An Analytical Solution of the Total Strain Energy Release Rate and Mode Partitioning of a Beam Type Delamination Specimen under High Speed Mixed-Mode Loading

In this work an analytical solution for the calculation of the total Stain Energy Release Rate and mode partitioning of beam type delamination specimen, at crack initiation, under high speed, mixed-mode loading is obtained for the first time. The analytical model is based on the dynamic response of a Mixed-Mode End Load Split type specimen subjected to loading with a constant velocity. The Timoshenko beam theory is used to model the specimen's kinematics and the mode partitioning method used is based on the Virtual Crack Closure Technique. To model the bonded region a method based on Lagrangian multipliers is utilized. The specimen is considered as a waveguide and the waves that are allowed to propagate are analytically obtained. Due to the complexity of the analytical form of the wavenumbers for the bonded region of the specimen, which makes the calculation of eigenfrequencies intractable, a series approximation method is used. The results of the proposed analytical solution are verified using a 2D Finite Element Model. The results show the dependency of the Strain Energy Release Rate and the mode mixity on the eigenfrequencies and the eigenmodes of the specimen rendering the value of the mode mixity highly inconsistent through time.

Automated summary

This work presents an analytical solution for calculating the total strain energy release rate and mode partitioning of a beam-type delamination specimen under high speed, mixed-mode loading. The dynamic response of a Mixed-Mode End Load Split specimen subjected to loading with a constant velocity is modeled using the Timoshenko beam theory. A Virtual Crack Closure Technique is used for mode partitioning, and a Lagrangian multiplier method is used to model the bonded region. The specimen is treated as a waveguide, and the allowed propagating waves are analytically obtained. Due to the complex form of the wavenumbers for the bonded region, a series approximation method is applied. The proposed analytical solution is validated using a 2D Finite Element Model, and the results demonstrate the dependency of the Strain Energy Release Rate and mode mixity on the eigenfrequencies and eigenmodes of the specimen, resulting in inconsistent mode mixity values over time.