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meso scale hydroforming process
International Journal of Mechanical Sciences 150 (2019) 265–276
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International Journal of Mechanical Sciences journal homepage: www.elsevier.com/locate/ijmecsci
An investigation on the formability of sheet metals in the micro/meso scale hydroforming process Zhutian Xu, Linfa Peng∗, Peiyun Yi, Xinmin Lai State Key Laboratory of Mechanical System and Vibration, Shanghai Jiao Tong University, Shanghai 200240, People’s Republic of China
a r t i c l e
i n f o
Keywords: Size effect Micro/meso scale Hydroforming Ductile fracture
a b s t r a c t The geometry and grain size effects have been revealed to affect the formability of metal materials during the micro/meso scale forming processes. To understand and characterize how these size effects influence practical forming process and further to utilize those knowledge in process design and optimization, an experimental and numerical investigation on a micro/meso scale hydroforming process of pure copper sheet metals was conducted as a case study. A hydroforming process experimental setup was first developed to form long multi-channel features with different dimensions. The experimental results reveal evident size effect: The pressure and maximum height onset of failure decrease as the grain size approaches the thickness. The size effect on the pressure was identified to be attribute to the reduction of flow stress of material as the grain size increases. The surface layer model has been employed to explain the mechanism. On the other hand, the decrease of ultimate height was revealed to be affected by the reduction of forming limit of sheet metals as the size effect becomes more significant. The interaction of geometry and grain sizes and the evolution of micro voids were discussed and a modified GTN–Thomason model with the consideration of grain size effect was employed in FE simulations to estimate the forming results. A reasonable agreement between the numerical and experimental results was observed. After that the method was further utilized in the process optimization for the fabrication of a fuel cell bipolar plate with typical micro/meso scale channel features. The dangerous area with a high risk of failure was predicted based on simulations. After optimizing the process parameters, the satisfying simulation result was obtained. Hence the hydroforming apparatus was developed accordingly and the bipolar plate was successfully fabricated with high quality, which verifies the applicability of the method in the present work.
1. Introduction With the increasing requirement of miniaturized products in various modern industrial applications such as electronic devices, micro reactors and fuel cells, micro/meso manufacturing processes aiming at the high accuracy and efficiency fabrication of these products are attracting the focus of researchers and engineers in the recent years [1, 2]. Among all the manufacturing techniques, micro/meso scale forming process is one of the most attractive methods due to its evident advantages of high productivity, low cost, near net shape, etc. [3, 4]. One important issue that must be addressed in the micro/meso scale forming process is the so-called size effect [3, 5]. The mechanism of size effect can be briefly summarized as follows [3, 5, 6]: During the miniaturization of forming process, some intrinsic dimensions of material such as the grain size and the surface roughness are not scaled down with the geometric dimensions. As the geometric dimensions approach those intrinsic ones, the overall material deformation response is affected by their interactions and differs from the results predicted
∗
Corresponding author. E-mail address: [email protected] (L. Peng).
by merely scaling down the traditional theories and models. In the recent two decades, the size effect has been widely explored from different perspectives. Among them, the size effect on the plastic deformation behavior, which is one of the most fundamental issues, has been the focus of researchers. One of the pioneering works was conducted by Geiger et al. [3] and Engel et al. [5] proposing the famous surface layer model. By dividing the deforming grains into surface and internal ones, the reduction of flow stress with forming scale is well-explained by considering that the proportion of the less-restricted surface grains increases as the grain size approaches the geometric dimensions. Based on the surface layer model, a lot of efforts were made by describing the constitutive behavior of material at micro/meso scale. Kim et al. [7] considered the effects of geometry and grain sizes by introducing the ratio between specimen/feature and grain sizes into the constitutive model. They also verified their model by comparing the analytical results to the experimental ones obtained by simple compression and tension tests. Mahabunphachai and Koc [8] investigated the micro hydroforming process of sheet metals by considering the size effect of flow stress. A quantitative model was further developed to capture the size effect. Lai et al. [9] also proposed a uniform size dependent constitutive model by describing the material with a scale factor. With the help
https://doi.org/10.1016/j.ijmecsci.2018.10.033 Received 18 June 2018; Received in revised form 15 October 2018; Accepted 16 October 2018 Available online 18 October 2018 0020-7403/© 2018 Elsevier Ltd. All rights reserved.
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International Journal of Mechanical Sciences 150 (2019) 265–276
of finite element (FE) tools, various micro forming processes were explored to investigate the influence of size effect on the flow stress. The experimental results were also compared with the FE results to verify the applicability [10, 11]. More recently, the mechanism of size effect in micro/meso scale forming processes is revealed more thoroughly by the comparison and analysis of both experimental and numerical results of the plastic deformation of crystal microstructures based on the crystalline plasticity theory. Wang et al. [12] developed a FE model of grain microstructures to investigate the flexible micro-bending process. The dislocation density is adopted to describe the flow stress of grain interior and grain boundaries quantitatively. The numerical results were found to agree with the experimental ones. Klusemann et al. [13] modeled the deformation behavior and grain orientation gradient development of a highly anisotropic thin sheet metal based on the single-crystal plasticity accounting for the dissipative hardening effect. Peng et al. [14] explored the grain orientation evolution during micro/meso scale forming process. By testing the samples before and after uniaxial tension with electron backscattered diffraction (EBSD) method, the variation of grain orientation was found to play an important role during the plastic deformation. Forming limit and failure prediction is another critical issue in the plastic forming scenario. Regarding the size effect on the failure behavior of ductile material in micro/meso scale forming process, much effort has been focused to explore both the phenomena and mechanism of failure along with the thorough investigations on the size effect of plastic deformation. Based on the bulging test of thin metal foils with the thickness from 500 to 25 𝜇m, Diehl et al. [15] revealed that the forming limit decreases with the thickness for the fine grain samples. In addition, Vollertsen et al. [16] also investigated the formability of aluminum foils by using the pneumatic bulge tests. They revealed that the strain-localization and fracture spot appears randomly in the dome as a result of the irregular material flow behavior affected by the crystalline microstructures as the forming scale decreases. Zhuang et al. [17] investigated the micro tube-hydroforming process both experimentally and numerically by employing a crystal plasticity model. They found that the co-effects of grain microstructure, crystal slip system and external load have a significant and complex impact on the localized necking of material. Regarding the volume microforming, Ran et al. [18, 19] studied the failure behavior in a flanged upsetting process of brass material. Based on the experiments, they revealed that the fracture in the flange surface is easier to form in macro scale flanged upsetting process. By conducting microstructural observations, they also found the dimple size at the transgranular surface is evidently affected by the size effect. In the previous researches of the present authors [20–22], the forming limits of copper sheet with different thicknesses and grain sizes were investigated experimentally. The forming limit curve (FLC) is revealed to shift down as the grain size approaches the thickness. The scatter of data is also found to increase with grain size. The applicability of several macro scale failure prediction theories were explored in micro/meso scale. A modified Gurson–Tvergaard–Needleman (GTN) model considering the as-observed geometry and grain size effects was also developed. As reviewed above, the size effects of plastic deformation and failure have been investigated a lot in recent years in the micro/meso scale forming scenario. However, a systematic research utilizing the existing models on a practical micro/meso scaled forming process to guide the process design and realization has seldom been reported. In the present work, the micro/meso scale hydroforming experimental apparatus was developed, based on which the constitutive and failure prediction models considering the size effects were first verified. After that, the process parameter design and optimization method were also developed based on the analytical models to achieve the fabrication of a protein exchanging membrane fuel cell (PEMFC) single polar plate prototype as a case study. This research could be helpful as an example for the development and process parameter design of practical micro/meso scale forming processes.
