Slow strain rate tensile tests on notched specimens of as-cast pure Cu and Cu–Fe–Co alloys

Journal Pre-proof Slow strain rate tensile tests on notched specimens of as-cast pure Cu and Cu–Fe– Co alloys Kaixuan Chen, Jiawei Zhang, Yajun Chen, Xiaohua Chen, Zidong Wang, Rolf Sandström PII:

S0925-8388(20)30010-4

DOI:

https://doi.org/10.1016/j.jallcom.2020.153647

Reference:

JALCOM 153647

To appear in:

Journal of Alloys and Compounds

Received Date: 10 September 2019 Revised Date:

30 December 2019

Accepted Date: 2 January 2020

Please cite this article as: K. Chen, J. Zhang, Y. Chen, X. Chen, Z. Wang, R. Sandström, Slow strain rate tensile tests on notched specimens of as-cast pure Cu and Cu–Fe–Co alloys, Journal of Alloys and Compounds (2020), doi: https://doi.org/10.1016/j.jallcom.2020.153647. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2020 Published by Elsevier B.V.

Kaixuan Chen: Conceptualization, Methodology, Formal analysis, Investigation, Funding

acquisition,

Writing-Original

draft

preparation,

Project

administration. Jiawei Zhang: Investigation, Writing-Original Draft. Yajun Chen: Resources;

Investigation. Xiaohua

Chen: Writing-Review

&

Editing. Zidong

Wang: Supervision, Validation. Rolf Sandström: Methodology, Software, Resources

Slow strain rate tensile (SSRT) performance of Cu-Fe-Co alloy reinforced by refined grains embedded with iron-rich nanoparticles (NPFG structure) NPFG structure in Cu-Fe-Co alloy

400µm

Fine grain

Nanoparticle 500nm

Fracture behavior in NPFG copper

20 µm

Engineering stress/MPa

180 160 140

SSRT performance of NPFG copper pure Cu Cu-1.0Fe-0.5Co Cu-2.0Fe-0.5Co Cu-3.0Fe-0.5Co

120 100 80 60 40 20 0 0.00

0.02

0.04

0.06

0.08

Engineering strain

0.10

Slow strain rate tensile tests on notched specimens of as-cast pure Cu and Cu-Fe-Co alloys Kaixuan Chena,b,*, Jiawei Zhanga, Yajun Chenc, Xiaohua Chend,*, Zidong Wanga,*, Rolf Sandströmb a

School of Material Science and Engineering, University of Science and Technology Beijing, Beijing 100083, P.R. China

b

Department of Materials Science and Engineering, KTH Royal Institute of Technology, SE-100 44 Stockholm, Sweden

c

Department of Costomer Development, Minmetals Development Co., LTD., Beijing 100044, P. R. China

d

State Key Laboratory for Advanced Metals and Materials, University of Science and Technology Beijing, Beijing 100083, P.R. China

Abstract Microstructure evolution in the as-cast pure Cu, Cu-(1.0, 2.0, 3.0)Fe-0.5Co (wt. %) alloys were characterized in the former work. The aim of the present study is to investigate the slow strain rate tensile (SSRT) performance and fracture behavior of the Cu-Fe-Co alloys reinforced with fined grains (FG) and iron-rich nanoparticles (NP), referred as NPFG structure. The plastic deformation and fracture characteristics were examined by multiaxial SSRT tests at 75 and 125 °C on notched specimens. The addition of Fe and Co enhanced the ultimate tensile strength and yield strength almost by double to triple times the properties compare to pure Cu, along with an acceptable reduction in ductility, both at 75 and 125 °C. The SSRT properties of the copper samples varied as a function of temperature and alloying content. The analysis of fracture surface indicates the effect of iron-rich nanoparticles and grain boundaries on the deformation and fracture processes. The Kocks-Mecking model was applied to *

Corresponding author. E-mail address: [email protected]; [email protected] (Kaixuan Chen) E-mail address: [email protected] (Zidong Wang) E-mail address: [email protected] (Xiaohua Chen)

2

describe the SSRT experimental results with fitting parameters. The model predicted the dynamic recovery ability of the copper samples with different Fe, Co content and temperature. The evolution mechanism of SSRT properties upon alloying content and temperature was discussed in terms of the microstructure characterization, fractographic observation, deformation modeling, strengthening models as well as the analysis

of strain-hardening curves.

The

results

indicate through

further

microstructural engineering the NPFG Cu-Fe-Co alloy is promising in utilization as the canister for the storage of the nuclear waste. Keywords: Copper; Slow strain rate tensile test; Microstructure; Fracture behavior; Strengthening mechanisms 1. Introduction In Sweden, the nuclear waste is in general to be placed in a package consisting of a cast iron insert and an outer 50 mm thick copper canister, 500 m below ground. Copper is selected because it is immune against corrosion under reducing conditions in the bedrock [1,2]. Creep in the copper canisters is expected to take place when the surrounding bentonite clay absorbs water, which gives rise to a swelling pressure. Specifically, the canisters will be subjected to temperatures up to 100 °C and external stresses up to 15 MPa for several decades [3,4]. Under the swelling pressure, the loading is essentially strain controlled but stress control will be activated after full pressure has been reached. To describe the deformation behavior of the canisters, slow strain rate tensile (SSRT) and creep tests were carried out on copper specimens under uniaxial [5-8] and multiaxial stress state [9,10]. The SSRT and creep tests were

3

applied to simulate the gradual loading and full loading in the swelling stage, respectively. Notably, the canisters are essentially suffered complex stress conditions, and thus it is natural to perform multiaxial stress tests. The basic models have been successfully developed for uniaxial and multiaxial tests on pure copper, which can simulate the stress and strain rate controlled plastic deformation without the use of any fitting parameter [7-9,11]. But the models have not been applied to describe SSRT or creep deformation of precipitation-strengthened copper. Initially high purity oxygen-free high conductivity copper (Cu-OF) was planned to be used for the canisters, but Cu-OF could have extra low creep ductility with elongation values less than 1% [12]. Then copper with additions of about 50 ppm phosphorus (Cu-OFP) has been creep tested extensively between 75 and 300

,

which has always exhibited an elongation larger than 14% [10]. Cu-OFP is now the main candidate material for the canister, owing to its good creep strength and ductility [13]. Meanwhile, creep may also occur if the canister is sheared during an earthquake [5,10], thus it is essential to further improve the creep properties of copper canisters, inclusive

of

enhancing

creep resistance

and

ductility.

