jeanflop/post-ocr-correction huggingface dataset:
by using other configurations. Despite the limited set of data provided in the Table and their relative inaccuracy, these results clearly demonstrate the efficiency of our algorithm. An important feature is that the convergence is always better when considering the material anisotropic instead of being isotropic. For instance, sometimes there is not even convergence, showing the incompatibility of treating the data with the isotropic hypothesis. In addition, the method can be extended to the full 3-dimensional problem [19]. For this problem, the set of non-linear equations is given by Equation (3), where new fourth degree terms appear. A supplementary difficulty
(3), where new fourth degree terms appear. A supplementary difficulty is due to the fact that propagation in non-principal planes has to be considered. In such a case, analytical expressions for the slowness curves are no longer available. The eigenvalues of the propagation tensor should be numerically computed, using for instance Jacobi method [14]. A stringent problem is related to the non-uniqueness of the solutions, which occur for some source/sensors configurations. These developments and further experimental data will be described elsewhere [20]. INTRODUCTION. — The localization of sources of acoustic emission is usually realized, for isotropic media, by triangulation techniques
emission is usually realized, for isotropic media, by triangulation techniques ([2], [3]). Whether it be for the localization of earthquake epicenters or for applications in Science of Materials/Mechanics of Fracture, least squares [4], and correlation ([5], [6]) techniques are commonly used. However, anisotropy was until then absent from these treatments which motivated the introduction of the optimization procedure described in a previous Note [1]. This method of localization of point sources of acoustic emission is tested in the present Note for a fiberglass-reinforced polyester resin composite material. The material chosen for this purpose, possesses an average anisotropy, and is by
for this purpose, possesses an average anisotropy, and is by the way very ordinary, lightly porous and rather inhomogeneous. Thus, we place ourselves deliberately in conditions rather unfavorable. Notably, the state of the surface of the material is rather mediocre and the condition of a thin plate with parallel faces required by the modeling appears at most as an approximation. For the experimental measurements, an ultrasonic system associating sources of acoustic emission point-like and a network of quasi-point-like transducers was used. Details concerning this apparatus are available elsewhere [10]. This testing bench opens interesting perspectives for experiments in mechanics of
testing bench opens interesting perspectives for experiments in mechanics of fracture ([11], [12]). The sources of acoustic emission are simulated by breaking 0.08 mm o.d. capillary glass tubes. The rise time for such acoustic emission events is typically in the range of 50 ns. The sensors used are large bandwidth piezoelectric transducers with a 1.3 mm diameter. The material used in this study, a fiberglass reinforced unidirectional composite material [15], has a medium anisotropy and is porous. Also, it has a poor homogeneity and rough surfaces. The location process is initiated by a calibration procedure which provides the necessary elastic
initiated by a calibration procedure which provides the necessary elastic constants given by Equations (1) and (2), in the case of a transversely isotropic solid [13]. These preliminary measurements are done in 4 particular directions of propagation as shown in Figure 1. To obtain accurate values of the elastic constants, averages are computed for that purpose. Then, by using the optimization procedure described in [1], which involves the solution of a non-linear set of equations with a Newton-Raphson numerical method [14], the location of the source is determined. The measurements were done in the near-field to limit the influence of
were done in the near-field to limit the influence of attenuation and dispersion of the transient waves. Figure 2 shows some characteristic waveforms. Attenuation and dispersion are clearly seen on these transient waves and might be detrimental to the precision of the results. Also, when moving to the far-field, plate modes ([16]-[18]) which become predominant are problematic, as the bulk modes have weaker amplitudes. This last problem is directly linked to the chosen geometry — a thin plate — and can be avoided by using other configurations. Despite the limited set of data provided in the Table and their relative
set of data provided in the Table and their relative inaccuracy, these results clearly demonstrate the efficiency of our algorithm. An important feature is that the convergence is always better when considering the material anisotropic instead of being isotropic. For instance, sometimes there is not even convergence, showing the incompatibility of treating the data with the isotropic hypothesis. In addition, the method can be extended to the full 3-dimensional problem [19]. For this problem, the set of non-linear equations is given by Equation (3), where new fourth degree terms appear. A supplementary difficulty is due to the fact that propagation
A supplementary difficulty is due to the fact that propagation in non-principal planes has to be considered. In such a case, analytical expressions for the slowness curves are no longer available. The eigenvalues of the propagation tensor should be numerically computed, using for instance Jacobi method [14]. A stringent problem is related to the non-uniqueness of the solutions, which occur for some source/sensors configurations. These developments and further experimental data will be described elsewhere [20]. NOTES POUR LA CORRECTION ### Abridged English Version — An original numerical scheme has been recently introduced for locating acoustic emission sources in anisotropic media