Table 1 The fitted results of Peng’s hybrid model [20]. Parameters
0.1 mm
0.2 mm
k1 n1 b k2 n2
162.58 0.75 47.60 20.0 0.10
142.19 0.64 17.24 12.9 0.24
2. Experimental analysis on the micro/meso scale hydrforming process 2.1. Sample preparation Sheet metals of Cu-FRHC with the thickness of 0.1 and 0.2 mm were employed as the testing material. To characterize the grain and geometry size effects on the formability in the micro/meso scale hydroforming process, the sheet metals were annealed at different temperatures to obtain different grain size conditions. The prepared samples in the present study are in accordance with those in our previous reports [20, 21]. The details of uniaxial tensile test setup, sample dimensions, heat treatments and true stress-true strain curves are summarized in Fig. 1. Peng’s hybrid model [23] was introduced to describe the grain and geometry sizes dependent hardening behavior. The model can be written as follows: ⎧𝜎̄ = 𝜎̄ 𝑖𝑛𝑑 + 𝜎̄ 𝑑𝑒𝑝 ⎪𝜎̄ 𝑖𝑛𝑑 = 𝑀 𝜏𝑅 (𝜀̄ ) + 𝑘√(𝜀̄) 𝑑 ⎪ ( ⎨ 𝜎 ̄ = 𝜂 𝑚 𝜏 𝜀 ̄ − 𝑀 𝜏𝑅 (𝜀̄ ) − ( ) 𝑅 ⎪ 𝑑𝑒𝑝 ⎪ 𝑑 ⎩𝜂 ≈ 𝑡
𝑘(𝜀̄ ) √ 𝑑
)
(1)
𝜎̄ 𝑖𝑛𝑑 and 𝜎̄ 𝑑𝑒𝑝 are the size independent and dependent parts of flow stress respectively. m and M can be assumed to be 2 and 3.06 respectively according to Peng et al. [23]. d and t are the average grain size and the thickness of sheet metal. 𝑘(𝜀̄ 𝑚 ) and 𝜏𝑅 (𝜀̄ 𝑚 ) were fitted to the following equations based on the least square method. The results are summarized in Table 1. { 𝑘(𝜀̄ ) = 𝑘1 (𝜀̄ )𝑛1 + 𝑏 (2) 𝜏𝑅 (𝜀̄ ) = 𝑘2 (𝜀̄ )𝑛2 Before test, the as-received sheet metals were first fabricated into round samples with the diameter of 60 mm by wire electric discharge machining (WEDM). The samples were then heat-treated by using the method shown in Fig. 1. After that they were employed in the hydroforming experiments. 2.2. Experimental setup To investigate the effects of both process parameters and material properties on the formability of samples during the micro/meso scale hydroforming process, the hydroforming apparatus shown in Fig. 2 was employed. The hydraulic pressure was provided by a Maximator high pressure oil pump (MHU-M111-G500-2-4500). Four dies with uniform channels of different dimensions were fabricated to test the samples as shown in Fig. 2. The dies were numbered from 1 to 4 with the reduction of channel width. The dies of No. 1, 2 and 3 were employed to test the formability of 0.2 mm samples while the ones of No. 2, 3 and 4 were used on 0.1 mm samples. This is because the channel width of die No. 4 (0.6 mm) is too small for 0.2 mm samples. It is difficult to form such small channels with 0.2 mm samples by using hydraulic pressure. On the other hand, the 0.1 mm sample could be hydroformed into the channels of die No. 1 easily attaching to the die surface closely. Hence it is also difficult to realize fracture of sample even at high hydraulic pressure. 266
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the samples formed against Die No. 1 is likely to exceed the measurable scope of the laser system. Therefore, a micrometer caliber with the accuracy of 10 𝜇m was used instead. The average height of the three channels in the center was recorded as the height onset of fracture. In addition, each hydroforming test was repeated three times to verify the repeatability of experiments. Since the focus of the present study lies on the exploration of the effect of process and size effect parameters on the failure behavior of sheet metals during the micro/meso scale hydroforming, the ultimate pressure and height of formed sample onset of failure were recorded. 2.3. Results and discussion The laser measurement results of the profile of the hydroformed samples onset of fracture are shown in Fig. 3. An evident reduction of limit height onset of failure with the increase of grain size can be observed under different geometric dimensions. This is in accordance with the observation made in the previous study [20] that the FLCs shift down with the increase of grain size. The deterioration of formability as the grain size approaches the geometric dimensions can be explained by incorporating the surface layer model with the ductile fracture theory. A brief illustration can be found in Fig. 4. It is well-accepted that the ductile fracture of metal is closely associated with the evolution of micro voids. In the beginning of plastic deformation, micro voids are generated at the defects of base material such as second phase particles, inclusions, grain boundaries, etc. As the deformation continues, the micro voids gradually grow until void coalescence occurs to form bigger cracks. The propagation and linkage of the cracks thus lead to the quick failure of material. At micro/meso scale, the grain size approaches to the geometric dimensions which lead to the significant size effect. The size effect has been well characterized by the surface layer model. According to this model, the metal material is regarded to be consisted of both surface and internal grains. The surface grains are less constrained due to their free surfaces. Hence the surface grains often perform close to single crystal during deformation. As a result, the deformation of surface grains is dependent on the grain orientation and other properties of individual grains. On the other hand, the deformation of internal grains is constrained by each other. Hence the overall behavior is more homogeneous. At micro/meso scale, the proportion of surface grains increases as the grain size approaches the geometric dimension. The overall deformation behavior of material is thus affected. Focusing on the ductile fracture behavior at micro/meso scale, the micro voids are mostly generated among the internal grains. This is because the rotation of surface grains could facilitate the motion of dislocations. The dislocations are thus less likely to localize at certain spots to form micro voids. In the micro/meso scale sheet metal forming progress, the internal layer becomes thinner as the grain size approaches the geometric dimensions. The void coalescence and crack linkage thus become easier. More importantly, the increase of grains size also leads to the easier strain localization. Hence the ductile fracture of sheet metal starts earlier and the formability of sheet metal decreases. In addition, when there is only one or two grains over the thickness, the various grain orientations and properties of individual grains could cause large uncertainty of forming limit. The maximum hydraulic pressure onset of failure was also recorded as shown in Fig. 5. It can be observed that the critical pressure decreases with the increase of grain size. This is mainly caused by the reduction of flow stress as revealed by the uniaxial tensile tests. According to the surface layer model, the surface grains are less restricted due to their free surfaces. Hence the rotation of grain orientation could facilitate the motion of dislocations, leading to the lower flow stress. As the grain size approaches the geometric dimensions, the surface layer takes a greater proportion. Therefore, the overall flow stress of material gradually decreases. Hence the lower deforming pressure was required during the
Fig. 1. True stress-true strain curves of sheet metals with different thicknesses and grain sizes after different heat treatments: (a) uniaxial tensile test setup; (b) 0.1 mm and (c) 0.2 mm samples results. The data were also analyzed by using the surface layer model to consider the grain size effect [20].
During the test, the samples were placed on top of the die and the die holder. The pieces were then clamped together by using eight thread bolts. After that the hydraulic pressure was applied at 0.2 MPa/s until the fracture of sample took place. Hence the limit height onset of fracture was measured by employing the KEYENCE KS-1100 laser measurement system with the resolution of 0.05 𝜇m. In addition, the height of 267
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Fig. 2. The hydroforming experimental setup.
hydroforming process. In addition, the limit height also decreases due to the deteriorated formability of samples as the increase of grain size. As a result, the ultimate pressure onset of failure decreases as the size effect becomes more evident.
A is the nucleation speed factor. d is the average grain size. t is the thickness of sheet metal. 𝜀̄ 𝑝𝑚 and 𝜀̄̇ 𝑝𝑚 are the equivalent plastic strain and strain rate respectively. 𝜀N and sN are the mean nucleation strain and the standard deviation of nucleation respectively. The growth of micro voids can be estimated by the modified GTN model:
3. Prediction and analysis of the failure behavior of micro/meso scale hydroforming process
( )2 ( ) ( ) ⎧ 𝑞 𝑝 ⎪Φ = 𝑞 + 2𝑞1 𝑓 ∗ cosh − 32 𝜎̄2 − 1 + 𝑞3 𝑓 ∗ 2 = 0 𝜎 ̄ 𝑚 ⎨ ( )𝑚 ( ) 𝑑𝑒𝑝 ( ) ⎪𝜎̄ 𝑚 𝜀̄ 𝑚 = 𝜎̄ 𝑚𝑖𝑛𝑑 𝜀̄ 𝑚 + 𝜎̄ 𝑚 𝜀̄ 𝑚 ⎩
According to the previous experimental investigations, it has been revealed that the deformation and failure behaviors of hydroformed sheet samples at micro/meso scale are affected by the size effect, which brings new challenges to the design and optimization of micro/meso scale hydroforming process. To obtained the robust design of process parameters to minimize the possibility of part failure during the forming process, a prior problem to be solved is finding a predictive model which could characterize the failure behavior of sheet metals affected by the size effects at micro/meso scale. In our previous study [22], M–K and GTN– Thomason models have been revealed to be accurate in describing the forming limit curves of sheet metals at different geometry and grain size conditions. In addition, a modified GTN–Thomason model considering the geometry and grain size effects was also developed [20]. In the following, both the modified GTN–Thomason and the M–K models were employed in predicting the failure behaviors of the samples subjected to uniform hydraulic pressure under different micro/meso scaled geometry and grain dimensions to verify their capability in the hydroforming process.
