Nondestructive Testing of Polyaramide Cables by Longitudinal Wave Propagation: Study of the Dynamic Modulus.
It has been observed that cables at different states of fatigue had their own speed of longitudinal propagation of acoustic waves . This speed can be measured with piezoelectric captors and is proportional to the square root of the sonic modulus. Our experiments, which have been carried out on Technora cables of diameter 2 mm, show that the modulus obtained from the wave speed has the same behavior in fatigue as the modulus obtained from tensile tests. Furthermore, our experiments also show that the residual strength in the cable is proportional to the modulus. A nondestructive control of cables can hence be made from these sonic modulus measurements.
Elastic properties of a material can be determined from the measurement of ultrasonic or acoustic wave propagation through this material. The speed of an ultrasonic wave in a material can lead to determination of the tensile and shear modulus .
Kwun  and Smith  have looked for a nondestructive control of synthetic and metallic cables by evaluating the speed of propagation of a transverse impulse vibrational wave. According to these authors, the presence of broken strands, which is easily perceptible, and defects in the cables produce a partial reflection of the wave. The propagation speed of this wave is proportional to [(F/M).sup.1/2], where F is load and M the linear density of the cable. The results indicate that the method of detection by transverse-impulse vibrational wave could constitute a simple and rapid method of detection for defects and for the determination of the ratio of load to average linear density of the cable. This method allows the detection of defects but does not give the state of fatigue. The tests of bending fatigue of the cables have shown that the modulus decreases when the fatigue increases, hence the interest in finding a relationship for the modulus. It is possible to determine the dynamic modulus with a method b ased on the propagation of longitudinal acoustic wave by determining the speed of propagation and using the following equation [5, 6]: [V.sup.2] = E/[rho] where V is speed of propagation, E is dynamic or sonic modulus and [rho] is density.
By measuring the time taken by the wave to travel between two piezoelectric sensors, the transmitter and receiver, for a given distance, one can determine the speed of propagation and thus calculate the modulus. The sonic modulus, which is the modulus obtained from the longitudinal propagation speed, is also used to determine the maturity of a cotton fiber , as well as to differentiate fabrics having undergone different finishing treatments [8-10]. Tensile tests as well as measurements of speed of propagation have been performed in parallel in order to compare the tensile modulus with that obtained from the speed of propagation. These tests have been carried out on cables at different states of fatigue. The aim is to find out whether the two moduli follow the same behavior with fatigue.
PROCEDURES AND RESULTS
The Technora cables tested had different constructions: they were either braided or had the so-called type A steel configuration. Technora is a polyaramide fiber that possesses ether groups. Poly(p-phenylene-co-3, 4'-oxydiphenylene terephthalamide) fiber was first developed by Teijin Corp. in 1974. The chemical structure is:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
The braided cable is a 1500 denier braid (twist angle of 30[degrees]). A spindle corresponds to 1000 parallel monofilaments. The cable is 2 mm in diameter.
The cable of type A is an assembly of 6 yarns wound together helically (left twist) around a central yarn, and each yarn is itself constituted of an assembly of yarns also wound together helically. The 7 yarns have the same count of 1500 dealers, and have undergone a surface treatment. Their diameter is 1.75 mm. These cables were manufactured by Cousin Trestec Company.
The tensile tests were conducted on a ZWICK 1456 universal mechanical testing machine, using extensometers that were in contact with the cable and that measured elongation without taking into account any slipping in the clamps. The load cell had a range of 0-10 kN and the strain rate was 100 mm/min, that is 0,5 [min.sup.-1].
The fatigue apparatus was developed in the GEMTEX laboratory: the test can be carried out with four cables at a time and in different ways. The cables, which are maintained under a 30 kg load (about 7% of the breaking strength), are placed on the pulleys of a truck that moves along the cables. The fatigue test occurs in flexure. The cables undergo fatigue that is a cycle of 6 simple flexures (Fig. 1) (simple flexure corresponds to the change of the position of the cable from a rectilinear to a curved one and vice versa; one cycle corresponds to one way of the truck on the cable).
The measurement device for the speed of propagation was developed by the GEMTEX laboratory. The cable is maintained under a load of 20 kg (approximately 5% of the breaking strength) (Fig. 2). Two piezoelectric sensors are in contact with the cable. The first one is a transmitter connected to a generator that can supply a square signal; the second one is a receiver. The signals emitted by the two piezoelectric sensors are transmitted to a digital oscilloscope. The distance between sensors can be adjusted.
Piezoelectric captors can emit and or receive waves. We have used captors with a resonance frequency of 6.6 kHz, an acoustic level of 90 dB at a distance of 30 cm, a diameter of 30 mm, and a thickness of 4.5 mm.
The impulse generator used was a TG 105 that allows a large change of frequency (0-5 MHz) and a range of impulse from 100 ns to 100 ms. An interface in series allows the recovery of experimental curves on computer. We have used the exit of synchronization of the generator that fathers an impulse of amplitude 5 volts and a duration 100 [micro]s.
