Steady-state Creep Deformation Research Articles

An isochronous stress ratio logarithmic strain curve based clay creep model considering the effects of hardening and damage

Creep is one of the typical mechanical properties of clay, and studying the creep mechanical properties of clay is of great significance to construction projects in clay sites. This study conducted creep tests on Chengdu clay and found that the soil mass underwent elastic deformation, decay creep deformation, steady-state creep deformation, and accelerated creep deformation. The isochronous stress ratio-logarithmic strain curves and their mathematical models were proposed to thoroughly analyze clay creep mechanical properties. Creep automatic feature points, such as linear elastic extreme point, initial yield point, long-term strength point, and plastic point, were identified on the curve. Considering the hardening and damage effects during creep loading, linear elastic and viscoelastic elements considering the time-dependent damage, a viscoplastic element considering the load hardening effect, and viscoplastic and plastic elements considering the load damage effect were established based on the element model and the Riemann–Liouville fractional derivative. Based on the mechanical properties of the whole clay creep process, the creep mechanical feature points, and the established element model, a clay creep model was proposed considering the hardening and damage effects. The rationality and regularity of the creep model were verified using the creep test data. This research accurately revealed the creep mechanical properties of clay and facilitated soil deformation prediction, thus providing technical guidance and references for construction projects in clay sites.

Dislocation structures after creep in an Al-3.85 %Mg alloy studied using EBSD-KAM technique

The electron backscatter diffraction (EBSD) technique is used to investigate the dislocation structures formed after steady-state creep deformation of an Al-3.85%Mg alloy. This material is crept at two different stress levels, corresponding to the so-called power-law and power-law breakdown regimes. The results show that, regardless of the creep stress level, the strain tends to localize, leading to the formation of intragranular bands. The thickness of such bands is larger when the material is tested at loads corresponding to the power-law breakdown. This suggests enhanced diffusion by dislocation pipes.

High temperature creep deformation of nanocrystalline diamond films

Abstract Diamond displays a combination of unique properties, including the highest hardness among materials, chemical inertness and high thermal conductivity. Therefore, nanocrystalline diamond films offer a huge potential for industrial applications. In fine-grained ceramics as well as metallic materials, high temperature creep deformation is dominated by grain-boundary-deformation mechanisms that become increasingly important with decreasing grain size. In this work we demonstrate that it is possible to inelastically deform nanocrystalline diamond films at elevated temperatures and stresses that are significantly lower than those reported for single-crystal diamond. The initial, isothermal, transient creep flow exhibits a logarithmic character, typical of creep in general. The isothermal steady state creep deformation, which follows transient creep, is analyzed using a physics-based model for grain boundary sliding rate controlled flow.

Nonlinear Elasto-Visco-Plastic Creep Behavior and New Creep Damage Model of Dolomitic Limestone Subjected to Cyclic Incremental Loading and Unloading

For many rock engineering projects, the stress of surrounding rocks is constantly increasing and decreasing during excavating progress and the long-term operation stage. Herein, the triaxial creep behavior of dolomitic limestone subjected to cyclic incremental loading and unloading was probed using an advanced rock mechanics testing system (i.e., MTS815.04). Then, the instantaneous elastic strain, instantaneous plastic strain, visco-elastic strain, and visco-plastic strain components were separated from the total strain curve, and evolutions of these different types of strain with deviatoric stress increment were analyzed. Furthermore, a damage variable considering the proportion of irrecoverable plastic strain to the total strain was introduced, and a new nonlinear multi-element creep model was established by connecting the newly proposed damage viscous body in series with the Hookean substance, St. Venant body, and Kelvin element. The parameters of this new model were analyzed. The findings are listed as follows: (1) When the deviatoric stress is not more than 75% of the compressive strength, only instantaneous deformation, transient creep, and steady-state creep deformation occur, rock deformation is mainly characterized by the instantaneous strain, whereas the irrecoverable instantaneous plastic strain accounts for 38.02–60.27% of the total instantaneous strain; (2) Greater deviatoric stress corresponds to more obvious creep deformation. The visco-elastic strain increases linearly with the increase of deviatoric stress, especially the irrecoverable visco-plastic strain increases exponentially with deviatoric stress increment, and finally leads to accelerated creep and delayed failure of the sample; (3) Based on the experimental data, the proposed nonlinear creep model is verified to describe the full creep stage perfectly, particularly the tertiary creep stage. These results could deepen our understanding of the elasto-visco-plastic deformation behavior of dolomitic limestone and have theoretical and practical significance for the safe excavation and long-term stability of underground rock engineering.

