RD-E: 4801 Solid Spotweld Validation

Introduces how to model a solid element spotweld using /MAT/LAW83 + /FAIL/SNCONNECT and validate results using experiment data.

One element test to validate solid spotweld material and failure behavior.

The following criteria are used to compare the results.

Maximum stress and force
Damage initiation displacement and failure displacement

Options and Keywords Used

Solid spotweld material (/MAT/LAW83)
Spotweld failure model (/FAIL/SNCONNECT)
Solid spotweld property (/PROP/TYPE43 (CONNECT))
Sheet metal material (/MAT/LAW1 (ELAST), /MAT/LAW2 (PLAS_JOHNS))
Self-impacting contact (/INTER/TYPE7)
Rigid body (/RBODY)

Input Files

The input files used in this example include:

<install_directory>/hwsolvers/demos/radioss/example/48_solid_spotweld/one_solid_test/One_solid_element_validation_law83*

Model Description

The spotweld is represented by one solid element connected the upper and lower sheets using a tied contact.

Spotwelds are difficult to test independently. They are normally tested together with upper and lower surface parts. A KS2 test specimen is used in this example. Four loads are tested to characterize the mechanical behavior in tension, shear and moment; except for the peel test, the name of the test is based on the angle between the loading direction and the sheet metal.

Shear test (angle of load and sheet is 0°, below also named with 0° test)
Normal test (90° test)
Shear and normal combined tests (30° and 90° tests)
Peel test

The spotweld thickness is half of the sum of the sheet metal thicknesses.(1)

t h i c k n e s s = \frac{2.0 + 1.5}{2} = 1.75

Although physical spotwelds are normally cylindrical, they are modeled using a hex element with the same area as the physical cylindrical spotweld. A tied contact is used to attached the spotweld nodes to the upper and lower sheet metal.

Units: mm, ms, Kg, kN, GPa

The upper and lower sheet metal use /MAT/LAW36, with the following characteristics:

Material Properties
Initial density: 7.85e-6 [Kg/mm³]
Young's modulus: 210 [GPa]
Poisson ratio: 0.3
Yield stress: 0.370 [GPa]

Simulation Iterations

The spotweld is modeled using the connection material /MAT/LAW83 and connection failure /FAIL/SNCONNECT.

In LAW83 the following parameters need to be determined and validated with the experimental data:

Yield curve, fct_ID₁
Young's modulus
Maximum stress in normal and shear direction with $R_{N}, R_{S}$
Maximum stress for loads that combine normal and shear loading $β$
Maximum stress in moment (peel test) $α$

In /FAIL/SNCONNECT, the beginning of displacement damage and final displacement failure needs to be determined and validated in the following experiments:

${\bar{u}}_{0}^{p l}$ and ${\bar{u}}_{f}^{p l}$ in normal and shear direction with $f_{0 S}$ (fct_ID_0S), $f_{F S}$ (fct_ID_FS), $f_{0 N}$ (fct_ID_0N), and $f_{F N}$ (fct_ID_FN)
${\bar{u}}_{0}^{p l}$ and ${\bar{u}}_{f}^{p l}$ in combined loading direction with $β_{0}, β_{f}$
${\bar{u}}_{0}^{p l}$ and ${\bar{u}}_{f}^{p l}$ in moment (peel test) with $α_{0}, α_{f}$

LAW83 Yield Curve

In an experiment, force vs displacement in normal direction (90° test), tangent direction (0° test, shear) and in combined direction (30° and 60° tests) are measured. These results are converted to true stress vs plastic displacement curves. Next, the test results are normalized and used as the yield curve in LAW83 (input in fct_ID₁). The stress should be normalized by maximum stress of shear test.

LAW83 Young's Modulus

The Young’s modulus in LAW83 could also take Young’s modulus from true stress vs displacement curve of 0° test.

LAW83 Maximum Stress Validation

The maximum stress in the normal direction and in tangent direction is extracted from the 90° test and 0° shear test and input as $R_{N}, R_{S}$ in LAW83.

The maximum stress in the combined direction is described by the parameter

β

which can be calculated using a fitting algorithm from the maximum stress in the 30° and 60° tests. The fitting is done using the following equation (ignoring

α

which is used in the peel test).(2)

σ_{y} = {[{(\frac{σ_{n}}{R_{N} \cdot f_{N}})}^{β} + {(\frac{σ_{s}}{R_{S} \cdot f_{S}})}^{β}]}^{\frac{1}{β}}

In this example, check the /MAT/LAW83 parameters

R_{N}, R_{S}

with the fitted parameter

β = 1.434

and no failure. This shows that the stress stays constant once it reaches the maximum stress. The maximum stress of 90° test, 0° test, 30° test and 60° test are close to experiment data.

The maximum stress in the peel test is scaled from the maximum stress in the test using the parameter

α

from the following equation which does not include shear.(3)

σ_{y} = {[{(\frac{σ_{n}}{R_{N} \cdot f_{N} (1 - α \cdot sym)})}^{β}]}^{\frac{1}{β}}

This equation shows that the maximum stress in the peel test is scaled by

(1 - α \cdot sym)

. Where

s y m = \sin (A)

and

A

is the angle between lower surface and upper surface of the solid element. This angle

A

is hard to measure from experiment. To determine

α

, several validation simulations should be ran to determine the

α

value that matches the experimental peel test results. Since the maximum force peel test is 0.5* the maximum force in the 90°, a good starting value is

α = 0.5

. After a few iterations, you will find that

α = 0.627

results in a maximum force in peel simulation that matches the experiment data.

