**5. Modified FEM with the consideration of material and lubrication characterization in MDD and MHDD**

**Figure 26** represents a typical EBSD microstructure. First, the EBSD image was input into the MATLAB software, and the binary image was obtained with black grain boundaries and white grains. Noise and small holes were eliminated in the transformation. Then, the Moore-Neighbor tracing algorithm modified by Jacob's stopping criteria was applied in the binary image treatment. As shown in **Figure 26b**, the information of grains and individual closed subareas, including single grain's area, geometrical center and geometrical orientation, was detected and sorted in MATLAB. The blue ports in **Figure 26b** are the grain's geometrical centers [9, 20, 21].

**Figure 27** displays the Voronoi structures and their corresponding FE models with average grain sizes of 10, 20, and 40 μm, respectively.

After annealed at 1100°C, the 50 μm thick blanks, with equiaxed crystals microstructure and average grain size of 40 μm, were drawn into micro cups. The drawn cup mouth is shown in **Figure 28a**, and the maximum thickness distributions of drawn cups are illustrated in **Figure 28b**–**d**, which represented the new developed model, a Voronoi model without the consideration of grain boundaries and a normal model in homogeneous material properties, respectively. The comparison of the maximum wall thickness between the simulation and the experimental results has been conducted. The localized deformation is ignored, and the maximum thickness was averaged with the lowest peak thickness values for all the simulation cases. It can be seen that the new model and the Voronoi model considered microscopic heterogeneity have higher maximum thickness than that in the normal model [9], where the largest thickness is obtained from the Voronoi model without grain boundaries buffer.

**Figure 26.** (a) Microstructure of a sample from EBSD, (b) its corresponding geometry detected by MATLAB and (c) corresponding simulation model.

The material surface consists of lots of peaks and valleys called roughness in microforming. The roughness and the extent of the valleys get larger compared to the scaled down workpiece size. As shown in **Figure 29**, the lubricant cannot be retained in the valleys connected to the edge of the blank, and this area is called open lubricant pockets (OLPs) [9, 18, 19]. The fraction of OLPs increases with the decrease in specimen size. The friction force increases because the lubricant cannot be kept during microscale forming process. Therefore, the OLPs must be taken into account when studying the tribological behavior of microforming.

with visualized, and liquid intruded area is taken out when the liquid dries out. After this, the blank surface is observed under a digital microscope, and the pictures are digitized [9, 17]. **Figure 31** illustrates the effects of scale factor on the normalized punch force-stroke curves at MDD with lubrication and MHDD with radial pressure. The shape of punch force-stroke curves in λ = 1, 2 is as similar as that with λ = 50 at MDD and MHDD. In these conditions, only the inner or outer pockets exist in the flange area. Therefore, the coefficient of friction in the flange area is almost uniform. On the other hand, in λ = 5, the inner and outer pockets are

**Figure 28.** (a) Drawn cup with 1100°C annealed blank and maximum thickness distribution from the simulation with (b)

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the developed new model, (c) the Voronoi model, and (d) the normal model.

**Figure 29.** The change of fraction of OLPs in flange area with the decrease of blank size.

**Figure 30** shows schematic of evaluation test for OLPs utilizing liquid where the blank is compressed by the tools under approximately 20 MPa contact pressure. During experiment, the liquid is filled into the tool first, and the liquid intruded area is colored. Then the blank

**Figure 27.** Voronoi structures (in the first line) and their corresponding FE models (in the second line): average grain sizes of (a) 10, (b) 20, and (c) 40 μm.

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**Figure 28.** (a) Drawn cup with 1100°C annealed blank and maximum thickness distribution from the simulation with (b) the developed new model, (c) the Voronoi model, and (d) the normal model.

