**1. Introduction**

Process modeling for the investigation and understanding of deformation mechanics has become a major concern in research, and the application of the finite element method (FEM) has been tremendously increased, particularly in the modeling of forming processes. There are many research studies on the principles and fundamentals of the simulation of metal forming, but only a few studies describe the application of FEM to the analysis and simulation of multiscale forming processes. The main objective of this chapter is to present the applications of FEM in metal forming analysis from macroscale to microscale.

Friction at the strip-roll interface is an important consideration in the metal-forming process. Traditionally, the frictional force is assumed to be proportional to the normal force, and the friction coefficient keeps the same in the roll bite. This assumption conflicts with the research

results where the friction is changeable in the roll bite [1], and the rolling pressure and model control accuracy will be influenced significantly. The deformation mechanics of thin foil [2] and the foil rolling with constant friction during cold rolling [3] have been investigated. The finite element method has been proposed in special-shaped strip rolling [4–6], particularly with variable friction models [5, 6]. Considering modeling accuracy, a friction variation model should be introduced in the cold rolling simulation of thin strip.

In the friction variation model, the friction varies along the contact length of the deformation

for forward slip zone and backward slip zone, respectively; *ki*

are the velocity components in the *x* and *y* directions, respectively, *β* is the

\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ (*vx sec* − *VR*)<sup>2</sup> + *vy*

angular position of the node, *VR* is the tangential velocity of the roll, and the distribution of

As shown in **Figure 2**, a quarter of the strip was studied. Isoparametric hexahedral elements were applied with eight Gauss points throughout the deformed workpiece. The element number in *x*, *y*, and *z* directions are 10, 8, and 5, respectively, and totally there are 594 nodes

From the simulation with low carbon steel, **Figures 3** and **4** show the effect of reduction on

value is below 0.1, the rolling pressure calculation value is in agreement with the measured

as shown in **Figures 5** and **6**. It can be seen that the calculated results are in good agreement

The rolling of copper strip is simulated with work roll diameter 158.76 mm, width of strip

simulation results significantly where the rolling pressure increases with decreased *k*<sup>2</sup>

= 0.1, the change of *k*<sup>1</sup>

for forward slip zone and backward slip zone, respectively; *Vg*

Application of Finite Element Analysis in Multiscale Metal Forming Process

and constant *k*<sup>1</sup>

= 0.1 is also close to the measured one when the reduc-

= 0.1. Therefore, the simulation results are close to measured

= 0.4. For case 1, *K*<sup>1</sup>

*ki* }) (1)

http://dx.doi.org/10.5772/intechopen.71880

2 (2)

= 0.1. *k*<sup>2</sup>

also has an effect on the simulation results,

= *K*<sup>2</sup>

= 1.0 and *k*<sup>1</sup>

is a posi-

influences the

 = *k*<sup>2</sup> = 0.1

. When

is

99

is a coefficient of the friction shear stress

*<sup>m</sup>*<sup>1</sup> *<sup>σ</sup>* \_\_\_\_*<sup>s</sup>* √ \_\_ 3 ( \_\_2 *<sup>π</sup> tan*<sup>−</sup><sup>1</sup> { *Vg* \_\_\_

yields stress; *Ki*

relative slip velocity between the strip and the roll and can be obtained by:

zone. The frictional shear stress model is modified as [5]:

these frictional shear stress models is shown in **Figure 1**.

rolling pressure and spread of strip for different *k*<sup>2</sup>

are less than 0.1.

76.2 mm, rolling speed 0.16 m/s, and friction factor *m*<sup>1</sup>

one. The spread calculation value for *k*<sup>2</sup>

tion is less than 43%. For *k*<sup>2</sup>

with the measured values for *k*<sup>1</sup>

**Figure 1.** Frictional shear stress models.

and *k*<sup>2</sup>

*τ<sup>f</sup>* = *Ki*

and *K*<sup>2</sup>

*Vg* <sup>=</sup> <sup>√</sup>

is the friction factor; *σ<sup>s</sup>*

and *k*<sup>2</sup>

where *m*<sup>1</sup>

where *vx*

*k*2

changes with *K*<sup>1</sup>

tive constant with *k*<sup>1</sup>

and *vy*

and 400 elements.

values when *k*<sup>1</sup>

The application of crystal plasticity finite element method (CPFEM) has been introduced in the simulation of surface asperity flattening in cold quasistatic uniaxial planar compression process. Rate-dependent crystal plasticity constitutive models have been established on the basis of experimental conditions [7], and the influences of the reduction and strain rate on the surface roughness are investigated using the 3D crystal plasticity finite element method [8]. The experimental results are also employed in the 3D CPFEM model and compared with the simulation results.

Microforming differs from the conventional forming technology in terms of materials, processes, tools, and machines and equipment due to the miniaturization nature of the whole microforming system [9]. It is impossible to scale down all parameters in the microforming process according to the theory of similarity due to the existence of size effects in microforming processes. A number of unexpected problems in key aspects of mechanical behavior, tribology, and scatter of material behavior are encountered [10, 11]. Challenges remain in the high efficiency manufacturing of high-quality microproducts due to the common problem of microscale size effects [9, 11], complexity of processes for making microproducts, and the ever increasing requirement to improve product quality and performance.

In Section 4, novel material model with grained heterogeneity in 3D Voronoi tessellation has been developed in the simulation of micro cross wedge rolling, springback analysis in micro flexible rolling and the micro V-bending processes considering grain boundary and generation process of grains in the workpiece [12–16]. The modified FE model in microforming has been applied with the consideration of size effects including material characterization, friction/contact characterization, and other size-related factors presented in Section 5. Open and closed lubricate pocket (OCLP) theory and size-dependent friction coefficient are proposed in micro deep drawing (MDD) and micro hydromechanical deep drawing (MHDD) [17–19]. Real microstructures and Voronoi structures are applied in microstructural models through the image-based modeling method [20, 21].