However,

further

strength-ductility enhancement in Cu-OF or Cu-OFP seems not promising. Recently, minor iron and cobalt reinforced copper and copper alloys (e.g. Cu–10Sn– 2Zn and Cu–3Sn–8Zn–6Pb (wt. %)), with large number of iron-rich nanoparticles embedded in refined micrometer-sized grain, achieve high strength and dramatic ductility over that of unreinforced copper samples at room temperature (RT) [14-21]. The nanoparticle (NP) - fined grain (FG) coupled microstructure in iron and cobalt

4

reinforced copper samples is deemed as NPFG structure. Iron-rich nanoparticles pre-precipitated in the melt serve as heterogeneous nucleation cores for copper grains during solidification [17] and restrict grain growth under the effect of Zener pinning after solidification [22]. Besides, iron-rich nanoparticles can be formed inside grains during casting, and consequently provide interior nano-reinforcements [23]. With such a NPFG structure, for instance, Cu-10Sn-2Zn-1.5Fe (wt. %) alloy had improved tensile strength of 483 MPa, and dramatic uniform elongation of 29.3% at RT, respectively, in contrast to conventional cast Cu-10Sn-2Zn tin bronze alloy [15]. Iron-rich nanoparticles were proposed to present substantial barriers for dislocation motion, which contributes to strength elevation. Meanwhile, the nanoparticles provide the easy motion of dislocations, which permits the simultaneous generation of significant plastic deformation [20,21]. The microstructural features and room-temperature tensile properties were investigated by examining the as-cast pure Cu and Cu-(1.0~3.0)Fe-0.5Co alloys [19-21]. Alloying of Fe, Co has a substantial effect on the internal microstructure in copper and allows the formation of the NPFG structure in the Cu-Fe-Co alloys. The NPFG structure improves both the strength and ductility at RT of the as-cast copper [19-21]. In addition, for the precipitate reinforced microstructure to maintain its mechanical properties at elevated temperatures, the precipitate requires chemical, crystallographic and microstructural stability at higher temperatures. This necessitates that the chosen precipitate has a high melting point, low solubility in the matrix, high elastic modulus, and a low diffusion rate of the reinforcing precipitate atoms in the

5

soft matrix [24]. Iron-rich nanoparticles in copper alloys can be well conformed with above requirements [17,19]. As a result, copper with additions of minor iron and cobalt, i.e. Cu-Fe-Co alloy, is anticipated to meet the demands for safe operation of the canisters. In order to describe the role of the Cu-Fe-Co alloy as the canister, both SSRT and creep tests should be carried out. The purpose of the present work is to perform SSRT tests for the pure Cu and Cu-(1.0, 2.0, 3.0)Fe-0.5Co (wt. %) alloys under multiaxial states at 75 and 125 °C. The deformation behavior of the copper samples, as influenced by the Fe content and microstructural evolution during casting, is discussed based on detailed micrographic and fractographic observations, and coupled with physically based models [7-9,11] for stress strain flow curves, the strain-hardening curves and strengthening models. 2. Experimental procedures The 50mm×65mm×195mm cuboid samples of pure Cu and Cu-(1.0, 2.0, 3.0)Fe-0.5Co (wt. %) alloys were fabricated by medium-frequency induction melting of high-purity elemental metals (99.99 Cu, 99.50 Fe, and 99.95 Co wt. %) and gravity casting in a vacuum chamber. Detailed information on the materials fabrication, microstructure characterization and room-temperature tensile tests can be found in our previous work [19-21], which will not be repeated here. The chemical compositions of the as-cast alloys were measured to be Cu-1.08Fe-0.49Co, Cu-2.12Fe-0.44Co, Cu-3.03Fe-0.53Co (wt. %), by inductively coupled plasma-atomic emission spectroscopy (ICP-AES).

6

In order to simulate the multiaxial stress state, double notched pure Cu and Cu-Fe-Co cylinder bars were used in the present tests (see Fig. 1). The specimens were 7.98 mm in diameter, 47 mm in gauge length, 1.41 mm in notch root radius and 2.82 mm in notch throat radius. The notch acuity is of 2, which is defined as the notch throat radius divided by the notch root radius. Note that the SSRT specimens were cut from fixed positions and orientations of the as-cast cuboid samples. Multiaxial SSRT tests were performed at 75 and 125 °C with a strain rate of 1.0×10-6 s-1 by using an electromechanical tensile/compression testing system, designed and delivered by Swetest Instrument AB. Test temperatures were chosen in line with the service condition of the canister. The maximum temperature is expected to be below 100 °C. The test temperature of 125 °C was chosen for extrapolation purpose [3]. Tests were performed according to standard procedures (SS-EN 10, 002-1). All the specimens were tested to rupture lasted for 18-33 hours. Yield strength was evaluated as the 0.2% off set in strain. All the fracture surfaces were observed using LEO1450 scanning electrical microscope (SEM) in order to identify the fracture behavior. The reduction in area A was evaluated from fracture SEM images coupled with the analysis by Photoshop CS5 and Image-Pro Plus [9]. The procedure has been described in Section 1 of Supplementary data.

