**3.1. Surface roughness model**

A cyclic triangular concavo-convex configuration is applied to the FE model of micro- deep drawing. Fig.8 shows a schematic view of the surface roughness model. The blank diameter is 1.1mm and 0.02mm in thickness. The axisymmetric FE mesh sizes of quadrilateral fournode elements are 1μm×0.5μm. A cyclic surface geometry is modelled as the height of the profile, *R*z, and the pitch, *P*, both of which are variables. This surface model is constructed on whole surface elements of blank and tools. Some of the virtues to consider the surface asperity in the FE model are as follows (Shimizu et al., 2009):


**Figure 8.** Schematic illustration of the surface roughness model and tool geometry

Fig.9 shows the distribution of equivalent plastic strain during the process with a surface roughness model (Shimizu et al., 2009). As shown in Fig. 9, plastic strain is observed at each local surface asperity. Particularly at a part of the sliding on the die corner and that of ironing, the amount of plastic strain of blank surface asperities is significant, due to the severe contact with the tool surface asperities.

Impact of Surface Topography of Tools and Materials in Micro-Sheet Metal Forming 119

118 Metal Forming – Process, Tools, Design

**3.1. Surface roughness model** 

**3. FE analysis of surface roughness model** 

asperity in the FE model are as follows (Shimizu et al., 2009):

properties, such as formability and forming accuracy.

**Dp=0.654mm**

**r**

**p**

**Blank holder**

**Dd=0.69mm**

**Figure 8.** Schematic illustration of the surface roughness model and tool geometry

**=0.1mm**

between the tool and the material.

**Punch**

**Blank**

severe contact with the tool surface asperities.

In order to analyse the influence of the surface asperities in wider range of roughness conditions of the tools and the materials, finite element (FE) analysis of the micro-deep drawing are carried out. To model from the microscopic roughness asperities to macroscopic material deformation behaviour, an advanced model with surface roughness is proposed.

A cyclic triangular concavo-convex configuration is applied to the FE model of micro- deep drawing. Fig.8 shows a schematic view of the surface roughness model. The blank diameter is 1.1mm and 0.02mm in thickness. The axisymmetric FE mesh sizes of quadrilateral fournode elements are 1μm×0.5μm. A cyclic surface geometry is modelled as the height of the profile, *R*z, and the pitch, *P*, both of which are variables. This surface model is constructed on whole surface elements of blank and tools. Some of the virtues to consider the surface

1. It is possible to input the geometry of surface asperity as a parameter of the process. 2. It is possible to represent the local deformation of surface asperity caused by contact

3. It is possible to investigate the effect of local contact behaviour on global deformation

**Die**

Fig.9 shows the distribution of equivalent plastic strain during the process with a surface roughness model (Shimizu et al., 2009). As shown in Fig. 9, plastic strain is observed at each local surface asperity. Particularly at a part of the sliding on the die corner and that of ironing, the amount of plastic strain of blank surface asperities is significant, due to the

**rd**

**=0.1mm**

**Die**

**Pitch "P"**μ**m**

**Amplitude "Ra"**

μ

**m**

**Blank**

**Figure 9.** Distribution of equivalent plastic strain and close up images on part of (a) sliding with die corner and (b) ironing

**Figure 10.** Comparison between punch force-stroke curves of "surface roughness model" and conventional "smooth surface model"

By comparing the surface roughness model with the smooth surface model, which is the conventional FE model with no roughness asperities, the difference with the surface roughness model can be recognized. As shown in Fig. 10, two peaks of maximum punch force are observed for the surface roughness model, while these peaks could not be observed in the smooth surface model. The first peak is under the sliding with a die corner (A) and the second peak is due to the ironing (C). Hence, by considering the local surface asperity on the model, effect of friction resistance of each surface asperity on global forming force are demonstrated.

Impact of Surface Topography of Tools and Materials in Micro-Sheet Metal Forming 121

Simulation Experiment

**Simulation**

**Experiment**

**1**

**2**

**3**

**FEM**

**4**

**5**

**6**

to the result of FE analysis, only the difference at the inner surface is remarkable. From the observation of inner surface roughness of drawn cup, the surface roughening phenomenon seems to largely affect the surface quality of micro drawn cup. Therefore, in order to evaluate the surface quality more precisely, the consideration of the roughening

0 100 200 300 400 500 600 700

Distance from cup center /μm

**0.153**

**0.053**

**0.115**

**0.1030.103**

**0.129**

**Figure 11.** Comparison data of thickness strain distributions of micro-drawn cup

**0.026**

**0.0440.038**

**0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16**

**0.028**

**Measurement**

**Figure 12.** Comparison of surface roughness on each part of micro-drawn cup

the effect of surface roughness for micro-deep drawing (Manabe et al. 2008).

**<sup>1</sup> <sup>2</sup> <sup>3</sup> <sup>4</sup> <sup>5</sup> <sup>6</sup>**

**part**

Thus, by comparison of the experimental and FE simulation results for micro-deep drawing, the validation of surface roughness model are qualitatively demonstrated for the study on

**0.079**

**0.097**

phenomenon would be required.

