Assessment of measurement uncertainty associated with fracture toughness calculation based on energy release rate in spherical indentation tests

This work aims to evaluate the uncertainty associated with the fracture toughness of 4130  M steel obtained via instrumented indentation tests and the methodology proposed by Zhang, Wang and Wang (2019). These authors take the energy release rate as a basis to determine fracture toughness. In this study, the uncertainty was assessed using the Guide to the Expression of Uncertainty of Measurement (GUM) and Monte Carlo methods. For uncertainty assessment, all measurands and input variables were identified based on the equations proposed by these authors. Then, the standard uncertainty associated with each input variable was calculated by applying the GUM method. To determine the uncertainty associated with the energy release rate J_SIT the Monte Carlo method was applied. The results obtained showed that the expanded uncertainty associated with J_SIT considering three tests was 1.486 N.mm⁻¹. This uncertainty represents 7.25 % of the average J_SIT value (20.490  N.mm⁻¹). The expanded uncertainty associated with K_IC was 7.520 MPa.m^0.5. These represent 3.82 % of the average K_IC (196.562 MPa.m^0.5) value obtained. This paper demonstrates that despite the complexity of the mathematical equation proposed by Zhang, Wang and Wang (2019), to obtain fracture toughness via instrumented indentation tests, the uncertainty associated can be successfully accessed by combining the GUM and Monte Carlo methods. This work showed that the application of the instrumented indentation technique with the methodology proposed by Zhang, Wang and Wang (2019) provided fracture toughness values with excellent quality under the experimental conditions used in this study.