Nonlocal and Coda Wave Quantification of Damage Precursors in Composite from Nonlinear Ultrasonic Response

Materials state awareness using conventional nondestructive evaluation (NDE) at the early stage of service life is extremely challenging because of the inherent material nonlinearity that initiates at the lower scales. Conventional NDE methods are limited by reporting location, size, and shape of the material discontinuities, e.g., cracks, voids, delamination, etc. In the past, several nonlinear ultrasonic methods are developed to detect the small discrete damages, whereas quantification of degraded material properties and detection of embryonic precursor damage in materials is currently challenging. Understanding the early stage of precursor damages using ultrasonic method inherently is to understand the material nonlinearity that arise from the bottom-up scales, which further requires to evaluate the ultrasonic signals with subtle nonlinearity in an innovative way that are essentially ignored in conventional ultrasonic NDE methods. Hence, in this chapter, it is hypothesized that such nonlinear effects at the early stage of damage at the lower scale are actually sensed by the ultrasonic NDE probes/sensors and hidden in the ultrasonic signals. Such hidden features are required to be extracted from the signals using innovative signal analysis method integrated with the microcontinuum physics. In this chapter defying the conventional nonlinear ultrasonic techniques, a newly formulated nonlocal approach is presented to quantify the damage precursor in materials at its early stage of the service life. Nonlocal parameter that carries information from the lower scale has a nonlinear dependency on the ultrasonic wave velocity at any particular frequency, which is assumed to be a constant in linear ultrasonics and no information could be extracted. Here, it should be noted that the nonlinear function of nonlocal parameter from a material that can be extracted from the material degradation state is not necessarily associated with the material discontinuities like cracks or delamination at the macroscale but due to distributed nonlocal effect of lower scale defects and damages. Thus, a new term called nonlocal damage entropy (NLDE) was coined by the authors in their recent publications to quantify the multiscale damage state in materials while exploiting the high-frequency ultrasonic (≥10 MHz) with microcontinuum field theory. In this chapter, first, a review of different “bottom-up” multiscale modeling approaches is discussed followed by the need of a “top-down” precursor quantification method is justified. Further, a review of the existing methods for quantifying damage precursor is presented followed by a mathematical and experimental derivation of NLDE is presented. To justify the findings with additional information from different scales, low-frequency (≤500 kHz) Guided wave ultrasonic NDE was performed. It is further hypothesized that the lower frequency ultrasonic guided wave signal that carries the nonlinear effect from the lower scale is essentially manifested but can only be extracted from the coda part of the signals and thus in this chapter the coda part of the signals were analyzed. Frequency transformation of the signals could result very low and almost undetectable higher harmonics due to the very early stage of damage and may not be useful for precursor quantification. Hence, a time domain analysis is required to find this information on the nonlinearity that could be manifested but are buried deep inside the signal. Thus, Guided coda wave interferometry (CWI) for composite is formulated for the first time using high-speed Taylor series expansion method. Precursor damage index is then formulated to quantify the damage state. Precursor damage index from Guided CWI and high-frequency NLDE are then correlated to evaluate the equivalency of information. To prove the positive indication of precursor damage from the newly coined NLDE, a set of benchmark studied are presented using optical microscopy and scanning electron microscopy (SEM). As metallic structures are well studied by many researchers, in this chapter the example study of precursor damage is restricted to the composite specimens under fatigue.