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This paper presents results for a new acoustic emission crack source model based on a finite element modelling approach which calculates the dynamic displacement field during crack formation. The specimen modelled is statically loaded until conditions for crack growth as defined by a failure criterion are fulfilled. Subsequently, crack growth is modelled by local degradation of the material stiffness utilizing a cohesive zone element approach. The displacements due to crack growth generate the acoustic emission signal and allow detailed examination of the principles of acoustic emission sources operation. Subsequent to crack growth signal propagation is modeled. The signal propagation is modeled superimposed on the static displacement field. The presented model comprises a multi-scale and multi-physics approach to consider the signal propagation from source to sensor, the piezoelectric conversion of the elastic wave to an electric signal and the interaction to the acquisition electronics. Validation of the modeling approach is done by investigating the acoustic emission signals of micromechanical experiments. Using a specifically developed load stage, carbon fiber filament failure and matrix cracking can be prepared as model sources. A comparison of the experimental signals to the modeled signals shows good quantitative agreement in signal amplitude and frequency content. A comparison between the present modeling work and analytical theories demonstrates the substantial differences not considered in previous modeling work of acoustic emission sources.
In recent years it has become convenient to use numerical methods to model acoustic emission sources. In this field, Prosser, Hamstad and Gary applied finite element modeling to simulate acoustic emission sources based on body forces acting as a point source in a solid [10, 17]. Hora and Cervena investigated the difference between nodal sources, line sources and cylindrical sources to build geometrically more representative acoustic emission sources . At the same time, we proposed a finite element approach using an acoustic emission source model taking into account the geometry of a crack and the inhomogeneous elastic properties in the vicinity of the acoustic emission source .
Based on these investigations we can categorize the different modelling strategies to describe acoustic emission sources of crack propagation as shown in Fig. 1. The first type of source models considers point-like sources explicitly defining the source dynamics utilizing analytical source functions (cf. Fig. 1a). As second type we can interpret those attempts that have been made to incorporate more accurate source geometries, while the modeled crack dynamics are still based on analytical source functions (cf. Fig. 1b). The third type uses accurate artificial source geometries and does not need an analytical source function to generate acoustic emission. Instead, this type of source model is capable to generate the crack dynamics based on experimentally accessible parameters and fracture mechanics laws.
Currently all source models proposed in literature are of type one or type two, since they all require the definition of an explicit source function. Therefore, no details of the dynamics arising from the crack formation process and the subsequent crack surface motion are predicted or considered by those models.
From a mathematical modeling and simulation point of view, there are two main challenges in providing a numerically based acoustic emission source model of the third type. The first challenge consists of the different scales involved in the problem (crack length of the order of microns versus signal wavelength of the order of millimeters to centimeters) and the proper scale bridging. Owing to the vastly different observations scales, a full multi-scale approach is thus necessary. The second challenge stems from the calculation of temporal and spatial evolution of the surfaces of the crack. This is a level of detail that is typically not studied in modeling approaches used to describe crack formation by means of cohesive zone elements, extended finite element methods or similar implementations.
In the present work, we first present the source model description and establish its principle of operation. Subsequently we validate the source description by modeling of acoustic emission sources to correspond to micromechanical experiments. The experimental work is based on a micromechanics test stage, which was constructed to allow the preparation of fiber breakage and matrix cracking as acoustic emission sources. We then apply the new acoustic emission source model concept in combination with in-situ modeling of the signal propagation process and the detection process of a piezoelectric sensor. Comparison is made between the experimental results and the results from the different types of acoustic emission source simulation.
