11 December 2015
The fatigue crack growth (FCG) behaviors of CueBeeCoeNi alloy subjected to interrupted aging (IA), normal aging (NA) and overaging (OA) treatment were discussed. The distinctions in microstructure of the alloys after various aging treatments led to different FCG behaviors. In order to understand the different FCG behaviors, a model based on the reversible plastic zone (RPZ) size and microstructural factors was applied in this study. At the relatively low stress intensity factor range (DK < 17 MPa m1/2), the RPZ size of each sample was smaller than the corresponding grain size, so the fatigue crack propagated inside the grain and adjacent to the grain boundaries (GBs). For the IA alloy, fine and coherent g00 precipitates which could be sheared by dislocations promoted the fatigue crack resistance, leading to the decrease of FCG rate. When the value of stress intensity factor range becomes higher (DK > 21 MPa m1/2), the RPZ size of each sample was 1e2 times of the corresponding grain size. Consequently, the crack trended to grow along GBs. For the OA alloy, the crack propagated along the interfaces between the discontinuous precipitation (DP) cells and parent phase. The tortuous interfaces hindered the propagation of the fatigue cracks, resulting in the reduction of FCG rate. © 2015 Elsevier B.V. All rights reserved.
Keywords: CueBeeCoeNi alloy Aging Microstructure Precipitate Fatigue crack growth behavior
1. Introduction The CueBeeCoeNi alloy has the most significant precipitation strengthening effect among copper alloys. After proper aging treatment, the alloy has high strength and elasticity but little elastic hysteresis. Meanwhile, it also possesses good electrical conductivity, thermal conductivity and is non-magnetic. Because of these attractive advantages, CueBeeCoeNi alloy has been widely used in key elastic parts, such as the springs, contactors and switches in the electronic components [1e3]. Since these components would withstand thousands even millions of repeated operations in service, the reliability of these components largely depends on the fatigue properties of the materials. Therefore, it is necessary to study the factors that affect the fatigue properties of CueBeeCoeNi alloy. When under the same service condition, the fatigue properties of the material are mainly affected by the microstructure. The
* Corresponding author. ** Corresponding author. E-mail addresses: [email protected] (G. Zhu), [email protected] (Y. Kang). http://dx.doi.org/10.1016/j.jallcom.2015.12.017 0925-8388/© 2015 Elsevier B.V. All rights reserved.
propagation path and growth rate of the fatigue crack are closely related to the characteristics of precipitates, grain size and the € ppel et al. [4] found that morphology of grain boundaries (GBs). Ho the fatigue properties were significantly affected by the size of precipitates. The size of precipitates in the over-aged alloy was larger than it in peak-aged and as-received alloy, resulting in lower fatigue limit and shorter fatigue life of the over-aged alloy. The interaction mechanisms between dislocations and precipitates also affect the fatigue properties. For the fine and coherent precipitates, dislocations can shear them and glide more-or-less reversibly during cyclic loading [5]. According to the research of Desmukh et al. on the aluminum alloys [6], this planar-reversible slip fosters the fatigue crack growth resistance, leading to the decrease of fatigue crack growth (FCG) rate. The precipitates in the over-aged alloy have relatively large size and semi-coherent or incoherent with the parent phase, which can't be sheared by dislocations. However, this allows the over-aged alloy to deform homogeneously, and as a result the over-aged alloy possesses a higher fatigue crack propagation threshold [6]. According to Qin et al. [7], the GH4169 alloy with coarser grain exhibits lower FCG rate and longer fatigue life. However, the slow expanding stage accounts for a larger fraction of the total fatigue life for the GH4169 alloy with
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finer grain size. Besides above factors, the existence of precipitatefree zones (PFZs) has a detrimental influence on the fatigue life and the decrease in the PFZ width brings about the increase in the fatigue life [6,8]. Since fatigue cracks usually propagate as a result of the accumulation of irreversible plastic deformation at a crack tip, the reversible crack tip displacement (CTODr) appears to be a proper method to characterize the crack propagation behavior. However, it is extremely difficult to measure CTODr in polycrystalline materials. Therefore, the reversible plastic zone (RPZ) size, which is closely related to CTODr, is often used to describe the crack propagation behavior. In the intermediate stage of crack growth in UFG steel, Kim et al. [9] showed that the RPZ size was much larger than the grain size, which permits the crack to interact with several grains during cyclic loading. Based on the RPZ size and microstructural factors, a quantitative model describing the crack growth mechanism was developed by Goto et al. [10]. The model successfully explained the fatigue crack growth behavior of the ultra-fine grained copper. In this study, different aging treatments were conducted on CueBeeCoeNi alloy (in solid solution state), resulting in various microstructural factors. The fatigue crack growth mechanisms were discussed based on the RPZ size at the crack tip and the microstructural factors of the alloys.
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Fig. 1. Schematic diagram of heat treatment procedures used in this study.
2. Experimental details 2.1. Material and processing The as-cast CueBeeCoeNi (composition in Table 1) alloy, in the shape of 120 mm 100 mm 70 mm, was subjected to homogenized annealing at 800 C for 180 min. Then the ingots were hotrolled to 9 mm (87% rolling reduction) at 650 Ce740 C, followed by quenching in water immediately. The hot-rolled sheets were intermediate annealed at 570 C for 240 min. Subsequently, the hot-rolled sheets were cold-rolled to a thickness of 2.0 mm (78% rolling reduction). The solution treatment was applied to coldrolled sheets at 780 C for 20 min, followed by water quenching to room temperature (RT). Finally, the cold-rolled sheets were subjected to different aging treatments, as shown schematically in Fig. 1. The first aging treatment is normal aging (marked as NA) with the treatment of aging at 320 C for 180 min. The second one is interrupted aging (marked as IA) with the treatment of underaging at 320 C for 30 min and rapid quenching to room temperature (RT) then interrupted aging at 280 C for 360 min. The last one is overaging (marked as OA) with the treatment of aging at 370 C for 60 min. The annealing and solution treatments were performed in the air circulating furnace, while the aging treatments were conducted in salt baths. 2.2. Tensile and fatigue crack growth (FCG) rate tests Samples for microstructural and mechanical properties examination were cut from the sheets subjected to different aging treatments, parallel to the rolling direction. All these tensile samples were prepared according to GB/T 228.1e2010. Tensile tests were carried out on a WDW200D test machine. FCG tests were performed on a MTS-810 test machine using compact tension, C(T),
Table 1 The composition of CueBeeNieCo alloy (wt. %). Element
Be
Ni
Co
Cu
Content
1.8e2.1
0.2e0.3
0.1e0.2
Bal.
Fig. 2. Geometry of the C(T) samples (dimensions in mm).
