Identification of 'Defects' in Epoxy Matrix Composites and Carbon Fiber by Ultrasound. Interaction of the Ultrasonic Beam with the Material

Non-Destructive Testing (NDT) methods, and especially, ultrasounds have gone from being a mere laboratory curiosity to an indispensable tool in the industry as a primary means of determining the level of quality achieved in its products (ASM, 1989; Barbero, 1999). This study will identify and apply the main physical phenomena of interaction of an ultrasonic wave in a composite material, to see if through this type of waves, you can detect defects of the type of porosity or delaminations in these materials. The percentages of reflected and transmitted waves in real cases of defects in the composite material will also be studied. It will be shown if the frequencies and intensities of the waves are adequate to find this type of defects or imperfections in the material. The theoretical study of the ultrasonic wave seeks to help researchers in the development of equipment that uses the methodology of immersion ultrasound for the inspection of materials in the search for 'defects' and to understand the physics of the test.


Introduction
In the last decades the operating requirements have increased, while at the same time trying to reduce the weight of the structures and mechanical components used for industrial purposes. This has led to the need to use advanced materials that have high mechanical properties along with a decrease in weight (Inasmet, 1998). The use of fiber reinforced polymeric matrix composites has replaced in many cases conventional materials (steel, plastic, aluminum, concrete, etc.). These materials have been used preferably in the aeronautical and space industry for the manufacture of floor panels, spoilers, rudders, depth rudders, interior and exterior ailerons, space shuttles, satellites, etc. where they have had a greater development because they are structures that require high values of resistance and specific rigidity, and in which the weight factor entails a great decrease in the cost (Sanglier et al., 2003;Ramírez & Col, 1982;Ramírez López et al., 1996).
These composite materials are characterized by high rigidity and mechanical resistance, high fatigue resistance, corrosion resistance, low weight and the possibility of selecting the appropriate orientation of the sheets for each specific application. Their low thermal conductivity and high dimensional stability give these materials a very interesting alternative in applications subject to low temperature conditions.
The structural components of this type are made up of plate and/or beam type elements, which are subjected to loads perpendicular to their plane that originate a state of work in bending in which tensile and compressive stresses appear (Padmanabhan & Kishore, 1995;Potel et al., 1998;Scarponi & Briotti, 2000;Vaccaro & Akers, 1996). For example, these tensile states can appear in the aerodynamic loads exerted on the wings of an aircraft. From the expression 11 it is deduced firstly that the reflected acoustic pressure will be of the same amplitude, whatever the side of the limit surface on which the wave is incident, that is to say, independently of the sequence of both materials; although in the case of being Z 2 >Z 1 , R' will be positive, which indicates that the incident wave and the reflected wave are in phase and, in the opposite case (Z 2 <Z 1 ), R' will be negative, which indicates an inversion of the phase of the reflected wave in relation to the incident wave.
From the expression 12 it is deduced that although the acoustic pressure transmitted in phase with the incident, it will not be independent of the sequence of the two materials, so that if Z 2 >Z 1 , then T'>1, which indicates that its amplitude will be greater than that of the incident wave and, in the opposite case (Z 2 <Z 1 , T'<1) less.
Finally, the balance of sound pressure, in contrast to energy or sound intensity, can be put as P i + P r = P t , either 1 +R' = T' which implies that for balance to be maintained, the sum of the pressures must be the same on both sides of the interface.

Methodology Applied to the Real Case
The determination of possible defects in composite materials widely used in the industrial sector, is the problem to be addressed once established the theoretical foundations of the physical interaction of an ultrasonic wave with matter.
It is important that the use of these materials at a technological and industrial level guarantees that they do not have defects that reduce their mechanical properties considerably, especially in critical structures.
The main defects to be evaluated are: • The punctual or generalized porosity that will be basically air inclusions within the polymeric matrix that could have been produced by a low pressure application in the resin curing process in its manufacturing process or by a movement between layers after the resin has started its molecular crosslinking process (Heru et al., 1997).
• In epoxy matrix carbon fiber laminates, low energy impacts cause damage that can result in dents, matrix cracking, fiber to matrix delamination and fiber breakage. Of all these, delamination is probably the most harmful due to the difficulty in detecting it and the reduction it causes in the properties (Baker;Jones & Callinan, 1985;Wróbel, Wierzbicki & Pawlak, 2005). The possible delaminations of a carbon fiber layer will be evaluated, these will be identified by the presence of air due to the detachment of successive layers of fiber due to lack of adhesion between them (Cantwell, Curtis, & Morton, 1986;Miyano et al., 1994).
In Table 1, some physical and mechanical properties of some materials that will be used in the ultrasonic inspection process to be developed on the chosen composite material have been collected.
In the technical inspection performed by ultrasound we will find, first the water layer, since it is an inspection by immersion in water, then the polymer matrix formed by an epoxy resin type, the carbon fiber used as reinforcement, and finally, the presence of air in the form of porosity or delamination.
The speed of sound propagation in the different media (C L ) and the acoustic impedance (Z) will be determined, since the amount of reflected and transmitted sound will be obtained from these parameters. It will be taken into account that the speed of sound in air is 340 m/s and in water 1435 m/s, and therefore, it is not necessary to calculate them.    shows the val resin). It also s will be the p mitted wave ( ent wave is eq ation, the refl of the transmi re is almost no pection for De is a delaminat , it will be tak he carbon fibe ber. The schem Distribution o tudy of delami phase the wate he third and las of wave that ation. Water + epox obtained for t ance of 132.55 value will be     Calculations of the percentages of acoustic intensities of reflected and transmitted waves allow more or less easily to determine if it is possible to detect defects (porosity and delaminations) in a material (composite). It will be taken into account that for the inspection of delaminations, an almost complete attenuation of the transmitted wave is produced, so in practice, for the search of this type of defects, it should be taken into account to work with higher frequencies, as well as acoustic intensities.

Discussion
Unidirectional components are not commonly used in aerospace structural components due to their high anisotropy of mechanical properties. Normally multidirectional laminates are used which are optimal for different load conditions (Miyano et al,,1986;Marsh, 2002;DobrzaÉski, 2002). Even so, it is necessary to study unidirectional laminates since this allows us to know how the material behaves in the direction of the fibers, since the sheet presents maximum properties in this direction and minimum properties in the transversal direction. The tested laminate presents the highest resistance and elastic module and the lowest possible thermal expansion coefficient in one direction.
The study of the use of the physical phenomena of interaction of the ultrasonic wave in the composite material is an excellent tool to identify defects by ultrasound in this type of materials. This will help the beginners who are initiated in the application of this type of methodologies (especially the ultrasounds) in the laboratories to be able to adjust in a theoretical way the measurement devices, one of the most pronounced difficulties in this type of measurements. This will also provide an approximate idea of the frequency and intensity of work for certain types of materials and defects, reducing preparation times and costs of testing.