# Advanced Structural Analysis/Part I - Theory/Failure Modes/Fatigue/Special Members/Welded Joints

Fatigue of welded joints is well in line with previously presented material on fatigue analysis, in the sense that it is a complex and local phenomena.

There are however both local and global approaches to assess the fatigue life of welded joints. Among the more famous local approaches are the Hot-spot stress method, Notch stress method and Linear Elastic Fracture Mechanics (LEFM). What ought to be the most commonly used method, the Nominal stress method, is a global method, although it is designed to indirectly account for the local effects.

These methods vary significantly regarding the accuracy they provide and the work effort they require. Below is a list where the methods are presented in order of increasing accuracy and work effort:

1. Nominal Stress Method
2. Hot-Spot Stress Method
3. Effective Notch Stress Method
4. Linear Elastic Fracture Mechanics

The three first methods are essentially based on common grounds, they only differ in how their features are emphasized. They all rely on reference empirical data, a measure of stress and the Basquin relation. The nominal method utilizes vast amounts of experimental reference material and a very coarse and limited measure of stress; and can be considered having a low abstraction level. The opposite extreme is the effective notch method which relies on a very concise empirical foundation and a very detailed and general stress measure. The linear elastic fracture mechanics method has an even greater abstraction level, but is essentially different than the other three methods.

Before we discuss these analysis methods any further, let us consider some important geometrical aspects of welded joints.

## Global Geometrical Factors

Need illustrations here

## Local Geometrical Factors

Need illustrations here

# Nominal Stress Method

The nominal stress method is a non-local fatigue assessment method. It is based on the notion that the fatigue life of a welded joint can be sufficiently specified by the characteristic global geometry of the joint and the history of nominal stresses at specified locations.

The characteristic global geometry of the joint is specified by a design category and one or several corresponding detail category numbers, see The Wöhler Curve and Basquin Relation.

## Hot-Spot Stress Method

The Hot-spot method is based on detail categories and detail category numbers, -very much in the same sense as the nominal stress method is. The only difference is that the hot-spot method incorporates the more competent measure geometrical stress, as opposed to the more limited measure nominal stress. As a Consequence, the hot-spot approach require fewer detail categories than the nominal stress in order to provide comparable versatility.

At present, there are only two applied detail category numbers: FAT100 MPa and FAT90 MPa.

## Geometrical Stress

Geometrical stress (also called structural stress) is defined as the summation of all stress rising effects except the notch effects of the weld. The concept is valid for linear-elastic models. The adopted mathematical "definition" is represented by the following to equations:

${\displaystyle \sigma _{hs}=1.67\sigma _{0.4t}-0.67\sigma _{1.0t}}$ (linear extrapolation)

or

${\displaystyle \sigma _{hs}=2.52\sigma _{0.4t}-2.24\sigma _{0.9t}+0.72\sigma _{1.4t}}$ (quadratic extrapolation)

Where ${\displaystyle \sigma _{0.4t}}$, ${\displaystyle \sigma _{0.67t}}$, ${\displaystyle \sigma _{0.72t}}$ etc. refer to the stress at the distances ${\displaystyle 0.4t}$, ${\displaystyle 0.67t}$, ${\displaystyle 0.72t}$ etc., from the hot-spot. The factor ${\displaystyle t}$ represents the thickness of the parent material.

Linear extrapolation is suitable when present bending is low or the mesh is coarse (element size in the order of ${\displaystyle >0.2t}$). Quadratic extrapolation should be used in other cases.

## Effective Notch Stress Method

The effective notch stress method represents a very generalized view of welds subjected to fatigue loads. The stress measure is defined as the local maximum stress in linear-elastic weld models where the true notches have been substituted by fictitious notches of radius ${\displaystyle r}$. This stress measure reflects the local effects very well and in a scalable manner. As a result only one detail category is necessary for a general analysis.

The value of ${\displaystyle r}$ is:

• ${\displaystyle r=1}$ mm for parent material thickness greater than 5 mm
• ${\displaystyle r=0.05}$ mm for parent material thickness smaller than 5 mm

The FAT = 240 MPa yields 97.7% survivor probability at ${\displaystyle 2\cdot 10^{6}}$ cycles.