Periodic Reporting for period 4 - FastMat (Fast determination of fatigue properties of materials beyond one billion cycles)
Période du rapport: 2022-01-01 au 2023-06-30
When a material is cyclically loaded, it can fail at a stress amplitude lower than its ultimate tensile strength. This phenomenon is known as fatigue. The fatigue of materials has been studied for a long time, but today it remains a crucial step in mechanical design. For example, in the transport and power generation industries, it is estimated that more than 80% of fractures are due to fatigue.
In addition, the increase in the service life of many structures leads to an increase in the number of cycles applied to the structure. Nowadays, it is quite common to find mechanical systems such as rotating machine components that can fail for a number of cycles greater than ten million and sometimes greater than one billion. In order to ensure the safety of the structures, it is necessary to characterise the fatigue properties of the material for this very high number of cycles.
Current fatigue design methods are based on standards that recommend plotting the evolution of the stress amplitude as a function of the number of cycles to failure (SN curve). Each point on this curve corresponds to a fatigue test performed to failure, usually at a low frequency, typically 10 Hertz. Drawing an SN curve to 10 million cycles can take more than a month. And to explore the VHCF range, the duration of just one test to one billion cycles is about 3 years. Therefore, to reduce test time, fatigue characterisation is limited to ten million cycles. In fact, the standards assume that the SN curve in the very high cycle fatigue range can be extrapolated by a horizontal asymptote called the fatigue limit. Many results in the literature show that this fatigue limit does not always exist. The objective of the FastMat project was to provide answers to these two technological challenges: the reduction of the testing time and the exploration of the VHCF domain. We thus suggested to develop a completely new method for fatigue characterization based on the analysis of short interrupted fatigue tests with complementary measurements like dissipation and mechanical work supplied to the material to estimate the stored energy closely linked to the fatigue damage. This new method will have the advantage to reduce drastically the testing time. It is an alternative technique to self-heating methods classically used in the literature.
One outcome of the project was to justify the feasibility of measuring stored energy during ultrasonic fatigue loading. To do this, in-situ synchrotron measurements were developed to simultaneously estimate the stress and total strain during a cycle. Although this experimental technique is difficult to perform, the results also showed that the stored energy is more sensitive than the energy, as it allows, for example, the formation of dislocation structures in the material to be identified.
Discrete dislocation dynamics calculations have allowed us to recover the trends observed experimentally in terms of the effect of stress amplitude and to gain a better understanding of the activation of the non-recoverable mechanisms activated during loading. The effect of the number of cycles is more difficult to simulate due to the limited computing power available.
In addition, the increase in the service life of many structures leads to an increase in the number of cycles applied to the structure. Nowadays, it is quite common to find mechanical systems such as rotating machine components that can fail for a number of cycles greater than ten million and sometimes greater than one billion. In order to ensure the safety of the structures, it is necessary to characterise the fatigue properties of the material for this very high number of cycles.
Current fatigue design methods are based on standards that recommend plotting the evolution of the stress amplitude as a function of the number of cycles to failure (SN curve). Each point on this curve corresponds to a fatigue test performed to failure, usually at a low frequency, typically 10 Hertz. Drawing an SN curve to 10 million cycles can take more than a month. And to explore the VHCF range, the duration of just one test to one billion cycles is about 3 years. Therefore, to reduce test time, fatigue characterisation is limited to ten million cycles. In fact, the standards assume that the SN curve in the very high cycle fatigue range can be extrapolated by a horizontal asymptote called the fatigue limit. Many results in the literature show that this fatigue limit does not always exist. The objective of the FastMat project was to provide answers to these two technological challenges: the reduction of the testing time and the exploration of the VHCF domain. We thus suggested to develop a completely new method for fatigue characterization based on the analysis of short interrupted fatigue tests with complementary measurements like dissipation and mechanical work supplied to the material to estimate the stored energy closely linked to the fatigue damage. This new method will have the advantage to reduce drastically the testing time. It is an alternative technique to self-heating methods classically used in the literature.
One outcome of the project was to justify the feasibility of measuring stored energy during ultrasonic fatigue loading. To do this, in-situ synchrotron measurements were developed to simultaneously estimate the stress and total strain during a cycle. Although this experimental technique is difficult to perform, the results also showed that the stored energy is more sensitive than the energy, as it allows, for example, the formation of dislocation structures in the material to be identified.
Discrete dislocation dynamics calculations have allowed us to recover the trends observed experimentally in terms of the effect of stress amplitude and to gain a better understanding of the activation of the non-recoverable mechanisms activated during loading. The effect of the number of cycles is more difficult to simulate due to the limited computing power available.
