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Material Characterization by Mechanical Point Contact Impact emitted Ultrasound Josip Stepanic jr., Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb, Croatia Contact

Abstract

As a result of mechanical impact on an object the elastic waves are emitted. In this article the intensities and frequency distributions of ultrasonic waves emitted after the point contact mechanical impact are theoretically modelled. The possibility of using these results for impacted object material type classification that could be used for buried landmines detection is discussed.

Keywords: ultrasound, material characterisation, contact region, point contact, elasticity

1. INTRODUCTION

Among the applications of the non-destructive testing methods there is a materials characterisation using ultrasound. In this method, mechanical characteristics of a material are determined through measurements of properties of an ultrasonic pulse that can propagate through the material. In order for the registered ultrasonic pulse to be intense enough, transfer losses in the system should be relatively low. Additionally, in order for information about the tested material to be fully extractable from the registered ultrasonic pulse, changes in the pulse occurring during propagation through various objects should be known.

This approach is being developed for the purpose of unknown, buried objects' material type determination [1]. The very presence of the object is obtained through the mechanical contact. In the realisation of the ultrasound characterisation for unknown, buried objects the ultrasonic pulse is brought from an ultrasonic transducer to a border of the tested material through the auxiliary object of known characteristics. The reflection in the region influenced by the tested material takes place, followed with the reflected pulse propagation through the material of known properties to the transducer.

The possible applications of the method include application in the humanitarian demining (HD) [2, 3], what is a set of operations conducted in order to decontaminate mine contaminated regions. The HD is presently rather slow and dangerous process. Particularly, the landmine detection is the operation causing most of the duration of and casualties during HD. There are several landmines detection methods used for HD landmines detection: hand-prodding, metal detection, ground penetrating radar and usage of specially trained dogs. Among the methods used there is no significant application of the ultrasound. This is a certain discrepancy considering the proportion of non-destructive testing applications where the ultrasound based methods are appropriate.

Earlier projects for realisation of the system for buried object characterisation using elastic waves have used the wave's propagation through a soil [3, 4]. Because of that, the registered ultrasonic pulse was modified significantly by the properties of the soil, its composition and microstructure. This approach has been very fruitful if large enough wavelengths were used so that detailed soil's microstructure influenced wave propagation in precisely predictable way [3]. However, in the range of ultrasonic wavelengths it was not possible to separate soil induced modifications of a signal from the part that contained information about the buried object [4].

The method discussed here solves the problem of the unknown transfer object explicit influence through formation of direct contact between the unknown object and the transfer object, fig. 1. However, then the registered pulse's properties are rather sensible to the characteristics of the contact region. This is not necessarily the method disadvantage as the contact region characteristics are determined partially with the unknown material properties.

Fig 1: a) Schematic representation of material characterisation using ultrasound. By generating the A pulse and analysing the C pulse, one tries to find out the properties of the object B; b) contact region between the known and the unknown materials K and U respectively in the simplified case of plane contact region. The two local co-ordinate systems sharing tangential plane of contact as xy plane are shown.

In order to understand more precisely the influences of the tested object composition and structure on the final ultrasound pulse properties we use representative geometry, thus simplifying the results' interpretation. By excluding explicitly the geometry from the considerations for the moment, we approach further to materials characterisation.

The topic of this paper is a description of the changes of ultrasonic pulses caused by the border between two objects in the particular case in which the pulses are emitted in the other object from a point source.

In the second section of the article the analysis of the factors influencing the ultrasonic propagation in the geometry used is given. The third section contains a preliminary and exemplary experimental set-up for materials characterisation and measured results. They are discussed in the fourth section, while in the fifth section the conclusions are summarised and lines of future development given.

2. MATHEMATICAL FORMULATION OF THE PROBLEM

The collection of the objects that could be found in the soil ranges from natural objects of various shapes (e.g. stones, roots) to artificial, non-purposely or purposely buried objects (e.g. bricks, cans, pipelines, landmines). Although their dimensions vary, we consider here the objects with characteristic dimensions of the order of several centimetres. Much larger objects could be characterised by other methods (e.g. ground penetrating radar), while much smaller objects are usually unimportant for the characterisation considered here.

