Relation comparison methodologies of the primary and secondary frequency components of acoustic events obtained from thermoplastic composite

laminates under tensile stress

N. Papadakis, N. Reynolds, C.Ramirez-Jimenez, M.Pharaoh

International Automotive Research Centre, Warwick Manufacturing Group, University of Warwick, CV4 7AL

ABSTRACT Acoustic emission (AE) methodologies have been successfully implemented for the monitoring of damage in monolithic materials (e.g. steel). Multiphase materials (such as composites) tend to exhibit more complex interactions than metals, and the processing of AE data into meaningful analyses (e.g. failure types) has until recently been impractical. However, recent advances in computer technology have made the acquisition, transmission, storage, and processing of data obtained from composite structures possible in real time. Two complimentary methodologies suitable for the investigation of the relationship of the primary and secondary frequency components of AE events are presented. The first methodology utilises the connecting vector between these two frequencies in the power-spectrum domain and allows visualisation the relationship independently of time. The second methodology is described that allows monitoring of the time-dependent evolution of the primary and secondary frequency and allows determination of any rapid changes.

1 Introduction Recent work at the University of Warwick has investigated the relationship between the primary frequency component of an event and the (micro-)failure mode present in a composite material [1]. In that work, a number of discrete primary frequency bands have been observed to be present, and it was proposed that they could be attributed to different failure events. It was also suggested that some of the AE events are the result the occurrence of a combination of different failure modes. The AE present due to the combined failure modes recorded within one AE waveform should have an effect on the final recorded event characteristics i.e. primary/secondary frequency components. This work focuses on the secondary frequency component of the AE events and presents the methodology that was used to investigate any correlation between secondary frequency component and failure modes.

2 Background As previously stated, it is accepted that compared to monolithic materials, composite materials exhibit more complex failure modes. Some of the most common failure modes are fibre breaking and fibre pull-out, matrix cracking, fibre-matrix debonding and local and global delamination [2]. Due to the differences in stiffness and density of the different composite phases (fibre, matrix, interface) – and other variables like geometry – it is postulated that the energy released by each failure mode is associated with a different frequency component. By applying a Fast Fourier Transform (FFT) to the transient waveform obtained for each AE event and analysing the resulting power spectrum, it is possible to obtain characteristic primary and secondary event frequency components - see Figure 1. The upper figure is the AE event waveform, whilst the lower figure

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presents the FFT power spectrum. The labels on the lower graph present the five successive highest power frequencies.

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Figure 1: (a) AE event transient waveform (Top), (b) power spectrum of a single AE event

(bottom) It can be seen from the FFT power spectrum (b) obtained from the complex transient waveform (a), the transient signal comprises many constituent frequencies. Observing this, it is obvious that the primary frequency might only represent the peak of a more complicated combination of micro failures, in which case any assumption that the primary frequency component alone is representative of an AE event might need to be reconsidered. Figure 2 plots the primary frequencies from a [+/- 45o]2s laminate tensile test vs. test time. The banding of the primary frequencies is obvious. This lends support to the assumption that the type of the failure mode type is associated with the primary event frequency.

Figure 2: Plot of primary event frequencies of a tensile test of [+/-45o]2s Plytron (14000 data

points).

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Figure 3 presents a plot of the secondary event frequencies vs. test time for the same test. The similarities of Figure 2 and Figure 3 are significant in both the central locations of the banding frequencies. One significant difference is the width of the bands is greater for the secondary event frequency, which indicates greater scatter. Due to the number of points it is impractical to do a visual comparison between the number of primary and secondary frequency components.

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Figure 3: Plot of secondary event frequencies of a tensile test of [+/-45o]2s Plytron (14000 data

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Figure 4: Secondary frequency vs. Primary Frequency

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The importance of the secondary frequency in an AE event is not yet determined in the literature. This paper proposes a methodology to establish if the secondary frequency component (when considered along with the primary frequency component) of an AE event directly relates to the failure mode type as with the primary event frequency. In order to investigate the possibility of such a relationship, the secondary event frequency is always examined in conjunction with the primary event frequency. Figure 4 presents a plot of the secondary frequency vs. the primary frequency for the results presented earlier. Points along the diagonal indicate that the secondary frequency and the primary frequency are similar. In such cases, the secondary frequency should be neglected. In the same graph, concentrations can also be observed in a number of areas. However, this representation is lacking, as it does not contain any information regarding the amplitude of the frequency components.

3 Methodologies The primary metrics used to determine the contribution of the secondary frequency component to the entire AE transient waveform are the following:

• Relative magnitude and frequency difference between components i.e. connecting vector between primary and secondary components;

• Evolution of primary and secondary event frequencies through the test-time domain. These metrics are used in the time-independent methodology which creates a field of likely vectors. The second methodology is complimentary to the first and takes into account the time-element.