recently introduced for locating acoustic emission sources in anisotropic media [1]. Generally, in the case of isotropic solids, such a localization process is done using triangulation techniques ([2], [3]). In principle, the approaches are similar for both acoustic emission source location as applied to fracture mechanics problems and for earthquake epicenter determinations [4]. Least-square methods are already used for such problems as well as signal processing techniques using correlation methods ([5], [6]). Furthermore, in the field of isotropic materials testing, several systems already exist ([7], [8]). To test our algorithm for anisotropic materials, an ultrasonic point-source/point-receiver materials testing system has
for anisotropic materials, an ultrasonic point-source/point-receiver materials testing system has been used in this study [9]. Recently, such an approach was successful to describe experimentally various problems in fracture mechanics ([11], [12]). The acoustic emission sources were simulated by breaking 0.08 mm o.d. capillary glass tubes. The rise time for such acoustic emission events is typically in the range of 50 ns. The sensors used here are large bandwidth piezoelectric transducers with a 1.3 mm diameter. The material used in this study, a fiberglass reinforced unidirectional composite material [15], has a medium anisotropy and is porous. Also, it has a
a medium anisotropy and is porous. Also, it has a poor homogeneity and rough surfaces. The location process is initiated by a calibration procedure which provides the necessary elastic constants given by Equations (1) and (2), in the case of a transversely isotropic solid [13]. These preliminary measurements are done in 4 particular directions of propagation as shown in Figure 1. To obtain accurate values of the elastic constants, averages are computed for that purpose. Then, by using the optimization procedure described in [1], which involves the solution of a non-linear set of equations with a Newton-Raphson numerical method [14],
non-linear set of equations with a Newton-Raphson numerical method [14], the location of the source is determined. The measurements were done in the near-field to limit the influence of attenuation and dispersion of the transient waves. Figure 2 shows some characteristic waveforms. Attenuation and dispersion are clearly seen on these transient waves and might be detrimental to the precision of the results. Also, when moving to the far-field, plate modes ([16]-[18]) which become predominant are problematic, as the bulk modes have weaker amplitudes. This last problem is directly linked to the chosen geometry — a thin plate — and can
the chosen geometry — a thin plate — and can be avoided by using other configurations. Despite the limited set of data provided in the Table and their relative inaccuracy, these results clearly demonstrate the efficiency of our algorithm. An important feature is that the convergence is always better when considering the material anisotropic instead of being isotropic. For instance, sometimes there is not even convergence, showing the incompatibility of treating the data with the isotropic hypothesis. In addition, the method can be extended to the full 3-dimensional problem [19]. For this problem, the set of non-linear equations is given
For this problem, the set of non-linear equations is given by Equation (3), where new fourth degree terms appear. A supplementary difficulty is due to the fact that propagation in non-principal planes has to be considered. In such a case, analytical expressions for the slowness curves are no longer available. The eigenvalues of the propagation tensor should be numerically computed, using for instance Jacobi method [14]. A stringent problem is related to the non-uniqueness of the solutions, which occur for some source/sensors configurations. These developments and further experimental data will be described elsewhere [20]. INTRODUCTION. — The localization of sources
be described elsewhere [20]. INTRODUCTION. — The localization of sources of acoustic emission is usually realized, for isotropic media, by triangulation techniques ([2], [3]). Whether it be for the localization of earthquake epicenters or for applications in Science of Materials/Mechanics of Fracture, least squares [4], and correlation ([5], [6]) techniques are commonly used. However, anisotropy was until then absent from these treatments which motivated the introduction of the optimization procedure described in a previous Note [1]. This method of localization of point sources of acoustic emission is tested in the present Note for a fiberglass-reinforced polyester resin composite material. The
present Note for a fiberglass-reinforced polyester resin composite material. The material chosen for this purpose, possesses an average anisotropy, and is by the way very ordinary, lightly porous and rather inhomogeneous. Thus, we place ourselves deliberately in conditions rather unfavorable. Notably, the state of the surface of the material is rather mediocre and the condition of a thin plate with parallel faces required by the modeling appears at most as an approximation. For the experimental measurements, an ultrasonic system associating sources of acoustic emission point-like and a network of quasi-point-like transducers was used. Details concerning this apparatus are available elsewhere
transducers was used. Details concerning this apparatus are available elsewhere [10]. This testing bench opens interesting perspectives for experiments in mechanics of fracture ([11], [12]). The sources of acoustic emission are simulated by breaking 0.08 mm o.d. capillary glass tubes. The rise time for such acoustic emission events is typically in the range of 50 ns. The sensors used are large bandwidth piezoelectric transducers with a 1.3 mm diameter. The material used in this study, a fiberglass reinforced unidirectional composite material [15], has a medium anisotropy and is porous. Also, it has a poor homogeneity and rough surfaces. The location
it has a poor homogeneity and rough surfaces. The location process is initiated by a calibration procedure which provides the necessary elastic constants given by Equations (1) and (2), in the case of a transversely isotropic solid [13]. These preliminary measurements are done in 4 particular directions of propagation as shown in Figure 1. To obtain accurate values of the elastic constants, averages are computed for that purpose. Then, by using the optimization procedure described in [1], which involves the solution of a non-linear set of equations with a Newton-Raphson numerical method [14], the location of the source is determined.