The unknown, buried objects could be rocks, wooden objects, polymeric objects and metallic objects. The magnitudes of mechanical characteristics for the various materials may differ for several orders.

For a particular geometry in this paper we take a slab of a large enough lateral dimensions, fig. 2. The slab is put into the environment having relatively very different acoustic impedance, in order to make the transmission of ultrasound between the slab and its environment negligible [6]. The boundary conditions include the transfer of the ultrasound from some material in the contact with the slab. Beside this contact the slab surfaces are taken free from stresses. Initially, there are no ultrasonic pulses propagating in the slab. This problem is easily formulated mathematically with the solution expressible in the closed form. However, the solution's form is rather complex and non-transparent so that usually a direct numerical modelling of the ultrasonic pulse propagation is more suitable.

Fig 2: Slab as the representation of the object B from Fig. 1 in the local probing configuration. The filled circle represents the region of initially generated ultrasonic pulse.

There are several reasons why this, rather artificial shape may be taken as a representative of the variety of shapes that unknown buried objects may have in the given configuration. For the ultrasonic pulse representative length we consider the length l the wave front passes during ultrasonic pulse duration t_p. We consider it be much smaller than slab width w as expressed in the relation

(1)

where v_w denotes the ultrasonic wave of one polarisation group velocity in the material of the unknown object and min{v_w} its predicted minimal value for a type of materials that are predicted to be possibly found. The requirement (1) brings about the local character of the discussed materials characterisation. The characterisation is to be performed on some randomly chosen, relatively small part of the surface and close enough subsurface region of the unknown, buried object. As a consequence all parts except the region probed directly are of no importance which is why the object's shape may be modelled to simplify experiment realisation and results interpretation. But, a sideways consequence is artificial enhancement of the probed material homogeneity because all the non-homogeneities shown on the distances much larger than w are not observable. Therefore, the characteristics of the probed region may not represent fully the material taken as a whole. Ultimately, this means that materials should be characterised according to the regions of parametric space formed by measured parameters in which values of a set of measured parameters could be found.

The precise description of propagation of generated ultrasonic pulse in an isotropic and homogeneous material of known characteristics is, in the range of linear elasticity, given with the vector equation [6]

(2)

combined with the appropriate initial and boundary conditions. Here l and m are Lamé's parameters, r is material density, is the field of elastic deformations and the dilatation. The general solution of (2) is a rather complex combination of normal modes that represents retarded travelling waves in lateral dimensions.

Boundary conditions include the given deformation field of the incoming ultrasonic pulse - pulse A in the figure 1. Therefore, ultrasonic pulse propagation in the characterised material is governed through the boundary conditions. They are a consequence of the dynamics of contact region [7]. In the contact region, the pulse A generates combined motions of materials K and U in addition to already existing transient motion of material K. A consequence of this combined motion of contact region and its neighbourhood is a generation of the reflected pulse, B on the figure 1, and a transmitted pulse. The transmitted pulse in not denoted explicitly in the figure 1 because it is not to be registered in the measurements.

Precise description of contact region between the materials K and U is by no means a trivial problem. The contact region is a non-stationary structure. The non-stationarity resembles the impact character of the contact region formation process. However, the similarity is not complete because here the forces are rather low. The contact is, at least partially, the adhesive phase. During the adhesive phase boundary conditions are easily written in terms of the equal values of projections of the strain tensor s _ij on the local normal axis, the axis z on figure 1. However, because of the ultrasonic pulse induced oscillatory motion generally repetitive adhesive and restitutive phases occur. In some cases the contact region motion could consist of decoupled normal and tangential direction motion, while in others there is a coupling between motions in these directions. Tangential motion is influenced by sliding friction. Usually, in case of dissimilar bodies tangential motion's importance rises. The overall contact region motion could significantly differ depending on whether the bodies in contact are elastic or viscoelastic.

The setting of boundary conditions requires knowledge of contact region surface roughness [8]. Initial condition for the contact region is expressed in its initial curvatures [7].

