Activation Energy For Creep Research Articles

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.

The microstructure and creep characteristics of cast Mg–3Si and Mg–3Si–1Gd alloys

The effect of 1wt% Gd addition on the creep behavior of a cast Mg–3Si alloy was investigated by impression creep testing in the temperature range of 448–523K under punching stresses in the range of 175–450MPa for dwell times up to 4200s. It was found that the creep strength of the Mg–3Si base alloy was improved by Gd addition. This was attributed to the modification of the primary Mg2Si particles, solid solution strengthening of Gd in the Mg matrix, and the formation of a new intermetallic phase with a composition close to Mg3Si2Gd2. Creep behavior of the binary Mg–3Si alloy can be divided into the low- and high-stress regimes, with the respective stress exponent values in the range of 5.1–6.0 and 8.8–11.5 and average activation energies of about 81kJmol−1 and 124.5kJmol−1. The creep behavior of the ternary Gd-containing alloy, however, was expressed by a single linear relationship over the whole stress and temperature ranges studied, with stress exponents in the range of 8.2–8.5 and an average activation energy of 111.1kJmol−1. The creep activation energies were all stress dependent, and thus in the binary alloy, stress-assisted climb of dislocations, controlled by pipe and lattice diffusion were the dominant creep mechanisms in the low- and high-stress regimes, respectively. In the ternary Gd-containing alloy, power law creep is valid and it can be suggested that the operative creep mechanism is dislocation climb controlled by lattice diffusion.

Creep microstructures and creep behaviors of pure molybdenum sheet at 0.7 Tm

The creep behavior of high purity molybdenum (99.995wt.%) is investigated at temperatures of 1600 to 2000°C (0.61–0.77 Tm) by direct ohmic heating. The stress and temperature dependency of creep strain and rupture time are described through optical microstructure observations. Under low load and low temperature conditions, coarse secondary recrystallized grains caused by dynamic recrystallization are observed far from the crack tip. In contrast, under high load and high temperature conditions, coarse secondary recrystallized grains are only fully formed near the crack tip, while coarse secondary recrystallized grains and small primary recrystallized grains coexisted further away from the tip. The recrystallized grain size of the Mo-B sheet is smaller than that of the Mo-A sheet, and small primary and large secondary recrystallized grains are mixed throughout whole specimens of the Mo-B sheet. Mo-A sheet shows elongated ductile fracture, but Mo-B sheet shows irregular brittle fracture under the same conditions. The steady-state creep strain rate at 1800°C is found to be 7.34×10−6, 2.83×10−5 and 1.53×10−4s−1 under a constant stress of 5, 10 and 20MPa, respectively. The stress exponent is estimated to be 3.85–3.98 and the strain activation energy for steady state creep is 362–413kJ/mol.

Creep Aging Behavior Characterization of 2219 Aluminum Alloy

In order to characterize the creep behaviors of 2219 aluminum alloy at different temperatures and stress levels, a RWS-50 Electronic Creep Testing Machine (Zhuhai SUST Electrical Equipment Company, Zhuhai, China) was used for creep experiment at temperatures of 353~458 k and experimental stresses of 130~170 MPa. It was discovered that this alloy displayed classical creep curve characteristics in its creep behaviors within the experimental parameters, and its creep value increased with temperature and stress. Based on the creep equation of hyperbolic sine function, regression analysis was conducted of experimental data to calculate stress exponent, creep activation energy, and other related variables, and a 2219 aluminum alloy creep constitutive equation was established. Results of further analysis of the creep mechanism of the alloy at different temperatures indicated that the creep mechanism of 2219 aluminum alloy differed at different temperatures; and creek characteristics were presented in three stages at different temperatures, i.e., the grain boundary sliding creep mechanism at a low temperature stage (T < 373 K), the dislocation glide creep mechanism at a medium temperature stage (373 K ≤ T < 418 K), and the dislocation climb creep mechanism at a high temperature stage (T ≥ 418 K). By comparative analysis of the fitting results and experiment data, they were found to be in agreement with the experimental data, revealing that the established creep constitutive equation is suitable for different temperatures and stresses.

