Ni clad foils

Ni clad foils

Author’s Accepted Manuscript Interactive effects of microstructure and interface on tensile deformation behaviors of Cu/Ni clad foils Chuanjie Wang, H...

2MB Sizes 0 Downloads 9 Views

Author’s Accepted Manuscript Interactive effects of microstructure and interface on tensile deformation behaviors of Cu/Ni clad foils Chuanjie Wang, Haiyang Wang, Fangfang Geng, Chen Gang, Lingjiang Cui, Peng Zhang www.elsevier.com/locate/msea

PII: DOI: Reference:

S0921-5093(17)31614-3 https://doi.org/10.1016/j.msea.2017.12.017 MSA35859

To appear in: Materials Science & Engineering A Received date: 2 November 2017 Revised date: 6 December 2017 Accepted date: 7 December 2017 Cite this article as: Chuanjie Wang, Haiyang Wang, Fangfang Geng, Chen Gang, Lingjiang Cui and Peng Zhang, Interactive effects of microstructure and interface on tensile deformation behaviors of Cu/Ni clad foils, Materials Science & Engineering A, https://doi.org/10.1016/j.msea.2017.12.017 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. 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.

Interactive effects of microstructure and interface on tensile deformation behaviors of Cu/Ni clad foils Chuanjie Wanga, Haiyang Wanga, Fangfang Genga, Chen Ganga, Lingjiang Cuia, Peng Zhang*a a

School of Materials Science and Engineering, Harbin Institute of Technology at Weihai, Weihai 264209, China



Correspondence information: Peng Zhang, E-mail address: [email protected] TEL:

+86 631 5687324, FAX: +86 631 5687305 Abstract: The plastic deformation behaviors are difficult to predict using the traditional theories because of the size effects induced by the interaction of intrinsic and extrinsic characteristics when the specimen sizes are scaled down to the micro/meso scale. In this study, uniaxial tensile tests of Cu/Ni clad foils under different heat treatments were carried out to investigate the coupling effects of microstructures and interface on the plastic deformation behaviors in the micro/meso scale. The traditional mixture rules, whether consider the interface layer or not, fail to analyze the strengths of Cu/Ni clad foils. The phenomenon was predicted via a proposed constitutive model which considers the interactive effect between the matrix microstructures and interface thickness of Cu/Ni clad foils, and the free surface effect in the micro/meso scale. A good agreement was seen between the calculated and experimental results. The experimental results also indicated that the ductility changed insignificantly with the annealing temperature and was enhanced compared to that of single-layer metal sheets. It was indicated by the experimental results of interrupt tests that the micro cracks originated from the interface and that the nickel layer and copper layer fractured successively due to their differences in mechanical properties and original micro voids at the interface between the Ni and Cu layers. The fracture mechanism was revealled by a proposed fracture model.

Key words: interface; Cu/Ni clad foils; constitutive model; micro-forming; fracture 1. Introduction In micro/meso-scale metal forming, the plastic deformation behaviors not only depend on microstructures but also the specimen sizes, which is different from the behaviors of macro-scale metallic polycrystals [1-4]. In the micro/meso scale, many 1

researchers have reported that the flow stress decreases gradually with the decrease of specimen size or the increase of grain size [5, 6], and vice versa [7, 8]. Constitutive models considering surface softening [1, 9] or strengthening effects [7, 10] are developed to interpret the flow stress size effects in the micro/meso scale. The ductibility decreases with the increase of the grain size while it decreases rapidly when there are only fewer grains across the thickness in the micro/meso scale. The inhomogeneous local strain distribution caused by the free surface roughening leads to an early fracture. Meanwhile, the fracture mechanism transforms from ductile fracture to brittle fracture due to the decrease of boundary fraction [11-16]. Precise bonding of dissimilar metals processes including rolling [17-19], extrusion [20] and explosive forming [21] are currently used to clad various materials with the rapid development of the electronic devices which require multifunction, high-speed, and reliable processes and materials in micrometer range. Because of the large deformation in these processes during clad metals preparation, interface layer is formed through atomic diffusion under high pressure and temperature [21-23]. Subsequent heat treatment is also used to enhance the interface bonding strength and formability of the clad metals. The thickness of the interface will increase after heat treatment. Both original preparing and subsequent heat treatment processes result in the production and development of the interface layer, which in turn influences the mechanical properties of the clad sheets [24-27]. When the thicknesses of the clad sheet are scaled down to the micro/meso scale, the free surface effect on mechanical properties of the clad sheets should be taken into account because of the size effects in the micro/meso scale. The coupling effects of the microstructures of the matrix materials and interface layer on the clad sheet in the micro/meso scale are more complicated than those of single-layer metal in the same scale. The prediction of the mechanical properties of clad sheet in macro scale usually uses the rule-of-mixture (ROM) model [28]. However, the ROM model does not involve the coupling influence of free surface and interface layer effects on clad shin sheets and fails to interpret the mechanical properties of the clad foils [29]. Few researches have been conducted on the influence of the coupling effects of the microstructures of the matrix materials and interface layer on the deformation behaviors of the clad sheet in the micro/meso scale. The coupling effects are still unclear up to now. Wang et al. [30] found that the engineering stress decreases at first and then increases with the increase of the interface layer thickness. The increase of the engineering stress can be explained by the increasing contribution of interface intermetallic compounds with 2