Effect of indentation depth in impression creep test: conversion relationships and correction functions

ABSTRACT The impression creep test method has been used extensively to determine the in-service creep properties of power plant components from a small volume of material. In the standardisation of the impression creep test, the determination of a maximum ‘allowable’ indentation depth is an important issue. This paper presents the results of finite element analyses obtained using a simplified method based on steady-state creep, for evaluating the variation of conversion factors with indentation depth. The results obtained show that the indentation depth has a significant influence on the conversion parameters and the steady-state creep deformation rate when the indentation depth is sufficiently large. On this basis, recommendation on practical application of these conversion relationships was made to the users, and empirical formulas were provided for the possible corrections of the conversion factors. The effect of plastic zone due to initial loading on the subsequent creep was found to be insignificant.

Elevated-temperature Deformation Mechanisms in a CrMnFeCoNi High-Entropy Alloy

Stress reduction creep experiments were performed on a CrMnFeCoNi high-entropy alloy at 1073 K to characterize the steady-state and transient creep properties of this material. From measurements of constant-structure creep, the activation area for deformation of CrMnFeCoNi was determined to be ∼100 b2 and to decrease with increasing applied stress, indicating the presence of both concentrated solid solution and forest dislocation control of high temperature plastic deformation. With the aid of a recent solid solution theory for high entropy alloys, quantitative separation of the two mechanisms was carried out using a Haasen plot and the results show that creep in CrMnFeCoNi relies heavily on thermal activation with the majority of creep strength coming from solid solution hardening, especially at low applied stresses. The overall analysis conducted in this study reveals that steady-state creep deformation of CrMnFeCoNi at 1073 K can be adequately described by existing concentrated solid solution hardening models and forest dislocation hardening models. This observation suggests it may be possible to develop a unified treatment of the dislocation glide kinetics for this alloy from cryogenic to elevated temperatures.

Indenter misalignment in impression creep test: Uncertainty, correction and recommendation

The impression creep test (ICT) method, as a miniature specimen test technique, has been used extensively to determine the in-service creep properties of power plant components. However, the experiment results of the ICT can be affected by some uncertainties associated with the inaccuracies of measurement, which have not been studied before. This paper presents some results of finite element analyses, to evaluate the effect of indenter misalignment on the results of the ICT, such as the steady-state creep deformation rate and the conversion parameters. The results obtained have shown that the angular misalignments of the indenter around horizontal directions have a relatively significant influence on the conversion parameters, and the misalignment around vertical direction has a much less significant effect. Empirical formulas were developed for the possible correction of the conversion factors. Finally, some recommendations on the control of the indenter and specimen alignment were given.

Investigation of tensile creep behavior of Mg–Gd–Y–Zr alloy based on creep constitutive model

The tensile creep behavior of as-extruded and T6 treated Mg–8Gd–3Y–0.3Zr (GW83) alloy was estimated under temperature at 170–200 °C and stress at 40–70 MPa. The results showed that the primary creep strain and steady state creep rate increased, while the duration of steady state creep decreased with increasing temperature and stress. The primary creep constitutive model of GW83 alloy kept an Andrade power law ε = βt k with k value of 0.24–0.6 for as-extruded alloy and 0.13–0.49 for T6 alloy, respectively. The steady state creep plastic deformation of as-extruded and T6 state alloys can be expressed by Arrhenius constitutive equations with stress exponents 5.6–5.9 and 8.9–9.8, creep activity energy 124.9–135.6 kJ/mol and 152.2–195.8 kJ/mol, respectively. The tensile creep resistance of GW83 alloy improved significantly by T6 heat treatment, the effect of temperature on steady state creep rate was relatively moderate, and the tensile creep plastic deformation of GW83 alloy mainly was controlled by applied stress. The steady state creep deformation mechanism of as-extruded GW83 alloy was regulated by Mg self-diffusion conducted by dislocation climb before heat treatment, and then transformed to dislocation cross-slip after T6 treated. The recrystallization and texture evolution of (10) , (10) played a non-ignorable effect on the tensile creep deformation. The creep rupture life can be predicted by steady state creep rate that will be controlled by temperature under low and intermediate stress and by stress under larger applied stress, respectively. The creep fracture surfaces with coarse dimples and tear ridges presented as ductile transgranular fracture features with the secondary cracks occurred.