**1st stage**





Thichkness strain

**Surface**

**roughness Ra**

**Surface roughness** 

**/**<sup>μ</sup>

**Ra /**

**m**

μ

**m**

0

0.05

0.1

0.15

0.2

## **3.2. Validation of surface roughness model**

To validate the surface roughness model, the results of FE analysis are compared with the experimental results. As a representative evaluation, the micro-drawn cups of stainless steel (Fig.6) are precisely evaluated. As an evaluate item to investigate the deformation behaviour during forming process, thickness strain distribution of the drawn cup is precisely evaluated by digital image processing. Additionally, surface roughness of the drawn cups is also measured by confocal laser scanning microscope (LEXT OLS-3000, Olympus Co.).

The simulation is carried out with an explicit dynamic finite element code, LS-DYNA ver.970. Tools and blank dimensions are the same as those in the experiment (Fig.5). The blank model is assumed as isotropic elastoplastic body and it is modeled as an *n*th power hardening law material (*σ*=*F*∙*εn*; *σ*: flow stress, *F*: strength coefficient, *ε*: true strain, *n*: n value). Tools such as a punch, a die and a blank holder are assumed as rigid bodies. All models are considered axisymmetric. Table 1 shows the mechanical properties of the blank and tools used in the simulation. The static and kinetic friction coefficients between the blank and the tools are assumed to be 0.05 and 0.03, respectively.


**Table 1.** Mechanical properties used in FE simulation

Fig.11 shows the comparison data of thickness strain distribution of both experiment and FE analysis (Manabe et al., 2008). General tendency of thickness variations in deep drawing process, such as the reduction at cup corner radius and the increase at cup edge, can be observed. Hence, the validation from the point of geometry and dimension of the model is demonstrated.

Fig.12 shows the comparison data of the surface roughness measured at defined 6 point of redrawn micro cups (Manabe et al., 2008). Although almost whole values are corresponded to the result of FE analysis, only the difference at the inner surface is remarkable. From the observation of inner surface roughness of drawn cup, the surface roughening phenomenon seems to largely affect the surface quality of micro drawn cup. Therefore, in order to evaluate the surface quality more precisely, the consideration of the roughening phenomenon would be required.

120 Metal Forming – Process, Tools, Design

force are demonstrated.

Olympus Co.).

demonstrated.

**3.2. Validation of surface roughness model** 

blank and the tools are assumed to be 0.05 and 0.03, respectively.

**Table 1.** Mechanical properties used in FE simulation

By comparing the surface roughness model with the smooth surface model, which is the conventional FE model with no roughness asperities, the difference with the surface roughness model can be recognized. As shown in Fig. 10, two peaks of maximum punch force are observed for the surface roughness model, while these peaks could not be observed in the smooth surface model. The first peak is under the sliding with a die corner (A) and the second peak is due to the ironing (C). Hence, by considering the local surface asperity on the model, effect of friction resistance of each surface asperity on global forming

To validate the surface roughness model, the results of FE analysis are compared with the experimental results. As a representative evaluation, the micro-drawn cups of stainless steel (Fig.6) are precisely evaluated. As an evaluate item to investigate the deformation behaviour during forming process, thickness strain distribution of the drawn cup is precisely evaluated by digital image processing. Additionally, surface roughness of the drawn cups is also measured by confocal laser scanning microscope (LEXT OLS-3000,

The simulation is carried out with an explicit dynamic finite element code, LS-DYNA ver.970. Tools and blank dimensions are the same as those in the experiment (Fig.5). The blank model is assumed as isotropic elastoplastic body and it is modeled as an *n*th power hardening law material (*σ*=*F*∙*εn*; *σ*: flow stress, *F*: strength coefficient, *ε*: true strain, *n*: n value). Tools such as a punch, a die and a blank holder are assumed as rigid bodies. All models are considered axisymmetric. Table 1 shows the mechanical properties of the blank and tools used in the simulation. The static and kinetic friction coefficients between the

Blank Tool

Fig.11 shows the comparison data of thickness strain distribution of both experiment and FE analysis (Manabe et al., 2008). General tendency of thickness variations in deep drawing process, such as the reduction at cup corner radius and the increase at cup edge, can be observed. Hence, the validation from the point of geometry and dimension of the model is

Fig.12 shows the comparison data of the surface roughness measured at defined 6 point of redrawn micro cups (Manabe et al., 2008). Although almost whole values are corresponded

Mass density (g∙μm-1) 8.00 x 10-11 8.00 x 10-7 Young's modulus (GPa) 177 206 Poisson's ratio 0.3 0.3 *F*-value (GPa) 1.55 *n*-value 0.14 -

Distance from cup center /μm

**Figure 11.** Comparison data of thickness strain distributions of micro-drawn cup

**Surface**

**Figure 12.** Comparison of surface roughness on each part of micro-drawn cup

Thus, by comparison of the experimental and FE simulation results for micro-deep drawing, the validation of surface roughness model are qualitatively demonstrated for the study on the effect of surface roughness for micro-deep drawing (Manabe et al. 2008).
