Minimum Creep Strain Rate Research Articles

High Temperature Behavior of Al-7Si-0.4Mg Alloy with Er and Zr Additions

In recent years, many efforts have been devoted to the development of innovative Al-based casting alloys with improved high temperature strength. Research is often oriented to the investigation of the effects of minor element additions to widely diffused casting alloys. The present study focuses on Al-7Si-0.4Mg (A356) alloy with small additions of Er and Zr. Following previous scientific works on the optimization of heat treatment and on tensile strength, creep tests were carried out at 300 °C under applied stress of 30 MPa, a reference condition for creep characterization of innovative high-temperature Al alloys. The alloys containing both Er and Zr displayed a lower minimum creep strain rate and a longer time to rupture. Fractographic and microstructural analyses on crept and aged specimens were performed to understand the role played by eutectic silicon, by the coarse intermetallics and by α-Al matrix ductility. The creep behavior in tension of the three alloys has been discussed by comparing them to tension and compression creep curves available in the literature for Al-7Si-0.4Mg improved by minor elemental additions.

A three-dimensional mesoscale model for progressive time-dependent deformation and fracturing of brittle rock with application to slope stability

An understanding of progressive time-dependent deformation is essential for determining appropriate measures to ensure the long-term integrity of rock-masses surrounding engineering structures. We propose a 3D numerical model, that uses the Norton-Bailey creep law and a time-independent damage evolution law, to investigate the progressive time-dependent deformation and fracturing of brittle rock. The model considers material heterogeneity and the concept of mesoscopic renormalization at the mesoscale. The cooperative interaction between microcrack distribution and damage evolution leads to local material degeneration as a function of increasing time in the model. First, the input parameters for the model were calibrated and the model was validated using laboratory experiments. Numerical creep simulations were then performed for a range of constant stresses. Our model can accurately replicate the evolution of strain and strain rate as a function of time, the output of acoustic emission energy, and the emergence of a macroscopic failure plane seen in laboratory experiments. Our simulations also show that the minimum creep strain rate and the time-to-failure increase and decrease, respectively, as stress is increased, also seen in laboratory experiments. For example, increasing the differential stress by 10 MPa increased the minimum creep strain rate increased by an order of magnitude. Finally, we use the proposed 3D model to investigate the time-dependent stability of an engineering-scale rock slope containing faults at the Fushun West Open Pit coal mine. A small increase in fault-adjacent damage was observed after 40 days and, between 60 and 120 days, the damage on the side of the slope increased. After 140 days, the localized growth of the damaged elements split the slope into two segments, resulting in slope failure. Our 3D numerical model highlights potential slope instability in the Fushun West Open Pit coal mine and can be used to investigate slope stability in engineering projects worldwide.

Influence of Ta content on microstructure and creep behavior of a Ni–Co base disc superalloy

Abstract This study investigated the influence of Ta content (i.e. 0 wt%, 2 wt%, and 4 wt%) on microstructure and creep behavior of a Ni–Co base disc superalloy at 760 °C/480 MPa. It was found that creep rupture life and the minimum creep strain rate showed a trend of first increase and then decrease with the increase of Ta content. The microstructure observations indicated that Ta addition promoted the increase of volume fraction of γ′, the precipitation of MC carbide and η-phase, but inhibited the growth of γ′ and the precipitation of M23C6 carbide at grain boundaries during creep. The mechanisms related to creep behavior were discussed, and it was deemed that the higher γ′ volume fraction, finer size of γ′, larger γ/γ′ misfit, lower atomic diffusion rate, inhibited M23C6 carbide and the palisade-like distribution of η-phase may be responsible for the enhancement of the primary and tertiary creep resistance.

High temperature creep behavior of a cast polycrystalline nickel-based superalloy K465 under thermal cycling conditions

Turbine blades in aircraft engines may suffer serious microstructural degradation and even failure due to sharp overheating during service. In this study, a microwave heating creep testing rig was designed and developed to conduct the high temperature thermal cycling creep experiments, to reveal the overheating effect on the creep behavior of a conventionally cast Ni-based superalloy K465. The thermal cycling creep experiments were conducted under (900 ℃/30 min–1100 ℃/3 min)/70 MPa, combined with the comparative isothermal creep references under 900 ℃/70 MPa and 1100 ℃/70 MPa. The thermal cycling creep exhibited unique characteristics namely short creep life, high creep strain rate and high fracture strain. During the thermal cycling creep, secondary γ′ precipitates dissolved rapidly at higher creep temperature, while recovered partially at lower creep temperature. The obvious microstructural degradation of secondary γ′ precipitates was primarily responsible for the short life of the thermal cycling creep. When secondary γ′ precipitates recovered and coarsened, early shearing of the γ′ phase by entrapped interfacial dislocations occurred, especially at the concave locations of the secondary γ′ precipitates. The evolution of dislocations was mainly responsible for the high minimum creep strain rate of the thermal cycling creep. The creep voids/cracks initiated quickly and located at the interface of M6C carbides and γ/γ′ eutectic pools in the interdendritic regions and grain boundaries during the thermal cycling creep, and finally caused the intergranular fracture.

