Effect of time on longitudinal fracture in functionally graded beam constructions

The present paper studies theoretically how the longitudinal fracture in functionally graded beam constructions is affected by the time. The beam explored has non-linear viscoelastic mechanical behaviour under static loading. Furthermore, the beam is functionally graded in the direction of thickness. To treat the viscoelastic deformation of the structure, a theoretical model representing a combination of linear and nonlinear dampers and springs is applied. This model has two parameters, namely the modulus of elasticity of the non-linear spring and the coefficient of viscosity of the non-linear dashpot which change with time. The time-dependent strain energy release rate is derived. A significant influence of the time factor on the strain energy release rate is detected. For example, it is found that the strain energy release rate – time graph has an upward slop. The question of the influence of the elastic modulus and the viscosity coefficient on the time-dependent behavior of the strain energy release rate is also clarified.