Characterization of nonlinear ultrasonic waves behavior while interacting with poor interlayer bonds in large-scale additive manufactured materials

https://doi.org/10.1016/j.ndteint.2022.102602Get rights and content

Abstract

Over the past decades, researchers have developed several nonlinear ultrasonic techniques for quality control of materials commonly used in different applications. Owing to the superior sensitivity of nonlinear ultrasound waves to small defects such as micro-cracks, their applicability in different nondestructive testing (NDT) problems has been investigated in numerous studies. These studies utilize frequency domain analysis to detect the generation of higher harmonics because of the formation of defects in the inspected medium. Frequency domain analysis based on the Fourier transform is a significant approach used in linear systems; however, it may not perform adequately on nonlinear systems. Hence, studies on nonlinear dynamics and physics consider analyzing systems' behavior in the phase-space domain. In contrast to the frequency domain analysis, which can result in information loss, analysis in the phase-space domain retains all the information regarding a system's states. In this study, the nonlinearities induced by poor interlayer bonding in polymer-based additive manufactured parts in the phase-space domain are investigated. It is convenient to characterize the nonlinearity in the phase-space domain because it provides a geometrical representation of a system's states. Two types of low quality interlayer bond are considered. The first type is simulated artificially while the second type is manufactured by reducing the bond quality during the printing process. The analysis verified that the received ultrasonic signals exhibit classical nonlinear behavior in the phase-space domain while interacting with simulated poor interlayer bonds. In addition, the results showed that the behavior of ultrasonic waves is amplitude-dependent and evolves into models that have not been previously reported. Furthermore, Largest Lyapunov Exponent (LLE) is used to quantify the behavior of nonlinear ultrasonic waves while interacting with poor interlayer bonds. Using LLE, it was observed that the divergence rate of the phase-space trajectories depends on the amplitude of the excitation. This observation quantitatively proves that nonlinear behavior of ultrasound while interacting with poor interlayer bonds can be amplitude-dependent. The results of both simulated and inherent poor interlayer bond cases showed that LLE can be used as a reliable quantitative damage-sensitive feature to detect and potentially characterize weak bonds, which are difficult to detect using conventional approaches. In addition, the reported results in the phase-space domain provide a basis for proposing a new mathematical model for ultrasonic waves interacting with poor interlayer bonds.

Introduction

Additive manufacturing (AM) is an emerging research topic in industry and academia owing to the advantages of rapid prototyping, flexibility in material properties, reduction in cost, an overall enhanced design, and manufacturing sector efficiency [1]. Polymer and metallic-based AM is used in several applications for building complex components in power, automotive, oil and gas, and aerospace industries [2]. Components that are manufactured using AM processes should be extensively examined to identify any existing defects that would render them nonfunctional. These defects include porosity, residual stresses, and poor interlayer adhesion. A significant demand exists in the field of quality control, particularly in nondestructive testing (NDT), to develop new techniques to overcome the limitations of conventional quality control, and characterize and detect defects in AM components.

The first type of defect is porosity, which is the presence of voids (microvoids and macrovoids) in polymer-based AM. Microvoids occur in a printed bead as a result of air trapped in the feedstock and during the mixing of polymer melt. Macrovoids are large diamond-shaped voids that occur between adjacent beads with a circular cross-section [2]. The AM components exhibit different properties in different directions owing to the anisotropic nature of the deposition process. Mechanical anisotropy is often observed within the boundaries of adjacent layers, creating regions with maximum residual stresses [3]. Another type of defect occurs because of the layered production of AM processes, where residual stresses tend to form around the boundaries of each layer (weak regions). Most AM processes produce the components in a heated chamber setup, which results in a high thermal gradient that adds to the residual stresses. Residual stresses lead to distortion, warpage, and microcracking [2]. Poor interlayer adhesion is a type of defect that occurs owing to improper bonding between layers in the AM. Appropriate bonding occurs by local re-melting of the solidified layers with the newly deposited layer. The deposition temperature and thermal properties of the feed stock material are the two major factors that control interlayer bonding. Layer time varies depending on the type of polymer used [4].

The interlayer bond weakness has undesirable limitations with respect to the practical implications of AM components [5]. An important challenge in the nondestructive evaluation of AM components is the ultrasonic assessment and characterization of weak interlayer bonding [6]. The residual stress in poor interlayer bonds poses an additional challenge to the detection process of weak interlayer bonds using ultrasonic testing [7]. Consequently, detecting and evaluating poor interlayer bonds using conventional linear ultrasonic approaches are difficult as the transmitted wave does not have sufficient energy to exhibit detectable changes in linear features such as amplitude owing to the change in stiffness. In contrast, a high-power ultrasonic approach can cause nonlinear behavior of ultrasonic waves when interacting with weak interlayer bonds.

