Demonstration Of Springback

Chapter 18: Demonstration of Springback

18

Demonstration of Springback



Summary



Introduction



Reference Solution



FEM Solutions



Modeling Tips



Input File(s)



Video

311

306 307

307 310 310

307

306 MD Demonstration Problems CHAPTER 18

Summary Title

Chapter 18: Demonstration of Springback

Contact features

Rigid-deformable contact, velocity driven rigid cylinder, load controlled rigid cylinder, and release of a contact bodies

Geometry

Rigid cylinder, D = 0.4375 in A

D

Material properties

6

4

E = 10.6 10 psi  = 0.33  y = 4.29 10 psi

Elastic plastic material with work-hardening Analysis type

Quasi-static analysis

Boundary conditions

• Left side is constrained with u x = 0 • A spring is used to constrain the motion in the y-degree of freedom • Contact between rigid cylinder and the deformable body

Applied loads

Two types of load introduction will be used: • Constant “velocity” vx = 0.1125 applied on the rigid body • Control node ux = 0.1125 applied on the load controlled rigid body

Element type

2-D 4-node plane strain elements

Contact properties

Friction coefficient =0.2

FE results

Contour of equivalent stress at the end of forming, equivalent stress after the springback; displacement history of point A. X-Displacement (in) Point A

0.20 forming

springback

0.15

0.10 MD Nastran Sol400 MSC.Marc

0.05

% of Load

0.00

0

50

100

150

200

CHAPTER 18 307 Demonstration of Springback

Introduction Significant permanent deformation and large strains occur during the forming step by moving a cylindrical rigid body into the metal structure. The metal structure springs back upon removal of the cylindrical rigid body using the contact table definition.

Reference Solution MSC.Marc 2005r3 will be used to create a reference solution.

FEM Solutions The finite element model is shown in Figure 18-1. There are two contact bodies: one deformable and one rigid body. BCBODY BSURF ... BCBODY

1 1

2D 1

DEFORM 2

4 0 RIGID NURBS2D .85875

2D 0. 0 -7 .51775

RIGID 0. 72 4

1 3 0. CYL 50 .85875

0 4

5

6

7

1 1.

0.1125

1 0.

0 0.

.95525

...

The deformable contact body is simply a collection of mutually exclusive elements and their associated nodes. The rigid cylindrical body is defined using 2-D NURBS line. Furthermore, the BCTABLE entries shown below identify that these bodies can touch each other. Since the master body is a rigid one, this actually means that the deformable body is the slave one. BCTABLE

BCTABLE

0 SLAVE

1 0 MASTERS 4 1 SLAVE 1 0 MASTERS 4

0. 0

1 0. 0

.2

0.

0

0.

0. 0

1 0. 0

.2

0.

0

0.

During the springback analysis, the contact forces on the deformable body due to the contact with the rigid body are removed immediately. It is done using BCMOVE option. To prevent the two bodies cylinder reclaims contact, a new BCTABLE has to be defined that does not include the cylinder. BCMOVE BCTABLE

2 4 2

RELEASE 0 1

1

The geometric nonlinear analysis is requested using the following LGDISP parameter. The large strain option is also set in this model PARAM NLMOPTS

LGDSIP LRGSTR

1 1

308 MD Demonstration Problems CHAPTER 18

To activate the friction behavior, the user should use the BCPARA option as follows: BCPARA

0 FTYPE

6

A

Figure 18-1

Finite Element Mesh

Plane strain elements for large strain elastic-plastic analyses are chosen by the PSHLN2 entry referring to the PLPLANE entry on the CQUAD4 option as shown below. PLPLANE 1 PSHLN2 1

1 1

1

The material property is isotropic and elastic-plastic with hardening. The Young’s modulus, Poisson’s ratio, and plasticity parameters are defined as follows: MAT1 MATEP TABLES1 * …

1 1 1 0.

1.06+7 TABLE 2

.33 1 42900.

ISOTROP ADDMEAN 0.001733

43110.2

The nonlinear procedure used during the forming and springback are set using the following options: NLPARM NLPARM

1 2

30 1

PFNT PFNT

U U

Here the PFNT option is selected to update the stiffness matrix during every recycle using the Newton-Raphson iteration strategy, and the default displacement convergence tolerances will be used. The simulation process is controlled by the case control section. The first step is the forming process and the second one is the springback analysis: BCONTACT=0 SPC = 2 STEP 1 TITLE=Forming Step NLPARM = 1 BCONTACT = 1 LOAD = 1

CHAPTER 18 309 Demonstration of Springback

STEP 2 TITLE=Springback Step NLPARM = 2 BCONTACT = 2

BCONTACT=0 is meant to bring both bodies just in contact. Since there is no explicit external load applied in this analysis, a dummy LOAD is introduced in the case control parameters.

The deformed structure plot (magnification factor 1.0) is shown in Figure 18-2 along with the von Misses stress contour. The maximum stresses are located at the expected location.

UNDEFORMED

DEFORMED

Figure 18-2

Deformed Configuration with von Misses Stress Contour at the End of the Forming Step

The deformation after the springback analysis is shown in Figure 18-3. There is significant permanent deformation during the forming process as obviously seen from this figure. The von Misses stresses of the residual stresses are also plotted.

UNDEFORMED

DEFORMED

Figure 18-3

Deformed Configuration with von Misses Stress Contour After the Springback

310 MD Demonstration Problems CHAPTER 18

The displacement of point A is plotted versus time (percentage of load) in Figure 18-4 illustrating the elastic springback upon unloading the structure. This behavior is compared with a reference plot obtained with MSC.Marc 2005r3. The result of MD Nastran matches the referenced one very nicely. X-Displacement (in) Point A

0.20 forming

springback

0.15

0.10 MD Nastran Sol400 MSC.Marc

0.05

% of Load

0.00

0

50

Figure 18-4

100

150

200

Displacement Plot for Point A During Forming and Springback Step

Modeling Tips Force control applied via a control node associated with the rigid cylinder may be used instead of displacement (or equivalently velocity) control. Using this technique, the release of the load requires less difficulty with the contact table (please see nug_18b.dat). In terms of CPU time, removing the rigid body from contact table is more efficient since there is no need to do contact manipulation (please see nug_18c.dat).

Input File(s) File

Description

nug_18a.dat

“Velocity” driven rigid body

nug_18b.dat

Load controlled rigid body without BCMOVE

nug_18c.dat

Load controlled rigid body with BCMOVE

CHAPTER 18 311 Demonstration of Springback

Video Click on the image or caption below to view a streaming video of this problem; it lasts approximately 18 minutes and explains how the steps are performed.

UNDEFORMED

DEFORMED

Figure 18-5

Video of the Above Steps