Microstructure and Mechanical Properties of Intercritically Treated Grade 91 Steel.

Premature creep failures at the intercritical heat affected zone (ICHAZ) of creep-resistant steel weldments have been frequently reported. However, the creep degradation mechanism of different microstructure constituents in ICHAZ is complicated and needs further clarification. In this work, Grade 91 steel was intercritically heat-treated at a temperature (860 °C) between the critical temperatures AC1 and AC3, and a correlation between microstructure and mechanical properties of the heat-treated specimen was built. The effects of austenitization and tempering resulting from the intercritical treatment (IT) differentiated the local strain energies between the two microstructure constituents: newly transformed martensite (NTM) and over-tempered martensite (OTM). The formation of NTM grains led to a hardness increase from 247 HV0.5 in the base metal to 332 HV0.5 in the IT specimen. The ultimate tensile strength (UTS) increased from 739 MPa in the base metal to 1054 MPa in the IT specimen. Extensive growth of the OTM grains and rapid recovery of NTM grains took place simultaneously in the IT specimen during a typical tempering at 760 °C. These microstructure degradations led to a lowered hardness of 178 HV0.5, a reduced UTS of 596 MPa, and a poor creep resistance with a minimum creep strain rate of 0.49 %/h at 650 °C in an IT + tempering (ITT) specimen.

Asymptotic creep deformation behavior of modified HP steel after long-term service

Creep behavior of modified HP steel was investigated through the tensile creep tests under the stress conditions of 25–55 MPa at 950 °C with four reformer tubes of different service periods: Unused (virgin), 8.50, 9.67, and 16.17 year aged. The minimum creep strain rates, creep rupture life, as well as elongation and reduction of area of the ruptured specimen were measured. It was observed that all the measured properties did not vary with different service periods. The creep deformation behavior was modeled based on the experimentally measured creep data utilizing the secondary creep (SC) model, the tertiary creep (TC) model, and the combined model of two latter ones (SC-TC model). The results indicated the asymptotic creep deformation behavior of the secondary creep strain rate. The tertiary creep also demonstrated asymptotic behavior, however, its strain rate slightly increased, as the service period increased. The creep curves predicted by the SC-TC model were more accurate than those obtained using the SC or TC model. Microstructural observations supported the observed asymptotic behavior.

Performance of 316L Stainless Steel Diffusion Welding during High Temperature Creep

The creep and rupture test were carried out on a non-standard specimen of 316L stainless steel (316L-SS) diffused bonding joint. And the θ-projection model was used to analyze the minimum creep strain rate and the remaining life at 500°C/6 MPa when the creep strain is 0.2%. According to the test results, design criterion for the diffusion bonding component at high temperature is established. The rupture experimental results show that the remaining life extrapolated by Larsen-Miller equation is relatively consistent with that calculated by the θ project concept method.

Mesoscopic time-dependent behavior of rocks based on three-dimensional discrete element grain-based model

Abstract A three-dimensional discrete element grain-based stress corrosion model incorporating the theories of subcritical crack growth and chemical reaction rate was built to explore the time-dependent behavior of damage evolution and fracture patterns of brittle rocks on a mesoscopic scale. The model was first validated and the model accurately captured the evolution of damage (tensile and shear microcracks) on the mesoscopic scale and the macroscopic mechanical behavior (the strength, and failure patterns) observed in laboratory experiments. The subcritical parameters of the model were calibrated to match the time-dependent damage deformation behavior observed in laboratory experiments. The time-dependent numerical results replicated the typical decelerating-accelerating axial strain behavior seen in laboratory brittle creep experiments. The crack propagation pattern in the simulation indicated that tension cracks were dominant. The results of numerical simulation showed that the time-to-failure during brittle creep decreased with the increase of the stress level, while the initial strain value, initial damage value, and minimum creep strain rate increased, as observed previously in the laboratory. We conclude therefore that the presented model supports a rich set of grain-scale discontinuities that can be related to microstructural features and provides a deeper understanding of the evolution of time-dependent damage on the mesoscale.