numerical method [14], the location of the source is determined. The measurements were done in the near-field to limit the influence of attenuation and dispersion of the transient waves. Figure 2 shows some characteristic waveforms. Attenuation and dispersion are clearly seen on these transient waves and might be detrimental to the precision of the results. Also, when moving to the far-field, plate modes ([16]-[18]) which become predominant are problematic, as the bulk modes have weaker amplitudes. This last problem is directly linked to the chosen geometry — a thin plate — and can be avoided by using other configurations. Despite
— and can be avoided by using other configurations. Despite the limited set of data provided in the Table and their relative inaccuracy, these results clearly demonstrate the efficiency of our algorithm. An important feature is that the convergence is always better when considering the material anisotropic instead of being isotropic. For instance, sometimes there is not even convergence, showing the incompatibility of treating the data with the isotropic hypothesis. In addition, the method can be extended to the full 3-dimensional problem [19]. For this problem, the set of non-linear equations is given by Equation (3), where new fourth degree
equations is given by Equation (3), where new fourth degree terms appear. A supplementary difficulty is due to the fact that propagation in non-principal planes has to be considered. In such a case, analytical expressions for the slowness curves are no longer available. The eigenvalues of the propagation tensor should be numerically computed, using for instance Jacobi method [14]. A stringent problem is related to the non-uniqueness of the solutions, which occur for some source/sensors configurations. These developments and further experimental data will be described elsewhere [20]. Ces résultats classiques sont : Pour déterminer les différentes vitesses de propagation entrant
sont : Pour déterminer les différentes vitesses de propagation entrant en jeu dans les équations (1) et (2), un certain nombre de mesures de différences des temps de transit pour une paire de transducteurs donnée sont réalisées en différentes positions repérées sur la figure 1. Une simple moyenne arithmétique est alors calculée fournissant avec précision les valeurs des vitesses nécessaires. Dès lors, une position arbitraire est retenue pour simuler l'emplacement de la source ponctuelle d'émission acoustique, et la procédure d'optimisation peut avoir lieu [14]. RÉSULTATS EXPÉRIMENTAUX. — Le déroulement des calculs est indépendant du nombre de senseurs (3 est le
calculs est indépendant du nombre de senseurs (3 est le minimum). Pour des raisons pratiques, les mêmes senseurs furent utilisés, à la fois pour la procédure de calibration et pour celle d'optimisation, bien que nous ayons la possibilité d'utiliser jusqu'à huit canaux. La figure 2 représente des ondes transitoires caractéristiques. Les mesures mettent en œuvre le tout début des formes d'ondes, correspondant au mode quasi longitudinal. L'amplitude de ces pics est très faible en comparaison avec les modes de plaques minces arrivant par la suite. Les ondes de Lamb [16] deviennent prépondérantes, spécialement dans le champ lointain pour lequel les
deviennent prépondérantes, spécialement dans le champ lointain pour lequel les modes de volume s'éteignent ([17], [18]). Notons en outre que les signaux sont dispersifs et atténués, ce qui ajoute une difficulté supplémentaire. Le tableau regroupe quelques résultats caractéristiques. Les vitesses de propagation des ondes acoustiques en diverses directions, ainsi que le rapport des modules d'Young dans les deux directions principales y figurent [15]. Les valeurs des constantes élastiques sont absentes. La raison vient du Fig. 1. — Géométrie utilisée au cours des mesures expérimentales. Cp, et Cp2 sont mesurées sur les droites en pointillés le long de la direction principale