In Eq. (4), the GTN model was incorporated with the constitutive model developed by Peng et al. [24] √ to describe the geometry and grain size effects of flow stress. 𝑞 =
3 𝑆 𝑆 2 𝑖𝑗 𝑖𝑗
is the von Mises equivalent
1 𝜎 3 𝑘𝑘
stress, 𝑝 = is the hydrostatic stress, Sij = 𝜎 ij − p𝛿 ij is the deviatoric component of Cauchy stress, 𝛿 ij is the Kronecker delta, 𝜎̄ 𝑚 is the equivalent stress of the base material which is contributed by both the size independent part 𝜎̄ 𝑚𝑖𝑛𝑑 and the size dependent one 𝜎̄ 𝑚𝑑𝑒𝑝 . q1 , q2 and q3 are the coefficients introduced. f∗ is the effective void volume fraction which is defined as: { 𝑓 ) 𝑓 < 𝑓𝑐 𝑓 −𝑓 ( 𝑓∗ = (5) 𝑓𝑐 + 𝑓 𝑢 −𝑓𝑐 𝑓 − 𝑓𝑐 𝑓 ≥ 𝑓𝑐 𝑓
𝑐
f is the void volume fraction.fc is the void volume fraction onset of coalescence, which could be determined according to the modified Thomason model as following: ( ( ))1∕3 ⎧ 3 3 ⎪𝜒 = 2 𝑓 𝜆0 2 𝑒𝑧𝑧 ⎪ √ 4 (𝜀̄𝑝𝑚 −𝜀𝑁 ) ⎨ 2𝜋𝑠𝑁 ⎪𝜆0 = 𝐶𝑑 𝑒 4 √ (𝜀̄𝑝𝑚 −𝜀𝑁 ) ⎪ 1+𝑒 2𝜋𝑠𝑁 ⎩
3.1. Modeling process 3.1.1. Modified GTN–Thomason model The modified GTN–Thomason model is established by describing the nucleation, growth and coalescence of micro voids with the consideration of size effect. The nucleation model can be written as: ⎧𝑓̇ = 𝐴𝜀̄̇ 𝑝𝑚 ( ) ⎪ 𝑛𝑢𝑐𝑙𝑒𝑎𝑡𝑖𝑜𝑛 ( ( 𝑝 𝑑 )2 ) 1− 𝑡 𝑓𝑛 ⎨ 1 𝜀̄ 𝑚 −𝜀𝑁 ⎪𝐴 = 𝑠 √2𝜋 exp − 2 𝑠𝑁 𝑁 ⎩
(4)
(6)
In Eq. (6), 𝜒 is a geometric factor representing the possibility of internal necking. ezz is the major principal strain. 𝜆0 is a factor denoting the spatial distribution of micro voids. C is a material constant. The void coalescence starts as soon as 𝜒 reaches a critical value of 𝜒 c . The key parameters of fn , 𝜆0 and fu − fc were determined by finding the coincidence of simulation and experimental engineering strain-
(3)
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3.1.2. M–K model The M–K model assumes that a surface defect exists during the forming process of sheet metals. With the plastic deformation increases, the stress and strain gradually concentrate at the defect area which further lead to the final necking and failure. As a preliminary research, the von Mises yield criterion and the hardening behavior described by using Peng’s hybrid model of size effect as presented in Eqs. (1) and (2) were employed. The following equations can be obtained based on the M–K modeling process as reported in Ref. [22]: ⎧ 𝜀2 = 𝑑 𝜀2 = 𝜌 𝑑 𝜀1 ⎪ 𝜀1 2 √ √ ⎪𝜀̄ = 3𝜀1 𝜌2 + 𝜌 + 1 3 ⎪ 𝜎𝐵 ⎪𝜂 𝐵 = 2𝐵 = 2𝜌𝐵 +1 2+𝜌 𝜎1 ⎪ √𝐵 ( )2 ⎪ 𝐵 𝜎̄ 𝐵 𝐵 𝐵 ⎨𝜑 = 𝜎 𝐵 = 1 − 𝜂 + 𝜂 1 ⎪ 2𝜑𝐵 Δ𝜀̄ 𝐵 ⎪𝜙 = Δ𝜀𝐵 = 2−𝜂 𝐵 1 ⎪ √ 3 𝜌+1 ⎛ 𝐵 | Δ𝜀̄𝐵 ⎪ − 2 √ 𝜀̄ 𝐴 ⎞ 𝐵 𝜎 ̄ 𝜀 + −1− 𝜌 | ( ) 𝜌+2 𝐵 𝜌2 +𝜌+1 ⎟=0 ⎪√ 𝜎̄ 𝐴 − 𝜑𝐵 𝑓0 ⎜𝑒 3 |𝑡 𝜙 −𝑒 2 ⎜ ⎟ ⎪ 3(𝜌 +𝜌+1) ⎝ ⎠ ⎩
(7)
In Eq. (7), f0 is the initial defect ratio. 𝜀̄ , 𝜀1 and 𝜀2 are the Mises, major and minor in-plane principal strains respectively while 𝜎, ̄ 𝜎 1 and 𝜎 2 are the corresponding Mises, major and minor in-plane principal stresses respectively. The superscripts A and B represent the states of out of and inside the defect area respectively. By combining with the constitutive model developed by Peng et al. [24]., an iteration calculation program was then developed to calculate the FLCs at different temperature and strain rate conditions. By using different f0 , the variation of FLC under different geometry and grain size conditions was well captured. The details of model establishment and parameter determination can be found in Ref. [22]. By finding the coincidence of experimental and predicted FLC at the smaller grain size condition, the optimized value of f0 was obtained for the sheet metals with different thicknesses. The parameters of M–K model are summarized in Table 3. 3.2. Simulation and analysis In order to obtain the predicted failure results at different conditions, FE simulations were conducted by using the commercial code of ABAQUS. A VUMAT subroutine was developed based on the modified GTN–Thomason model and incorporated in the simulations. Meanwhile, ordinary ABAQUS/Explicit plastic deformation simulations for different conditions were also conducted, based on which the FLDs predicted by M–K model were incorporated to simulate the failure behavior during hydroforming. C3D8R elements were used for the deforming sample while R3D4 ones were employed for the die. The constant friction coefficient 0.15 was also set. The simulation results of the GTN–Thomason model onset of necking were shown in Fig. 6, in which the fields of effective void volume fraction f∗ (indicated by SDV3) and major principal strain were illustrated. It can be observed that the necking and failure position is at the radius area. In addition, the strain and f∗ distributions become more concentrated and localized at that area with the reduction of forming dimensions for both 0.1 and 0.2 mm-thick samples. A direct consequence is that ductile fracture is easier to initiate and the dome height onset of failure thus decreases, which is in accordance with the experimental results as reported in Section 2. Actually, this is because the thickness of sheet metal cannot be ignored as the forming scale decreases, especially when the geometric process parameters are in the same level with the thickness. In that case, the stress/strain distribution across the thickness direction can no longer be regarded as uniformly-distributed. As a result, many traditional methods developed based on the sheet metal, including the traditional FLD method, may not work well in the micro/meso scale forming scenario. Modifications of these methods need to be addressed to consider the geometric size effects before applying on the micro/meso scale forming processes. In the present work, FE tools
Fig. 3. Profile measurement of the hydroformed samples: (a) the profile of laser measurement results; (b) the average limit height of 0.2 mm samples and (c) the average limit height of 0.1 mm samples.
stress curves based on the analysis of a series of five-level orthogonal numerical experiments. The rest of parameters were identified based on previous researches. The parameters determination procedure has been reported in Ref. [20]. The parameters values are summarized in Table 2. The modified GTN–Thomason model was also incorporated into ABAQUS via VUMAT subroutine. 269
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Fig. 4. A brief illustration of the effects of grain and geometry sizes on the ductile fracture behavior during micro/meso scale sheet metal forming process.
were employed to predict the failure behavior to address this problem. On the one hand, the GTN–Thomason model was incorporated into the simulations to estimate the whole-field strain and void volume fraction distribution during the forming process. Hence the localized fracture can be estimated with the consideration of the geometric size effect. On the other hand, the localized major and minor strains of FE simulation were taken to compare with the forming limit predicted by the M–K model. With the increase of grain size, it can also be found that the ultimate pressure onset of necking decreases. This is mostly because the flow stress decreases due to the grain size effect. A clearer representation of this effect is summarized in Fig. 7 which illustrates the forming pressure vs. bulge height curves at different geometric and grain size conditions. FE simulations of the material with the grain size of 0.1 𝜇m were employed to estimate the conditions without the grain size effect. It can be observed that the height increases more rapidly with the increase of grain size. This is because the flow stress reduction was well-captured by the modified GTN–Thomason model. In addition, it can also be seen that the ultimate forming height decreases with the increase of grain size, which is in accordance with the experimental observation that the forming limit of sheet metal decreases with the increase of grain size. Hence the modified GTN–Thomason model can estimate the trend of formability deterioration as the geometry and grain size effects become more significant. Nevertheless, further quantitative compare of numerical and experimental results is still needed to verify the applicability of the failure prediction methods adopted. 3.3. Compare of numerical and experimental results The predicted ultimate height and pressure onset of failure are compared with the experimental results as shown in Fig. 8. In general, there is a good agreement between the experimental and the modified GTN–Thomason model results. With the increase of grain size, the model is able to capture the reduction of both the limit bulge height and ultimate forming pressure. This is because the interactive effects of geometry and grain sizes on the hardening behavior as well as the void evolution are considered in the modified GTN–Thomason model. The experimental results also verified the applicability of this model in the micro/meso scale hydroforming process. On the other hand, the M–K model tends to overestimate the limit height with the increase of grain size. This is because the same surface defect factor was used for different grain size conditions. Even though more accurate analytical results can be calculated by adjusting the surface defect factor,
Fig. 5. The ultimate pressure results of (a) 0.2 mm samples and (b) 0.1 mm samples onset of failure. 270
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Table 2 The parameters of the modified GTN–Thomason model [20].
0.1 mm 0.2 mm
𝜀N
sN
q1
q2
q3
𝜅
𝜒c
fn
C
ff − fc
0.25
0.1
1.5
1
2.25
1
0.9
0.0607 0.0516
0.445 0.607
0.115 0.125
Fig. 6. The FE simulation results onset of necking by using the modified GTN–Thomason model for the samples with the thickness of: (a) 0.2 mm and (b) 0.1 mm.
4. Application of micro/meso scale hydrforming process on the fabrication of PEMFC single polar plates
the mechanism of size effect on the ductile fracture behavior could not be well described with promising numerical method. Hence in the following, the modified GTN–Thomason model is applied in the case study of a hydroforming process of PEMFC bipoloar plates with typical micro/meso scale features to guide the process parameter design to avoid the fracture of sheet metal during the forming process.
The PEMFC single polar plate was designed as shown in Fig. 9(a). To realize its fabrication, the radius of edges is the most important geometric factor which determines the formability since the dimensions
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Fig. 7. The bulge height vs. pressure curves and the failure points under different grain sizes conditions in the hydroforming process: (a) Sheet metal with the thickness of 0.1 mm bulged into Channel No. 2; (b) Sheet metal with the thickness of 0.2 mm bulged into Channel No. 2; (c) Sheet metal with the thickness of 0.1 mm bulged into Channel No. 3; and (d) Sheet metal with the thickness of 0.2 mm bulged into Channel No. 3.
erty parameters for 0.1 mm sheet metals with the grain size of 27.5 𝜇m were employed during the calculation. The friction coefficient between the sheet metal and the die was set as 0.15. The strain and void volume fraction fields just before failure happens with the ultimate pressure of 28.76 MPa are shown in Fig. 10. As shown in Fig. 10, the void volume fraction and strain are extremely concentrated at the edges of features, especially at the corner areas as indicated. According to the measurement, the formed height in the channel area before failure was 0.253 mm, 64% of the designed height of 0.4 mm. The small radius in the initial case could be the direct reason. To find out the proper radius of edge, simulations with the radius of 0.15, 0.2 and 0.25 mm were then conducted and the results onset of failure are shown in Fig. 11. It can be observed that the maximum height formed with the radius of 0.15 mm was less than the designed height. With the increase of edge radius to 0.2 mm, the designed height was reached. However, it can be observed that the flat area formed at the bottom was limited. Much greater flat area can be obtained by further increasing the edge radius to 0.25 mm. The promising contact area could lead to easier assembly and better performance of bipolar plates. It should be noticed that the upper flat area of formed plate decreases evidently with the increase of edge radius. As a compromise, the edge radius of 0.25 mm was employed to obtain both the promising upper and bottom contact area. In addition, to avoid the failure behavior at the dangerous areas near the turning corners of channels as shown in Fig. 10, the corner radius was also in-
Table 3 The parameters of the M–K model [22].
