Peel stress singularities occur at the bi-material interface of the free edges of, for example, a steel-adhesive-steel sandwich specimen of say 500 mm in length, 100 mm in width, and 10 mm thickness (5 mm adhesive thickness) under longitudinal cyclic tension due to the difference in Young's modulus and Poisson's ratio of the two materials.

The singularity can be relatively economically investigated in a very fine cross-sectional finite element (FE) model representing the as manufactured geometry using the generalized plain strain approach (ANSYS), for example, see attached picture. The finer the mesh gets the larger gets the local peel stress peak at the bi-material free edge interface. The graph shows the equivalent stress according to Beltrami (similar to von Mises).

The load amplitude is chosen from a fatigue load spectrum of a cyclic test and is thus that small that linear elasticity holds for the average stress according to classical laminated plate theory (CLPT) in the adhesive. Now, this local stress peak, however, gets already as large (factor of 10 of the average equivalent stress) that it could be dedicated to a plastic deformation and failure. In reality, i.e., in the experiment, we would not see such a failure after say the first 100 load cycles. Thus, there is a discrepancy between linear elasticity theory and reality. The material seems to withstand these peaks.

For the static strength analysis one could use a non-linear stress-strain curve to circumvent the "problem" and lower the peaks and use then fracture mechanics to quantitatively evaluate such situations, but this requires the modeling and relatively expensive analysis of possible crack orientations in all possible dimensions due to the multi-axial stress state. Therefore, fracture mechanics does not seem to be an applicable method to evaluate the fatigue damage for a load spectrum whose stress vector components vary over time and thus with them the critical crack planes .

Another technique is to extract the stress value at a critical distance from the edge and then extrapolate a "more realistic" stress peak. But how to define such a critical distance on a physically sound basis and how does the extrapolation function look?

Do you have any other ideas how to extract a realistic stress value from the finite element model for a fatigue analysis?