PSI - Issue 83

Victor Rizov et al. / Procedia Structural Integrity 83 (2026) 105–114

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at  60   the resultant is perpendicular to the beam. Another conclusion from the graphs in Fig. 3 is that the J integral grows as a result of increase of 2 1 / m m ratio. Figure 4 shows how the J -integral behaves when the ratio, a l / , and the parameter,  , vary. Increasing the ratio, a l / , leads to an increase in the risk of delamination growth, as the J -integral increases (Fig. 4). The risk of delamination growth also increases as a result of increasing the parameter,  .

Fig. 5. Plots of the J -integral as a function of 1.05   (curve 3). Figure 5 illustrates the effects of increasing the ratio, 1 2 / B B , and the parameter of motion,  , on the J -integral. Increasing the ratio, 1 2 / B B , reduces the risk of delamination growth as the J -integral decreases, as can be observed in Fig. 5. Increasing the parameter,  , value worsens the moving beam delamination behavior as it leads to an increase in the J -integral. 4. Conclusion A delamination analysis of a moving stepwise functionally graded beam is presented. The analysis is based on a theoretical model which considers the beam as a multilayered structural component with a delamination crack between layers. A solution of the J -integral is obtained, taking into account the non-linear viscoelastic behavior of the beam structure under inertia loading. Based on the analysis performed, the following conclusions are made: ( a ) For the considered law of motion of the beam, the J -integral reaches maximum when the angle of inclination of the beam is  60   . ( b ) The J -integral grows as a result of increase of 2 1 / m m ratio. ( c ) Increasing the ratio, a l / , as well as the parameter,  , leads to an increase in the risk of delamination growth, as the J -integral increases. ( d ) The risk of delamination growth decreases with increasing the ratio, 1 2 / B B , since the J -integral decreases. ( e ) Increasing the parameter,  , worsens the delamination behavior as it leads to an increase in the J -integral. 2 1 / B B ratio at 0.35   (curve 1), 0.70   (curve 2) and