Effect of Y and Ca addition on the creep behaviors of AZ61 magnesium alloys

The creep behaviors of AZ61-1.2Y and AZ61-1.2Y-1.0Ca alloys under the temperature 125 °C–175 °C and the applied stress 50–70 MPa for 100 h were investigated in a typical creep testing machine. The stress exponent n at different stresses and creep activation energy Q at different temperatures for the two alloys were discussed also. Results showed that the creep resistance of AZ61 alloy can be significantly improved by the addition of Y and Ca. The steady creep rates of AZ61-1.2Y and AZ61-1.2Y-1.0Ca alloys increased obviously with increasing applied stress and temperature. The creep rate of AZ61-1.2Y alloy was significantly larger than that of AZ61-1.2Y-1.0Ca alloy under all experimental conditions. The creep life of AZ61-1.2Y alloy under 150 °C and 70 MPa was only 82.4 h corresponding to the large creep rate 1.6841 × 10−7. But the creep life of AZ61-1.2Y-1.0Ca alloy was always greater than 100 h, exhibiting excellent creep resistance at this experimental condition. The creep constitutive equation of AZ61-1.2Y alloy and AZ61-1.2Y-1.0Ca alloy can be expressed as ε˙=2.6067×10−10σ5.623exp(−50510/RT) and ε˙=3.7708×10−8σ3.901exp(−60820/RT), respectively.

High temperature creep properties of low-Ag Cu/Sn-Ag-Cu-Bi-Ni/Cu solder joints by nanoindentation method

Purpose This paper aims to investigate the creep properties of the bulks of low-Ag Cu/Sn-Ag-Cu-Bi-Ni/Cu micro solder joints from 298 to 358 K. The creep constitutive modelling was developed. Meanwhile, the creep mechanism of the bulks of Cu/Sn-Ag-Cu-Bi-Ni/Cu micro solder joints was discussed. Design/methodology/approach The creep properties of the bulks of low-Ag Cu/Sn-Ag-Cu-Bi-Ni/Cu micro solder joints from 298 to 358 K were investigated using the nanoindentation method. Findings The results of the experiments showed that the indentation depth and area increased with increasing temperatures. At the test temperature of 298-358 K, the creep strain rate of the bulks of the micro solder joints increases with the rising of the tested temperature. The values of creep stress exponent and activation energy calculated for the bulks of Cu/Sn-Ag-Cu-Bi-Ni/Cu micro solder joints were reasonably close to the published data. At the tested temperatures, dislocation climb took place and the dislocation climb motion was controlled by the dislocation pipe mechanism, and the second-phase particles enhancement mechanism played a very important role. Originality/value This study provides the creep properties of low-Ag Cu/Sn-Ag-Cu-Bi-Ni/Cu solder joints at different temperatures. The creep constitutive modelling has been developed for low-Ag Cu/Sn-Ag-Cu-Bi-Ni/Cu solder joints.

Creep Properties of the As-Cast Al-A319 Alloy: T4 and T7 Heat Treatment Effects

In this work, the creep behavior of a commercial Al-A319 alloy was investigated in the temperature range of 413 K to 533 K (140 °C to 260 °C). Tensile creep specimens in the as-cast condition and after heat treating by solid solution (T4) and by aging (T7) were tested in a stress range varying from 60 to 170 MPa. It was found that steady-state creep strain rate was significantly low in the T7 condition when compared with either the T4 or as-cast alloy conditions. As a result, the time to failure behavior considerably increased. The experimentally determined creep exponents measured from the stress–strain curves were 4 for the as-cast alloy, 7.5 in the solid solution, and 9.5 after aging. In particular, after solid solution a grain substructure was found to develop which indicated that creep in a constant subgrain structure was active, thus accounting for the n exponent of 7.5. In the aged condition, a stress threshold is considered to account for the power law creep exponent n of 9.5. Moreover, It was found that the creep activation energy values were rather similar for the alloys in the as-cast (134 kJ/mol) and T4 (146 kJ/mol) conditions. These values are close to the one corresponding to pure Al self-diffusion (143 kJ/mol). In the aged alloy, the apparent creep activation energy (202 kJ/mol) exceeded that corresponding to Al self-diffusion. This deviation in activation energy is attributed to the effect of temperature on the alloy elastic modulus. Microstructural observations using transmission electron microscopy provided further support for the various dislocation-microstructure interactions exhibited by the alloy under the investigated creep conditions and implemented heat treatments.