0.2 mm 0.1 mm
Parameter
Value
𝑓0 𝑓0
0.973 0.986
of features (i.e., the width, height and length of channel features) have been determined during the design procedure. It should be noticed that the design of feature dimensions was estimated with the consideration of the previous discussion on the formable window of hydroforming process in the present work. By applying the radius as shown in Fig. 9(b), the trial 3D die CAD model was developed. As an initial case study, the low level of radius was expected which could lead to greater contact area. According to Qiu et al. [25], limited contact area could lead to easier mis-assembly of adjacent bipolar plates and may cause the leak of gas due to the less constrained sealing ring. Hence greater contact area with smaller edge radius is beneficial during the design of PEMFC bipolar plates. However, as revealed previously, the smaller radius could prevent the flow of material leading to the earlier fracture. Hence an optimized point satisfying both the requirements of PEMFC function and formability is the target. FE simulations were then conducted based on the VUMAT subroutine developed according to the modified GTN–Thomason model. The prop272
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Fig. 8. Compare of the experimental and analytical results: (a) The formed height results of sheet metals with the thickness of 0.1 mm; (b) The formed height results of sheet metals with the thickness of 0.2 mm; (c) The ultimate pressure results of sheet metals with the thickness of 0.1 mm; and (d) The ultimate pressure results of sheet metals with the thickness of 0.2 mm.
Fig. 9. Development of die profile: (a) The design of bipolar plate sample; (b) the developed die by using the initial parameters.
creased from 0.6 to 0.9 mm. The optimized 3D die geometry was then imported into ABAQUS for simulation. The results are shown in Fig. 12. The maximum pressure applied onset of failure was 47.5 MPa and it can be observed that the strain distribution is more uniform due to the improvement made on the initial parameters. Hence the necking moment could be postponed leading to the greater forming height. Accord-
ing to the observation, the maximum height was reached at the channel area. In addition, the flat area formed at the bottom of channel is large enough to support the bipolar plate during stack assembly. Hence the optimized parameters could satisfy both the functional and formability requirements.Based on the as-obtained parameters, the die prototype was fabricated as shown in Fig. 13(a). Verification hydroforming test 273
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Fig. 10. FE results onset of failure by using the initial geometry parameters.
Fig. 11. Determination of the edge radius by conducting simulations.
Fig. 12. FE results onset of failure after the modification of parameters.
of copper sheet metal with the thickness of 0.1 mm and the grain size of 27.5 𝜇m was then conducted. Successful forming of samples could be obtained by raising the hydraulic pressure to 45 MPa and maintained for 10 s. No fracture is found and the average height in the channel area is 0.394 mm. In addition, fracture of sheet metal occurred at higher pressure as shown in Fig. 13(b). As the pressure increases to 51 MPa, fracture of sample is observed at the corner area of gas inlet features. This observation is in agreement with the FE results that illustrates the dangerous area is at the corner of channel and the gas inlet features when
the pressure increases to 47.5 MPa. The profile in the center section of formed sample was also scanned by using the KS-1100 laser measurement system. The compare of experimental and FE results were shown in Fig. 14. It can be observed that the bottom of the outer channel is flat in the experimental profile which could be the proof that the sheet metal was in close contact with the die surface during hydroforming. Nevertheless, there is a slight difference between the FE and experimental profiles at the bottom of the channels in the middle. On the 274
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Fig. 13. The die and the formed sample of PEMFC single polar plate: (a) the fabricated die; (b) the hydroformed sample.
Fig. 14. Compare of FE and experimental section profiles in the center of formed sample.
5. Conclusions
one hand, this could be attributed to the springback behavior of sheet metals and measurement error. On the other, the damage model employed in the simulations could overestimate the formability. Hence the failure actually initiated at an earlier stage in the hydroforming experiments and the hydroformed channel height was lower than expected. Further investigation on the accurate failure prediction in micro/meso scale hydroforming process is still needed to address this problem. In addition, it should be mentioned that copper sheet metal is not a satisfying candidate for the application of PEMFC bipolar plates due to its weak anti-corrosion capability. In this study, the copper sheet metal was employed as a testing material for the verification of modeling method. Further study regarding the application of the modified GTN–Thomason model on stainless steels, Ti alloys, etc. which have been proved to be the suitable material for bipolar plates, should be conducted in the future to further verify the accuracy of the model. In addition, it should be mentioned that the present study is still a preliminary one which did not include the interacting effect of individual grains. That could be one of the major reasons for the error between the numerical and experimental results in the presented research. Further research regarding the deformation and ductile failure behaviors in the micro/meso scale forming process considering the polycrystalline microstructure and the interaction of individual grains should be conducted to explore the mechanism behind.
In this work, micro/meso scale hydroforming experiments of copper sheet metals with different thickness and grain sizes were conducted to investigate the geometry and grain size effects on the deformation and failure behaviors. A modified GTN–Thomason model was also employed to describe the size effect affected deformation and failure behaviors. In addition, a case study regarding the hydroforming process design of a PEMFC single polar plate prototype was also conducted based on the model. The following remarks could be obtained from this study: 1) According to the hydroforming experiments at different geometric and grain size conditions, the evident size effects are observed. The maximum forming height and the ultimate pressure are revealed to decrease as the grain size approaches the thickness of sheet metal. 2) The modified GTN–Thomason model by including the effects of geometry and grain sizes on the evolution of damage was employed to predict the maximum height and pressure onset of failure. The results are found to be in accordance with the experimental ones. 3) The model was employed in the process parameter design and optimization for the fabrication of a PEMFC single polar plate. Based on the failure prediction obtained by utilizing the modified GTN–Thomason model, the parameters were optimized and the 275
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successful fabrication of product was realized. In addition, the failure of sample at a higher forming pressure was also captured by this model, which verifies the applicability of the presented method.
[10] Peng L, Lai X, Lee HJ, Song JH, Ni J. Analysis of micro/mesoscale sheet forming process with uniform size dependent material constitutive model. Mater Sci Eng A 2009;526:93–9. [11] Peng LF, Hu P, Lai XM, Mei DQ, Ni J. Investigation of micro/meso sheet soft punch stamping process - simulation and experiments. Mater Des 2009;30:783–90. [12] Wang X, Qian Q, Shen Z, Li J, Zhang H, Liu H. Numerical simulation of flexible micro-bending processes with consideration of grain structure. Comput Mater Sci 2015;110:134–43. [13] Klusemann B, Svendsen B, Vehoff H. Modeling and simulation of deformation behavior, orientation gradient development and heterogeneous hardening in thin sheets with coarse texture. Int J Plast 2013;50:109–26. [14] Peng L, Xu Z, Gao Z, Fu MW. A constitutive model for metal plastic deformation at micro/meso scale with consideration of grain orientation and its evolution. Int J Mech Sci 2018;138-139:74–85. [15] Diehl A, Engel U, Geiger M. Influence of microstructure on the mechanical properties and the forming behaviour of very thin metal foils. Int J Adv Manuf Tech 2010;47:53–61. [16] Vollertsen F, Hu Z, Wielage H, Blaurock L. Fracture limits of metal foils in micro forming. In: Proceedings of the 36th International MATADOR Conference:. Springer; 2010. p. 49–52. [17] Zhuang W, Wang S, Cao J, Lin J, Hartl C. Modelling of localised thinning features in the hydroforming of micro-tubes using the crystal-plasticity FE method. Int J Adv Manuf Tech 2010;47:859–65. [18] Ran JQ, Fu MW, Chan WL. The influence of size effect on the ductile fracture in micro-scaled plastic deformation. Int J Plast 2013;41:65–81. [19] Ran JQ, Fu MW. A hybrid model for analysis of ductile fracture in micro-scaled plastic deformation of multiphase alloys. Int J Plast 2014;61:1–16. [20] Xu ZT, Peng LF, Fu MW, Lai XM. Size effect affected formability of sheet metals in micro/meso scale plastic deformation: experiment and modeling,. Int J Plast 2015;68:34–54. [21] Xu ZT, Peng LF, Lai XM, Fu MW. Geometry and grain size effects on the forming limit of sheet metals in micro-scaled plastic deformation. Mater Sci Eng A 2014;611:345–53. [22] Peng LF, Xu ZT, Fu MW, Lai XM. Forming limit of sheet metals in meso-scale plastic forming by using different failure criteria. Int J Mech Sci 2017;120:190–203. [23] Peng L, Liu F, Ni J, Lai X. Size effects in thin sheet metal forming and its elastic— plastic constitutive model. Mater Des 2007;28:1731–6. [24] Peng L, Lai X, Lee H-J, Song J-H, Ni J. Analysis of micro/mesoscale sheet forming process with uniform size dependent material constitutive model. Mater Sci Eng A 2009;526:93–9. [25] Qiu D, Yi P, Peng L, Lai X. Study on shape error effect of metallic bipolar plate on the GDL contact pressure distribution in proton exchange membrane fuel cell. Int J Hydrogen Energy 2013;38:6762–72.
