Creep crack growth behavior in materials is a complex phenomenon that depends on many factors, including the properties of the material, the environment in which it is used, and the loading conditions to which it is subjected. To predict creep crack growth behavior in materials, one typically uses a combination of experimental testing and mathematical modeling. Experimental testing involves subjecting the material to different loading conditions and monitoring its behavior over time, using techniques such as optical microscopy, electron microscopy, or X-ray diffraction. The results of these tests provide information about the material’s mechanical properties, such as its strength, ductility, and fracture toughness, as well as its resistance to environmental factors such as temperature, humidity, and chemical exposure. Mathematical modeling involves using computer simulations to predict how the material will behave under different loading and environmental conditions. These simulations typically involve solving a set of differential equations that describe the behavior of the material over time, taking into account factors such as stress, strain, temperature, and environmental exposure. The simulations can be used to predict the rate at which cracks will grow in the material, as well as the time and conditions under which they will propagate to failure.
A minor disparity between an established mathematical model to predict creep crack growth behavior in materials in high-temperature environments and actual data has prompted Dr. Warwick Payten to reassess the approach and revise the model. In research published in Engineering Fracture Mechanics, Dr. Warwick Payten reported the design of a new model to predict creep growth rates that was validated in a range of materials. Being able to more accurately predict crack growth in real components is highly useful because it allows you to potentially extend the life of operating industrial plants and conventional, solar and nuclear power stations with confidence,” said Payten, a senior nuclear fuel cycle researcher.
The NSW equations were derived from original mathematical work done in the 1960s by Hutchinson Rice and Rosengren (HRR). In the NSW equation to determine plane strain crack growth, which is used in all the engineering codes, you multiply the plane stress crack growth by a multiaxial factor of 30 or 50. This produces a high estimate for failure, or shorter operational life for the component. When you use a factor of 30 or 50 in the equation, it might produce a result that says you have to retire the part in three years when in reality it is more likely to last 30 years. Although Nikbin came up with another method that used a factor between three and eight, it was difficult to use and was dependent on how you interpreted a critical angle.
Because of this disparity between the model and actual life expectancy, Dr. Warwick Payten decided to take a new approach. He had an idea because everything we use is based on ductility. Rather than ductility, he looked at energies. The author went back to the original HRR equations, in order to make an assessment based on the amount of energy in the singular fields associated with crack propagation. Using the original logarithm tables from the HRR paper and the Lemaitre damage model, the author was able to calculate the energy for each of the singular fields. According to the author the factor fell out at 2.9, which he rounded up to three. This suggested the factor he multiply by would be three and not 30 or 50, which is a significant difference.
After testing and validating the new model a range of different materials, including carbon, steels, stainless steels, inconels and superalloys, the materials used to construct current and future power reactors. The author recommended that the universal crack growth equations and the FEA code be changed to provide a more realistic prediction of component life.
Overall, predicting creep crack growth behavior in materials is a challenging task that requires a deep understanding of the material’s properties and behavior under different loading and environmental conditions. By combining experimental testing with mathematical modeling, researchers can gain valuable insights into the mechanisms of crack growth in materials and develop strategies to prevent or mitigate this behavior in engineering applications.
Warwick Payten (2023). A reassessment of the multiaxial ductility C* creep crack growth equation based on the strain energy integral of the HRR singular field terms, Engineering Fracture Mechanics, Volume 217, 2019, 106530.