International Symposium (NDT-CE 2003)Non-Destructive Testing in Civil Engineering 2003
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THREE-DIMENSIONAL VISUALISATION OF ACOUSTIC EMISSION MOMENT TENSOR SOLUTIONS BY VRMLMitsuhiro SHIGEISHI, Kumamoto University, Japan
Masayasu OHTSU, Kumamoto University, Japan
Jun SHIMAZAKI, Kumamoto University, Japan
SiGMA-AE is developing as a reasonable and powerful technique for the moment tensor analysis of acoustic emission (AE). By SiGMA-AE analysis, crack kinematics of locations, types and orientations are quantitatively determined. Because these kinematical outcomes are obtained as three-dimensional (3D) locations and vectors, Virtual reality modelling language (VRML) application is examined for 3D visualisation of moment tensor solutions. As a test case, failure processes of a few of concrete specimens are discussed by using 3D visualisation of SiGMA-AE solutions in the virtual reality world.
The generalized theory of acoustic emission (AE) has been established on the basis of elastodynamics . Thus, it is clarified that AE waves are elastic waves due to dynamic dislocation in a solid. Theoretical treatment of AE in concrete was studied as elastic waves in a homogeneous medium . In accordance with these studies, an application software named 'SiGMA' to determine AE source kinematics of AE source location, crack orientation, crack-motion direction and crack type has been developed . Although this reasonable and powerful tool has been applied to a variety of AE experiments in concrete engineering , numerical results from computed moment tensor solutions had a lot of difficulty to satisfy analysts or owners. Because these kinematical outcomes are obtained as three-dimensional (3D) locations and vectors, 3D visualisation of results is desirable.
Otherwise, when the commercial version of SiGMA software released up to market in 1997 , a community, the Web3D Consortium has been in action to represent all aspects of 3D technologies on the Internet. Virtual Reality Modelling Language (VRML) is a file format for describing interactive 3D objects and worlds. VRML is designed for using on the Internet, intranets, and local client systems. VRML is also intended to be a universal interchange format for integrated 3D graphics and multimedia. VRML may be used in a variety of application areas such as engineering and scientific visualisation, multimedia presentations, entertainment and educational titles, web pages, and shared virtual worlds . In this paper, the visualisation using VRML (Virtual Reality Modelling Language) for moment tensor solutions is proposed.
MOMENT TENSOR ANALYSIS BY AE-SIGMA
By taking into account only P wave motion of the far field of Green's function in an infinite space, the displacement Ui(x, t) of P wave motion is obtained from,
Here, r is the density of the material and vp is the velocity of P wave. R is the distance between the source y and the observation point x, of which direction cosine is r = (r1, r2, r3). S(t) is the source-time function of crack motion. Considering the effect of reflection at the surface and neglecting the source-time function, amplitude A(x) of the first motion is represented,
where Cs is the calibration coefficient including material constants in Eq. (1). q is the direction of the sensor sensitivity. Ref(t, r) is the reflection coefficient at the observation location x. Since the moment tensor is symmetric, the number of independent unknowns Mij to be solved is six. Thus, multi-channel observation of the first motions at more than six channels is required to determine the moment tensor components.
CRACK KINEMATICS REPRESENTATION
In the case of an isotropic material, the moment tensor, Mpq, is defined by,
where l and m are Lame's elastic constants. l is the unit direction vector and n is the unit normal vector to the crack surface. DV is the crack volume. Then, the classification of a crack is performed by the eigenvalue analysis of the moment tensor.
