Issue34

L. E. Kosteski et alii, Frattura ed Integrità Strutturale, 34 (2015) 226-236; DOI: 10.3221/IGF-ESIS.34.24 234 In Fig.7 (right) the graphic illustrates fluctuations of kinetic, elastic and dissipated energy during all the damaged process, where abrupt changes in such values of energy are associated to local instabilities in main crack grow, denoting the spasmodic character of simulated subcritical growth. Aiming to improve visualization of the energetic fluctuations during simulated crack growth, the dissipated energy curve (red) is multiplied by a 0.02 scaling factor and elastic energy (green) by a 0.04 scaling factor. Kinetic energy curve (blue) is shown in original scale. Observing Fig. 7 it is possible to conclude that the macro crack propagates in subcritical way from (t/tmax=0,70) untill (t/tmax=0.96) when the process becomes unstable. Within subcritical growth, in the next subsection, fatigue life is characterized according to the classic Paris law. Figure 7: (Left) Main crack configuration during six moments of simulation, where   * / max 100 t t t   ; (Right) The fluctuations of kinetic, elastic and dissipated energy during simulated damage process. Fatigue Life Characterization: The Paris Law, based in a potencial law, presents subcritical crack growth velocity (da/dN) as a function of the delta of stress intensity factor (  K) acting at the main crack tip. For this work,  was computed using the expresion presented in Gdoutos [14] which is adequate to the model geometry, boundary conditions and pre-crack configuration here adopted. The value of  K  changes (grows) during the simulation process, as  K also depends on the crack length, a .  Having obtained crack propagation velocity (da/dN) and stress intensity factor (  K) by mean of the LDEM tool, the values can be subtituted in Paris equation [ (da/dN) = C  K m ] to model fatigue life during subcritical crack growth. Applying log operation in both sides of Paris expression it is possible to obtain the constants and that characterize fatigue behavior for the simulated material.  The velocity (da/dN) is obtained in the LDEM model using the x coordinate of every element and the instant in time when it reaches the critical strain value  p , becoming damaged. This strategy implies in assuming that the microfissure cluster which precedes the main crack advances through the plate in the same velocity as the crack itself. Thus, (da/dN) is measured computing the time in which each bar reaches the critical strain  p , versus the x coordinate of the element central point. Also, the same procedure is realized when rupture strain  r is achieved. The resulting graphic is seen in Fig. 8 (left). Figure 8 : (Left) Normalized time versus the x coordinate of the central points of elements that reached (red dots) and (blue dots) during the simulation, the curve equivalent to is denoted by the green dots; (Right) Plot versus where the straight line indicates subcritical crack growth. The velocity is expressed in µm per cycle.