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Experimental and simulation based study on micro-scaled sheet metal deformation behavior in microembossing process
Materials Science & Engineering A 556 (2012) 60–67
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Materials Science & Engineering A journal homepage: www.elsevier.com/locate/msea
Experimental and simulation based study on micro-scaled sheet metal deformation behavior in microembossing process W.L. Chan, M.W. Fu n Department of Mechanical Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong
a r t i c l e i n f o
a b s t r a c t
Article history: Received 11 February 2012 Received in revised form 12 June 2012 Accepted 19 June 2012 Available online 28 June 2012
In microforming, the workpiece size is in microscale and has only a few grains involved in a deformation zone, leading to the deformation behaviors different from those in macroscale. The researches on micro-scaled plastic deformation behavior and microforming process are thus needed. In this research, the tensile test and the embossing of microchannels using pure copper foils with different grain sizes are conducted to investigate the material size effect on the flow stress, surface roughening and local deformation behavior. It is revealed that the surface roughness increases with strain and its change rate increases with grain size. This phenomenon results from the deformation incompatibility among grains with different properties in material surfaces. In addition, the size effect on the measurement of material properties in tensile test is analyzed based on the Monte Carlo simulation. It is found that the longer the gage length and the lesser the number of grains in the specimen section in tensile test, the higher the probability to have a significantly large fraction of soft grains in the section of specimen. The decrease of flow stress with the increase of grain size is partly caused by the decrease of Taylor factor, which leads to the underestimation of the averaged flow stress of the grains along the gage length. By using the flow stress curves obtained via tensile test to simulate the microembossing process, the simulation result shows an underestimation of the deformation load and the deviation tends to increase with the increase of grain size. This further validates the occurrence of size effect leading to the error of the measurement of material flow stress in tensile test. & 2012 Elsevier B.V. All rights reserved.
Keywords: Metal forming Size effect Plastic deformation Microembossing Taylor factor
1. Introduction Production miniaturization is an emerging global trend in many industrial clusters. Metallic microparts are becoming more and more important in practical applications due to their mechanical properties and thermal stability superior to those of polymeric microparts. Forming is a promising approach to fabricating metallic microparts for its advantages of high productivity, low production cost, good mechanical properties, stable dimensional accuracy, and the near-net- or net-shape characteristics [1]. The well-established tools for analysis of macro-scaled material deformation behavior have been widely used in metal forming industries [2–4]. When the part geometry size is decreased to microscale, however, the deformation behaviors of material change and the so-called size effect occurs [5–9], which has a close relationship with the anisotropic properties of grain and surface topography of forming material. The design and fabrication of microparts cannot rely on the knowledge of macro-scaled deformation behavior. The occurrence of size effect makes the
n
Corresponding author. Tel.: þ852 276 65 527. E-mail address: [email protected] (M.W. Fu).
0921-5093/$ - see front matter & 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.msea.2012.06.058
design and development of micropart difficult due to the lack of understanding of this phenomenon. To investigate the material size effect in microforming processes, some prior researches have been conducted. Messner et al. [10] examined the size effect via compression of cylinder and ring specimens. They found that the flow stress and frictional behavior are affected by size effect. Kals and Eckstein [11] studied the size effect on the sheet metal forming process. They revealed that the flow stress and the ductility decrease with miniaturization. Gau et al. [12] investigated the size effect based on the bending of thin foil. They observed that the amount of springback increases with the decreasing ratio of specimen thickness to grain size. Parasiz et al. [13] explored the size effect in the microextrusion process. They concluded that the location, size and orientation of individual grains affect the deformation behavior significantly when the grain size approaches to the formed part feature size. In addition, Krishnan et al. [14] revealed that the conventional material model in Finite Element (FE) simulation overestimates the deformation load in the microextrusion process. Kang et al. [15] investigated the micro-formability of Al5083 by using the microforging method. They identified that the micro-formability is closely related to the number of grains involved in the deformation process. Kim et al. [16] examined the material deformation
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behavior in the microcoining process. They found that the grain size and the geometry of preform affect the micro-sized feature formation on the specimen surface. Vollertsen and Hu [17] investigated the strip drawing process and developed a model to estimate the material size effect on tribology. Their model was then further validated in analysis of the micro deep drawing of rectangular part [18]. Based on the above review of prior arts, many researches have been conducted on various microforming processes. The investigation of size effect on the microembossing process, however, has not yet been extensively conducted. Only a few researchers tried the microembossing with the aid of rubber pad [19–21]. The deformation system which couples the rubber and metal deformations actually could affect the investigation of size effect on the deformation behavior in the microembossing process. In addition, most of the investigations of size effect on the flow stress of sheet metal are based on the tensile test of thin foils [22–26]. There is a lack of researches on evaluating the influence of size effect on the accuracy of measurement of the intrinsic material properties in
Fig. 1. Microstructures of the testing specimens. (a) 500 1C annealed, (b) 650 1C annealed and (c) 800 1C annealed.
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tensile test. Obtaining the intrinsic material properties is critical for modeling of the deformation behaviors in various microforming processes. In tandem with this, the embossing of micro-scaled channels with rigid dies and the tensile test of thin foils are conducted, and their micro-scaled deformation behaviors are investigated. The FE simulation of the microembossing process is further conducted and how the accuracy of the simulation affected by the size effect is also discussed.
