Effect of fastener pre-tension on fatigue relevant stresses | CDGudas
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Pressurised Box

Effects of fasteners pretension in a contact enabled analysis

A 20 inch [508 mm] cubic box modelled with 2D shell located at mid plane of the parts was used to assess the effect of fasteners pretension over a wide range of deformations and stress levels in the components. For this purpose two models representing one quarter of the box were used:

  •  The first model, representative of classical sizing practices, did not include details at the fastener holes with the fasteners being idealised by short springs connecting the parts at the appropriate locations. In this representation the initial fastener pretension was not accounted for because the end nodes of the spring elements belong also to the panels.
  • The second model used a more detailed discretization at the holes in the panels with the fasteners modelled in detail with 3D solid elements.  In this representation a pretension of 500 lbf or 2224 N was applied prior to the main loads to all fasteners in several stages approximately follow a live assembly process.

A unique bulk mesh was used for the box in both models with the differences being localised to the zones immediately adjacent to the holes.   The image gallery on the right side shows representative pictures for the common and model specific elements.  The material properties used and samples of the stiffness values used for the fasteners in the first model are also included.

Excluding the pretension faze, the same loading of 25 psi external pressure was applied to the models in four stages (0-10, 10-15, 15-20 and 20-25) followed by pressure removal for evaluation of the permanent set in the panels and comparative assessment of residual stresses.   Just touching contact was enforced at all surfaces prior to loads application in both models.

Isometric view of the model with 3 detail views for assembly and supports

Click any pictures to enlarge

Internal view of top corner (wireframe edges removed for clarity)
Internal view of lower corner - showing fast. at the base installed from inside
Systematised numbering for fasteners (used also for elements and nodes)

Contact definitions:  In the first representation there are only six sets of contact surfaces between the parts the last one being the upper rigid surface (contact body body 51).  In this case a single additional list of contact pairs (defined through a BCTABL1 entry) is sufficient for the entire loading-unloading cycle after the enforcement of the initial contact conditions (just-touching) with BCTABL1=0.

When enlarged, the figure to the right shows at the bottom the above two entry cards.  Above there are the cards for the definition of the touching and touched contact bodies (BCONECT) and the physical contact parameters between these bodies (BCONPRP).   The geometrical contact parameters used by the solver to determine when contact occurs between two bodies are defined in the card with id 3012.

In the detailed model, the bolts and collars of the 51 fasteners were each separated in two bodies each to enable threads locking after pretension and the gluing of the bolt heads and nut bases to their bases prior to pretension to prevent rigid body singularities.  In this arrangement the model has 251 contact bodies, with 313 contact surfaces and over 450 contact configurations that required a more elaborated approach in model building and for the definition of the contact characteristics during the pretension loading which was applied in 27 steps.  A colour sample of the tables for definition of contact parameters during the pretension and main loading-unloading is shown in the adjacent image gallery.  The supplementary pre-processing work required by the inclusion of 102 additional contact bodies was more than compensated during the solution time and for post-processing of results.

Codification and colour codes

Short brief of results:

  • In elastic range, the predictions for maximum principal stresses on the outer surface of the top panel were up to 60% smaller when fastener pretension was not accounted for. The maximum stresses occurred near the supports (pivoting line) at the free ends of the flanges in the vertical panels and are quite remote from fastener holes. The large differences in values occur for the entire elastic range of the material.  Support configurations for large un-flanged panels supported and loaded in similar manner are quite common in many practical situations (eg. pressure bulkhead, rib webs in wet wings).    The implications of these differences from a fatigue and damage tolerance perspective are clear.    In plastic range the stress differences between the two  models are negligible from an engineering perspective.
  • For the front and lateral panels the maximum stresses develop, as expected, at the flange fillets and the first model provides conservative results in the elastic range. However a stress pattern similar to that described above is noticeable at the front panel, along the edge of the flange in the lateral panel.   In plastic range the differences in maximum principal stresses are also negligible.

The reason for differences in elastic range for the two types panels (un-flanged vs flanged) resides in the restraint role of the fasteners that can be captured only by the second model.  Explanations of these restrains together with additional graphs for the stress envelopes and maximum deformations are presented in this video clip.

% Difference in max principal stress - top panel outer surface

Front panel

Lateral panel

  • Incorporating fasteners pretension in a contact enabled analysis reduces the maximum deformations by more than 20% in the elastic range and less than 10% in plastic.  The overall deformed shape is also affected with the most noticeable differences at the free edges and, in this case, after the initiation of buckling between two consecutive fasteners
Yellow mesh shows the unreformed shape

Iso view (8psi)

Yellow mesh shows the unreformed shape

Side view (8psi)

Yellow mesh shows the unreformed shape

Iso view (10psi)

Yellow mesh shows the unreformed shape

Side view (10psi)

First model at 25 psi -Yellow mesh shows the unreformed shape

Buckled views (25psi)

Second model at 25 psi -Yellow mesh shows the unreformed shape

Buckled views (25psi)

  • In relation to the normal contact stresses developed at the interfaces between the surfaces and the shear stresses occurring during the relative sliding at these locations, it is obvious that fasteners pretension is a major factor in their magnitude. The two models showed that the distribution of these stresses is largely affected not only immediately underneath the pin heads and the bases of the collars, but also further away, near the flange edges, fillets or corners.  In the images on the right a brief exemplification is shown for the upper corner of the lateral panel for pressures up to 8 psi.                                           In these images black indicates that there is no contact, dark blue – juts touching normal contact and red stresses equal or larger than the upper value of the scale used. The same scale in used for both models is kept constant.  In the case of shear stresses, dark blue indicates that the is no sliding while the other colours show the shear stresses developed due to friction during sliding.

Contact stresses

(2 psi)

Friction shear stresses at 2 & 4 psi

Shear stresses

(2 & 4 psi)

Shear stresses

(6 & 8 psi)

The evolution of the surface shear stress due to inter surface sliding from zero to 25 psi is included at the end of the video clip mentioned above or by pressing the play button below.

Two larger video clips presenting the box configuration, stresses and internal loads in the parts the evolution of the contact status for all components are available at locations marked below:

  • Model 1 (without pretension – 12′:39″)
  • Model 2 (with pretension – 20′:40″):

On fasteners pretension, contacts and shell structures… in a fatigue and sizing context