Crack growth in a 0.5 inch UNC threaded connection
This example shows a crack growing under fatigue loading from the root of a thread in a bolted connection. The model is a simplified one in which the circumferential effect of the pitch is not included i.e. the model is a 3D equivalent of an axi-symmetric model. A 90 degree sector is modelled with the crack extending around the full 90 degrees of the model.
The geometry is defined for a coarse (UNC) 0.5 inch major diameter thread (see https://en.wikipedia.org/wiki/Unified_Thread_Standard). In terms of the definitions in Figure 1, the major diameter is Dmaj=0.5" and the pitch is P=1/13" (i.e. 13 threads per inch).
The geometry of the 90 degree sector, expanded to 180 degrees for visualisation, is shown in Figure 2. The uncracked mesh for the model is shown in Figure 3. The load is applied via displacement controlled boundary conditions: one end of the bolt is held in the axial direction and a face of the nut is pushed axially. The nut is also constrained to prevent radial motion of the outer surface. Four contact pairs are defined between the appropriate inclined thread surfaces of the bolt and nut. The resulting displacement magnitudes and Von Mises stress at the maximum load condition are shown in Figures 4 and 5 for the uncracked component. For the crack growth analysis a zero to maximum (constant amplitude) cycle is defined in the Zencrack input file.
The thread at the first contacting tooth has peak stress at the root. As shown in the maximum principal stress plot of Figure 6, this peak is slightly offset from the geometric base of the root. The position of this peak is used to define the initial crack position as shown in the first mesh of the crack growth analysis in Figure 7.
As the crack growth proceeds, the crack advances through the mesh. Animations of the crack growth are shown in Figure 8 and Figure 9.
Each individual crack configuration analysed during the growth sequence can be saved and re-analysed as a stand-alone finite element run with a modified loading sequence. In the example of Figure 10, a more detailed load incrementation is used to allow generation of a Von Mises contour plot through a single loading cycle.
Figure 1 - Thread definition (ref. https://en.wikipedia.org/wiki/Unified_Thread_Standard)
Figure 2 - Geometry showing a section of bolt surrounded by a nut
Figure 3 - Mesh for the uncracked component
Figure 4 - Contours of displacement magnitude for the uncracked component
Figure 5 - Contours of Von Mises stress for the uncracked component
Figure 6 - Contours of maximum principal stress used to determine a likely initial crack location
Figure 7 - Mesh containing the initial crack