Acknowledgment This work was supported by the General Research Fund of National Natural Science Foundation of China (No. 51522506 and No. 51575465), National Key Research and Development Program of China (No. 2017YFB0103001) and “Shu Guang” project supported by Shanghai Municipal Education Commission and Shanghai Education Development Foundation (No. 17SG13). It was also supported by Research Project of State Key Laboratory of Mechanical System and Vibration (No. MSV201704). References [1] Qin Y, Brockett A, Ma Y, Razali A, Zhao J, Harrison C, Pan W, Dai X, Loziak D. Micro-manufacturing: research, technology outcomes and development issues. Int J Adv Manuf Technol 2010;47:821–37. [2] Razali AR, Qin Y. A Review on micro-manufacturing, micro-forming and their key issues. Procedia Eng 2013;53:665–72. [3] Geiger M, Kleiner M, Eckstein R, Tiesler N, Engel U. Microforming. CIRP Ann. 2001;50:445–62. [4] Vollertsen F, Schulze Niehoff H, Hu Z. State of the art in micro forming. Int J Mach Tools Manuf 2006;46:1172–9. [5] Engel U, Eckstein R. Microforming—from basic research to its realization. J Mater Process Technol 2002;125–126:35–44. [6] Fu MW, Chan WL. A review on the state-of-the-art microforming technologies. Int J Adv Manuf Tech 2013;67:2411–37. [7] Kim GY, Ni J, Koç M. Modeling of the size effects on the behavior of metals in microscale deformation processes. J Manuf Sci Eng 2007;129:470. [8] Mahabunphachai S, Koç M. Investigation of size effects on material behavior of thin sheet metals using hydraulic bulge testing at micro/meso-scales. Int J Mach Tools Manuf 2008;48:1014–29. [9] Lai X, Peng L, Hu P, Lan S, Ni J. Material behavior modelling in micro/meso-scale forming process with considering size/scale effects. Comput Mater Sci 2008;43:1003–9.
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Contents lists available at ScienceDirect
International Journal of Mechanical Sciences journal homepage: www.elsevier.com/locate/ijmecsci
An investigation on the formability of sheet metals in the micro/meso scale hydroforming process Zhutian Xu, Linfa Peng∗, Peiyun Yi, Xinmin Lai State Key Laboratory of Mechanical System and Vibration, Shanghai Jiao Tong University, Shanghai 200240, People’s Republic of China
a r t i c l e
i n f o
Keywords: Size effect Micro/meso scale Hydroforming Ductile fracture
a b s t r a c t The geometry and grain size effects have been revealed to affect the formability of metal materials during the micro/meso scale forming processes. To understand and characterize how these size effects influence practical forming process and further to utilize those knowledge in process design and optimization, an experimental and numerical investigation on a micro/meso scale hydroforming process of pure copper sheet metals was conducted as a case study. A hydroforming process experimental setup was first developed to form long multi-channel features with different dimensions. The experimental results reveal evident size effect: The pressure and maximum height onset of failure decrease as the grain size approaches the thickness. The size effect on the pressure was identified to be attribute to the reduction of flow stress of material as the grain size increases. The surface layer model has been employed to explain the mechanism. On the other hand, the decrease of ultimate height was revealed to be affected by the reduction of forming limit of sheet metals as the size effect becomes more significant. The interaction of geometry and grain sizes and the evolution of micro voids were discussed and a modified GTN–Thomason model with the consideration of grain size effect was employed in FE simulations to estimate the forming results. A reasonable agreement between the numerical and experimental results was observed. After that the method was further utilized in the process optimization for the fabrication of a fuel cell bipolar plate with typical micro/meso scale channel features. The dangerous area with a high risk of failure was predicted based on simulations. After optimizing the process parameters, the satisfying simulation result was obtained. Hence the hydroforming apparatus was developed accordingly and the bipolar plate was successfully fabricated with high quality, which verifies the applicability of the method in the present work.
1. Introduction With the increasing requirement of miniaturized products in various modern industrial applications such as electronic devices, micro reactors and fuel cells, micro/meso manufacturing processes aiming at the high accuracy and efficiency fabrication of these products are attracting the focus of researchers and engineers in the recent years [1, 2]. Among all the manufacturing techniques, micro/meso scale forming process is one of the most attractive methods due to its evident advantages of high productivity, low cost, near net shape, etc. [3, 4]. One important issue that must be addressed in the micro/meso scale forming process is the so-called size effect [3, 5]. The mechanism of size effect can be briefly summarized as follows [3, 5, 6]: During the miniaturization of forming process, some intrinsic dimensions of material such as the grain size and the surface roughness are not scaled down with the geometric dimensions. As the geometric dimensions approach those intrinsic ones, the overall material deformation response is affected by their interactions and differs from the results predicted
∗
Corresponding author. E-mail address: [email protected] (L. Peng).
by merely scaling down the traditional theories and models. In the recent two decades, the size effect has been widely explored from different perspectives. Among them, the size effect on the plastic deformation behavior, which is one of the most fundamental issues, has been the focus of researchers. One of the pioneering works was conducted by Geiger et al. [3] and Engel et al. [5] proposing the famous surface layer model. By dividing the deforming grains into surface and internal ones, the reduction of flow stress with forming scale is well-explained by considering that the proportion of the less-restricted surface grains increases as the grain size approaches the geometric dimensions. Based on the surface layer model, a lot of efforts were made by describing the constitutive behavior of material at micro/meso scale. Kim et al. [7] considered the effects of geometry and grain sizes by introducing the ratio between specimen/feature and grain sizes into the constitutive model. They also verified their model by comparing the analytical results to the experimental ones obtained by simple compression and tension tests. Mahabunphachai and Koc [8] investigated the micro hydroforming process of sheet metals by considering the size effect of flow stress. A quantitative model was further developed to capture the size effect. Lai et al. [9] also proposed a uniform size dependent constitutive model by describing the material with a scale factor. With the help
https://doi.org/10.1016/j.ijmecsci.2018.10.033 Received 18 June 2018; Received in revised form 15 October 2018; Accepted 16 October 2018 Available online 18 October 2018 0020-7403/© 2018 Elsevier Ltd. All rights reserved.
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of finite element (FE) tools, various micro forming processes were explored to investigate the influence of size effect on the flow stress. The experimental results were also compared with the FE results to verify the applicability [10, 11]. More recently, the mechanism of size effect in micro/meso scale forming processes is revealed more thoroughly by the comparison and analysis of both experimental and numerical results of the plastic deformation of crystal microstructures based on the crystalline plasticity theory. Wang et al. [12] developed a FE model of grain microstructures to investigate the flexible micro-bending process. The dislocation density is adopted to describe the flow stress of grain interior and grain boundaries quantitatively. The numerical results were found to agree with the experimental ones. Klusemann et al. [13] modeled the deformation behavior and grain orientation gradient development of a highly anisotropic thin sheet metal based on the single-crystal plasticity accounting for the dissipative hardening effect. Peng et al. [14] explored the grain orientation evolution during micro/meso scale forming process. By testing the samples before and after uniaxial tension with electron backscattered diffraction (EBSD) method, the variation of grain orientation was found to play an important role during the plastic deformation. Forming limit and failure prediction is another critical issue in the plastic forming scenario. Regarding the size effect on the failure behavior of ductile material in micro/meso scale forming process, much effort has been focused to explore both the phenomena and mechanism of failure along with the thorough investigations on the size effect of plastic deformation. Based on the bulging test of thin metal foils with the thickness from 500 to 25 𝜇m, Diehl et al. [15] revealed that the forming limit decreases with the thickness for the fine grain samples. In addition, Vollertsen et al. [16] also investigated the formability of aluminum foils by using the pneumatic bulge tests. They revealed that the strain-localization and fracture spot appears randomly in the dome as a result of the irregular material flow behavior affected by the crystalline microstructures as the forming scale decreases. Zhuang et al. [17] investigated the micro tube-hydroforming process both experimentally and numerically by employing a crystal plasticity model. They found that the co-effects of grain microstructure, crystal slip system and external load have a significant and complex impact on the localized necking of material. Regarding the volume microforming, Ran et al. [18, 19] studied the failure behavior in a flanged upsetting process of brass material. Based on the experiments, they revealed that the fracture in the flange surface is easier to form in macro scale flanged upsetting process. By conducting microstructural observations, they also found the dimple size at the transgranular surface is evidently affected by the size effect. In the previous researches of the present authors [20–22], the forming limits of copper sheet with different thicknesses and grain sizes were investigated experimentally. The forming limit curve (FLC) is revealed to shift down as the grain size approaches the thickness. The scatter of data is also found to increase with grain size. The applicability of several macro scale failure prediction theories were explored in micro/meso scale. A modified Gurson–Tvergaard–Needleman (GTN) model considering the as-observed geometry and grain size effects was also developed. As reviewed above, the size effects of plastic deformation and failure have been investigated a lot in recent years in the micro/meso scale forming scenario. However, a systematic research utilizing the existing models on a practical micro/meso scaled forming process to guide the process design and realization has seldom been reported. In the present work, the micro/meso scale hydroforming experimental apparatus was developed, based on which the constitutive and failure prediction models considering the size effects were first verified. After that, the process parameter design and optimization method were also developed based on the analytical models to achieve the fabrication of a protein exchanging membrane fuel cell (PEMFC) single polar plate prototype as a case study. This research could be helpful as an example for the development and process parameter design of practical micro/meso scale forming processes.
