Creep Stress Exponent Research Articles

Indentation strain rate sensitivity of ball-milled spark-plasma sintered Cu-C metal matrix composite

Bulk ultrafine grained metal matrix composites (MMC) have attracted much attention of many researchers due to their potential in terms of excellent mechanical properties for engineering applications, such as high strength, which can be two or more times of that of their coarse grained counterpart. Bulk ultrafine grained Cu-3wt.%C MMC samples were produced by Ball-Milling (BM) followed by Spark Plasma Sintering (SPS), at a temperature of 900 °C. The Cu-C MMC was compacted progressively by repeating the BM + SPS procedure without changing the weight ratio between Cu and graphite. The room temperature creep behavior, and the strain rate sensitivity (SRS) were inspected by using nanoindentation measurements. Strain rate ranged 0.0025-to-0.5 s−1, and the contact dwelling times ranged 5-to-300 s. A secondary steady-state regime was reached starting from a dwelling time of 120 s irrespective of the strain rate and Cu-C compaction level. A negative trend of the SRS exponent with Cu-C compaction was obtained, with creep stress exponent as high as 28. These results were discussed according to the microstructure features that differentiated the Cu-3wt.%C MMC obtained by the progressive BM + SPS compaction levels.

Tensile Creep Characterization and Prediction of Zr-Based Metallic Glass at High Temperatures

The high temperature creep behaviors of a Zr-based bulk metallic glass (BMG) are studied by uniaxial tensile creep experiments under applied stresses of 50–180 MPa at temperatures of 660–700 K. The microstructural observations of the BMG samples after creep tests show that crystalline phases can be detected under high temperature or high applied stress. Constitutive models for predicting the high temperature creep behaviors of the studied Zr-based BMG are established based on the θ projection method. The creep activation energy and stress exponent are also calculated to establish the creep model. The parameters of the established models are found to be closely associated with the applied stress and temperature. The results show an excellent agreement between the measured and predicted results, confirming the validity of the established model to accurately estimate the high temperature creep curves for the Zr-based BMG. Moreover, based on the classical diffusion creep theory, a schematic model is proposed to describe the creep behaviors of BMGs from the framework of free volume theory.

Operando Nanoindentation: A Perfect Platform to Measure the Mechanical Properties of Electrodes during Electrochemical Reactions

We present an experimental platform of operando nanoindentation that probes the dynamic mechanical behaviors of electrodes during real-time electrochemical reactions. The setup consists of a nanoindenter, an electrochemical station, and a custom fluid cell integrated in an inert environment. We evaluate the influence of the argon atmosphere, electrolyte solution, structural degradation and volumetric change of electrodes upon Li reactions, as well as the surface layer and substrate effects by control experiments. Results inform on the system limitations and capabilities, and provide guidelines on the best experimental practices. Furthermore, we present a thorough investigation of the elastic-viscoplastic properties of amorphous Si electrodes, during cell operation at different C-rates and at open circuit. Pure Li metal is characterized separately. We measure the continuous evolution of the elastic modulus, hardness, and creep stress exponent of lithiated Si and compare the results with prior reports. Operando indentation will provide a perfect platform to understand the fundamental coupling between mechanics and electrochemistry in energy materials.

A study of the nanoindentation creep behavior of (La0.5Ce0.5)65Al10Co25 metallic glass based on fractional differential rheological model

A fractional differential rheological model was proposed to describe the nanoindentation creep behavior of metallic glasses (MGs) at room temperature. The model had been proved to not only include the conventional rheological model, but can be used to obtain the empirical formula that has been commonly used to characterize nanoindentation creep behavior of MGs. The reversible and irreversible parts of time-dependent deformations of (La0.5Ce0.5)65Al10Co25 metallic glass were obtained through nanoindentation creep experiments, and the results were used to investigate the effects of the creep load Pmax and the loading rate Ṗ on the creep behavior and the variations of the model parameters. The results indicate that the fractional differential rheological model can describe the creep deformation quite well. Parameters analysis shows that viscoelastic part of creep and β relaxation has many common points. The variation of irreversible viscoplastic part of creep with creep load is the main cause of indentation size effect. The load rate Ṗ has effect on all components of creep deformation, which is reflected by the variations of the rheological model parameters. The viscosity and retardation time are related to the loading history as indicators that characterize the system's instantaneous viscosity at the onset of creep. The fractional order and creep stress exponent varies with loading rate have similar pattern, which could reflect the flowing ability upon the completion of the creep experiment.

