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The single scattering of P- and SV-waves by a cylindrical fiber with a partially imperfect bonding to the surrounding matrix is investigated, which benefits the characterization of the behavior of elastic waves in composite materials. The imperfect interface is modelled by the spring model. To solve the corresponding single scattering problem, a collocation point (CP) method is introduced. Based on this method, influence of various aspects of the imperfect interface on the scattering of P- and SV-waves is studied. Results indicate that (i) the total scattering cross section (SCS) is almost symmetric about the axis

A large number of interfaces exist in composite materials and play a very important role in the performance of composite materials, for example, the transmission of the load between the matrix and fibers. To simplify the analysis and calculation, the fibers/particulates are generally assumed to be perfectly bonded to the surrounding matrix [

The perfect bonding and the debonding are the two extreme cases of the bonding conditions of interfaces. Actually, there are other conditions which extensively exist between the perfect bonding and the debonding, that is, imperfect condition. For this reason, several theoretical models were proposed during the past few years [

Using the above-introduced spring model, the effective mechanical properties of composite materials, such as the effective modulus [

It is worthwhile to mention that, in most of the previous studies, the whole interface between each fiber/particulate and the matrix was usually assumed to simultaneously enter the imperfect bonding condition. However, this is not real case, assuming that the interface between each fiber and the surrounding matrix deteriorates as a process would be more reasonable. In this regard, less attention has been paid except for the partial debonding case. The limited works include those of Lopez-Realpozo et al. [

In the following sections, firstly, the single scattering problem is formulated. Then, the CP method is introduced to solve the single scattering problem. After that, the influence of various aspects of the partially imperfect bonding on the single scattering is extensively studied numerically. Finally, a short conclusion is drawn.

The governing equations for P- and SV-waves in 2D problems with a homogeneous medium are decoupled based on the Helmholtz decomposition. In harmonic analysis, the two equations for P- and SV-waves can be expressed as

Figure

Scattering of a plane P- or SV-wave by a cylindrical fiber with a partially imperfect bonding to the matrix. The range of the imperfect bonding is denoted by the red solid arc.

The total displacement potential in the matrix is the summation of the incident wave and the scattered wave, while the quantities in the fiber are only of the refracted one. By substituting the total displacement potentials in the matrix and the fiber expressed in (

In order to characterize the overall behavior of coherent waves in composites with randomly distributed fibers/particulates, over the past several decades, extensive theoretical models have been proposed including the

In this study, the CP method is adopted to solve (

Distribution of CPs denoted by the “

To check the convergence of this CP method, the total SCS by a partially debonded fiber (

Materials used in the current work [

Material | | | ^{3}) |
---|---|---|---|

SiC | 92.1 | 177.0 | 3200 |

Ti-alloy | 103.0 | 44.8 | 5400 |

Glass | 0.7367 | 1.43 | 2550 |

Epoxy | 0.8895 | 1.28 | 1250 |

Convergence study of the CP method using the debonding case considered in [

Next, three examples are calculated to validate the application of the CP method. Figure

The calculated SCS by a partially imperfectly bonded fiber as a function of the stiffness in the range of ^{4}.

The far-field scattering magnitude patterns of the scattered (a) P- and (b) SV-waves by a fiber with a partially imperfect bonding to the matrix, under a plane P-wave incidence (dashed line:

Figure

Comparison of the calculated far-field scattering patterns of the scattered (a) P-wave and (b) SV-wave by a fiber with a fully imperfect bonding to the matrix under a P-wave incidence versus those of the debonding case (cavity).

Figures

In this section, the influence of

Relative difference (%) of the calculated

The corresponding results under the SV-wave incidence are plotted in Figure

Relative difference (%) of the calculated

In this section, influence of stiffness

The influence of stiffness

Definitely, the sensitivity of

A schematic to define the sensitivity of

The sensitivity of

The corresponding results under the SV-wave incidence are plotted in Figure

The sensitivity of

The single scattering of P- and SV-waves by a cylindrical fiber with a partially imperfect bonding to the matrix is investigated using the CP method. This study benefits the characterization of coherent waves in composites with randomly distributed inclusions. In this study, the imperfect interface is modelled using the spring model. Three examples are calculated and the results show that this CP method performs well. Also, the parametric analysis of location, width, and bonding level of the imperfect bonding on the total SCS is extensively studied. From this study, the following conclusions are obtained:

The influence of the partially imperfect bonding on the single scattering of P- and SV-waves is almost symmetric about the axis

Under the P-wave incidence, the

When

In summary, besides its significance in the understanding of the single scattering, the present study also benefits for the application of the theoretical models to evaluate phase velocity and attenuation coefficient of coherent elastic waves in composites with randomly distributed inclusions and the nondestructive evaluation of composites using the ultrasonic techniques.

with

The data used to support the findings of this study are available from the corresponding author upon request.

The authors declare that they have no conflicts of interest.

This work was supported by the National Natural Science Foundation of China (Grants 11502036 and 51708434) and the Natural Science Fund of the City of Chongqing (Grant cstc2015jcyjA0577). Guangxi Key Laboratory of Manufacturing Systems and Advanced Manufacturing Technology (no. 16-380-12-014k) also provided partial financial support.