For all cases investigated the first part of the preparation is to position a small droplet of RTM6 epoxy resin on top of the aluminum pin. To facilitate the positioning of the epoxy resin droplet a small depression was machined into the end of the aluminum pin. To prepare the micromechanical stage for generation of a matrix crack a tensile bar made from polyether ether ketone (PEEK) of 2 mm diameter and 80 mm length is used. The tensile bar is first moved into the liquid epoxy resin and then retracted to yield a tapered contour of 380 to 800 \(\mu \)m (see Fig. 3). Subsequently, curing of the liquid resin is carried out using heating foils attached to the aluminum block and an additional heating sleeve wrapped around a small cylinder covering the aluminum pin and parts of the tensile bar. We use a curing cycle comprising a heating rate of 2 \(^\circ \)C/min up to the curing temperature of 180 \(^\circ \)C. The curing temperature is kept constant for 150 minutes with subsequent cooling to room temperature at a rate between 0.5 and 2 \(^\circ \)C/min. Due to its low thermal conductivity the tensile bar made from PEEK minimizes the dissipative heat flux and therefore assures a constant temperature of the resin during curing. The tensile bar and the aluminum block are mounted in a universal test machine so that thermal expansion of the components and chemical shrinkage of the resin can be compensated by a closed loop force control. The test machine control adjusts the tensile bar position to assure zero force acting during curing, which is necessary to avoid excessive forces acting on the filament causing preliminary failure due to thermal expansion and cure shrinkage of the resin.
After preparation of the test geometry, the universal test machine is used to apply a tensile force using a displacement controlled mode with velocities dependent on the selected failure mechanism. We choose a velocity of 20 \(\mu \)m/min for fiber breakage and 50 \(\mu \)m/min for matrix cracking. The failure was monitored by an optical microscope using a magnification factor of 100. The images obtained after failure are shown in Fig. 3 for the two failure types. The respective acoustic emission signal is detected by a type WD piezoelectric sensor coupled by temperature stable Apiezon-L grease at the bottom of the aluminum block. The dimensions of the aluminum block allow an observation window of the primary acoustic emission signal of 18 \(\mu \)s free of reflections from the surfaces of the aluminum block. The detected acoustic emission signals are digitized by 40 MS/s using a bandpass range between 20 kHz and 1 MHz. Triggering of the signals was carried out with 10 \(\mu \)s Peak-Definition-Time, 80 \(\mu \)s Hit-Definition-Time and 300 \(\mu \)s Hit-Lockout-Time at a threshold level of 45 dB\(_AE\). The preamplification factor was chosen as 40 dB\(_AE\) for fiber breakage and as 20 dB\(_AE\) for matrix cracking.
The source model description proposed herein consists of three sequential modeling steps as schematically presented in Fig. 4. The first step is derived from classical structural mechanics. Suitable displacement boundary conditions are defined for the geometry considered to restrict some of the displacement components on one end (cf. Fig. 2). The other end is loaded by a force high enough to initiate fracture at the crack plane considered. If this force value is unknown, the implementation of a fracture criterion (e.g. fracture toughness, max. stress, etc.) to deduce the onset load for crack initiation is a straight forward procedure using a stationary solver sequence with incremental loading. If the external force is known from experiments, the measured force value can directly be used for the stationary solver. For the example shown in Fig. 4, the presence of the notch causes stress concentration at the tip of the notch, which will cause crack initiation at this point.
In the second step, the initial conditions for the displacement \(\vec u\) and stress states \(\vec \sigma \) are chosen to be identical to the static values \(\vec u_static\) and \(\vec \sigma _static\) as calculated in the previous step. Boundary conditions for restricted displacement components and external loads are kept identical to the previous step. In contrast to the previous step, now a transient calculation of the displacement field is performed. In addition, boundary conditions at the crack plane are chosen to allow for crack opening according to a fracture mechanics law. The duration of this transient calculation \(t_frac \) is chosen to be sufficient until crack propagation has come to a rest. As seen from Fig. 4, the presence of the static displacement field causes crack propagation with an accompanying excitation of an acoustic emission wave. This spatial movement is seen best in the velocity field, since the static displacement dominates the displacement scale and therefore inhibits the identification of the very small displacements caused by the acoustic emission wave. A detailed discussion of the crack growth implementation is given in Sect. 3.1. 350c69d7ab