Fig. 1. Geometry of the specimen, from top to bottom notch acuity 2

3. Results

7

3.1. Microstructure The features of the matrix grain and iron-rich nanoparticles in the as-cast pure Cu and Cu-Fe-Co alloys were characterized by optical microscopy (OM) and transmission electron microscopy (TEM), respectively [19]. Due to the heterogeneous nucleation effect of iron-rich nanoparticles, the addition of Fe and Co provoked the grain refinement and the grain size reduced with the increase of Fe+Co content (Fig. 2a-d and Table 1). Meantime, the number density, mean radius, volume fraction and particle–matrix interface area of the iron-rich nanoparticle varied with the alloying content (Fig. 2e-g and Table 1). In the Cu-1.0Fe-0.5Co alloy, the spot-like and spherical nanoparticles were dispersed in the matrix copper (Fig. 2e). Whilst in the Cu-(2.0, 3.0)Fe-0.5Co alloys, the larger-sized rhombic nanoparticles appeared accompanied with the spot-like and spherical ones (Fig. 2f, g). The spot-like nanoparticles (<20 nm) were more apparent in enlarged TEM image (see Fig. S2 in Supplementary data). Most of iron-rich nanoparticles were uniformly distributed throughout the copper matrix, but some of the nanoparticles including coarse ones were precipitated at grain boundaries (GBs) marked with black and white arrows in Figs. 2f and 3, respectively. (a)

400 µm

8

(e)

(b)

Spherical

Spot-like

400 µm (c)

500 nm (f) Spherical

Rhombic

400 µm (d)

500 nm (g)

Rhombic Spherical

400 µm

500 nm

Fig. 2. Evolution of (a-d) grain and (e-g) iron-rich nanoparticle in (a) pure Cu and (b, e) Cu-1.0Fe-0.5Co, (c, f) Cu-2.0Fe-0.5Co, (d, g) Cu-3.0Fe-0.5Co alloys.

Fig. 3. SEM image showing coarse rhombic iron-rich nanoparticles at the GB in the Cu-3.0Fe-0.5Co alloy, which are marked by white arrows (InLens mode).

9

Table 1. Grain size (d) of the as-cast samples, and statistic results for the number density (Nv), mean radius (rmean), volume fraction (f ) and particle–matrix interface area per cubic meter (S) of spherical and rhombic nanoparticles in the Cu-Fe-Co alloys [19]. Samples/wt. %

d/µm

Nv/1020 m-3

rmean/nm

S/106 m2

f/vol. %

Pure Cu

603.4±114.8

-

-

-

-

Cu-1.08Fe-0.49Co

588.2±24.6

1.4

21.8

0.84

0.6

Cu-2.12Fe-0.44Co

49.9±6.4

0.5

44.3

1.23

1.8

Cu-3.03Fe-0.53Co

26.2±2.3

0.3

59.1

1.18

2.3

3.2. SSRT properties The multiaxial SSRT test results are shown in Fig. 4a, b and the values of SSRT properties are summarized in Fig. 4c, d and Table S1 (Supplementary data). The ultimate tensile stress σb of Cu-Fe-Co alloys under multiaxial stress state was much higher than that of pure Cu both at 75 and 125 °C. The σb increased with increasing Fe+Co content at a given temperature. Besides, the σb of pure Cu and Cu-Fe-Co alloys at 75 °C was higher than that at 125 °C, similar as the trend observed by Sui et al. on Cu-OFP [9]. Meantime, the yield strength σs performed identical trends with σb as a function of Fe+Co composition and temperature. With regard to the uniform elongation δu for the Cu-Fe-Co alloys, it enhanced with the increase of Fe+Co content at 75 °C, which is consistent with the trend during uniaxial tensile test at RT [19,21]. At 125 °C, however, δu reduced with the increasing Fe+Co content. In addition, δu of Cu-Fe-Co alloys was lower than that of pure Cu both at 75 and 125 °C. δu of all the alloy samples performed higher value at 75 °C than that at 125 °C. For pure Cu, δu at 75 °C was less than that at 125 °C, which is inconsistent with the normal result [9]. This anomy may be correlated to the shrinkage

10

pores (marked by black arrows in Fig. S1a in Supplementary data) formed during casting process. The reduction in area A presented a similar trend as δu. In general, the as-cast Cu-(1.0, 2.0, 3.0)Fe-0.5Co alloys exhibited better combined SSRT properties in comparison with the properties of the as-cast pure Cu, as the comparison of SSRT data presented in Table. S1. pure Cu Cu-1.0Fe-0.5Co Cu-2.0Fe-0.5Co Cu-3.0Fe-0.5Co

140 120 100 80 60 40 20 0 0.00

0.02

0.04

0.06

0.08

160

pure Cu Cu-1.0Fe-0.5Co Cu-2.0Fe-0.5Co Cu-3.0Fe-0.5Co

140 120 100 80 60 40 20

0.10

0 0.00

0.02

Engineering strain

Strength/MPa

200 180 160 140 120 100 80 60 40 20 0.0

100

75°C yield strength/MPa 75°C tensile strength/MPa 125°C yield strength/MPa 125°C tensile strength/MPa

0.5

1.0

1.5

2.0

2.5

(d)90 Reduction in area/%

240

(c) 220

0.04

0.06

0.08

0.10

0.12

Engineering strain

3.0

Fe+Co/wt.%

3.5

80 70 60 50 40 30 20 10 0

75 °C Reduction in area A 125 °C Reduction in area A 75 °C Uniform elongation δu 125 °C Uniform elongation δu

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

20 18 16 14 12 10 8 6 4 2 0

Uniform elongation/%

160

(b) Engineering stress/MPa

Engineering stress/MPa

(a) 180

Fe+Co/wt.%

Fig. 4. Stress strain curves for cylinder bars of the as-cast pure Cu and Cu-Fe-Co alloys tested at (a) 75 and (b) 125 °C with a strain rate of 1×10-6 s-1. □: uniform elongations, ○: 0.2% offset yield strengths; (c) Yield strength σs, tensile strength σb and (d) uniform elongation δu, reduction in area A as a function of temperature and actual Fe+Co content.

