Los efectos sociales y culturales de los medios de comunicación y sus implicaciones educativas

A simplified defect model of a v-shaped surface-breaking defect aligned nor- mal to the sample surface of a plate was used to begin to develop an understanding of the interactions of Lamb waves with defects, without the added complications of the complex branching structure present in real defects. Aluminium plates, of dimensions 300 x 300 x d mm, were chosen as a test material following considera- tions of material costs, ease of machining and an understanding of the mechanical properties of aluminium[141]. The v-shaped defects were produced by laser micro-

x

Figure 5.1: A schematic diagram showing both plan view and side profile of simple v-shaped defects, of depth x in mm, in aluminium plates. The percentage defect depth is given byh = ₁x_.5.100%.

machining (see section 1.4.3), propagating normal to the sample surface to give a different defect percentage depth, h, in each plate, ranging from 15% _≤h _≤100% of the plate through-thickness. A schematic diagram of these simplified defects is given in figure 5.1. The defects were angled with respect to the plate edges so as to reduce the sidewall reflections that were received at the detector.

Plate thicknesses covering the range 0.5_≤d_≤1.5 mm, so as to cover a range of typical sheet thicknesses as may be used in industry, were used in this study. For the 0.5 mm sheets the laser micro-machining process caused large levels of localised heating, which meant that the depths of the defects could not be reliably guaran- teed, and therefore these defects were produced by milling using a fine drill head. An example of a defect produced through each machining process is shown in figure 5.2 for a 50% through-thickness defect, where it can be seen that the milling process produced defects with wider openings than the laser micro-machining.

Experiments were carried out using the linear scanning experimental setup outlined in section 3.1, with the aluminium sheets held in a specially designed holder such that the defect was orientated perpendicular to the direction of the scan, as shown in figure 3.4. The sheet was scanned past the fixed laser generator and de- tector in increments of 50µm such that the IOS detector passed over the midpoint of the defect, as shown on figure 5.1. At each scan position an A-scan was recorded, as shown in figure 5.3a.

The fixed separation that was maintained between the source and the detec- tor minimises the influence of attenuation of the Lamb waves between each A-scan, as the distance travelled at each scan position is the same. This also minimises the effect of dispersion between scans, and prevents the arrival times of different Lamb modes, which travel at different speeds, at the detector from diverging between each

0.5mm thick sheet

211μm 248μm

311μm Defect line profile

(a) 0.5 mm thickness

125μm

107μm 125μm

1.5mm thick sheet Defect line profile

(b) 1.5 mm thickness

Figure 5.2: Top view of machined defects in 0.5 mm (a) and 1.5 mm (b) thickness sheets, for a 50% through-thickness defect produced by milling with a fine drill tip (a) and by laser micro-machining (b). Defect line profiles are shown as a guide for the eye.

scan.

FEM simulations using PZFlex were performed in tandem with the experi- ments to validate the results. An explanation of the FEM technique was provided in section 3.2. The models had reduced dimensions compared to the experimental samples and symmetry was applied about the defect midpoint, so as to reduce the computational time, as was previously used in section 4.2. All of the sheet edges were set to have absorbing boundary conditions to reduce the sidewall reflections at the detection point. The top and bottom of the sheet were given free boundary con- ditions, allowing the propagation of the Lamb waves. A dipole force, as described in section 3.2, was used at a fixed position to simulate the laser source and the out-of-plane displacement was obtained from a series of nodes, in a line across the mid-point of the defect, separated by 50µm steps. A fixed generation position for the FEM process was used so as to avoid the lengthy recalculation of the boundary conditions of generation at each scan position, thereby allowing the simulations to be carried out over a reasonable time scale.

For both experimental and simulated data, the broadband laser generation mechanism (see section 2.2.4) produces multiple Lamb wave modes in the sheet, with significant frequency-thickness content up to 10 MHz.mm (see section 2.1.4.2). As can be seen in figure 5.3 for both the experiment and FEM simulation this produces complicated A-scans with some wave modes arriving simultaneously at the detector, with the arrival times of these waves dictated by the frequency-thickness dependent velocity shown in figure 2.1b. From B-scans produced during the experiments, such as that shown in figure 5.4, the appearance of reflected, mode converted and trans-

(a) Experimental

(b) FEM

Figure 5.3: Experimental (a) and FEM (b) A-scans for a defect free plate with a thickness of 1.5 mm, showing simultaneous arrival of several Lamb wave modes.

mitted Lamb waves at the defect can be seen, which will be shown to produce an enhancement in the near-field of the defect, similar to that seen for Rayleigh waves in chapter 4.