2. Experiment In this research, the pure copper, which has an excellent formability and wide applications in microparts fabrication, is selected as the testing material. The specimens with the thickness of 100 mm were annealed in the chamber filled with argon gas. The annealing treatment using the temperatures of 500, 650 and 800 1C were conducted to obtain different grain sizes. Fig. 1 shows the obtained microstructures of the annealed specimens. It can be seen that the grain size increases with the increasing annealing temperature. The dog bone shaped specimens with a reduced section length of 36 mm and width of 7 mm were used in tensile test to obtain the flow stress curves. An extensometer with a gage length of 25 mm was used to measure the elongation of the testing specimens, while a 1 kN load cell was used to measure the deformation load. Tensile test was conducted using a slow strain rate of 0.002 s 1 and the specimens were deformed until fracture. The die assembly for microembossing and the detailed dimensions are shown in Fig. 2. The experiment of this study is to form three microchannels and the influence of neighboring material flow is considered. The punch and die are made of JIS SK3 tooling
Fig. 3. Microchannels on the die.
Fig. 2. Die assembly and the detailed tooling dimensions.
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incompatibility zone at the grain boundary, Chan et al. [33] investigated the flow stress of material with mixture models. It is found that the fraction of grain boundary increases with strain and the ratio of specimen size to grain size. The grain size increases with annealing temperature in this study. This decreases the number of grains over the specimen thickness and fraction of grain boundary in the material. It eventually leads to the decrease of flow stress as shown in Fig. 5. 3.2. Grain statistics Fig. 4. Microembossing platform.
320 280
Flow stress
240 200 160 Grain size
120
28 µm
80
46 µm 153 µm
40 0 0.0
0.1
0.2 Plastic strain
0.3
0.4
Fig. 5. Flow stress curves of specimens with various grain sizes.
steel which was heat-treated to obtain the hardness of 56–60 HRC. The microchannels on the tooling were fabricated via electrical-discharge wire cutting (wire EDM) by using the wire with the diameter of 100 mm. Fig. 3 shows the machined microchannels on the die. The testing platform is shown in Fig. 4. To minimize the friction in the process and facilitate the ejection of the deformed part, machine oil was applied at the tooling– workpiece interface. A slow compression speed of 0.005 mm/s was used in this research. The punch stroke was measured based on the crosshead movement by using a built-in displacement sensor.
3. Results and discussion 3.1. Grain boundary strengthening Flow stress actually determines the material flow behavior in the forming process, which can be observed based on the amount of upward and downward material flows in the extrusion process using materials with different flow stresses [27]. Fig. 5 shows the flow stress curves obtained via tensile test in this study. It can be seen that the flow stress decreases with the increase of grain size. This phenomenon can be explained based on grain boundary strengthening effect. The grain boundary plays a significant role on the material strength in microforming process [28,29]. The most well-known empirical equation to model the grain boundary strengthening effect is Hall–Petch relation [30,31]. Attention has been paid to the properties and deformation mechanisms at grain boundary and grain interior for a long time. It is found that the hardness at grain boundary is higher than that of grain interior [32]. Based on the assumption that there is a microscopic
Apart from the grain boundary strengthening effect, the grain orientation also affects the flow stress in tensile test. The grain deformation is accomplished by slip movement. Sachs [34] assumed that all the grains in polycrystal are deformed by slip on a single slip system. However, this hypothesis neglects the strain compatibility at grain boundary, leading to the material separation at grain boundary. Taylor [35] suggested that each grain undergoes the same homogeneous strain in the case that at least five independent slip systems are activated. He predicted the grain orientation factor (Taylor factor), which relates macroscopic tension stress (s) and shear stress (t), has a value of 3.06 for random FCC polycrystal. This is in contrast to the value of 2.24 predicted by Sachs. Pure copper has an FCC crystal structure with 12 slip systems {111} /110S. In the case that the grain is subject to uniaxial loading, the work increment (dw) by the slips in all the activated slip systems within a grain is X dw ¼ tc 9dgn 9 ¼ sx dex ð1Þ n
where the critical resolved shear stress (tc) is the same in all the slip systems and dgn is the incremental slip in the nth slip system. The Taylor factor (m) which depends on the grain orientation is given by P 9dgn 9 sx ¼ n ð2Þ m¼ tc dex The Taylor factor can be represented in terms of von Misses stress (sv) and strain (ev) in the multiaxial stress state P 9dgn 9 sv dw s : de ¼ n ¼ ¼ ð3Þ m¼ tc tc dev tc dev dev The averaged Taylor factor is commonly used to represent the ratio of the macroscopic flow stress to the critical resolved shear stress for polycrystalline materials. This is based on the assumption that the soft grains cannot deform unless the hard grains deform simultaneously and the shape change performs in the way of minimizing energy expenditure, i.e., min{dw}¼ tc[min P { n 9dgn 9}]. In the tensile test, plastic deformation begins when the local yield stress is reached. The testing specimen can be considered as a chain illustrated in Fig. 6. Each specimen section perpendicular to the loading direction acts as a link member. The section of specimen yields when all the grains in that section yield. The initial yielding occurs at the weakest section [36]. The yield stress of the jth section is X X sj ¼ sG,i ai,j ¼ tc mi ai,j ¼ tc mAvg,j ð4Þ i
i
where sG,i, ai,j and mi are the yield stress, area fraction and Taylor factor of the ith grain in the jth section, respectively. mAvg,j is the averaged Taylor factor in the jth section. The force applied in the jth section is F j ¼ sj Aj ¼ tc mAvg,j Aj
ð5Þ
where Aj is the jth section area. The weakest section should be the one with min{mAvg,jAj}. In the testing specimen, the grains with the favorable orientation to deform along the loading direction
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3.00
Taylor factor
2.95 2.90 2.85 Gauge length : Width (l:w)
1:2 1:1 2:1
2.80 2.75
102 103 104 Number of grains in specimen section Fig. 7. Change of minimum Taylor factor (min{mAvg,j}) in the tensile testing specimen.