Nonlinear ultrasonic testing has become popular in the field of NDT because it is more attuned to detecting small defects, such as microcracks, when compared with conventional ultrasound testing. Large wave amplitude and traveling long distances are two fundamental factors that can enhance nonlinearities in ultrasonic waves [8]. Two different classes of nonlinear models that are widely used to explain nonlinear ultrasound behavior are: 1. The classical nonlinear theory, which relies on the generation of higher harmonics, and 2. Non-classical nonlinear theories [8]. The classical nonlinear theory of elasticity considers Hooke's law with higher-order elastic terms [8]. Non-classical models are used owing to an assumption that the stiffness is asymmetric across the near-surface of a bond or crack interface [9]. Based on this assumption, contact acoustic nonlinearity (CAN) models have been proposed. Models based on bi-linear stiffness (stiffness asymmetry) are some of the most popular and simple nonlinear models [[8], [9], [10]]. A bi-linear nonlinear model has successfully used to represent breathing cracks given that the stiffness of the system changes with the position of the two faces of the crack. When the crack experiences tension, it opens, which results in global stiffness reduction; however, when it is under compressive loads, the crack closes, and the global stiffness of the system remains constant.

Most of the reported research in the nonlinear ultrasonic field relies on the generation of higher harmonics in the frequency domain [8,11]. Analyzing ultrasonic waves in the frequency domain is a common approach and has been used in several studies to analyze different disbonds and imperfect interfaces successfully [7,[12], [13], [14], [15], [16], [17]]. Furthermore, nonlinear ultrasound has also been used in defect evaluation of parts manufactured with AM processes. The feasibility of online ultrasound measurement using ultrasonic testing during the selective laser melting process has been demonstrated by Rieder et al. using time and frequency domain analysis of received ultrasound signals [18,19]. Ultrasound testing has been used successfully for quality control of metal and plastic based additive manufactured parts [[20], [21], [22], [23]]. The ultrasonic tests have been successfully conducted on samples made from powdered-aluminum alloy, and AlSi10Mg samples manufactured by selective laser melting (SLM) with implanted defects [24,25]. Also, immersion ultrasonic testing has been performed on 3D printed samples made from acrylonitrile butadiene styrene (ABS) by fused deposition modeling (FDM) [26]. While the frequency domain successfully used in several application using nonlinear ultrasound, analyzing a system response in the frequency domain using the Fourier transform has several shortcomings [27,28]. The Fourier transform divides the signal into individual harmonic signals with different frequencies. Because the Fourier transform is a linear function, the Fourier transform of nonlinear systems changes a set of complex differential equations into integral equations in the frequency domain with convolutions among dependent variables [27]. Thus, studies are being conducted to enhance the frequency-based methods [29] or suggest new approaches to analyze a system response [27]. A well-known and effective method for analyzing system behavior is the phase-space analysis. The phase-space analysis provides a powerful domain for analyzing the complex nonlinear behavior of dynamic systems and physical phenomena [30].

By plotting systems' independent states with respect to each other, it is possible to construct and depict the systems' behavior in the phase-space domain with unique geometric features. In this domain, time is implicit. The phase-space domain enables visualization of the system behavior. Furthermore, because of the unique geometric representation of a dynamic system in this domain, different signal processing techniques and mathematical tools can be utilized to analyze a system's nonlinear response. Recurrence quantification analysis (RQA) can be used to demonstrate the determinism of a system behavior [[30], [31], [32]]. In other words, it is possible to determine if a system behavior is stochastic or deterministic. The instability of a system can be quantified by calculating the Lyapunov exponent. A fractal dimension analysis can be used to assign dimensions to a system behavior geometry. In addition, the phase-space domain analysis is a powerful method for determining chaotic motion and studying the system behavior transition to chaos [[30], [31], [32]].