ultra-high strengths. The elongation decreases monotonically with the increase of the interface layer thickness accordingly. Jung et al. [29] investigated the tensile properties of a Cu/Ni fine clad sheets under different heat treatments and found that the yield strength values calculated by the rule-of-mixture model was lower than experimental yield strength. At the same time, a model considering the diffusion layer and friction at the interfaces between various phases was proposed without comparison among experimental results. Fan et al. [31-33] found that the strength-ductility synergy originated from the contribution of the interface on the local stress/strain transfer behavior, the constrained crack propagation behavior and strain non-localization conveyed by multilayered structure. In this study, the uniaxial tensile tests of Cu/Ni clad foils under different heat treatments were conducted to find out the coupling effects of microstructures and interface layer on the plastic deformation behaviors in the micro/meso scale. A constitutive model considering the free surface effect and the interactive effect between the matrix microstructures and interface layer thickness of Cu/Ni clad foils in the micro/meso scale was developed to predict the abnormal strength of Cu/Ni clad foils. The enhanced ductility was analyzed through the proposed necking process model and the fracture behavior was investigated by the proposed fracture process model. 2. Experimental Cold rolled Cu/Ni clad foils with a thickness of 100 μm and an original thickness ratio of copper to nickel being 5.5:4.5 were selected in the research. The tensile specimens with a gauge length of 25 mm and width of 6 mm were manufactured with electrical discharge machining (EDM) method. In order to secure various microstructures, the specimens were annealed in vacuum for 1.0 h at the temperatures among 600 ℃ and 850 ℃ and then cooled in air. The microstructures of the matrix materials along the plane and through-thickness directions are shown in Fig. 1 and Fig. 2 respectively. The obtained grain sizes of the copper and nickel layers are shown in Fig. 3. It can be seen that the grain sizes of the copper and nickel layers increase with the annealing temperature and there is only one grain across the copper layer when the annealing temperature reaches 700 ℃ . The thicknesses of copper, nickel and interface layers after heat treatment are shown in Fig. 4. The thickness of interface layer increases with the increase of annealing temperature because of the atomic diffusion under high temperatures. In contrast, the thickness of copper and nickel layers decreases accordingly with the increase of annealing temperature. Micro uniaxial tension tests were carried out by an INSTRON 5967 testing machine with a 3

load cell of 1 kN, as shown in Fig. 5. The specimens were strained to fracture under a low strain rate of 1×10-3s-1.

Fig. 1 Microstructures in plane direction after heat treatment (a) 600℃ (b) 650℃ (c) 700℃ (d) 750℃ (e) 800℃ (f) 850℃

Fig. 2 Microstructures in through-thickness direction after heat treatment

Grain size(m)

120 Ni

100

Cu

80

60

40 0

600

650

700

750

Temperature(ºC) 4

800

850

Fig. 3 Grain sizes of copper and nickel layers after heat treatment 50

Thickness (m)

40 Copper Nickel Interface layer

30 20 10 0

600

650

700

750

800

850

Annealing temperature (C)

Fig. 4 Variation of thicknesses of copper, nickel and interface layers with annealing temperature

Fig. 5 Micro tensile platform of Cu/Ni clad foils

3. Results and discussions 3.1 Flow stress Fig. 6 (a) shows the flow curves of specimens under different heat treatments. The flow curves decrease with the increase of the annealing temperature or grain size of the component monotonously. To analyze the results in detail, the relationship between the annealing temperature and true stress with different strain is depicted in Fig. 6 (b). The flow stress firstly decreases slightly with the increase of the annealing temperature from 600 ℃ to 800 ℃, and then decreases sharply when the annealing temperature reaches 850 ℃ at a given strain. The reduction tendency of the flow stress with annealing temperature is consistent with the Hall-Petch relationship, and similar to those in tensile tests of single-layer metals [5, 6, 9, 11-16].

5

Fig. 6 Variation of flow stress with annealing temperature (a) Flow curve (b) True stress-true strain with different strain

The strength of clad metals can be formulated by a mixing rule which depends on the area-weighted averages of component properties [28], the flow curve of two component clad sheets is formulated as follows. 𝜎𝐶 (ε) = 𝑓𝐴 𝜎𝐴 (𝜀) + 𝑓𝐵 𝜎𝐵 (𝜀)

(1)

The subscripts C, A, B refer to clad sheet, metal layer A and metal layer B respectively. SA and SB are the cross-sectional area fractions of metal A and B. The rule of mixture averaging technique has been applied to both continuous filamentary composites [28, 34] and sandwich sheet materials [35, 36]. The flow curves were then calculated by the ROM model (Eq. 1), circumstances considering the thickness of the interface layer and not are both shown in Fig. 7 (The data used in the calculation were from the refs [14, 16, 37]). It indicated that the flow stress was overestimated when using the traditional ROM model without considering the effect of interface layer thickness, as illustrated in Fig. 7 (a). The thickness of the interface layer was around 10 μm and about 1/4-1/5 of the single matrix layer thickness. Different from macro-scale circumstance, the effect of interface layer cannot be neglected in the calculation of the strength in the micro/meso scale. Then the flow stress was calculated by the traditional ROM model considering the effect of interface layer, as shown in Fig. 7 (b). It indicated that the flow stress was also underestimated when using the traditional ROM model considering the effect of interface layer. Coupling effects of the two factors: the matrix microstructures and interface layer thickness are the main reasons for the departure of the flow curve from the mixing rule. In summary, both of the models mentioned are not suitable to predict the flow stress size effect in micro tension of Cu/Ni clad foils based on the analysis above.

