Vol.20, No.2, 2020, pp. 137–142
UDC:

The paper deals with longitudinal fracture analysis of an inhomogeneous beam of linearly varying height of cross-section along the beam length. The beam is under three-point bending. The beam height increases linearly from the two ends towards the mid-span. A longitudinal crack is located arbitrary along the beam height. The beam exhibits continuous (smooth) material inhomogeneity along its height and length. The material is nonlinear elastic. Longitudinal fracture behaviour of the beam is studied in terms of strain energy release rate. Energy balance is analysed in order to derive a solution to the strain energy release rate. The solution is verified by applying the J-integral approach. The solution is used to investigate influences of linearly varying beam height in length direction; material inhomogeneity along the beam height and length; location of crack along beam height and crack length on longitudinal fracture behaviour. Longitudinal fracture analysis developed here can be used in the preliminary design of load-bearing inhomogeneous nonlinear elastic beam structures with continuously varying height in the length direction.

Keywords: inhomogeneous beam, longitudinal fracture, material nonlinearity, bending