A Finite Element study of the Deformability of Steel

Jiadi Fana, Qi Ruib, Jingyi Wangc

aMechanical Engineering, Master of Engineering, jf653@cornell.edu bMechanical Engineering, Master of Engineering, qr24@cornell.edu

cMechanical Engineering, Master of Engineering, jw956@cornell.edu

Deep drawing is a widely used manufacturing method in industrial area. However, improper

method to simulate a certain deep drawing process of 42CrMo high-strength steel. We studied the

mechanism of common defects, simulate different forming conditions (forming temperature,

forming rate, and holding force), and refine the blank size. Finally, we found the most proper

forming conditions and blank size for this process. Our study will optimize forming condition,

enhance productivity, and reduce waste.

1. Introduction

1.1 There are three major parts in a stamping

mold- punch, die and blank holder. In a

normal stamping process, the blank would

deform under the constraints of the blank

holder and ide as the punch goes down.

Several parameters (forming temperature,

forming rate, and holding force) which

determine the forming condition should be

considered to avoid the potential defects like

the wrinkling and fracture. Also, improper

forming conditions may raise the cost of

manufacture and waste time. This report uses

finite element method to analyze the process

and get the proper range of important

parameters by using ABAQUS-a finite element

analysis software.

1.2 Mechanism of common defects

1.2.1 Wrinkling

During deep drawing process, metal flows

from large perimeter area to small perimeter

area. Under minimum principal stress 3 [1],

the blank will be thickened. Uneven

thickening will lead to wrinkling. Wrinkling

increases the surface friction coefficient, and

stop metal from flowing inside. In application,

we need a reasonable holding force to

provide a restriction to avoid wrinkling.

Figure 1 Wrinkling during deep drawing

1.2.2 Fracture

The friction between holder and blank, die

and holder will block metal from flowing. If

the friction is too big, the metal at the bottom

corner will over-thinning, lead to fracture.[2]

Figure 2 Fracture during deep drawing

1.3 The influence of different forming

condition.

1.3.1 Temperature influence

The deformability of metal will improve as

temperature rises, shows in figure 3. [3]

Figure 3 Relation between temperature and

Maximum strentch depth.

Under higher temperature, the deformability

of metal is better. However, good

deformability may lead to over-thinning at

the corner, and reduce the quality of product.

What is more, higher temperature is also

more temperature expensive. From former

research, the suggested forming temperature

of 42CrMo steel is 550-850℃[3]

1.3.2 Holding force influence

Oversize holding force can lead to fracture

defect. And undersize holding force can lead

to wrinkling defect, which will both reduce

the fluidity of metal, shows in Figure 4.

Figure 4 Relation between holding force and

Maximum strength depth.

1.3.3 Strain rate influence

Under large strain rate, the deformability of

metal is poor, which is more like to lead to

fracture. Under small strain rate, the

deformability of metal is good. However,

small strain rate will reduce the productivity.

1.4 Material

In this study, we use 42CrMo high-strength

steel as material. 42CrMo (American Grade:

AISI 4140) is one of the representative

medium carbon and low alloy steels. Its good

comprehensive mechanical properties lead to

the application of many universal parts. Some

of its mechanical parameters are shown in

Table 1 below.

Max

imu

m s

tret

ch d

epth

(m

m)

Simulation Experiment

Temperature ℃

Max

imu

m s

tret

ch d

epth

(m

m)

Simulation Experiment

Holding Force (MPa)

Density (Kg/m^3)

Young’s Modulus (Gpa)

Poison’s ratio

7,830 210 0.31

Table 1 mechanical parameters of 42CrMo

The true stress-strain cure in different

temperatures and strain rate are shown in

Figure 5. [4] We can see that the

deformability of 42CrMo increase as

temperature increases and strain rate

decreases.

Figure 5 true stress-strain curve in different

temperatures and strain rate[4]

2. Case description

We specifically use ABAQUS to simulate the

manufacturing process of bakeware. The

geometry of bakeware shows in Figure 6.