6

Fig. 7 Predicted flow curves using (a) ROM model without considering interface layer (b) ROM model with considering interface layer

3.2 Constitutive model The softening effect induced by free surface and the strengthening effect induced by interface layer play an increasingly important role in the overall flow stress of the clad sheet with miniaturization. The coupling effects of the microstructures of the matrix materials and interface layer on the clad sheet in the micro/meso scale are more complicated than those of single-layer metal in the same scale. In this section, by employing the mixing rule and considering the free surface and interface effects, a new constitutive model for clad foil was developed. 3.2.1 Modeling The traditional mixing rule is usually used for thick clad sheets [35, 36] and is unable to interpret the phenomena of clad foils even if the effect of the influence of the interface layer in the study is considered. The total thickness of the Cu/Ni clad foil is only 100 μm, the copper layer thickness and nickel layer thickness are in the range of several tens of microns. They are in the micro/meso scale. Previous researches have also implied that the free surface effect played a more crucial role in the mechanical properties of the specimens with dimensions in the micro/meso scale [5-16]. Thus, the free surface effect should be discussed in developing the constitutive model for Cu/Ni clad foils in this study. To reveal the flow stress size effects led by the coupling effects of the matrix microstructures, interface layer thickness and the free surface effect in the micro/meso scale, a polycrystalline model was established considering the distribution of grains as shown in Fig. 8. Then the constitutive model for Cu/Ni clad foils based on the traditional mixing rule was proposed as follows. 𝜎𝐶 (ε) = 𝑆𝐶𝑢 𝜎𝐶𝑢 (𝜀) + 𝑆𝑁𝑖 𝜎𝑁𝑖 (𝜀) + 𝑆𝐼 𝜎𝐼 (𝜀)

(2)

where SCu, SNi and SI are the cross-sectional area fractions component copper, nickel and interface layer respectively. 𝜎𝐶𝑢 (𝜀), 𝜎𝑁𝑖 (𝜀) and 𝜎𝐼 (𝜀) are the flow stresses of 7

pure copper [14], pure nickel [37] and interface layer [16] respectively at a given strain. SCu, SNi and SI are from the EDS analysis, and original thicknesses (SCu0 and SNi0) considering the effect of counterdiffusion of copper and nickel under heat treatment [29].

Fig. 8 Scheme of polycrystalline model of clad foil in the micro/meso scale

For polycrystalline metals, the relationship between flow stress and grain size can be formulated by the Hall-Petch relation [38, 39]: σ(ε, d) = 𝜎0 (𝜀) +

𝐾(𝜀)

(3)

√𝑑

where σ0(ε) and K(ε) are materials constants at a given strain ε. d is average grain size. The material strength is only dependent on the grain size in the macro scale. In the micro/meso scale deformation, a geometrical parameter η was introduced into the traditional constitutive model to reveal the flow stress size effect induced by the free surface effect. The modified Hall-Petch relation is as follows: σ(ε, d) = 𝜂𝑚𝜏0 (𝜀) + (1 − 𝜂)(𝑀𝜏0 (𝜀) +

𝐾(𝜀) √𝑑

)

(4)

  2d / t

(5)

where η is the cross-sectional area fraction of surface grains for single-layer sheet, for clad sheet η equals to d/t. m of 2.5 and M of 3.1 are the Taylor factors of the grains with free surfaces and inner grains respectively. t is the specimen thickness. 𝜏0 (𝜀) is the critical resolved shear stress at a given strain. Thus, the constitutive relationships of copper and nickel layer for Cu/Ni clad foil can be formulated as follows: 𝜎𝐶𝑢 (ε, d) = 𝜂𝐶𝑢 𝑚𝜏𝐶𝑢 0 (𝜀) + (1 − 𝜂𝐶𝑢 )(𝑀𝜏𝐶𝑢 0 + 8

𝐾𝐶𝑢 (𝜀) √𝑑𝐶𝑢

)

(6)

𝜎𝑁𝑖 (ε, d) = 𝜂𝑁𝑖 𝑚𝜏𝑁𝑖 0 (𝜀) + (1 − 𝜂𝑁𝑖 )(𝑀𝜏𝑁𝑖 0 +

𝐾𝑁𝑖 (𝜀) √𝑑𝑁𝑖

)

(7)

where 𝜎𝐶𝑢 (ε, d) and 𝜎𝑁𝑖 (ε, d) are the flow stresses, 𝜏𝐶𝑢0 and 𝜏𝑁𝑖0 the critical resolved shear stresses, 𝑑𝐶𝑢 and 𝑑𝑁𝑖 the grain sizes, 𝐾𝐶𝑢 and 𝐾𝑁𝑖 the grain boundary strengthening material constants, 𝜂𝐶𝑢 and 𝜂𝑁𝑖 the cross-sectional area fractions of surface grains of copper and nickel layers for Cu/Ni clad foil in the micro/meso scale, respectively. As for the interface layer, the flow stress can be regarded as that in the macro scale because of no free surface: 𝜎𝐼 (ε, d) = 𝑀𝜏𝐼 (𝜀) +

𝐾𝐼 (𝜀)

(8)

√𝑑𝐼

where 𝜎𝐼 (ε, d), 𝜏𝐼0 , 𝑑𝐼 , and 𝐾𝐼 are the flow stress, critical resolved shear stress, grain size and grain boundary strengthening material constant of the interface layer for Cu/Ni clad foil. Thus, the proposed constitutive model can be formulated as follows: 𝜎𝐶 (ε) = 𝑆𝐶𝑢 [𝜂𝐶𝑢 𝑚𝜏𝐶𝑢 0 (𝜀) + (1 − 𝜂𝐶𝑢 )(𝑀𝜏𝐶𝑢 0 + (1 − 𝜂𝑁𝑖 )(𝑀𝜏𝑁𝑖 0 +