Table 1 The fitted results of Peng’s hybrid model [20]. Parameters
0.1 mm
0.2 mm
k1 n1 b k2 n2
162.58 0.75 47.60 20.0 0.10
142.19 0.64 17.24 12.9 0.24
2. Experimental analysis on the micro/meso scale hydrforming process 2.1. Sample preparation Sheet metals of Cu-FRHC with the thickness of 0.1 and 0.2 mm were employed as the testing material. To characterize the grain and geometry size effects on the formability in the micro/meso scale hydroforming process, the sheet metals were annealed at different temperatures to obtain different grain size conditions. The prepared samples in the present study are in accordance with those in our previous reports [20, 21]. The details of uniaxial tensile test setup, sample dimensions, heat treatments and true stress-true strain curves are summarized in Fig. 1. Peng’s hybrid model [23] was introduced to describe the grain and geometry sizes dependent hardening behavior. The model can be written as follows: ⎧𝜎̄ = 𝜎̄ 𝑖𝑛𝑑 + 𝜎̄ 𝑑𝑒𝑝 ⎪𝜎̄ 𝑖𝑛𝑑 = 𝑀 𝜏𝑅 (𝜀̄ ) + 𝑘√(𝜀̄) 𝑑 ⎪ ( ⎨ 𝜎 ̄ = 𝜂 𝑚 𝜏 𝜀 ̄ − 𝑀 𝜏𝑅 (𝜀̄ ) − ( ) 𝑅 ⎪ 𝑑𝑒𝑝 ⎪ 𝑑 ⎩𝜂 ≈ 𝑡
𝑘(𝜀̄ ) √ 𝑑
)
(1)
𝜎̄ 𝑖𝑛𝑑 and 𝜎̄ 𝑑𝑒𝑝 are the size independent and dependent parts of flow stress respectively. m and M can be assumed to be 2 and 3.06 respectively according to Peng et al. [23]. d and t are the average grain size and the thickness of sheet metal. 𝑘(𝜀̄ 𝑚 ) and 𝜏𝑅 (𝜀̄ 𝑚 ) were fitted to the following equations based on the least square method. The results are summarized in Table 1. { 𝑘(𝜀̄ ) = 𝑘1 (𝜀̄ )𝑛1 + 𝑏 (2) 𝜏𝑅 (𝜀̄ ) = 𝑘2 (𝜀̄ )𝑛2 Before test, the as-received sheet metals were first fabricated into round samples with the diameter of 60 mm by wire electric discharge machining (WEDM). The samples were then heat-treated by using the method shown in Fig. 1. After that they were employed in the hydroforming experiments. 2.2. Experimental setup To investigate the effects of both process parameters and material properties on the formability of samples during the micro/meso scale hydroforming process, the hydroforming apparatus shown in Fig. 2 was employed. The hydraulic pressure was provided by a Maximator high pressure oil pump (MHU-M111-G500-2-4500). Four dies with uniform channels of different dimensions were fabricated to test the samples as shown in Fig. 2. The dies were numbered from 1 to 4 with the reduction of channel width. The dies of No. 1, 2 and 3 were employed to test the formability of 0.2 mm samples while the ones of No. 2, 3 and 4 were used on 0.1 mm samples. This is because the channel width of die No. 4 (0.6 mm) is too small for 0.2 mm samples. It is difficult to form such small channels with 0.2 mm samples by using hydraulic pressure. On the other hand, the 0.1 mm sample could be hydroformed into the channels of die No. 1 easily attaching to the die surface closely. Hence it is also difficult to realize fracture of sample even at high hydraulic pressure. 266
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the samples formed against Die No. 1 is likely to exceed the measurable scope of the laser system. Therefore, a micrometer caliber with the accuracy of 10 𝜇m was used instead. The average height of the three channels in the center was recorded as the height onset of fracture. In addition, each hydroforming test was repeated three times to verify the repeatability of experiments. Since the focus of the present study lies on the exploration of the effect of process and size effect parameters on the failure behavior of sheet metals during the micro/meso scale hydroforming, the ultimate pressure and height of formed sample onset of failure were recorded. 2.3. Results and discussion The laser measurement results of the profile of the hydroformed samples onset of fracture are shown in Fig. 3. An evident reduction of limit height onset of failure with the increase of grain size can be observed under different geometric dimensions. This is in accordance with the observation made in the previous study [20] that the FLCs shift down with the increase of grain size. The deterioration of formability as the grain size approaches the geometric dimensions can be explained by incorporating the surface layer model with the ductile fracture theory. A brief illustration can be found in Fig. 4. It is well-accepted that the ductile fracture of metal is closely associated with the evolution of micro voids. In the beginning of plastic deformation, micro voids are generated at the defects of base material such as second phase particles, inclusions, grain boundaries, etc. As the deformation continues, the micro voids gradually grow until void coalescence occurs to form bigger cracks. The propagation and linkage of the cracks thus lead to the quick failure of material. At micro/meso scale, the grain size approaches to the geometric dimensions which lead to the significant size effect. The size effect has been well characterized by the surface layer model. According to this model, the metal material is regarded to be consisted of both surface and internal grains. The surface grains are less constrained due to their free surfaces. Hence the surface grains often perform close to single crystal during deformation. As a result, the deformation of surface grains is dependent on the grain orientation and other properties of individual grains. On the other hand, the deformation of internal grains is constrained by each other. Hence the overall behavior is more homogeneous. At micro/meso scale, the proportion of surface grains increases as the grain size approaches the geometric dimension. The overall deformation behavior of material is thus affected. Focusing on the ductile fracture behavior at micro/meso scale, the micro voids are mostly generated among the internal grains. This is because the rotation of surface grains could facilitate the motion of dislocations. The dislocations are thus less likely to localize at certain spots to form micro voids. In the micro/meso scale sheet metal forming progress, the internal layer becomes thinner as the grain size approaches the geometric dimensions. The void coalescence and crack linkage thus become easier. More importantly, the increase of grains size also leads to the easier strain localization. Hence the ductile fracture of sheet metal starts earlier and the formability of sheet metal decreases. In addition, when there is only one or two grains over the thickness, the various grain orientations and properties of individual grains could cause large uncertainty of forming limit. The maximum hydraulic pressure onset of failure was also recorded as shown in Fig. 5. It can be observed that the critical pressure decreases with the increase of grain size. This is mainly caused by the reduction of flow stress as revealed by the uniaxial tensile tests. According to the surface layer model, the surface grains are less restricted due to their free surfaces. Hence the rotation of grain orientation could facilitate the motion of dislocations, leading to the lower flow stress. As the grain size approaches the geometric dimensions, the surface layer takes a greater proportion. Therefore, the overall flow stress of material gradually decreases. Hence the lower deforming pressure was required during the
Fig. 1. True stress-true strain curves of sheet metals with different thicknesses and grain sizes after different heat treatments: (a) uniaxial tensile test setup; (b) 0.1 mm and (c) 0.2 mm samples results. The data were also analyzed by using the surface layer model to consider the grain size effect [20].
During the test, the samples were placed on top of the die and the die holder. The pieces were then clamped together by using eight thread bolts. After that the hydraulic pressure was applied at 0.2 MPa/s until the fracture of sample took place. Hence the limit height onset of fracture was measured by employing the KEYENCE KS-1100 laser measurement system with the resolution of 0.05 𝜇m. In addition, the height of 267
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Fig. 2. The hydroforming experimental setup.
hydroforming process. In addition, the limit height also decreases due to the deteriorated formability of samples as the increase of grain size. As a result, the ultimate pressure onset of failure decreases as the size effect becomes more evident.
A is the nucleation speed factor. d is the average grain size. t is the thickness of sheet metal. 𝜀̄ 𝑝𝑚 and 𝜀̄̇ 𝑝𝑚 are the equivalent plastic strain and strain rate respectively. 𝜀N and sN are the mean nucleation strain and the standard deviation of nucleation respectively. The growth of micro voids can be estimated by the modified GTN model:
3. Prediction and analysis of the failure behavior of micro/meso scale hydroforming process
( )2 ( ) ( ) ⎧ 𝑞 𝑝 ⎪Φ = 𝑞 + 2𝑞1 𝑓 ∗ cosh − 32 𝜎̄2 − 1 + 𝑞3 𝑓 ∗ 2 = 0 𝜎 ̄ 𝑚 ⎨ ( )𝑚 ( ) 𝑑𝑒𝑝 ( ) ⎪𝜎̄ 𝑚 𝜀̄ 𝑚 = 𝜎̄ 𝑚𝑖𝑛𝑑 𝜀̄ 𝑚 + 𝜎̄ 𝑚 𝜀̄ 𝑚 ⎩
According to the previous experimental investigations, it has been revealed that the deformation and failure behaviors of hydroformed sheet samples at micro/meso scale are affected by the size effect, which brings new challenges to the design and optimization of micro/meso scale hydroforming process. To obtained the robust design of process parameters to minimize the possibility of part failure during the forming process, a prior problem to be solved is finding a predictive model which could characterize the failure behavior of sheet metals affected by the size effects at micro/meso scale. In our previous study [22], M–K and GTN– Thomason models have been revealed to be accurate in describing the forming limit curves of sheet metals at different geometry and grain size conditions. In addition, a modified GTN–Thomason model considering the geometry and grain size effects was also developed [20]. In the following, both the modified GTN–Thomason and the M–K models were employed in predicting the failure behaviors of the samples subjected to uniform hydraulic pressure under different micro/meso scaled geometry and grain dimensions to verify their capability in the hydroforming process.