Spotweld Failure (/FAIL/SNCONNECT)

After validating the maximum stress with LAW83, the spotweld failure needs to be validated using the failure model /FAIL/SNCONNECT. In this failure model, you need the displacement value where damage begins

{\bar{u}}_{0}^{p l}

and displacement at failure

{\bar{u}}_{f}^{p l}

from the experiment.

Spotweld failure in 90° (normal) and 0° (shear) test
Input the displacement where damage begins ${\bar{u}}_{0}^{p l}$ and displacement at failure ${\bar{u}}_{f}^{p l}$ from the 90° test into functions ( $f_{0 N}$ (fct_ID_0N) and ( $f_{F N}$ (fct_ID_FN) and from test into functions ( $f_{0 S}$ (fct_ID_0S) and $f_{F S}$ (fct_ID_FS). Since there is no rate effect data, the curves will be constant.

Figure 10. Beginnining and Failure Damage Displacements

Using these values in a simulation, the beginning damage displacement and failure displacement match very well to the 0° test results. However, the simulation does not match very well to the 90° test. This is due to the deformation of upper and lower sheet metal. In the 0° test, the sheet metal barely deforms.

Figure 11. Simulation with Damage and Experimental Results. 0° and 90° tests

Using the displacement of the sheet metal from the simulation results, the sheet metal displacement is subtracted from the ${\bar{u}}_{0}^{p l}$ and ${\bar{u}}_{f}^{p l}$ of the 90° test. After doing this, the force displacement curves in the simulation match the test.

Figure 12. Improved Failure Results
Spotweld Failure in Combined Tests
The beginning and failure damage in the 30° and 60° tests (combined normal and shear loading) can be defined using the parameters $β_{0}, β_{f}$ in the following equations, which do not consider $α_{0}, α_{f}$ which are for peel test.(4) $1 = {[{(\frac{{\bar{u}}_{0, n}^{p l}}{f_{0 N}})}^{β_{0}} + {(\frac{{\bar{u}}_{0, s}^{p l}}{f_{0 S}})}^{β_{0}}]}^{\frac{1}{β_{0}}}$ (5) $1 = {[{(\frac{{\bar{u}}_{f, n}^{p l}}{f_{F N}})}^{β_{f}} + {(\frac{{\bar{u}}_{f, s}^{p l}}{f_{F S}})}^{β_{f}}]}^{\frac{1}{β_{f}}}$

Taking ${\bar{u}}_{0}^{p l}$ and ${\bar{u}}_{f}^{p l}$ from experiment data:

Figure 13. Test Results - 30° and 60°

Using the results from the 30° and 60° tests, the $β_{0} = 2.389$ and $β_{f} = 2.249$ values are calculated using an equation fitting routine.

Figure 14. Damage and Failure Surface Fit

Figure 15. Results Initial Beta Parameter Fitting

Using the calculated fitted parameters $β_{0}, β_{f}$ , the simulation shows that the start of the damage does not match the experimental data. Similar to the 90° test, the deformation of sheet metal needs to be excluded from the damage displacements. The sheet metal displacement from the simulation is subtracted from the damage displacement and new parameters $β_{0} = 3.2$ and $β_{f} = 3.721$ are calculated using the fitting algorithm.

Figure 16. Damage and Failure Surface Fit

Figure 17. Validation - 30° and 60° Tests

Using the updated $β_{0}, β_{f}$ parameters, the beginning of the damage better matches the experiment data.
Spotweld Failure in Peel Test
To correctly simulate the moment loads that occur in the peel test, the $α_{0}, α_{f}$ scale factor parameters must be calculated.

If the shear terms are ignored, the beginning and failure damage is represented as:(6) $1 = \frac{{\bar{u}}_{0, n}^{p l}}{f_{0 N} (1 - α_{0} \cdot s y m)}$ (7) $1 = \frac{{\bar{u}}_{f, n}^{p l}}{f_{F N} (1 - α_{f} \cdot s y m)}$

The $(1 - α_{0} \cdot sym)$ and $(1 - α_{f} \cdot sym)$ terms scale the normal term in the equation. As done before for LAW83, the $α_{0}, α_{f}$ terms can be determined using the simulation and optimization or trial and error to match the peel test results. Starting with $α_{0} = 0.5; α_{f} = 0.5$ and the knowledge that increasing these terms decreases the ${\bar{u}}_{0}^{p l}$ and ${\bar{u}}_{f}^{p l}$ values, you determine that the parameters $α_{0} = 1.2; α_{f} = 1.3$ (peel test 2) result in ${\bar{u}}_{0}^{p l}$ and ${\bar{u}}_{f}^{p l}$ values that match the experimental peel test data.

Figure 18. Validation - Peel Test

Results

With a minimum of 4 different experimental tests, input data for /MAT/LAW83 + /FAIL/SNCONNECT can be validated for use with solid brick element spotwelds.

Using a KS2 test specimen, a 0° test, 90° test, peel test and at least one combined loading (30, 45 or 60 degree) test is needed. Since there can be variations in the test data, it is better to have multiple test results for each test.

If upper and lower sheets deformed during the test, the simulations results can be used to modify the damage displacements during the validation of the spotweld failure displacement in /FAIL/SNCONNECT.