Influence of varying nitrogen on creep deformation behaviour of 316LN austenitic stainless steel in the framework of the state-variable approach

Abstract Primary and steady-state creep deformation of 316LN stainless steel with four different nitrogen weight percent (0.07, 0.11, 0.14, and 0.22% N) have been examined in the framework of internal stress based kinetic creep law. The interrelationship between activation area or activation volume and effective stress has been employed in the present model, rather than the applied stress dependency on these thermodynamic quantities. The model predicted the decrease in obstacle spacing and the increase in internal stress with nitrogen at all the applied stress levels. Across the nitrogen content, the evaluated activation volume ranging from 400 to 900 b3 suggested the dominance of forest dislocation intersections coupled with the non-conservative motion of jogged dislocations during steady-state creep. The rate constant parameter of the model associated with the dynamic recovery exhibited a decreasing trend with nitrogen. The variations in the strength enhanced activation volume and length of the dislocation segment against the applied stress/yield strength exhibited the unified power law relationships, irrespective of nitrogen content. The model appropriately predicted the creep strain/rate vs. time curves and steady-state creep rate vs. internal stress and effective stress quantities. By incorporating the damage term into the creep rate equation, the developed model is extended for the prediction of entire creep strain-time curves.

Effect of primary creep on the relationship between indentation and uniaxial creep: A theoretical model

In this work, a theoretical model is developed to address the effect of primary creep on the relationship between indentation and uniaxial creep tests. By considering the expansion of a spherical cavity in the materials following the primary creeping law, a general expression of the conversion factor is deduced during the primary creep stage. For creep tests with spherical and flat punch indenters, a closed-form formula is specified for the conversion factor that is determined by the stress exponent and hardening exponent. By further considering the difference of the critical time at the onset of steady-state creep deformation between uniaxial and indentation creep tests, it becomes available to convert the indentation creep data into uniaxial creep results during the steady-state creep stage. The rationality and accuracy of the proposed model are verified by comparing with the experimental data of Sn37Pb solder, AZ31 Mg alloy and Succinonitrile. Furthermore, the comparison with previous theoretical models indicates that the ignoring of primary creep effect could lead to the deviation of converted indentation creep data from uniaxial creep results.

An experimental and modeling investigation of tensile creep resistance of a stable nanocrystalline alloy

Nanocrystalline (NC) materials possess excellent room temperature properties, such as high strength, wear resistance, and toughness as compared to their coarse-grained counterparts. However, due to the excess free energy, NC microstructures are unstable at higher temperatures. Significant grain growth is observed already at moderately low temperatures, limiting the broader applicability of NC materials. Here, we present a design approach that leads to a significant improvement in the high temperature tensile creep resistance (up to 0.64 of the melting temperature) of a NC Cu-Ta alloy. The design approach involves alloying of pure elements to create a distribution of nanometer sized solute clusters within the grains and along the grain boundaries. We demonstrate that the addition of Ta nanoclusters inhibits the migration of grain boundaries at high temperatures and reduces the dislocation motion. This leads to a highly unusual tensile creep behavior, including the absence of any appreciable steady-state creep deformation normally observed in almost all materials. This design strategy can be readily scaled-up for bulk manufacturing of creep-resistant NC parts and transferred to other multicomponent systems such as Ni-based alloys.

Study of accelerated shear creep behavior and fracture process of micro-scale ball grid array (BGA) structure Cu/Sn–3.0Ag–0.5Cu/Cu joints under coupled electro-thermo-mechanical loads

