Thermodynamic models for the study of viscoelastic deformation and failure in metals at high temperatures - Lavie, William J (2024)
Current trends in the power generation and distribution sectors suggest an ever-increasing need for flexibility in the loading of components. In both cases, this implies that components will increasingly be subjected to both creep and fatigue loading conditions. The damage caused by this type of loading is notoriously difficult to predict, with empirical models and large safety factors often being used. Advances in damage modelling of mechanical deformation in the past years have led to the establishment of entropy-based damage prediction methods. These methods postulate that a given amount of entropy can be generated within a material before failure occurs and have been used to model fatigue and wear damage, for instance. The use of thermodynamically-based models allows entropy generation to be computed as a function of the state and dual variables of the model. By using thermodynamically-based material models that can replicate the behaviour of metals at high temperatures, generated entropy can then be computed and used as a parameter for determining the damage caused by phenomena such as creep, fatigue and their combination. One particular high temperature behaviour of metals that has received little attention in the scientific literature is viscoelasticity. Overshadowed by viscoplasticity, it is nonetheless a behaviour that has been observed in metals and that may be key to understanding and predicting the damage caused in metals by deformation at high temperatures and low loads. The purpose of this thesis is to provide tools for the development of thermodynamically-based material models for the deformation and damage of metals at high temperatures. Particular attention is given to the modelling of viscoelastic behaviours. Since thermodynamically-based material models typically derive state and evolution laws from dissipation potentials and free energies with arbitrarily chosen formulations, insight into the thermodynamics of deformation are helpful in determining appropriate potentials. In particular, the dissipation of energy as heat during deformation can be monitored using thermography and Taylor-Quinney values determined. A testing method is proposed in this thesis for determining Taylor-Quinney coefficients for use in checking the validity of thermodynamic potentials. The method uses inverse analysis of small ring testing through finite element simulations to determine coefficients at low cost. Values of Taylor-Quinney coefficients ranging from 0.48 to 0.61 are obtained for AA7175, far from the value of 0.9 often assumed for metals in the literature. The state variables used in thermodynamically-based material models are chosen such that they fully determine the state of a material at a point in time. The choice of variables is therefore complex and should reflect the microstructural state of the material. To determine the best state variables to use when modelling viscoelastic behaviours, investigations into the microstructural causes of viscoelasticity are led in this thesis. Small ring specimens of C110 Copper are subjected to displacement holds at displacements that result in viscoelastic or viscoplastic states within the specimens. It is found that dislocation densities measured in the specimens are consistently higher after the specimens are subjected to relaxation than before, even when the initial relaxation load is supposed to be below what would usually be considered the yield strength of the material. Dislocation densities are further found to reduce over time during relaxation. Stresses within certain grains are found to reach levels where creep minimum strain rates are sizeable, explaining the reduction in dislocation density. The observed viscoelastic relaxation is therefore determined to be related to a localised form of plasticity occurring in favourable grains. To model the constitutive viscoelastic deformation behaviour of metals, models employ state and evolution laws that must be calibrated using material parameters. To aid in determining such parameters, a novel inverse analysis testing method is also proposed in this thesis. The method uses inverse analysis to interpret the results of small ring relaxation experiments. The inverse analysis uses finite element simulations, with a viscoelastic material model implemented in Abaqus using a Fortran UMAT with a bespoke time incrementation scheme. The method is tested on AA7175, with the resulting material model reproducing experimental viscoelastic behaviour well. Finally, a viscoelastic-viscoplastic material model for P91 at 600 °C is implemented into a purpose-written Matlab solver to compute generated entropy for a range of deformation loadings. A database of creep, fatigue and dwell-fatigue test data obtained for tests performed until failure for P91 at 600 °C is compiled. Total and viscoelastic failure entropy are computed for each test using the solver. It is found that linear laws relate the loading condition (nominal creep load or strain amplitude) to the total failure entropy for creep, fatigue and dwell-fatigue, proving the usefulness of generated entropy as a damage criterion for all three loading types. Furthermore, the ratio of the viscoelastic failure entropy to the total failure entropy is large for fatigue and dwell-fatigue tests performed at low loads, illustrating the importance of understanding viscoelastic phenomenon when modelling the deformation behaviour of metals at high temperatures and highlighting the need to account for viscoelastic contributions to damage.