In Eq. (4), the GTN model was incorporated with the constitutive model developed by Peng et al. [24] √ to describe the geometry and grain size effects of flow stress. 𝑞 =
3 𝑆 𝑆 2 𝑖𝑗 𝑖𝑗
is the von Mises equivalent
1 𝜎 3 𝑘𝑘
stress, 𝑝 = is the hydrostatic stress, Sij = 𝜎 ij − p𝛿 ij is the deviatoric component of Cauchy stress, 𝛿 ij is the Kronecker delta, 𝜎̄ 𝑚 is the equivalent stress of the base material which is contributed by both the size independent part 𝜎̄ 𝑚𝑖𝑛𝑑 and the size dependent one 𝜎̄ 𝑚𝑑𝑒𝑝 . q1 , q2 and q3 are the coefficients introduced. f∗ is the effective void volume fraction which is defined as: { 𝑓 ) 𝑓 < 𝑓𝑐 𝑓 −𝑓 ( 𝑓∗ = (5) 𝑓𝑐 + 𝑓 𝑢 −𝑓𝑐 𝑓 − 𝑓𝑐 𝑓 ≥ 𝑓𝑐 𝑓
𝑐
f is the void volume fraction.fc is the void volume fraction onset of coalescence, which could be determined according to the modified Thomason model as following: ( ( ))1∕3 ⎧ 3 3 ⎪𝜒 = 2 𝑓 𝜆0 2 𝑒𝑧𝑧 ⎪ √ 4 (𝜀̄𝑝𝑚 −𝜀𝑁 ) ⎨ 2𝜋𝑠𝑁 ⎪𝜆0 = 𝐶𝑑 𝑒 4 √ (𝜀̄𝑝𝑚 −𝜀𝑁 ) ⎪ 1+𝑒 2𝜋𝑠𝑁 ⎩
3.1. Modeling process 3.1.1. Modified GTN–Thomason model The modified GTN–Thomason model is established by describing the nucleation, growth and coalescence of micro voids with the consideration of size effect. The nucleation model can be written as: ⎧𝑓̇ = 𝐴𝜀̄̇ 𝑝𝑚 ( ) ⎪ 𝑛𝑢𝑐𝑙𝑒𝑎𝑡𝑖𝑜𝑛 ( ( 𝑝 𝑑 )2 ) 1− 𝑡 𝑓𝑛 ⎨ 1 𝜀̄ 𝑚 −𝜀𝑁 ⎪𝐴 = 𝑠 √2𝜋 exp − 2 𝑠𝑁 𝑁 ⎩
(4)
(6)
In Eq. (6), 𝜒 is a geometric factor representing the possibility of internal necking. ezz is the major principal strain. 𝜆0 is a factor denoting the spatial distribution of micro voids. C is a material constant. The void coalescence starts as soon as 𝜒 reaches a critical value of 𝜒 c . The key parameters of fn , 𝜆0 and fu − fc were determined by finding the coincidence of simulation and experimental engineering strain-
(3)
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3.1.2. M–K model The M–K model assumes that a surface defect exists during the forming process of sheet metals. With the plastic deformation increases, the stress and strain gradually concentrate at the defect area which further lead to the final necking and failure. As a preliminary research, the von Mises yield criterion and the hardening behavior described by using Peng’s hybrid model of size effect as presented in Eqs. (1) and (2) were employed. The following equations can be obtained based on the M–K modeling process as reported in Ref. [22]: ⎧ 𝜀2 = 𝑑 𝜀2 = 𝜌 𝑑 𝜀1 ⎪ 𝜀1 2 √ √ ⎪𝜀̄ = 3𝜀1 𝜌2 + 𝜌 + 1 3 ⎪ 𝜎𝐵 ⎪𝜂 𝐵 = 2𝐵 = 2𝜌𝐵 +1 2+𝜌 𝜎1 ⎪ √𝐵 ( )2 ⎪ 𝐵 𝜎̄ 𝐵 𝐵 𝐵 ⎨𝜑 = 𝜎 𝐵 = 1 − 𝜂 + 𝜂 1 ⎪ 2𝜑𝐵 Δ𝜀̄ 𝐵 ⎪𝜙 = Δ𝜀𝐵 = 2−𝜂 𝐵 1 ⎪ √ 3 𝜌+1 ⎛ 𝐵 | Δ𝜀̄𝐵 ⎪ − 2 √ 𝜀̄ 𝐴 ⎞ 𝐵 𝜎 ̄ 𝜀 + −1− 𝜌 | ( ) 𝜌+2 𝐵 𝜌2 +𝜌+1 ⎟=0 ⎪√ 𝜎̄ 𝐴 − 𝜑𝐵 𝑓0 ⎜𝑒 3 |𝑡 𝜙 −𝑒 2 ⎜ ⎟ ⎪ 3(𝜌 +𝜌+1) ⎝ ⎠ ⎩
(7)
In Eq. (7), f0 is the initial defect ratio. 𝜀̄ , 𝜀1 and 𝜀2 are the Mises, major and minor in-plane principal strains respectively while 𝜎, ̄ 𝜎 1 and 𝜎 2 are the corresponding Mises, major and minor in-plane principal stresses respectively. The superscripts A and B represent the states of out of and inside the defect area respectively. By combining with the constitutive model developed by Peng et al. [24]., an iteration calculation program was then developed to calculate the FLCs at different temperature and strain rate conditions. By using different f0 , the variation of FLC under different geometry and grain size conditions was well captured. The details of model establishment and parameter determination can be found in Ref. [22]. By finding the coincidence of experimental and predicted FLC at the smaller grain size condition, the optimized value of f0 was obtained for the sheet metals with different thicknesses. The parameters of M–K model are summarized in Table 3. 3.2. Simulation and analysis In order to obtain the predicted failure results at different conditions, FE simulations were conducted by using the commercial code of ABAQUS. A VUMAT subroutine was developed based on the modified GTN–Thomason model and incorporated in the simulations. Meanwhile, ordinary ABAQUS/Explicit plastic deformation simulations for different conditions were also conducted, based on which the FLDs predicted by M–K model were incorporated to simulate the failure behavior during hydroforming. C3D8R elements were used for the deforming sample while R3D4 ones were employed for the die. The constant friction coefficient 0.15 was also set. The simulation results of the GTN–Thomason model onset of necking were shown in Fig. 6, in which the fields of effective void volume fraction f∗ (indicated by SDV3) and major principal strain were illustrated. It can be observed that the necking and failure position is at the radius area. In addition, the strain and f∗ distributions become more concentrated and localized at that area with the reduction of forming dimensions for both 0.1 and 0.2 mm-thick samples. A direct consequence is that ductile fracture is easier to initiate and the dome height onset of failure thus decreases, which is in accordance with the experimental results as reported in Section 2. Actually, this is because the thickness of sheet metal cannot be ignored as the forming scale decreases, especially when the geometric process parameters are in the same level with the thickness. In that case, the stress/strain distribution across the thickness direction can no longer be regarded as uniformly-distributed. As a result, many traditional methods developed based on the sheet metal, including the traditional FLD method, may not work well in the micro/meso scale forming scenario. Modifications of these methods need to be addressed to consider the geometric size effects before applying on the micro/meso scale forming processes. In the present work, FE tools
Fig. 3. Profile measurement of the hydroformed samples: (a) the profile of laser measurement results; (b) the average limit height of 0.2 mm samples and (c) the average limit height of 0.1 mm samples.
stress curves based on the analysis of a series of five-level orthogonal numerical experiments. The rest of parameters were identified based on previous researches. The parameters determination procedure has been reported in Ref. [20]. The parameters values are summarized in Table 2. The modified GTN–Thomason model was also incorporated into ABAQUS via VUMAT subroutine. 269
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Fig. 4. A brief illustration of the effects of grain and geometry sizes on the ductile fracture behavior during micro/meso scale sheet metal forming process.
were employed to predict the failure behavior to address this problem. On the one hand, the GTN–Thomason model was incorporated into the simulations to estimate the whole-field strain and void volume fraction distribution during the forming process. Hence the localized fracture can be estimated with the consideration of the geometric size effect. On the other hand, the localized major and minor strains of FE simulation were taken to compare with the forming limit predicted by the M–K model. With the increase of grain size, it can also be found that the ultimate pressure onset of necking decreases. This is mostly because the flow stress decreases due to the grain size effect. A clearer representation of this effect is summarized in Fig. 7 which illustrates the forming pressure vs. bulge height curves at different geometric and grain size conditions. FE simulations of the material with the grain size of 0.1 𝜇m were employed to estimate the conditions without the grain size effect. It can be observed that the height increases more rapidly with the increase of grain size. This is because the flow stress reduction was well-captured by the modified GTN–Thomason model. In addition, it can also be seen that the ultimate forming height decreases with the increase of grain size, which is in accordance with the experimental observation that the forming limit of sheet metal decreases with the increase of grain size. Hence the modified GTN–Thomason model can estimate the trend of formability deterioration as the geometry and grain size effects become more significant. Nevertheless, further quantitative compare of numerical and experimental results is still needed to verify the applicability of the failure prediction methods adopted. 3.3. Compare of numerical and experimental results The predicted ultimate height and pressure onset of failure are compared with the experimental results as shown in Fig. 8. In general, there is a good agreement between the experimental and the modified GTN–Thomason model results. With the increase of grain size, the model is able to capture the reduction of both the limit bulge height and ultimate forming pressure. This is because the interactive effects of geometry and grain sizes on the hardening behavior as well as the void evolution are considered in the modified GTN–Thomason model. The experimental results also verified the applicability of this model in the micro/meso scale hydroforming process. On the other hand, the M–K model tends to overestimate the limit height with the increase of grain size. This is because the same surface defect factor was used for different grain size conditions. Even though more accurate analytical results can be calculated by adjusting the surface defect factor,
Fig. 5. The ultimate pressure results of (a) 0.2 mm samples and (b) 0.1 mm samples onset of failure. 270
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Table 2 The parameters of the modified GTN–Thomason model [20].
0.1 mm 0.2 mm
𝜀N
sN
q1
q2
q3
𝜅
𝜒c
fn
C
ff − fc
0.25
0.1
1.5
1
2.25
1
0.9
0.0607 0.0516
0.445 0.607
0.115 0.125
Fig. 6. The FE simulation results onset of necking by using the modified GTN–Thomason model for the samples with the thickness of: (a) 0.2 mm and (b) 0.1 mm.
4. Application of micro/meso scale hydrforming process on the fabrication of PEMFC single polar plates
the mechanism of size effect on the ductile fracture behavior could not be well described with promising numerical method. Hence in the following, the modified GTN–Thomason model is applied in the case study of a hydroforming process of PEMFC bipoloar plates with typical micro/meso scale features to guide the process parameter design to avoid the fracture of sheet metal during the forming process.
