Capítulo 5: Materiales y métodos
5.5 Cultivo de Bacillus thuringiensis en modo semicontinuo (Draw-fill)
Acoustic Emissions (AE) are elastic waves produced by sudden movement in stressed materials, which can be detected with appropriate surface-mounted sensors. The dominant sources of acoustic emissions in materials are defect-related deformation processes such as crack initiation, growth and plastic deformation [101]. Of particular interest to this thesis include crack initiation and growth, dislocation motion, slip, twinning, grain boundary sliding as well fracture and inclusion decohesion. Familiar examples of the phenomenon occur when a twig breaks or a piece of paper is torn. We can hear these examples without the use of specialized sensors since these types of emissions are in the audible range. AE testing differs foremost from other non- destructive testing methods in two significant respects. First, AE testing is passive; this means the energy that is detected is released from within the specimen, rather being actively supplied by the test method, as ultrasonic testing, x-rays or radiographic testing. Second, the AE method can detect the dynamic process associated with the progressive damage development. Material related AE are caused by external stimuli such as changes in load pressure, strain or temperature [102, 103]. In this framework, AE has held promise for quantitative evaluation of the crack initiation and growth in metals during fracture and fatigue. For instance, by finding a correlation between AE hits and the stress intensity factor, a relationship is proposed to predict the crack growth [104]. In addition, several studies have attempted to reframe Paris-Erdogan equation by relating AE parameters such as events, count, amplitude and energy to material behavior [104- 106]. In fatigue the crack growth rate can be described using Paris-Erdogan equation
( )m
da
C K
dn
(2.46)
where da dn is the change of the crack length per load cycle is (ais the crack length and nis the number of fatigue cycles). Furthermore, kis the stress intensity factor range, C and m are assumed to be constant for particular material. These studies suggest a linear relationship between the log of the crack propagation rate da dnand the log of the AE count rate.
The detectability of the mechanism depends on the amplitude of the elastic wave emitted by the source of background noise over the frequency range of the sensors. To discriminate the AE emission from background noise, data processing techniques are necessary. The first part of data processing includes the Fourier spectral analysis of each recorded AE event. Aspects of spectral signal processing is explained in Ref. [107] and their implementation to AE is reported in Ref. [108]. After obtaining digital time-domain data, Fast Fourier transform is applied to AE waveform in order to convert it to the frequency-domain. Better estimation of AE power spectral density ( )G f can be calculated when the noise spectrum Gn( )f is subtracted from each power
spectral density G f i( )
( ) i( ) n( )
G f G f G f (2.47)
From the AE power spectral density function, the energy and median frequency are computed for each event: E is the energy measured as an integral of G f over a whole frequency range of ( ) 50-1000 kHz: max
min
( )
f f
E
G f df and f is the median frequency given by [109]. mmax max min ( ) ( ) m f f f G f df f G f df
(2.48)Friesel and Carpenter [110] found that deformation twinning and dislocation glide are the major sources of AE in pure magnesium and AZ31 magnesium alloys. Based on this result Lu et al. [111] associated AE signals with different deformation mechanisms in Mg alloys. AE generated by twinning was characterized by short rise time and high amplitude, both of which lead to the burst type emissions shown in Figure 17b. In contrast, deformation caused by slip results in continuous type emissions similar to the ones displayed in Figure 17a [111].
Figure 17 AE signal waveform (a) sliding (b) twinning [111].
The appearance of burst type AE can be conveniently identified by introducing a parameter known as the ‘peakedness’ of the waveform in the time domain. This parameter quantifies a shape of a random signal in the same way that the forth moment of a random variable describes the sharpness of its probability distribution. The AE signal is considered as a set of fluctuation of random amplitudeUj, mean amplitude U and varianceU2. Thus, kurtosis (q) of the AE signal as given in mathematical statistics is [111].
4 1 1 3 N j j U U U q N
(2.49)Processes with normal amplitude distribution, i.e. noise-like continuous signals, have q-values close to zero. Those continuous signals, which have a ‘flatter’ amplitude distribution than normal, have negative kurtosis. The signals with q 0 have the amplitude distribution ‘sharper’ than normal, and they will be recognized therefore as burst-type signals. The deviation of the positive q magnitude from zero serves as a measure of peakedness of the signal.
First, assume that different sources produce the AE signals with different waveforms and power spectral densities. Since AE is a random process, there will be some scatter in spectra and waveforms that makes it difficult sometimes to distinguish between different sources. This distinction, however, can be feasible by grouping signals of a similar kind. One possibility is to determine all records in terms of a limited number of parameters such as an energy, peak amplitude, median or central frequency, etc., measured in both time and frequency domain, without limiting ourselves to any a priory assumptions concerning characteristics of AE events caused by sources of different nature. Vinogradov et al. [109] proposed a following statistical procedure for unsupervised categorizing or ‘clustering’. As a measure of the distance between two events A and Bin the n-dimensional space of AE parameters, a simple metric is chosen as
2 2 1 ( , ) n j i i U a b r A B
(2.50)Where