samples according to ASTM E647 standard. Fig. 2 shows the geometry of the C(T) samples. The samples were machined from the sheets in the transverse-longitudinal (T-L) direction, maintaining the crack propagation direction along the rolling direction. Before the FCG rate tests, each C(T) sample was subjected to fatigue loading in order to obtain a pre-crack with the length of approximately 1.0 mm. Tests were conducted in air at room temperature, using a constant amplitude sinusoidal loading with a load ratio of R ¼ 0.1 at a frequency of 10 Hz. The fatigue crack length measurements were carried out using the compliance method by employing a clip gauge at the notch mouth. 2.3. Microstructural and differential scanning calorimetry (DSC) investigation The microstructures and fracture surfaces of the samples under different aging conditions were examined in detail using a field emission gun scanning electron microscope (FEG-SEM) Hitachi S4800 and Cambridge S-360 SEM operating at 20 kV. The DSC experiments were carried out in a SDT-Q600 simultaneous thermal analyzer. Disc-shaped samples with 20e40 mg in weight were prepared from the sheets by an electro discharge machine. The DSC samples were examined with a heating rate of 10 C/min between 20 and 550 C. A baseline scan was recorded from a pure Cu sample and subsequently subtracted from the alloy scans. Transmission electron microscope (TEM) observation was carried out using an H8100 TEM operating at 200 kV. For this observation, thin foils were prepared by a twin-jet polishing method with a solution of 70%
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methanol and 30% nitric acid in volume fraction at 25 to 30 C, 9.5 V and 20 mA. The sizes in the long axis and short axis of the precipitates were measured from 5 TEM images by image processing software. For each aging condition, the TEM images were taken from different areas under the same magnification. 3. Results 3.1. Tensile properties and related microstructure As the tensile properties presented in Table 2, the yield strength (YS) and ultimate tensile strength (UTS) of the alloy under the IA condition are similar to those of the alloy under the NA condition, but the elongation of the alloy under the IA condition was about 12% higher than it under the NA condition. The alloy subjected to OA treatment had the relatively low strength, the YS and UTS were about 180 MPa lower than those of the alloys under the NA and IA conditions. However, the elongation of OA samples was about 2 times as it of NA and IA samples and the yield ratio of the OA alloy was the lowest. Fig. 3 shows the microstructure of the alloys subjected to different aging treatments, using the backscattered electron (BSD) mode of SEM. After the aging treatments, it could be observed that the microstructure was consisted of a phase (solid solution phase) and the discontinuous precipitation (DP) cells located at the grain boundaries (GBs) of a phase. For the IA samples, the GBs could be clearly observed while there were few DP cells at the GBs. The microstructure of the NA samples was composed of a phase with small numbers of DP cells at the GBs. However, the DP cells accounted for a considerable percentage in the microstructure of the OA samples, and a phase was surrounded by the DP cells. The microstructural characteristics of the studied alloys, including the average size of a phase and the volume fraction of DP cells, were measured by image processing software and the results are summarized in Table 3. The alloys under the IA, NA and OA conditions had similar average grain sizes of a phase, with the value of 10.9, 12.8 and 9.5 mm respectively. The volume fraction of DP cells under the OA condition was 13.4%, compared with less than 5% under the NA and IA conditions. DP cells involve the formation of a solute-depleted matrix phase (a0 ) and a precipitate phase (g) as a duplex transformation product and they usually nucleate at the GBs and grow into one side of the supersaturated matrix (a phase) [11,12]. The DP cells consumed huge numbers of solute atoms and they contained coarse equilibrium phase of g instead of fine metastable g00 and g0 phases, resulting in weakening the precipitation strengthening of the alloy. Consequently, the strength of the alloy would decrease with the increase of the volume fraction of DP cells, which was in line with the relatively low strength of the OA alloy as compared to the NA and IA alloy. 3.2. DSC and TEM study of CueBeeCoeNi alloy under different aging conditions As shown in Fig. 4, a series of DSC scans was recorded from the samples of the alloys subjected to different aging treatments, and then compared with the scan from the solution treated and
Table 2 Tensile properties of the CueBeeCoeNi alloys under different aging conditions. Aging condition
YS (MPa)
UTS (MPa)
UEl (%)
El (%)
Yield ratio
IA NA OA
1157 1167 990
1320 1329 1161
5.7 5.1 8.4
7.5 6.7 13.0
0.876 0.878 0.853
quenched sample. The scan from the solution treated and quenched sample showed four characteristic exothermic reactions which were consistent with results reported by Donoso and Varschavsky [13]. Peak 1 (the center of peak 1: ~210 C) corresponded to the formation of G.P. zones; peak 2 (~260 C) indicated the formation of g00 precipitates; peak 3 (~340 C) represented the formation of g0 precipitates; peak 4 (~400 C) indicated the formation of g precipitates. The DSC trace for the sample subjected to the OA treatment prior to heating in the DSC cell didn't show any exothermic peaks or endothermic peaks, which meant that the solute atoms in the OA sample were totally precipitated, and the precipitates were thermodynamic stable during the DSC test. As a result, the alloy under the OA condition should be mainly consisted of g phase (equilibrium phase). The DSC scans of the samples under NA and IA conditions showed the endothermic peaks at about 385 C, and then the exothermic peaks at about 440 C. The endothermic reaction suggested that the g00 precipitates formed during aging treatments dissolved on heating, and the exothermic reaction indicated the formation of g precipitates. However the area under the endothermic peak of the IA sample was much larger than that of the NA sample, suggesting more g00 precipitates dissolved on heating, thereby larger numbers of g00 precipitates precipitated during the IA treatment. TEM observation was used to characterize the precipitates in the alloys after different aging treatments, and the results were in line with the DSC scans. After the IA treatment (Fig. 5a and c), the microstructure was mainly composed of fine granular precipitates with the habit plane of (100)a. From the corresponding selected area diffraction pattern (SADP) in <001>Cu matrix orientation (Fig. 5b), the extra diffraction spots which represented the precipitates could be observed, indicating the lattice parameter of the precipitates (a ¼ 0.254 nm). The result was fairly close to the lattice parameter of g00 phase reported by Monzen et al. [14]. Furthermore, the “arrowheads” with its ‘‘tip’’ at the position of the (010)a reflection and its “base” at 2/3(020)a could be observed, which were considered as the formation of the g0 precipitates [15]. In summary, the microstructure of the alloy subjected to IA treatment was mainly consisted of fine g00 precipitates with tiny amounts of g0 precipitates. As shown in Fig. 5d and f, the main phase precipitated after the NA treatment appeared to be slender strips of g0 phase, which precipitated after the g00 phase according to the precipitation sequence of CueBe alloys [16]. The ‘‘arrowheads’’ considered as the formation of the g0 precipitates could also be observed in the corresponding SADP (Fig. 5e), indicating a change in habit planes from the matrix [15]. The slender strips of g0 precipitates were parallel to (131)a and (121)a, while the habit plane of g00 precipitates was (100)a. After the OA treatment (Fig. 5g and i), the microstructure was composed of coarse g precipitates, with the length of approximately 100 nm. The equilibrium g phase was formed by the transformation of metastable g0 phase, with no changes in the orientations and habit planes of precipitates [17]. According to the corresponding SADP (Fig. 5h), the g precipitates were parallel to (211)a and (311)a, which had the same habit planes as the g0 precipitates. The sizes of the precipitates after different aging treatments are shown in Table 4. After the IA treatment, the main phase was granular g00 phase. The g00 precipitates had relatively small size, whose average length of the long axis was only 5.3 nm. The dominate precipitates after the NA treatment were slender strips of g0 precipitates. Compared with g00 precipitates, g0 precipitates had much larger size, especially in the long axis (with average length of 25.3 nm). The main precipitates after the OA treatment were coarse g precipitates, with the even larger size in the long axis (with
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Fig. 3. SEM images of the CueBeeCoeNi alloys under different aging conditions: (a) IA, (b) NA and (c) OA.
Table 3 Microstructural characteristics of the alloys. Aging condition
Average grain size of a phase (mm)
Volume fraction of DP cells (%)
IA NA OA
10.9 12.8 9.5
2.2 4.8 13.4
3.3. Fatigue crack growth (FCG) behavior
Fig. 4. DSC curves of the as-quenched alloy and the alloys under different aging conditions.
average length of 66.9 nm). Above all, the sizes in the long axis of the precipitates showed a broad range after different aging treatments. However, the sizes in the short axis of the precipitates didn't change much after different aging treatments. The average sizes in the short axis ranged from 3.0 nm to 8.5 nm. As a result, the ratio of the long axis to the short axis of the precipitates changed from 1.8 to 8.1 when the aging treatment turned from IA to OA.
Fig. 6 presents the fatigue crack growth rates of the samples under different aging conditions in terms of FCG rate versus stress intensity factor range (da/dN-DK) curves. The da/dN-DK curves can usually be divided into three regions, i.e. the slow expanding region (I), stable expanding region (II) and rapid expanding region (III). According to the FCG rate in Fig. 6, the da/dN-DK curves in this study are mainly consisted of stable expanding region and rapid expanding region. When DK value was below 17 MPa m1/2, the FCG rate (da/dN) of the samples subjected to IA was the lowest under the same DK and da/dN of the OA samples was higher than it of the NA samples. When DK value was between 17 and 21 MPa m1/2, da/ dN of the IA samples was still the lowest, but da/dN of the OA samples became lower than it of the NA samples. When DK value was above 21 MPa m1/2, da/dN of the NA samples was still higher than it of the IA and OA samples. However, da/dN of the OA samples kept a stable growth rate, while da/dN of the IA samples represented a much higher growth rate compared with the growth rate when DK value was below 21 MPa m1/2. As a result, the IA samples exhibited a significant higher FCG rate when compared the OA samples at the relatively high stress intensity factor range (DK > 21 MPa m1/2). The conventional Paris model [18] was applied to describe the FCG behavior of the alloys subjected to different aging treatments, given by Eq. (1).
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Fig. 5. TEM micrographs of the CueBeeCoeNi alloys under different aging conditions: (a) IA, (b) SADP in <001>Cu matrix orientation corresponding to (a), (c) the morphology of the precipitates after the IA treatment; (d) NA, (e)<013>Cu SADP corresponding to (d), (f) the morphology of the precipitates after the NA treatment; (g) OA, (h)<011>Cu SADP corresponding to (g), (i) the morphology of the precipitates after the OA treatment.
