Investigation of the friction behavior between dry/infiltrated glass fiber fabric and metal sheet during deep drawing of fiber metal laminates

Different types of glass fibers and of metal sheets are selected to analyze the friction coefficients. The aluminum alloy AA 5182-H111 and cold rolled DC04 sheet metal blank with a thickness of 1.0 mm are common materials for body-in-white in the automotive industry. The metal sheets have a surface roughness of approximately \({R}_{\mathrm{a}}=1\) µm. Two fabrics with different weave types, plain woven fabric and twill woven fabric, are selected to investigate the influence of the weave type under load (Fig. 1). In order to investigate the influence of the laminate thickness and the geometry, which affects the weight per unit area, on the fabric under load, two different weights per unit area are selected for the twill woven fabric: 80 g/m² and 280 g/m². The plain woven fabric has a weight of 280 g/m².

The flat strip drawing tests are carried out on a test facility as described by Mennecart [15] and shown in Fig. 2. The sheet metal strip is clamped between two friction elements, whereby a defined force \(F\) is applied in the normal direction. The two specimens with a contact area of 30 mm (width) × 40 mm (height) = 1200 mm² are covered with a layer of the glass fabric to be examined. The sheet metal strips used have a length of 300 mm and a width of 40 mm. The sheet metal strip is pulled at a constant velocity v while the compaction force N in thickness direction is kept constant and the pulling force F is measured. The applied transverse force and the drawing velocity are controlled. The forces are measured by piezo load cells (type 0911A 0–15 kN in drawing direction and type 9021A 0–35 kN in clamping direction) from Kistler. The displacement is determined by using a potentiometric position transducer from Novotechnik (type LWH-0200). Assuming Coulomb friction, the following formula is used to obtain the dynamic coefficient of friction \({\mu }_{D}\):

The strip is clamped with a force of 2000 N, which corresponds to a contact pressure of p = 1.67 MPa, and pulled at a velocity of 600 mm/min. The determination of the coefficient of friction ends after five seconds. In order to detect an influence on the fiber orientation, the coefficients of friction for fibers which are clamped in 0°/90° and in \(\pm\) 45° are determined as shown in Fig. 3a.

Substitute fluids of different dynamic viscosities are used to determine the influence of viscosity on the coefficient of friction, because the reactive matrix system would polymerize and change its viscosity while testing. Silicone oils with viscosities of 160 mPa s, 10,000 mPa s and 100,000 mPa s are used. The viscosity of the low viscous oil corresponds to the initial viscosity of the matrix system used in deep drawing of fiber metal laminate with in-situ hybridization. With the current in-situ hybridization process, the deep drawing is completed after 90 s with a low viscous matrix. With lower drawing velocities, the matrix would polymerize further during the deep drawing. Higher viscosities are intended to reflect the increase in viscosity during polymerization, as shown in Fig. 4. The fabrics are completely infiltrated with the oils. Excess oil is pressed out by the contact pressure. Three to four evaluable tests for each configuration are carried out.

Figure 5 shows a selection of the coefficients of friction of the dry and infiltrated fabrics for a fiber orientation of 0°/90° to the drawing direction of the sheets against the displacement. The mean values and standard deviations of all evaluable tests are plotted to compare different fabric and metal types under the influence of oils with different viscosities. The dry fabric in interaction with both the AA 5182-H111 and DC04, respectively, shows the highest friction. With up to µ = 0.23, this is the highest value for the heavy twill woven fabric and the plain woven fabric. The friction coefficients are similar for the combination with DC04 and with AA 5182-H111. The coefficient of friction drops slightly by approx. 0.03 in the wet condition with 160 mPa s oil compared to the dry state. The friction in dry state and with 160 mPa s viscous oil is mostly independent of the fabric typ. With higher viscous oils, the friction coefficient is much lower. The friction associated with the oil with a viscosity of 10,000 mPa s produces contact friction coefficients between µ = 0.05 (light twill woven fabric) and µ = 0.12 (plain woven fabric). At 10,000 mPa s viscosity, a sharp increase in the friction coefficient during the draw path for the friction pairing of plain woven fabric and sheet metal can be noticed. The coefficient of friction increases from an initial value of µ = 0.07 to µ = 0.12. This effect is not observed for the twill woven fabric at 10,000 mPa s in combination with the AA5182-H111. Here, the friction coefficient is slightly lower (µ = 0.05) than for the plain woven fabric and steady over the displacement. However, a similar effect is observed in the twill woven fabric in combination with DC04 at 160 mPa s, where the initial friction coefficient is lower than in combination with AA5182-H111 but increases to the same value at further displacement. The coefficient of friction is lowest in the case of the friction pairing between fibers infiltrated with the highly viscous oil (100,000 mPa s) and the sheet metal. Here, the coefficient of friction is between µ = 0.02 and µ = 0.04. Again, the friction coefficient is slightly lower for the twill woven fabric. It is steady over the displacement for both plain and twill woven fabric at 100,000 mPa s. Standard deviations are around ± 10% for most material combinations with slightly higher deviations for DC04 with twill woven fabric and 160 mPa s as well as 100,000 mPa s viscous oil. Higher deviations in these cases are caused by considerably higher (for 160 mPa s) or lower (for 100,000 MPa) measured friction coefficients in one of the three performed tests. They were not excluded from the analysis as outliers as they are still in a reasonable range.

