Negative Creep Research Articles

Negative Creep of Single Crystals of Nickel–Based Superalloys

Negative Creep of Single Crystals of Nickel–Based Superalloys

Effect of temperature on ferroelastic and creep behavior of LaCoO3

The study investigates the time-dependent deformation of LaCoO3 under constant uniaxial compressive stresses at various temperatures ranging from room temperature to 880 °C. Through the acquisition of stress-strain curves at different temperatures, it has been observed that LaCoO3 exhibits non-linear ferroelastic behavior. The stiffness of LaCoO3 increases with temperature, up to 600 °C, after which it starts to decrease at higher temperatures. Furthermore, negative creep occurs at lower temperatures, whereas positive creep is observed at temperatures exceeding 600 °C. This can be attributed to transitioning from a ferroelastic creep at low temperatures to a combination of ferroelastic and high-temperature conventional creep at temperatures above 600 °C. The magnitude of both negative and positive creep is proportional to the temperature. The structural stability of LaCoO3 under creep loading at all temperatures has been assessed by comparing pre-test and post-test X-ray diffraction analyses, which showed the texture formation after testing.

Characteristics of negative creep aging and its microstructure-oriented tensile behavior

UNS S17400 steel was creep-aged under a constant stress of 300 MPa at 480 °C and 600 °C for 1, 3, and 5 h, and its microstructural phase evolution was investigated. During the initial creep aging at 480 °C for 15 min, negative creep strain occurred because of the stress-assisted precipitation, which resulted in Cu-rich precipitates impeding the movement of dislocations. By contrast, the sample creep-aged at 600 °C had a typical creep-strain curve comprising a primary creep stage and secondary steady-state stage. The creep stress accelerated the growth of Cu-rich precipitates and austenite γ phase reversion, which were clearly observed in samples creep-aged at 600 °C. The reverted γ phase formed due to the stress-assisted aging at 480 °C for 3 h, as well as at 600 °C due to the elevated temperature aging. The samples with the longer creep aging times decreased in tensile yield strength but increased in strain hardening rate. Strain hardening after strain softening was observed in the sample creep-aged at 600 °C for 5 h, which had the highest strain hardening rate. Strain hardening was attributed to the dislocations becoming entangled with nanoscale Cu-rich precipitates, the formation of microtwins, and the presence of deformation-induced martensite.

Effect of creep deformation on the microstructure evolution of Inconel 625 nickel-based superalloy additively manufactured by laser powder bed fusion

The microstructure evolution of Inconel 625 additively manufactured by laser powder bed fusion during creep tests at the temperature range 600–800 °C and under a constant stress of 100 MPa was studied using scanning and transmission electron microscopy, X-ray diffraction and dilatometry. Before creep tests, the samples were stress relieved at 980 °C for 1 h and the initial as-built microstructure was preserved. The results show that the cellular microstructure of the Inconel 625 LPBF is stable even after 2000 h of creep at 600 °C. The negative creep strain phenomenon was revealed at 600 °C, which was associated with the intense precipitation of the γʺ phase along the cell boundaries and in their interior. XRD, dilatometry and TEM studies revealed that the negative strain is caused by a precipitation-assisted stress-relaxation process enhanced by rearrangement of a dislocation substructure. In the samples creep tested at the temperature range 700–800 °C, numerous plate-like particles of the δ phase precipitated inside of grains as well as coarse δ, Laves phase, M6C and M23C6 particles at the grain boundaries were present. Based on the microstructural analysis of the samples from the interrupted creep test at 700 °C and 750 °C it was concluded that the creep deformation in the secondary stage is controlled by the thermally activated dislocation movement and its effective hindering, mainly by the plate-like δ phase precipitates densely distributed inside the grains. In addition, as a consequence of the diffusion of vacancies, the formation of cavities along grain boundaries occurs. The analysis of the sample creep ruptured at 800 °C revealed that the formation of microcracks at the grain boundaries and the intergranular fracture mode in the tertiary creep of Inconel 625 LPBF is controlled mainly by the diffusion mechanism.

