Non‐linear fracture study of single cantilever beam specimen

Non‐linear fracture of single cantilever beam (SCB) is studied theoretically using J ‐integral. It is assumed that the beam is made of unidirectional fiber reinforced polymer composite which obeys the stress‐strain relation of an elastic‐perfectly plastic material. The lower crack arm is loaded by an external moment while the upper crack arm is stress free. Closed form analytical solutions of J ‐integral are found for different magnitudes of the external load corresponding to the different distribution of stresses and strains in the beam cracked and un‐cracked portions. For this purpose, a mechanics of materials based model is used. The validity of the solution is proved by comparison with formula for strain energy release rate in the linear‐elastic stage of the work of the material. A numerical example is presented to illustrate the influence of the material non‐linearity on J ‐integral. It is found that the material non‐linearity leads to the increase of J ‐integral values. This is attributed to the strain energy dissipation due to the non‐linear deformation.