Abstract: Three-point bending (TPB) specimens can realise out-of-plane fracture through pre-establishing a crack surface which is perpendicular to the under-surface while inclined to the front and back surfaces. The finite element method (FEM) software ABAQUS is applied to calculate stress intensity factors (SIFs) of mode I, mode II and mode III crack front along the thickness of the specimen with different inclined angles θ. It is clear that mode I and mode III dimensionless SIFs can get a larger value, while mode II dimensionless SIF is insignificant when it is close to the mid-point of the specimen thickness. As a result, this kind of specimen can be used to investigate mixed-mode I/III of materials. Numerical results are compared with the analytical formula of the conventional TPB specimen and the approximate formula of the TPB specimen with the inclined crack surface. The accuracy of numerical results is proved and the problems of the approximate formula are discussed. Mixed-mode I/III fracture behaviour of sandstone is studied in 7 groups of 28 specimens. The results show that the critical SIFs of mode I and mode III increase with the increase of inclined angle then decrease, while the variation tends are different; mixed-mode I/III effective fracture toughness also changes with the inclined angle and reaches the maximum value when θ=20°. The crack surface tilts when the crack propagates, and the lager θ is, the greater tilted angle can get.

Key words: three-point bending (TPB), sandstone, numerical analysis, mixed-mode I/III