Shear creep deformation and fracture behavior of micro-scale ball grid array (BGA) structure Cu/Sn–3.0Ag–0.5Cu/Cu joints under electro-thermo-mechanical coupled loads with high-density current stressing (6.0 × 103 A/cm2) at different temperatures (40, 60, 80, 100 and 120 °C) and various shear stress levels (12.5, 15, 17.5, 20 and 22.5 MPa) were studied intensively. The results show that electric current stressing can significantly accelerate the creep deformation and fracture process of BGA solder joints in terms of increasing steady-state creep stain rate and shortening creep lifetime of the joints. Garofalo hyperbolic-sine function has shown to be a suitable creep constitutive equation, which can be well used to formulate the creep deformation behavior of micro-scale Cu/Sn–3.0Ag–0.5Cu/Cu joints under electro-thermo-mechanical coupled loads, and the equation has the increased stress exponent of 8.6 and creep activation energy of 90.8 kJ/mol, respectively. Combined theoretical analysis and experimental characterization suggest that electric current stressing leads to the change of the dominant steady-state creep deformation mechanism from dislocation climb to lattice diffusion. The interruption creep tests demonstrate that crack initiates at the interface between the solder and intermetallic compounds (IMC) near the position of electrons entering or exiting the solder matrix when the steady-state creep stage approaches the limit, and then the crack first propagates along the solder/IMC interface and gradually turns to the solder matrix under combined shear and tensile stresses. The joint fractographies exhibit a mixed brittle-ductile fracture mode with one part in the interface and the other part in the solder matrix.

Influence of varying nitrogen on creep deformation and damage behaviour of type 316L in the framework of continuum damage mechanics approach

In the present study, Kachanov–Rabotnov continuum damage model has been employed to describe the steady state and tertiary creep deformation and damage behaviour of 316L austenitic stainless steel with different nitrogen contents of 0.07, 0.11 and 0.22 wt%, at 923 K. For all the nitrogen contents, the model appropriately predicts the creep strain–time data, creep rupture strain and rupture life. The model parameters such as characteristic strain and damage rates systematically decrease with the increase in nitrogen content. The derived iso-damage contours superimposed on creep strain–time data indicate that the evolution kinetics of strain, as well as damage, are unique at each applied stress level. For nitrogen added type 316L SS, the critical damage value ( ωcr) at which creep failure takes place is found to be less than 1 and is in the range of 0.35–0.60. It is observed that the dominance of damage rate ([Formula: see text]) over the strain rate ([Formula: see text]) increases with increasing nitrogen content from 0.07 to 0.22% N for the steel. A direct correlation has been established between the creep rupture ductility and the ratio of strain rate to damage rate, i.e. [Formula: see text]/[Formula: see text] using the Kachanov–Rabotnov model for different nitrogen contents and stress levels.

An Experimental and Modeling Investigation of Tensile Creep Resistance in a Stable Nanocrystalline Alloy

Nanocrystalline materials possess excellent room temperature properties, such as high strength, wear resistance, and toughness as compared to their coarse-grained counterparts. However, due to excess free energy, nanocrystalline microstructures are unstable at higher temperatures. Significant grain growth is observed already at moderately low temperatures, limiting their broader applicability. Here, we present a design approach that leads to a significant improvement in the high temperature tensile creep resistance (up to 0.64 of the melting temperature Tm) of a nanocrystalline Cu-Ta alloy. The design approach involves alloying of pure elements for engineering nanometer sized solute clusters within the solvent grains as well as along the grain boundaries. Using a chemically optimized nanocrystalline Cu-3at.%Ta alloy as a model material system, we demonstrate that the addition of Ta nanoclusters inhibits the migration of the planar defects at higher temperatures and reduces the dislocation motion, leading to extraordinary high temperature properties. For instance, the NC Cu-3Ta alloy tested under tensile creep conditions up to the temperature of 873 K (0.64Tm) displays highly unusual behavior, including the absence of any appreciable steady-state creep deformation which is normally observed in almost all materials. This approach can be readily scaled-up for bulk manufacturing of creep resistant nanocrystalline parts. Moreover, this design strategy can be transferred to other multicomponent systems such as Ni-based alloys for making nanocrystalline materials with tailored properties.