Fig. 6. Schematic illustration of yielding at the weakest section in the tensile testing specimen.
could be considered as a soft portion, while other grains with the unfavorable orientation are considered as a hard portion. Minimization of plastic work can be achieved by selecting the specimen section with the smallest yield stress. Based on the above analysis, the Monte Carlo simulation is conducted to study the grain and specimen size effects on the material yielding behavior. To simplify the model, it is assumed that the grain geometry in the specimen can be represented as a cubic and the cross-section area is the same in each section. Therefore, it is not necessary to consider different area fractions of different grains in each section and the weakest section is the one with the lowest averaged Taylor factor (min{mAvg,j}). The Taylor factors of the grains ranging from 2.3 to 3.7 [37] are given by a random number generator to model the random characteristic of grain properties. 50 samples are modeled for each case with a specified number of grains in the specimen section and the ratio of gage length to specimen width. The change of min{mAvg,j} with different numbers of grains in the specimen section and different gage lengths is simulated and the mean values are presented in Fig. 7. It can be seen that the min{mAvg,j} decreases with the decreasing number of grains in the specimen section. It has a good correlation to the experimental result on the change of flow stress with the change of grain size in this study. In addition, the min{mAvg,j} increases with the decrease of gage length that has a good agreement with the experimental results reported in prior studies [38,39] that the hardening rate and tensile strength increase with the increase of specimen thickness and the decrease of gage length. The result of simulation implies that the longer the gage length, the smaller the number of grains in the specimen section, the higher the probability to have a section with a significantly large fraction of soft grains, as illustrated in Fig. 8. This could be attributed to the fact that the distribution of different grains becomes nonuniform when there are only a few grains constituting the specimen. Significant large deformation could concentrate at the soft grains.
Fig. 8. Grain and specimen size effects on the distribution of different grains.
This further leads to the small fracture strain in the tensile test, which can be observed in Fig. 5. 3.3. Surface roughening The surface finish of the micro-formed part could be critical to its functional performance. The poor surface quality of the microformed bipolar plates could result in a high contact resistance and a low corrosion resistance [40]. Surface roughness on the deformed specimen is thus examined in this study. Fig. 9 shows the surface texture of the micro-embossed parts. It can be seen that the surface roughness increases with the grain size. Since the size of embossed channel is small and the profile is curved, it is difficult to measure its surface roughness. The surface roughness of the elongated copper foils with different strains is thus measured to quantify the size effect on the surface deformation behavior as shown in Fig. 10. It can be seen that the surface roughness increases with strain and the change rate increases with the grain size. This result has a good agreement with the ones reported in prior studies [41,42]. Chandrasekaran and Nygards [41] studied the surface deformation behavior by atomic force microscopy (AFM) and electron backscatter diffraction (EBSD). It is found that the surface roughness and the misorientation increase linearly with strain. Furthermore, Wouters et al. [42] investigated the surface roughening behavior based on the white light confocal microscopy. They found that the surface roughening effect could be affected by grain size. The phenomenon
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Fig. 9. Embossed microchannels with different grain sizes. (a) 28 mm, (b) 46 mm and (c) 153 mm.
embossed part. Therefore, the thicknesses of the embossed microchannels are measured as shown in Fig. 12. From the figure, it can be seen that the significant thinning occurs at the corner region of the microchannel. The thinning behavior is associated with the tensile force applied at the corner and the friction that prohibits material flow, resulting in the occurrence of the localized strain.
2.4 Surface roughness - Ra (µm)
Grain size 2.0
28 µm 46 µm
1.6
153 µm
1.2 3.5. Simulation
0.8 0.4 0.0 0.00
0.05
0.10 Plstic strain
0.15
0.20
Fig. 10. Change of the surface roughness with strain.
results from the deformation incompatibility among grains with different properties in material surface. In the material surface, soft grains could undergo a larger deformation than the hard grain does. The less constrained grains could move normal to the surface, resulting in the occurrence of surface roughening. Based on the experimental results of this research, it can be seen that the roughening effect becomes much obvious when the grain size approaches to the formed part feature size in microforming process. Such kind of size effect could decrease the formability by triggering the strain instability and localized necking [43]. 3.4. Thickness variation Fig. 11 shows the microstructures of the embossed microchannels, it is revealed that the inhomogeneous deformation occurs with the increase of grain size. It is due to the fact that when there are only a few grains constituting the deformation zone, the deforming material cannot be considered as continuum due to the strong anisotropic properties of grains. It makes the embossed channel asymmetric. During the microembossing process, the thickness of the foil changes, which is critical to the formation of cracking defect and the structural rigidity of the
The FE simulation of the microembossing process with different friction coefficients (m) is conducted. The flow stress curves obtained from tensile test are used as the material model in simulation. However, the flow stress curves obtained by tensile test can only have a small true strain due to the necking occurrence, especially in the case with a small ratio of specimen size to grain size. The flow stress curve with a large true strain is needed for analysis of the large plastic deformation in most metal forming processes. Therefore, the flow stress curves obtained in this study are formulated based on the saturation model:
s ¼ sy þ Q ð1expðbeÞÞ
ð6Þ
where sy is the initial yield stress, Q is the saturation stress and b is the change rate of flow stress. Based on the tensile test results, it does not show any obvious trend about the change of initial yield stress (sy) with the change of grain size. Therefore, a mean value of 45 MPa is used for the three curve fitting cases. The fitted curves are shown in Fig. 13. The simulation is conducted using the commercial CAE system, Abaqus. The forming tools are modeled as rigid bodies while the forming material as an elastic–plastic body. The 4-node bilinear plane stress quadrilateral element is used in meshing of the deformation body. It is found that the simulated variation of the thickness with the friction coefficient of 0.3 qualitatively agrees with the experimental values as shown in Fig. 14, but the grain size effect is not as obvious as the one in the experiment. This result can be explained based on the fact that there are only a few grains over the thickness of the specimens in the three case studies, as shown Figs. 1 and 11. This leads to the fact of the individual grain properties becoming dominant and the occurrence of inhomogeneous deformation, which further makes the thickness of formed microchannel uneven. The conventional FE simulation does not take such kind of size effect into account.
