3.3 Simulation of finite elements of square towers with different angles

After collecting experimental data, this data is used as input parameters for the simulation process. To determine the accuracy of the simulation process compared to the corresponding experiment, the square tower shape with different angles was simulated to predict the forming height obtained until the appearance of the tear of products for materials.

Figure 13 describes the simulation results. From the simulation results, we can observe the ductile fracture phenomenon occurs with the wall angle of 80° and the forming height of 25 mm (Figure 13a). While forming with a square shape with 45° wall angle, the fracture is not observed even until the end of forming process with the final forming height of 40 mm (Figure 13b). In order to verify the predictability of the simulation process, the corresponding experiments were also conducted as shown in Figure 13. The experimental results are in good agreement with corresponding simulation results.

However, commercial software is inconvenient to simulate an incremental forming process for a complex shape because the various programs only support simple movements such as linear or circular motions. To overcome this inconvenience, the combination of CAM and computer-aided engineering (CAE)

> simulation using MATLAB programming to modify input ABAQUS file has been proposed. This method was also applied in previous study to simulate ISF for

The evolution of deformed shape in FEM of ISMF [3]. (a) Deformation at tool stroke h = 8.5 mm, (b) Deformation at tool stroke h = 17 mm, and (c) Final results at tool stroke h = 22 mm.

Today, sheet metal forming methods based on the deformation of materials play an important role in mechanical production and metallurgy. The growing applications of numerical simulations in the field of sheet metal forming have helped engineers solve various problems in improving the formability and reducing the cost and time of products. Accurate simulation results are necessary for mold and product design. Many factors affect the final simulation results, but the most important input data for the ductile fracture prediction of a product is the forming limit curve of the sheet material. Several studies have been carried out to predict and evaluate the FLC by using experimental and theoretical methods. In addition, this concept has been widely applied in various commercial finite element software packages for technical studies. According to the experimental approach, Keeler [15, 16] tests are popular methods that have been widely used to clarify the levels of FLCs for sheet metals. However, time-consuming and high-cost computing is the

complex part (Figure 14).

Rapid Prototyping for Sheet Metal Products DOI: http://dx.doi.org/10.5772/intechopen.88435

Figure 14.

109

#### Figure 13.

Simulation and experimental results for square shape with different wall angles. (a) The wall angle of 80°. (b) The wall angle of 45°.

Rapid Prototyping for Sheet Metal Products DOI: http://dx.doi.org/10.5772/intechopen.88435

molds are modeled by rigid surface elements (R3D4). The average size of the elements can be selected to suit the calculation time and desired accuracy.

coefficients between the forming tool and the material sheet have hardly been measured and determined correctly by previous researches. Measuring forming forces and converting them into corresponding friction coefficients are also difficult. In general, the friction coefficient of the forming process could be assumed in the range from 0.05 to 0.2 depending on the specific conditions of the forming process. Another difficult issue is how to obtain reliable material data. Most studies use standard materials and conduct experiments using conventional tension or compression test methods. However, these experimental data only provide results with lower strain values than those observed during ISMF. Therefore, the representation of the stress-strain curve for higher deformation levels is necessary to

3.3 Simulation of finite elements of square towers with different angles

shown in Figure 13. The experimental results are in good agreement with

However, commercial software is inconvenient to simulate an incremental forming process for a complex shape because the various programs only support simple movements such as linear or circular motions. To overcome this inconvenience, the combination of CAM and computer-aided engineering (CAE)

Simulation and experimental results for square shape with different wall angles. (a) The wall angle of 80°. (b)

After collecting experimental data, this data is used as input parameters for the simulation process. To determine the accuracy of the simulation process compared to the corresponding experiment, the square tower shape with different angles was simulated to predict the forming height obtained until the appearance of the tear of

Figure 13 describes the simulation results. From the simulation results, we can observe the ductile fracture phenomenon occurs with the wall angle of 80° and the forming height of 25 mm (Figure 13a). While forming with a square shape with 45° wall angle, the fracture is not observed even until the end of forming process with the final forming height of 40 mm (Figure 13b). In order to verify the predictability of the simulation process, the corresponding experiments were also conducted as

Obtaining input data for the simulation of ISMF is not an easy task. The friction

3.2 Material and friction coefficient

Mass Production Processes

simulate the ISMF process.

products for materials.

Figure 13.

108

The wall angle of 45°.

corresponding simulation results.

#### Figure 14.

The evolution of deformed shape in FEM of ISMF [3]. (a) Deformation at tool stroke h = 8.5 mm, (b) Deformation at tool stroke h = 17 mm, and (c) Final results at tool stroke h = 22 mm.

simulation using MATLAB programming to modify input ABAQUS file has been proposed. This method was also applied in previous study to simulate ISF for complex part (Figure 14).

Today, sheet metal forming methods based on the deformation of materials play an important role in mechanical production and metallurgy. The growing applications of numerical simulations in the field of sheet metal forming have helped engineers solve various problems in improving the formability and reducing the cost and time of products. Accurate simulation results are necessary for mold and product design. Many factors affect the final simulation results, but the most important input data for the ductile fracture prediction of a product is the forming limit curve of the sheet material. Several studies have been carried out to predict and evaluate the FLC by using experimental and theoretical methods. In addition, this concept has been widely applied in various commercial finite element software packages for technical studies. According to the experimental approach, Keeler [15, 16] tests are popular methods that have been widely used to clarify the levels of FLCs for sheet metals. However, time-consuming and high-cost computing is the

main drawback of this testing method. Therefore, considerable effort has been made to obtain FLCs theoretically. Swift [17] can be recognized as a pioneering study on predicting FLC. Hill [18] then proposed a way to improve the accuracy of FLC prediction by adopting necking point criteria. Stören and Rice [19] developed a solution for FLC prediction by applying a force equilibrium between necking and uniform deformed regions. Banabic et al. [20] observed and developed a pre-defect in the material and developed a theory of limited deformation based on

imperfections of material thickness. Hora et al. [21] upgraded the Swift diffuse necking criteria and set a modified maximum force criterion (MMFC) by effectively examining the instant deformation state changes until the forming force achieved a maximum value. Some new MMFC models proposed to improve the accuracy of FLC prediction based on theoretical models by solving systems of

Rapid Prototyping for Sheet Metal Products DOI: http://dx.doi.org/10.5772/intechopen.88435

Simulation and rapid prototyping of complex surfaces. (a) Intermediate deformations, and (b) Final shape.

Figure 17.

111

#### Figure 15.

Experiments of incremental forming for various square shape sizes with (a) 80° wall angle, (b) 85° wall angle, and (c) 60° wall angle.

Figure 16. Obtained forming limit based on the maximum wall angle versus maximum deformed height [18].