𝐾𝑁𝑖 (𝜀)

𝐾𝐼 (𝜀)

√𝑑𝑁𝑖

√𝑑𝐼

)] + 𝑆𝐼 [𝑀𝜏𝐼 (𝜀) +

𝐾𝐶𝑢 (𝜀) √𝑑𝐶𝑢

)] + 𝑆𝑁𝑖 [𝜂𝑁𝑖 𝑚𝜏𝑁𝑖 0 (𝜀) +

]

(9)

3.2.2 Parameters in constitutive model In the proposed constitutive model (Eq. 9), some parameters need to be assigned to calculate the flow stress, including the geometrical parameters SCu, SNi, SI , ηCu and 𝜂𝑁𝑖 . The critical resolved shear stresses of copper, nickel and interface layers 𝜏𝐶𝑢0 (𝜀), 𝜏𝑁𝑖0 (𝜀) and 𝜏𝐼 (𝜀). The grain boundary strengthening material constants of copper, nickel and interface layers 𝐾𝐶𝑢 , 𝐾𝑁𝑖 and 𝐾𝐼 . 3.2.2.1 Geometrical parameters The geometrical parameters SCu, SNi and SI can be obtained according to Fig. 3 and Fig. 4. The relationship between the cross-sectional area fractions of the component copper, nickel, interface layer and the annealing temperature is shown in Fig. 9. It indicates that the cross-sectional area fractions of the component copper and nickel decrease with the increase of the annealing temperature and that the cross-sectional area fraction of the component interface layer increase with the increase of the annealing temperature. The geometrical parameters ηCu and ηNi can be calculated by d/t. Since d>t, the geometrical parameters ηCu and ηNi equal to 1.

9

0.5

Fraction

0.4 Copper layer Nickel layer Interface layer

0.3 0.2 0.1 0.0

600

650

700

750

800

850

Annealing temperature (C)

Fig. 9 SCu, SNi and SI with annealing temperature

3.2.2.2 Mechanical parameters For metallic materials, the critical resolved shear stress can be formulated by 𝜏0 = 𝑎 ∙ εb or 𝜏0 = 𝑎 + 𝑏 ∙ εc [40], where a, b and c are the material constants. For pure metals, 𝐾Cu and 𝐾Ni are constants in a certain range of strain. For Cu-Ni alloys in the interface layer, 𝐾I can be formulated by 𝐾I = 𝑒 ∙ εc , where e is a material constant. Thus, 𝐾Cu and 𝐾Ni , 𝜏Cu0 and 𝜏Ni0 , can be obtained by the previous researches of pure nickel and pure copper, as shown in Fig. 10. (a)

(b)400 True stress (MPa)

True stress (MPa)

300

200

100

t=200μm t/d=4.5 t/d=9.7 t/d=14.5

0 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45

300

200

t=500μm t/d=14 t/d=5 t/d=0.9

100

0 0.00

0.05

0.10

0.15

0.20

0.25

True strain

True strain

Fig.10 True stress-true strain curves a) Pure copper[14] b) Pure nickel[37]

For pure copper: 𝜏 = 248.481𝜀 0.71146 (MPa) { 𝐶𝑢0 𝐾𝐶𝑢 = 30.1 (MPa ∙ μm0.5 )

(10)

𝜏𝑁𝑖0 = 306𝜀 0.5208815 (MPa) 𝐾𝐶𝑢 = 23.0 (MPa ∙ μm0.5 )

(11)

For pure nickel: {

The flow stress of the interface layer changes with its positions or composition distributions. To simplify the calculation, the flow stress of the interface layer is divided into two parts (trapezoidal regions) by the peak stress location [41]. Based on data in the ref. [16] (as shown in Fig. 11) and Eqs. (4-8) and 𝜏0 = 𝑎 + 𝑏 ∙ 𝜀 𝑐 , 10

𝐾𝐼 = 𝑒 ∙ 𝜀 𝑐 , the critical resolved shear stress of Monel 400 𝜏𝑀400 and grain boundary strengthening material constant of Monel 400 𝐾𝑀400 are as follows: 𝜏 = 2.8269 + 254.097𝜀 0.69447 (MPa) { 𝑀400 𝐾𝑀400 = 601.9554𝜀 0.042412 (MPa ∙ μm0.5 )

(12)

Fig.11 True stress-true strain curves of Monel 400 [14]

3.2.3 Experimental verification and analysis The comparison between the calculated and experimental flow curves is shown in Fig. 12 (a). The variation of the calculated flow stress is similar to the experimental result. Then the correlation between experimental values and values by the proposed model is shown in Fig. 12 (b). The fitting accuracy is higher than 0.99. The predict precision is very high except under the early plastic deformation stage. This may result from the non-conforming of the mechanical properties of copper and nickel. On the whole, there is a good agreement between the experimental and the calculated results by the proposed model considering the coupling effects of the matrix microstructures, interface layer thickness and the free surface effect.

