# 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 OptiStruct 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 on FATPARM Bulk Data.
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 on FATPARM Bulk
Data. 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 FATDEF Bulk and Subcase entries can be used to identify the
elements for which fatigue analysis should be
performed. For spot weld fatigue, the
PWELD, PBAR,
PBEAM,
PBARL,
PBEAML, and
PSOLID continuation lines are
available for the definition of the spot weld
elements via the
`PTYPE`continuation. Additionally, the`ELSET`field also supports the CBAR, CWELD, CBEAM, CHEXA entries. The sheets can be defined using the`PSHELL`continuation line. - The FATDEF Bulk Data Entry also provides the corresponding PFATSPW Bulk Data Entry references for each spot weld element to define the spot weld fatigue properties.
- If PWELD references are used, then the
`TYPE`field on the PWELD entry should be set to SPOT for spot weld fatigue. - The
`DTAB`continuation line on the PWELD entry can be used to define the weld element diameter as a function of the minimum shell thickness. - 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. For more information on the element and the grinding number, refer to the CHEXA Bulk Data Entry.

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

- The FATPARM Bulk Data and Subcase Entries can be used to specify fatigue parameters for the Spot Weld Fatigue Analysis.
- The
`SPWLD`continuation line on the FATPARM entry allows you to input the spot weld fatigue method and identify various parameters. - The PFATSPW Bulk Data Entry allows the definition of some properties for Spot Weld Fatigue Analysis.

### Fatigue Material

- The MATFAT Bulk Data Entry can be used to specify the material properties for Spot Weld Fatigue Analysis.
- The
`SPWLD`continuation line allows you to specify mean stress sensitivity value, and separate SN curve attributes for sheet 1, sheet 2, and the nugget.

### Fatigue Loads

- Similar to regular fatigue analysis, the FATLOAD, FATSEQ, and FATEVNT entries can be used to define loading sequences.

### Optimization

- The weld element diameter (
`D`on PWELD entry) can be used as a design variable in optimization runs using the DVPREL1/DVPREL2 Bulk Data Entries. - The
`ATTB`field on the DRESP1 entry can be set to SPWLD to activate spot weld fatigue optimization.

### Output

Output for Spot Weld Fatigue Analysis is
provided similar to regular Fatigue Analysis results. Damage and
Life results for the sheet 1, sheet 2, and nugget are available in the H3D file
via the Spot Weld Damage(s) and Spot Weld Life(s) result types in HyperView. The damage calculation location can be set in OptiStruct via the
`SPTFAIL`=SHEET, NUGGET,
or ALL options on the PFATSPW Bulk Data
Entry. Additionally,
you can choose to only display the worst damage out of the three damage
locations (sheet 1, sheet 2, or nugget) by choosing the Damage(s) result
type.

You can similarly choose to view results at the sheet locations for Spot Weld Damage and Life.