**2.7. Mechanical property of the formed billet**

The hardness distribution of the formed billet becomes to be no uniform in microforming (**Figure 36**) when the grain size is coarse [45, 46]. More even material flow and hardness distribution can be achieved using the ultrafine-grained material. This implies the potential applications of the ultrafine-grained materials in metal microforming processes.

**Figure 36.** Left: Illustration of nanoindentation; Right: statistical distribution of *α*-value, *α*—ratio of the hardness at each class to the average hardness [25].

Billet formability increases with the decrease of workpiece size for a constant grain size [21]. It needs a larger strain to initiate cracking in microforming (**Figure 37**). Common assumption is that the damage energy to initiate fracturing is the same in macro- and microscale. The flow stress decreases with the billet size, so the larger deformation is needed to obtain the critical damage energy in microforming.

**Figure 37.** Different size-scaled central headed parts [21].

#### **2.8. Summary**

features decreases. The uniform distribution of different grains no longer exists. Each grain with each property plays a significant role to the overall material deformation behavior. Different crystallographic orientations, different shapes, and sizes of neighboring grains lead to inhomogeneous deformation, which result in the scatter of achieved material properties.

**Figure 35.** Schematic illustration of the modeling of the scatter effect with a normal distribution function [12].

applications of the ultrafine-grained materials in metal microforming processes.

The hardness distribution of the formed billet becomes to be no uniform in microforming (**Figure 36**) when the grain size is coarse [45, 46]. More even material flow and hardness distribution can be achieved using the ultrafine-grained material. This implies the potential

**Figure 36.** Left: Illustration of nanoindentation; Right: statistical distribution of *α*-value, *α*—ratio of the hardness at

Billet formability increases with the decrease of workpiece size for a constant grain size [21]. It needs a larger strain to initiate cracking in microforming (**Figure 37**). Common assumption

**2.7. Mechanical property of the formed billet**

22 Modeling and Simulation in Engineering Sciences

each class to the average hardness [25].

Microforming is considered as an economically competitive process for production of metallic microcomponents. The scaling down of a forming system from macro to micro leads to the occurrence of size effect. This phenomenon differs microforming from forming in macroscale and do not allow applying conventional knowledge. The anisotropic properties of each grain, the random nature of grain distribution, and orientation as well as tool surface roughness become significant. This leads to the inhomogeneous deformation and the scatter of the achieved flow stress. Experimentally recognized size effects, such as flow stress size effect, deformation behavior size effect, or interfacial friction size effect are numerically modeled, giving the ability to more accurately identify their mechanics and to predict the results of the microforming process.

For the microforming process simulations, commercial FE systems such as DEFORM, QFORM, ABACUS, or ANSYS/LS-DYNA are used. Nonlinear code ADINA (developed by KJ Bathe and his team at MIT Mechanical Engineering) may be also recommended to solve some of the complex multiphysical micromechanics phenomena associated with metal forming. Grain structures are modeled based on metallographies or using Voronoi tessellation and the tool surface roughness using rigid waves. Ortiz atomistic models of material behavior based on atomistic energy laws may be an alternative way to resolve the mechanics of microforming of metals.

Although the polycrystalline material deformation behaviors have been extensively studied and adopted in numerical simulations, the size effects physics is not yet thoroughly under‐ stood. The influence of size effect on deformation mechanics in microforming processes is still a challenging issue to be investigated.