Fig. 12 (a) Flow curves predicted by the proposed model (b) Comparison of experimental and calculated values by proposed model 11

3.3 Ductility and fracture behavior Fig. 13 (a) shows the engineering stress - engineering strain curves of Cu/Ni clad foils. Fig. 13 (b) shows the variation of the elongation with annealing temperature of Cu/Ni clad foils. It indicates that the elongation changes modestly with annealing temperature. Fig. 13 (c) shows the variations of the strength and yield ratio with annealing temperature of Cu/Ni clad foils. It also indicates that the yield ratio is insensitive to the annealing temperature. The consistency between the yield ratio and the elongation is consistent with traditional metal plastic deformation theories for single-layer metals. However, the ductility is different from that in micro tension of single-layer metals [5-7, 11-14, 16]. The comparison between previous data and this research is shown in Fig. 14. It indicates the ductility of Cu/Ni clad foil in this research is more excellent than that of pure copper or pure nickel under the same ratio of specimen thickness to grain size N. The better ductility of Cu/Ni clad foil results from the restriction effect induced by the interface layer [29-33]. The ductility of Cu/Ni clad foil cannot be predicted by the mixture rule, the stress gradient and interface constraint between layers can enhance the ductility [42-45]. 300

(b) 30

250 200

Elongation(%)

Engineering stress (MPa)

(a)

25

150

Heat treatment (ºC) 600ºC 650ºC 700ºC 750ºC 800ºC 850ºC

100 50 0 0.00

20

0

0.05

0.10

0.15

0.20

0.25

600

0.30

650

Engineering strain

700

750

Temperature(



800

850

)

0.5

(c)

300

Strength (MPa)

200

0.3

150

Yield strength Tensile strength Yield ratio

100

0.1

50 0

0.2

Yield ratio

0.4

250

600

650

700

750

Temperature(



800

850

0.0

)

Fig. 13 (a) Engineering stress vs engineering strain (b) Relationship of elongation with annealing temperature (c) Relationship of yield, tensile strength and yield ratio with annealing temperature 12

30

Elongation (%)

25 20 15 10

Wang et al. [11] Keller et al. [37] Fu et al. [16] This study

5 0

0

2

4

6

8

10

12

14

16

Ratio of specimen thickness to grain size N

Fig. 14 Comparison of elongation with previous research [11, 16, 37]

Fig. 15 shows the microstructures of Cu/Ni clad foils in the through-thickness direction after tension. It indicates that the microstructures approaching the fracture regions are deformed severely and obvious necking zone appears at the fracture regions. Also with the increase of the annealing temperature, grooves appear in the fractured specimen surface of the coarse grained layer - copper layer. However, no distinct grooves are found in the nickel layer surface, because of the fine grains located in the nickel layer. To investigate the inhomogeneous deformation behavior at the necking region in depth, the necking angle and length are measured according to the diagrammatic sketch as shown in Fig. 16 (a). This figure also shows the variations of the necking angle with the annealing temperature. It indicates that both the necking angles in the copper and nickel layers decrease with the increase of the annealing temperature, while the necking angle in the copper layer increases inversely when the annealing temperature reaches 850 ℃. The abnormal phenomenon may result from the inhomogeneous distribution of microstructure of pure copper layer when the annealing temperature reaches 850 ℃. The necking angle in the nickel layer is bigger than that in the copper layer. The necking length in the copper layer is bigger than that in the nickel layer and decreases with the increase of the annealing temperature. The necking length in the nickel layer changes little with the annealing temperature and is in the range of about 40 μm to 46 μm. The strength of copper layer is lower than that of the nickel layer. Strain-hardening rate (θ=dσ/dε) reflects the uniform deformation ability of metal. The gradual decrease of strain-hardening rate with strain indicates the plastic instability. Local necking begins to occur in the specimen. Fig. 17 shows the strain-hardening rates of Cu/Ni clad foil, pure copper [14] and pure nickel [37]. It indicates that the strain-hardening rate of the Cu/Ni clad foil is higher than that of the pure copper or pure nickel when the strain is higher than 0.2. This demonstrates that the clad foil sustains more strain hardening when elongated uniformly. The stress 13

concentration at the nickel layer can be released by the plastic deformation of the copper layer through the interface layer. The compression stress induced by the interface layer also results in the increase of the ductility through suppressing the nucleation and expansion of crack effectively. The copper layer and nickel layer cannot reach the plastic instability at the same time and in the same cross-section along the through-thickness direction because of the random distribution of the microstructure of both layers. The existence of the interface layer not only can disperse the local strain effectively by reducing stress concentration when a small necking appeared in one layer, but also can prevent a crack from passing into another layer [46, 47].

Fig. 15 Microstructures in through-thickness direction after tension (a) 600℃ (b) 650℃ (c) 700℃ (d) 750℃ (e) 800℃ (f) 850℃ 35

t=100μm Cu Ni

30

27.2 25

81.75 74.65 69.26

21 Angle (°)

t=100μm Cu Ni

86.96

80

23.6 20.7 19.1

20

15

90.08

(b)

15.1

14.9 10.2

10

68.44

60

18.1

11.3

Length (μm)

(a)

46.35

43.22

43

41.14

40

42

40.18

9.2 7.5 20

5

0 600

650

700

750

Temperature (



800

0

850

600

650

)

700

750

Temperature (



800

850

)

Fig. 16 (a) Necking angles in through-thickness plane after fracture (b) Necking length in through-thickness plane after fracture

A schematic illustration of the difference in the process until failure between the clad 14

foil and the single-layer metal is shown in Fig. 18. For single-layer metal sheet (Fig. 18 a), when plasticity becomes unstable, the local necking cannot easily spread to the whole sample and just develops in a specific region to form a diffuse necking region. For Cu/Ni clad foil (Fig. 18 b), the copper layer and nickel layer cannot easily form a whole diffuse necking region in the same cross-section along the thickness because of inhomogeneous distribution of microstructures and loadings. The relatively independent necking of each layer of the clad foil delayed the whole necking which results in the enhancement of ductility of clad foil compared to single-layer metal. The pure copper exhibits a slower decrease in dσ/dε with increasing strain than pure nickel. This is corresponding to the smaller necking angle and the bigger necking length as shown in Fig. 16. Based on the analysis above, the existence of the interface layer is helpful to enhance the ductility of clad foil even though in the micro/meso scale.

