Damage mechanics model for correlating notch toughness in Charpy impact tests with fracture toughness in cracked static fracture tests

Abstract

Empirically derived Charpy energy to fracture toughness ($J$-integral) correlations are often used to estimate the fracture toughness of steels from Charpy tests due to the higher testing costs and time associated with direct fracture toughness tests, but analytical insight into these correlations is lacking. Accounting for differences in the strain rates and stress states in these tests to simulate the correct response in both while keeping model complexity and calibration effort manageable presents an obstacle to a numerical approach for this problem. This paper hence establishes a modelling and calibration approach that could be used to contribute mechanics-based insight into the correlations between the Charpy energy, $J$-integral, yield-to-tensile strength ratio and tensile test fracture elongation. A phenomenological rate-dependent plasticity model coupled with damage and temperature effects is developed by implementing the strain-based modified Mohr–Coulomb damage-softening model with Johnson–Cook thermal softening in a thermodynamically consistent Cowper–Symonds viscoplasticity model. The validity of the modelling framework is shown by its ability to simultaneously model the tensile test, the Charpy V-notch test and the precracked single-edge notched bending test. This is demonstrated for two steels, AH36 and S690QL, capturing the force–displacement responses and the characteristic ductile fracture mechanism of slant fracture in all three tests. Accounting for thermal softening due to adiabatic heating proves to be important for the accurate simulation of ductile Charpy tests involving high impact energies. Capitalising on weak triaxiality dependence in the middle-to-high triaxiality ranges in the given materials and adopting a triaxiality-independent assumption is found to be effective for reducing the damage model complexity while maintaining its ability to simulate the mechanical response in key tests covering an important range of stress states. The importance of the role of the Lode angle in ductile fracture modelling in weakly triaxiality-dependent regimes is further substantiated. Key similarities in the fracture behaviour of the Charpy and single-edge notched bending tests are identified: they span a similar range of stress states over a large range of their response despite the initial notched versus cracked difference—an insight that could be used to reduce the calibration effort of damage mechanics models for these tests, assuming that the key differentiating factors of rate-dependence and adiabatic heating are correctly accounted for.