Kinetics of grain growth in La-doped ultrapure Al2O3

Kinetics of grain growth was measured in dense polycrystalline ultrapure alumina doped with 100 ppm of lanthanum. The evolution of grain size followed cubic kinetics, which can be attributed to the influence of solutes. Based on the increase of Gibbsian excess of segregating dopants with increase in the average grain size, it can be approximated that boundary velocity scales as inverse-square of grain size, leading to cubic grain growth kinetics. The activation energy of grain growth was found to be 418 ± 22 kJ mol−1 for La-doped alumina; comparable to that of undoped ultrapure alumina, and much lower than the activation energy of creep in La-doped alumina. The grain boundary mobility was found to be almost an order of magnitude lower than that of undoped ultrapure alumina, which can be attributed to the drag of oversized dopants segregated to the grain boundary core. These findings provide a basic understanding of the effects of segregating dopants on grain growth, and can be exploited in the production of coarsening resistant nanograined materials.

Probability analysis of the fire structural resistance of aluminium plate

An experimental and numerical study into the intrinsic scatter in the fire structural resistance of aluminium plate supporting tension loads is presented. Small-scale simulated fire structural tests performed on two aluminium alloys (AA5083 and AA6061) show for the first time a large amount of scatter in the tensile deformation rate and rupture stress. Multiple simulated fire tests conducted under identical heat flux exposure and tensile load conditions reveal scatter in the softening behaviour of the two aluminium alloys; there is large variability in the deformation rate, rupture stress and time-to-rupture, particularly at low stresses when creep dominates the softening process. Finite element analysis (incorporating elastic, plastic and creep softening effects) and elevated temperature material testing reveals that the scatter is caused mainly by variability in creep properties such as creep activation energy. A probability density function is used to quantify the scatter in the creep activation energy, and the finite element model using Monte Carlo simulations computes the scatter in the fire structural resistance of aluminium, which is not possible with existing deterministic models.

Rationalization of Creep Data of Creep-Resistant Steels on the Basis of the New Power Law Creep Equation

The conventional power law creep equation (Norton equation) relating the minimum creep rate to creep stress and temperature cannot be used to predict the long-term creep strengths of creep-resistant steels if its parameters are determined only from short-term measurements. This is because the stress exponent and activation energy of creep determined on the basis of this equation depend on creep temperature and stress and these dependences cannot be predicted using this equation. In this work, it is shown that these problems associated with the conventional power law creep equation can be resolved if the new power law equation is used to rationalize the creep data. The new power law creep equation takes a form similar to the conventional power law creep equation but has a radically different capability not only in rationalizing creep data but also in predicting the long-term creep strengths from short-term test data. These capabilities of the new power law creep equation are demonstrated using the tensile strength and creep test data measured for both pipe and tube grades of the creep-resistant steel 9Cr-1.8W-0.5Mo-V-Nb-B (P92 and T92).

High-temperature creep behavior of a SiOC glass ceramic free of segregated carbon

In this study we present the high-temperature creep behavior of a dense SiOC glass ceramic free of segregated carbon. Solid-state NMR spectroscopy, XRD and TEM investigations indicate that the sample consists of β-SiC nanoparticles homogeneously dispersed in an amorphous silica matrix. Compression creep experiments were performed at 1100–1300°C and stresses of 50–100MPa. The calculated creep viscosity of SiOC is two orders of magnitude higher than that of pure silica. Whereas the activation energy for creep (696kJ/mol) is close to that determined in pure silica glass. However, a stress exponent of 1.7 was calculated, suggesting that other mechanisms might contribute to the creep in addition to the Newtonian viscous flow. The strong difference in the creep rates and creep mechanism of the SiOC glass ceramic and amorphous silica is discussed in terms of possible contributions of the interface between the silica matrix and the β-SiC nanoparticles.

Superplastic creep of AuSn eutectic solder alloy

The large-strain tensile creep behavior of Au80Sn20 wt.% eutectic was studied at temperatures between 125°C and 200°C. Constant load creep experiments were performed and a power law relationship was created from this data to predict creep as a function of stress and temperature with a best-fit stress exponent n=2.1 and activation energy for creep of Q=148.4kJ/mol. Results show that the favorable creep resistance of AuSn reduces considerably at temperatures above 125°C, having 1000× higher creep rate at 200°C than 125°C. Of particular note is the observation of superplasticity in AuSn, with failure strains reaching 740% at 200°C.