3.1 Connecting vector The vector connecting the primary frequency component to the secondary frequency component in the power spectrum (similar to Figure 1b) was selected to measure the relative magnitude and the distance between the frequency components. The vector is determined by the log of the magnitude (Euclidean distance) and the log of the gradient – see following equations:

Magnitude=log| 22 )()( Af ∆+∆ |

Gradient=log|fA

∆∆ |

Where ∆f is the difference between the primary and secondary frequencies (f1 – f2), and ∆A is the difference between amplitudes (A1 – A2). It is very important to have a normalized power spectrum. To achieve this, the area under the power spectrum curve is calculated and then the amplitude value for each frequency component is divided by the area (i.e. in the normalised power spectrum the area under the curve equals to one). The secondary frequency has a greater effect on the acoustic waveform for decreasing values of the gradient. The interpretation of the magnitude depends on the value of the gradient. For small values of gradient, increasing values of magnitude indicate that the difference between primary and secondary frequency increases – i.e. the secondary frequency has a significant contribution. For high values of gradient, increasing values of magnitude indicate that the difference between primary and secondary amplitude increases – i.e. only the primary frequency is important.

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Using the connecting vector it is possible to visualise the relationship and determine whether there are predominant trends – see Figure 5 for an example. By plotting the vectors for each individual event, trends are expected to emerge. However, due to the large number of points it is not possible to directly use this method (the attempt resulted in a black image). Therefore a screening process is required, which utilises the density of magnitude and the gradient – see Error! Reference source not found..

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Figure 5: Visualisation of connecting vectors (using a magnitude screening filter with values

greater than 1.5).

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Figure 6: Bi-variate kernel density estimation (KDE) of the gradient and magnitude of a

vector connecting the primary and secondary frequency.

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Error! Reference source not found. presents a bivariate kernel density of the magnitude and the gradient. The peaks in the plot represent the areas of magnitude and gradients that are most common. As mentioned earlier, the areas of interest are those with high values of magnitude and also low gradient values. In the case at hand, the highest values of magnitude are exhibited for related to the lowest values of magnitude; this is partly due to a scaling effect (when the magnitude and gradient were calculated the values were not normalised). Using the information in Figure 6, it is possible to implement a filter that utilises both the magnitude and the gradient in order to reduce the amount of information to the relevant point. To implement the filter a minimum value of the gradient can be used and/or a maximum value for the gradient. The results presented in Figure 5 suggest that in this test the secondary frequency is very near to the primary one and therefore there is no reason to investigate further.

3.2 Evolution of kernel density estimations (KDEs) of the primary and secondary frequency The parallel evolution of the kernel density estimations of the primary and secondary frequency can also be utilised to reveal time-dependent relationships between the primary and secondary frequency. A typical KDE of the primary frequency for the entire test is presented in Figure 7. The interpretation of figure 7 is that the majority of the AE events had a primary frequency of 100[kHz]. Other common primary frequencies are at 250[kHz], 280[kHz] (a point of inflection), at 550[Hz] and finally around 450[Hz].

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Figure 7: KDE of the primary frequency component

By plotting the KDEs for the primary and secondary frequency, at different stages of the test (e.g. increasing the number of acoustic events under consideration by 100) it is possible to determine if any significant changes in the proportion of the primary and secondary frequency occur. The plots can be either cumulative or differential. Cumulative KDE plots (see Figure 8-top) take into account increasing number of acoustic events and as a result in the beginning can vary rapidly

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but soon develop stable patterns, which as the number of events increases the KDE becomes more insensitive to influences from the recent inputs.

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8*Cumulative* PDF of 1st Frequency [kHz] for 12989 events.

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Figure 8: Cumulative (top) and differential (bottom) KDE plots.

Contrary to the cumulative KDE, the differential KDE plot (see Figure 8-bottom) is only influenced by the last N specimens and therefore exhibit at any given time the same degree of sensitivity.

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Figure 9: Cumulative KDE of the primary frequency.

As a result, the cumulative KDE can be used to give a time dependent overview of the progress of the frequencies in the test. The differential KDE is preferred to monitor more accurately the changes in proportion at different times through-out the test; e.g. in the case that there are unusual frequencies occurring near failure then a differential KDE plot will be preferable.

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Figure 9 and Figure 10 respectively represent projections of the cumulative and differential KDEs of the primary event frequency. They allow visualisation of the evolution of the primary event frequency distribution. Another surface could be added to represent the secondary event frequency, however for clarity reasons is will not be shown on this paper.

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Figure 10: Differential KDE of the primary frequency

4 Conclusion Two methodologies suitable for the investigation of the relationship of the primary and secondary frequency components of recorded AE events have been presented. The first methodology utilises the connecting vector between the two frequencies in the power-spectrum plot. Although this direct connection between primary and secondary frequency on a graph showed certain interesting trends, this methodology was proven to be inefficient when considering the large amount of points resulting from the tests (up to 20000 AE events recorded per test). A second methodology is described that that allows monitoring of the time dependent evolution of the primary and secondary frequency.

5 References [1] C.R. Ramirez-Jimenez, M.Pharaoh, N.Reynolds, N. Papadakis, “A methodology for the identification of tensile failure mode types in thermoplastic composite laminates by means of acoustic emission monitoring”, ECCM-11 (submitted) Rhodes, Greece, May 2004. 2 Hull D. & Clyde T.W., An introduction to Composite Materials (Second Edition), Cambridge University Press 1996, p 159

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