PSI - Issue 54

Victor Rizov et al. / Procedia Structural Integrity 54 (2024) 468–474 Victor Rizov/ Structural Integrity Procedia 00 (2019) 000 – 000

473

6

3 f (curve 1 – at

0.8

1.8 4  f and curve 3 – at

2.4

4  f

4  f

Fig. 5. Variation of the SERR with

, curve 2 – at

).

The ascendancy of 3 f and 4 f over the SERR is visualized with the aid of the graphs in Fig. 5.

4. Conclusions Application of a non-linear rheological model in longitudinal fracture analysis of a viscoplastic functionally graded engineering beam structure is studied theoretically. The rheological model is made of two consecutive units structured by springs, dashpots and a frictional slider. The latter is added in the model in order to take into account plastic strains in the beam structure. The model is loaded by stress that increases with time. The material properties involved in the model alter smoothly in the width direction of the structure. The beam is with arbitrary number of longitudinal vertical cracks. Solutions of the time-dependent SERR which take into account the viscoplastic behaviour are obtained for each crack. The energy balance is examined for control of the solutions. The effect of continuous material inhomogeneity is studied. The time-dependent SERR contracts at growth of 1 f , 2 f , 3 f , 4 f , 5 f , 6 f and 7 f (these parameters control the inhomogeneity in the structure). The research illuminates the strong relation between the longitudinal fracture and the properties continuous distribution in functionally graded materials which have viscoplastic mechanical behaviour under time-dependent loading. Therefore, by forming suitable distribution of material properties during manufacturing process, one can improve significantly the longitudinal fracture behaviour of viscoplastic engineering structures. References Ganapathi, M., 2007, Dynamic stability characteristics of functionally graded materials shallow spherical shells, Composite Structures 79, 338 343. Gururaja Udupa, Shrikantha Rao, S., Rao Gangadharan, K., 2014. Functionally Graded Composite Materials: An Overview. Procedia Materals Science 5, 1291-1299. Hirai, T., Chen, L., 1999. Recent and prospective development of functionally graded materials in Japan. Mater Sci. Forum 308-311, 509-514. Kieback, B., Neubrand, A., Riedel, H., 2003. Processing techniques for functionally graded materials. Materials Science and Engineering: A 362,