# Spot Weld Fatigue Analysis

Allows for the study of fatigue performance of spot welds in structures.

The length of the spot weld is determined by the attached shell thicknesses. If T1 and T2 are the thicknesses of the two shells, then the length of the spot weld element, L is equal to (T1+T2)/2.

## Implementation

The simplified representation of a spot weld is used in HyperLife to model the fatigue behavior at the weld.

A single weldment may contain a number of sections welded together with welds of different types. However, in this section you only look at analyzing the sections that contain spot welds. Refer to Seam Weld Fatigue Analysis for details about other weld types.

### Simplified Spot Weld Representation

A spot weld is represented as a CBAR, CBEAM, CWELD, or CHEXA elements connected to two sheets of shell elements (PSHELL). The CWELD and CBEAM elements are equivalent to a CBAR element internally. The CHEXA element grid point forces are resolved as beam forces at the geometric centers of each face and then they are considered similar to other 1D elements for fatigue calculations.

### Spot Weld Fatigue

The following sections illustrates how stresses and subsequently damage are calculated at each of the three locations shown in Figure 3.

### Sheet Location (1 or 2)

At sheet location 1 or 2, damage is calculated at the point where the weld is attached to the sheet/shell.

The sheet location 1 is identified by the end A (grid GA) of the nugget (for 1D element nugget) and the face corresponding to the lowest ID’s of the nugget (for CHEXA element nugget). For the structure of CHEXA nugget, refer to Fatigue Input/Output.

The sheet location 2 is identified by the end B (grid GB) of the nugget (for 1D element nugget) and the face corresponding to the highest ID’s of the nugget (for CHEXA element nugget). For the structure of CHEXA nugget, refer to Fatigue Input/Output.

Radial stresses are calculated at the sheet locations by considering weld element forces at the attachment points. The radial stresses $\sigma (\theta )$ are calculated as a function of $\theta $ for each point in the load-time history as:

Where,

$\sigma ({f}_{x})=\kappa \left(\frac{1.744{f}_{x}}{{T}^{2}}\right)$ for ${f}_{x}>0.0$

$\sigma ({f}_{x})=0.0$ for ${f}_{x}\le 0.0$

- $D$
- Diameter of the weld element
- $T$
- Thickness of the sheet under consideration for damage calculation
- $\kappa $
- Calculated as $\kappa =0.6\sqrt{T}$

The equivalent radial stresses are
calculated at intervals of
$\theta $
(Default =18 degrees). The value of
$\theta $
can be modified by varying the
`NANGLE` field in the Assign Material tool.
Subsequently, Rainflow cycle counting is used to
calculate fatigue life and damage at each angle
(
$\theta $
). The worst damage value is
then picked for output. A similar approach is
conducted for the other sheet.

### Nugget Location

The absolute maximum principal stresses are calculated using the shear stress and bending stress of the beam element as a function of θ for each point in the load-time history as:

Where,

$\sigma ({f}_{x})=\frac{4{f}_{x}}{\pi {D}^{2}}$ for ${f}_{x}>0.0$

$\sigma ({f}_{x})=0.0$ for ${f}_{x}\le 0.0$

$D$ is the diameter of the weld element.

$T$ is the thickness of the sheet under consideration for damage calculation.

The stresses are calculated at intervals of
$\theta $
(Default =18 degrees). The value of
$\theta $
can be modified by varying the `NANGLE`
field in the Assign Material tool. The
equivalent maximum absolute principal stresses are
calculated for each
$\theta $
from
$\tau (\theta )$
and
$\sigma (\theta )$
. These stresses are
used for subsequent fatigue analysis. Rainflow cycle
counting is used to calculate fatigue life and damage at
each angle (
$\theta $
). The worst damage value is
then picked for output. A similar approach is conducted for
the other sheet.

## Fatigue Input/Output

Fatigue input for Spot Weld Fatigue Analysis can be divided into the following categories:

### Fatigue Element Identification

- The spot welds (CBAR, CWELD, CBEAM) are referenced with the connected sheets as groups. These groups are currently referenced through components.
- The spot weld diameter, which is a function of the minimum shell element thickness, should be input in the Assign Material dialog.
- The result file should contain the shell thickness output to be automatically referred to the HyperLife Assign Material tool.
- CHEXA elements can be used to define the weld element for Spot Weld Fatigue Analysis. In such cases, the grid point forces are resolved into corresponding forces and moments at the face centers of the opposing faces connected to the shells. The faces of the CHEXA element attached to the sheets should always consist of grid points in the following order.

Additionally, the default weld element diameter of the CHEXA element for spot weld fatigue is equal to two times the smallest distance from the attachment face centroid to the edges.

### Fatigue Parameters (Spot Weld Fatigue Dialog)

- The RUPP method is currently applied to calculate the spot weld fatigue analysis.
- The spot weld fatigue parameters are applied in this dialog.
- Mean stress and thickness corrections
are to be activated if the corresponding
parameters are to be applied in the Assign
Material dialog.
For more information on FKM mean stress correction, see the FKM section under Uniaxial S-N Fatigue.

- FE Model units are specified in this dialog. The default unit specified is MPa. Thickness reference will be automatically modified based in the FE model unit selection.
- Type of loading supported are time series, transient response, and random (Input PSD with FRF).

### Fatigue Material

- The material properties (SN curve attributes for sheet 1, sheet 2, and the nugget) to be associated with the spot weld group are specified in the Assign Material dialog (SN attributes from the My Material or Material Database tab).
- The mean stress sensitivity value and the thickness correction values are specified in the Assign Material dialog.
- By default, the shell thickness of the sheets is referenced from the model. The sheets are editable in HyperLife.
- The spot weld diameter is to be specified in the Thick/Dia entry in the Assign Material dialog.
- TREF is set to 25mm by default, which is equivalent to 1 inch, as specified by the standard.
- Spot Weld group is assigned with a
default material Mat_SpotWeld_default, which can be changed with materials from
Material DB and My Material databases.
Mat_SpotWeld_default has the following properties: SR1 = 14109, b1 = -0.3400, Nc1 = 2000000.00 and Stress Ratio (R) = 0.0

- SPTFAIL
- Damage assessment option type
- ALPHA
- The value of α used to determine the AUTO option on the SPTFAIL field
- TREF
- Reference thickness for thickness effect consideration
- TREF_N
- Exponent for the thickness effect consideration
- SF
- Stress scale factor.

### Fatigue Loads

- Similar to regular fatigue analysis, the fatigue loads are specified in the Load Map tool.
- Time series, transient, and random fatigue events are supported in LoadMap for spot weld fatigue analysis.

### Output

Output for Spot Weld Fatigue Analysis is
provided similar to regular Fatigue Analysis results. Damage and Life results
for the SHEET, NUGGET, ALL or
Auto are available based on the `SPTFAIL`
selection in the Assign Material dialog. The damage calculation lists the worst damage if Auto is
selected. The Damage calculation lists Worst (Sheet1, Sheet2 or Nugget), SHEET
and NUGGET damages if ALL is selected. Sheet damage to show
contour at connected nodes for 1D welds. .