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Analytical formulation for the evaluation of frequency of CFRP sandwich beam with debond, following the split beam theory, generally underestimates the stiffness, as the contact between the honeycomb core and the skin during vibration is not considered in the region of debond. The validation of the present analytical solution for multiple-debond size is established through 3D finite element analysis, wherein geometry of honeycomb core is modeled as it is, with contact element introduced in the debond region. Nonlinear transient analysis is followed by fast Fourier transform analysis to obtain the frequency response functions. Frequencies are obtained for two types of model having single debond and double debond, at different spacing between them, with debond size up to 40% of beam length. The analytical solution is validated for a debond length of 15% of the beam length, and with the presence of two debonds of same size, the reduction in frequency with respect to that of an intact beam is the same as that of a single-debond case, when the debonds are well separated by three times the size of debond. It is also observed that a single long debond can result in significant reduction in the frequencies of the beam than multiple debond of comparable length.

Sandwich construction is formed by bonding two thin facings to a thick core and has very high strength and stiffness properties achieved by increasing the thickness of the core without any weight penalty. The manufacturing defects like incomplete wetting or entrapped air pockets into resin-dominant layer can result in nonuniform adhesion between the face sheets and the core or skin-to-core debond. In-service circumstances such as low velocity impact by foreign objects or accidental tool drops during maintenance operations can lead to local debond. Overloading and elevated temperature regime may also induce debond at the weakest point of skin-to-core interface. During service, the debond may propagate and trigger new damage modes such as face sheet wrinkling, dimpling, and core shear cracks. As the structures using sandwich materials require extremely high level of reliability, debond must be detected immediately after its occurrence to ensure safety and the durability of the structures.

In the author’s recent analytical study on vibration characteristics of sandwich beams with debond, the well-known split beam theory was modified considering the core stiffness of sandwich beam and accordingly the equations of motion were derived [

Goswami and Becker used the finite element method to study the cause and the effects of debonding phenomena in between the face sheet and the core of a sandwich plate under in-plane loading [

The aim of the present study is to find out the limit of debond length up to which the analytical prediction of frequency is valid for the case of a CFRP sandwich beam with multiple debonds. For this purpose, finite element analysis is carried out and the results are compared with analytical solution for multiple debond of different lengths and spacing between them. In the numerical analysis using finite element method, contact elements are introduced between the skin and core in the debond region and nonlinear transient analysis is performed and frequency response functions are obtained through fast Fourier transform analysis.

Honeycomb sandwich beams with laminated carbon-epoxy (CFRP) skins are considered in the present study. All the beams are of size

Properties of materials used.

Carbon-epoxy skin | Aluminium honeycomb core |
---|---|

Plate shear modulus | |

Cell size = 6 mm (inscribed circle diameter) | |

^{3} | Cell wall thickness = 1/1000 of an inch (.00254 mm), ^{3}) |

Schematic representation of the beam with debond.

Figure

The centre line displacements of the top and bottom layers in the longitudinal direction are

(a) Displacements of the sandwich beam. (b) Forces and moments in the sandwich beam.

The longitudinal forces acting in the midplanes of each face plate, denoted by

When no external loads are applied,

For the debonded beam segment, the equation of motion according to Euler beam theory is

Assuming free harmonic vibration,

Similarly, the solution of (

For the CFRP skinned honeycomb sandwich beam, the geometry of the honeycomb core is retained as it is and 2D shell element with six degrees of freedom per node is used to model the core. It is necessary to use 3D brick element (with three translational degrees of freedom per node) for top and bottom skins to incorporate through-width interface debond regions at predetermined symmetric locations more precisely. Contact elements are introduced between the elements of skin and core at the debond locations to prevent the debonded skin from overlapping with the core during vibration. The contact elements are capable of supporting only compression in the direction normal to the surfaces and have three translational degrees of freedom at each node. The finite element model is shown in Figure

Finite element model of the honeycomb sandwich structure.

In the case of debonded beams, as the contact elements introduce nonlinearity, transient analysis (time-history analysis) is performed. Time-history analysis is a technique used to determine the dynamic response of a structure under the action of any general time-dependent loads. A constant impulse force

Time-displacement response curve.

Frequency response curve.

Study is carried out for eight cases of single debond with

Comparison of fundamental frequency of CFRP sandwich beam with single debond obtained by analysis and numerical approach.

For higher modes, a similar agreement in frequencies up to 15% of debond length is observed as in Figure

Comparison of higher mode frequencies of CFRP sandwich beam with single debond obtained by analysis and numerical approaches.

Fundamental frequency obtained by analytical solution is compared with finite element analysis for CFRP sandwich beams with multiple debond and given in Table

Comparison of fundamental frequency of cantilever CFRP sandwich beam with multiple debonds.

Debond length (mm) | First mode frequency (Hz) | Spacing | First mode frequency (Hz) | ||||

Analytical* | FEM* | Experiment [ | Analytical* | FEM* | Experiment [ | ||

Nil | 183.1 | 187.89 | 182.8 | — | — | — | — |

100 | 88.93 | 98.7 | 82.5 | 50 | 73.34 | 78.65 | 69 |

100 | — | — | — | 150 | 79.23 | 84.98 | 81.9 |

*Present results.

Study is further extended for sandwich beam with two debonds at different spacing between them, keeping the first debond location same as mentioned earlier (

Variation in frequency with respect to spacing between debonds.

It can be concluded that, in the case of double debonds, even though total debond length is 30% of beam length, when they are well separated (by about three times the single debond length), frequency of the sandwich beam is reduced only as much as in the presence of single debond.

Analytical formulation for the evaluation of frequency of CFRP sandwich beam with debonds, using the split beam theory, has been carried out considering honeycomb core stiffness and validated the range of debond size through 3D nonlinear transient analysis. Honeycomb core is modeled with the contact element introduced between the core and the skin during vibration, following fast Fourier transform analysis to obtain the Frequency Response Functions. Comparison of fundamental frequencies of a cantilever beam with a single debond obtained by the test, analysis, and numerical method show a reasonably good agreement between them up to a debond length of 15% of beam length. Analytical model has also been validated for the case of double debonds and it is observed that reduction in frequency of the sandwich beam is only as much as with the presence of single debond when two debonds (of sum total length up to 30% of beam length) are separated by three times single-debond size. However, when the double-debond size is very small up to a value of 5% of the beam length, then the distance in between can be retained to 1.5 time the debond size to obtain a value corresponding to a single debond.