A New Approach for Severity Estimation of Transversal Cracks in Multi-layered Beams

Abstract

Nowadays, the damage severity evaluation in mechanical structures is mostly performed by analyzing the natural frequency shift. The non-isotropic materials, as the multi-layered ones, are widespread in industrial applications, due to their interesting physicmechanical properties. Thus, a deeper approach of multi-layered beams becomes an important request in the research domain. This paper introduces a damage severity estimator by expressing the crack evolution as a function of stored energy. It is well known that the energy stored in a beam without damage is greater than the energy of that damaged beam. As a consequence, the beam deflection can be related to the stored energy. In this regard, the possibility to split the damage localization and the damage severity assessment has been proven, and also the graphical evolution of the natural frequency shift has been achieved as a function of the crack depth. The results achieved by the finite element method (FEM) and experimental tests are given in tables and graphics. For the first five vibration modes, a comparison was made between frequencies accomplished by analytical, numerical and experimental analyses, in order to give more credibility to the accuracy of the research data presented in this paper.

Numerical study on complex shaped cracks in cantilever beams concerning frequency and stiffness changes

“…From paper [15], the beam's free end deflection for the healthy and damaged state is expressed by the mathematical relations:…”

“…In previous studies [15][16][17][18], the authors developed a robust method for detecting, locating and evaluating transverse cracks in all types of beams, regardless of the constraining method, based on the natural frequency changes.…”

Estimation of the severity of damage produced by a transverse crack

“…In our previous research we approached this topic and found a relation to express the frequency of cracked beams in respect to the damage severity [9] - [11]. The severity is found involving Castigliano's second theorem [12], and it was shown that the severity does not directly depend on the moment of inertia of the damaged cross-section [13].…”

Fragmentation model for the tensile response of unidirectional composites based on the critical number of fiber breaks and the correction of the fiber-matrix interfacial strength.

“…In this point, it is worth-mentioning that previous works has introduced damage estimators as a function of the strain energy. For instance, Gillich et al expressed the damage severity produced by cracks located in a cantilever, multi-layered beam as a function of the stored energy, in order to study the influence of the crack depth on the natural frequency ship at several longitudinal positions of the beam (Gillich et al 2016). Accurate results were obtained in that work for some vibration modes when compared to experiments.…”