Indentation-based rate-dependent plastic deformation of polycrystalline pure magnesium

Using a Berkovich pyramidal indenter and an instrumented nanoindentation platform, dual stage nanoindentation creep tests, including loading to a pre-set load and holding at the constant load then unloading, were performed on polycrystalline pure magnesium at 300K. Indentation tests were performed at four indentation loading rates of 0.05, 0.5, 5, and 50mN/s at constant load of 45mN and holding time of 400s. These were performed to assess indentation force-displacement response along with average indentation stress, indentation strain rate sensitivity and ambient temperature rate dependent plastic deformation response of the material. To this end, activation volume, a kinetic characteristic of plastic deformation, and density of mobile dislocations in plastically deforming material in the plastic zone around the indenter are discussed in detail. Uncertainties and sources of error, i.e. indentation size effect, surface roughness, and thermal drift, and pile-up/sink-in measuring creep response through nanoindentation are provided in the current paper as well. The microstructure of the material was also studied through optical and scanning electron microscopy to further investigate the microstructure/property correlations in the tested polycrystalline pure magnesium. The results show the dependency of indentation stress, strain rate sensitivity, and activation volume upon depth and loading rate. According to the creep stress exponent measurements, the dominant mechanism of rate dependent plastic deformation for polycrystalline pure Mg at ambient temperature is attributed to obstacle limited dislocation glide. Finally, the contribution of mechanical twins in the plastic zone around the indenter in the studied polycrystalline pure magnesium is briefly discussed.

Deformation behavior relationship between tensile and nanoindentation tests of SAC305 lead-free solder wire

PurposeThe relationship between the bulk and localized mechanical properties is critically needed, especially to understand the mechanical performance of solder alloy because of smaller sizing trend of solder joint. The purpose of this paper is to investigate the relationship between tensile and nanoindentation tests toward the mechanical properties and deformation behavior of Sn-3.0Ag-0.5Cu (SAC305) lead-free solder wire at room temperature.Design/methodology/approachTensile test with different strain rates of 1.5 × 10-4 s-1, 1.5 × 10-3 s-1, 1.5 × 10-2 s-1 and 1.5 × 10-1 s-1 at room temperature of 25°C were carried out on lead-free Sn-3.0Ag-0.5Cu (SAC305) solder wire. Stress–strain curves and mechanical properties such as yield strength (YS), ultimate tensile strength (UTS) and elongation were determined from the tensile test. Load-depth (P-h) profiles and micromechanical properties, namely, hardness and reduced modulus, were obtained from nanoindentation test. In addition, the deformation mechanisms of SAC305 lead-free solder wire were obtained by measuring the range of creep parameters, namely, stress exponent and strain rate sensitivity, using both of tensile and nanoindentation data.FindingsIt was observed that qualitative results obtained from tensile and nanoindentation tests can be used to identify the changes of the microstructure. The occurrence of dynamic recrystallization and the increase of ductility obtained from tensile test can be used to indicate the increment of grain refinement or dislocation density. Similarly, the occurrence of earliest pop-in event and the highest occurrence of pop-in event observed from nanoindentation also can be used to identify the increase of grain refinement and dislocation density. An increment of strain rates increases the YS and ultimate UTS of SAC305 solder wire. Similarly, the variation of hardness of SAC305 solder wire has the similar trend or linear relationship with the variation of YS and UTS, following the Tabor relation. In contrast, the variation of reduced modulus has a different trend compared to that of hardness. The deformation behavior analysis based on the Holomon’s relation for tensile test and constant load method for nanoindentation test showed the same trend but with different deformation mechanisms. The transition of responsible deformation mechanism was obtained from both tensile and nanoindentation tests which from grain boundary sliding (GBS) to grain boundary diffusion and dislocation climb to grain boundary slide, respectively.Originality/valueFor the current analysis, the relationship between tensile and nanoindentation test was analyzed specifically for the SAC305 lead-free solder wire, which is still lacking. The findings provide a valuable data, especially when comparing the trend and mechanism involved in bulk (tensile) and localized (nanoindentation) methods of testing.