Figure 6 2D geometry of model

In the implement of ABAQUS, a quarter of

entire model is used, because geometrical

symmetry. The ABAQUS model, including

punch, die, holder, and blank, shows in Figure

7.

Figure 7 ABAQUS model

The punch, holder, and die are defined as

rigid shell. Blank is deformed shell with

thickness of 1mm. The symmetry boundary

condition (BC) is implemented for all parts. A

load is implemented on the holder as holding

force. For the die, all degree of freedom are

fixed. Blank and punch can only move in y

direction. The BC of punch is a displacement -

50mm in y direction, which is the depth of the

bakeware. The plastic data is from

experiment data from figure 5.

(b)

3.Result

3.1 Different temperatures

Strain rate was set as 1, holding force was

10kN. The forming process under 600℃ and

650℃ were compared. Shows in Figure 8.

(a)

(b)

Figure 8 forming results in 600℃(a),

650℃(b)

The scale in figure 8 is thickness after forming.

The blue area is the bottom corner, which is

the thinnest area after forming. At 600℃, the

corner thickness is 0.6848, at 650℃, the

corner thickness is 0.6604.

3.2 Different strain rates

The temperature was chosen as 600℃,

holding force was 10kN. The forming

processes under strain rate 0.1 and 1

were compared. Figure 9. After forming , at

=0.1, the corner thickness is 0.7057, at

=1, the corner thickness is 0.6848.

(a)

(b)

Figure 9 Results in =0.1(a) and =1(b)

3.3 Different holding forces

The temperature was chosen as 600℃, strain

rate was 0.1. Choose different holding

force and compared the result. Figure 10.

(a)

(c)

Figure 10. (a)F=5kN, (b)F=10kN, (c)F=30kN

In (a), we can see the uneven thickness after

forming, it is wrinkling. In (c) the corner

thickness became 40% of original thickness,

which can be treated as fracture. In (b), the

corner thickness is 0.7067.

3.4 refine the size of blank

After deep drawing process, the extra blank

needs to be cut off. If the original blank size is

too big, it will be a huge waste. The

temperature was chosen as 600℃, strain

rate was 0.1. Holding force is 10kN.

Choose different original blank size.

(a)

(b)

(c)

Figure 11 (a)400*400mm, (b)300*300mm, (c)

240*240mm.

4.Discussion

From the simulation results, we notice that all

the thinnest area occur at the bottom corner.

So, the corner is the area that most likely to

generate fracture. In this paper, if the

thickness after forming becomes 70% or low

of the original thickness, it can be treated as

fracture.

In Figure 8, the thickness at corner influence

that 42CrMo’s deformability at higher

temperature is better. However, as the

thickness ratio are both under 0.7, it is

unnecessary to simulate at temperature

higher than 650℃.

In Figure 9, the results reflect that

42CrMo’s deformability at lower strain

rate is better. However, at =1, the

thickness ratio is <0.7, so we choose =0.1

as optimized strain rate.

Figure 10 shows the influence of holding

forces. After several simulations, we found

reasonable holding force range is 7-13kN.

Figure 11 shows the blank size refining. For

the given bakeware size, 240*240mm original

blank size is good enough.

5.Conclusions

The critical criterion when we choose

forming condition is 1) Guarantee the

production quality. 2) Reduce the waste of

energy and material. 3)Enhance the

productivity. So, we choose the optimized

forming condition as followings:

Forming temperature T=600 ℃

Strain rate =0.1

Holding force F=7-13kN

Original blank size 240*240mm

In these forming conditions, the simulation

result shows in Figure 12.

Figure 12 Result in optimized forming

conditions

References [1]James A Szumera. (2003). The Metal

Stamping Process

[2] Lim, Y. Process Control for sheet-metal

stamping

[3]Gu, T. (2012). Research on ductile fracture

criterion of hot stamping. China

Academic Journal Electronic Publishing

House, 50-64.

[4]Guo-Zheng, Q. (2013). Characterization for

Dynamic Recrystallization Kinetics

Based on Stress-Strain Curves. In Recent

Developments in the Study of

Recrystallization (p. 9). Intech.