Closed/Semi-Closed Form Solutions for Face/Core Debonds in Sandwich Beams

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Niranjan Babu, Siddarth
Kardomateas, George A.
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Sandwich beams are highly susceptible to debonding at the interface between face and core. These debonds can grow and eventually lead to complete failure of the structure. To understand and study such debonds analytically, an Elastic Foundation Analysis (EFA) can be used to incorporate the effects of crack tip deformation in beam theory. In this model, EFA is extended further to better capture the effects of transverse shear. Unlike most models, this approach can be applied for both isotropic and orthotropic face & core materials. The approach uses both normal and rotational springs in the elastic foundation in the bonded region of the beam to capture transverse shear effects. Timoshenko beam theory introduces a rotational degree of freedom to the beam element and the rotational springs are used to capture it. The model is comprehensive and include both the deformation of the debonded part and the substrate. Double Cantilever Beam (DCB) and Single Cantilever Beam (SCB) specimens are chosen to demonstrate the procedure to obtain Mode-I fracture parameters. In the case of Mode-II fracture, the effects of crack face contact can affect the fracture parameters and are usually neglected in analytical approaches. The proposed model extends EFA by introducing a tensionless spring foundation in the cracked region. Tensionless springs are used to capture the compressive stresses across the interface between the debonded face sheet and the substrate. The absence of tensile stresses in the foundation is because when there is tension the debonded face sheet lifts away from the substrate. Apart from compressive stresses, there will also be frictional forces acting between the crack faces. So, the governing equations are modified to capture the friction tractions in the crack faces. An End Notched Flexure (ENF) specimen is chosen to demonstrate Mode-II fracture. Expressions for energy release rates are obtained using J-Integral approach and it is modified to capture the energy lost due to the friction tractions. Solutions for mode partitioning are obtained using the axial and transverse displacements near the crack tip. Results obtained from these expressions are compared with results from finite element models. The model is comprehensive, efficient and would provide accurate results when compared with the other models (from literature).
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