Implementation

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

Fatigue analysis for spot welds involves examining the weld at three distinct locations, the center planes of the two attachment sheets at the points of attachment and at the center of the nugget and is based on a paper by Rupp et al. The cross-sectional forces and moments at each of the three locations is determined and used to calculate corresponding stresses. These stresses are then used to calculate Fatigue Damage using Rainflow counting and the SN approach.

Figure 1. Spot Weld Fatigue Locations

The following sections illustrates how stresses and subsequently damage are calculated at each of the three locations shown in Figure 2.

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.

Sheet Location 1

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.

Sheet Location 2

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.

Forces and Moments are generated as output from the applied loading for the weld element (CWELD, CBAR, CBEAM, or CHEXA). As explained previously, the calculation process involves an extra step for CHEXA elements, and except for this difference, the procedure is identical for all spot weld elements. Even though the sheet fatigue behavior point is being examined, the forces at the ends of the weld element are used since they are equivalent.

Figure 2. Forces and Moments of Interest at the Sheet Locations

Radial stresses are calculated at the sheet locations by considering weld element forces at the attachment points. The radial stresses

σ (θ)

are calculated as a function of

θ

for each point in the load-time history as follows:(1)

σ (θ) = - σ_{\max} (f_{y}) \cos θ - σ_{\max} (f_{z}) \sin θ + σ (f_{x}) - σ_{\max} (m_{y}) \sin θ - σ_{\max} (m_{z}) \cos θ

Where,(2)

σ_{\max} (f_{y}) = \frac{f_{y}}{π D T}

(3)

σ_{\max} (f_{z}) = \frac{f_{z}}{π D T}

$σ (f_{x}) = κ (\frac{1.744 f_{x}}{T^{2}})$ for $f_{x} > 0.0$

σ (f_{x}) = 0.0

for

f_{x} \leq 0.0

(4)

σ_{\max} (m_{y}) = κ (\frac{1.872 m_{y}}{D T^{2}})

(5)

σ_{\max} (m_{z}) = κ (\frac{1.872 m_{z}}{D T^{2}})

Where,

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

The equivalent radial stresses are calculated at intervals of $θ$ (Default =18 degrees). The value of $θ$ 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 ( $θ$ ). The worst damage value is then picked for output. A similar approach is conducted for the other sheet.

Nugget Location

The nugget location is at the center of the weld element. Forces and moments are generated as output from the applied loading for the weld element (CWELD, CBAR, CBEAM, or CHEXA). As explained previously, the calculation process involves an extra step for CHEXA elements, and except for this difference, the procedure is identical for all spot weld elements.

Figure 3. Forces and Moments of Interest at the Nugget Cross-Section

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:(6)

τ (θ) = τ_{\max} (f_{y}) \sin θ + τ_{\max} (f_{z}) \cos θ

(7)

σ (θ) = σ (f_{x}) - σ_{\max} (m_{y}) \sin θ - σ_{\max} (m_{z}) \cos θ

Where,(8)

τ_{\max} (f_{y}) = \frac{16 f_{y}}{3 π D^{2}}

(9)

τ_{\max} (f_{z}) = \frac{16 f_{z}}{3 π D^{2}}

$σ (f_{x}) = \frac{4 f_{x}}{π D^{2}}$ for $f_{x} > 0.0$

σ (f_{x}) = 0.0

for

f_{x} \leq 0.0

(10)

σ_{\max} (m_{y}) = \frac{32 m_{y}}{π D^{3}}

(11)

σ_{\max} (m_{z}) = \frac{32 m_{z}}{π D^{3}}

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