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