Articles

A new constitutive equation predicting the evolution of oxide thickness is proposed and implemented in a crystal plasticity framework with a hardening-based damage density function. The oxidation model depends on the initial surface roughness as well as on the amount of accumulated plastic strain and stress triaxiality. The description for the effect of oxidation on the mechanical behavior and damage is at the flow-stress level by modifying the amplitude of the kinematic hardening. The oxidation-altered kinematic hardening can predict the effect of oxidizing environments on mechanical behavior, specifically the plastic strain rate in the secondary creep stage, and lifetime. Finally, the oxidation model is verified to predict surface roughness and oxide thickness distributions by performing a finite-element simulation on a notched specimen subjected to creep and developing a complex multiaxial stress field.

The kinematics of an inelastic solid established in terms of Laplace stretch and its rate are decomposed into one stretch that describes an elastic response, another stretch that describes an inelastic response, and their rates. These kinematics are a direct consequence of Laplace stretch belonging to the group of all real, 3×3, upper-triangular matrices with positive diagonal elements. The Laplace stretch follows from a Gram–Schmidt decomposition of the deformation gradient.

The mechanical response of Ni-based single-crystal superalloys is known to be sensitive to the microstructural state, i.e., the shape and size of the γ′ precipitates when exposed to high-temperature conditions. The magnitude and sign of the natural lattice misfit between the γ and γ′ phases play the most crucial role in establishing a controlled size, shape, and distribution of γ′ precipitates during heat treatments as well as in defining the direction of rafting, viz. the directional coalescence of the γ′ precipitates. In this study, a bottom-up scale bridging strategy of using phase-field informed finite-element (FE) crystal plasticity on realistic microstructures is followed to better understand the effect of the microstructural state on the macro-scale performance of a ⟨001⟩-oriented Ni-based single-crystal superalloy. Strain-controlled tensile tests using FE crystal plasticity were performed on a set of different microstructural states: cuboidal, rafted, and topologically inverted imported from 3D phase-field simulations. The study revealed that a cuboidal microstructure with a natural lattice misfit of − 0.004 is the most ductile. As observed experimentally, the microstructure with rafts perpendicular to the loading axis (N-type) is more ductile than the cuboidal one. The P-type microstructure, i.e., with rafts parallel to the loading axis, is found to have the lowest ductility, which was attributed to lesser dislocation mobility.

A phenomenological hardening-based damage density function built on a Rabotnov-Kachanov’s formulation and coupled to a microstructure-sensitive viscoplastic crystal plasticity model is developed for ductile materials experiencing fast-evolving microstructures. The model seats on the fact that classical continuum damage models, that only consider discontinuities of matter; viz. voids and cracks; as damage, are not able to predict the non-isothermal creep and isothermal dwell/fatigue lifetimes of materials exposed to temperature/stress conditions that trigger microstructure evolutions faster than the nucleation and growth of voids. The hereby-proposed damage model depends on microstructure-sensitive hardening variables that were previously tailored to model changes in the mechanical behavior of a Ni-based single crystal superalloy during non-isothermal loading. Furthermore, the model also proposes to predict lifetime scattering during creep by considering the initial volume fraction of pores obtained by X-ray tomography. Isothermal and non-isothermal uniaxial creep and dwell/fatigue experiments on a Ni-based single crystal superalloy are used to calibrate and validate the model. Finite element simulations are also carried out to confirm the lifetime predictive capabilities of the model on an in-plane multiaxial creep test and on multiaxial torsion and tension/torsion dwell/fatigue tests. The numerical results show that the damage model well predicts the lifetime of isothermal and non-isothermal creep as well as dwell/fatigue experiments in uniaxial and multiaxial states of stresses.

A lattice-misfit-dependent damage density function is developed to predict the non-linear accumulation of damage when a thermal jump from 1050 °C to 1200 °C is introduced somewhere in the creep life. Furthermore, a phenomenological model aimed at describing the evolution of the constrained lattice misfit during monotonous creep load is also formulated. The response of the lattice-misfit-dependent plasticity-coupled damage model is compared with the experimental results obtained at 140 and 160 MPa on the first generation Ni-based single crystal superalloy MC2. The comparison reveals that the damage model is well suited at 160 MPa and less at 140 MPa because the transfer of stress to the γ′ phase occurs for stresses above 150 MPa which leads to larger variations and, therefore, larger effects of the constrained lattice misfit on the lifetime during thermo-mechanical loading.