3.2. Fracture surface observations Metallographic studies were carried out on the fracture surfaces of the specimens to examine the failure mode. Typical ductile failure with cup and cone type appearance

11

was obtained (Fig. S1 in Supplementary data). Outer shear lip and center dimple parts were present in the left-column images of Fig. S1. Within dimple part, dimpled rupture mode were observed (Fig. 5). The fracture mode was found to be dependent of Fe+Co content and test temperature, but all the failed specimens showed similar ductile failure appearance (Fig. S1 and Fig. 5). In general, the dimples of pure Cu were much bigger in size and deeper in depth compared with those of the Cu-Fe-Co alloys (Fig. 5). Meantime, for the alloy specimens, typical bimodal distribution of dimples was observed, in contrast to the unimodal distribution of relatively large dimples for the pure copper specimens (Fig. 5). The present SEM fractographs demonstrated that relatively fine dimples (mostly <1 µm) are associated with the iron-rich nanoparticles (see insets in Fig. 6b-d). The nanoparticles were embedded in copper matrix and partially protruded from dimple surface. This means that crack preferred the nanoparticle/matrix interface as a preferential extension path, which is identical with the crack propagation process at room temperature [20]. The size of dimples in the Cu-Fe-Co alloys increased with the Fe+Co content (Fig. 6b-d), which is attributed to the coarsening of iron-rich nanoparticles (see Fig. 2e-g and Table 1). The finer dimples always result in the higher ductility [25]. The high-angle GBs are reported to decrease the crack propagation rate [26], thus it is considered to improve the tensile elongation with more Fe+Co content due to the finer grain structure (Fig. 2a-d and Table 1). As a whole, on account of the combinatorial effect of iron-rich nanoparticles and GBs, the tensile elongation varied with increasing Fe+Co content and at different temperatures (Fig. 4a, b) [26,27].

12

(a)

75 °C

40 µm

40 µm

(b)

75 °C

40 µm

(c)

40 µm

125 °C

40 µm

125 °C

75 °C

40 µm

(d)

125 °C

40 µm

125 °C

75 °C

40 µm

Fig. 5. The SEM fractographs of tensile-fractured as-cast copper specimens within dimple part: (a) pure Cu and (b) Cu-1.0Fe-0.5Co, (c) Cu-2.0Fe-0.5Co, (d) Cu-3.0Fe-0.5Co alloys.

13

(a)

125 °C

75 °C

4 µm

4 µm

75 °C

(b)

125 °C

1 µm

1 µm

4 µm

4 µm

75 °C

(c)

125 °C

1 µm

1 µm

4 µm

4 µm

75 °C

(d)

125 °C

1 µm

4 µm

1 µm

4 µm

Fig. 6. The SEM fractographs documented on the unimodal and bimodal distributions of dimples in the tensile-fractured (a) pure Cu and (b) Cu-1.0Fe-0.5Co, (c) Cu-2.0Fe-0.5Co, (d) Cu-3.0Fe-0.5Co alloys. The insets in (b-d) showing the small and shallow dimpled area in the alloy samples, with debonded nanoparticles embedded in dimples as marked by white arrows.

14

Crack propagation process was further examined at the cross sections near the ruptured notches, see Fig. 7a-c. Intergranular and transgranular fracture modes were both observed in Fig. 7b. The transgranular and intergranular facets both were covered with dimple voids (Fig. 7b), suggesting that iron-rich nanoparticles precipitated homogeneously throughout the alloy samples. The size variation (from micro to nano scale) of dimple voids in different area of Fig. 7b arises from the polished depth during metallographic sample preparation. However, within a small region, e.g. Grain 1 area in Fig. 7b, the larger dimple voids observed intermittently inside the grain or at GBs were more possibly due to the presence of coarse iron-rich nanoparticles. Coarse precipitates are preferential sites for crack initiation ascribed to local concentration of internal stresses, especially when these precipitates segregate at GBs, which can considerably degrade ductility and fatigue strength [25,28-30]. The bright-field TEM (Fig. 2f) and SEM (Fig. 3) micrographs present the microstructure around GB areas; large iron-rich nanoparticles precipitated along the GBs can be observed. Micro-void nucleation occurred first at the largest nanoparticles at the GBs, in particular at triangular GBs, as shown by black arrows in Fig. 7b, c. After the initiation, the cracks first tended to propagate along the GB (intergranular mode, indicated by yellow curves in Fig. 7b, c) through coalescence of nano- to micro- voids [31] induced by debonded interface between iron-rich nanoparticle and GB, and then grew with shear mode along the slip orientation of adjacent grains (transgranular mode, indicated by red curves in Fig. 7b). To achieve optimized performance, extra attention must be paid to refine the iron-rich nanoparticles and avoid the precipitation