Setting the ratio of the maximum shear contribution as X, three eigenvalues for the shear crack become X, 0, -X. Likewise, the ratio of the maximum deviatric tensile component is set as Y and the isotropic tensile as Z. It is assumed that the principal axes of the shear crack are identical to those of the tensile crack. Then, the eigenvalues of the moment tensor for a general case are represented by the combination of the shear crack and the tensile crack. Because relative values are determined in the SiGMA, three eigenvalues are normalized and decomposed,
where X, Y, and Z denote the shear ratio, the deviatric tensile ratio, and the isotropic tensile ratio, respectively. In the present SiGMA code, AE sources of which the shear ratios X < 0.4 are classified into tensile cracks. Otherwise, the sources of X > 0.6 are classified into shear cracks. Also, the sources of X are between 40% and 60% are referred to as mixed mode.
Figure 3 shows geometry among the unit eigenvectors corresponding to three eigenvalues, normal to crack surface n and crack motion direction l as e1 = l +n, e2 = l ´ n and e3 = l - n. The vectors l and n can be recovered from the following relations,
By applying a conventional SiGMA code, numerical results for one AE event are listed in Table 1.
VRML APPLICATION TO MICRO-CRACK VISUALISATION
Just as Hyper Text Mark-up Language (HTML) led to a population explosion on the Internet by implementing a graphical interface, VRML adds the next level of interaction, structured graphics, and extra dimensions (z-axis and time) to the online experience. The applications of Web3D technologies are broad, ranging from prosaic business graphics to entertaining web page graphics, to manufacturing, scientific, entertainment, and broadcast and educational applications, and of course to 3D shared virtual worlds and communities.
The release of software such as CosmoPlayer  made viewing VRML models a practical reality for the average computer owner. CosmoPlayer can view VRML 2.0/97 models and comes in the form of a plug-in for use with Web browsers such as Netscape. The dashboard controls (Figure 4) are probably familiar.
In usual, AE events are displayed at their locations with symbols. A tensile crack is denoted by arrow symbol ("), of which direction is identical to that of crack opening. A shear crack is denoted by cross symbol (´), of which two directions correspond to two vectors l and n. As can be seen, classification of cracks is readily made, whereas crack orientation is not easily recognized. This is because two-dimensional plotting is adopted and results are inherently suitable for 3D visualisation . In this respect, VRML is introduced. Crack modes of tensile, mixed-mode and shear are given in Figure 5. Here, an arrow vector indicates a crack motion vector, and a circular plate corresponds to a crack surface, which is perpendicular to a crack normal vector.
Using these objects shown in Figure 5, VRML application was applied to practical results of AE-SiGMA analysis. A bending test of a reinforced concrete (RC) beam specimen was carried out (Fig 6). 6 sensors and 6ch. AE waveform recording system were used. Bending failure of the RC beam was generated. Without reinforcement, concrete beams break suddenly into two blocks when the stress at the bottom side reaches the tensile strength. Sudden crack propagation from the bottom to the top is prevented with reinforcement.
As a result, failure process is visually divided into several stages. Combining all results analyzed, Figure 7 is obtained. As shown, actually all figures can be moved and rotated. So, locations and orientations of the source can be visually identified. This is a good point by means of VRML.
Nucleation of cracks can be quantitatively analyzed from AE waveforms, applying SiGMA code. Crack kinematics on locations, types and orientations are determined three-dimensionally. Because visualisation of results is desirable, using VRML develops 3D visualisation,Times procedure for SiGMA analysis. As discussed, failure process of a reinforced concrete beam is successfully visualisation and studied.
Other cases of concrete failure processes are viewed by VRML. Due to expansion of corrosive products, cracks are nucleated around reinforcement in concrete. Initiation and propagation of cracks are studied experimentally.
Figure 9 and 10 show the results of SiGMA Analysis of the 2 types of specimens, which were fractured by internal expansive power at the holes. The specimen Type A has a hole at distance of 40 mm from the nearest side. Another specimen Type B has a hole at distance of 20 mm from the nearest side. The difference of cracking development pattern could be corresponding to the restriction effect by the distance between the hole and the side.
Very remarkably, the difference of crack propagation pattern is shown. Also, it is found that cracking mechanisms due to expansion of holes are mostly associated with the tensile type micro cracking.