3. MEASUREMENTS

Considering a large number of parameters influencing the description it is appropriate to present a toy-model as a beginnery example. In it, the experimental set-up consists of an ultrasonic transducer coupled to a signal analyser. The immersion pulse-echo technique is applied. Measured variable was the amplitude of the registered pulse that was reflected from the upper side of a known specimen. The 7 specimens, shown on figure 3a, all of same dimensions and surface roughness up to the preparation tolerance, were used. The distances between the transducer and specimens was always equal to the transducer near field length. Parameters influencing the registered amplitude are the ultrasonic attenuation coefficient in water a and the acoustic impedance of the specimen expressed through the amplitude reflection coefficient r for the water-specimen interface. The coefficient r is the only quantity through which the material of the specimen enters the description. Hence this is an example of one-parameter materials characterisation using ultrasound. Although in this measurement specimens of same dimensions, surface planarity and roughness were used, there could be some weakening of these requirements. Specimen lateral dimensions are unimportant as long as they are larger than some dimension defined by the ultrasonic pulse width after propagation of a known distance in water and relatively small non-planarity are admissible. The surface roughness does not influence the registered signal intensity significantly if smaller than a critical roughness [9].

The relationship between the registered amplitude A_r, the initial amplitude A_i and the amplitude reflection coefficient r for the water-specimen interface is

(3)

The results obtained are shown on graph in figure 3b.

Fig 3: a) specimens used, b) graph of the amplitude dependence on the reflection coefficient.

As can be inferred from the graph for this particular example, there are some well separated regions. However, there are some specimens that can not be reliably differentiated on the basis of the measurement performed. For more complete differentiation one needs more than one parameter to be measured.

In this example all the previously mentioned influences like contacts, boundaries, transients and other are missing. This is a consequence of the contact object K which is here fluid so the contact region is identically equal to the unknown object surface shape. Unless cavitations occur, there is no restitutive phase in the contact region.

Surface conditions may additionally influence the experimental results through the surface ageing. It invokes an additional question - in what amount does the contact established for the characterisation erase the previously existing contact that was determined by soil adhesion.

SUMMARY AND CONCLUSIONS

The principle of the materials characterisation using ultrasound, concentrated on the surface properties is discussed. The possibility of material characterisation using local surface and subsurface properties depends highly on the detailed understanding of complex combination of transient, mutually dependent processes. There is a need for further, more detailed experiments and numerical simulations in order to formulate precisely the set of relevant boundary conditions applicable for various contact regions possible. The crucial point in the analysis is the description of the mechanical contact established. In the method discussed the formation of contact region enables the transfer of characteristics about the buried object with the high enough resolution to a neighbouring objects, particularly the one that is used for controlled propagation of ultrasound pulses between the transducer and the contact region.

Acknowledgements

This work is a part of the author's Dissertation. The author is grateful to the mentor Prof. V. Krstelj for encouragement, advice and many helpful discussions; D. Markucic, Ph.D. for many discussions and M. Omelic and R. Basara for experiment preparation. The work was financed by the project MZT 120098.

References

1. Krstelj, V.; Stepanic jr., J.: Humanitarian de-mining detection equipment and working group for antipersonnel landmines detection, INSIGHT, Vol 42(3), pp. 187-190,
2. Krstelj, V.; Stepanic jr., J.: Non-Destructive Testing in Antipersonnel Landmine Detection, MATEST '99, Proceedings, 1999., pp. 109-115,
3. Ganji, V.; Gucunski, N.; Maher, A.: Detection of Underground Obstacles by SASW Method - Numerical Aspects, Journal of Geotechnical and Geoenvironmental Engineering, Vol. 123(3), 1997., pp. 212-219,
4. Van Kempen, L. et al.: Digital Signal/Image Processing For Mine Detection. Part 2: Ground based Approach, MINE '99, Firenze, Proceedings, pp. 54-59,
5. McAslan, A. R. R.; Bryden, A. C.: Humanitarian demining in Southeastern Europe, The Geneva International Centre for Humanitarian Demining, 2000.,
6. Mason, W. P.: Physical Acoustics and the Properties of Solids, D. Van Nostrand, Princeton , 1958.,
7. Jaeger, J.: Analytical contact impact phenomena, Applied Mechanics Review, Vol. 47(2), 1994., pp. 35-54,
8. Markucic, D.; Runje, B.: Reproducibility of Ultrasonic Attenuation Measurement Results, MATEST '99, Proceedings, 1999., pp. 47-52,
9. Markucic, D.: Possibilities of Material Classification by Means of Ultrasound, these Proceedings.

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