A viscoelastic-viscoplastic constitutive model for high-temperature response of an advanced steel verified by biaxial measurement experiments

This paper presents a viscoelastic-viscoplastic constitutive model for representing different aspects of the high-temperature deformation response of advanced martensitic steel. The model decomposes the strain into three components of elastic, viscoelastic, and viscoplastic. The elastic behaviour is represented by Hooke's law; 2 K-Voigt models in series are used for the viscoelastic response, and a variant of the two back-stress terms Chaboche model is employed for the viscoplastic part. The effectiveness of the proposed model has been examined for representing the deformation behaviour of a 10%Cr martensitic steel at 600 °C. It has been shown that the developed model provides a sufficiently accurate description of i) constant-load creep after various prior loadings, ii) constant-strain stress-relaxation, iii) anelastic recovery, and iv) negative creep behaviour of the 10%Cr steel. The model results are compared with those from a three back-stress terms Chaboche viscoplastic model to indicate the importance of considering the viscoelastic component. Furthermore, observations from biaxial measurements of axial and radial deformation for a uniaxially loaded testpiece were used to demonstrate the necessity of considering the viscoelastic contribution for accurately representing the high-temperature deformation response of steels.

Creep adjustment of strain gauges based on granular NiCr-carbon thin films

Abstract. An important property of high-precision mechanical sensors such as force transducers or torque sensors is the so-called creep error. It is defined as the signal deviation over time at a constant load. Since this signal deviation results in a reduced accuracy of the sensor, it is beneficial to minimize the creep error. Many of these sensors consist of a metallic spring element and strain gauges. In order to realize a sensor with a creep error of almost zero, it is necessary to compensate for the creep behavior of the metallic spring element. This can be achieved by creep adjustment of the used strain gauges. Unlike standard metal foil strain gauges with a gauge factor of 2, a type of strain gauges based on sputter-deposited NiCr-carbon thin films on polymer substrates offers the advantage of an improved gauge factor of about 10. However, for this type of strain gauge, creep adjustment by customary methods is not possible. In order to remedy this disadvantage, a thorough creep analysis is carried out. Five major influences on the creep error of force transducers equipped with NiCr-carbon thin-film strain gauges are examined, namely, the material creep of the metallic spring element (1), the creep (relaxation) of the polymer substrate (2), the composition of the thin film (3), the strain transfer to the thin film (4), and the kind of strain field on the surface of the transducer (5). Consequently, we present two applicable methods for creep adjustment of NiCr-carbon thin- film strain gauges. The first method addresses the intrinsic creep behavior of the thin film by a modification of the film composition. With increasing Cr content (at the expense of Ni, the intrinsic negative creep error can be shifted towards zero. The second method is not based on the thin film itself but rather on a modification of the strain transfer from the polyimide carrier to the thin film. This is achieved by controlled cutting of well-defined deep trenches into the polymer substrate via a picosecond laser.

Micro-plasticity in a fragile model binary glass

Atomistic deformation simulations in the nominally elastic regime are performed for a model binary glass with strain rates as low as 104/s (corresponding to 0.01 shear strain per 1 µs). A strain rate dependent elastic softening due to a micro-plasticity is observed, which is mediated by thermally-activated localized structural transformations (LSEs). A closer inspection of the atomic-scale structure indicates the material response is distinctly different for two types of local atomic environments. A system spanning iscosahedrally coordinated substructure responds purely elastically, whereas the remaining substructure admits both elastic and microplastic evolution. This leads to a heterogeneous internal stress distribution which, upon unloading, results in negative creep and complete residual-strain recovery. A detailed structural analysis in terms of local stress, atomic displacement, and SU(2) local bonding topology shows such microscopic processes can result in large changes in local stress and are more likely to occur in geometrically frustrated regions characterized by higher free volume and softer elastic stiffness. The thermally-activated LSE activity also mediates structural relaxation, and in this way should be distinguished from stress-driven shear transformation activity which only rejuvenates glass structure. The frequency of LSE activity, and therefore the amount of micro-plasticity, is found to be related to the degree to which the glassy state is relaxed. These insights shed atomistic light onto the structural origins that may govern recent experimental observations of significant structural evolution in response to elastic loading protocols.

The influence of Cr, Al, Co, Fe and C on negative creep of Waspaloy

Abstract Negative creep using precision dilatation experiments is investigated on a broad variety of single, dual and multiphase nickel-based superalloys. Pure nickel and dilute binary nickel-based alloys show no signs of negative creep. However, with higher contents of Cr and Al and in highly alloyed ternary and multicomponent nickel-based alloys negative creep is observed. Short range ordering of Cr and/ or Al are identified to cause negative creep at 550 °C. Carbon additions leading to retarded carbide precipitation or transformation can enhance negative creep.

Room Temperature Ferroelastic Creep Behavior of Porous (La0.6Sr0.4)0.95Co0.2Fe0.8O3-δ

The time-dependent deformation of porous (La0.6Sr0.4)0.95Co0.2Fe0.8O3-δ (LSCF) under constant uniaxial compressive stress at room temperature has been studied. Both axial and lateral stress–strain deformation curves clearly show the non-linear ferroelastic behavior of LSCF perovskite during compression. The ferroelastic characteristics of deformation curves such as coercive stress and apparent loading moduli decrease when the porosity of the samples increases. Ferroelastic creep deformations at applied stresses of 25 and 50 MPa demonstrate that stress and porosity are influencing factors on creep deformation, which increases with increasing stress and porosity. A negative creep or axial expansion and lateral contraction were observed in the sample with 35% porosity under 50-MPa constant compression stress.

Effect of prior deformation on the subsequent creep and anelastic recovery behaviour of an advanced martensitic steel: Unified constitutive modelling

This paper presents an elastic-viscoplastic constitutive model formulation for the representation of different aspects of high-temperature deformation behaviour of an advanced martensitic steel under various loading conditions. The model is a variant of the well-known Chaboche constitutive model and uses a bi-term power-law equation for describing the stress dependency of the viscoplastic strain rate. Isotropic and kinematic hardening/softening considerations have been incorporated through the employment of drag-stress and back-stress concepts. The evolution equations for drag-stress and back-stress consider contributions from strain hardening, dynamic strain softening, and static recovery. The effectiveness of the model formulation has been examined for the representation of the deformation behaviour of a 10%Cr martensitic steel at 600 °C. It has been demonstrated that the developed model could provide a fairly accurate description for i) constant-load creep, ii) constant-strain stress-relaxation, iii) anelastic recovery, and iv) negative creep behaviour of the alloy. More importantly, evidence on the capability of the model for taking into consideration the effect of prior-loading on the subsequent viscoplastic response has been presented.

Investigation of chaotic instabilities in railway wheel squeal

The occurrence of chaotic motion in a railway instability phenomenon known as wheel squeal is investigated. The analysis is motivated and applied to predicting the large amplitude friction excited oscillations of the coupled wheel and rail motion. The equations of motion reduce to two autonomous coupled nonlinear second-order systems. Instabilities of the wheel and rail motions are shown to be due to the friction coupling which at low amplitudes causes limit cycle behaviour via a Hopf bifurcation. When the amplitude grows large enough, full nonlinear creep oscillations are shown to occur causing oscillations about positive and negative sliding conditions. Chaos is shown to occur when the motion meanders and jumps between large positive and negative creep and is characterised by a Poincare map with fractal nature. The route to chaos is shown to be via quasiperiodicity. Based on this insight, necessary analytical conditions for wheel squeal chaos are developed and verified using numerical simulations over a range of angles of attack and wheel/rail contact angles. Conditions under which chaotic instability is more likely to occur are identified and discussed, including mode coupling and parametric excitation. The results may describe why some very loud occurrences of wheel squeal are not characterised by a pure tone.

Piezoelectric creep in LiNbO3, PMN-PT and PZT-5A at low temperatures

Creep and hysteresis were directly measured for shear displacements of three widely used piezoelectric materials: 41° X-cut lithium niobate (LiNbO3), single crystal lead magnesium niobate-lead titanate (PMN-PT), and ceramic lead zirconium titanate (PZT-5A). Measurements were made at temperatures between 0.1 K and 310 K and at voltages up to 150 V. No creep or hysteresis was seen for the single domain lithium niobate transducer. PMN-PT exhibited large creep and hysteresis with a strong temperature dependence even at temperatures as low as 10 K. The temperature dependence was complicated and included an unusual region of negative creep around 250 K. The ceramic PZT-5A had significant creep near room temperature, which disappeared below about 35 K. The widths of the measured hysteresis loops mirrored the magnitudes of the creep that produces the hysteresis. We discuss the behavior of the three materials in terms of intrinsic and extrinsic mechanisms of piezoelectricity. Our results provide guidance in selecting materials for piezoelectric actuators for precise positioning applications like scanning tunneling microscopy. Although it is seldom used in actuator stacks, lithium niobate is the best choice for many cryogenic applications.

Influence of Stress on Creep Behavior of Ni60Zr40 Glass-Reinforced Ni Nanocomposite Investigated by Atomistic Simulations

In this present study, molecular dynamics simulations of creep deformation at 1200 K temperature and different stresses have been performed to study the influence of stress on the creep behavior of Ni60Zr40 glass-reinforced nanocrystalline (NC) Ni nanocomposite using embedded atom method potential. Adaptive common neighbor analysis, centro-symmetry parameter estimation, Voronoi polyhedra, atomic trajectory and radial distribution functions are implemented to present structural evolution during creep process, thereby providing an insight into the underlying mechanism. The specimen is observed to undergo substantial amorphization with the progress of creep deformation owing to stress-induced diffusion of Zr atoms to NC Ni through the Ni60Zr40 glass–NC Ni interface and thickening of grain boundaries, which eventually causes a negative creep phenomenon at the later stage of tertiary creep regime. Calculated stress exponent for Ni60Zr40 glass-reinforced nanocrystalline (NC) Ni nanocomposite is equal to 0.64.

Negative creep of soils

After unloading, the deformation of soils cannot be stable immediately, but continues to expand over time even under constant pressure. In this paper, the expansive deformation over time when effective stress is kept constant is defined as the negative creep, while the compressive creep is described as the positive creep. The division between positive creep and negative creep is named the stable normal compression line (SNCL), on which the stress–strain behaviour of the soil is time-independent. Based on the concept of the SNCL and test results, a new formula for creep is proposed. This formula is simple in form and has less parameters, and both negative creep and positive creep can be well predicted. By incorporating this formula into the current yield function of the unified hardening model, a new time-dependent current yield function is built. Combining the yield function, a flow rule, and transformed stress method, a new three-dimensional time-dependent constitutive model considering both positive and negative creep for clays is derived and presented. The new model is then validated by test results, including multistage loading oedometer tests, triaxial undrained creep tests, and triaxial undrained compression tests at the constant strain rates.

Transient Effects in Creep of Sanicro 25 Austenitic Steel and Their Modelling

Transient effects upon stress changes during creep of the new Sanicro 25 steel were investigated experimentally using the helicoid spring specimen technique. The creep behaviour was found to be qualitatively the same as that observed earlier with the creep-resistant 9% Cr ferritic-martensitic P-91 steel, but the transient strains are considerably smaller. Negative creep rate, which is strain running against the applied stress, was observed with any stress decrease. Parameters for the complex creep model were estimated and model results were compared to the creep rates measured experimentally. The model can be used for the finite element method modelling of the creep and stress relaxation effects in the components made from the Sanicro 25 steel.

Time and frequency dependent mechanical properties of LaCoO3-based perovskites: Internal friction and negative creep

The internal friction and creep deformation behavior of La0.8Ca0.2CoO3 and pure LaCoO3 mixed ionic electronic conducting perovskite ceramics have been studied by Dynamic Mechanical Analysis and uniaxial compression under constant applied load, respectively. It was found that both the internal friction and creep strain were almost an order of magnitude higher for Ca2+ doped LaCoO3 as compared to pure undoped LaCoO3. The difference in Ca2+ doped LaCoO3 behavior was attributed to the much higher concentration of point defects (e.g., oxygen vacancies) in the structure and their interaction with other mobile defects, such as ferroelastic domain/twin walls, stacking faults, dislocations, etc. Such interactions of numerous point defects with domain walls produce energetic barriers and slow down the movement of ferroelastic domain walls under applied stress. At the same time, the defects' interactions increase the internal friction resulting in a much higher creep strain of La0.8Ca0.2CoO3 as compared to pure LaCoO3, as the creep strain is determined by the distance between the domain wall and its equilibrium position at the onset of the creep process. Therefore, the high friction will result in the larger distance the wall has to move to reach the equilibrium which in turn results in higher creep strain. The expansion of LaCoO3 under constant applied compressive stress, named here as negative creep, was also discovered to occur during room temperature creep experiments.

Time and frequency dependent mechanical properties of LaCoO3-based perovskites: Neutron diffraction and domain mobility

The study of domain wall movement and texture formation in ferroelastic LaCoO3 perovskite under constant applied compressive stress has been performed using in situ neutron diffraction. It was established that under constant applied compressive stress the domain walls show mobility that may lead both to the shrinkage (creep strain) and to the expansion (negative creep strain) of LaCoO3 perovskite. The domain wall movement and texture formation can be explained by the availability, mobility, and interaction of twins, stacking faults, antiphase boundaries, dislocations, and point defects, such as oxygen vacancies and their complexes as well as impurity atoms. The equation of motion was used to describe the possible mechanisms of domain wall movement under applied stress, and it was determined that the available solutions of this equation allow both for the shrinkage (creep strain) and for the expansion (negative creep strain) of LaCoO3 perovskite to occur.

Study of precipitation-assisted stress relaxation and creep behavior during the ageing of a nickel-iron superalloy

To study the stress relaxation and creep behavior of a nickel-iron base superalloy during the ageing process, solution annealed microstructures were subjected to loading experiments at various temperatures. Neutron diffraction (ND) measurements were carried out during the loading process to record the elastic lattice strain response of the γ, γ″ and γ′ phases. The results show that over time, increased length contraction occurred at all three temperatures and the sample tested at 720 °C experienced the most significant shrinkage. During the precipitation of the γ″ phase, the chemical composition of the γ matrix will change as the niobium atoms migrate to the form γ″ precipitates, which directly contributes to a change in the lattice parameter of the matrix and governs the samples' volume shrinkage. The creep strain at 720 °C was positive, while negative creep could be seen at 500 °C and 620 °C. The observed negative creep at 500 °C and 620 °C was caused by the samples' shrinkage, and the creep strain at 720 °C was positive because creep plastic strain is relatively large and thus dominates the measured creep deformation. The stress relaxation results exhibited a significant increase with the increase in test duration at 500 °C, 620 °C and experienced a normal decrease at 720 °C. Stress increase during the relaxation tests is a manifestation of the phenomenon of “negative creep”. The precipitation induced volume shrinkage was found to be the key reason for the observed negative creep and abnormal stress relaxation.

Micromechanics of primary creep in Ni base superalloys

The initial stages of creep in nickel base superalloy deserve a special attention since they prevail in most of the service live of critical jet engine components. In nickel base superalloys, a very sharp minimum in creep rate is observed at strains less than 0.5% in a wide range of temperatures: the lower the applied stress the steeper the minimum, often referred to as incubation period. In this paper, the primary creep stage of Ni superalloy is investigated using 3D discrete dislocation dynamics modeling. The simulated volume corresponds to a 3D periodic cell of the cubic arrangement of γ−γ′ NiAl loaded along the (001) direction. Misfit stresses induced by the lattice mismatch (δ = -3.10−3) between the precipitate and the matrix are taken into account through a coupling of the dislocation dynamics code with a finite element code. Frank-Read sources are positioned in the horizontal channel. It is shown that most of the dislocations propagate in the horizontal channels by repeated cross-slip on activated {111} glide planes and a few invade the vertical channels. This behavior is rationalized by the model. In the γ-γ′ interfaces, the zigzagging lines of dislocations straighten out into [100] and [010] directions leading to a dislocation microstructure similar to the ideal misfit dislocation network needed to compensate the lattice mismatch. Calculations of internal stresses in the channels show that this dislocation microstructure induces biaxial planar stresses in the horizontal γ channels leading to an elastic contraction of the sample along the loading direction. Three-dimensional DDD simulations show that the plastic strain induced, in the loading direction, by the movement and multiplication of dislocations is less important than the elastic relaxation it produces along that same direction. Hence, for very low applied tensile stresses, Ni superalloys display an abnormal behavior often referred to as negative creep that can be evidenced experimentally, even in polycrystalline materials. This last observation clearly implies that the first active batches of dislocations, during creep, or static high temperature ageing are mobilized to cancel out the numerous and pervading internal elastic strain fields generated within the crystals by the γ’ precipitates due to their misfit with the γ matrix.

Modeling of creep and stress relaxation of the nickel‐base alloy NiCr20TiAl at isothermal and non‐isothermal loading conditions

AbstractThe design and dimensioning of new as well as the assessment of operating high‐temperature components in service require a precise prediction of creep and stress relaxation. The increasing share of renewable energies forces fossil‐fired power plants for increasing numbers of start‐ups and shut‐downs. Consequently, transient loading conditions need to be taken into account. In order to meet this demand, non‐isothermal creep equations are necessary, which enables a consistent prediction of creep strain and stress relaxation in a wide range of temperatures and stresses. In this paper, an approach for the visco‐plastic modeling of creep and stress relaxation for non‐isothermal loading conditions is presented. The strain portions creep, “negative creep” and initial plasticity, occurring at elevated temperatures are described by temperature‐dependent phenomenological equations. Within this paper, the adjustment of the parameters is based on a wide database of hot tensile tests, creep and annealing experiments. The nickel‐base alloy NiCr20TiAl has been examined in a temperature range from 450 °C to 650 °C. The developed material models have been successfully validated with isothermal and non‐isothermal relaxation experiments. Further, the recalculation of a staged relaxation test demonstrates the capability of the defined material laws in a wide stress range under isothermal and non‐isothermal loading conditions.