Transmission of ultrasonic waves at oblique incidence to composite laminates with spring-type interlayer interfaces

Abstract

The transmission characteristics of ultrasonic waves at oblique incidence to composite laminates are analyzed theoretically by the stiffness matrix method. The analysis takes into account the presence of thin resin-rich regions between adjacent plies as spring-type interfaces with normal and shear stiffnesses. The amplitude transmission coefficient of longitudinal wave through a unidirectional laminate immersed in water is shown to be significantly influenced by the frequency, the interlayer interfacial stiffnesses, and the incident angle. Using Floquet's theorem, the dispersion relation of the infinitely extended laminate structure is calculated and compared to the transmission coefficient of laminates of finite thickness. This reveals that the ranges of frequency and interfacial stiffnesses where the Floquet waves lie in the band-gaps agree well with those where the transmission coefficient of the finite layered structure is relatively small, indicating that the band-gaps appear even in the laminate with a finite number of plies. The amplitude transmission coefficient for an 11-ply carbon-epoxy unidirectional composite laminate is experimentally obtained for various frequencies and incident angles. The low-transmission zones observed in the experimental results, which are due to the critical angle of the quasi-longitudinal wave and the Bragg reflection, are shown to be favorably compared with the theory.

Second-harmonic generation in an infinite layered structure with nonlinear spring-type interfaces

“…Elastic wave propagation in multilayered structures with spring-type interlayer interfaces has also been analyzed in order to clarify the effect of thin interlaminar resin-rich regions in fiber-reinforced composite laminates [18][19][20][21][22][23].…”

Influence of porosity on ultrasonic wave velocity, attenuation and interlaminar interface echoes in composite laminates: Finite element simulations and measurements

“…The spring boundary conditions [35][36][37][38][39][40][41] are applied to the double nodes on the interlaminar interfaces located at x2 = Hw + mh (m = 1, 2,…, N -1, h = H/N: ply thickness). The material properties used in the present analysis are summarized in Table 2.…”

“…The complex elastic constants as well as the interlayer interfacial stiffnesses were determined experimentally for the porosity-free specimen. Namely, they were determined so that the theoretical amplitude transmission coefficients [41] fit best to those measured for the porosity-free specimen at different incident angles in the plane normal to the fiber direction.…”

“…This is of particular advantage when incorporating the viscoelastic properties of CFRP exhibiting nearly linear frequency dependence of the attenuation coefficients [32][33][34]. Thin interlaminar resin-rich regions are modeled as spring-type interlayer interfaces with equivalent normal and shear stiffnesses [35][36][37][38][39][40][41].…”

Nondestructive Evaluation of Porosity Content in the Curved Corner Section of Composite Laminates Using Focused Ultrasonic Waves

“…The stiffness property of each point in the curved laminate structure is determined by carrying out appropriate transformations of the stiffness components accounting for the stacking direction of each ply and the curvature of the structure. Although thin resin layers between the plies have some significant effects on the wave propagation behavior at higher frequencies around the stop band of the layered structure [22,23], such effects are ignored in the present simulations as the frequency range of the present interest is sufficiently low. Consequently, the plies are assumed to be perfectly bonded to each other without the resin layers in this analysis.…”