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Fig. 11. Microstructures of the embossed microchannels with different grain sizes. (a) 28 mm, (b) 46 mm and (c) 153 mm.
Grain size (Simulation) 28 µm,
Grain size 28 µm 46 µm
a
e
f
d b 0
100
200
g
c 300 400 500 Distance (µm)
Thickness (µm)
Thickness (µm)
153 µm 100 90 80 70 60
600
46 µm,
153 µm
46 µm,
153 µm
Grain size (Experiment)
700
28 µm,
110 100 90 80 70 60
µ = 0.3
0 800
Fig. 12. Thickness distribution of the embossed microchannels.
Fig. 13. The fitted models of flow stress curves.
This could result in the discrepancy between the experimental and simulation results. The simulated forming stages and the stress distribution are shown in Fig. 15. When the punch moves down, the outside material is bent, and then drawn into to the die cavity. The inner material is pushed downwards and the tension force is applied at the corner region. The interfacial friction resists the material flow and further accelerates the material thinning. The high interfacial friction could attribute to the fact that the tooling–workpiece interface at the micro-sized deformation zone might not hold the lubricant efficiently [44]. Furthermore, the asperity size of the tooling is determined by the machining method and its
100
200
300 400 500 Distance (µm)
600
700
800
Fig. 14. The simulated thickness distribution.
parameters. Fig. 16 shows the surface topography of microembossing tooling which was machined by wire EDM. Since the asperity size is independent of the forming system size, the ratio of the specimen size to the asperity size decreases with the decrease of specimen size. The decrease of both the lubricant efficiency and the ratio of specimen size to asperity size leads to the increase of tooling–workpiece interfacial friction. Fig. 17 shows the comparison of deformation load. It can be seen that the simulated results underestimate the deformation load and the deviation tends to increase with the grain size. This could attribute to the fact that a significantly large deformation of specimen in tensile test is localized at the region where most grains are favorable to deform in tensile direction as explained in the previous section. This further leads to the underestimation of the averaged flow stress of the grains along the gage length. The influence of such grain statistics effect is much significant with the increase of grain size based on the change of Taylor factor presented in Fig. 7. In microembossing, the tooling presses on a large number of grains simultaneously which are different from the case in tensile test. The soft grain would not deform unless the hard grain deforms. The effect of grain statistics is less significant in such case. Therefore, the underestimation of the deformation load could happen when using the flow stress curve obtained from tensile test to simulate the microembossing process.
4. Conclusions In this research, the embossing of microchannels is conducted to study the microscale deformation behavior of sheet metal. It is
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Fig. 15. The simulated forming stage and stress distribution.
Fig. 16. Surface topography of the wire EDM machined microembossing tooling.
450 Grain size (Experiment) 28 µm 46 µm 153 µm
400 350 Load (N)
300 250 200
Grain size (Simulation) 28 µm 46 µm 153 µm
150 100 50 0 0
50
100 150 Stroke (µm)
200
different properties in material surfaces. In addition, a significant thinning occurs at the corner regions of the formed microchannel. The thinning behavior is associated with the tensile force applied at the corner and the friction that prohibits material flow, resulting in occurrence of localized strain. The tensile test specimen can be considered as a chain and each specimen section perpendicular to the loading direction acts as a link member. The section of material yields when all the grains in that section yield and the initial yielding occurs at the weakest section. It is shown that the longer gage length and the smaller number of grains in the section, the higher probability to have a section of specimen with a significantly large fraction of soft grains. Therefore, there is an interactive effect of the grain and specimen sizes on the material deformation behavior in tensile test. The decrease of flow stress with the increase of grain size could be caused by the decrease of both the Taylor factor and the grain boundary strengthening effect. By using the flow stress curves obtained from tensile test to simulate the microembossing process, the simulation underestimates the deformation load and the deviation tends to increase with the grain size. This could be attributed to the nonuniform deformation along the gage length in tensile test, which results in a significantly large strain localized at the region where most grains are favorable to deform in tensile direction. This further leads to small fracture strain and underestimation of the averaged flow stress of the grains along the gage length.
Acknowledgments The authors would like to thank the funding support to this research from the Innovation Technology Commission of Hong Kong government under the project of ITS 313/09 and the projects of G-U923 and A-PJ29 from The Hong Kong Polytechnic University.
