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Engineering Advantage

Is My Contact Stress Real?

August 23, 2016 By: Steven Hale

How many times have you run a model that includes contact and found that the peak stress occurs in the contact zone? While this can be a real stress that should be evaluated, it can sometimes be an artifact of the modeling methodology. In some cases, stresses near the contact zone are not a concern because the critical region being evaluated isn’t near the contact site or the contact stresses are overwhelmingly compressive. In other cases, the maximum shear or tensile stresses in the contact zone are so much lower than stresses in other locations that additional effort to improve the accuracy of the contact stress is likely unnecessary. But what about cases where a contact stress is high and a real threat to part failure? In such cases, you need to determine if the contact stress is real: In other words, is it accurate enough to be useful in determining failure potential. 

The accuracy of contact stresses can be evaluated with the following criteria:

1. Is the contact interface modeled appropriately?
2. Is the peak contact stress at a singularity point?
3. Is the mesh fine enough to accurately predict the contact stress? 

To answer all of these questions in detail would require a lengthy discussion, so I’ll focus on just a few significant points. There are several contact methods and results that indicate that a contact stress is not real. Here are some situations where they may not be real, or grossly inaccurate at best:

1. Sharp corners in contact. Any sharp corner in contact will create a numerical singularity (See additional bog titled “Why Worry About Sharp Corners and Point Loads” for information regarding numerical singularities).
   A. Under tensile load: Bonded or no separation contact effectively creates a sharp internal corner.  As with any sharp internal corner, a numerical singularity is present and the results will not be accurate even with a very dense mesh.
   B. Under compressive load: A numerical singularity is also present at a sharp corner regardless of the contact type. This may not be intuitively obvious but it’s documented in the literature [1] and can be shown with a test model such as the one described below.

2. Only a few elements are in contact:
   A. Increasing the number of elements that are in contact with each other will usually improve the accuracy of a near-field contact solution by more accurately representing the distribution of contact forces across the interface.  Another complementary approach is to use a projection-based contact algorithm such as the one available for surface-to-surface contact elements in the ANSYS finite element code.

3. At frictional contact interfaces, it’s possible to have part of the surface slide while another part sticks.  This can create a very uneven distribution of shear stress across the interface.
   A. Once again, increasing the mesh density in these regions can improve the results by more accurately representing the distribution of contact shear load across the interface.

The issue with stress singularities at sharp corners under compressive loads can be demonstrated with a test model such as the one shown in Figure 1, below.  This model consists of two plane stress blocks where the upper block is pushed into the lower block and the upper block contains both a sharp corner and a blend in contact. The interface was modeled with surface-to-surface contact elements and frictionless conditions. Two load cases were evaluated: the first (Case 1) consists of a 10000 lb vertical load applied to the line above the sharp corner while the second (Case 2) consists of a 10000 lb vertical load applied to the line above the blend.  The highest stress state is a shear stress at the contact surface directly adjacent to the corner for Case 1 and the intersection with the blend radius for Case 2, as shown in Figure 1.

Figure 1: Test Model - Load Cases and Max. Stress Locations


Figure 2 shows the maximum shear stress in the lower block as a function of mesh density.  It’s clear that the stress at the sharp corner continues to increase with increasing mesh density (indicating a stress singularity) while the stress at the edge of the blend levels out with increasing refinement.  However, while the stress at the edge of the blend is real, it requires a very fine mesh to be accurate because of the extremely high stress gradients in such a small region of the model. 

Figure 2: Test Model - Maximum Shear Stress Variation with Increasing Mesh Density


This discussion has addressed a few situations that can adversely affect contact stress results or invalidate them altogether.  However, it’s important to remember that it’s not always necessary to predict accurate contact stresses, which is typically the case when the region of interest is outside of a contact zone or the contact stresses are well below other stresses in the model.  Another point to note is that high contact stresses tend to be very localized, which can create a small zone of plasticity, thus redistributing the stress to the adjacent material.  It’s also important to emphasize that a very fine mesh is required in the contact zone to accurately predict contact stresses.  As an analyst, you need to determine if the level of effort and computation time required for this kind of mesh is really necessary to obtain a useful solution.  An alternate approach is to use the analytical solution for Hertzian contact.  This method provides contact stress equations for common geometries which can be described locally as having orthogonal radii of curvature, such as cylinders and spheres.

We are very interested to hear about any experience you have in dealing with contact stresses.  How have you evaluated these stresses to determine their relevance and accuracy, or how have you changed the model to improve your contact stress solution?

 

 

 

 

 

 

 

 

References:
J. Dunders and M.S. Lee, “Stress Concentration at a Sharp Edge in Contact Problems”Journal of Elasticity 2, 109-112 (1972)