Strain hardening rate (MPa)

4000 Cu/Ni clad foil [This work] Copper [14] Nickel [37]

3000

2000

1000

0

0.0

0.1

0.2

0.3

0.4

True strain

Fig. 17 Work hardening rate with strain of Cu/Ni clad foil, pure copper and pure nickel [14, 37]

To investigate the fracture process in micro tension of Cu/Ni clad foil, a special test was carried out. The special test is to stop the tensile test when the load reaches the maximum value and drops by 5%. It means that the tensile specimen has come into the inhomogeneous deformation stage and that local necking appears without distinct macro fracture. Then the topography along the thickness direction approaching the local necking region is analyzed. Three cross sectional areas along transverse direction of the specimen are selected for analysis as shown in Fig. 19 (a). Fig. 19 (b) shows the topography of the selected three cross sectional areas in the thickness direction. It indicates that there is a specific void between the copper layer and the nickel layer. The nickel layer fractured apparently, however, the copper layer is just necked without fracture. The nickel layer and copper layer of the clad foil in micro tension are still unfractured at the same time but successively. 15

Fig. 18 Schematic illustration of difference in process of necking (a) single-layer metal (b) clad foil

Fig. 19 (a) Scheme of three selected cross sectional areas along transverse direction (b) Topography of selected areas in thickness direction

For clad metals during the plastic deformation, the crack originates at the interface and extends to the matrix with strain [48-50]. During the heat treatment, there are also some micro voids formed at the interface [51], which are also found in the study as shown in Fig. 20. The existence of the micro voids at the interface results in stress concentration and produce initial crack when the stress reaches the critical value during plastic deformation. The fracture topography of specimen under heat treatment of 700 ℃ (as shown in Fig. 21) also indicates that there are some micro voids at the interface of the clad foil after tension to fracture. Based on the analysis above, the fracture process of Cu/Ni clad foil during 16

plastic deformation follows the sequence below. At the initial stage of loading, both the Cu and Ni layers of the Cu/Ni clad foil undergo elastic deformation. The original stress concentration applies at the micro voids at the interface between the Cu and Ni layers. The Cu layer, which is softer than Ni layer, yields firstly with the increase of strain. The local stress in the Ni layer increases faster than that in the Cu layer with the further increase of strain induced by the differences in elastic modulus and strength between the Ni and Cu layers. Then the stress incompatibility at the interface occurs. The stress concentration applied to the micro voids will release with strain by the plastic deformation of the micro void, Cu and Ni layers. The dimensions of the original micro void and formed micro void during plastic deformation will enlarge with strain. When the strain reaches the fracture stress limit, the micro void fractures. Because the work hardening rate of pure nickel is larger than that of pure copper under the same strain (as shown in Fig.17) [14, 37], the nickel layer firstly reaches the fracture strain limit with the accumulation of the plastic deformation. The further increase of strain would finally cause premature fracture of the Ni layer while the Cu layer at the moment is still subjected to plastic deformation as shown in Fig. 17 (b). Based on the analysis above, a fracture model of Cu/Ni clad foil under tension is proposed as shown in Fig. 22.

Fig. 20 Micro voids at interface for specimens after heat treatment

17

Fig. 21 Fracture topography of specimen under heat treatment of 700 ℃

Fig. 22 Fracture model of Cu/Ni clad foil under tension

4. Conclusions In this research, the coupling effects of the microstructure and interface on the mechanical properties of Cu/Ni clad foils are investigated by uniaxial tensile tests. Then the flow stress size effect, ductility and fracture behaviors of Cu/Ni clad foils in micro tension are analyzed systematically through experimental and theoretical analysis. The conclusions are drawn as follows: (1) The flow stress decreases with the increase of annealing temperature in micro tension of Cu/Ni clad foils. However, this cannot be predicted by the ROM model whether the interface layer is considered or not. A flow stress size effect occurs. (2) A new constitutive model considering the interactive effects between the matrix microstructures and interface thickness of Cu/Ni clad foils is built to reveal the flow stress size effect. A good agreement between the calculated and experimental results is obtained. (3) The ductility of Cu/Ni clad foil is more excellent than that of pure copper or pure nickel under the same ratio of specimen thickness to grain size which cannot be predicted by the mixture rule. The better ductility of Cu/Ni clad foil is a result of the 18

stress gradient and interface constraint induced by the interface layer. (4) A fracture model considering the original micro voids at the interface and the mechanical properties incompatibility of the copper and nickel layers of Cu/Ni clad foil under tension is proposed. The nickel and copper layers won’t fracture at the same time, but the nickel and copper layers will fracture successively after the micro void at the interface reaches the fracture limit.

Acknowledgements The authors gratefully acknowledge the financial support of the National Natural Science Foundation of China (No. 51505101) and China Postdoctoral Science Foundation (No. 2017T100238 and No. 2015M571407).