250
Fig. 17. Comparison of the experimental and simulation results of the deformation load in microembossing process.
found that the surface roughness increases with strain and the variation rate increases with the grain size. The phenomenon results from the deformation incompatibility among grains with
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Contents lists available at SciVerse ScienceDirect
Materials Science & Engineering A journal homepage: www.elsevier.com/locate/msea
Experimental and simulation based study on micro-scaled sheet metal deformation behavior in microembossing process W.L. Chan, M.W. Fu n Department of Mechanical Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong
a r t i c l e i n f o
a b s t r a c t
Article history: Received 11 February 2012 Received in revised form 12 June 2012 Accepted 19 June 2012 Available online 28 June 2012
In microforming, the workpiece size is in microscale and has only a few grains involved in a deformation zone, leading to the deformation behaviors different from those in macroscale. The researches on micro-scaled plastic deformation behavior and microforming process are thus needed. In this research, the tensile test and the embossing of microchannels using pure copper foils with different grain sizes are conducted to investigate the material size effect on the flow stress, surface roughening and local deformation behavior. It is revealed that the surface roughness increases with strain and its change rate increases with grain size. This phenomenon results from the deformation incompatibility among grains with different properties in material surfaces. In addition, the size effect on the measurement of material properties in tensile test is analyzed based on the Monte Carlo simulation. It is found that the longer the gage length and the lesser the number of grains in the specimen section in tensile test, the higher the probability to have a significantly large fraction of soft grains in the section of specimen. The decrease of flow stress with the increase of grain size is partly caused by the decrease of Taylor factor, which leads to the underestimation of the averaged flow stress of the grains along the gage length. By using the flow stress curves obtained via tensile test to simulate the microembossing process, the simulation result shows an underestimation of the deformation load and the deviation tends to increase with the increase of grain size. This further validates the occurrence of size effect leading to the error of the measurement of material flow stress in tensile test. & 2012 Elsevier B.V. All rights reserved.
Keywords: Metal forming Size effect Plastic deformation Microembossing Taylor factor
1. Introduction Production miniaturization is an emerging global trend in many industrial clusters. Metallic microparts are becoming more and more important in practical applications due to their mechanical properties and thermal stability superior to those of polymeric microparts. Forming is a promising approach to fabricating metallic microparts for its advantages of high productivity, low production cost, good mechanical properties, stable dimensional accuracy, and the near-net- or net-shape characteristics [1]. The well-established tools for analysis of macro-scaled material deformation behavior have been widely used in metal forming industries [2–4]. When the part geometry size is decreased to microscale, however, the deformation behaviors of material change and the so-called size effect occurs [5–9], which has a close relationship with the anisotropic properties of grain and surface topography of forming material. The design and fabrication of microparts cannot rely on the knowledge of macro-scaled deformation behavior. The occurrence of size effect makes the
n
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design and development of micropart difficult due to the lack of understanding of this phenomenon. To investigate the material size effect in microforming processes, some prior researches have been conducted. Messner et al. [10] examined the size effect via compression of cylinder and ring specimens. They found that the flow stress and frictional behavior are affected by size effect. Kals and Eckstein [11] studied the size effect on the sheet metal forming process. They revealed that the flow stress and the ductility decrease with miniaturization. Gau et al. [12] investigated the size effect based on the bending of thin foil. They observed that the amount of springback increases with the decreasing ratio of specimen thickness to grain size. Parasiz et al. [13] explored the size effect in the microextrusion process. They concluded that the location, size and orientation of individual grains affect the deformation behavior significantly when the grain size approaches to the formed part feature size. In addition, Krishnan et al. [14] revealed that the conventional material model in Finite Element (FE) simulation overestimates the deformation load in the microextrusion process. Kang et al. [15] investigated the micro-formability of Al5083 by using the microforging method. They identified that the micro-formability is closely related to the number of grains involved in the deformation process. Kim et al. [16] examined the material deformation
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behavior in the microcoining process. They found that the grain size and the geometry of preform affect the micro-sized feature formation on the specimen surface. Vollertsen and Hu [17] investigated the strip drawing process and developed a model to estimate the material size effect on tribology. Their model was then further validated in analysis of the micro deep drawing of rectangular part [18]. Based on the above review of prior arts, many researches have been conducted on various microforming processes. The investigation of size effect on the microembossing process, however, has not yet been extensively conducted. Only a few researchers tried the microembossing with the aid of rubber pad [19–21]. The deformation system which couples the rubber and metal deformations actually could affect the investigation of size effect on the deformation behavior in the microembossing process. In addition, most of the investigations of size effect on the flow stress of sheet metal are based on the tensile test of thin foils [22–26]. There is a lack of researches on evaluating the influence of size effect on the accuracy of measurement of the intrinsic material properties in
Fig. 1. Microstructures of the testing specimens. (a) 500 1C annealed, (b) 650 1C annealed and (c) 800 1C annealed.
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tensile test. Obtaining the intrinsic material properties is critical for modeling of the deformation behaviors in various microforming processes. In tandem with this, the embossing of micro-scaled channels with rigid dies and the tensile test of thin foils are conducted, and their micro-scaled deformation behaviors are investigated. The FE simulation of the microembossing process is further conducted and how the accuracy of the simulation affected by the size effect is also discussed.
