Bonded Joints

The foundation of HyperX Bonded Joint Analysis is based on work by Mortensen in 1998. We at Collier have built extensively on that base; significantly expanding its capability to make it a practical, production tool.

HyperX Bonded Joint Analysis is not a FEM-based approach; it’s a rapid numerical solution. However, it produces results in a point-by-point manner that is analogous to FEA. It involves solving a system of ODEs to compute forces and displacements at discrete points with optional VCCT implementation for cracked adhesives. The figures below show the stresses in a joint predicted by the rapid tool.

The result of HyperX Bonded Joint Analysis is a full 3D stress state calculated at many locations throughout the Joints. The following images are examples of the level of detail considered by the tool.

Here is a bonded T stiffener, taking multiple slices through the thickness with ply-by-ply stresses

Peel stress in this joint. Each curve is a different through-thickness cut.

Transverse shear stiffness.

Nonlinear Adhesive Model

It is widely known that using linear adhesive properties can be overly conservative. So, HyperX supports the incorporation of nonlinear adhesive properties leading to more realistic stress predictions as shown in the graph below. Note that peaking is much more severe (unrealistic) with linear adhesive for both peel and transverse shear.

A Ramberg-Osgood curve is used to predict stress-strain response.

Collier and several industry partners have been using HyperX Bonded Joint Analysis on production structures for years now. Notably, they were used to model bonded spars, skin lap joints/joggles, and miscellaneous structural connections in UAM eVTOLs. Engineers both internally at Collier and externally at our customers have identified the tool's value and capabilities in the following areas:

The Virtual Testing application is particularly useful for complex loading scenarios where automatic load extraction might not work as well. Especially in cases with complex joint geometry, Non-FEA Joints can be used to derive running load allowables to build that Joint Configuration Library. HyperX's Bonded Joint capabilities simplify that process to three steps:

When analyzing a Bonded Joint in HyperX, the software is assessing stresses / strains at many hundreds or thousands of points through the Joint, but the data provided in the interface only corresponds to the critical point for each criterion. Users can more deeply interrogate the simulated stresses and strains throughout the entire Joint through a dedicated series of output files.

Detailed Outputs

For performance reasons, detailed file outputs are not produced at all times. To produce them:

1. Run a single Joint with a single candidate (no Sizing).

2. Run with a User FEA or User General Load with a single load case.

3. Look for the files in the project TEMP directory (C:/HyperX/Projects/Temp/[Project Name]).

There you will find 5 files:

1. BondedJointResult.BDF - A “surrogate FEM” to visualize the simulation results. This is not a “real” FEM and cannot be run in Nastran. It is only used to provide a way to view and import the tool’s outputs.

2. BondedJointResult.f06 - An empty file, not needed.

3. BondedJointResult.csv - Discrete Field data that can be imported into HyperX and visualized on the surrogate FEM.

4. BondedJointResult.OUT - Adherend midplane forces and displacements. Adhesive stresses and strains. Strain energy release rates (if running VCCT).

5. BondedJointResult_LOC.OUT - Full ply-by-ply stresses and strains.

Postprocessing

Understanding Coordinate Systems

The Joint coordinate system used in the output files is slightly different than the one referred to in HyperX when applying loads and boundary conditions.

The X-axis runs along the overlap, starting at the left side, with Z-axis pointing upward, (\(\sigma_{zz}\) is the peel stress, \(\tau_{xz}\) is transverse shear stress, etc.). There are other minor differences in the output geometry (e.g. some joints may appear “upside down” compared to HX figures).

Surrogate FEM and Discrete Fields

1. Create a new Project in HyperX.

2. Import the surrogate FEM (BondedJointResult.bdf).

3. Select the entire Joint in the Viewport and create a Structure out of it.

4. Edit the Discrete Field CSV header to say “Grid ID” so HyperX can import it.

   

5. Import the Discrete Field data (“Model” tab in HyperX 2023.3.1+, otherwise “Result” tab of the Ribbon).

6. Plot via the Legend.

   

OUT File

The OUT file contains a series of 1D datasets, organized into distinct groups:

• One group per adherend, with midplane plate displacements, curvatures, forces, and moments.

• One group per adhesive with midline stresses and strains.

The file also contains computed strain energy release rates at the crack tip for VCCT runs (at the top of the file). This file can be loaded into Excel to generate plots for further postprocessing the analysis results.

Note

This file uses “a” in the adhesive to indicate the through-thickness (z) direction.

E.g. SIGa == \(\sigma_{zz}\) ; TAUax = \(\tau_{xz}\) ; etc.

_LOC.OUT File

This file typically is best post-processed with Scripts. It contains 2D blocks of data showing the full ply-by-ply stresses and strains throughout the Joint. The basic format is:

A walkthrough of how to setup and size Bonded Joints can be found in the Training Module #4: HyperX Entities - Joints (Click-Along) training.

Failure Analysis of Adhesively Bonded Composite Joints via the Virtual Crack Closure Technique

3D Stress Analysis of Adhesively Bonded Composite Joints

Failure Analysis of Adhesively Bonded Composite Joints

Verification, Validation, and Limits of Applicability of a Rapid Bonded Joint Analysis Tool