Recently, studies in the ultrasonic field have utilized the phase-space domain to analyze signals and assess damages. Carrión et al. [33] implemented RQA to assess the damage severity effect on system behavior in concrete materials. They concluded that by increasing the damage level and with higher frequency ultrasonic waves, the determinism of a system decreases significantly. This implies that the system behavior transforms from a deterministic behavior to stochastic behavior [33]. Zamen et al. analyzed the complex behavior of multimode friction-based Lamb waves using recurrence plots and RQA. They used recurrence plots to detect the arrival of different modes in multimode Lamb waves [34]. Dehghan-Niri and Al-Beer used the phase-space reconstruction to categorize the interaction of nonlinear ultrasonic waves with closed interfaces on high-strength aluminum material [35]. In the phase-space domain, Zamen and Dehghan-Niri applied different signal processing techniques to verify the chaotic motion of nonlinear ultrasonic waves while interacting with a closed interface crack due to residual stress in concrete materials [36]. Additionally, they used fractal dimension analysis to extract a quantitative damage-sensitive feature from nonlinear ultrasonic wave in the phase-space domain [37,38].

The main contribution of this study is to propose a method to classify behavior of nonlinear ultrasonic waves imposed by the poor interlayer bond in AM components; the method should be convenient and reliable without relying on the frequency domain response. Because the phase-space approach considers all possible states of a system, it would result in superior accuracy when compared with the frequency domain-based approaches. In addition, the phase-space representation provides geometrical information that facilitates easy interpretation of complex data. Furthermore, to quantitatively identify ultrasonic waves behavior when interacting with poor interlayer bond, Largest Lyapunov Exponent (LLE) [39] is used. Lyapunov exponent measures the rate of divergence and convergence of system's trajectories in the phase-space domain, locally. Since for a dynamical system, there exists a spectrum of Lyapunov Exponents [31], maximum value is selected to represent the maximum amount of divergence or convergence in received ultrasound signals. The paper is further organized as follows: Section 2 presents a brief discussion on phase-space reconstruction of recorded data. In addition, the phase-space representation of well-known nonlinear models is presented. Section 3 presents the experimental setup of this study. The results and discussions are presented in Section 4, and the conclusions are presented in Section 5.

Section snippets

Phase-space reconstruction of nonlinear ultrasonic models

This section introduces the phase-space domain fundamentals, well-known ultrasonic models, and their corresponding behavior in the phase-space domain. To transform ultrasonic signals (X(t)) from the time domain to the phase-space domain, the delay method proposed by Packard et al. [[30], [31], [32],40] was used. The delay method is based on calculating the embedding dimension (E) and time lag (τ). X(t), which represents the displacement or pressure fields of the ultrasonic waves, is one state

Experimental setup

A big area additive manufacturing (BAAM) system at the U.S. Oak Ridge National Laboratory was used in this work. The BAAM system deposition head is shown in Fig. 6. It is a four-heating zone single-screw polymer extruder mounted on a large gantry system with a build volume of 6 m in length, 2.5 m in width, and 1.8 m in height. In the extrusion deposition process used in BAAM, a semi-molten polymer is extruded through a nozzle mounted at the end of the extruder and deposited layer-by-layer. The

Sample with simulated poor interlayer bond

Here, the time and frequency domain analysis as well as phase-space representation of the received ultrasound signals of the intact sample and the sample with the simulated defect are presented. Fig. 10 presents the windowed time domain response and frequency responses of the received ultrasonic signal with excitation amplitude of 170 V for the intact sample. From the time domain response of the intact sample, a simple harmonic response is observed. Additionally, according to the frequency

Conclusion

This study considers the resulting nonlinear behavior in the phase-space domain of ultrasonic waves while interacting with poor interlayer bonds. Two different samples with poor interlayer bonds were considered. In the first case, two 3D-printed polymer cubic samples with a liquid polymer between them were used to simulate a poor interlayer bond. Then, the samples were placed inside a compressive tool that applies compressive force on both sides of the sample. Simultaneously, ultrasonic testing

Author statement

Sina Zamen: writing the paper, analyzing the data, developing the algorithm, performing ultrasound test, developing the numerical program.

Ehsan Dehghan Niri: writing the paper, developing the algorithm, developing the program used in analyzing the data.

Helem Al-Beer: literature review, revising the paper, performing ultrasound tests.

John Lindahl: changing the 3D printing process parameters, printing experimental samples.

Ahmed Arabi Hassen: 3D printing the samples, writing the paper, revising

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

Research was sponsored in part by the U.S. Department of Energy, Office of Energy Efficiency and Renewable Energy, Advance Manufacturing Office, under contract DE-AC05-00OR22725 with UT-Battelle, LLC. Large scale AM machine used in this research was sponsored by Cincinnati Inc., OH, USA. Feedstock materials used in this work were provided by Techmer PM., TN, USA. We also gratefully acknowledge the funding support from the Department of Energy/National Nuclear Security Agency (Grant DE-NA0003987

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