RD-E: 4802 Solid and Spring Spotweld in Crash Box

The purpose of this example is to introduce solid element modeling for spotweld connection.

Solid spotweld defined with /MAT/LAW59 and /FAIL/CONNECT connect two metal sheets with tied contact.
Figure 1.

ex48_solid_spotweld

Options and Keywords Used

  • Rigid body and Boundary conditions

    One end of the crash box is modeled using a rigid body and this rigid body is completely fixed using translations and rotations.

  • Rigid wall

    The impactor is modeled using a moving rigid wall having a fixed velocity (5 m/s) in a X direction and is fixed for other translations and rotations.

  • Interface

    The structure interaction is modeled using a TYPE7 interface on the full structure with self-impact, where the main surface is defined using the complete model and the secondary nodes group is defined using the main surface.

Input Files

Before you begin, copy the file(s) used in this example to your working directory.

Model Description

A steel crash box with solid spotweld, fixed at one end, is impacted at the other end by a rigid wall. The dimensions of the crash box are 333.6 mm x 122.7 mm x 68.28 mm, and its thickness is 1.8 mm.
Figure 2. Problem Description and Beam Cross Section

ex48_problem_description

Units: mm, s, Mg , N , MPa

Using the Johnson-Cook plasticity model (/MAT/LAW2), the sheet metal material has the following characteristics:
Material Properties
Value
Initial density
7.8e-9 [Mg/mm3]
Young's modulus
210000 [ MPa ] MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaadaWadaqaai Gac2eacaGGqbGaaiyyaaGaay5waiaaw2faaaaa@3BE6@
Poisson's ratio
0.3
Yield stress
250 [ MPa ] MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaadaWadaqaai Gac2eacaGGqbGaaiyyaaGaay5waiaaw2faaaaa@3BE6@
Hardening parameter
350 [ MPa ] MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaadaWadaqaai Gac2eacaGGqbGaaiyyaaGaay5waiaaw2faaaaa@3BE6@
Hardening exponent
0.3

In this connection material (/MAT/LAW59) use stress - plastic strain curve to describe the material characters of spot-weld. With failure model (/FAIL/CONNECT) it is possible to use two different failure criteria to describe the failure of solid spot.

In this example, use the following characteristics:
Material Properties
Value
Initial density
7.8e-9 [Mg/mm3]
Young's modulus
210000 [ MPa ] MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaadaWadaqaai Gac2eacaGGqbGaaiyyaaGaay5waiaaw2faaaaa@3BE6@
Failure relative displacement in normal direction
1.0
Failure relative displacement in tangential plane
1.8
Figure 3. Material Curve of Sheet Metal and Solid Spotweld

ex48_material_curve

In this example a linear behavior of spotweld has just been assumed. For more accurate results, you can also put nonlinear behavior of spotweld through real physic test and CAE validation.

Model Method

Figure 4.

ex48_spotweld_model
Solid spotweld will be modeled as:
  • /MAT/LAW59 to define the material
  • /FAIL/CONNECT to define the rupture criteria
  • /PROP/TYPE43 to define the spotweld property, which should be only used with /MAT/LAW59
  • /INTER/TYPE2 to define the connection between spotweld and sheet metal
Note:
  1. In this spotweld modeling surface 1 (Node 1, 2, 3, and 4) and surface 2 (Node 5, 6, 7, and 8) are defined. The normal direction has been defined from surface 1 to surface 2.
  2. Surface 1 and 2 for each solid spotweld should always connect with a shell element. If one surface of one solid spotweld is not connected with a shell element, then the stiffness will not be computed correctly and an error may occur.

Results

With /ANIM/BRICK/TENS/STRAIN and /ANIM/BRICK/TENS/STRESS you get the strain and stress results of the solid spotweld (Figure 5, Figure 6).
Figure 5. Strain of Solid Spotweld

ex48_spotweld_strain
Figure 6. Stress of Solid Spotweld

ex48_spotweld_stress

Here in the model you define max. relative displacement in normal direction EPS_N_MAX=1.0 in option /FAIL/CONNECT. Therefore, two solid spotwelds (circled in red) failed after reaching this criterion.

Figure 7. Strain of Solid Spotweld (display eroded element in HyperView)

ex48_spotweld_strain2
Figure 8. Force versus Displacement of Crashbox

ex48_force_vs_disp

Performance

Compared with spring beam spotweld molding, the following performance could be observed:

If you use this solid spotweld modeling, it shows less sheet metal mesh size dependence compared with spring beam element.
  • With coarse sheet metal mesh size, you got similar deformation and similar Force versus Displacement curve for solid spotweld modeling and spring beam spotweld modeling.
    Figure 9.

    ex48_performance
  • Once you remesh the sheet metal shell element with fine mesh size (for example with 2.5mm mesh size here), then you still get similar deformation and Force versus Displacement curve in solid spotweld modeling but not in spring beam spotweld modeling. This means less sheet metal mesh size dependence for this new solid spotweld modeling.
    Figure 10.

    ex48_performance2
  • The solid spotweld element is time step is free. The element stability is assured by its nodal connection. The node of the solid element must be connected (tied interface, common nodes, and rigid connection).
  • The solid spotweld element height (length in local Z direction) can be null and the spotweld results are independent from its height.
  • Strain rate of solid spotweld can be taken into account.