15

of the coarse nanoparticles at GBs. Note that as a growing crack encountered with GB, it either coalesced with voids along GB or grew across the GB into the adjacent grain (see Fig. S3 in Supplementary data). Cracks mostly grew along the slip planes of grains, as the dominant transgranular crack propagation path shown in Fig. 7b. The crack propagation along crystallographic slip planes is commonly observed in Cu– 6Ni–1.5Si [32], 6061-T6 aluminum [33,34] and Cu–6Ni–2Mn–2Sn–2Al [35] alloys. As a summary, the SEM fractographs (Fig. 6b-d) and cross-section metallography of fracture surface (Fig. 7b) demonstrate that the coarse nanoparticles and the increased tendency for intergranular fracture mode reduced the tensile elongation for the alloy specimens. Notably, this deteriorating effect enhances with the increase of Fe+Co content caused by the coarsening of the nanoparticles. (a)

200 µm

(b)

(c)

20 µm

20 µm

Fig. 7. (a) The cross-section of the tensile region around 1 mm beneath the fracture surface of Cu-3.0Fe-0.5Co alloys tested at 125 °C with a strain rate of 1×10-6 s-1. The etched specimen

16

was polished off a layer of around 1 mm from the top of fracture surface; (b) The enlargement of white dashed rectangle area I in (a) showing the crack initiation and propagation at GBs (outlined by yellow dashed curves) and inside grains (outlined by red dashed curves); (c) The enlargement of white dashed rectangle area II in (a). The area II, which is a relatively far away from the fracture surface, was documented to uncover the remained phenomena of crack initiation from GBs (particularly triangular GBs) and early-stage propagation along GBs as indicated by black arrows and yellow dashed curves, respectively.

The cross sections near the ruptured notches of the pure Cu were also detected. Crack propagation across coarse grains (450~650 µm) dominated the fracture process with no observable intergranular cracks (see Fig. 8a, b). Noteworthy, cavitation was not observed along the GBs (Fig. 8c). Intergranular creep cavitation has been found by Wu [10,36] and Sui [9] on Cu-OF and Cu-OFP samples in creep tests. Comparing the present SSRT test with the previous creep tests, the duration is shorter. The longest SSRT test in the present study lasted for 33 hours (Table S1) while the creep tests were conducted for up to 10,000 h [10,36]. With shorter duration, there is less possibility to form creep cavities [9], which is in agreement with the cavity-free GBs in Fig. 8. While in the Cu-Fe-Co alloys, the debonding between GB and iron-rich nanoparticles facilitates the cavitation, producing undesirable voids (or cavities) in Figs. 7 and S3.

17

(a)

400 µm

Transgranular cracking

Fig. 8. (a) The cross-section of the tensile region around 1 mm beneath the fracture surface of pure Cu tested at 125 °C with a strain rate of 1×10-6 s-1. The etched specimen was polished off a layer of around 1 mm from the top of fracture surface; (b) The enlarged image showing the crack propagation across the coarse grain; (c) The enlargement of black dashed rectangle zone in (b) showing no cavity along GB. 4. Discussions

4.1. Deformation modeling for as-cast copper samples during multiaxial SSRT tests The plastic deformation in room-temperature uniaxial tensile test and multiaxial SSRT test represents the same physical phenomenon, i.e. work/strain hardening and recovery. Kocks-Mecking model [6,7,9] is used to describe plastic deformation by taking these two factors into account, see Eq. (1). ωρ

2τ

ρ /ε

(1)

ρ is the dislocation density (m-2), ε the strain, M the Taylor factor, b the Burger’s

18

vector and L the “spurt” distance (m) which the dislocation moves when it is released during deformation. ω is a dimensionless parameter representing the rate constant for dynamic recovery, τL the dislocation line tension (N), m the dislocation mobility (m2/Ns), and ε the strain rate (s-1). The first term on the right-hand side of Eq. (1) describes the work hardening that the dislocation density multiplies during plastic deformation and the strength is therefore increased. The second and last terms represent the static (time dependent) and dynamic (strain dependent) recovery, respectively. During recovery process, dislocations with opposite signs annihilate each other and thereby the dislocation density is reduced. Actually, the last term is usually negligible in the present case. Kocks-Mecking model for stress-strain curves can be obtained by integrating Eq. (1) [6,7,9]: σ

σ + (1

e

/

)

(2)

σ is the strength which has an exponential dependence on the strain (ε). B=σmax-σs, wherein σmax and σs are the maximum and yield strength in the stress-strain flow curve, respectively. ω describes the dynamic recovery ability as a function of ε. Kocks-Mecking model has been reported to represent the stress and strain rate controlled plastic deformation of Cu-Fe-Co alloys (uniaxial tensile state at RT) [21], Cu-OF (uniaxial and multiaxial SSRT state) [9,37] and Cu-OFP (uniaxial and multiaxial SSRT state) [7,9]. But the application of the model in multiaxial SSRT test for precipitation-strengthened copper is lacking. Here, Kocks-Mecking model was applied to compare with the SSRT tests at 75 and 125 °C of the present as-cast copper samples under multiaxial stress state. The model

19

for flow curves, Eq. (2), was fitted to the SSRT testing data using σs, B and ω as adjustable parameters. The comparisons between the modeling and experimental stress-strain curves (engineering case) of the copper specimens tested at different temperatures are shown in Fig. 9. The model represented the multiaxial SSRT stress-strain curves quite well (Fig. 9). Table 2 illustrates the adjustable parameters B and ω of the copper samples. The Cu-Fe-Co alloys exhibited close fitting values of ω approximately double and triple those of the pure Cu at 75 and 125 °C, respectively. This suggests the enhanced dynamic recovery in the alloys. The higher ω values derive from the iron-rich nanoparticles which force dislocation together regionally and annihilation each other, and hence improve the dynamic recovery rate during deformation of the alloys. At the same temperature, all the alloys presented minor differences among their ω values. For the same copper sample, the pure copper presented a lower ω value at higher temperature, but quite the reverse for all the Cu-Fe-Co alloys. The former data of pure Cu implies the matrix copper including GBs yields a lower dynamic recovery rate at higher temperature. The latter suggests iron-rich nanoparticles, in comparison with the matrix copper, contribute more strongly to the dynamic recovery rate of the alloys at higher temperature, correspondingly resulting in a higher ω value in total. It is noteworthy the enhanced dynamic recovery, viz. higher ω, contributes to the more persistent plastic deformation in the copper samples.