Figure 6 shows the coefficients of friction for the dry and for the infiltrated fabrics for a fiber orientation of \(\pm\) 45° to the drawing direction of the sheet. In general, the friction shows a similar behavior in \(\pm\) 45° direction as in 0°/90° direction. The friction coefficients are higher for dry fabrics and decrease with increasing viscosity. Friction coefficients are slightly higher in \(\pm\) 45° direction, in particular for the twill woven fabric. Smaller differences can be observed for the plain woven fabric, where the main difference is an even larger increase of the friction coefficient over the displacement for the fabric that is infiltrated with the 10,000 mPa s oil. For the twill woven fabric, a sharp increase in friction coefficient can be seen during the initial displacement in combination with the 160 mPa s oil and both DC04 and AA5182-H111. In 0°/90° direction, this increase is not observed in combination with AA5182-H111 except for a small increase in the very beginning, whereas in combination with DC04, the increase in friction coefficient is spread out place over the whole displacement length. Similar to the experiments conducted in 0°/90°-direction, the standard deviations are around ± 10% or lower. Standard deviations are slightly lower for the experiments performed in ± 45° direction.

One compression test from 0.005 to 5 MPa was performed on three layers of the twill woven fabric 280 g/m² to verify the assumption of contact with plastic deformation for the application of Coulomb’s friction law. The initial thickness of the fabric at 0.005 MPa amounts to 0.32 mm. The compression behavior is assumed to be similar for the plain woven fabric 280 g/m² and twill woven fabric 80 g/m². The obtained thickness-pressure curve is shown in Fig. 7. According to Yousaf et al. [27], it consists of three parts. First a linear part and second an exponential part, where the majority of the compression takes place by rearranging of the fibers and interlayer nesting. The last part of the compression curve is determined by the elastic deformation of the fibers itself as almost all possible nesting took place at lower compression loads. For the tested fabric, this is the case for pressures higher than approximately 1 MPa. Bowden and Young’s friction is dependent on the contact area and type of contact between the friction partners. At high pressures, the contact area between metal sheet and fibers can be seen as constant, since only very little elastic deformation is occurring in the brittle and stiff glass fibers. The contact between metal sheet and glass fibers can be seen as almost entirely plastic. While the glass fibers should exhibit almost no deformation compared to the metal sheets, the deformation of the surface irregularities on the metal sheet should be almost entirely plastic at high pressures as they are occurring in the in-situ hybridization process and the strip drawing tests. Coulomb friction [with \(n=1\) in Eq. (2)] can therefore be assumed. Under low contact pressures, Coulomb’s law could not be applied for the determination of the friction coefficient because the change in contact area would have to be considered.

The standard deviations of approximately ± 10% are low compared to the differences observed for different material combinations. The number of tests carried out can therefore assumed to be sufficient for this investigation. Slightly lower standard deviations were observed in ± 45° direction. Although being almost the same in warp and weft direction (133 g/m² and 143 g/m²), a slight anisotropy in the fabric might lead to small differences between 0° and 90° direction that could explain the higher deviations. The friction coefficient measurements for the dry fabrics and for the fabrics infiltrated with the low viscous fluid show that the friction coefficients are approx. 0.01 to 0.02 higher when the fiber orientation is \(\pm\) 45°. A possible cause of friction in fiber metal contact could be that the fibers rotate in the direction of tension due to friction (Fig. 8). Due to less undulations and better drapability, a greater rotation of the roving in the twill woven fabric compared with plain woven fabric is to be expected. For the fiber rotation, additional force is needed which explains the measured higher friction coefficient for fabrics in \(\pm\) 45° direction. At the crossing points of the rovings, the contact pressure is much higher than the average pressure.

For some specimens, an increase in the friction coefficient can be observed with further displacement. This effect occurs in particular for the \(\pm\) 45° fiber orientation to the drawing direction. This can be explained by the fact that the liquid is quickly discharged to the outside in a V-shape, as Hahn et al. [11] also found in bending processes. A faster squeezed out fluid leads to an increasing number of fibers interacting with the metal sheet and a continuously increased coefficient of friction (Fig. 9). Without fluid, the contact pressure is very high at the crossing points of the fabric. Because the matrix is transported forward with a fiber orientation of 0°/90°, the fluid is not as easily squeezed out of the fabric. The displacement of the fluid is also more difficult with medium viscosity. The matrix film is dragged along before displacement of the fluid occurs over time. This means that the friction coefficient in this case changes from a low to a higher value. Using a highly viscous fluid, no matrix is squeezed out and the matrix is in contact with the sheet during the entire draw path. With increasing viscosity, the pressure is more evenly distributed and gets closer to the average area pressure. As a result, the friction factor is low when the viscosity is high.

The influence of fluids with different viscosities on the friction between fabric and metal was investigated under a high normal pressure. Dry friction without viscous matrix is independent of the drawing velocity. However, when using a viscous matrix, the friction decreases with decreasing velocity. In this work, a high drawing velocity of 600 mm/min was investigated. For lower drawing velocities, as occurring in the in-situ hybridization process, the difference in friction between dry and infiltrated fabrics is therefore assumed to be even higher.

As of now, a low reactive matrix system is used in the in-situ hybridization process. During the deep drawing process, only little polymerization takes place with increasing matrix viscosity from initial 100 mPa s to approximately 200–300 mPa s [14], as shown in Fig. 4. Most of the viscosity increase takes place during polymerization when holding the position after deep drawing. This investigation shows that lower friction values hinder the metal sheet less in the forming process and allow greater degrees of forming. As lower frictions can be achieved with a higher viscous matrix, lower drawing velocities or using a matrix system with faster polymerization time could improve the forming behavior in the in-situ hybridization process. When polymerization already takes place during the forming process, the friction is reduced due to higher matrix viscosity, in particular towards the end of the forming process. However, a high viscosity is also counterproductive for forming of the fabric layer, as other studies have shown [28]. High viscosities reduce the friction between fabric and metal sheet, but lead to higher fluid forces. The higher fluid forces lead to fiber washing and thus poorer forming results in the fabric due to fiber misorientation. Therefore, further research has to be conducted to find a process window for the in-situ hybridization process.