Compressive creep behavior of a γ-TiAl based Ti–45Al–8Nb–2Cr-0.2B alloy: The role of β(B2)-phase and concurrent phase transformations

The primary and steady-state compressive creep deformation behavior of an as-cast high Nb containing γ-TiA1 alloy having remnant β(B2)-phase has been studied over the temperature range of 750–850 °C at constant initial applied stress levels between 75-200 MPa. The creep curves derived over the entire creep testing conditions show a prominent primary creep regime which is attributed to the presence of dislocation debris of the coarse γ-grains at the colony boundaries. The stress and temperature dependence of the steady-state creep rate follows the Norton-Bailey power law and the corresponding average value of the stress exponent and apparent activation energy are estimated to be 3.6 and 375 kJ/mol, respectively. The average value of the stress exponent in conjunction with the dislocation substructure of the crept samples suggests that the kinetics of creep deformation within the studied experimental conditions is controlled by the non-conservative motion (climb) of dislocations. Further misorientation analyses of the phase-resolved EBSD maps imply that for most of the conditions creep strain is carried by the γ-TiAl phase. Consequently, contrary to the commonly believed idea, the β(B2)-phase does not appear to deteriorate the creep resistance of the present alloy below suitable combinations of temperature and stress. Beyond these conditions, the concurrent deformation of γ-TiAl and β(B2)-phases is found to enhance the steady-state creep rate. In addition, characteristics of the dynamic transformation of β(B2) phase into γ and α2 phases during creep and its effect on the steady-state creep rate are further considered. Finally, the application potential of the present alloy is compared through a composite plot of Larson-Miller parameter with several other potential alloys reported in the literature.

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.

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.

Creep behavior and deformation mechanisms of a novel directionally solidified Ni-base superalloy at 900 °C

A novel directionally solidified Ni-base superalloy with excellent creep-rupture strength has been developed. By means of measurement of the creep properties and microstructural observations, the variations of the creep deformation behavior and corresponding deformation mechanisms of the new superalloy with the applied stress are investigated at 900 °C. As the applied stress increases from 300 to 375 MPa, the steady-state creep rate increases gradually, whereas the creep-rupture life decreases. Transmission electron microscope observations on the crept specimens reveal that dislocation climb plays an important role in the steady-state creep deformation, and the process which two matrix dislocations with different Burgers vectors combine into one a〈001〉 dislocation and subsequently shear through γ′ precipitates operates more actively with increasing the applied stress. Based on the experimental observations, the reasons that account for the variation of the creep properties with the applied stress are discussed.

Electric current-assisted creep behaviour of Sn–3.0Ag–0.5Cu solder

The creep behaviour of Sn–3.0Ag–0.5Cu lead-free solder specimens with a diameter of 1.0 mm is investigated subjected to tensile forces from 10 to 25 N under electric currents ranging from 0 to 20 A. Due to the Joule heating effect, the solder temperature induced by electric current is measured to quantify the deterioration of tensile behaviour. Based on the observed steady-state creep deformation, the creep strain rate varies linearly with the tensile stress in the natural logarithmic coordinate with a stress threshold for the electric current between 0 and 10 A, and the natural logarithm of creep rate has a linear relationship with the square of current density. By revealing the dislocation climbing as the dominate creep mechanism under the coupled mechanical–electric–thermal loading, a modified Norton’s model is proposed which shows exponential dependence on the square of current density and the natural logarithm of tensile stress with the stress exponent enriched as a quadratic function of current density.

The High Temperature Creep Properties of a Thermally Sprayed CoNiCrAlY Coating via Small Punch Creep Testing

Thermal barrier coatings (TBC’s) protect superalloy components from excessively high temperatures in gas turbines. TBC’s comprise of a ceramic top coat, a metallic bond coat and a thermally grown oxide (TGO). The creep behaviour of the MCrAlY bond coat, which is sensitive to the composition and the method of deposition, has a significant effect on the life of the TBC. High velocity oxy-fuel (HVOF) thermal spraying is a popular deposition method for MCrAlY bond coats however the creep properties of HVOF MCrAlY coatings are not well documented. The creep behaviour of a HVOF thermally sprayed CoNiCrAlY coating has been determined by small punch creep (SPC) testing. Tests were conducted between an equivalent uniaxial stress range of 37-80 MPa at 750 °C on two different SPC rigs and between 30-49 MPa at 850 °C on a single SPC rig. The measured steady-state creep deformation rates at 750 °C were consistent across the two rigs. A comparison with previous work demonstrated that the creep behaviour of HVOF CoNiCrAlY coatings is not sensitive to the manufacturing variability associated with HVOF thermal spraying. The CoNiCrAlY coating exhibited typical SPC deformation at 750 °C. At 850 °C the CoNiCrAlY coating showed significantly different creep behaviour which could be attributed to the onset of superplasticity.