Indentation Size Effect on Ag Nanoparticle-Modified Graphene/Sn-Ag-Cu Solders

This paper presents the results for the indentation size effect (ISE) on the creep stress exponent and hardness of 0.03 wt.% Ag-modified graphene nanosheet Sn-Ag-Cu solder alloys, using constant loading/holding and multi-cycle (CMC) loading methods, respectively. At each maximum load, with increasing indentation depth, the creep exponent first decreased and then increased. At the same strain rate, the stress exponent also showed the same tendency, increasing as the indentation depth (peak load) increased and then decreased. The hardness was measured continuously with increasing indentation depth by the CMC loading method. The hardness did not exhibit a decrease as the indentation depth increased, which differs from the classical description of the ISE. After an initial decrease, the hardness then increased and finally decreased as the indentation depth increased. This study reviews the existing theories and formulations describing ISE with hardening effects. The experimental results fit well with the empirical formulation. The phenomenon of ISE accompanied by hardening effects has been explained physically via the interaction between geometrically necessary dislocations and grain boundaries.

Effect of crystallographic orientation on impression creep behaviors of single crystal based on crystal plasticity theory

The present work aims to reveal the effect of crystallographic orientation on impression creep responses of single crystal alloys. For this purpose, crystal plasticity finite element (FE) method was employed to simulate the process of impression creep performed on [001]-, [011]- and [111]- oriented nickel based single crystal alloys. The determination of crystallographic creep parameters by impression creep was explored and compared among differently oriented single crystals. The result shows that the stress distribution and surface morphology induced by impression creep exhibit anisotropic patterns which are strongly dependent on crystallographic orientation. The determination of creep stress exponent is independent on crystallographic orientation.

Creep Behavior of CP-Ti TA2 at Low Temperature and Intermediate Temperature

Significant temperature and stress dependent creep behavior of commercial pure titanium TA2 was observed at low and intermediate temperature. According to the variation of creep strain with applied stress level, the relationship between threshold stress level and the corresponding creep temperature was determined. Based on short time creep tests, the constitutive equation containing steady state creep strain rate was used to extrapolate the minimum creep rate. The existence of steady state creep of commercial pure titanium TA2 was confirmed by subsequent long time creep experiments. Through the minimum creep strain rates, creep stress exponent was obtained which also indicates the accuracy of the extrapolated minimum creep strain rates. The activation energy of primary creep (approximately 60 kJ/mol) at different creep strains level was higher than the activation energy for slip controlled creep, which demonstrates the importance of twinning for the development of creep behavior of TA2 at low temperature. Moreover, according to the variation of twinning structure with deformed temperature in creep tested specimens, the temperature dependent creep behavior was interpreted and the importance of twinning for creep behavior of TA2 was confirmed.

Nanoindentation creep behavior of coarse-grained and ultrafine-grained pure magnesium and AZ31 alloy

Ultrafine-grained (UFG) pure magnesium and AZ31 alloy were prepared by sliding friction treatment (SFT). Nanoindentation tests of UFG Mg and AZ31 alloy were performed under a wide range of loading strain rates from 0.004/s to 0.4/s with a holding time of 500s at room temperature to study the grain size and alloy element influence on the creep behavior and the corresponding deformation mechanisms. It is shown that the refined grain size could promote creep behavior, while the alloy elements would enhance the creep resistance. Creep stress exponent deduced in the ending of the holding regime were used to illustrate the creep diversity in these materials. The UFG samples exhibit a reduced creep stress exponent because of significantly increased grain boundary activities. Besides that, the solute atoms of Al and Zn endow the material with an improved creep resistance by limiting interactions between dislocations and boundaries.