20

160

Exp. Model

140 120 100 80 60 40

pure Cu, 75 °C

20 0 0.00

0.02

0.04

0.06

0.08

0.10

(b) 160 Engineering stress (MPa)

Engineering stress (MPa)

(a)

0.12

Exp. Model

140 120 100 80 60 40

pure Cu, 125 °C

20 0 0.00

0.02

160

Exp. Model

140 120 100 80 60 40 20 0 0.00

Cu-1.0Fe-0.5Co, 75 °C 0.02

0.04

0.06

0.08

0.10

0.12

Exp. Model

140 120 100 80 60

0 0.00

Cu-2.0Fe-0.5Co, 75 °C 0.02

0.04

0.06

0.08

0.10

120 100 80 60 40 20

Cu-1.0Fe-0.5Co, 125 °C

0 0.00

0.02

100 80 60

Cu-3.0Fe-0.5Co, 75 °C 0.04

0.06

0.08

0.10

Engineering strain

0.12

(h) Engineering stress (MPa)

Engineering stress (MPa)

120

0.02

0.06

0.08

0.10

(f) 160

0.12

Exp. Model

140

0 0.00

0.04

0.12

Exp. Model

140 120 100 80 60 40 20 0 0.00

Cu-2.0Fe-0.5Co, 125 °C 0.02

0.04

0.06

0.08

0.10

0.12

Engineering strain

(g) 160

20

0.12

Exp. Model

Engineering strain

40

0.10

Engineering strain

Engineering stress (MPa)

Engineering stress (MPa)

(e) 160

20

0.08

140

Engineering strain

40

0.06

(d) 160 Engineering stress (MPa)

Engineering stress (MPa)

(c)

0.04

Engineering strain

Engineering strain

160

Exp. Model

140 120 100 80 60 40 20 0 0.00

Cu-3.0Fe-0.5Co, 125 °C 0.02

0.04

0.06

0.08

0.10

0.12

Engineering strain

Fig. 9. The comparisons of the engineering stress-strain curves between the modeling and experiment at (a, c, e, g) 75 and (b, d, f, h) 125 °C of (a, b) Pure Cu and (c, d)

21

Cu-1.0Fe-0.5Co, (e, f) Cu-2.0Fe-0.5Co, (g, h) Cu-3.0Fe-0.5Co alloys. Here engineering stress σ(Eng.) and strain ε(Eng.) are converted from the true stress σ(True) and strain ε(True) by using Standard textbook equations, i.e. σs(True)=σs(Eng.)(1+ε(Eng.)) and ε(True)=ln(1+ε(Eng.)). From the curves the strength and uniform elongation values can be found directly. The modeling curves do not consider the necking process of the SSRT testing curves, so here the comparison to the curves after necking is meaningless.

Table 2. The adjustable parameters B, ω and σs in Kocks-Mecking modeling for the SSRT testing of the copper samples. Samples pure Cu

Temperature/°C

ω

σs(True)+B/MPa

B/MPa

σs(True)/MPa

σs(Eng.)/MPa

75

19.98

92.26

60.59

31.67

31.61

125

13.21

94.50

72.8

21.70

21.66

Cu-1.0Fe-0.5Co

75

40.43

163.23

85.83

77.40

77.25

alloy

125

47.83

134.88

68.86

66.01

65.88

Cu-2.0Fe-0.5Co

75

40.12

184.47

109.98

74.49

74.34

alloy

125

46.38

158.87

87.9

70.975

70.83

Cu-3.0Fe-0.5Co

75

44.05

184.80

108.04

76.76

76.61

alloy

125

46.65

166.30

94.18

72.12

71.98

4.2. Multiple effects on the evolution of SSRT strength and ductility The high strength of the Cu-Fe-Co alloys is due to grain boundary (GB) strengthening and the interaction of moving dislocation and dispersed iron-rich nanoparticles when tested at low temperatures (<200 °C). Diffusion takes place easily through the GBs and the nanoparticle/matrix interfaces for the irregular arrangement of atoms on them, thus the GB and precipitation strengthening both decrease dramatically with the increasing temperature [38]. The reduced strengthening of GB and the nanoparticles causes the lower yield strength σs of the pure Cu and Cu-Fe-Co

22

alloys at 125 °C (Fig. 4). Grain-refined strengthening ∆σgrain can be calculated from Hall-Petch relation (Eq. (S1), see Supplementary Data) [39,40], the ∆σgrain increased along with the grain size reduction. The presence of a substantial amount of iron-rich nanoparticles plays a dominant role in the yield strength. The spherical and rhombic nanoparticles are effective in Orowan strengthening (∆σOrowan) at both 75 and 125 °C (Eq. (S2) in Supplementary data) [21,31]. Here, Eq. (S2) is simplified as ∆σ $

%& '