The cables were submitted to 6 simple flexure cycles on three aluminum pulleys, of 29 mm in diameter and a groove radius of 0.9 mm. We noticed progressive bending fatigue of the cables after a given number of fatigue cycles, then a tensile test (destructive control) was performed and the breaking stress and strain as well as the different moduli were calculated. A fatigue test was performed on each type of cable (braided and type A) till the breaking point was reached, so as to study its behavior to bending fatigue.
When the modulus is plotted as a function of the number of cycles (Fig. 3) for the braided cable, the curves obtained show that differences in two moduli are obtained for the number of cycles is small ([sim]500 cycles). These moduli are characterized by two distinct slopes of the tensile curve (Fig. 4). The modulus E1 corresponds to the first slope, and the modulus E2 corresponds to the one near break. This behavior recalls the one obtained with monofilaments that we have studied in another article .
The modulus E1 of the cable increases while the modulus E2 decreases during the first few hundreds of cycles. Around 500 cycles, they merge into only one modulus, which corresponds to a single slope on the tensile curve (Fig. 5). This modulus then decreases gradually with the fatigue.
Measurement of the Speed of Propagation
We now proceed to the measurement of the traveling time of a signal in Technora cables with the device described previously. We applied a square signal of period 60 ms giving impulses of 100 [micro]s in breadth. the piezoelectric sensors being in contact with the cable .
The signal [a] emitted by the generator of the transmitter was sent to the digital oscilloscope (square signal), in addition to the signal of the receiver [b]. The signals from the two sensors are shown on a same graph (Fig. 6). We can thus deduce the propagation time between the two marks, the first mark being at the increase in amplitude of the pulse of input signal  and the second at the deformation of the signal of the receiver .
The time of propagation was measured for braided and type A Technora cables, the distance between sensors being fixed. The speed of propagation, V, and hence the modulus E, was calculated from: [V.sup.2] = E/[rho] ([rho] Technora = 1.39 g/[cm.sup.3]).
Ten tests were carried out for each state of fatigue, these states being identical to those studied in the tensile tests. We thus compared the dynamic modulus obtained from the speed of propagation with the modulus obtained from the tensile tests for each type of cable at different states of fatigue.
When the modulus is plotted against the number of fatigue cycles, the curves obtained with the 2 methods show that for the braided cable (Fig. 7), apart from the value obtained for 500 cycles, the behaviors are very similar. The tensile moduli are slightly higher. For the cable of type A (Fig. 8), higher values of modulus are obtained from the speed of propagation compared with those obtained from tensile tests. This difference between the two cables is probably due to the different construction of the cables, but the fatigue effect on the moduli obtained with the two methods is identical.
We also observe a decrease of the dynamic modulus obtained from the speed of propagation for the two types of cables.
Relationship Between Modulus and Residual Strength
Since the evolution of both the tensile modulus and the residual strength as a function of number of fatigue cycles is almost identical for the cables (Fig. 9), we can expect to obtain a relationship between Fr (residual strength) and E (modulus). To this end, we have plotted the modulus against the residual strength, so E = f(Fr) (Fig. 10). A straight line is obtained whatever the construction of the cables. If we consider the value of the modulus and the residual strength near the breaking point, it can be observed that these values are far from the E = f (Fr) line. We call this point critical point. (It is the point of the modulus versus residual strength graph where the graph is no longer linear. This point indicates the point nearest the breaking of the cable.) We can therefore conclude that this straight line can be used as a means of monitoring the cables. This straight line is not respected when the cable is in critical state; a limit can therefore be established when the critical state of fatigue is reached; that is when E is no longer proportional to Fr. This value having been determined for a given cable, E or Fr can become indifferently a parameter for the fatigue limit.
The fatigue effect on the two dynamic moduli, obtained respectively from the speed of propagation and from the tensile test, is similar for the two types of Technora cables. We can therefore envisage a nondestructive control of Technora cables, with the longitudinal propagation speed measuring technique. The residual strength Fr and the tensile modulus E have the same behavior following the state of fatigue. We even endup with a relationship between these two parameters that is independent of the construction of the cable.
We obtain a linear relationship for E = f(Fr) in the domain of use of the cable. This relationship can be used as a means to control the state of the cable since the behavior deviates from this linearity when the cable is in a critical state. Since the tensile modulus presents the same behavior as the sonic modulus, this nondestructive method can thus be used to determine the residual strength in the cables by using the E = f(Fr) straight lines.
We acknowledge the financial support of the NordPas de Calais Region council and Patrick Labache for his help in the conception of the fatigue apparatus.
(*.) To whom correspondence should be addressed.
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|Author:||FERREIRA, M.; LAM, T.M.; KONCAR, V.; DELVAEL, Y.|
|Publication:||Polymer Engineering and Science|
|Date:||Jul 1, 2000|
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