Using a spark plasma sintering apparatus as a tool in a compressive creep study of fine-grained alumina

Abstract A spark plasma sintering (SPS) apparatus was used to perform uniaxial compressive creep tests on dense SPS-processed fine-grained alumina. Experiments were carried out in the 1125–1250 °C temperature range under an applied stress of 80–120 MPa. Creep rates, stress exponent and apparent activation energy were determined. The microstructure of deformed samples was characterized by HRSEM. The creep rates, stress exponent (1.9–2.1) and apparent activation energy (454 kJ/mol) values obtained are in a good agreement with data reported in the literature regarding creep of fine-grained polycrystalline alumina. These results, together with microstructural observations, suggest that the creep mechanism involved was grain boundary sliding (GBS), accommodated by dislocation climb, controlled by diffusion along the grain boundaries. It was thus demonstrated that an SPS apparatus can be employed as an accurate high-temperature creep testing system.

Effect of Q-Al5Cu2Mg8Si6 phase on mechanical properties of Al-Si-Cu-Mg alloy at elevated temperature

The effect of Q-Al5Cu2Mg8Si6 phase on creep and tensile properties of Al-Si-Cu-Mg alloy at elevated temperatures was investigated. Microstructure observation clarifies that the Q-Al5Cu2Mg8Si6 phase is distributed in the Al matrix. The creep stress exponent is in the range of 4.20–4.67 and activation energy for creep varies from 218 to 226kJ/mol with increasing the volume fraction of Q-Al5Cu2Mg8Si6 phase. The stress exponent and activation energy suggest that dislocation climb is the dominant creep mechanism. In addition, slight variation of the stress exponent and activation energy indicates that the creep mechanism do not change with the increase of Q-Al5Cu2Mg8Si6. The relation between the minimum creep rate and creep fracture life are fitted by Monkman-Grant equation, which indicates that the creep fracture life is increased with the increase of Q-Al5Cu2Mg8Si6 phase. The ultimate tensile strength at 250°C increases from 157MPa to 199MPa with the volume fraction of Q-Al5Cu2Mg8Si6 phase varying from 3.2% to 6.4%. However, the ultimate tensile strength at 350°C only increases 9MPa with increasing the Q-Al5Cu2Mg8Si6 phase. The slight increase in ultimate tensile strength at 350°C indicates that the Q-Al5Cu2Mg8Si6 phase is not effective in improving the ultimate tensile strength at 350°C.

Indenter load effects on creep deformation behavior for Ti-10V-2Fe-3Al alloy at room temperature

Abstract Indentation creep behavior at room temperature and its mechanism of Ti-10V-2Fe-3Al alloy with dual phase structure were investigated. Micro-indentation creep tests were performed under the maximum indenter load ranging from 1500 mN to 4500 mN and the holding time of 300 s. The effect of indenter load on creep behavior and creep parameters, like creep rate, creep strain rate, indentation stress and creep stress exponent, were analyzed at the steady-state creep. The results revealed that creep parameters exhibited significantly indentation depth dependent. At the secondary stage of creep, creep strain rate and creep rate increased with the increase of maximum indenter load, while creep stress and creep stress exponent exhibited an opposite trend. Especially, creep stress exponent of 7.65 ± 1.25 in power-law creep behavior of Ti-10V-2Fe-3Al alloy, which was consistent with dislocation process, indicated that the secondary stage of creep may be dominated by dislocation climb. Furthermore, experimental data and figures were used to evaluate and comprehend likely creep mechanisms during a micro-indentation scheme of Ti-10V-2Fe-3Al alloy.