The development of creep damage constitutive equations for high Cr steel

ABSTRACTThis paper reports (1) an application of the modified hyperbolic sine law to P92 for the minimum creep strain rate over a wider range of stress level, and 2) the calibration of the creep cavity fracture model and its applications to such as P92, E911 and MARBN alloys. It was motivated by the original development of creep cavitation based creep rupture model and application to other alloys, and the need of creep strain and stress relation over a wider range of stress. The results include: (1) the calibration of creep cavity fracture model for E911, and the pre-required cavity nucleation and growth models, for E911, (2) the creep lifetime and stress relation coefficient U’ for P92, and (3) the relationship of the cavity nucleation rate coefficient A2 and stress level for MARBN cross-welds. This paper contributes to the specific knowledge and the methodology. It anticipates that this methodology will find its value and application in modelling other fractures such as ductile and fatigue.

Towards a comprehensive understanding of creep: Microstructural dependence of the pre-exponential term in Al

We show that the equation proposed by Takeuchi and Argon to explain the creep behavior of Al–Mg solid solution can be used to describe also the creep behavior of pure aluminum. In this frame, it is possible to avoid the use of the classic pre-exponential fitting parameter in the power law equation to predict the minimum creep strain rate. The effect of the fractal arrangement of dislocations, developed at the mesoscale, must be considered to fully explain the experimental data. These ideas allow improving the recently introduced SSTC model, fully describing the primary and secondary creep regimes of aluminum alloys without the need for fitting. Creep data from commercially pure Al99.8% and Al–Mg alloys tested at different temperatures and stresses are used to validate the proposed ideas.

Study on the expression of the rate constant α of the creep equation by modified θ projection applied to turbine materials

It is well-known that the creep equation obtained by the modified θ projection [2] describes well from the primary creep region to the tertiary creep region. However, unlike the power law such as that applied by the Bailey-Norton method, the stress variables and temperature variables are not found in the equation coefficients. Therefore, the users of this equation must find functions containing temperature variables and stress variables to display the equation coefficients. Thus, among the three coefficients A, α, and B included in the equation of the modified θ projection, the rate constant α, which exerts the largest influence on the curvature and the minimum creep strain rate of the creep curve [3], was selected as the object of investigation. Moreover, by considering the Cr-Mo-V steel and the Ni-based superalloy as examples, the expression of α was investigated. As a result, it was found that the discrete cosine transform and series can be applied not only to the coefficients of the creep equation but also to the creep equation itself. It is very important that the Fourier transform, which is considered to be applicable only to periodic functions, can be applied to non-periodic functions like a creep equation or its coefficients without apodizing such as windowing [9].

A unified constitutive model in simulating creep strains in addition to fatigue responses of Haynes 230

A unified constitutive model (UCM) specifies that its flow rule for inelasticity computes both the plastic and creep strains as a single state variable. A Chaboche framework based UCM with the modeling features of strain range-dependence, strain rate-dependence, static recovery and mean stress evolution was developed and experimentally validated against a broad set of fatigue and fatigue-creep responses of Haynes 230 (HA 230) under isothermal and anisothermal temperature conditions. This article demonstrates that this advanced Chaboche-based UCM can simulate the secondary minimum creep strain rates reasonably, but is unable to predict the tertiary creep strain responses. To simulate the tertiary creep strain responses a continuum damage model is needed to be coupled to the UCM. This study also evaluated three different unified flow rules, Norton's power law, exponential Norton and sine-hyperbolic Norton for calculating the inelastic strain rates. It is found that the choice of flow rule is important in simulating the stress amplitude saturation rate of fatigue responses, but has minimal effect in simulating the tertiary creep strains. However, the damage coupled UCM independent to the unified flow rules listed above can adequately simulate fatigue, fatigue-creep including the stress relaxation during strain dwell, and creep strain up to the tertiary range for HA 230. The drawbacks of the damage coupled UCM are the hysteresis loop softening at very high temperatures and asymptotic simulation at low creep temperatures, which are identified as challenges to be overcome towards developing a universal UCM for robust design and analysis of high temperature components.

