Issue34

K.L. Yuan et alii, Frattura ed Integrità Strutturale, 34 (2015) 476-486; DOI: 10.3221/IGF-ESIS.34.53 481 Simulation of UIT process After welding simulation in SYSWELD, the results of cruciform joint including element information, as-weld residual stress distribution and plastic strain are imported into LS-DYNA. The tips of 3-mm-diamter pins are modelled as elastic body with an elastic modulus of 206 GPa, Poisson’s ratio of 0.3 and measured mass of 1.5 gram [16]. The pins are angled at 67.5° to the top and bottom surfaces of the specimen. According to Eq. 2, the impact velocity V imp is estimated as 5m/s with corresponding equipment parameters (oscillation frequency of 27 kHz and amplitude of 30 μm under loaded condition [1]). The pin is controlled to continuously impinge the weld toe at the same location for 30 times (equivalent to one ultrasonic impact as mentioned before) by using restart analysis option of LS-DYNA. After each ultrasonic impact, the pin is moved 0.4 mm along weld line to achieve a smooth peened groove with reasonable calculation efforts. This leads to at least four overlapping indentations for the contact area of pin. The weld toe on the top surface is first peened, and that on the bottom surface is subsequently treated. a) b) Figure 8 : (a) Finite element model of UIT, (b) Mechanical properties considering acoustic softening. The material of the weld joint is assumed to follow linear kinematic hardening behavior. To consider the acoustic softening effect in Eq.3, the parameter η is selected as 40% by trial and error, so that predicted groove depth fits to the experimental results. The softening zones (SZ) around the weld toe in Fig.8 are assumed to be affected by acoustic softening during peening, of which each depth is determined as 8mm according to measured stress reduction in 16-mm- thickness specimen [14], and the remain zones (NSZ) are not affected by softening. It should be noted that the apparent yield stress dominantly affected by acoustic softening reveals reduction, although the strain-rate effect due to oscillatory stress has been implicitly included in the above mentioned ultrasonic-assisted test [12]. In order to prevent unnecessary long post-impact residual oscillations, which may lead to numerical instability, in this model the material proportional damping is employed as follow: 0 2      C M M (4) 0 2 E T     (5) where C is the damping matrix, M is the mass matrix, α is the mass proportional Rayleigh damping, ω 0 is the lowest natural frequency, ξ is the corresponding damping ratio, E is elastic modulus, ρ and T are density and thickness of the plate, respectively. According to [19], the adopted value of ξ=0.5 is adequate for the rapid stress convergence. Moreover, the contact surfaces are set between the pin tip and the specimen with a Coulomb friction coefficient μ=0.5. V ALIDATION OF WELDING -UIT SIMULATION Determination of acoustic softening parameter he acoustic softening parameter η is firstly selected by trial and error so as to match the experimentally measured indentation depth d and weld toe radius r [20] on a cross-section with the predicted ones after one ultrasonic impact, as shown in Fig.9. It can be seen that it is easier to form a smooth change of the shape at the weld toe T