Operando Nanoindentation: A New Platform to Measure the Mechanical Properties of Electrodes during Electrochemical Reactions

We present an experimental platform of operando nanoindentation that probes the dynamic mechanical behaviors of electrodes during real-time electrochemical reactions. The setup consists of a nanoindenter, an electrochemical station, and a custom fluid cell integrated into an inert environment. We evaluate the influence of the argon atmosphere, electrolyte solution, structural degradation and volumetric change of electrodes upon Li reactions, as well as the surface layer and substrate effects by control experiments. Results inform on the system limitations and capabilities, and provide guidelines on the best experimental practices. Furthermore, we present a thorough investigation of the elastic-viscoplastic properties of amorphous Si electrodes, during cell operation at different C-rates and at open circuit. Pure Li metal is characterized separately. We measure the continuous evolution of the elastic modulus, hardness, and creep stress exponent of lithiated Si and compare the results with prior reports. operando indentation will provide a reliable platform to understand the fundamental coupling between mechanics and electrochemistry in energy materials.

Creep behavior of Sn–Bi solder alloys at elevated temperatures studied by nanoindentation

The creep mechanisms of eutectic Sn–Bi alloy were evaluated with indentation constant strain rate (CSR) method at elevated temperatures. The activation energy (Q) and creep stress exponent (n) of eutectic Sn–Bi alloy and other alloy compositions were measured in the temperature range from 25 to 100 °C. Prior to this, the indentation CSR testing protocol for evaluation of Q and n was validated through evaluating the pure Sn (grain size >100 µm) at various temperatures. The creep mechanism of large grain-sized Sn was found to be dislocation climb controlled by core diffusion in bulk. Dislocation climb though core diffusion and power-law breakdown were suggested to be the deformation mechanism for pure Bi and Sn–3%Bi alloy, respectively. For the two-phased eutectic Sn–Bi alloy, the creep mechanism was found to be strain rate and temperature dependent. Individual constituent phases were found to take turns to dominate the creep rate at different strain rates.

Creep deformation behavior of 9Cr1MoVNb (ASME Grade 91) steel

Detailed investigations have been performed to examine the creep deformation behavior and microstructural evolution of modified 9Cr-1Mo steel which is widely used in high temperature power plant component. The creep data were analysed in terms of the temperature compensated power law and Monkman-Grant relation. The creep activation energy of Grade 91 steel was determined with 543±30kJ/mol without threshold stress compensation, while after correcting the threshold stress; the activation energy is decreased to 303±15kJ/mol. This value is close to the activation energy of creep in α-Fe. The calculated threshold stress showed a strong dependence on temperature. The creep behavior of the steel was described by the modified Bird-Mukherjee-Dorn relation. The rate controlling creep deformation mechanism was identified as the edge dislocation climb with stress exponent of n=5. Further, the value of creep damage tolerance factor (λ) and stress exponent was used to identify the cause of creep damage, showed significant difference in the high and low stress regimes. The fracture surface morphology of the ruptured specimens was studied by scanning electron microscopy to further elucidate the failure mechanisms. Whereas deformed microstructure was examined by transmission electron microscopy. The significant decrease in creep strength in the alloy has been attributed to microstructural degradation associated with precipitates and dislocation substructure.

Ambient-temperature nanoindentation creep in ultrafine-grained titanium processed by ECAP

Ultrafine-grained (UFG) Ti was prepared by equal channel angular pressing (ECAP) through 1 and 4 passes at room temperature. The ambient-temperature creep behavior and mechanism of UFG Ti were studied by nanoindentation creep tests at the loading strain rate of 0.005 and 0.1s−1. The effect of grain size on creep behavior and relevant creep parameters such as steady creep strain rate and creep stress exponent (n) was estimated for coarse-grained (CG) and UFG Ti. The results show that the creep resistance of UFG Ti is enhanced with respect to CG Ti. UFG Ti after 1 pass of ECAP exhibits the highest creep resistance. The creep resistance of UFG Ti decreases with increasing the number of ECAP passes. The creep stress exponents of UFG Ti are much higher than those of CG Ti while steady creep strain rates do not vary much with grain size. The creep stress exponents of CG and UFG Ti are dependent on the loading strain rate and increase with increasing the loading strain rate. The power-law creep with a stress exponent of 18.1–24.6 is consistent with dislocation process, especially for dislocation emission and annihilation at grain boundaries, which is a key mechanism in creep deformation of UFG Ti. Grain boundaries may play an important role in the creep behavior of UFG Ti.

