PSI - Issue 68

Victor Rizov et al. / Procedia Structural Integrity 68 (2025) 139–145 V. Rizov / Structural Integrity Procedia 00 (2025) 000–000

144

6

!

The curves shown in Fig. 3 indicate how the normalized SERR is affected by the spring constant, , and the value of the parameter of the physical law (1) describing the spring mechanical behaviour. It is evident that the normalized SERR can be reduced considerably by increasing the value of (Fig. 3). Thus, the longitudinal fracture behaviour can be regulated quite effectively by using springs with appropriate rigidity. The growth of the parameter however, leads to rise of the normalized SERR as indicated by curves in Fig. 3. ! !

!

µ ! ! !

# ! $ = " !

!"

# % $ = " !

!"

Fig. 4. The normalized SERR versus

ratio (curve 1 – for

, curve 2 – for

and curve 3 – for

!

# % $ = " !

!"

).

µ ! ! !

" ! # " ! µ ! ! !

The change of the normalized SERR when

and

ratios grow is examined too. The curves are non-linear for each of the

!

corresponding curves are shown in Fig. 4. The normalized SERR -

!

" ! # " !

" ! # " !

considered

ratios (Fig. 4). Besides, the rise of

ratio causes significant growth of the normalized

SERR (Fig. 4). 4. Conclusions

Longitudinal fracture of an L-shaped structural member located in the vertical plane is examined theoretically. The shaft is functionally graded along the radius of its cross-section and has non-linear viscoelastic behaviour under twist angle that grows non-linearly with time. The SERR problem is solved. It is explored how the SERR is affected by the rigidity of the rotational spring (this rigidity is modelled by the parameter, , in the non-linear physical law relating the moment in the spring and the angle of twist of the shaft cross-section in which the spring is located) and the parameters of the loading, geometry and material inhomogeneity. The exploration shows clearly that the spring rigidity has considerable effect on the SERR. By increasing the spring rigidity, one can achieve significant reduction of the SERR. In this manner, the longitudinal fracture behaviour of the L-shaped shaft can be efficiently controlled. The influence of the other parameter, , of the physical law of the spring on the SERR is explored too. It is found that the SERR rises when grows. The SERR rises also when and ratios increase. An opposite behaviour, i.e. reduction of the SERR is observed when ratio increases. ! ! ! " ! # " ! ! µ ! ! !

µ ! ! !

!