References [1] M. Geiger, M. Kleiner, R. Eckstein, N. Tiesler, U. Engel. Microforming. CIRP Annals-Manufacturing Technology, 2001, 50(2): 445-462. [2] U. Engel, R. Eckstein. Microforming-from basic research to its realization. Journal of Materials Processing Technology, 2002, 125-126: 35-44. [3] Y. Qin, A. Brockett, Y. Ma, A. Razali, J. Zhao, C. Harrison, W. Pan, X. Dia, D. Loziak. Micro-manufacturing: research, technology outcomes and development issues. International Journal of Advanced Manufacturing Technology, 2010, 47(9): [4]

[5]

[6]

[7] [8]

[9]

821-837. M.W. Fu, J.L. Wang, A.M. Korsunsky. A review of geometrical and microstructural size effects in micro-scale deformation processing of metallic alloy components. International Journal of Machine Tools and Manufacture, 2016, 109: 94-125. C. Keller, E. Hug, X. Feaugas. Microstructural size effects on mechanical properties of high purity nickel. International Journal of Plasticity, 2011, 27(4): 635-654. M.G.D. Geers, W.A.M. Brekelmans, P.J.M. Janssen. Size effects in miniaturized polycrystalline FCC samples: strengthening versus weakening. International Journal of Solids and Structures, 2006, 43(24): 7304-7321. X.X. Chen, A.H.W. Ngan. Specimen size and grain size effects on tensile strength of Ag microwires. Scripta Materialia, 2011, 64(8): 717-720. C.J. Wang, C.J. Wang, B. Guo, D.B. Shan, G. Huang. Size effect on flow stress in uniaxial compression of pure nickel cylinders with a few grains across thickness. Materials Letters, 2013, 106: 294-296. W.L. Chan, M.W. Fu, B. Yang. Experimental studies of the size effect affected microscale plastic deformation in micro upsetting process. Materials Science and Engineering: A, 2012, 534: 374-383. 19

[10] C.J. Wang, C.J. Wang, J. Xu, P. Zhang, D.B. Shan, B. Guo. Plastic deformation size effects in micro-compression of pure nickel with a few grains across diameter. Materials Science and Engineering: A, 2015, 636: 352-360. [11] C.J. Wang, C.J. Wang, J. Xu, P. Zhang, D.B. Shan, B. Guo, Z.L. Wang. Tensile deformation behaviors of pure nickel fine wire with a few grains across diameter. Transactions of Nonferrous Metals Society of China, 2016, 26(7): 1765-1774. [12] T. Furushima, H. Tsunezaki, K. Manabe, S. Alexsandrov. Ductile fracture and free surface roughening behaviors of pure copper foils for the micro/meso scale forming. International Journal of Machine Tools & Manufacture, 2014, 76: 34-48. [13] Z. Fang, Z.Y. Jiang, X.G. Wang, C.L. Zhou, D.B. Wei, X.H. Liu. Grain size effect of thickness/average grain size on mechanical behaviour, fracture mechanism and constitutive model for phosphor bronze foil. International Journal of Advanced Manufacturing Technology, 2015, 79(9): 1905-1914. [14] B. Meng, M.W. Fu. Size effect on deformation behavior and ductile fracture in microforming of pure copper sheets considering free surface roughening. Materials & Design, 2015, 83: 400-412. [15] R. Zhao, X.J. Li, M. Wan, J.Q. Han, B. Meng, Z.Y. Cai. Fracture behavior of Inconel 718 sheet in thermal-aided deformation considering grain size effect and strain rate influence. Materials & Design, 2017, 130: 413-425. [16] C.J. Wang, S.X. Xue, G. Chen, P. Zhang. Constitutive model based on dislocation density and ductile fracture of Monel 400 thin sheet under tension. Metals and Materials International, 2017, 23(2): 264-271. [17] D. Pan, K. Gao, J. Yu. Cold roll bonding of bimetallic sheets and strips. Materials Science and Technology, 1989, 5(9): 934-939. [18] H. R. Akramifard, H. Mirzadeh, M. H Parsa. Cladding of aluminum on AISI 304L stainless steel by cold roll bonding: Mechanism, microstructure, and mechanical properties. Materials Science and Engineering: A, 2014, 613(34): 232-239. [19] X. B. Li, G. Y. Zu, M. M. Ding, Y. L. Mu, P. Wang. Interfacial microstructure and mechanical properties of Cu/Al clad sheet fabricated by asymmetrical roll bonding and annealing. Materials Science and Engineering: A, 2011, 529(1): 485-491. [20] J.M. Story, B. Avitzur, W.C. Hahn. The effect of receiver pressure on the observed flow pattern in the hydrostatic extrusion of bimetal rods. Journal of Engineering for Industry, 1976, 98(3): 909-913. [21] H. Yan, J.G. Lenard. A study of warm and cold roll-bonding of an aluminium alloy. Materials Science and Engineering: A, 2004, 385(1): 419-428. 20

[22] H.Y. Wu, S. Lee, J.Y. Wang. Solid-state bonding of iron-based alloys, steel–brass, and aluminum alloys. Journal of Materials Processing Technology, 1998, 75(1): 173-179. [23] N.D. Lucaschkin, A.P. Borissow, A.I. Elrikh. The system analysis of metal forming technique in welding processes. Journal of materials processing technology, 1997, 66(1-3): 264-269. [24] M. Tayyebi, B. Eghbali. Study on the microstructure and mechanical properties of multilayer Cu/Ni composite processed by accumulative roll bonding. Materials Science and Engineering: A, 2013, 559: 759-764. [25] M. Talebian, M. Alizadeh. Manufacturing Al/steel multilayered composite by accumulative roll bonding and the effects of subsequent annealing on the microstructural

and

mechanical

characteristics.