les droites en pointillés le long de la direction principale 1, respectivement 2. Cs est mesurée d'une manière analogue sur le mode transverse. C45 est mesurée le long des diagonales D, et D2. Fig. 1. — Geometry used during experiments. Detected Waveforms Fiberglass/ Epoxy Spécimen fait que la masse volumique du matériau, non indispensable pour la suite des calculs, ne fut pas mesurée. Dans ce même tableau figurent quelques résultats de la détermination optimale de la position de la source d'émission acoustique supposée ponctuelle. Ces résultats sans être excellents démontrent clairement que la procédure d'optimisation se déroule correctement. Il faut
clairement que la procédure d'optimisation se déroule correctement. Il faut noter par exemple que le nombre d'itérations est faible, augmentant lorsque la source est éloignée de l'origine du référentiel, résultat déjà connu en simulation [1]. De plus, la comparaison des cas isotropes/anisotropes, sans ambiguïté atteste de l'incompatibilité à considérer ce matériau isotrope, et ce malgré un rapport d'anisotropie modeste. Insistons sur le fait que la relative imprécision de ces résultats est liée à plusieurs limitations expérimentales du système tel qu'il fut utilisé, à savoir quatre senseurs au lieu de huit, une fréquence d'échantillonnage de 10 MHz qui ne permet pas
une fréquence d'échantillonnage de 10 MHz qui ne permet pas d'obtenir une précision suffisante en simple chronométrie. Des expériences complémentaires sont en cours, pour divers matériaux n'ayant pas tous une dispersion et une atténuation aussi sévère. Fig. 2. — Exemple d'une série d'ondes transitoires obtenues : (a) par le senseur # 1; (b) par le senseur #2; (c) par le senseur #3; (d) par le senseur #4. Fig. 2. — Example of a set of transient waveforms obtained: (a) by sensor #1; (b) by sensor #2; (c) by sensor #3, (d) by sensor #4. C. R. Acad. Sci. Paris, t.
(d) by sensor #4. C. R. Acad. Sci. Paris, t. 307, Série II, p. 1595-1600, 1988 1599 TABLEAU Rapport des modules d'Young, vitesses de propagation, et localisation de sources d'émission acoustique. Young moduli ratio, wavespeeds, and AE source location. Module d'Young direction 1 Module d'Young direction 2 = 1,50 Vitesses de propagation Cpl = 3770 m/s Cs = 1750 m/s Cp2 = 3 350 m/s C45 = 3460 m/s Position de la source Calcul de la position de la source Source située en : Isotropie Anisotropie Xs= 0,000 mm Xs= 1,448 mm Xs= 0,867 mm Ys = 50,800 mm Ys
1,448 mm Xs= 0,867 mm Ys = 50,800 mm Ys = 86,589 mm Ys = 51,333 mm Xs = 25,400 mm Divergence Xs = 34,620 mm Ys = 76,200 mm Xs = +oo Ys = 87,787 mm EXTENSION AU CAS TRIDIMENSIONNEL. — L'extension de cette approche au problème à trois dimensions est particulièrement attractive pour détecter des défauts situés à l'intérieur d'un matériau non transparent. Sur le papier, cette généralisation ne pose pas de problème majeur : la démarche décrite en [1] reste la même. Au lieu d'obtenir le système d'équations quadratiques (2) de la référence [1], l'introduction de la
d'équations quadratiques (2) de la référence [1], l'introduction de la troisième coordonnée aboutit à un système de degré 4 donné par l'équation : avec : n : nombre de senseurs (n est 4) où Ka = R2 + d2, et Kkm=Atp (k, m) Cp (6t) Cp (6m), et où les autres coefficients A;, i=5, ..., 10 sont donnés en [1] par A;, avec i= 1, ..., 6. Une difficulté supplémentaire est qu'il faut absolument considérer la propagation s'effectuant dans des plans non principaux. Pour ce problème, les formes analytiques des courbes de lenteurs ne sont plus disponibles, et les valeurs