Prediksi Laju Perambatan Retak Melar pada Baja Austenitik 316L Menggunakan Data Uji Melar dan Metode NSW

In this study, an experimental creep crack growth rate (CCGR) of austenitic steel AISI 316L was predicted from the creep constant values and Nibkin Smith Webster (NSW) method. The experimental CCGR data were obtained from the CCG test under four different load conditions ranging from 6000 to 7000 N at 525 o C. The creep constants, A and n were obtained from the uniaxial creep rupture test under various load conditions, ranging from 180 to 225 Mpa at 525 o C. The creep constants were determined both from the minimum and average creep strain rate data. By applying the creep constants and NSW method, the predicted CCGR curve was generated and compared with the experimental CCGR curve. The result showed that the predicted CCGR curve based on the minimum creep strain rate data was found to be close to the experimental CCGR curve. The significant portion of creep crack growth’s lifetime of austenitic steel AISI 316L was occupied by the crack propagation (steady stage) period rather than crack initiation and/or fracture periods. In addition, plane stress and strain conditions could also be determined from the predicted CCGR curve. It was observed that the experimental CCGR curve was located near the plane strain condition where no deformation occurred in the lateral direction.

Microstructural Stability During Creep Exposure of 9Cr-1Mo Steel Treated at Different Normalization Temperatures

A modified 9Cr-1Mo steel has been exposed to three separate austenitization temperatures, i.e., at 950, 1025, and 1100 °C for normalization. After subsequent tempering at 750 °C, the normalized and tempered samples were creep-tested at temperatures of 550, 600, and 650 °C. The creep strength of the investigated samples was evaluated in terms of minimum creep strain rate and time to rupture. The effects of microstructure, precipitate and boundary misorientation on the creep behavior of the samples have been studied with TEM and EBSD analyses. Further, the evolution of crystallographic texture after creep tests has also been studied. The presence of an intermediate size of martensitic microstructural units (i.e., prior-austenite grain, martensitic packets, etc.) and combination of fine coherent and incoherent Nb(C,N) precipitates has provided superior creep strength for the samples normalized at 1025 °C, when these are subsequently subjected to low-temperature (i.e., 550 °C) and high-temperature (i.e., 650 °C) creep tests, as compared to other conditions of normalizing heat treatment.

Microstructure, creep deformation behavior and reliability of Sn-6.5wt%Zn-0.3wt%Cu lead free solder after Bi additions

Creep characteristics of Sn-6.5Zn-0.3Cu plain solder was studied and compared with Sn-6.5Zn-0.3Cu-1Bi and Sn-6.5Zn-0.3Cu-3Bi solder alloys. The results show that 3Bi-containing alloy solder has the higher creep resistance (~80 times) than the other two solders at the same stress level and testing temperatures. The higher creep resistance was attributed to the solid solution and precipitations strengthen effects of Bi atoms. The precipitation of Bi atoms or particles can significantly refine the microstructure, blocks the movement of dislocations and increases the creep resistance of Bi-containing solders. Moreover, the creep life time of plain SZC plain solder alloy was extremely enlarged ~23.7 times with the addition of 3 wt. % Bi, which could result in improving the reliability of Bi-containing solders. Additionally, the minimum creep strain rate in the steady state flow is developed during secondary creep and Garofalo model was created from the experimental data to predict the creep deformation mechanism. According to the obtained stress exponents and activation energies, it is proposed that the dominant deformation mechanism is dislocation climb over the whole temperature range investigated.

Comparative analysis of the sin-hyperbolic and Kachanov–Rabotnov creep-damage models

In this study, the Sin-Hyperbolic (Sinh) and the classic Kachanov-Rabotnov (KR) creep-damage models are fit to creep data for 304 stainless steel at 600 and 700 °C. The ability of the models to predict minimum creep strain rate, creep deformation, damage evolution, and rupture are compared. It is shown that both models can predict the creep deformation accurately; however, the minimum creep strain rate, damage evolution, and rupture predictions of the KR model is deficient. Using the KR model, critical damage is often less than unity; a violation of continuum damage mechanics (CDM). The KR minimum creep strain rate and rupture predictions do not exhibit the sigmoidal bend on a log-log scale that is observed in experimental data. In the Sinh model, critical damage is always unity and the sigmoidal bend in the minimum creep strain rate and stress-rupture curves is present. Overall the Sinh model is more accurate.