2. Experiment In this research, the pure copper, which has an excellent formability and wide applications in microparts fabrication, is selected as the testing material. The specimens with the thickness of 100 mm were annealed in the chamber filled with argon gas. The annealing treatment using the temperatures of 500, 650 and 800 1C were conducted to obtain different grain sizes. Fig. 1 shows the obtained microstructures of the annealed specimens. It can be seen that the grain size increases with the increasing annealing temperature. The dog bone shaped specimens with a reduced section length of 36 mm and width of 7 mm were used in tensile test to obtain the flow stress curves. An extensometer with a gage length of 25 mm was used to measure the elongation of the testing specimens, while a 1 kN load cell was used to measure the deformation load. Tensile test was conducted using a slow strain rate of 0.002 s 1 and the specimens were deformed until fracture. The die assembly for microembossing and the detailed dimensions are shown in Fig. 2. The experiment of this study is to form three microchannels and the influence of neighboring material flow is considered. The punch and die are made of JIS SK3 tooling
Fig. 3. Microchannels on the die.
Fig. 2. Die assembly and the detailed tooling dimensions.
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incompatibility zone at the grain boundary, Chan et al. [33] investigated the flow stress of material with mixture models. It is found that the fraction of grain boundary increases with strain and the ratio of specimen size to grain size. The grain size increases with annealing temperature in this study. This decreases the number of grains over the specimen thickness and fraction of grain boundary in the material. It eventually leads to the decrease of flow stress as shown in Fig. 5. 3.2. Grain statistics Fig. 4. Microembossing platform.
320 280
Flow stress
240 200 160 Grain size
120
28 µm
80
46 µm 153 µm
40 0 0.0
0.1
0.2 Plastic strain
0.3
0.4
Fig. 5. Flow stress curves of specimens with various grain sizes.
steel which was heat-treated to obtain the hardness of 56–60 HRC. The microchannels on the tooling were fabricated via electrical-discharge wire cutting (wire EDM) by using the wire with the diameter of 100 mm. Fig. 3 shows the machined microchannels on the die. The testing platform is shown in Fig. 4. To minimize the friction in the process and facilitate the ejection of the deformed part, machine oil was applied at the tooling– workpiece interface. A slow compression speed of 0.005 mm/s was used in this research. The punch stroke was measured based on the crosshead movement by using a built-in displacement sensor.
3. Results and discussion 3.1. Grain boundary strengthening Flow stress actually determines the material flow behavior in the forming process, which can be observed based on the amount of upward and downward material flows in the extrusion process using materials with different flow stresses [27]. Fig. 5 shows the flow stress curves obtained via tensile test in this study. It can be seen that the flow stress decreases with the increase of grain size. This phenomenon can be explained based on grain boundary strengthening effect. The grain boundary plays a significant role on the material strength in microforming process [28,29]. The most well-known empirical equation to model the grain boundary strengthening effect is Hall–Petch relation [30,31]. Attention has been paid to the properties and deformation mechanisms at grain boundary and grain interior for a long time. It is found that the hardness at grain boundary is higher than that of grain interior [32]. Based on the assumption that there is a microscopic
Apart from the grain boundary strengthening effect, the grain orientation also affects the flow stress in tensile test. The grain deformation is accomplished by slip movement. Sachs [34] assumed that all the grains in polycrystal are deformed by slip on a single slip system. However, this hypothesis neglects the strain compatibility at grain boundary, leading to the material separation at grain boundary. Taylor [35] suggested that each grain undergoes the same homogeneous strain in the case that at least five independent slip systems are activated. He predicted the grain orientation factor (Taylor factor), which relates macroscopic tension stress (s) and shear stress (t), has a value of 3.06 for random FCC polycrystal. This is in contrast to the value of 2.24 predicted by Sachs. Pure copper has an FCC crystal structure with 12 slip systems {111} /110S. In the case that the grain is subject to uniaxial loading, the work increment (dw) by the slips in all the activated slip systems within a grain is X dw ¼ tc 9dgn 9 ¼ sx dex ð1Þ n
where the critical resolved shear stress (tc) is the same in all the slip systems and dgn is the incremental slip in the nth slip system. The Taylor factor (m) which depends on the grain orientation is given by P 9dgn 9 sx ¼ n ð2Þ m¼ tc dex The Taylor factor can be represented in terms of von Misses stress (sv) and strain (ev) in the multiaxial stress state P 9dgn 9 sv dw s : de ¼ n ¼ ¼ ð3Þ m¼ tc tc dev tc dev dev The averaged Taylor factor is commonly used to represent the ratio of the macroscopic flow stress to the critical resolved shear stress for polycrystalline materials. This is based on the assumption that the soft grains cannot deform unless the hard grains deform simultaneously and the shape change performs in the way of minimizing energy expenditure, i.e., min{dw}¼ tc[min P { n 9dgn 9}]. In the tensile test, plastic deformation begins when the local yield stress is reached. The testing specimen can be considered as a chain illustrated in Fig. 6. Each specimen section perpendicular to the loading direction acts as a link member. The section of specimen yields when all the grains in that section yield. The initial yielding occurs at the weakest section [36]. The yield stress of the jth section is X X sj ¼ sG,i ai,j ¼ tc mi ai,j ¼ tc mAvg,j ð4Þ i
i
where sG,i, ai,j and mi are the yield stress, area fraction and Taylor factor of the ith grain in the jth section, respectively. mAvg,j is the averaged Taylor factor in the jth section. The force applied in the jth section is F j ¼ sj Aj ¼ tc mAvg,j Aj
ð5Þ
where Aj is the jth section area. The weakest section should be the one with min{mAvg,jAj}. In the testing specimen, the grains with the favorable orientation to deform along the loading direction
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3.00
Taylor factor
2.95 2.90 2.85 Gauge length : Width (l:w)
1:2 1:1 2:1
2.80 2.75
102 103 104 Number of grains in specimen section Fig. 7. Change of minimum Taylor factor (min{mAvg,j}) in the tensile testing specimen.