courbes de lenteurs ne sont plus disponibles, et les valeurs propres du tenseur de propagation doivent être calculées numériquement à l'aide d'une méthode de Jacobi [14], par exemple. Une autre difficulté, plus sérieuse celle-là, tient du fait qu'il y a des configurations source/senseurs pour lesquelles il n'y a pas unicité des solutions [19]. Par un travail en simulation numérique analogue à celui décrit en [1], il a été possible de constater que la convergence est plus délicate. Pourtant des améliorations semblent possible, notamment par un choix judicieux de la disposition des senseurs. Des développements ultérieurs sont en cours [20]. 1600
des senseurs. Des développements ultérieurs sont en cours [20]. 1600 C. R. Acad. Sci. Paris, t. 307, Série II, p. 1595-1600, 1988 CONCLUSION. — La localisation d'événements d'émissions acoustiques dans des solides anisotropes, et en particulier dans des matériaux composites semble possible. Des limitations dues à la réponse acoustique (atténuation et dispersion) du matériau, néanmoins existent. Celles-ci sont reliées au comportement viscoélastique du matériau, qui n'est pas pris en compte par une description strictement élastique. Pour ce faire, des modèles existent, qui pourraient éventuellement être incorporés dans notre démarche. Plusieurs applications potentielles existent en mécanique de la rupture et en
applications potentielles existent en mécanique de la rupture et en contrôle non destructif. Il s'agit de plaques de 12 mm d'épaisseur de composites à résine polyester isophthalique de la série EXTREN 500, commercialisé par Joseph T. Ryerson & Son, Inc., Chicago, Illinois 60680. Note reçue le 27 juin 1988, acceptée le 13 septembre 1988. RÉFÉRENCES BIBLIOGRAPHIQUES [1] B. CASTAGNEDE, W. SACHSE et K. Y. KIM, C. R. Acad. Sci. Paris, 307, série II, 1988, p. 1473-1478. [2] A. TOBIAS, Nondestructive Testing Int., 10, 1976, p. 9. [3] M. ASTY, Nondestructive Testing Int. 12, 1978, p. 223. [4] Y. H. PAO,
Testing Int. 12, 1978, p. 223. [4] Y. H. PAO, Theory of acoustic emission in Elastic and nondestructive testing of materials, A.M.D., 29, Y. H. PAO éd., A.S.M.E., New York, 1978, p. 107-127. [5] I. GRABEC, Ultrasonics, 16, 1978, p. 111. [6] R. N. BRACEWELL, The Fourier transform and its applications, McGraw-Hill, New York, 1986, p. 98-123. [7] S. P. YING, D. R. HAMLIN et D. TANNEBERGER, J. Acoust. Soc. Am., 55, (2), 1974, p. 350. [8] W. SACHSE et S. SANKAR, United States Patent, 4, 592, 034, 1986. [9] W. SACHSE et K. Y. KIM, J. Appl Phys. (à
W. SACHSE et K. Y. KIM, J. Appl Phys. (à paraître). [10] W. SACHSE et K. Y. KIM, Ultrasonics, 25, 1987, p. 195. [11] K. Y. KIM et W. SACHSE, J. Appl. Phys., 55, (8), 1984, p. 2847. [12] K. Y. KIM et W. SACHSE, J. Appl. Phys., 59, (8), 1986, p. 2704. [13] E. DIEULESAINT et D. ROYER, Ondes élastiques dans les solides, Masson, Paris, 1974, p. 113-166. [14] W. H. PRESS, B. P. FLANNERY, S. A. TEUKOLSKY et W. T. VETTERLING, Numerical recipes, Cambridge University Press, New York, 1986, p. 240-269. [15] Brochure Technique sur les matériaux à
1986, p. 240-269. [15] Brochure Technique sur les matériaux à fibres de la série Extren 500, J. T. Ryerson & Sons Inc., Plastics Division, Chicago, 1987. [16] Y. H. PAO et R. K. KAUL, Waves and vibrations in isotropic and anisotropic plates, in R. D. MINDLIN and Applied Mechanics, G. HERMANN éd., Pergamon Press, New York, 1974. [17] A. N. CERANOGLU et Y. H. PAO, J. Appl. Mech., 48, 1981, p. 125-147. [18] R. L. WEAVER et Y. H. PAO, J. Appl. Mech., 49, 1982, p. 821. [19] B. CASTAGNEDE et W. SACHSE, 31th Meeting of the acoustic emission working