The material surface consists of lots of peaks and valleys called roughness in microforming. The roughness and the extent of the valleys get larger compared to the scaled down workpiece size. As shown in **Figure 29**, the lubricant cannot be retained in the valleys connected to the edge of the blank, and this area is called open lubricant pockets (OLPs) [9, 18, 19]. The fraction of OLPs increases with the decrease in specimen size. The friction force increases because the lubricant cannot be kept during microscale forming process. Therefore, the OLPs must be

**Figure 26.** (a) Microstructure of a sample from EBSD, (b) its corresponding geometry detected by MATLAB and (c)

**Figure 30** shows schematic of evaluation test for OLPs utilizing liquid where the blank is compressed by the tools under approximately 20 MPa contact pressure. During experiment, the liquid is filled into the tool first, and the liquid intruded area is colored. Then the blank

**Figure 27.** Voronoi structures (in the first line) and their corresponding FE models (in the second line): average grain

taken into account when studying the tribological behavior of microforming.

116 Finite Element Method - Simulation, Numerical Analysis and Solution Techniques

corresponding simulation model.

sizes of (a) 10, (b) 20, and (c) 40 μm.

with visualized, and liquid intruded area is taken out when the liquid dries out. After this, the blank surface is observed under a digital microscope, and the pictures are digitized [9, 17].

**Figure 31** illustrates the effects of scale factor on the normalized punch force-stroke curves at MDD with lubrication and MHDD with radial pressure. The shape of punch force-stroke curves in λ = 1, 2 is as similar as that with λ = 50 at MDD and MHDD. In these conditions, only the inner or outer pockets exist in the flange area. Therefore, the coefficient of friction in the flange area is almost uniform. On the other hand, in λ = 5, the inner and outer pockets are

**Figure 29.** The change of fraction of OLPs in flange area with the decrease of blank size.

**Figure 30.** Schematic of evaluation test for OLPs utilizing liquid.

caused the decrease in friction force in MHDD. **Figure 32b** shows the effect of the lubrication type on friction force in MHDD. The decrease of friction force in radial pressure condition is much larger than that in leakage condition. Also in radial pressure condition, the friction force significant decreases from λ = 5–1. It is because the contact pressure between the blank and die at die shoulder is higher than that between the blank and blank holder in the small Dp/t. Therefore, the decrease in coefficient of friction at die shoulder is especially important to decrease the friction force in MHDD. According to the above-mentioned results, the friction force can decrease with the decrease in size in MHDD, while it only increases in MDD. The friction force can be reduced by filling the fluid medium in the outer pockets in MHDD [19].

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**Figure 32.** Tribological size effects at different lubrication conditions in MDD and MHDD.

This chapter presents the applications of FEM in metal-forming analysis from macroscale to microscale, including FEA software programs used, simulation approach and results obtained, and their validation for metal-forming processes. A 3D rigid plastic FEM is used with the consideration of friction variation models in the case of work roll kiss occurrence during cold rolling of thin strip. The modeling of the friction variation can produce a more accurate model that can improve the accuracy of simulation results. In the CPFEM, the simulation results show that with an increase in reduction, the cubic texture {001}<100> is weak, while the brass orientation {110}<112> becomes strong. The simulation result agrees with the experimental one. When reduction exceeds 60%, most grains have plastic slips. With an increase in reduction, both the grain size and surface roughness decrease while the flow stress increases. Novel material model with grained heterogeneity in 3D Voronoi tessellation has been developed in the simulation of micro cross wedge rolling, springback analysis in thickness direction during micro flexible rolling process and the micro V-bending process considering grain boundary and generation process of grains in the workpiece. Real microstructures and Voronoi structures are applied in microstructural models through image-based modeling method and

**6. Conclusions**

**Figure 31.** Effects of scale factor λ on normalized punch force-stroke curve at different lubrication conditions (a) MDD with lubrication, and (b) MHDD with radial pressure.

mixed in the flange area. In the initial process, the inner pockets mainly exist at die shoulder and flange area and affect the tribological behavior significantly. Therefore, the punch forcestroke curves are as similar with that in macroscale. However, in the middle process, the ratio of outer pockets increases. As a result, the tribological behavior shifts to that in microscale. This behavior appears at both MDD and MHDD. This causes the maximum punch force shifts as shown in **Figure 31a**. These results indicate the ratio of the outer pockets to the flange area during the forming process influences the tribological behavior of the MHDD as shown in **Figure 31b**.