Table 4 The sizes of the precipitates after different aging treatments. Aging treatments
l (lmin - lmax) (nm)
h (hmin - hmax) (nm)
R
IA NA OA
5.3 (2.6e14.4) 25.3 (5.4e61.9) 66.9 (26.8e187.8)
3.0 (1.2e9.1) 4.8 (2.0e11.0) 8.5 (3.9e17.3)
1.8 5.5 8.1
Note: l, lmin and lmax are average, minimum and maximum size in long axis, respectively; h, hmin and hmax are average, minimum and maximum size in short axis, respectively; R is the average ratio of long axis to short axis.
da=dN ¼ C,ðDKÞm
(1)
where da/dN is the FCG rates, m is the Paris exponent, C is the Paris constants and DK is the stress intensity factor range. By taking the common logarithm on both sides of Eq. (1), the following linear equation can be obtained:
lgðda=dNÞ ¼ lgC þ mlgðDKÞ
(2)
The linear region in Fig. 6 was used to obtain the value of C and m, the fitting parameters and the correlative coefficient are given in Table 5 for each aging condition. As can be seen from Table 5, C and m values are different for various aging conditions. Since the
Fig. 6. Fatigue crack growth rate as a function of stress intensity factor range under different aging conditions.
experiment conditions were nearly the same, it could be inferred that the parameters were closely related to the microstructural factors of the alloys. As shown in Fig. 7, the curves were made up of the linear region and accelerating region, representing the stable expanding region
Y. Tang et al. / Journal of Alloys and Compounds 663 (2016) 784e795 Table 5 Fitting results of samples under different aging conditions. Aging condition
Value of C
Value of m
Correlative coefficient
IA NA OA
1.973 1012 4.684 1014 2.872 1010
6.175 7.725 4.611
0.996 0.996 0.993
and rapid expanding region respectively. The experimental data in the linear region were in good agreement with the calculations, indicating the conventional Paris model precisely describe the stable expanding stage of the alloys. The range of DK in stable expanding region of the IA samples was 14.4e23.6 MPa m1/2, the NA samples in the range of 14.2e23.1 MPa m1/2 and the OA samples in the range of 14.4e27.1 MPa m1/2. As shown in Fig. 8, the growth curve (a vs. N) of major cracks can be separated into two stages. The crack length grows gradually during the first stage, which accounts for about 90% of the fatigue cycles to failure. During the second stage, the crack length grows rapidly, resulting in fracture finally. The NA and IA alloy had almost the same value of critical crack length (ac) and both were lower than the value of ac of the OA alloy. However the number of fatigue cycles to failure (Nf) of the IA alloy was the highest among the alloys under the three aging conditions. 3.4. Morphological features of fracture surface Fig. 9 shows the fatigue fracture surfaces of the alloys under different aging conditions at the initial stage of stable expanding region. Due to the relatively low stress intensity factor, the size of the plastic zone at crack tip is small, resulting in the shearing propagation of the crack along the primary slip system direction.
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For the IA alloy (Fig. 9a), the fracture surface was composed of facets. Unlike the cleavage surface, these facets were caused by the cracks propagated strictly along the {111} slip plane inside the grains [19]. The fracture surface of the NA alloy (Fig. 9b) showed the typical feature of intergranular fracture, and the size of the small surfaces was coincided with the grain size of the NA alloy. Instead of the relatively smooth surfaces, the small surfaces were composed of the voids caused by the segregation of precipitates. The fracture surface of the OA alloy (Fig. 9c) was made up by characteristic crystallographic planes (FCC metal) and slip bands. Furthermore, the river patterns indicating the feature of brittle fracture were visible on the fracture surface. Fig. 10 represents the fatigue fracture surfaces of the alloys under different aging conditions at the later stage of stable expanding region. Since the stress intensity factor is relatively high at this stage, the plastic zone at crack tip can cover multiple grains and the crack begins to propagate along dual slip systems simultaneously or alternatively. The relatively smooth facets and a small number of dimples could be observed on the fracture surface of both the IA and NA alloys (Fig. 10a and c). However, the fracture surface of the IA alloy had a higher proportion of relatively smooth facets compared to the NA alloy. The adjacent relatively smooth facets were connected by the tearing ridges. Furthermore, some secondary cracks propagated along the grain boundaries could be found on the fracture surface of both alloys, suggesting the fracture type was intergranular mode. The fracture surface of the OA alloy (Fig. 10e) was composed of relatively smooth facets and few dimples were observed. The secondary cracks could also be observed on the fracture surface of the OA alloy, but they propagated along the boundaries of different facets instead of grain boundaries. Fig. 10b, d and f show the morphology of the relatively smooth facets under higher magnification. The fatigue striations uniformly
Fig. 7. Logarithm of the fatigue crack growth rate as a function of the logarithm stress intensity factor range: (a) IA; (b) NA; (c) OA.
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materials. As shown in Fig. 12, the fatigue fracture surface at the unstable expanding region represents the characters of static tensile fracture. Lots of dimples, tearing ridges and protuberant facets could be observed in the alloy under the IA (Fig. 12a) and NA (Fig. 12b) conditions, indicating the fracture mechanism was microvoids coalescence fracture couple with intergranular fracture. However, the fatigue fracture surface of the OA alloy at the unstable expanding region (Fig. 12c) exhibited the significant features of ductile transgranular fracture due to the tensile stresses. The dimples and tearing ridges on the fracture surface suggested that large amount of plastic deformation occurred at the unstable expanding region. The plastic deformation led to the formation and coalescence of microvoids, finally resulting in fracture [20]. 4. Discussion Fig. 8. Crack growth curve (a vs. N relation).
distributed on the facets and they were perpendicular to the local FCG direction. In addition, the fatigue steps parallel to the local FCG direction could also be seen on the facets. They were caused by the confluence of the fatigue propagation region with different height [19]. The fatigue fracture surface at the rapid expanding region presents the mixed features of fatigue striations and static tensile, as shown in Fig. 11. Relatively smooth face, dimples couple with fatigue striations could be observed in the alloy subjected to different aging treatments. Furthermore, the striation widths of the rapid expanding region were much larger than those of the stable expanding region, indicating the FCG rate was much higher. According to the K-concept, the unstable propagation of crack would happen when the stress intensity factor at crack tip reaches the critical value of the material (KC) and result in the fracture of
As indicated in the curves of FCG rates vs. DK and morphological features of fracture surfaces of the alloys subjected to different aging treatments, the growth behavior of the fatigue cracks is strongly influenced by microstructural inhomogeneity. Thus, it is important to clarify the relationship between the reversible plastic zone (RPZ) size at the crack tip and microstructural factors for analyzing the growth mechanisms of the fatigue cracks. The RPZ size (rp) under plane stress condition was defined as [21]:
rp ¼
1 DK 2 10p s0:2
(3)
where DK is the stress intensity factor range, and s0.2 is the yield strength. Calculated values of rp and the ratios of rp to the grain size of a phase (rp/d), together with the corresponding values of DK and FCG rates (da/dN) are shown in Table 6. At the relatively low stress intensity factor range (DK < 17 MPa m1/2), the RPZ size of each sample is smaller than the
Fig. 9. SEM fractographs of fatigue fracture surfaces at the initial stage of stable expanding region: (a) IA, (b) NA and (c) OA. The black arrows show the crack propagation direction.
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Fig. 10. SEM fractographs of fatigue fracture surfaces at the later stage of stable expanding region: (a) and (b) IA; (c) and (d) NA; (e) and (f) OA. The black arrows show the crack propagation direction and the white arrows indicate the secondary cracks.
corresponding grain size, so the fatigue crack propagates by a mechanism that follows the individual deformation mode of the localized area inside the grain and adjacent to the grain boundaries (GBs) [10]. Therefore, the characteristics of the precipitates inside the grains and adjacent to the GBs have significant influence on the FCG rates. For the IA alloy, the microstructure was composed of the granular g00 precipitates with the average long axis length of about 5 nm. The g00 precipitates are completely coherent with the parent phase [14], which are shearable by dislocations [22]. In the loading halfcycle, dislocations move in the loading half-cycle from the crack tip into the depth of the plastic zone, and the dislocations that remain on their original slip plane can leave the material as they move back towards the crack tip in the unloading half-cycle when the precipitates can be sheared [23]. These “reversed” dislocations neither contribute to damage accumulation in the plastic zone nor promote crack growth in the following loading cycles [24]. As a result, the IA alloy (with coherent and shearable precipitates) had the lowest FCG rate at the relatively low stress intensity factor range (DK < 21 MPa m1/2).
The dominate precipitates in the NA alloy were slender strips of
g0 precipitates (with average long axis length of 25.3 nm), which were semi-coherent with the parent phase [15]. Furthermore, a small number of g00 precipitates existed in the NA alloy according to the DSC results (Fig. 4). The main precipitates in the OA alloy were coarse g precipitates (with average long axis length of 66.9 nm). The g precipitates were totally incoherent with parent phase and not shearable in nature [17]. According to Hornbogen et al. [24], the alloy with lower reversibility of dislocation motion would present a higher FCG rate. Due to the non-shearable g precipitates, the dislocations in the OA alloy have to bypass them during the loading half-cycle, leaving dislocation loops around the precipitates [25]. The dislocations keep piling up at the crack tip, which would cause the stress concentration and then lead to the initiation of microvoids [26]. Hence, the OA alloy with the coarser and non-shearble g precipitates showed the highest FCG rate when the value of the stress intensity factor range is lower than 17 MPa m1/2. When the value of stress intensity factor range becomes higher (DK > 21 MPa m1/2), the RPZ size of each sample is 1e2 times of the corresponding grain size. Consequently, the crack trends to grow
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Fig. 11. SEM fractographs of fatigue fracture surface at the rapid expanding region: (a) IA, (b) NA and (c) OA. The black arrows show the crack propagation direction.