A direct comparison of high temperature nanoindentation creep and uniaxial creep measurements for commercial purity aluminum

Measuring the uniaxial creep response from nanoindentation has been of great interest to the small scale mechanics community. However, several experimental and modeling challenges pose obstacles to direct comparison of indentation and uniaxial results. In this work, new experimental procedures are developed to improve the precision and accuracy of high temperature nanoindentation tests. Indentation creep experiments are performed on commercial purity aluminum alloy at a number of temperatures up to 550 °C. The activation energy for creep was found to be 140.2KJ/mol/K, matching the value determined with high temperature uniaxial creep experiments extremely well. Uniaxial power-law creep parameters (stress exponent and pre-exponential term) are calculated from the indentation data for direct comparison of results to the uniaxial data. The results are in good agreement with the literature values for uniaxial compression/torsion tests over a wide range of strain rates and temperatures demonstrating the capabilities of high temperature indentation creep experiments. The relative contributions and interplay of indentation size effect, strain rate and temperature on the creep response is also explored.

Tensile creep behavior of Sn–Ag–Cu–Ni multicomponent lead-free solder alloy

In the process of electronic packaging, the dissolution of under bump metallizations, such as Cu and Ni, into liquid solder occurs during soldering, which can change the original solder to a multicomponent one. Under the trend of miniaturization, it is quite necessary to evaluate the properties of multicomponent solder with excessive Cu and Ni compositions. In this study, the tensile creep behavior of Sn–3.5Ag–2.0Cu–0.5Ni multicomponent lead-free solder alloy is investigated at three temperatures, i.e., 303, 348 and 393 K. The steady-rate creep rates are obtained in the range of 10−4–10−8 s−1, when the normalized stress, σ/E, is in the range of 10−4–10−3. Based on the Dorn equation, the apparent stress exponent (n a), threshold stress (σ th), and activation energy of creep (Q C) are calculated at the three temperatures. It is found that the Sn–3.5Ag–2.0Cu–0.5Ni solder alloy shows a better creep performance than pure tin and eutectic Sn–3.5Ag solder due to the strengthening effect of Ag3Sn and (Cu,Ni)6Sn5 IMC precipitations. The true stress exponent for creep is identified to be 7, indicating that the creep behave is controlled by the dislocation-pipe diffusion in the tin matrix.

Effect of final heat treatment on creep behaviors of Zr-Nb-Cu alloy cladding tubes

Creep properties of annealed and stress-relieved Zr-1.1Nb-0.05Cu cladding tubes were studied and compared. The creep rates of Zr-1.1Nb-0.05Cu cladding tubes stress-relieved at 560°C were found to be appreciably higher than those of Zr-1.1Nb-0.05Cu annealed at 700 °C. The stress exponents for steady state creep were observed to be 5.0~7.0 for both stress-relieved and annealed Zr-1Nb-0.05Cu, supporting that the dislocation-climb-controlled creep operates at the intermediate temperatures (450~500 °C). The creep activation energy increased appreciably in the annealed Zr-1.1Nb-0.05Cu alloy compared to those of stress-relieved alloy. The increase of activation energy in the annealed Zr-1.1Nb-0.05Cu alloy is attributed to the decreasing contribution of faster diffusion path such as grain boundaries and dislocations. The creep rate of Zr-1.1Nb-0.05Cu decreased at intermediate temperatures with the increase of grain size with heat treatment, supporting the creep performance can be improved by the modification of microstructure through annealing.

High‐Temperature Compression Deformation Behavior of Fine‐Grained Carbon‐Bonded Alumina

Carbon‐bonded alumina with 33 wt% residual carbon was tested in compression at room temperature and at temperatures between 700°C and 1500°C in quasi‐static tests, creep tests, and stress relaxation tests. Therefore, a new high‐temperature test set up with inert gas chamber and inductive heating was used. The tests were accomplished by investigations of microstructure and Young's modulus. At room temperature, the results exhibit a pronounced hysteresis for the first loading cycle, which almost completely disappeared in subsequent cycles. The creep tests showed characteristic curves for compression whereas primary and secondary (stationary) creep occurred. Above 1000°C, a strong increase in creep rate was detected, whereas almost no creep was observed below this temperature. All creep curves were approximated with the models of logarithmic and Andrade creep. The activation energy for creep was found to be 263 kJ/mol above 1150°C. The resistance against stress relaxation showed an anomaly with a minimum between 1000°C to 1200°C and a maximum between 1300°C and 1400°C.