Effect of α<sub>2</sub> Precipitation on Creep and Tensile Properties of Ga-Added Near-α Titanium Alloys

The effect of α2 precipitation on the creep and tensile properties was investigated for bimodal and lamellar microstructures in two Ga-added near-α Ti alloys with Al equivalences of 10.6 and 11.5. Fine α2 phase formed in the α phase of both alloys. The volume fraction of the α2 phase for the Al equivalences of 10.6 and 11.5 is equivalent to 57.6 % and 73.3 %, respectively, in the binary Ti-Al system at 600 °C. Creep tests were carried out under a constant stress of 310 MPa at 600 °C and tensile tests were performed at room temperature. Lamellar microstructure showed lower minimum creep strain rates than bimodal microstructure for both alloys. The increase in Al equivalence increased creep life by a factor of 1.6 and decreased the minimum creep strain rate from 6.51 × 10-8 s-1 to 3.99 × 10-8 s-1 in bimodal microstructure. In addition, the increase in Al equivalence decreased room temperature tensile elongation although both alloys contained a similar volume fraction of equiaxed α in a bimodal microstructure.

The development of a novel technique for small ring specimen tensile testing

The wide scale use of small specimens in routine testing programs could significantly reduce material resource requirements (factors of 10 are easily achievable). This is a major benefit to situations where there is not enough material to manufacture conventional, full-size specimens, such as first-stage gas turbine blade roots. However, limitations exist due to concerns over size effects, manufacturing difficulties, uncertainties related to the application of representative loading conditions and complex interpretation procedures of non-standard data. Due to these limitations, small specimen testing techniques have been mostly applied in ranking exercises and to determine approximate or simple material parameters such as Young’s modulus, minimum creep strain rate and fracture toughness. The small ring method is a novel, high sensitivity small specimen technique for creep testing that has been extended in the present work to the determination of tensile material properties. The main advantages of the small ring specimen are that it is self-aligning and has a large equivalent gauge length in comparison to other small specimens, resulting in much higher testing sensitivity. In the present work, this specimen type mimics conventional, full-size, monotonic testing, allowing for observations of elastic and plastic material response to be made. Wrought aluminium alloy 7175-T7153 small rings were tested at room temperature at 5 different loading (displacement) rates and the results compared to conventional, full-size, monotonic specimen equivalents. Finite element analysis was conducted in order to evaluate the equivalent gauge section and equivalent gauge length in the small ring specimen (which varied between circa 0.35–1.4 mm2 and 25–45 mm, respectively) to facilitate these comparisons. An analytical solution has also been derived in order to validate the finite element analysis.

Tensile, creep and fracture testing of prospective Fe-Al-based alloys using miniature specimens

Mechanical properties of prospective Fe-Al- based alloys were investigated using miniature specimens. This enables testing of material from experimental heats that did not allow preparation of standard specimens. Small punch test and mini-tensile test were applied for estimation of the mechanical properties of Fe-22 Al and Fe-22Al-7Ti (at.%) at high temperatures. It is shown that the force applied in the small punch test can be successfully converted into the equivalent applied stress using the empirical formula suggested by the new European standard for small punch testing. The minimum deflection rate can be converted into the minimum creep strain rate as well. The improvement of the latter conversion based on the Monkman-Grant relationship is proposed. The small punch testing enables evaluation of rupture properties including the creep rupture strength. This can effectively complement previous investigations of Fe-Al-Ti alloys performed predominantly in uniaxial compression. It is shown that a significant increase in creep resistance is achieved by addition of titanium and a two-phase microstructure analogical to that in γ′-strengthened nickel-based superalloys is observed.

Characterization of creep deformation and rupture behaviour of P92 steel weldment at 600°C

P92 steel is a potential candidate for ultra-supercritical (USC) plant component. Thus, its suitability and performance for future service are still under investigation. Understanding the creep behaviour is essential to design the components that can sustain in service over a certain period. With the intention to investigate the creep deformation and rupture behaviour of P92 steel weldment, four cross-weld creep specimens were prepared and tested at 600°C at different stress levels. All specimens ruptured between 400 and 4,000 hours. Following the creep test, fractography examination was performed. P92 steel weldment exhibits clear primary, secondary and tertiary creep deformation stages. At long-term, the time portion for primary deformation as compared to rupture time reduces, however, secondary stage is observed to dominate. Deformation and rupture data obeys the power law relation which indicates the material deforms at a higher rate and rupture earlier as the stress increases. Ductility of P92 steel weldment reduces as the stress decreases. A strong correlation between minimum creep strain rate and time to rupture is observed when the data is fitted using original Monkman-Grant (MG) and Modified Monkman-Grant (MMG) relations. Examination of fracture surface reveals that at high stress, transgranular-type of fracture is dominant. As creep time increases, a mixture between the intergranular and transgranular fracture is evidence.