Fig. 6. Schematic illustration of yielding at the weakest section in the tensile testing specimen.
could be considered as a soft portion, while other grains with the unfavorable orientation are considered as a hard portion. Minimization of plastic work can be achieved by selecting the specimen section with the smallest yield stress. Based on the above analysis, the Monte Carlo simulation is conducted to study the grain and specimen size effects on the material yielding behavior. To simplify the model, it is assumed that the grain geometry in the specimen can be represented as a cubic and the cross-section area is the same in each section. Therefore, it is not necessary to consider different area fractions of different grains in each section and the weakest section is the one with the lowest averaged Taylor factor (min{mAvg,j}). The Taylor factors of the grains ranging from 2.3 to 3.7 [37] are given by a random number generator to model the random characteristic of grain properties. 50 samples are modeled for each case with a specified number of grains in the specimen section and the ratio of gage length to specimen width. The change of min{mAvg,j} with different numbers of grains in the specimen section and different gage lengths is simulated and the mean values are presented in Fig. 7. It can be seen that the min{mAvg,j} decreases with the decreasing number of grains in the specimen section. It has a good correlation to the experimental result on the change of flow stress with the change of grain size in this study. In addition, the min{mAvg,j} increases with the decrease of gage length that has a good agreement with the experimental results reported in prior studies [38,39] that the hardening rate and tensile strength increase with the increase of specimen thickness and the decrease of gage length. The result of simulation implies that the longer the gage length, the smaller the number of grains in the specimen section, the higher the probability to have a section with a significantly large fraction of soft grains, as illustrated in Fig. 8. This could be attributed to the fact that the distribution of different grains becomes nonuniform when there are only a few grains constituting the specimen. Significant large deformation could concentrate at the soft grains.
Fig. 8. Grain and specimen size effects on the distribution of different grains.
This further leads to the small fracture strain in the tensile test, which can be observed in Fig. 5. 3.3. Surface roughening The surface finish of the micro-formed part could be critical to its functional performance. The poor surface quality of the microformed bipolar plates could result in a high contact resistance and a low corrosion resistance [40]. Surface roughness on the deformed specimen is thus examined in this study. Fig. 9 shows the surface texture of the micro-embossed parts. It can be seen that the surface roughness increases with the grain size. Since the size of embossed channel is small and the profile is curved, it is difficult to measure its surface roughness. The surface roughness of the elongated copper foils with different strains is thus measured to quantify the size effect on the surface deformation behavior as shown in Fig. 10. It can be seen that the surface roughness increases with strain and the change rate increases with the grain size. This result has a good agreement with the ones reported in prior studies [41,42]. Chandrasekaran and Nygards [41] studied the surface deformation behavior by atomic force microscopy (AFM) and electron backscatter diffraction (EBSD). It is found that the surface roughness and the misorientation increase linearly with strain. Furthermore, Wouters et al. [42] investigated the surface roughening behavior based on the white light confocal microscopy. They found that the surface roughening effect could be affected by grain size. The phenomenon
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Fig. 9. Embossed microchannels with different grain sizes. (a) 28 mm, (b) 46 mm and (c) 153 mm.
embossed part. Therefore, the thicknesses of the embossed microchannels are measured as shown in Fig. 12. From the figure, it can be seen that the significant thinning occurs at the corner region of the microchannel. The thinning behavior is associated with the tensile force applied at the corner and the friction that prohibits material flow, resulting in the occurrence of the localized strain.
2.4 Surface roughness - Ra (µm)
Grain size 2.0
28 µm 46 µm
1.6
153 µm
1.2 3.5. Simulation
0.8 0.4 0.0 0.00
0.05
0.10 Plstic strain
0.15
0.20
Fig. 10. Change of the surface roughness with strain.
results from the deformation incompatibility among grains with different properties in material surface. In the material surface, soft grains could undergo a larger deformation than the hard grain does. The less constrained grains could move normal to the surface, resulting in the occurrence of surface roughening. Based on the experimental results of this research, it can be seen that the roughening effect becomes much obvious when the grain size approaches to the formed part feature size in microforming process. Such kind of size effect could decrease the formability by triggering the strain instability and localized necking [43]. 3.4. Thickness variation Fig. 11 shows the microstructures of the embossed microchannels, it is revealed that the inhomogeneous deformation occurs with the increase of grain size. It is due to the fact that when there are only a few grains constituting the deformation zone, the deforming material cannot be considered as continuum due to the strong anisotropic properties of grains. It makes the embossed channel asymmetric. During the microembossing process, the thickness of the foil changes, which is critical to the formation of cracking defect and the structural rigidity of the
The FE simulation of the microembossing process with different friction coefficients (m) is conducted. The flow stress curves obtained from tensile test are used as the material model in simulation. However, the flow stress curves obtained by tensile test can only have a small true strain due to the necking occurrence, especially in the case with a small ratio of specimen size to grain size. The flow stress curve with a large true strain is needed for analysis of the large plastic deformation in most metal forming processes. Therefore, the flow stress curves obtained in this study are formulated based on the saturation model:
s ¼ sy þ Q ð1expðbeÞÞ
ð6Þ
where sy is the initial yield stress, Q is the saturation stress and b is the change rate of flow stress. Based on the tensile test results, it does not show any obvious trend about the change of initial yield stress (sy) with the change of grain size. Therefore, a mean value of 45 MPa is used for the three curve fitting cases. The fitted curves are shown in Fig. 13. The simulation is conducted using the commercial CAE system, Abaqus. The forming tools are modeled as rigid bodies while the forming material as an elastic–plastic body. The 4-node bilinear plane stress quadrilateral element is used in meshing of the deformation body. It is found that the simulated variation of the thickness with the friction coefficient of 0.3 qualitatively agrees with the experimental values as shown in Fig. 14, but the grain size effect is not as obvious as the one in the experiment. This result can be explained based on the fact that there are only a few grains over the thickness of the specimens in the three case studies, as shown Figs. 1 and 11. This leads to the fact of the individual grain properties becoming dominant and the occurrence of inhomogeneous deformation, which further makes the thickness of formed microchannel uneven. The conventional FE simulation does not take such kind of size effect into account.
