**3. Models used to describe friction**

To describe the friction phenomenon in forming, it is important to use a model that reasonably describes the reality, especially when the analysis surface is large. For this case, the friction force makes a relevant contribution to the total force

required in the operation. Despite the great development in models that describe the behavior of materials, conventional computational numerical simulations generally do not provide correct results regarding friction. This is due to the use of very simplified friction models.

Two models are generally used to describe friction at the interface between tool and work material depending on the process being considered. The first is the Amontons-Coulomb model shown in Eq. (1), where there is a linear relationship between normal pressure and shear stress.

$$
\pi = \mu \cdot p \tag{1}
$$

where μ is the coefficient of friction (COF), p is the normal pressure and τ is the frictional shear stress.

Eq. (1) is valid only for relatively small shear stresses, because when τ exceeds the shear strength, k, of the workpiece material, the second model must be used. This second model was proposed by Orowan [7] and is shown in Eq. (2).

$$
\tau = m \cdot k \tag{2}
$$

where m is the shear factor, where its value ranges from 0 to 1 and k is the maximum shear strength of the work material.

**Figure 5** represents the combination of the Amontons-Coulomb model and the limit shear stress model proposed by Orowan [7]. Shear stress is shown as a function of normal pressure. The first part of the figure is considered to be the Coulomb part. The relationship between the frictional force and the normal force, defined as the friction coefficient μ, is constant in this part of the curve.

When the normal pressure increases, the lubricant pockets start to leak and promote a decrease in friction visualized by the decrease in the slope of the curve, until reaching a constant value that is given by the maximum shear stress of the material. At this point, the friction coefficient no longer makes sense, and the concept of friction factor appears. This phenomenon is represented by the horizontal part of the curve (**Figure 5**).

#### **Figure 5.**

*Relationship between contact pressure and frictional shear stress. Source: Based on Rodrigues and Martins [8] and Altan and Tekkaya [9].*

*The Role of Friction on Metal Forming Processes DOI: http://dx.doi.org/10.5772/intechopen.101387*

In terms of metal forming processes, the coulombian friction coefficient is more used in sheet metal fabrication since the pressures cannot be so great as there is not enough material in the thickness to be deformed. As for the forming processes in bulk deformation, the shear friction factor must be used because in this case the pressures are always close to the maximum shear stresses of the work material.