Creep Behavior and Microstructure Evolution of Sand–Cast Mg–4Y–2.3Nd–1Gd–0.6Zr Alloy Crept at 523–573 K

High temperature tensile–creep behavior of Mg–4Y–2.3Nd–1Gd–0.6Zr (wt%, WE43(T6)) alloy at 523–573 K was investigated. The creep stress exponent is equal to 4.6, suggesting the underlying dislocation creep mechanism. The activation energy is (199 ± 23) kJ/mol, which is higher than that for self-diffusion in Mg and is believed to be associated with precipitates coarsening or cross slip. The creep mechanism is further suggested to be dislocation climb at 523 K, while a cross slip at 573 K is possible. The metastable β′ and β1 phases in the WE43(T6) alloy were relatively thermal stable at 523 K and could be effective to hinder the dislocation climb, which contributed to its excellent creep resistance. However, at 573 K it readily transforms into equilibrium βe phase and coarsens within two hours, thereby causing a decrease of creep resistance. In addition, precipitate free zones approximately normal to applied stress direction (directional PFZs) developed during the creep deformation, especially at 573 K. Those zones became preferential sites to nucleate, extend and connect microcracks and cavities, which lead to the intergranular creep fracture. Improving the thermal stability of precipitates or introducing thermally stable fine plate-shaped precipitates on the basal planes of Mg matrix could enhance the high temperature creep resistance.

Creep behavior of micro-scale Cu/Sn–3.0Ag–0.5Cu/Cu joints under electro-thermo-mechanical coupled loads

The creep behavior of line-type micro-scale Cu/Sn–3.0Ag–0.5Cu/Cu joints under electro-thermo-mechanical coupled loads with a high current density of 1.0 × 104 A/cm2 was characterized, in comparison with those without current stressing. Results show that under electro-thermo-mechanical coupled loads all joints exhibit typical three-stage creep characteristics similar with that of joints under the mechanical stress only, implying that the mechanical stress still dominates the creep deformation process of joints. The steady-state creep rate increases with the externally applied stress and temperature regardless of current stressing. Notably, the creep of joints under electro-thermo-mechanical coupled loads is accelerated in terms of an increase in the steady-state creep rate, compared with that without current stressing. The essential factors influencing the steady-state creep rate of joints are the damage effect and Joule heating induced by electro-thermo-mechanical coupled loads. Moreover, the results manifest that the creep activation energy and stress exponent of joints are independent of current stressing. The creep mechanisms of solder joints under electro-thermo-mechanical coupled loads and without current stressing are lattice diffusion.

Limit case analysis of the \u201cstable indenter velocity\u201d method for obtaining creep stress exponents from constant load indentation creep tests

This study concerns a commonly-used procedure for evaluating the steady state creep stress exponent, n, from indentation data. The procedure involves monitoring the indenter displacement history under constant load and making the assumption that, once its velocity has stabilised, the system is in a quasi-steady state, with stage II creep dominating the behaviour. The stress and strain fields under the indenter are represented by “equivalent stress” and “equivalent strain rate” values. The estimate of n is then obtained as the gradient of a plot of the logarithm of the equivalent strain rate against the logarithm of the equivalent stress. Concerns have, however, been expressed about the reliability of this procedure, and indeed it has already been shown to be fundamentally flawed. In the present paper, it is demonstrated, using a very simple analysis, that, for a genuinely stable velocity, the procedure always leads to the same, constant value for n (either 1.0 or 0.5, depending on whether the tip shape is spherical or self-similar). This occurs irrespective of the value of the measured velocity, or indeed of any creep characteristic of the material. It is now clear that previously-measured values of n, obtained using this procedure, have varied in a more or less random fashion, depending on the functional form chosen to represent the displacement–time history and the experimental variables (tip shape and size, penetration depth, etc.), with little or no sensitivity to the true value of n.