Numerical calculation the fracture toughness of square section beam under three-point bending test

Abstract

A universal equation is proposed to determine specific fracture energy based on numerical calculations by finite element methods in the ANSYS system referring to the three-point bending of a square beam arranged edgewise on supports. Numerical dependences of the specimen compliance on the crack length were represented as the 5th and 6th degree polynomials on the relative value of Δl/h, where Δl is the crack length and h is the half length of the square diagonal. To calculate the specific fracture energy, we used the derivative of specimen compliance by the crack length. The analysis has shown that finite value of specific fracture energy at Δl→0 is obtained when the decomposition term at Δl/h is equal to 0. A satisfactory agreement between the specific fracture energy values for the 5th and 6th degree decompositions is observed only at Δl/h ≈ 1. As the values of Δl decrease, the difference becomes increasingly significant. The averaging of coefficients at corresponding Δl/h degrees of two considered decompositions allows us to find a power function that weakly depends on the Δl/h ratio and leads to a consistent dependence of the specific fracture energy on the crack length. Due to the performed calculations, a universal equation is obtained to determine the specific fracture energy according to the test data of square beams by three-point bending in a wide range of geometric dimensions.