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Fig. 11. Microstructures of the embossed microchannels with different grain sizes. (a) 28 mm, (b) 46 mm and (c) 153 mm.
Grain size (Simulation) 28 µm,
Grain size 28 µm 46 µm
a
e
f
d b 0
100
200
g
c 300 400 500 Distance (µm)
Thickness (µm)
Thickness (µm)
153 µm 100 90 80 70 60
600
46 µm,
153 µm
46 µm,
153 µm
Grain size (Experiment)
700
28 µm,
110 100 90 80 70 60
µ = 0.3
0 800
Fig. 12. Thickness distribution of the embossed microchannels.
Fig. 13. The fitted models of flow stress curves.
This could result in the discrepancy between the experimental and simulation results. The simulated forming stages and the stress distribution are shown in Fig. 15. When the punch moves down, the outside material is bent, and then drawn into to the die cavity. The inner material is pushed downwards and the tension force is applied at the corner region. The interfacial friction resists the material flow and further accelerates the material thinning. The high interfacial friction could attribute to the fact that the tooling–workpiece interface at the micro-sized deformation zone might not hold the lubricant efficiently [44]. Furthermore, the asperity size of the tooling is determined by the machining method and its
100
200
300 400 500 Distance (µm)
600
700
800
Fig. 14. The simulated thickness distribution.
parameters. Fig. 16 shows the surface topography of microembossing tooling which was machined by wire EDM. Since the asperity size is independent of the forming system size, the ratio of the specimen size to the asperity size decreases with the decrease of specimen size. The decrease of both the lubricant efficiency and the ratio of specimen size to asperity size leads to the increase of tooling–workpiece interfacial friction. Fig. 17 shows the comparison of deformation load. It can be seen that the simulated results underestimate the deformation load and the deviation tends to increase with the grain size. This could attribute to the fact that a significantly large deformation of specimen in tensile test is localized at the region where most grains are favorable to deform in tensile direction as explained in the previous section. This further leads to the underestimation of the averaged flow stress of the grains along the gage length. The influence of such grain statistics effect is much significant with the increase of grain size based on the change of Taylor factor presented in Fig. 7. In microembossing, the tooling presses on a large number of grains simultaneously which are different from the case in tensile test. The soft grain would not deform unless the hard grain deforms. The effect of grain statistics is less significant in such case. Therefore, the underestimation of the deformation load could happen when using the flow stress curve obtained from tensile test to simulate the microembossing process.
4. Conclusions In this research, the embossing of microchannels is conducted to study the microscale deformation behavior of sheet metal. It is
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Fig. 15. The simulated forming stage and stress distribution.
Fig. 16. Surface topography of the wire EDM machined microembossing tooling.
450 Grain size (Experiment) 28 µm 46 µm 153 µm
400 350 Load (N)
300 250 200
Grain size (Simulation) 28 µm 46 µm 153 µm
150 100 50 0 0
50
100 150 Stroke (µm)
200
different properties in material surfaces. In addition, a significant thinning occurs at the corner regions of the formed microchannel. The thinning behavior is associated with the tensile force applied at the corner and the friction that prohibits material flow, resulting in occurrence of localized strain. The tensile test specimen can be considered as a chain and each specimen section perpendicular to the loading direction acts as a link member. The section of material yields when all the grains in that section yield and the initial yielding occurs at the weakest section. It is shown that the longer gage length and the smaller number of grains in the section, the higher probability to have a section of specimen with a significantly large fraction of soft grains. Therefore, there is an interactive effect of the grain and specimen sizes on the material deformation behavior in tensile test. The decrease of flow stress with the increase of grain size could be caused by the decrease of both the Taylor factor and the grain boundary strengthening effect. By using the flow stress curves obtained from tensile test to simulate the microembossing process, the simulation underestimates the deformation load and the deviation tends to increase with the grain size. This could be attributed to the nonuniform deformation along the gage length in tensile test, which results in a significantly large strain localized at the region where most grains are favorable to deform in tensile direction. This further leads to small fracture strain and underestimation of the averaged flow stress of the grains along the gage length.
Acknowledgments The authors would like to thank the funding support to this research from the Innovation Technology Commission of Hong Kong government under the project of ITS 313/09 and the projects of G-U923 and A-PJ29 from The Hong Kong Polytechnic University.
250
Fig. 17. Comparison of the experimental and simulation results of the deformation load in microembossing process.
found that the surface roughness increases with strain and the variation rate increases with the grain size. The phenomenon results from the deformation incompatibility among grains with
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