Fig. 12. SEM fractographs of fatigue fracture surfaces at the unstable expanding region: (a) IA, (b) NA and (c) OA. The black arrows show the crack propagation direction.
along GBs where an incompatibility of plastic deformation in adjacent grains is concentrated, presenting an intergranular fracture [10]. Therefore, the features of the GBs become the main factor that influences the FCG rates. Fig. 13 represents the morphology of
the GBs of the alloys after different aging treatments. For the alloy under the IA condition, DP cells could hardly be found at the GBs (Fig. 13a). However, a few DP cells could be observed at the GBs of the NA alloy (Fig. 13b). The DP cells distributed discontinuous at the
Y. Tang et al. / Journal of Alloys and Compounds 663 (2016) 784e795 Table 6 Values of reversible plastic zone (RPZ) sizes and their ratio to the grain size. Sample
DK (MPa$m1/2)
rp (mm)
rp/d
da/dN (104 mm/cycle)
IA (d ¼ 10.9 mm)
15 17 21 25 15 17 21 25 15 17 21 25
5.5 6.9 10.7 14.9 5.5 6.8 10.4 14.5 7.6 9.6 14.8 20.2
0.51 0.63 0.98 1.37 0.43 0.53 0.81 1.14 0.80 1.01 1.56 2.13
0.40 0.79 3.03 11.95 0.74 1.49 8.02 61.21 0.95 1.32 3.33 9.47
NA (d ¼ 12.8 mm)
OA (d ¼ 9.5 mm)
GBs and they grew from only one side of the GBs into the parent phase. When it came to the OA condition (Fig. 13c), the GBs were almost replaced by the DP cells. The DP cells distributed continuous at the both sides of the GBs and there were clear interfaces between the DP cells and the parent phase. Fig. 14 illustrates the crack growth mechanisms in the alloys under different aging conditions, when the RPZ size of each sample is 1e2 times of the corresponding grain size. Meanwhile, the fatigue cracks were in the later stage of stable expanding region and the rapid expanding region according to the da/dN-DK curves (Fig. 6). When the alloy is subjected to the IA treatment (Fig. 14a), the crack appears to propagate along the GBs. For the NA alloy (Fig. 14b), the crack propagates preferentially along the GBs which have DP cells on one side of them. As a consequence, these grains are separated from the matrix, leading to fracture quickly. Due to that few DP cells exist at the GBs in the IA alloy, the compatibility of the plastic deformation of the GBs in the IA alloy is much higher than it in the NA alloy. Therefore, the FCG rate of the IA alloy was much lower as compared to the NA alloy. When under the OA condition (Fig. 14c), the crack propagates along the interfaces
793
between the DP cells and parent phase. Since the interfaces between the DP cells and parent phase are tortuous, the propagation of the crack demands more energy [5]. This is the reason why the FCG rate of the OA alloy was the lowest at the relatively high stress intensity factor range (DK > 21 MPa m1/2). The surface morphology near the fracture (the later stage of stable expanding region and the rapid expanding region) was observed on samples after FCG tests. As shown in Fig. 15, the characteristics of the microcracks in each sample confirm the rationality of the crack growth mechanisms illustrated above. The microcrack propagated along the GBs with a relatively straight path in the IA alloy (Fig. 15a). For the NA alloy (Fig. 15b), the microcrack propagated preferentially along the GBs which have DP cells on one side of them. As a result, the grain was almost separated from the matrix. However, the microcrack propagated along the interfaces between the DP cells and parent phase in the OA alloy (Fig. 15c). Compared with the microcrack in the IA alloy, the microcrack in the OA alloy represented a significantly more tortuous propagation path. As shown in the curves of crack length vs. number of cycles (Fig. 8), the alloys subjected to different aging treatments exhibited different fatigue lives. Table 7 presents the relationship between the ratio of the RPZ size to the grain size (rp/d) and the residual fatigue life. For the IA and NA alloy, the number of cycles (N) accounted for over 90% of the fatigue cycles to failure (Nf) when the RPZ size was equal to the grain size. This means that the crack propagating inside the grain and adjacent to the GBs takes up most of the fatigue life. Then the crack propagated along the GBs when the RPZ size was larger than the grain size, leading to the rapid fracture of the sample. Since the FCG rate of the IA alloy is much lower than those of the other two alloys when the crack propagates inside the grain, the IA alloy has the longest fatigue life. However, for the OA alloy, N made up only 60% of Nf when the RPZ size was equal to the grain size. The FCG rate increased with the RPZ size. Until the RPZ size was about twice as large as the grain size, N
Fig. 13. TEM morphology of the GBs after (a) IA treatment, (b) NA treatment and (c) OA treatment.
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Fig. 14. Schematic illustration of the crack growth mechanism in the alloy subjected to the (a) IA treatment, (b) NA treatment and (c) OA treatment. The RPZ size of each sample is 1e2 times of the corresponding grain size.
reached more than 90% of Nf. According to the effect of RPZ size on the FCG mechanism, the propagation of the fatigue crack in the OA alloy can be divided into two parts, the propagation inside the grain and the propagation along the interfaces between the DP cells and parent phase. These interfaces hinder the propagation of the fatigue cracks effectively when the cracks propagate from the area inside the grains to the interfaces, which contribute to the decrease of FCG rate. 5. Conclusions The effects of microstructure on the fatigue crack growth behavior of CueBeeCoeNi alloy after IA, NA and OA treatment are investigated in this paper. The conclusions are made as follows: (1). After IA treatment, the microstructure of the CueBeeCoeNi alloy was mainly consisted of fine g00 precipitates with tiny amounts of g0 precipitates. The main precipitates of the alloy treated by NA and OA were g0 precipitates and g precipitates,
respectively. The average long axis length of the g0 precipitates was 25.3 nm while it of g precipitates was 66.9 nm, and both were much larger than the average long axis length of g00 precipitates (5.3 nm). The IA alloy had few DP cells at the GBs, while the NA alloy had a quantity of DP cells which distributed discontinuous at the GBs. The GBs of the OA alloy were almost replaced by the DP cells which distributed continuous at the both sides of the GBs. (2). The FCG rate was closely related to the crack growth mechanism in each alloy, which could be successfully explained by the model based on the RPZ size and microstructural factors. Because that g00 precipitates in the IA alloy were completely coherent with the parent phase and they could be sheared by the dislocations, the IA alloy had the lowest FCG rate at the relatively low stress intensity factor range (DK < 21 MPa m1/ 2 ). When the stress intensity factor range became higher (DK > 21 MPa m1/2), the tortuous interfaces between the DP cells and parent phase in the OA alloy hindered the
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Fig. 15. SEM observations of the regions below the fracture surfaces of the FCG test samples subjected to the (a) IA treatment, (b) NA treatment and (c) OA treatment. The black arrows indicate the microcracks.
Table 7 Relationship between the ratio of the reversible plastic zone (RPZ) size to the grain size and the residual fatigue life. Aging condition
Fatigue cycles to failure Nf (cycle)
rp/d
da/dN (104 mm/cycle)
Number of cycles N (cycle)
N/Nf
IA NA OA
66288 39409 40052
0.98 0.99 1.01 1.33 2.13
3.03 27.93 1.32 2.45 9.47
62354 39125 24086 32565 38622
0.94 0.99 0.60 0.81 0.96
propagation of the fatigue cracks, correspondingly resulted in the lowest FCG rate. (3). For the IA and NA alloy, the fatigue crack propagating inside the grain and adjacent to the GBs accounted for over 90% of the fatigue life. Owing to the lowest FCG rate when the crack propagated inside the grain, the IA alloy had the longest fatigue life. The propagation of the fatigue crack in the OA alloy could be divided into the propagation inside the grain (made up 60% of the fatigue life) and the propagation along the interfaces between the DP cells and parent phase (took up the rest 40% of the fatigue life). Acknowledgments The authors gratefully acknowledge the financial support from Project U1460101 supported by National Natural Science Foundation of China. References [1] F. Berto, P. Lazzarin, P. Gallo, J. Strain Anal. Eng. Des. 49 (2014) 244e256. [2] P. Behjati, H. Vahid Dastjerdi, R. Mahdavi, J. Alloys Compd. 505 (2010)
[3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26]
739e742. J.R. Davis, Copper and Copper Alloys, ASM International, Ohio, 2011. € ppel, L. May, M. Prell, M. Go €ken, Int. J. Fatigue 33 (2011) 10e18. H.W. Ho Y.L. Wang, Q.L. Pan, L.L. Wei, et al., Mater. Des. 55 (2014) 857e863. M.N. Desmukh, R.K. Pandey, A.K. Mukhopadhyay, Mater. Sci. Eng. A 435e436 (2006) 318e326. C.H. Qin, X.C. Zhang, S. Ye, S.T. Tu, Eng. Frcat. Mech. 142 (2015) 140e153. C. Watanabe, R. Monzen, K. Tazaki, Int. J. Fatigue 30 (2008) 635e641. H.K. Kim, M. Choi, C.S. Chung, D.H. Shin, Mater. Sci. Eng. A 340 (2003) 243e250. M. Goto, S.Z. Han, K. Euh, et al., Acta Mater 58 (2010) 6294e6305. D.B. Williams, E.P. Butler, Int. Met. Rev. 26 (1981) 153e183. I. Manna, S.K. Pabi, W. Gust, Int. Mater. Rev. 46 (2001) 53e91. E. Donoso, A. Varschavsky, J. Therm. Anal. Calorim. 63 (2001) 249e266. R. Monzen, S. Okawarab, C. Watanabe, Philos. Mag. 92 (2012) 1826e1843. R.J. Rioja, D.E. Laughlin, Acta Metall. 28 (1980) 1301e1313. G.L. Xie, Q.S. Wang, X.J. Mi, et al., Mater. Sci. Eng. A 558 (2012) 326e330. R. Monzen, T. Seo, T. Sakai, C. Watanabe, Mater. Trans. 47 (2006) 2925e2934. P. Paris, F. Erdogan, J. Basic Eng. Trans. ASME (1963) 528e534. U. Krupp, Fatigue Crack Propagation in Metals and Alloys: Microstructural Aspects and Modelling Concepts, John Wiley & Sons, 2007. A. Weck, D.S. Wilkinson, E. Maire, Mater. Sci. Eng. A 488 (2008) 435e445. B. Budianski, J.W. Huchinson, J. Appl. Mech. Trans. ASME 45 (1978) 267e276. Y.C. Tang, Y.L. Kang, L.J. Yue, et al., Mater. Des. 85 (2015) 332e341. K. Hockauf, M.F.-X. Wagner, T. Halle, et al., Acta Mater 80 (2014) 250e263. E. Hornbogen, K.H. Zum Gahr, Acta Metall. 24 (1976) 581e592. T. Gladman, Mater. Sci. Technol. 15 (1999) 30e36. Y. Satoh, T. Yoshiie, H. Mori, et al., Mater. Sci. Eng. A 350 (2003) 44e52.