The first part of this project was to develop a measurement technique to estimate the stored energy. The principle of this method was based on the energy dissipated from self-heating measurements on the one hand, and on the mechanical work performed by the fatigue machine on the specimen on the other. Self-heating was measured in a fairly conventional way using an infrared camera. The energy dissipated was then obtained by inverse solution of the heat equation. The originality of the project lay in the estimation of the mechanical work done. This was estimated by integrating the product of stress and total strain rate over a cycle. The strain rate was measured using strain gauges placed on the specimen. A time-resolved X-ray diffraction technique has been specially developed to measure the strain during a cycle. It uses an intense continuous X-ray source obtained on a synchrotron beamline (continuous method). The diffraction patterns were observed with a camera synchronised with the ultrasonic fatigue machine. The displacement of the diffraction peaks was used to estimate the elastic strain and stress. The time evolution of stress during a cycle was then reconstructed by synchronising the camera at different positions in a cycle. A stroboscopic method was also used to obtain diffraction images with a sufficient signal-to-noise ratio. This method successfully reconstructed the stress evolution over a cycle for stress amplitudes close to the conventional fatigue limit. It was also possible to correctly estimate the evolution of the Bragg peak width over a cycle for different stress amplitudes.
However, this continuous method was limited in its ability to measure the stored energy at low strain amplitudes because its temporal resolution, coupled to the minimum aperture time of the camera (0.1µs), was no longer sufficient. An alternative time-resolved X-ray diffraction method, called the flash method, was therefore developed in this project. It was similar to the continuous method but used a pulsed synchrotron source (pulse width 0.1ns). The difference with the continuous method was that the fatigue machine was then synchronised with the synchrotron so that the pulse was always positioned at the same moment in a loading cycle. This method significantly reduced the time resolution, which was estimated to be a few tens of nanoseconds. However, it required more stress cycles to obtain a reconstructed cycle than the continuous method.
The latter method allowed the stored energy to be estimated for very low stress amplitudes compared to the conventional fatigue limit. Two materials were tested, single crystal copper and a pearlitic steel. Both materials show an overall exponential increase with stress amplitude. In addition, a local maximum of stored energy is observed to dissipate at a stress amplitude most likely due to dislocation structure formation as a precursor to fatigue crack initiation. This maximum is also associated with a change in the shape of the Bragg peak width evolution during a cycle.
In parallel with the experimental study, discrete dislocation dynamics calculations were carried out using the Tridis code. A new cross slip law, where the energy barrier depends on the stress components applied to the dislocation, was implemented to better model the non-recoverability of cyclic slip. The results of the simulation with cyclic loading at different stress amplitudes were post-processed to obtain the stored and dissipated energies and compared with experimental results.
However, this continuous method was limited in its ability to measure the stored energy at low strain amplitudes because its temporal resolution, coupled to the minimum aperture time of the camera (0.1µs), was no longer sufficient. An alternative time-resolved X-ray diffraction method, called the flash method, was therefore developed in this project. It was similar to the continuous method but used a pulsed synchrotron source (pulse width 0.1ns). The difference with the continuous method was that the fatigue machine was then synchronised with the synchrotron so that the pulse was always positioned at the same moment in a loading cycle. This method significantly reduced the time resolution, which was estimated to be a few tens of nanoseconds. However, it required more stress cycles to obtain a reconstructed cycle than the continuous method.
The latter method allowed the stored energy to be estimated for very low stress amplitudes compared to the conventional fatigue limit. Two materials were tested, single crystal copper and a pearlitic steel. Both materials show an overall exponential increase with stress amplitude. In addition, a local maximum of stored energy is observed to dissipate at a stress amplitude most likely due to dislocation structure formation as a precursor to fatigue crack initiation. This maximum is also associated with a change in the shape of the Bragg peak width evolution during a cycle.
In parallel with the experimental study, discrete dislocation dynamics calculations were carried out using the Tridis code. A new cross slip law, where the energy barrier depends on the stress components applied to the dislocation, was implemented to better model the non-recoverability of cyclic slip. The results of the simulation with cyclic loading at different stress amplitudes were post-processed to obtain the stored and dissipated energies and compared with experimental results.
The main results of the FastMat project are:
- The development of a time-resolved X-ray diffraction technique using synchrotron in pulsed mode to estimate the stored energy and its evolution as a function of the number of cycles in the gigacycle fatigue regime.
- To improve the control of the ultrasonic fatigue machine and the reliability of its results.
- The identification of damage mechanisms during fatigue loading such as dislocation structure formation from stored energy data.
- To study the non-recoverable cyclic motion of dislocations and the consequences on the stored energy using discrete dislocation dynamics simulations.
- The development of a time-resolved X-ray diffraction technique using synchrotron in pulsed mode to estimate the stored energy and its evolution as a function of the number of cycles in the gigacycle fatigue regime.
- To improve the control of the ultrasonic fatigue machine and the reliability of its results.
- The identification of damage mechanisms during fatigue loading such as dislocation structure formation from stored energy data.
- To study the non-recoverable cyclic motion of dislocations and the consequences on the stored energy using discrete dislocation dynamics simulations.