, where $

!"#

,

0.8+( -)./ μ0"1 23 4 which is estimated to be a constant for the

Cu-Fe-Co alloys. The values of

%& '

were calculated to be 0.0355, 0.0303, 0.0257 nm-1

for the Cu-(1.0, 1.5, 2.0)Fe-0.5Co alloys by using the statistic results in Table 1, respectively. This values indicate the ∆σOrowan of the spherical and rhombic nanoparticles suffered from a decrease as Fe content increases. The spot-like nanoparticles which are shearable impede the motion of gliding dislocations by chemical strengthening ∆σChemical (Eq. (S3)), modulus strengthening ∆σModulus (Eq. (S4)) or coherency strengthening ∆σCoherency (Eq. (S5)). Due to the low spatial resolution and the background noise, the spot-like nanoparticles can only be roughly measured and counted. But it was qualitatively estimate that the size and volume fraction of the spot-like nanoparticles increased with more Fe content, which induced the enhanced precipitate strengthening ∆σshear by shearing models (Eq. (S3-S5)). Presumably, the total increase of ∆σshear and ∆σgrain outbalances the decline of ∆σOrowan, which causes the overall ∆σs increase with the increment of Fe content (Fig. 4). The ultimate tensile strength σUTS and uniform elongation δu are significantly affected by the strain-hardening rate (Θ) [41]. The Cu-Fe-Co alloys had higher work

23

hardening at limit strains during SSRT deformation at either 75 or 125 °C (see Fig. 10a, b). Dislocations accumulate when they intersect or by-pass the iron-rich nanoparticles, which produces higher strain hardening and consequently higher tensile strength and ductility [42]. Upon increasing Fe content with a constant testing temperature, the increase in nanoparticle/matrix interface and decrease in grain size promote the dislocation-interface interactions and create more place for dislocation storage, which results in more pronounced strain hardening effect (strain-hardening curve shifted upwards upon increasing Fe content in Fig. 10a, b). The Θ enhancement correspondingly leads to the enhanced σUTS (Fig. 4). However, despite the higher strain hardening effect (at limit strains) and enhanced dynamic recovery rate (Table 2) of the Cu-Fe-Co alloys, the pure Cu produce a more stable strain hardening and thus a higher Θ, when ε>ca. 4.6% at 75 °C or ε>ca. 5.3% at 125 °C, than the alloys (Fig. 10a, b). Note that the stability of strain hardening means a strain range that the strain-hardening rate Θ does not decrease dramatically, say, Θ exhibits a higher stable degree in a certain strain range. Strain hardening Θ continued to the true stain ε of ca. 8.9% at 75 °C and 10.9% at 125 °C in the pure Cu, by contrast in the Cu-Fe-Co alloys Θ dramatically dropped to zero as ε<5.2% at 75 °C and 5.0% at 125 °C. In consequence, the unstable strain hardening limits the continuous plastic deformation, viz. results in lower ductility of the alloys (Fig. 4). This limited strain hardening in the Cu-Fe-Co alloys is correlated to the iron-rich nanoparticles which facilitate micro-void nucleation and crack propagation either within grain interior or at GBs during deformation (Figs. 6 and 7).

24

It is noted that the Θ become more stable with the increase of Fe+Co content at 75 °C, but quite the reverse at 125 °C (Fig. 10a, b). This evolution trend of the Θ in the Cu-Fe-Co alloys is consistent with the trend of the ductility δu as a function of Fe+Co content at 75 °C (Fig. 4a, c, d) or 125 °C (Fig. 4b, c, d). In other word, the more stable strain hardening, the higher δu in the alloys. This rule is also applicable to explain the difference of δu for a given copper samples tested at 75 and 125 °C (Fig. 4c, d and Fig. 10c-f). For instance, at higher temperature the Cu-Fe-Co alloys presented a higher ω value (Table 2), i.e. higher dynamic recovery rate, but the less stable strain hardening at higher temperature (Fig. 10d-f) overweighs the effect of dynamic recovery rate, causing the overall reduction of ductility. With respect to the evolution mechanism of the degree and stability of strain hardening, grain refinement upon the increase of Fe+Co content produces more GBs and thereby enhances the strain hardening effect. Meantime, the addition of more Fe+Co content creates more interphase interfaces between iron-rich nanoparticles and the matrix (see Table 1), causing more pronounced strain hardening likewise. Nevertheless, the increased tendency for intergranular fracture owing to the coarse nanoparticles reduces the stability of strain hardening (Fig. 6b-d and Fig. 7b, c), thus the lower elongation is attained in the alloy specimens. Particularly, the deteriorating effect from intergranular fracture enhances with the increase of Fe+Co content due to the coarsening of the nanoparticles as described in Section 3.2. As a result, the combined effect of iron-rich nanoparticles and GBs, which are influenced by the Fe+Co content and temperature, produces the overall strain hardening results.

25

The combined effect of the nanoparticles and GBs generates a remarkable enhancement of the Θ degree within a limit strain range, which is stronger with the increasing Fe+Co content no matter at 75 or 125 °C (Fig. 10a, b). The enhancement of the Θ degree correspondingly improves the ultimate tensile strength (Fig. 4). Nevertheless, the higher temperature weakens the cohesion between iron-rich nanoparticle and the matrix copper, which means micro-voids more easily nucleate and propagate at the nanoparticle/matrix interfaces under SSRT tensile stress at 125 °C. Consequently, the Cu-Fe-Co alloys exhibited a lower stability of strain hardening (Fig. 10d-f) at 125°C and thus the lower ductility δu (Fig. 4c, d), which is contradicted to the situation of the pure Cu (Figs. 4c, d and 10c). Besides, the deteriorating effect arising from the particle coarsening with the increasing Fe+Co content behaves more dramatically on the stability of strain hardening at higher temperature. The deteriorating effect of coarse iron-rich nanoparticles triumphs over the stabilizing effect of refining grains and fine iron-rich nanoparticles at 125 °C (Fig. 10a), which is quite reverse at 75 °C (Fig. 10b). In consequence, for the Cu-Fe-Co alloys, Θ stability (Fig. 10b) and δu (Fig. 4b, c, d) declined at 125 °C, but enhanced at 75 °C (Fig. 10a and Fig. 4a, c, d), with the increase of Fe+Co content. (b) 100