**Figure 32a** shows the tribological size effects in MDD and MHDD. With the decrease in the size, the friction force increases in case of MDD with lubrication because the ratio of outer pockets increases. When λ = 1, 2, the maximum effective punch forces in MDD with the dry friction and lubrication become the same because only the outer pockets exist at flange area. On the other hand, with the decrease in the size, the friction force in MHDD decreases. It can be seen the tribological size effects in MHDD have an opposite behavior with MDD. In MHDD, the fluid medium is provided to the outer pockets whose ratio is high in microscale. This

**Figure 32.** Tribological size effects at different lubrication conditions in MDD and MHDD.

caused the decrease in friction force in MHDD. **Figure 32b** shows the effect of the lubrication type on friction force in MHDD. The decrease of friction force in radial pressure condition is much larger than that in leakage condition. Also in radial pressure condition, the friction force significant decreases from λ = 5–1. It is because the contact pressure between the blank and die at die shoulder is higher than that between the blank and blank holder in the small Dp/t. Therefore, the decrease in coefficient of friction at die shoulder is especially important to decrease the friction force in MHDD. According to the above-mentioned results, the friction force can decrease with the decrease in size in MHDD, while it only increases in MDD. The friction force can be reduced by filling the fluid medium in the outer pockets in MHDD [19].

### **6. Conclusions**

mixed in the flange area. In the initial process, the inner pockets mainly exist at die shoulder and flange area and affect the tribological behavior significantly. Therefore, the punch forcestroke curves are as similar with that in macroscale. However, in the middle process, the ratio of outer pockets increases. As a result, the tribological behavior shifts to that in microscale. This behavior appears at both MDD and MHDD. This causes the maximum punch force shifts as shown in **Figure 31a**. These results indicate the ratio of the outer pockets to the flange area during the forming process influences the tribological behavior of the MHDD as shown in

**Figure 31.** Effects of scale factor λ on normalized punch force-stroke curve at different lubrication conditions (a) MDD

**Figure 30.** Schematic of evaluation test for OLPs utilizing liquid.

118 Finite Element Method - Simulation, Numerical Analysis and Solution Techniques

with lubrication, and (b) MHDD with radial pressure.

**Figure 32a** shows the tribological size effects in MDD and MHDD. With the decrease in the size, the friction force increases in case of MDD with lubrication because the ratio of outer pockets increases. When λ = 1, 2, the maximum effective punch forces in MDD with the dry friction and lubrication become the same because only the outer pockets exist at flange area. On the other hand, with the decrease in the size, the friction force in MHDD decreases. It can be seen the tribological size effects in MHDD have an opposite behavior with MDD. In MHDD, the fluid medium is provided to the outer pockets whose ratio is high in microscale. This

**Figure 31b**.

This chapter presents the applications of FEM in metal-forming analysis from macroscale to microscale, including FEA software programs used, simulation approach and results obtained, and their validation for metal-forming processes. A 3D rigid plastic FEM is used with the consideration of friction variation models in the case of work roll kiss occurrence during cold rolling of thin strip. The modeling of the friction variation can produce a more accurate model that can improve the accuracy of simulation results. In the CPFEM, the simulation results show that with an increase in reduction, the cubic texture {001}<100> is weak, while the brass orientation {110}<112> becomes strong. The simulation result agrees with the experimental one. When reduction exceeds 60%, most grains have plastic slips. With an increase in reduction, both the grain size and surface roughness decrease while the flow stress increases. Novel material model with grained heterogeneity in 3D Voronoi tessellation has been developed in the simulation of micro cross wedge rolling, springback analysis in thickness direction during micro flexible rolling process and the micro V-bending process considering grain boundary and generation process of grains in the workpiece. Real microstructures and Voronoi structures are applied in microstructural models through image-based modeling method and modified FE with the consideration of size effects including material characterization, friction/ contact characterization, and other size-related factors. Open and closed lubricate pocket theory and size-dependent coefficient of friction are also proposed in micro deep drawing and micro hydromechanical deep drawing.

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