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Journal of Alloys and Compounds journal homepage: http://www.elsevier.com/locate/jalcom
Effect of microstructure on the fatigue crack growth behavior of CueBeeCoeNi alloy Yanchuan Tang a, Guoming Zhu a, **, Yonglin Kang a, *, Lijuan Yue b, Xiaoliang Jiao b a b
School of Materials Science and Engineering, University of Science and Technology Beijing, Beijing 100083, China CNMC Ningxia Orient Group Co. Ltd., Shizuishan 753000, China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 17 September 2015 Received in revised form 16 November 2015 Accepted 5 December 2015 Available online 11 December 2015
The fatigue crack growth (FCG) behaviors of CueBeeCoeNi alloy subjected to interrupted aging (IA), normal aging (NA) and overaging (OA) treatment were discussed. The distinctions in microstructure of the alloys after various aging treatments led to different FCG behaviors. In order to understand the different FCG behaviors, a model based on the reversible plastic zone (RPZ) size and microstructural factors was applied in this study. At the relatively low stress intensity factor range (DK < 17 MPa m1/2), the RPZ size of each sample was smaller than the corresponding grain size, so the fatigue crack propagated inside the grain and adjacent to the grain boundaries (GBs). For the IA alloy, fine and coherent g00 precipitates which could be sheared by dislocations promoted the fatigue crack resistance, leading to the decrease of FCG rate. When the value of stress intensity factor range becomes higher (DK > 21 MPa m1/2), the RPZ size of each sample was 1e2 times of the corresponding grain size. Consequently, the crack trended to grow along GBs. For the OA alloy, the crack propagated along the interfaces between the discontinuous precipitation (DP) cells and parent phase. The tortuous interfaces hindered the propagation of the fatigue cracks, resulting in the reduction of FCG rate. © 2015 Elsevier B.V. All rights reserved.
Keywords: CueBeeCoeNi alloy Aging Microstructure Precipitate Fatigue crack growth behavior
1. Introduction The CueBeeCoeNi alloy has the most significant precipitation strengthening effect among copper alloys. After proper aging treatment, the alloy has high strength and elasticity but little elastic hysteresis. Meanwhile, it also possesses good electrical conductivity, thermal conductivity and is non-magnetic. Because of these attractive advantages, CueBeeCoeNi alloy has been widely used in key elastic parts, such as the springs, contactors and switches in the electronic components [1e3]. Since these components would withstand thousands even millions of repeated operations in service, the reliability of these components largely depends on the fatigue properties of the materials. Therefore, it is necessary to study the factors that affect the fatigue properties of CueBeeCoeNi alloy. When under the same service condition, the fatigue properties of the material are mainly affected by the microstructure. The
* Corresponding author. ** Corresponding author. E-mail addresses: [email protected] (G. Zhu), [email protected] (Y. Kang). http://dx.doi.org/10.1016/j.jallcom.2015.12.017 0925-8388/© 2015 Elsevier B.V. All rights reserved.
propagation path and growth rate of the fatigue crack are closely related to the characteristics of precipitates, grain size and the € ppel et al. [4] found that morphology of grain boundaries (GBs). Ho the fatigue properties were significantly affected by the size of precipitates. The size of precipitates in the over-aged alloy was larger than it in peak-aged and as-received alloy, resulting in lower fatigue limit and shorter fatigue life of the over-aged alloy. The interaction mechanisms between dislocations and precipitates also affect the fatigue properties. For the fine and coherent precipitates, dislocations can shear them and glide more-or-less reversibly during cyclic loading [5]. According to the research of Desmukh et al. on the aluminum alloys [6], this planar-reversible slip fosters the fatigue crack growth resistance, leading to the decrease of fatigue crack growth (FCG) rate. The precipitates in the over-aged alloy have relatively large size and semi-coherent or incoherent with the parent phase, which can't be sheared by dislocations. However, this allows the over-aged alloy to deform homogeneously, and as a result the over-aged alloy possesses a higher fatigue crack propagation threshold [6]. According to Qin et al. [7], the GH4169 alloy with coarser grain exhibits lower FCG rate and longer fatigue life. However, the slow expanding stage accounts for a larger fraction of the total fatigue life for the GH4169 alloy with
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finer grain size. Besides above factors, the existence of precipitatefree zones (PFZs) has a detrimental influence on the fatigue life and the decrease in the PFZ width brings about the increase in the fatigue life [6,8]. Since fatigue cracks usually propagate as a result of the accumulation of irreversible plastic deformation at a crack tip, the reversible crack tip displacement (CTODr) appears to be a proper method to characterize the crack propagation behavior. However, it is extremely difficult to measure CTODr in polycrystalline materials. Therefore, the reversible plastic zone (RPZ) size, which is closely related to CTODr, is often used to describe the crack propagation behavior. In the intermediate stage of crack growth in UFG steel, Kim et al. [9] showed that the RPZ size was much larger than the grain size, which permits the crack to interact with several grains during cyclic loading. Based on the RPZ size and microstructural factors, a quantitative model describing the crack growth mechanism was developed by Goto et al. [10]. The model successfully explained the fatigue crack growth behavior of the ultra-fine grained copper. In this study, different aging treatments were conducted on CueBeeCoeNi alloy (in solid solution state), resulting in various microstructural factors. The fatigue crack growth mechanisms were discussed based on the RPZ size at the crack tip and the microstructural factors of the alloys.
785
Fig. 1. Schematic diagram of heat treatment procedures used in this study.
2. Experimental details 2.1. Material and processing The as-cast CueBeeCoeNi (composition in Table 1) alloy, in the shape of 120 mm 100 mm 70 mm, was subjected to homogenized annealing at 800 C for 180 min. Then the ingots were hotrolled to 9 mm (87% rolling reduction) at 650 Ce740 C, followed by quenching in water immediately. The hot-rolled sheets were intermediate annealed at 570 C for 240 min. Subsequently, the hot-rolled sheets were cold-rolled to a thickness of 2.0 mm (78% rolling reduction). The solution treatment was applied to coldrolled sheets at 780 C for 20 min, followed by water quenching to room temperature (RT). Finally, the cold-rolled sheets were subjected to different aging treatments, as shown schematically in Fig. 1. The first aging treatment is normal aging (marked as NA) with the treatment of aging at 320 C for 180 min. The second one is interrupted aging (marked as IA) with the treatment of underaging at 320 C for 30 min and rapid quenching to room temperature (RT) then interrupted aging at 280 C for 360 min. The last one is overaging (marked as OA) with the treatment of aging at 370 C for 60 min. The annealing and solution treatments were performed in the air circulating furnace, while the aging treatments were conducted in salt baths. 2.2. Tensile and fatigue crack growth (FCG) rate tests Samples for microstructural and mechanical properties examination were cut from the sheets subjected to different aging treatments, parallel to the rolling direction. All these tensile samples were prepared according to GB/T 228.1e2010. Tensile tests were carried out on a WDW200D test machine. FCG tests were performed on a MTS-810 test machine using compact tension, C(T),
Table 1 The composition of CueBeeNieCo alloy (wt. %). Element
Be
Ni
Co
Cu
Content
1.8e2.1
0.2e0.3
0.1e0.2
Bal.
Fig. 2. Geometry of the C(T) samples (dimensions in mm).
samples according to ASTM E647 standard. Fig. 2 shows the geometry of the C(T) samples. The samples were machined from the sheets in the transverse-longitudinal (T-L) direction, maintaining the crack propagation direction along the rolling direction. Before the FCG rate tests, each C(T) sample was subjected to fatigue loading in order to obtain a pre-crack with the length of approximately 1.0 mm. Tests were conducted in air at room temperature, using a constant amplitude sinusoidal loading with a load ratio of R ¼ 0.1 at a frequency of 10 Hz. The fatigue crack length measurements were carried out using the compliance method by employing a clip gauge at the notch mouth. 2.3. Microstructural and differential scanning calorimetry (DSC) investigation The microstructures and fracture surfaces of the samples under different aging conditions were examined in detail using a field emission gun scanning electron microscope (FEG-SEM) Hitachi S4800 and Cambridge S-360 SEM operating at 20 kV. The DSC experiments were carried out in a SDT-Q600 simultaneous thermal analyzer. Disc-shaped samples with 20e40 mg in weight were prepared from the sheets by an electro discharge machine. The DSC samples were examined with a heating rate of 10 C/min between 20 and 550 C. A baseline scan was recorded from a pure Cu sample and subsequently subtracted from the alloy scans. Transmission electron microscope (TEM) observation was carried out using an H8100 TEM operating at 200 kV. For this observation, thin foils were prepared by a twin-jet polishing method with a solution of 70%
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methanol and 30% nitric acid in volume fraction at 25 to 30 C, 9.5 V and 20 mA. The sizes in the long axis and short axis of the precipitates were measured from 5 TEM images by image processing software. For each aging condition, the TEM images were taken from different areas under the same magnification. 3. Results 3.1. Tensile properties and related microstructure As the tensile properties presented in Table 2, the yield strength (YS) and ultimate tensile strength (UTS) of the alloy under the IA condition are similar to those of the alloy under the NA condition, but the elongation of the alloy under the IA condition was about 12% higher than it under the NA condition. The alloy subjected to OA treatment had the relatively low strength, the YS and UTS were about 180 MPa lower than those of the alloys under the NA and IA conditions. However, the elongation of OA samples was about 2 times as it of NA and IA samples and the yield ratio of the OA alloy was the lowest. Fig. 3 shows the microstructure of the alloys subjected to different aging treatments, using the backscattered electron (BSD) mode of SEM. After the aging treatments, it could be observed that the microstructure was consisted of a phase (solid solution phase) and the discontinuous precipitation (DP) cells located at the grain boundaries (GBs) of a phase. For the IA samples, the GBs could be clearly observed while there were few DP cells at the GBs. The microstructure of the NA samples was composed of a phase with small numbers of DP cells at the GBs. However, the DP cells accounted for a considerable percentage in the microstructure of the OA samples, and a phase was surrounded by the DP cells. The microstructural characteristics of the studied alloys, including the average size of a phase and the volume fraction of DP cells, were measured by image processing software and the results are summarized in Table 3. The alloys under the IA, NA and OA conditions had similar average grain sizes of a phase, with the value of 10.9, 12.8 and 9.5 mm respectively. The volume fraction of DP cells under the OA condition was 13.4%, compared with less than 5% under the NA and IA conditions. DP cells involve the formation of a solute-depleted matrix phase (a0 ) and a precipitate phase (g) as a duplex transformation product and they usually nucleate at the GBs and grow into one side of the supersaturated matrix (a phase) [11,12]. The DP cells consumed huge numbers of solute atoms and they contained coarse equilibrium phase of g instead of fine metastable g00 and g0 phases, resulting in weakening the precipitation strengthening of the alloy. Consequently, the strength of the alloy would decrease with the increase of the volume fraction of DP cells, which was in line with the relatively low strength of the OA alloy as compared to the NA and IA alloy. 3.2. DSC and TEM study of CueBeeCoeNi alloy under different aging conditions As shown in Fig. 4, a series of DSC scans was recorded from the samples of the alloys subjected to different aging treatments, and then compared with the scan from the solution treated and
Table 2 Tensile properties of the CueBeeCoeNi alloys under different aging conditions. Aging condition
YS (MPa)
UTS (MPa)
UEl (%)
El (%)
Yield ratio
IA NA OA
1157 1167 990
1320 1329 1161
5.7 5.1 8.4
7.5 6.7 13.0
0.876 0.878 0.853
quenched sample. The scan from the solution treated and quenched sample showed four characteristic exothermic reactions which were consistent with results reported by Donoso and Varschavsky [13]. Peak 1 (the center of peak 1: ~210 C) corresponded to the formation of G.P. zones; peak 2 (~260 C) indicated the formation of g00 precipitates; peak 3 (~340 C) represented the formation of g0 precipitates; peak 4 (~400 C) indicated the formation of g precipitates. The DSC trace for the sample subjected to the OA treatment prior to heating in the DSC cell didn't show any exothermic peaks or endothermic peaks, which meant that the solute atoms in the OA sample were totally precipitated, and the precipitates were thermodynamic stable during the DSC test. As a result, the alloy under the OA condition should be mainly consisted of g phase (equilibrium phase). The DSC scans of the samples under NA and IA conditions showed the endothermic peaks at about 385 C, and then the exothermic peaks at about 440 C. The endothermic reaction suggested that the g00 precipitates formed during aging treatments dissolved on heating, and the exothermic reaction indicated the formation of g precipitates. However the area under the endothermic peak of the IA sample was much larger than that of the NA sample, suggesting more g00 precipitates dissolved on heating, thereby larger numbers of g00 precipitates precipitated during the IA treatment. TEM observation was used to characterize the precipitates in the alloys after different aging treatments, and the results were in line with the DSC scans. After the IA treatment (Fig. 5a and c), the microstructure was mainly composed of fine granular precipitates with the habit plane of (100)a. From the corresponding selected area diffraction pattern (SADP) in <001>Cu matrix orientation (Fig. 5b), the extra diffraction spots which represented the precipitates could be observed, indicating the lattice parameter of the precipitates (a ¼ 0.254 nm). The result was fairly close to the lattice parameter of g00 phase reported by Monzen et al. [14]. Furthermore, the “arrowheads” with its ‘‘tip’’ at the position of the (010)a reflection and its “base” at 2/3(020)a could be observed, which were considered as the formation of the g0 precipitates [15]. In summary, the microstructure of the alloy subjected to IA treatment was mainly consisted of fine g00 precipitates with tiny amounts of g0 precipitates. As shown in Fig. 5d and f, the main phase precipitated after the NA treatment appeared to be slender strips of g0 phase, which precipitated after the g00 phase according to the precipitation sequence of CueBe alloys [16]. The ‘‘arrowheads’’ considered as the formation of the g0 precipitates could also be observed in the corresponding SADP (Fig. 5e), indicating a change in habit planes from the matrix [15]. The slender strips of g0 precipitates were parallel to (131)a and (121)a, while the habit plane of g00 precipitates was (100)a. After the OA treatment (Fig. 5g and i), the microstructure was composed of coarse g precipitates, with the length of approximately 100 nm. The equilibrium g phase was formed by the transformation of metastable g0 phase, with no changes in the orientations and habit planes of precipitates [17]. According to the corresponding SADP (Fig. 5h), the g precipitates were parallel to (211)a and (311)a, which had the same habit planes as the g0 precipitates. The sizes of the precipitates after different aging treatments are shown in Table 4. After the IA treatment, the main phase was granular g00 phase. The g00 precipitates had relatively small size, whose average length of the long axis was only 5.3 nm. The dominate precipitates after the NA treatment were slender strips of g0 precipitates. Compared with g00 precipitates, g0 precipitates had much larger size, especially in the long axis (with average length of 25.3 nm). The main precipitates after the OA treatment were coarse g precipitates, with the even larger size in the long axis (with
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787
Fig. 3. SEM images of the CueBeeCoeNi alloys under different aging conditions: (a) IA, (b) NA and (c) OA.
Table 3 Microstructural characteristics of the alloys. Aging condition
Average grain size of a phase (mm)
Volume fraction of DP cells (%)
IA NA OA
10.9 12.8 9.5
2.2 4.8 13.4
3.3. Fatigue crack growth (FCG) behavior
Fig. 4. DSC curves of the as-quenched alloy and the alloys under different aging conditions.
average length of 66.9 nm). Above all, the sizes in the long axis of the precipitates showed a broad range after different aging treatments. However, the sizes in the short axis of the precipitates didn't change much after different aging treatments. The average sizes in the short axis ranged from 3.0 nm to 8.5 nm. As a result, the ratio of the long axis to the short axis of the precipitates changed from 1.8 to 8.1 when the aging treatment turned from IA to OA.
Fig. 6 presents the fatigue crack growth rates of the samples under different aging conditions in terms of FCG rate versus stress intensity factor range (da/dN-DK) curves. The da/dN-DK curves can usually be divided into three regions, i.e. the slow expanding region (I), stable expanding region (II) and rapid expanding region (III). According to the FCG rate in Fig. 6, the da/dN-DK curves in this study are mainly consisted of stable expanding region and rapid expanding region. When DK value was below 17 MPa m1/2, the FCG rate (da/dN) of the samples subjected to IA was the lowest under the same DK and da/dN of the OA samples was higher than it of the NA samples. When DK value was between 17 and 21 MPa m1/2, da/ dN of the IA samples was still the lowest, but da/dN of the OA samples became lower than it of the NA samples. When DK value was above 21 MPa m1/2, da/dN of the NA samples was still higher than it of the IA and OA samples. However, da/dN of the OA samples kept a stable growth rate, while da/dN of the IA samples represented a much higher growth rate compared with the growth rate when DK value was below 21 MPa m1/2. As a result, the IA samples exhibited a significant higher FCG rate when compared the OA samples at the relatively high stress intensity factor range (DK > 21 MPa m1/2). The conventional Paris model [18] was applied to describe the FCG behavior of the alloys subjected to different aging treatments, given by Eq. (1).
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Fig. 5. TEM micrographs of the CueBeeCoeNi alloys under different aging conditions: (a) IA, (b) SADP in <001>Cu matrix orientation corresponding to (a), (c) the morphology of the precipitates after the IA treatment; (d) NA, (e)<013>Cu SADP corresponding to (d), (f) the morphology of the precipitates after the NA treatment; (g) OA, (h)<011>Cu SADP corresponding to (g), (i) the morphology of the precipitates after the OA treatment.
Table 4 The sizes of the precipitates after different aging treatments. Aging treatments
l (lmin - lmax) (nm)
h (hmin - hmax) (nm)
R
IA NA OA
5.3 (2.6e14.4) 25.3 (5.4e61.9) 66.9 (26.8e187.8)
3.0 (1.2e9.1) 4.8 (2.0e11.0) 8.5 (3.9e17.3)
1.8 5.5 8.1
Note: l, lmin and lmax are average, minimum and maximum size in long axis, respectively; h, hmin and hmax are average, minimum and maximum size in short axis, respectively; R is the average ratio of long axis to short axis.
da=dN ¼ C,ðDKÞm
(1)
where da/dN is the FCG rates, m is the Paris exponent, C is the Paris constants and DK is the stress intensity factor range. By taking the common logarithm on both sides of Eq. (1), the following linear equation can be obtained:
lgðda=dNÞ ¼ lgC þ mlgðDKÞ
(2)
The linear region in Fig. 6 was used to obtain the value of C and m, the fitting parameters and the correlative coefficient are given in Table 5 for each aging condition. As can be seen from Table 5, C and m values are different for various aging conditions. Since the
Fig. 6. Fatigue crack growth rate as a function of stress intensity factor range under different aging conditions.
experiment conditions were nearly the same, it could be inferred that the parameters were closely related to the microstructural factors of the alloys. As shown in Fig. 7, the curves were made up of the linear region and accelerating region, representing the stable expanding region
Y. Tang et al. / Journal of Alloys and Compounds 663 (2016) 784e795 Table 5 Fitting results of samples under different aging conditions. Aging condition
Value of C
Value of m
Correlative coefficient
IA NA OA
1.973 1012 4.684 1014 2.872 1010
6.175 7.725 4.611
0.996 0.996 0.993
and rapid expanding region respectively. The experimental data in the linear region were in good agreement with the calculations, indicating the conventional Paris model precisely describe the stable expanding stage of the alloys. The range of DK in stable expanding region of the IA samples was 14.4e23.6 MPa m1/2, the NA samples in the range of 14.2e23.1 MPa m1/2 and the OA samples in the range of 14.4e27.1 MPa m1/2. As shown in Fig. 8, the growth curve (a vs. N) of major cracks can be separated into two stages. The crack length grows gradually during the first stage, which accounts for about 90% of the fatigue cycles to failure. During the second stage, the crack length grows rapidly, resulting in fracture finally. The NA and IA alloy had almost the same value of critical crack length (ac) and both were lower than the value of ac of the OA alloy. However the number of fatigue cycles to failure (Nf) of the IA alloy was the highest among the alloys under the three aging conditions. 3.4. Morphological features of fracture surface Fig. 9 shows the fatigue fracture surfaces of the alloys under different aging conditions at the initial stage of stable expanding region. Due to the relatively low stress intensity factor, the size of the plastic zone at crack tip is small, resulting in the shearing propagation of the crack along the primary slip system direction.
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For the IA alloy (Fig. 9a), the fracture surface was composed of facets. Unlike the cleavage surface, these facets were caused by the cracks propagated strictly along the {111} slip plane inside the grains [19]. The fracture surface of the NA alloy (Fig. 9b) showed the typical feature of intergranular fracture, and the size of the small surfaces was coincided with the grain size of the NA alloy. Instead of the relatively smooth surfaces, the small surfaces were composed of the voids caused by the segregation of precipitates. The fracture surface of the OA alloy (Fig. 9c) was made up by characteristic crystallographic planes (FCC metal) and slip bands. Furthermore, the river patterns indicating the feature of brittle fracture were visible on the fracture surface. Fig. 10 represents the fatigue fracture surfaces of the alloys under different aging conditions at the later stage of stable expanding region. Since the stress intensity factor is relatively high at this stage, the plastic zone at crack tip can cover multiple grains and the crack begins to propagate along dual slip systems simultaneously or alternatively. The relatively smooth facets and a small number of dimples could be observed on the fracture surface of both the IA and NA alloys (Fig. 10a and c). However, the fracture surface of the IA alloy had a higher proportion of relatively smooth facets compared to the NA alloy. The adjacent relatively smooth facets were connected by the tearing ridges. Furthermore, some secondary cracks propagated along the grain boundaries could be found on the fracture surface of both alloys, suggesting the fracture type was intergranular mode. The fracture surface of the OA alloy (Fig. 10e) was composed of relatively smooth facets and few dimples were observed. The secondary cracks could also be observed on the fracture surface of the OA alloy, but they propagated along the boundaries of different facets instead of grain boundaries. Fig. 10b, d and f show the morphology of the relatively smooth facets under higher magnification. The fatigue striations uniformly
Fig. 7. Logarithm of the fatigue crack growth rate as a function of the logarithm stress intensity factor range: (a) IA; (b) NA; (c) OA.
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materials. As shown in Fig. 12, the fatigue fracture surface at the unstable expanding region represents the characters of static tensile fracture. Lots of dimples, tearing ridges and protuberant facets could be observed in the alloy under the IA (Fig. 12a) and NA (Fig. 12b) conditions, indicating the fracture mechanism was microvoids coalescence fracture couple with intergranular fracture. However, the fatigue fracture surface of the OA alloy at the unstable expanding region (Fig. 12c) exhibited the significant features of ductile transgranular fracture due to the tensile stresses. The dimples and tearing ridges on the fracture surface suggested that large amount of plastic deformation occurred at the unstable expanding region. The plastic deformation led to the formation and coalescence of microvoids, finally resulting in fracture [20]. 4. Discussion Fig. 8. Crack growth curve (a vs. N relation).
distributed on the facets and they were perpendicular to the local FCG direction. In addition, the fatigue steps parallel to the local FCG direction could also be seen on the facets. They were caused by the confluence of the fatigue propagation region with different height [19]. The fatigue fracture surface at the rapid expanding region presents the mixed features of fatigue striations and static tensile, as shown in Fig. 11. Relatively smooth face, dimples couple with fatigue striations could be observed in the alloy subjected to different aging treatments. Furthermore, the striation widths of the rapid expanding region were much larger than those of the stable expanding region, indicating the FCG rate was much higher. According to the K-concept, the unstable propagation of crack would happen when the stress intensity factor at crack tip reaches the critical value of the material (KC) and result in the fracture of
As indicated in the curves of FCG rates vs. DK and morphological features of fracture surfaces of the alloys subjected to different aging treatments, the growth behavior of the fatigue cracks is strongly influenced by microstructural inhomogeneity. Thus, it is important to clarify the relationship between the reversible plastic zone (RPZ) size at the crack tip and microstructural factors for analyzing the growth mechanisms of the fatigue cracks. The RPZ size (rp) under plane stress condition was defined as [21]:
rp ¼
1 DK 2 10p s0:2
(3)
where DK is the stress intensity factor range, and s0.2 is the yield strength. Calculated values of rp and the ratios of rp to the grain size of a phase (rp/d), together with the corresponding values of DK and FCG rates (da/dN) are shown in Table 6. At the relatively low stress intensity factor range (DK < 17 MPa m1/2), the RPZ size of each sample is smaller than the
Fig. 9. SEM fractographs of fatigue fracture surfaces at the initial stage of stable expanding region: (a) IA, (b) NA and (c) OA. The black arrows show the crack propagation direction.
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Fig. 10. SEM fractographs of fatigue fracture surfaces at the later stage of stable expanding region: (a) and (b) IA; (c) and (d) NA; (e) and (f) OA. The black arrows show the crack propagation direction and the white arrows indicate the secondary cracks.
corresponding grain size, so the fatigue crack propagates by a mechanism that follows the individual deformation mode of the localized area inside the grain and adjacent to the grain boundaries (GBs) [10]. Therefore, the characteristics of the precipitates inside the grains and adjacent to the GBs have significant influence on the FCG rates. For the IA alloy, the microstructure was composed of the granular g00 precipitates with the average long axis length of about 5 nm. The g00 precipitates are completely coherent with the parent phase [14], which are shearable by dislocations [22]. In the loading halfcycle, dislocations move in the loading half-cycle from the crack tip into the depth of the plastic zone, and the dislocations that remain on their original slip plane can leave the material as they move back towards the crack tip in the unloading half-cycle when the precipitates can be sheared [23]. These “reversed” dislocations neither contribute to damage accumulation in the plastic zone nor promote crack growth in the following loading cycles [24]. As a result, the IA alloy (with coherent and shearable precipitates) had the lowest FCG rate at the relatively low stress intensity factor range (DK < 21 MPa m1/2).