70 60

pure Cu Cu-1.0Fe-0.5Co Cu-2.0Fe-0.5Co Cu-3.0Fe-0.5Co

50 40 30 20

75 °C

10 0 -10 0.00

0.02

0.04

0.06

True strain

0.08

0.10

Strain hardening rate Θ/GPa

Strain hardening rate Θ/GPa

(a)

pure Cu Cu-1.0Fe-0.5Co Cu-2.0Fe-0.5Co Cu-3.0Fe-0.5Co

80 60 40

125 °C 20 0 0.00

0.02

0.04

0.06

0.08

True strain

0.10

0.12

26

(d)

40

Strain hardening rate Θ/GPa

Strain hardening rate Θ/GPa

(c) 75 °C 125 °C

30 20

Pure Cu 10 0 -10 0.00

0.02

0.04

0.06

0.08

0.10

0.12

60 50

30

10 0 -10 0.00

(f) 75 °C 125 °C

40

Cu-2.0Fe-0.5Co 20

0 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

True strain

Strain hardening rate Θ/GPa

Strain hardening rate Θ/GPa

0.01

0.02

0.03

0.04

0.05

0.06

0.07

True strain

80

60

Cu-1.0Fe-0.5Co

20

True strain

(e)

75 °C 125 °C

40

100

75 °C 125 °C

80 60 40

Cu-3.0Fe-0.5Co

20 0 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

True strain

Fig. 10. (a, b) The comparisons of the strain-hardening curves between the copper specimens with different alloying contents at (a) 75 and (b) 125 °C; (c-f) Strain-hardening rate as a function of temperature in the as-cast pure Cu and Cu-Fe-Co alloys. Strain-hardening rate Θ=dσ/dε, where σ and ε are true stress and true strain, respectively [41].

5. Conclusions In this work, SSRT tests of the pure Cu and Cu-Fe-Co alloys have been performed under multiaxial stress state at 75 and 125 °C with a strain rate of 1×10-6 s-1. The main conclusions are summarized as follows: (1) The NPFG structure, i.e. the refined grains embedded with interior nanoparticles, gives enhanced tensile strength σb and yield strength σs, almost double to triple values on the properties compare to coarse-grained (CG) pure Cu during SSRT tests both at 75 and 125 °C, accompanied with an acceptable loss in ductility δu. The properties

27

alter as a function of temperature and alloying content. (2) The fracture surface analysis indicates that the coarse nanoparticles and the increased tendency for intergranular fracture reduce the tensile elongation for the alloys. This deteriorating effect enhances with the increase of Fe+Co content due to the coarsening of the nanoparticles. The finer grain structure induced by the addition of more Fe+Co content is considered to improve the tensile elongation. (3) The Kocks-Mecking model for stress strain flow curves can describe the SSRT data by using σs, B and ω as adjustable parameters. The Cu-Fe-Co alloys exhibit close fitting values of ω higher than that of the pure Cu at 75 or 125 °C. The pure copper presents a lower ω value at higher temperature, but quite the reverse for all the Cu-Fe-Co alloys. (4) The evolution of SSRT properties arises from synergistic effect of NPFG structure. The enhancements of σs and σb values in the alloys result from the higher strengthening effects (Orowan, shear and GB) and higher strain hardening rate, respectively. The overall ductility depends on the integrative effect of strain hardening and dynamic recovery rate. The reduction of ductility δu of the alloys is caused by the unstable work hardening at large strains due to the deteriorating effect of iron-rich nanoparticles. (5) The NPFG Cu-Fe-Co alloys in casting state yield an improved combination of SSRT strength and ductility, in comparison with the as-cast pure Cu. More excellent properties are promising if the microstructures are optimized further by the alloying modification or with the following heat treatment and/or deformation processing.

28

NPFG Cu-Fe-Co alloy is expected to be used as the canister for the storage of the nuclear waste. Appendix A. Supplementary data Supplementary data to this article can be found online. Acknowledgements This work was performed at the USTB University of Science and Technology Beijing and KTH Royal Institute of Technology. This work was supported by the Project funded by China Postdoctoral Science Foundation (No. 2019M660451), the Fundamental Research Funds for the Central Universities (No. FRF-TP-19-002A1), Domain Foundation of Equipment Advance Research of 13th Five-year Plan (No. 61409220124). One of the authors, KXC, is grateful to the China Scholarship Council (CSC) for the financial support. The authors acknowledge Huahai Mao and Pavel Korzhavyi for inspiring discussions. References [1] B. Rosborg, L.Werme, The Swedish nuclear waste program and the long-term corrosion behavior of copper, J. Nucl. Mater. 379 (2008) 142–153. [2] L.Z. Jin, R. Sandström, Creep of copper canisters in power-law break down, Comput. Mater. Sci. 43 (2008) 403–416. [3] R. Sandström, Extrapolation of creep strain data for pure copper, J. Test. Eval. 27 (1999) 31–35. [4] H. Raiko, R. Sandström, H. Rydén, M. Johansson, Design Analysis Report For the Canister, Swedish Nuclear Fuel and Waste Management Co., Technical Report

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Highlights • Refined grain embedded with interior nanoparticles is obtained in as-cast Cu-Fe-Co alloys. • Slow strain rate tensile (SSRT) tests were conducted on the Cu-Fe-Co alloys. • SSRT fracture behaviors were investigated. • Strengthening mechanism of the alloys during SSRT test was discussed. • The alloy was proposed to be used as the canister for the storage of the nuclear waste.

Declaration of interests ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: