Steady-state Creep Behavior Research Articles

Investigation of three-step heat treatments on the microstructure and steady-state creep behaviors of (TiB + TiC + Y2O3)/α-Ti composite

The microstructure and steady-state creep behaviors of as-cast and heat-treated (TiB + TiC + Y2O3)/α-Ti composites were systematically investigated in this study. The relevant properties of the matrix alloy are also provided for comparative analysis. The matrix alloy exhibits the coarse Widmannstatten structure. After heat treatment, the microstructure of the composite transforms from the basket-weave structure to a trimodal structure with spheroidized TiC and Y2O3 particles and some merged TiB whiskers. Compared to the matrix alloy, the steady-state creep rates of the as-cast and heat-treated composites are decreased by 29% and 40%, respectively. After creep, serious β-Ti dissolution in the matrix alloy and the as-cast composite contributes to the instability of α/β interfaces and precipitated silicides. The morphology of β-Ti phases in the heat-treated composite remains stable during creep and many dislocations are observed inside the secondary α-Ti phases, which is the main reason for the improvement of the creep performance. Extensive dynamic recrystallization occurred during the steady-state creep stage, and the dislocation structure undergoes significant evolution, along with a large number of sub-grains and dislocation walls. The coarse reinforcements play a role in the particle stimulated nucleation, while the small TiC and Y2O3 spherical particles provide little contribution to dynamic recrystallization. Dislocation climbing is the main creep control mechanism, and the creep rate keeps the constant through dislocation rearrangement and dislocation annihilation.

Unravelling the microstructure – indentation creep resistance relationships for friction stir welded modified 9Cr-1Mo steel and LN-type 316 stainless-steel dissimilar joints

In this article, the indentation creep characteristics and the microstructures are assessed for the friction stir welded modified 9Cr-1Mo steel and LN-type 316 SS dissimilar joint. Microstructures are characterized for the post-weld heat treated and indentation crept samples at different conditions with optical microscopy, scanning electron microscope and energy dispersive X-ray spectroscopy. Distinct heat-affected zones were revealed with the refined and reformed martensite (α′) and austenite (γ) structures that formed in view of the distinct thermal conductivity property and the differences in lower critical(Ac1) and upper critical(Ac3) transformation temperatures. The size of prior austenite grain sizes was found to be varied significantly at the different regions. Indentation creep data were acquired in distinct weld zones at 873, 898 and 923 K. Zone-wise indentation depth, steady-state creep behaviour (SSCR) and activation energy ( Q) were evaluated and correlated with the microstructures. The formation of small prior austenitic grain (PAG) structures and the grain boundary vacancies has led to maximum creep deformation (86.83%) at the heat affected zone of the modified 9Cr-1Mo steel. Furthermore, the reduction in lath structures and the formation of tiny α′ with soft substructures have lowered the hardness values to around 210 ± 21 HV, which is 20 HV less than the post weld heat treated sample. In the stir zone, the presence of dynamically refined and rich γ along with fine α′ layers has improved the steady-state creep rate of 9.112 E-7, which is less than the modified 9Cr-1Mo steel and the heat affected zone at modified 9Cr-1Mo side. The coarse austenite structures that existed in the LN-type 316 base metal have resisted more creep damage and exhibited high activation energy (i.e. 490 kJ mol−1) than the stir zone and heat affected zone of the LN-type 316 SS.

Impression creep behavior of different zones in friction stir welded ZE41 magnesium-rare earth alloy

The ability of the impression tests to obtain localized creep data is exploited to study the creep behavior of the friction stir welded (FSWelded) joints made on 15 mm thick plates of ZE41 magnesium alloy. The three zones of the FSWelded joint, Nugget zone (NZ), Thermo-Mechanically Affected Zone (TMAZ), and Heat Affected Zone (HAZ), were divided into ten different parts and their local steady-state creep behavior was studied. Impression tests were carried out at stresses of 350, 400, and 450 MPa and temperatures of 513 K, 533 K, and 553 K. Optical and SEM micrographs were used to study the microstructure of various zones of the FSWelded joint both before and after the impression test. Power law was used to obtain the creep exponent (n) and activation energy (Q) for different parts of the weld and the weld zones as a whole. The creep exponent was found to vary from 3.6 to 10.45 and the activation energy from ∼81 kJ/mol to ∼226 kJ/mol. The creep rate was found to vary between the upper and lower surfaces of the weld zones and also among the advancing and retreating sides. The weak zone was found to be temperature-dependent and varied when the temperature or stress changes. Within the parameters studied, the lower part of the TMAZ on the AS showed poor creep resistance at a lower temperature, while the lower part of TMAZ on the RS showed poor creep resistance at higher temperatures. The upper part of the TMAZ on the RS showed better creep resistance throughout the range of temperatures studied. To rationalize the high n and Q values, the threshold stress approach and the Eyring relationship were adopted. Using the threshold approach, creep exponents of 4.87 and 5.17 were obtained for TMAZ and HAZ, respectively. Using Eyring hyperbolic sine relationship, single activation energies of 143.5 kJ/mol and 261.5 kJ/mol were obtained for TMAZ and HAZ, respectively. Based on the obtained n and Q values, it is proposed that two mechanisms, namely climb and cross-slip of dislocations, are operative in the creep of the ZE41 FS weld joint. However, the dominant/rate controlling mechanism could not be arrived at conclusively.

Multi-scale Crystal Viscoplasticity Approach for Estimating Anisotropic Steady-State Creep Properties of Single-Crystal SnAgCu Alloys

Creep can have a significant impact on the reliability of Sn-based solder alloys even at room temperature because of their relatively low melting temperatures. SnAgCu (SAC) solder joints used in electronic packaging typically consist of only a few highly anisotropic grains, which consist of Sn dendrites embedded in a near-eutectic Sn-Ag component. The unique grain structure of each joint leads to stochastic variations in the thermomechanical response of such joint. Therefore, grain-scale testing and modeling are recommended to better characterize the anisotropic behavior and to estimate the influence of stochastic variability of grain structure on the viscoplastic response of the joint. This work aims to investigate the anisotropic steady-state creep behavior of single-crystal SAC solder joints. The orientation-dependent viscoplastic behavior of individual SAC grains is modeled with a multi-scale crystal-viscoplasticity approach for representing the relevant dislocation mechanics. The response predicted by the crystal viscoplasticity model is then captured in an equivalent homogenized continuous-scale constitutive model (Hill-Garofalo formulation).This modeling strategy was implemented in numerical simulations, as an illustrative example, to analyze the behavior of single-grain solder joints subjected to combined steady compression (from heat-sink clamping force) and thermal cyclic loading. The cyclic ratcheting in the presence of the steady compressive force causes: (i) transverse expansion of the solder ball, potentially leading to eventual short circuits; and (ii) cyclic fatigue damage leading to eventual failure of the solder joint. The proposed grain-scale modeling approach is shown to be able to address the stochastic variability of both these damage mechanisms, as a function of grain orientation. The present methodology can be used to predict the realistic behavior of solder joints, based on their microstructure, and provide valuable insights for their reliability analysis.

High-temperature creep behavior and hot-pressing consolidation of NiAl

AbstractThe steady-state creep behavior of NiAl was studied by constant strain-rate tests in the strain-rate regime 1.5 × 10−4≤ ɛ̇ ≤ 1.0 × 10−2s−1.Primary creep of NiAl was investigated at different stresses (10 MPa−40 MPa) in the temperature range from 1200 to 1400°C. The steady-state creep rate was fitted to a temperature-compensated power-law expression ɛ̇ =B(σ/μ)nexp(−Q/RT), from which a stress exponent n≈3.5 and an activation energy Q ≈ 398 kJ/mol were derived, respectively. The obtained activation parameters indicate that dislocation creep dominates the creep behavior of NiAl at temperatures above 1200°C up to 1400°C. The transient creep behavior at 40 MPa could be fitted to a power-law equationε=ε0+btmwithbα σ3:5and 0.52<m<0.68. The creep data of NiAl obtained in this study were utilized for modeling and simulation of the consolidation process of NiAl composites during hot pressing by finite-element analysis.

The effect of aspect ratio on the mechanical behavior of Li metal in solid-state cells

The Li metal anode is necessary for solid-state batteries to dramatically exceed the energy density of state-of-the-art conventional Li-ion batteries. To enable the Li metal anode, the mechanical properties of Li metal under compression in a commercially relevant cell configuration must be determined. This work examines the compression creep behavior of Li metal coupled with a relevant model solid-state electrolyte (Li 6.5 La 3 Ta 0.5 Zr 1.5 O 12 ) and current collector (Ni) as a function of applied stress (1–10 MPa) and Li foil thickness (100–700 μm). At 1 MPa applied stress, the strain rate of all Li foil thicknesses under compression was almost four orders of magnitude lower than what is predicted from tensile creep tests. Steady-state creep behavior was observed for Li foil ≥350 μm at 5 MPa and ≥250 μm at 10 MPa. Conversely, sustained creep deformation was not observed for 100 and 150 μm Li foils at any applied stress. It is suggested that friction at the Li/LLZO and Li/Ni interfaces leads to the formation of hydrostatic stress that controls Li deformation at low aspect ratios. These results have implications for battery pack stack pressure requirements, particularly relating to void formation during stripping and Li metal filament penetration during plating. • Compressive creep measurements of Li metal foils in solid-state cell configuration. • Strain and strain rate decreased with decreasing Li foil thickness. • The strain rate of Li measured in compression was lower than predicted from tension. • Friction at Li interfaces prevents substantial creep deformation for thin Li foils.

Short-Term Creep-Rupture Behaviour of AISI 310S Austenitic Stainless Steel Sheets Manufactured in Salem Steel Plant, a Special Steels Unit of Steel Authority of India Limited, Ministry of Steel, Government of India

The creep behavior of AISI 310S stainless steel taken from SAIL’s Salem stainless steel plant has been investigated by constant load tensile creep test at the temperatures of 973, 1023, and 1073 K and loads of 66.6, 74.8, 86.6, and 94.8 MPa. It exhibits steadystate creep behavior in most test conditions. The double logarithm plot of rupture life and applied stress yielded straight lines at all the three test temperatures indicating that power-law creep due to dislocation climb is the operating mechanism of creep deformation. Linear relationship was obtained for plots of logarithm of rupture life against inverse temperature obeying Arrhenius type of temperature dependence with activation energy of 340 kJ/mol. The stress-rupture data yielded a master curve of Larson-Miller parameter. The plot of Monkman-Grant relationship is typical indicating that rupture is controlled by growth of grain boundary cavities. The metallographic examination of crept samples revealed formation of grain boundary voids and cracks leading to intergranular creep fracture. Deformation twins and carbide precipitates were also observed. Creep-rupture properties are compared with that of AISI 600 ironbased superalloy to analyze quantitatively its behavior

Anisotropic steady-state creep behavior of Single-crystal β-Sn: A continuum constitutive model based on crystal viscoplasticity

Body-center tetragonal (BCT) β-Sn crystals exhibit highly anisotropic properties such as stiffness and thermal expansion, which significantly affect their thermal-mechanical behavior. The homologous temperature of β-Sn is relatively high under common applications due to its low melting point, which renders Sn and Sn-based alloys viscoplastic even at room temperature. The orientation-dependent creep behavior of β-Sn specimens have been previously measured by different research groups. A dislocation mechanics based crystal viscoplasticity model is applied in this study to describe this anisotropic steady-state creep behavior of β-Sn single crystals. The model constants are calibrated with single-crystal creep test results available in the literature. The resulting creep behavior of β-Sn single-crystal is also represented with a homogenized continuum-scale finite element approach based on the use of a combined Hill-Norton approach where the creep anisotropy is represented with Hill's anisotropic potential and the creep flow rule is represented with Norton's power-law model. Estimation of the six Hill's constants for β-Sn requires multiple creep tests under specific stress states, for single crystals along crystal principal directions. In this study, these physical creep tests are replaced with ‘virtual tests’ conducted with the developed dislocation-based crystal-viscoplasticity model. To assess the ability of the Hill-Norton finite element approach to represent dislocation creep, the finite element simulation results are compared with results of: (i) physical tests on single crystal specimens reported in the literature; and (ii) crystal-viscoplasticity modeling along many crystal orientations (beyond the fundamental calibration cases conducted along crystal principal directions). In future studies, this approach will be used for anisotropic finite element modeling of creep in polycrystalline specimens.

Thermomechanical response of an ultrafine-grained nickel-yttrium alloy

Thermomechanical behavior of an ultrafine-grained nickel-yttrium alloy has been investigated through quasi-static (10−4 s−1) and high temperature creep experiments under uniaxial compression along with post-deformed transmission electron microscopy (TEM) characterization. While the alloy possesses a quasi-static flow stress of ~1255 MPa at room temperature, the flow stress drops by about 80% at 873 K. TEM analysis showed negligible average grain growth over the entire temperature range tested. Furthermore, the alloy showed exceptional steady–state creep behavior owing to the relative stability of the grain size and interactions between dislocations/grain boundary and inclusions/dispersoids.

Influence of annealing on the creep behavior of GlidCop Al-15

The steady-state creep behavior of annealed GlidCop Al-15 (100 h, 1273 K) was studied at 973 K and compared to the extruded version. The Rösler-Arzt model applies well to both extruded and annealed alloys, suggesting the major deformation mechanism to be dislocation detachment from particles. However, threshold behavior was also observed at low stresses for both material conditions, which can be phenomenologically described by the threshold stress model. The annealed GlidCop samples exhibited better creep resistance than their extruded counterparts, the reason behind which was carefully examined in terms of the annealing effects on grain size, texture, dislocation density, and particle size and distribution. This investigation reveals that none of the above are the primary factors affecting the difference in the creep behavior of the two forms of GlidCop. Instead, the transformation of Al2O3 particles to 9Al2O3–B2O3 after long-term annealing is considered to be the major cause of the difference in steady-state creep rates, as the resulting less-coherent particle/matrix interface increases the energy required for the dislocation detachment process.

Creep Mechanisms of an Al-Cu-Mg Alloy at the Macro- and Micro-Scale: Effect of the S'/S Precipitate.

A novel methodology combining the macro- and micro-creep techniques was employed to study the effect of S′/S precipitate growth on the creep mechanism of an Al–Cu–Mg alloy. An AA2524 alloy was pre-aged at 180 °C to obtain S′/S precipitates with various sizes. The results showed that the precipitate size increased approximately linearly to ≈32 nm, ≈60 nm, and ≈105 nm after 3 h, 6 h, and 12 h of pre-aging, respectively. The growth of precipitate could significantly shorten the primary creep stage, despite the fact that the steady-state creep behavior was similar to that of the as-received alloy, as revealed by the macro tensile creep tests at 180 °C and 180 MPa. This led to a stress exponent (2.4–2.5) of the Al alloy with various precipitate sizes that was quite close to that of the as-received Al alloy, implying a steady-state creep mechanism dominated by grain boundary sliding and dislocation interactions. Finally, the micro-creep tests showed a minor role of the precipitate size on the steady-state creep mechanism, as evidenced by the similar strain rate sensitivity (0.0169–0.0186), activation volume (≈27 b3), and the results of a detailed transmission electron microscopy analysis of all tested alloys.

Constitutive modelling of transient and steady state creep behaviour of type 316LN austenitic stainless steel

In the present study, sine hyperbolic creep rate law coupled with the evolution of internal stress with time has been employed for modelling transient and steady state creep deformation behaviours of type 316LN austenitic stainless steel (SS). The model predicts the creep strain-time and creep rate-time data appropriately for the stress levels ranging from 120 to 225 MPa at 923 K, with good agreement between experimental and predicted steady state creep rates. At all the stress levels, the predicted internal stress increases with time during transient creep, and it approaches saturation at steady state creep. The predicted increase in internal stress was interrelated to the increase in dislocation density and a decrease in the mean free path during creep deformation. At steady state condition, a decrease in activation volume with an increase in applied stress levels has been observed for the steel. The estimated value of activation volume for the steel demonstrates the dominance of intersection of forest dislocations and non-conservative motion of jogs during transient creep in type 316LN SS. The applicability of the present model has been demonstrated towards the prediction of stress-relaxation behaviour of type 316LN SS based on the power law interrelation between internal stress and applied stress.

A phenomenological understanding of the influence of processing methods on creep of Cu-8Cr-4Nb (GRCop-84)

Steady-state creep behavior of rolled Cu-8Cr-4Nb (GRCop-84) production sheet was systematically studied at temperatures from 673 to 1073 K (0.50–0.79 Tm). Threshold behavior was observed at high temperatures and low stresses which can be phenomenologically described by a threshold stress model. The threshold stress obtained by a non-linear regression method ranges from 0.2 to 0.3 of the Orowan stress, which suggests that dislocations locally climb over particles with an activation energy approximately equal to that of lattice diffusion. Power-law breakdown was observed at low temperatures and high stresses, which can be phenomenologically described by a hyperbolic sine model. A unifying model is proposed to predict the creep properties of both the production sheet and previously-studied extruded material. Generally, GRCop-84 production sheet creeps faster than the extruded form due to the difference in crystallographic texture. No observable effects caused by microstructural differences are noted to influence the steady-state creep behavior of the two differently processed forms of GRCop-84. The post-fracture morphology of the production sheet closely resembles that of the extruded material indicating ductile fracture caused by micro-void coalescence.

Creep analysis of a rotating functionally graded simple blade: steady state analysis

Initial thermo-elastic and steady state creep deformation of a rotating functionally graded simple blade is studied using first-order shear deformation theory. A variable thickness model for cantilever beam has been considered. The blade geometry and loading are defined as functions of length so that one can define his own blade profile and loading using any arbitrary function. The blade is subjected to a transverse distributed load, an inertia body force due to rotation and a distributed temperature field due to a thermal gradient between the tip and the root. All mechanical and thermal properties except Poisson's ratio are assumed to be longitudinally variable based on the volume fraction of reinforcement. The creep behaviour is modelled by Norton's law. Considering creep strains in stress strain relation, Prandtl-Reuss relations, Norton' law and effective stress relation differential equation in term of effective creep strain is established. This differential equation is solved numerically. By effective creep strain, steady state stresses and deflections are obtained. It is concluded that reinforcement particle size and form of distribution of reinforcement has significant effect on the steady state creep behavior of the blade.

Computational modeling of creep in complex plane for reinforced materials

AbstractComputational modeling for predicting the steady state creep behavior is presented in complex plane for reinforced materials by complex variable method. Both the fiber and matrix simultaneously creep at elevated temperatures and loading. We suppose that one dimension of the short fiber is small enough in comparison with the other two (see Fig. 1). In this formulation, plane stress state is used. Finally, displacement rate behaviors are predicted using compatibility, equilibrium, constitutive, and governing equations by complex variable method. One of the considerable applications of the method is in nano-composites analysis in elasticity or plasticity research.

Effect of thermal gradation on steady state creep of functionally graded rotating disc

Abstract The paper presents the steady state creep behavior of isotropic rotating disc made of parabolically varying functionally graded material in the presence of thermal gradient. The creep rates have been obtained for the discs rotating at elevated temperatures. Investigations for disc rotating at uniform temperature from inner to outer radii has been done using von Mises’ yield criterion. Further, work has been extended for discs rotating at parabolically decreasing temperature. The results are exhibited graphically for the said temperature profiles. A small variation is observed for radial and tangential stresses for said thermal gradations. However, in the presence of thermal gradation the strain rates vary significantly as compared to disc at uniform temperature. Thus in functionally graded rotating disc the temperature gradation significantly effect the creep behavior of a rotating disc.

Steady State Creep of Isotropic Rotating Composite Disc Under Thermal Gradation

An attempt has been made to investigate steady state creep behavior of thermally graded isotropic discs rotating at elevated temperatures. For this purpose, composite discs of aluminum matrix reinforced with silicon carbide particulate have been taken. Modeling of stress and strain rate distributions for discs operating under linear thermal gradient has been done using von Mises’ yield criterion and threshold stress-based creep law. Similarly modeling has been done for discs operating under non-linear thermal gradient. The results are compared with the disc having a uniform temperature profile from inner to outer radius and are displayed graphically in designer friendly format for the said temperature profiles. A small variation is observed for radial and tangential stresses for the said thermal gradations. However, the strain rates vary significantly in the presence of thermal gradations as compared to a disc having uniform temperature throughout the radial distance. Thus, it is observed that there is a need to extend the domain of thermal gradation for designing rotating discs.

Creep behavior of the solid acid fuel cell material CsHSO4

Solid acid materials have recently shown great promise as solid-state electrolytes in intermediate temperature fuel cells. However, little is currently known about their mechanical properties, some of which could severely limit their application. In this study, the steady state creep behavior of the prototypical solid acid, CsHSO4, is characterized. In its highly conductive superprotonic state (>141°C), the material creeps at very high rates, as high as 10−2s−1, at stresses in the application design range of only a few MPa. The steady state creep stress exponent n≅3.6 and activation energy Q≅1.02eV=98.8kJ/mol are consistent with a dislocation-based creep mechanism.

Modified Constitutive Creep Laws With Micromechanical Modeling of Pb-Free Solder Alloys

This paper explicitly establishes a modified creep model of a Sn–3.8Ag–0.7Cu alloy using a physical-based micromechanical modeling technique. Through experimentation and reformulation, steady-state creep behavior is analyzed with minimum strain rates for different temperatures 35 °C, 80 °C, and 125 °C. The new modified physical creep model is proposed, by understanding the respective precipitate strengthened deformation mechanism, seeing the dependency of the activation energy over the temperature along with stress and, finally, by integrating the subgrain-size dependency λss. The new model is found to accurately model the creep behavior of lead-free solder alloy by combining the physical state variables. The features of the creep model can be explored further by changing the physical variable such as subgrain size to establish a structure–property relationship for a better solder joint reliability performance.

Modeling the Effect of Thermal Gradation on Steady-State Creep Behavior of Isotropic Rotating Disc Made of Functionally Graded Material

Modeling the Effect of Thermal Gradation on Steady-State Creep Behavior of Isotropic Rotating Disc Made of Functionally Graded Material