Materials

Science

and

Engineering: A, 2014, 590: 186-93. [26] T.T. Sasaki, R.A. Morris, G.B. Thompson, Y. Syarif, D. Fox. Formation of ultra-fine copper grains in copper-clad aluminum wire. Scripta Materialia, 2010, 63(5): 488-491. [27] H. R. Akramifard, H. Mirzadeh, M. H. Parsa. Estimating interface bonding strength in clad sheets based on tensile test results. Materials & Design, 2014, 64(9): 307-309. [28] A. Kelly, G.J. Davies. The principles of the fibre reinforcement of metals. Metallurgical Reviews, 1965, 10: 1-77. [29] T.K. Jung, K.H. Kim, D.W. Joh, K.Y. Heo, H.S. Lee, S.C. Lim, H.C. Kwon. Tensile properties of copper-nickel fine clad prepared by surface activation bonding and subsequent heat treatment. Electronic Materials Letters, 2013, 9(6): 767-770. [30] C.J. Wang, S.X. Xue, G Chen, X.Y. Lin, H.W. Liu, H. Liu, P. Zhang. Effect of annealing on mecahnical properties and formability of Cu/Al clad bipolar plates in proton exchange membrane fuel cells. Advanced Engineering Materials, 2016, 18(10): 1770-1776. [31] M. Huang, G.H. Fan, L. Geng, G.J. Cao, Y. Du, H. Wu, T.T. Zhang, H.J. Kang, T.M. Wang, G.H. Du, H.L. Xie. Revealing extraordinary tensile plasticity in layered Ti-Al metal composite. Scientific Reports, 2016, 6: 38461. [32] G.H. Fan, L. Geng, H. Wu, K.S. Miao, X.P. Cui, H.J. Kang, T.M. Wang, H.L. Xie, T.Q. Xiao. Improving the tensile ductility of metal matrix composites by laminated structure: A coupled X-ray tomography and digital image correlation study. Scripta Materialia, 135, 2017, 63-67. 21

[33] H. Wu, G.H. Fan, M. Huang, L. Geng, X.P. Cui, H.L. Xie. Deformation behavior of brittle/ductile multilayered composites under interface constraint effect. International Journal of Plasticity, 2017, 89: 96-109. [34] H.R. Piehler. Plastic deformation and failure of silver-steel filamentary composite materials[R].

MASSACHUSETTS

INST

OF

TECH

CAMBRIDGE

AEROELASTIC AND STRUCTURES RESEARCH LAB, 1963. [35] R. Hawkins, J.C. Wright. Mechanical properties and press-formability of copper/mild steel sandwich sheet materials. Journal of the Institute of Metals, 1971, 99: 357-371. [36] J.G. Beese, G.M. Bram. Prediction of the tensile properties of sheet metal composites. Journal of Engineering Materials and Technology, 1975, 97(1): 10-13. [37] C. Keller, E. Hug, D. Chateigner. On the origin of the stress decrease for nickel polycrystals with few grains across the thickness. Materials Science and Engineering: A, 2009, 500(1): 207-215. [38] E.O. Hall. The deformation and ageing of mild steel: III discussion of results. Proceedings of the Physical Society. Section B, 1951, 64(9): 747. [39] N.J. Petch. The cleavage strength of polycrystals. The Journal of the Iron and Steel Institute, 1953, 174: 25-28. [40] D. Kuhlmann-Wilsdorf. Theory of plastic deformation:-properties of low energy dislocation structures. Materials Science and Engineering: A, 1989, 113: 1-41. [41] W.D. Jenkins, T.G. Digges, C.R. Johnson. Tensile properties of copper, nickel, and 70 – percent – copper – 30 – percent - nickel and 30 – percent – copper – 70 – percent - nickel alloys at high temperatures. Journal of Research of the National Bureau of Standards, 1957, 58(4): 201-211. [42] B. Zhang, Y. Kou, Y.Y. Xia, X. Zhang. Modulation of strength and plasticity of multiscale Ni/Cu laminated composites. Materials Science and Engineering: A, 2015, 636: 216-220. [43] S.S. Chakravarthy, W.A. Curtin. Stress-gradient plasticity. Proceedings of the National Academy of Sciences, 2011, 108(38): 15716-15720. [44] H.F. Tan, B. Zhang, X.M. Luo, X.D. Sun, G.P. Zhang. Strain rate dependent tensile plasticity of ultrafine-grained Cu/Ni laminated composites. Materials Science and Engineering: A, 2014, 609: 318-322. [45] J. Y. Jin, S. I. Hong. Effect of heat treatment on tensile deformation characteristics and properties of Al3003/STS439 clad composite. Materials Science and Engineering: A, 2014, 596(3): 1-8. [46] H.S. Liu, B. Zhang, G.P. Zhang. Delaying premature local necking of high-strength Cu: A potential way to enhance plasticity. Scripta Materialia, 2011, 64(1): 13-16. 22

[47] M. Bannister, M.F. Ashby. The deformation and fracture of constrained metal sheets. Acta Metallurgica et Materialia, 1991, 39(11): 2575-2582. [48] M. Merzkirch, M. Meissner, V. Schulze, K.A. Weidenmann. Tensile behaviour of spring steel wire reinforced EN AW-6082. Journal of Composite Materials, 2015, 49(3): 261-274. [49] S.L. Semiatin, H.R. Piehler. Deformation of sandwich sheet materials in uniaxial tension. Metallurgical and Materials Transactions A, 1979, 10(1): 85-96. [50] I.K. Kim, S.I. Hong. Effect of heat treatment on the bending behavior of tri-layered Cu/Al/Cu composite plates. Materials & Design, 2013, 47: 590-598. [51] I.D. Choi, D.K. Matlock, D.L. Olson. An analysis of diffusion-induced porosity in Cu-Ni laminate composites. Materials Science and Engineering: A, 1990, 124(2): L15-L18.

23