Influence of microstructure modification on the circumferential creep of Zr–Nb–Sn–Fe cladding tubes

Out-of-reactor, non-irradiated thermal creep performances and lives of annealed and stress-relieved Zr-1.02Nb-0.69Sn-0.12Fe cladding tubes were studied and compared. The creep rates of annealed Zr-1.02Nb-0.69Sn-0.12Fe cladding tubes were appreciably slower than those of stress-relieved annealed counterpart. The stress exponent increased slightly from 5.1 to 6.1 in the stress-relieved cladding to 5.3–6.3 in the annealed cladding. The creep activation energy of the annealed Zr-1.02Nb-0.69Sn-0.12Fe alloy (300–330 kJ/mol) was larger compared to that of the stress-relieved alloy (210–260 kJ/mol). The creep activation energy of annealed alloy is close to that of self-diffusion in α-Zr (336 kJ/mol). The smaller activation energy in the stress-relieved alloy is attributed to the increasing contribution of faster diffusion path such as grain boundaries and dislocations. The presence of dislocation arrays with higher dislocation density and smaller grain size in the stress-relived alloy was confirmed by TEM analysis. The creep rupture time increased dramatically in the annealed Zr–1Nb- 0.7Sn-0.1Fe alloy compared to that of stress-relieved alloy, supporting the decrease of creep rate by annealing. The creep life of Zr-1.02Nb-0.69Sn-0.12Fe claddings can be extended through microstructure modification by annealing at intermediate temperatures in which dislocation creep dominates.

Thermal activation in the Zr65Cu18Ni7Al10 metallic glass by creep deformation and stress relaxation

In the current study, jump stress creep and stress relaxation experiments were performed to Zr65Cu18Ni7Al10 metallic glass below the transition temperatures Tg. The viscoplasticity effect and transition between the Newtonian and non-Newtonian flow are investigated. The activation energy of creep is obtained from two theoretical methods. It is found that the activation volume of creep is more than that of stress relaxation, which is mainly caused by different organizational behaviors.

High-temperature Deformation Behavior of HP40Nb Micro-alloyed Reformer Steel

Reformer tubes are designed for prolonged service conditions at high temperatures and pressures in petrochemical industries for the production of hydrogen-rich gas. Frequent premature failures of reformer tubes are encountered due to the microstructural degradation of the material. Analysis of the tensile and creep deformation behavior of HP40Nb micro-alloyed steel at temperatures ranging from 800 to 1200 °C is presented in this paper. The Young’s modulus, yield strength, and ultimate tensile strength of the micro-alloyed steel decreased, and the ductility increased with the increase in temperature up to 1000 °C. The stress–temperature-dependent steady state creep rate obeys Young’s modulus compensated power-law relationship. The stress exponent and activation energy for creep were determined to be 7.96 and 332.65 kJ/mol. The predicted minimum creep rates were compared with the experimental values. It is possible to predict the value of minimum creep rate within an error less than ±7%. Analysis of fractured surfaces reveals brittle fracture up to 800 °C, while at higher temperature, dimple fractures are predominant.

Short-term creep of Cт3 steel

The behavior of Cт3 structural steel in brief heating (no more than 2 h) at 450–650°C is investigated, when the initial stress is below the yield point. In these conditions, the initial ferrite–pearlite structure of the steel is relatively stable, and no recrystallization is observed. At a test temperature of 450°C, when the stress is ~0.8 of its yield point at 20°C, Cт3 steel may fail within a matter of hours or days. At 650°C, when the stress is σ/σ0.220 > 0.8 of the yield point at 20°C, failure sets in within minutes. The calculated activation energy of creep for steel is 310.8–387.8 kJ/mol, which is comparable with the activation energy for Cт3 the self-diffusion of α iron.