·Table of Contents
·Conservation and Restoration in Art and Architecture
Marble monuments examination using the NDT method of ultrasoundsI. N. Prassianakis, S. K. Kourkoulis, I. Vardoulakis
National Technical University of Athens,
School of Applied Sciences, Department of Mechanics,
5 Heroes of Polytechnion Avenue, Zografou Campus, Theocaris Bld., 157 73 Athens, Greece
Marble is regarded as being the product of the metamorphism of limestone beds. Metamorphism takes place under the action of heat or pressure independently or of both heat and pressure simultaneously. It is a kind of rather hard rock consisting mainly of crystallized grains of calcite (CaCO3) or dolomite (MaCO3) or a mixture of them. Its color is mainly due to admixtures of foreign substances like muscovite and chlorite. The very good physical and mechanical properties of marble, such as its high resistance to abrasion, its translucence and its capability to be polished (as opposed to other type of rock materials), as well as its high strength and hardness render it one of the most widely used structural materials even today for the construction of both buildings and sculptures.
Unfortunately, most varieties of marble are of anisotropic nature (Corres 1993, Theocaris and Coroneos 1979, Zambas 1994) and extremely brittle and, thus, the determination of their mechanical properties becomes an extremely difficult experimental task in case ones uses the conventional destructive Strength of Materials tests (Vardoulakis et al. 1998, Kourkoulis et al. 1999, Franzini 1998). On the other hand, it is obvious that the destructive control is inapplicable at all in case one studies the behaviour of marble monuments of invaluable archaeological value.
The above mentioned inapplicability of the destructive methods for the quality chara cterization of such structures, in conjunction with the advantage of the NDT methods to maintain the integrity of the tested specimens, led to the application of the NDT method of ultrasounds for the study of marble and marble structures.
In a recent paper (Prassianakis et al. 2000) this method was applied for the mechanical characterization of prismatic specimens prepared from a specific type of marble, that is called Dionysos-Pentelikon (D-P) marble, which were subjected to three point bending. The mechanical constants were estimated and the damage evolution of the material in both the tension and the compression-regime of the bent beam was determined (Prassianakis 1994, 1997). The results obtained were in very good agreement with the respective ones obtained on the basis of a hybrid elastic-damage model, introduced recently by Exadaktylos et al. (2000) based on Hartig's approach (Hartig 1893). Motivated by the success of this work, the application of the NDT method of ultrasounds is extended in the present paper for the mechanical characterization of marble specimens that are to be subjected to direct tension.
|Fig 1: Shape and dimensions of the three types of specimens.|
The exact dimensions of the "dogbone" specimens are described analytically by Vardoulakis et al. (1995). Specimens were prepared that were cut along all different anisotropy directions of the materials studied. Indeed, as it can be seen in Fig.2, marble has three distinct anisotropy directions (one parallel to the material layers, a second one along the width of the web and a third one along the thickness of the web) and thus it appears to be an orthotropic material (Corres 1993). After a long series of direct tension tests (Vardoulakis and Kourkoulis, 1997) it has been concluded that the mechanical properties along the first two anisotropy directions are very similar to each other. Thus, the material can be considered as transversely isotropic and it can be described with the aid of five elastic constants: the two elastic moduli in the plane of transverse isotropy and normal to it, the two Poisson's ratios characterizing the lateral strain response in the plane of transverse isotropy to a tensile stress acting parallel and normal to it, and the shear modulus in planes normal to the plane of isotropy (Lekhnitskii 1977).
|Fig 2: Anisotropy of Dionysos-Pendelikon marble and specimen sampling. Both 'beams' and 'architraves'have been employed in the present experimental analysis|
The destructive tension tests were carried out using a very stiff INSTRON loading frame with maximum loading capacity 250 kN. On the other hand, the non destructive measurements were performed using the ultrasonic device USIP-11 of Krautkramer. The probes used were the K2G ones of Krautkramer again and the frequency of both the longitudinal and the transverse waves produced by the respective probes were 2 MHz.
Using the values of the velocities, cl and ct, of the longitudinal and transverse elastic stress waves, respectively, propagating within the mass of marble specimens, as they were determined with the aid of ultrasonic measurements, and knowing that the density of D-P marble varies around the value of r=2730 gr/cm3, one can proceed to the estimation of the values of the elastic constants, i.e. of the modulus of elasticity, E, of the modulus of rigidity, G, and Poisson's ratio, n, using the familiar formulae (Prassianakis 1994, 1997):
|Direction of |
|E (GPa)||n (-)||sf(MPa)|
|Table I: The mechanical properties of D-P marble loaded statically in direct tension|
It is clear from this table that the assumption concerning the transversally isotropic nature of D-P marble is fully justified, since the constants along the strong and the intermediate anisotropy direction are very close to each other.
On the other hand all information that has been obtained from the NDT method of ultrasounds using the prismatic type of specimens are included in Table II. The code indicates the order and the relative direction of the material layers of each individual specimen.
|2a|| 1 |
|Table II: Elastic constants of the prismatic marble specimens obtained with the aid of the NDT method of ultrasounds.|
The ultrasonic measurements have been performed at three different points (one at the middle section and two close to the edges) on each one of the sides (1) and (1') see Figure 2a) of the prismatic type specimens. The values of the above Table II have been determined as the average value of the three measurements on each side of the specimen and for each one of the three anisotropy direction. The symbol (||) characterizes quantities obtained from measurements that have been performed along a direction parallel to the material layers of the specimens, while the symbol (^
) characterizes quantities obtained from measurements that have been performed along a direction perpendicular to the material layers of the specimens.
In next Table III the values of the velocities, cl and ct, of the longitudinal and transverse elastic waves, respectively are recapitulated, as well as the corresponding values of the elastic constants, as they have been determined with the aid of Eqs.(1), again as the average of the ultrasonic measurements performed at two points of each specimen (see Fig.2b). In this case all measurements were exclusively performed along the direction parallel to the longitudinal axis of each cylindrical specimen. Both the individual measurements and their average value have been included in the table. It is mentioned at this point that the specimens of this type were cut along directions forming angles 0o, 45o and 90o with the direction perpendicular to the material layers of the marble.
|1st , 45o||1||5722,7||3141,7||69,5||27,0||0,29|
|Table III: Elastic constants of the cylindrical marble specimens obtained with the aid of the NDT method of ultrasounds.|
Finally, in Table IV the results have been summarized from the study of the specimens of the third type (Fig.2c). The specimens of this category were subjected to direct tensile loading for the parallel destructive determination of the values of the elastic constants E, G, and n, after having been tested with the aid of the NDT method of ultrasonics All specimens were cut along a direction parallel to the material layers. The values of the same constants were, also, determined using the respective values of the elastic waves velocities and Eqs.(1) using the results of two measurements performed at two points of each specimen (Fig.3c). Again both the individual measurements and their average value have been included in Table IV. The measurements were performed at points (1) along directions parallel to the longitudinal axis of each specimen, while at points (2) they were performed along directions perpendicular to the bases of the specimens.
|No||Measurement||Non-destructive testing||Destructive testing|
|Table IV: Comparison of the values of the elastic constants of :dogbone" cylindrical marble specimens obtained with the aid of the NDT method of ultrasounds and the destructive tension experiment|
Concerning the code of the specimens of this category, the first number indicates whether their surface was artificially polished (1) or not (0), the second one indicates the diameter of the specimens measured in cm, while the last two numbers indicate the order of the specimen. For example the code 1206 indicates the sixth specimen surface polished specimen of diameter two centimeters. It is mentioned, also, that all specimens in all three cases were obtained from the same batch of marble.
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