The dominate precipitates in the NA alloy were slender strips of
g0 precipitates (with average long axis length of 25.3 nm), which were semi-coherent with the parent phase [15]. Furthermore, a small number of g00 precipitates existed in the NA alloy according to the DSC results (Fig. 4). The main precipitates in the OA alloy were coarse g precipitates (with average long axis length of 66.9 nm). The g precipitates were totally incoherent with parent phase and not shearable in nature [17]. According to Hornbogen et al. [24], the alloy with lower reversibility of dislocation motion would present a higher FCG rate. Due to the non-shearable g precipitates, the dislocations in the OA alloy have to bypass them during the loading half-cycle, leaving dislocation loops around the precipitates [25]. The dislocations keep piling up at the crack tip, which would cause the stress concentration and then lead to the initiation of microvoids [26]. Hence, the OA alloy with the coarser and non-shearble g precipitates showed the highest FCG rate when the value of the stress intensity factor range is lower than 17 MPa m1/2. When the value of stress intensity factor range becomes higher (DK > 21 MPa m1/2), the RPZ size of each sample is 1e2 times of the corresponding grain size. Consequently, the crack trends to grow
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Fig. 11. SEM fractographs of fatigue fracture surface at the rapid expanding region: (a) IA, (b) NA and (c) OA. The black arrows show the crack propagation direction.
Fig. 12. SEM fractographs of fatigue fracture surfaces at the unstable expanding region: (a) IA, (b) NA and (c) OA. The black arrows show the crack propagation direction.
along GBs where an incompatibility of plastic deformation in adjacent grains is concentrated, presenting an intergranular fracture [10]. Therefore, the features of the GBs become the main factor that influences the FCG rates. Fig. 13 represents the morphology of
the GBs of the alloys after different aging treatments. For the alloy under the IA condition, DP cells could hardly be found at the GBs (Fig. 13a). However, a few DP cells could be observed at the GBs of the NA alloy (Fig. 13b). The DP cells distributed discontinuous at the
Y. Tang et al. / Journal of Alloys and Compounds 663 (2016) 784e795 Table 6 Values of reversible plastic zone (RPZ) sizes and their ratio to the grain size. Sample
DK (MPa$m1/2)
rp (mm)
rp/d
da/dN (104 mm/cycle)
IA (d ¼ 10.9 mm)
15 17 21 25 15 17 21 25 15 17 21 25
5.5 6.9 10.7 14.9 5.5 6.8 10.4 14.5 7.6 9.6 14.8 20.2
0.51 0.63 0.98 1.37 0.43 0.53 0.81 1.14 0.80 1.01 1.56 2.13
0.40 0.79 3.03 11.95 0.74 1.49 8.02 61.21 0.95 1.32 3.33 9.47
NA (d ¼ 12.8 mm)
OA (d ¼ 9.5 mm)
GBs and they grew from only one side of the GBs into the parent phase. When it came to the OA condition (Fig. 13c), the GBs were almost replaced by the DP cells. The DP cells distributed continuous at the both sides of the GBs and there were clear interfaces between the DP cells and the parent phase. Fig. 14 illustrates the crack growth mechanisms in the alloys under different aging conditions, when the RPZ size of each sample is 1e2 times of the corresponding grain size. Meanwhile, the fatigue cracks were in the later stage of stable expanding region and the rapid expanding region according to the da/dN-DK curves (Fig. 6). When the alloy is subjected to the IA treatment (Fig. 14a), the crack appears to propagate along the GBs. For the NA alloy (Fig. 14b), the crack propagates preferentially along the GBs which have DP cells on one side of them. As a consequence, these grains are separated from the matrix, leading to fracture quickly. Due to that few DP cells exist at the GBs in the IA alloy, the compatibility of the plastic deformation of the GBs in the IA alloy is much higher than it in the NA alloy. Therefore, the FCG rate of the IA alloy was much lower as compared to the NA alloy. When under the OA condition (Fig. 14c), the crack propagates along the interfaces
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between the DP cells and parent phase. Since the interfaces between the DP cells and parent phase are tortuous, the propagation of the crack demands more energy [5]. This is the reason why the FCG rate of the OA alloy was the lowest at the relatively high stress intensity factor range (DK > 21 MPa m1/2). The surface morphology near the fracture (the later stage of stable expanding region and the rapid expanding region) was observed on samples after FCG tests. As shown in Fig. 15, the characteristics of the microcracks in each sample confirm the rationality of the crack growth mechanisms illustrated above. The microcrack propagated along the GBs with a relatively straight path in the IA alloy (Fig. 15a). For the NA alloy (Fig. 15b), the microcrack propagated preferentially along the GBs which have DP cells on one side of them. As a result, the grain was almost separated from the matrix. However, the microcrack propagated along the interfaces between the DP cells and parent phase in the OA alloy (Fig. 15c). Compared with the microcrack in the IA alloy, the microcrack in the OA alloy represented a significantly more tortuous propagation path. As shown in the curves of crack length vs. number of cycles (Fig. 8), the alloys subjected to different aging treatments exhibited different fatigue lives. Table 7 presents the relationship between the ratio of the RPZ size to the grain size (rp/d) and the residual fatigue life. For the IA and NA alloy, the number of cycles (N) accounted for over 90% of the fatigue cycles to failure (Nf) when the RPZ size was equal to the grain size. This means that the crack propagating inside the grain and adjacent to the GBs takes up most of the fatigue life. Then the crack propagated along the GBs when the RPZ size was larger than the grain size, leading to the rapid fracture of the sample. Since the FCG rate of the IA alloy is much lower than those of the other two alloys when the crack propagates inside the grain, the IA alloy has the longest fatigue life. However, for the OA alloy, N made up only 60% of Nf when the RPZ size was equal to the grain size. The FCG rate increased with the RPZ size. Until the RPZ size was about twice as large as the grain size, N
Fig. 13. TEM morphology of the GBs after (a) IA treatment, (b) NA treatment and (c) OA treatment.
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Fig. 14. Schematic illustration of the crack growth mechanism in the alloy subjected to the (a) IA treatment, (b) NA treatment and (c) OA treatment. The RPZ size of each sample is 1e2 times of the corresponding grain size.
reached more than 90% of Nf. According to the effect of RPZ size on the FCG mechanism, the propagation of the fatigue crack in the OA alloy can be divided into two parts, the propagation inside the grain and the propagation along the interfaces between the DP cells and parent phase. These interfaces hinder the propagation of the fatigue cracks effectively when the cracks propagate from the area inside the grains to the interfaces, which contribute to the decrease of FCG rate. 5. Conclusions The effects of microstructure on the fatigue crack growth behavior of CueBeeCoeNi alloy after IA, NA and OA treatment are investigated in this paper. The conclusions are made as follows: (1). After IA treatment, the microstructure of the CueBeeCoeNi alloy was mainly consisted of fine g00 precipitates with tiny amounts of g0 precipitates. The main precipitates of the alloy treated by NA and OA were g0 precipitates and g precipitates,
respectively. The average long axis length of the g0 precipitates was 25.3 nm while it of g precipitates was 66.9 nm, and both were much larger than the average long axis length of g00 precipitates (5.3 nm). The IA alloy had few DP cells at the GBs, while the NA alloy had a quantity of DP cells which distributed discontinuous at the GBs. The GBs of the OA alloy were almost replaced by the DP cells which distributed continuous at the both sides of the GBs. (2). The FCG rate was closely related to the crack growth mechanism in each alloy, which could be successfully explained by the model based on the RPZ size and microstructural factors. Because that g00 precipitates in the IA alloy were completely coherent with the parent phase and they could be sheared by the dislocations, the IA alloy had the lowest FCG rate at the relatively low stress intensity factor range (DK < 21 MPa m1/ 2 ). When the stress intensity factor range became higher (DK > 21 MPa m1/2), the tortuous interfaces between the DP cells and parent phase in the OA alloy hindered the
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Fig. 15. SEM observations of the regions below the fracture surfaces of the FCG test samples subjected to the (a) IA treatment, (b) NA treatment and (c) OA treatment. The black arrows indicate the microcracks.
Table 7 Relationship between the ratio of the reversible plastic zone (RPZ) size to the grain size and the residual fatigue life. Aging condition
Fatigue cycles to failure Nf (cycle)
rp/d
da/dN (104 mm/cycle)
Number of cycles N (cycle)
N/Nf
IA NA OA
66288 39409 40052
0.98 0.99 1.01 1.33 2.13
3.03 27.93 1.32 2.45 9.47
62354 39125 24086 32565 38622
0.94 0.99 0.60 0.81 0.96
propagation of the fatigue cracks, correspondingly resulted in the lowest FCG rate. (3). For the IA and NA alloy, the fatigue crack propagating inside the grain and adjacent to the GBs accounted for over 90% of the fatigue life. Owing to the lowest FCG rate when the crack propagated inside the grain, the IA alloy had the longest fatigue life. The propagation of the fatigue crack in the OA alloy could be divided into the propagation inside the grain (made up 60% of the fatigue life) and the propagation along the interfaces between the DP cells and parent phase (took up the rest 40% of the fatigue life). Acknowledgments The authors gratefully acknowledge the financial support from Project U1460101 supported by National Natural Science Foundation of China. References [1] F. Berto, P. Lazzarin, P. Gallo, J. Strain Anal. Eng. Des. 49 (2014) 244e256. [2] P. Behjati, H. Vahid Dastjerdi, R. Mahdavi, J. Alloys Compd. 505 (2010)
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