The PEMFC single polar plate was designed as shown in Fig. 9(a). To realize its fabrication, the radius of edges is the most important geometric factor which determines the formability since the dimensions
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Fig. 7. The bulge height vs. pressure curves and the failure points under different grain sizes conditions in the hydroforming process: (a) Sheet metal with the thickness of 0.1 mm bulged into Channel No. 2; (b) Sheet metal with the thickness of 0.2 mm bulged into Channel No. 2; (c) Sheet metal with the thickness of 0.1 mm bulged into Channel No. 3; and (d) Sheet metal with the thickness of 0.2 mm bulged into Channel No. 3.
erty parameters for 0.1 mm sheet metals with the grain size of 27.5 𝜇m were employed during the calculation. The friction coefficient between the sheet metal and the die was set as 0.15. The strain and void volume fraction fields just before failure happens with the ultimate pressure of 28.76 MPa are shown in Fig. 10. As shown in Fig. 10, the void volume fraction and strain are extremely concentrated at the edges of features, especially at the corner areas as indicated. According to the measurement, the formed height in the channel area before failure was 0.253 mm, 64% of the designed height of 0.4 mm. The small radius in the initial case could be the direct reason. To find out the proper radius of edge, simulations with the radius of 0.15, 0.2 and 0.25 mm were then conducted and the results onset of failure are shown in Fig. 11. It can be observed that the maximum height formed with the radius of 0.15 mm was less than the designed height. With the increase of edge radius to 0.2 mm, the designed height was reached. However, it can be observed that the flat area formed at the bottom was limited. Much greater flat area can be obtained by further increasing the edge radius to 0.25 mm. The promising contact area could lead to easier assembly and better performance of bipolar plates. It should be noticed that the upper flat area of formed plate decreases evidently with the increase of edge radius. As a compromise, the edge radius of 0.25 mm was employed to obtain both the promising upper and bottom contact area. In addition, to avoid the failure behavior at the dangerous areas near the turning corners of channels as shown in Fig. 10, the corner radius was also in-
Table 3 The parameters of the M–K model [22].
0.2 mm 0.1 mm
Parameter
Value
𝑓0 𝑓0
0.973 0.986
of features (i.e., the width, height and length of channel features) have been determined during the design procedure. It should be noticed that the design of feature dimensions was estimated with the consideration of the previous discussion on the formable window of hydroforming process in the present work. By applying the radius as shown in Fig. 9(b), the trial 3D die CAD model was developed. As an initial case study, the low level of radius was expected which could lead to greater contact area. According to Qiu et al. [25], limited contact area could lead to easier mis-assembly of adjacent bipolar plates and may cause the leak of gas due to the less constrained sealing ring. Hence greater contact area with smaller edge radius is beneficial during the design of PEMFC bipolar plates. However, as revealed previously, the smaller radius could prevent the flow of material leading to the earlier fracture. Hence an optimized point satisfying both the requirements of PEMFC function and formability is the target. FE simulations were then conducted based on the VUMAT subroutine developed according to the modified GTN–Thomason model. The prop272
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Fig. 8. Compare of the experimental and analytical results: (a) The formed height results of sheet metals with the thickness of 0.1 mm; (b) The formed height results of sheet metals with the thickness of 0.2 mm; (c) The ultimate pressure results of sheet metals with the thickness of 0.1 mm; and (d) The ultimate pressure results of sheet metals with the thickness of 0.2 mm.
Fig. 9. Development of die profile: (a) The design of bipolar plate sample; (b) the developed die by using the initial parameters.
creased from 0.6 to 0.9 mm. The optimized 3D die geometry was then imported into ABAQUS for simulation. The results are shown in Fig. 12. The maximum pressure applied onset of failure was 47.5 MPa and it can be observed that the strain distribution is more uniform due to the improvement made on the initial parameters. Hence the necking moment could be postponed leading to the greater forming height. Accord-
ing to the observation, the maximum height was reached at the channel area. In addition, the flat area formed at the bottom of channel is large enough to support the bipolar plate during stack assembly. Hence the optimized parameters could satisfy both the functional and formability requirements.Based on the as-obtained parameters, the die prototype was fabricated as shown in Fig. 13(a). Verification hydroforming test 273
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Fig. 10. FE results onset of failure by using the initial geometry parameters.
Fig. 11. Determination of the edge radius by conducting simulations.
Fig. 12. FE results onset of failure after the modification of parameters.
of copper sheet metal with the thickness of 0.1 mm and the grain size of 27.5 𝜇m was then conducted. Successful forming of samples could be obtained by raising the hydraulic pressure to 45 MPa and maintained for 10 s. No fracture is found and the average height in the channel area is 0.394 mm. In addition, fracture of sheet metal occurred at higher pressure as shown in Fig. 13(b). As the pressure increases to 51 MPa, fracture of sample is observed at the corner area of gas inlet features. This observation is in agreement with the FE results that illustrates the dangerous area is at the corner of channel and the gas inlet features when
the pressure increases to 47.5 MPa. The profile in the center section of formed sample was also scanned by using the KS-1100 laser measurement system. The compare of experimental and FE results were shown in Fig. 14. It can be observed that the bottom of the outer channel is flat in the experimental profile which could be the proof that the sheet metal was in close contact with the die surface during hydroforming. Nevertheless, there is a slight difference between the FE and experimental profiles at the bottom of the channels in the middle. On the 274
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Fig. 13. The die and the formed sample of PEMFC single polar plate: (a) the fabricated die; (b) the hydroformed sample.
Fig. 14. Compare of FE and experimental section profiles in the center of formed sample.
5. Conclusions
one hand, this could be attributed to the springback behavior of sheet metals and measurement error. On the other, the damage model employed in the simulations could overestimate the formability. Hence the failure actually initiated at an earlier stage in the hydroforming experiments and the hydroformed channel height was lower than expected. Further investigation on the accurate failure prediction in micro/meso scale hydroforming process is still needed to address this problem. In addition, it should be mentioned that copper sheet metal is not a satisfying candidate for the application of PEMFC bipolar plates due to its weak anti-corrosion capability. In this study, the copper sheet metal was employed as a testing material for the verification of modeling method. Further study regarding the application of the modified GTN–Thomason model on stainless steels, Ti alloys, etc. which have been proved to be the suitable material for bipolar plates, should be conducted in the future to further verify the accuracy of the model. In addition, it should be mentioned that the present study is still a preliminary one which did not include the interacting effect of individual grains. That could be one of the major reasons for the error between the numerical and experimental results in the presented research. Further research regarding the deformation and ductile failure behaviors in the micro/meso scale forming process considering the polycrystalline microstructure and the interaction of individual grains should be conducted to explore the mechanism behind.
In this work, micro/meso scale hydroforming experiments of copper sheet metals with different thickness and grain sizes were conducted to investigate the geometry and grain size effects on the deformation and failure behaviors. A modified GTN–Thomason model was also employed to describe the size effect affected deformation and failure behaviors. In addition, a case study regarding the hydroforming process design of a PEMFC single polar plate prototype was also conducted based on the model. The following remarks could be obtained from this study: 1) According to the hydroforming experiments at different geometric and grain size conditions, the evident size effects are observed. The maximum forming height and the ultimate pressure are revealed to decrease as the grain size approaches the thickness of sheet metal. 2) The modified GTN–Thomason model by including the effects of geometry and grain sizes on the evolution of damage was employed to predict the maximum height and pressure onset of failure. The results are found to be in accordance with the experimental ones. 3) The model was employed in the process parameter design and optimization for the fabrication of a PEMFC single polar plate. Based on the failure prediction obtained by utilizing the modified GTN–Thomason model, the parameters were optimized and the 275
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successful fabrication of product was realized. In addition, the failure of sample at a higher forming pressure was also captured by this model, which verifies the applicability of the presented method.
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Acknowledgment This work was supported by the General Research Fund of National Natural Science Foundation of China (No. 51522506 and No. 51575465), National Key Research and Development Program of China (No. 2017YFB0103001) and “Shu Guang” project supported by Shanghai Municipal Education Commission and Shanghai Education Development Foundation (No. 17SG13). It was also supported by Research Project of State Key Laboratory of Mechanical System and Vibration (No. MSV201704). References [1] Qin Y, Brockett A, Ma Y, Razali A, Zhao J, Harrison C, Pan W, Dai X, Loziak D. Micro-manufacturing: research, technology outcomes and development issues. Int J Adv Manuf Technol 2010;47:821–37. [2] Razali AR, Qin Y. A Review on micro-manufacturing, micro-forming and their key issues. Procedia Eng 2013;53:665–72. [3] Geiger M, Kleiner M, Eckstein R, Tiesler N, Engel U. Microforming. CIRP Ann. 2001;50:445–62. [4] Vollertsen F, Schulze Niehoff H, Hu Z. State of the art in micro forming. Int J Mach Tools Manuf 2006;46:1172–9. [5] Engel U, Eckstein R. Microforming—from basic research to its realization. J Mater Process Technol 2002;125–126:35–44. [6] Fu MW, Chan WL. A review on the state-of-the-art microforming technologies. Int J Adv Manuf Tech 2013;67:2411–37. [7] Kim GY, Ni J, Koç M. Modeling of the size effects on the behavior of metals in microscale deformation processes. J Manuf Sci Eng 2007;129:470. [8] Mahabunphachai S, Koç M. Investigation of size effects on material behavior of thin sheet metals using hydraulic bulge testing at micro/meso-scales. Int J Mach Tools Manuf 2008;48:1014–29. [9] Lai X, Peng L, Hu P, Lan S, Ni J. Material behavior modelling in micro/meso-scale forming process with considering size/scale effects. Comput Mater Sci 2008;43:1003–9.
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