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5.2. LASER SHCOK MICROFORMING SIMULATION
• HARDSHOCK code (based in the FEM commercial code ABAQUS®) solves the shock propagation problem into the solid material, with specific consideration of the material response to thermal and mechanical alterations induced by the propagating wave itself (i.e. effects as elastic–plastic behaviour, changes in elastic constants, phase changes, etc.). For the kind of problems considered in this tutorial, a 3D version of the HARDSHOCK code is used. From the point of view of time differencing, the usual strategy of explicit differencing for the initial fast shock propagation phase followed by standard implicit differencing for the analysis of the final residual stresses equilibrium is used. The onset of the implicit phase is defined to apply once all plastic deformation has taken place.
Concerning material behaviour a dynamic elastic limit has to be used. In the reported calculations such limit has been fixed according to Johnson-Cook model [61], applicable to the typical behaviour shown by the different materials through their dynamic strain–stress curve. The actual material yield strength is taken according to Von Mises’ criterion.
A sample of the 3D simulated geometry is shown in figure 5.3. It corresponds to the incidence of a uniform laser beam of cylindrical shape on a planar surface with a pinned end as boundary condition. The FEM element used for the mechanical simulation is an 8-node brick reduced integration with hourglass control, namely C3D8R.
Figure 5.3. Geometrical properties of a typical FEM Model used for the numerical simulation of one-end pinned thin metal strip subject to laser shock microforming.
5.2.2 Numerical results.
The described model has been applied to study the mechanical effect of laser pulse energy and laser spot position on the net metal sheets bending angle under the reasonable hypothesis of weak thermal influence.
All the results presented in this tutorial refer to Stainless Steel AISI 304 and samples of 50 μm thickness and 200 μm width irradiated with a 10 ns pulsed Nd:YAG laser operating at 1064 nm and with a spot diameter of 175 μm.
5.2.2.1 Analysis of the influence of laser energy on the net bending angle.
As a first step in the analysis, the influence of the laser pulse total energy on the bending angle of typical specimens has been analyzed. In figure 5.5 the thin sheet deformations for different laser pulse energies are displayed. One only laser pulse incident on a selected area of the specimen (laser spot centered at d = L/3) has been considered for this simulation.
The study of net bending angle of the metal sheet as a function of the laser energy pulse (see figure 5.6) shows that, after a critical value of pulse energy, the bending angle (b) produced by the bending moment starts to have a deleterious effect on the net bending angle (〈).
5.2.2.2 Analysis of the influence of laser spot position on the net bending angle
In this point, the analysis of the influence of the laser incident position (laser spot centre position) on the final specimens bending is performed.
In figure 5.7 the deformed profiles of the clamped sheet subject to an equal-energy laser pulse (0,048 J) applied at different distances from the clamping base are displayed.
The study of the net bending angle of the metal sheet as a function of the laser spot position d (see figure 5.8) shows that, as a consequence of the combination of the two main deformation effects, a maximum is obtained when the laser spot is applied at a given distance from the pinned end (about d = L/3 for this process parameter).
The residual stress distribution produced by shock waves is the same in all these cases, but when the laser is near the bulk material the bending angle is reduced because it has to deform more material while the bending moment increases linearly with laser spot position.
Figure 5.8. Net bending angle of reference thin sheet specimens subject to 0.048 J, 10 ns laser pulses irradiation as a function of spot center distance from base, d.