Multiaxial high-temperature creep tests have been performed at 1050 °C on a first-generation Ni-based single-crystal superalloy through the use of asymmetric notched specimens. Mechanical twins have been observed by EBSD and TEM analyses. A finite element simulation in a crystal plasticity framework has also been carried out to better understand the presence of mechanical twins at stress concentrators depending on stress triaxiality, plastic strain rate, and damage level.

Creep damage by void nucleation and growth limits the lifetime of components subjected to mechanical loads at high temperatures. For the first time, the porosity of a Ni-based single crystal superalloy subjected to high temperature creep tests (T≥1000 °C) is followed by ex-situ X-ray computed tomography. A large experimental campaign consisting of nine temperature/stress conditions is carried out to determine the kinetics of the damage accumulation by voids. It is, indeed, essential to characterize their evolution to create internal variables describing properly the evolution of damage in a Continuum Damage Mechanics framework. Nonetheless, it is pointed out that the increase in the plastic strain rate during the tertiary creep stage is not necessarily related to the increase in the pore volume fraction for the alloy and temperature range explored (1000–1100 °C). Therefore, it seems that the changes in the microstructure, i.e. precipitation coarsening and γ/γ′ topological inversion, and the shearing of the γ′ particles have to be considered further to properly describe the damage evolution. Thus, the Continuum Damage Mechanics theory is undermined and should be replaced by a transformative paradigm taken into consideration microstructural evolutions in order to improve the predictability of further damage models.

In a recent paper, Sisi Xiang & al. [Acta Materialia 116 (2016) 343] studied microstructure evolutions of γ′ precipitates during creep of a Ni-based single crystal superalloy, with a special focus on hyperfine γ′ particles nucleating in the γ matrix channels. This paper is misleading, claiming that hyperfine γ′ particles nucleate during high temperature creep exposure at 1100 °C. The aim of the present comments is to reconsider these results based on the available literature on hyperfine γ′ particles nucleation mechanisms and subsequent morphological evolutions at high temperature.

Dwell-fatigue tests and variable strain rate tensile tests followed by cycling tests were performed using 〈0 0 1〉-oriented specimens made of a first-generation Ni-based single crystal superalloy. A short thermal jump from the nominal temperature of 1050 to 1200 °C was introduced along the lifetime of dwell-fatigue experiments and at the beginning of tensile tests. A fine γ′ precipitation occurred in the γ matrix upon such event which induced a large transient strengthening effect on the mechanical properties. In fact, a transient decrease of the plastic strain rate, corresponding to a reduced magnitude in the hysteresis loops, was measured after the temperature peak during the dwell-fatigue experiments. In addition, a temperature peak produced a large hardening effect and a mechanical behavior change during the tensile tests since a hardening of 160 MPa was recorded and a perfectly plastic behavior was obtained. These transient phenomena were due to a temporary additional strengthening provided by fine γ′ precipitates lasting for the time necessary to not hinder dislocation motions anymore. Furthermore, the experimental results were also used to determine how fine γ′ precipitates modified the magnitude and the saturation speed of the isotropic and kinematic hardenings.

The viscoelasticity of a variety of active materials is controllable, e.g., by the application of electric or thermal fields. However, their viscoelastic behavior cannot be fully explored by current methods due to limitations in their control of mechanical, electrical, and thermal fields simultaneously. To close this gap, we introduce Broadband Electromechanical Spectroscopy (BES). For the specific apparatus developed, specimens are subjected to bending and torsional moments with frequencies up to 4 kHz and amplitudes up to 10⁻⁴ Nm (the method is sufficiently general to allow for higher and wider frequency ranges). Deflection/twist is measured and moments are applied in a contactless fashion to minimize the influence of the apparatus compliance and of spurious damping. Electric fields are applied to specimens via surface electrodes at frequencies up to 10 Hz and amplitudes up to 5 MV/m. Experiments are performed under vacuum to remove noise from the surrounding air. Using BES, the dynamic stiffness and damping in bending and torsion of a ferroelectric ceramic, lead zirconate titanate, were measured at room temperature, while applying large, cyclic electric fields to induce domain switching. Results reveal large increases of the specimen’s damping capacity and softening of the modulus during domain switching. The effect occurs over wide ranges of mechanical frequencies and permits lowering of the resonance frequencies. This promises potential for using ferroelectrics for active vibration control beyond linear piezoelectricity. More generally, BES helps improve current understanding of microstructure kinetics (such as during domain switching) and how it relates to the macroscopic viscoelastic response of materials.

Complex thermomechanical loadings at high temperature (T ⩾ 950 °C) on the AM1 single-crystal superalloy were studied by X-ray diffraction under synchrotron radiation. This technique enables in situ access to the evolutions of the lattice mismatch as well as the volume fraction and the dislocation density of the γ and γ′ phases during high-temperature non-isothermal creep loadings. It is shown that the large microstructure evolutions through the growth/shrinkage of γ/γ′ interfaces due to the γ′ volume fraction changes and the associated variations in the density of dislocations at these interfaces during temperature jumps are key parameters controlling the whole behavior (distribution of internal stresses and constitutive laws) of both phases. We propose an empirical constitutive law linking the strain rate of the γ′ phase to its stress state as well as a way to determine it. During our experiments, the plastic behavior of the γ′-rafts is related to the entry of dislocations with Burgers vectors perpendicular to the tensile axis and controlled by the overcoming of a threshold stress corresponding to the internal stress components perpendicular to the tensile axis.

We show that the viscoelastic properties of polycrystalline ferroelectric ceramics can be significantly altered over a wide range of mechanical frequencies when domain switching is controlled by cyclic electric fields. The dynamic stiffness of lead zirconate titanate is shown to vary by more than 30%, while damping increases by an order of magnitude. Experimental results are interpreted by the aid of a continuum-mechanics model that captures the nonlinear electro-mechanically coupled material response for the full electric hysteresis.

The prediction of the viscoplastic behavior of nickel-based single crystal superalloys remains a challenging issue due to the complex loadings encountered in aeronautical engine components such as high pressure turbine blades. Under particular in-service conditions, these materials may experience temperature cycles which promote the dissolution of the strengthening γ′ phase of the material on (over)heating, and subsequent precipitation on cooling, leading to a transient viscoplastic behavior.

Within this context, a model was recently developed by Cormier and Cailletaud (2010) to fulfill the effects of fast microstructure evolutions occurring upon high temperature non-isothermal loadings. New internal variables were introduced in the crystal plasticity framework to take into account microstructure evolutions such as γ′ dissolution/precipitation and dislocation recovery processes which are known to control the creep behavior and life. Nevertheless, this model did not consider the γ′ directional coarsening, one of the main microstructural evolutions occurring specifically at high temperature. In addition, no kinematic hardening was considered to describe the mechanical behavior, leading to a poor description of cyclic loadings.

This paper details the development of a new model by introducing new internal variables for both modeling the γ′ directional coarsening and the evolutions of isotropic and kinematic hardening under complex loading paths.

This model was calibrated using monotonous and cyclic experiments performed on [0 0 1] oriented single-crystal samples and both under isothermal and non-isothermal conditions. Thereby, it is able to predict microstructural evolutions for complex thermal and mechanical loadings as well as internal stress evolutions whatever the thermomechanical history. The model efficiency was highlighted by comparing FEM simulation and experimental results of a non-isothermal creep test on a notched sample (i.e. under complex mechanical stress state).

Specific non-isothermal creep conditions were applied to a 1st generation single crystal nickel based superalloy at very high temperature. Creep tests were conducted under 120 and 160 MPa at 1050 °C with one overheating under stress at 1200 °C for 30 s. Results were compared to the ones already obtained under 140 MPa on the same alloy as well as on a fourth generation of alloy.

It is shown that the residual creep life after a single overheating is optimal after a specific prior-creep time. The impact of the creep degradation prior to an overheating on the creep life is dependent on the magnitude of the effective γ/γ′ lattice mismatch. Indeed, an overheating performed when the effective γ/γ′ mismatch magnitude is maximum leads to longer creep lives, even better than without overheating.

The influence of both topologically close-packed (TCP) phase precipitation and pores on the creep life of a single-crystal superalloy has been studied at 1323 K (1050 °C)/160 MPa. Despite very reproducible primary and secondary creep stages, the creep life is scattered for this specific condition where a very steep tertiary creep stage is observed, corresponding to a highly localized failure process. Image processing was performed after failure to determine the stereological parameters characterizing pores and TCP-phase particles. It was determined that pores are major determinants of creep life under these temperature and stress conditions. It was also observed that the average surface area or the density of pores is not sufficient to explain creep life variability. A homogenization method including modified γ/γ′ microstructure area surrounding pores and TCP-phase particles was developed and correlated to creep life. It is shown that the greater the extent of the modified microstructure, the lower the creep life. Moreover, a better understanding of the TCP-phase role in controlling the creep life was obtained: TCP-phase particles modified the local stress field and disturbed the local γ/γ′ microstructure. They enhance the generation of vacancies and subsequent nucleation and growth of pores.

The evolution of the γ/γ′ lattice mismatch of the AM1 single-crystal superalloy was measured during in situ non-isothermal very high-temperature creep tests under X-ray synchrotron radiation. The magnitude of the effective lattice mismatch in the 1273 K to 1323 K (1000 °C to 1050 °C) temperature range always increased after overheatings performed at temperatures lower than 1403 K (1130 °C). In contrast, a decrease of its magnitude was observed after overheatings at temperatures greater than 1453 K (1180 °C) due to massive dislocation recovery processes occurring at very high temperature.

The dissolution kinetics of an ultra-fine γ’ precipitation occurring in the γ matrix between the standard secondary precipitates of MC2 Ni-based single crystal superalloy was investigated. Creep-fatigue experiments at 1050°C including an overheating at 1200°C were performed on <111> oriented specimens to study the effects of fine γ’ particles on the plastic deformation. During these experiments, a decrease of the plastic deformation rate was observed just after the temperature peak. This hardening effect disappears once the fine γ’ precipitates had been dissolved. A mean time for this hyperfine precipitation dissolution could then be highlighted. Based on both simple binary diffusion and complex diffusion analysis, the mean time for the dissolution of the fine γ’ precipitates is analyzed and compared to the experimental ones. It is shown that considering only a simple binary diffusion is not sufficient and it should be considered a more complex diffusive analysis involving additional interplays.

The influence of topologically close packed-phase (TCP-phase) precipitation on the γ/γ′ microstructure evolution of a single crystal superalloy has been studied. Four representative configurations of needle-shaped μ-phase particles observed in the MC2 alloy after creep deformation at 1050 °C/160 MPa have been selected.

Finite element modeling was performed on the selected configurations using a crystal plasticity framework and a viscoplastic approach.

The local calculated stress/strain fields in the vicinity of TCP-phase precipitates, especially stress concentration, allow an interpretation of the observed microstructural evolutions (γ′-precipitate orientation and thickness).

Moreover, our numerical simulation brings a fruitful contribution to the understanding of the phenomenon often observed beyond needle-like μ-phase: the formation of a distorted γ/γ′ microstructure in lieu of the expected γ/γ′-rafted structure.

A novel technique, combining on the one hand creep-fatigue tests with an overheating and creep tests with thermal cycling in the other hand, performed on γ/γ′ nickel base single crystal superalloy MC2 have led to an increased understanding of fine γ′ precipitation and its strengthening effect.

Both creep and creep-fatigue tests were conducted at 1050 °C with 1200 °C overheating for creep-fatigue experiments and with repeated overheatings at 1100 °C and 1150 °C for creep.

The resulting microstructures of these experiments were examined using both scanning electron microscopy (SEM) and transmission electron microscopy (TEM). It appears, both on creep or creep-fatigue, once an overheating is experienced a fine γ′ precipitation occurs in γ matrix. These precipitates seem to have a transient strengthening effect on the mechanical properties. For the creep-fatigue experiments a decrease of the plastic strain rate was measured at once after the temperature peak. In the case of the creep tests under thermal cycling, no extra deformation induced by the overheating at 1100 °C was recorded. However, overheatings at 1150 °C lead to a plastic strain jump which progressively decreases upon thermal cycling, due to the formation of fine γ′ precipitates. Furthermore, the γ′ fine particles seem to have a hardening effect that vanishes once they dissolve.