Minimum Creep Strain Rate Research Articles

An Advanced Sine-Hyperbolic Creep-Damage Model Incorporating Threshold Strength

Abstract This study aims at improving the classic sine-hyperbolic (Sinh) creep-damage model to predict minimum-creep-strain-rate (MCSR), rupture, damage, and creep deformation. The Sinh model employs a continuum-damage-mechanics-based framework to model secondary and tertiary creep regimes. In Sinh, the creep strain and damage rate equations exhibit an implicit threshold stress that arises during numerical optimization. Herein, the Sinh model is modified to include an explicit threshold strength as a material property and the tensile strength. Threshold strength is defined as the lower limit for creep activation at a given temperature. Stresses are applied below the threshold, resulting in infinite life. The advanced Sinh offers several advantages including a physical significance of stress ratios where the onset of creep is defined by threshold strength, a closed-form solution where the rate equations remain finite at any combination of stress and temperature, and adaptability in finite element analysis where the solution space remains numerically stable. Experimental creep data of 304 SS at multiple isotherms are gathered from prior literature. The advanced Sinh is calibrated to the MCSR and SR data of 304 SS. The calibration of threshold strength follows a standard procedure from literature and is observed to be realistic for stainless steel at elevated temperatures. The MCSR and SR predictions illustrate the Sigmoidal bend and demonstrate zero creep rate and infinite life at or below threshold strength. The creep deformation and damage predictions exhibit agreement with experimental data. The advanced Sinh is validated by employing finite element simulation to ensure the applicability of the model across a range of applications. The advanced Sinh improved creep response prediction and added physical realism to the model's framework.

Investigation on the room temperature compressive creep behavior of TC4 titanium alloy joints with vacuum electron beam welding

The room temperature compressive creep behavior is a key issue for the titanium alloys welded structural components served in deep-sea environment. In the present work, the compressive creep behavior of different areas for TC4 titanium alloy joints with vacuum electron beam welding was systematically studied, and it is found that the fusion zone (FZ) of TC4 titanium alloy joints has the minimum creep strain rate. This is mainly because the creep deformation of TC4 titanium alloy is mainly controlled by the movement of dislocations in the α or α′ phases, the size of α′ phase in FZ is small, and thus the dislocation slip is limited. MD simulation results have further revealed that the room temperature compressive creep nature of α-Ti can be regarded as a dynamic hysteresis phenomenon in plastic strain and is dominated by the dislocation movement.

Thermo-mechanical creep-fatigue damage evolution and life assessment of TiAl alloy

Thermo-mechanical creep-fatigue (TMCF) behaviors of a TiAl alloy were investigated by conducting various creep, creep-fatigue, and thermo-mechanical tests and performing detailed microstructural analysis. A new creep model was proposed to unify primary strain hardening and tertiary accelerating damage effects. The TMCF failure of TiAl alloys is accompanied by the crack initiation from surface oxides/carbides and mixed transgranular and intergranular cracking. It revealed that introducing thermo-mechanical cycles significantly reduces the creep damage rate during the creep dwell stage and the fatigue process, i.e., the creep-delaying effect, which is attributed to the non-proportional strengthening effect induced by thermal cycles. A life model based on the average minimum creep strain rate was proposed to predict the creep-dominated TMCF life. This model incorporates the complex creep-fatigue interactions on creep damage and demonstrated good agreement with experimental results under varying loading conditions. The present work provides new insights into understanding the creep-dominant thermo-mechanical damage evolution of TiAl alloys.

Creep life assessment of modified 9Cr-1Mo steel based on Monkman–Grant relationship considering temperature and stress dependences of strain required for rupture

ABSTRACT Regarding the application of the Monkman-Grant relationship to creep strength enhanced ferritic steels such as modified 9Cr-1Mo and 12Cr steels, there have been many reports showing that results tend to be an overestimation of the creep life in the long-term region. To address this issue, an author conducted a study to improve the estimation accuracy in the long-term region by the Monkman Grant relationship. Analysing the published creep test data for modified 9Cr-1Mo steel, the author found that the product of the minimum creep strain rate and rupture time (Ɛ MG ) is not constant but depends on the loading conditions, which are test temperature and stress. Then, the author proposed an extended Monkman-Grant relationship considering the dependence of Ɛ MG on the loading conditions. When this model was applied to the data for modified 9Cr-1Mo and 12Cr steels, the creep life was predicted with good accuracy from the short-term to long-term regions.

Microstructural effects on the ambient temperature indentation creep behavior of metastable β Ti-5Al-5V-5Mo-3Cr alloy

Ti-5553 alloy is considered as a potential candidate for heavy structural components such as landing gears in aerospace industries, that operate particularly at room temperature. For achieving the targeted performance, microstructural modification and corresponding improvement in mechanical properties, particularly room temperature creep behavior of Ti-5553 alloy is of significant concern. In this regard, an optimized thermomechanical processing (TMP) schedule is employed to tailor the microstructure of as-cast Ti-5553 alloy. Typical bimodal microstructure containing both α and β phases is noted to evolve upon TMPing, as compared to its as-cast counterpart, having sole β phase. The size and volume fraction of αp are noted to be 0.85 ± 0.39 µm and 11.7 ± 0.5%, respectively. Such pronounced variation in the microstructural features is expected to alter the localized mechanical properties significantly. To assess that, room temperature small-scale creep behavior of as-cast and TMPed Ti-5553 alloys is investigated using nanoindentation technique. The effect of maximum load on different creep parameters are analyzed and correlated with the corresponding microstructures. It is noted that at any particular applied load level, creep deformation of TMPed Ti-5553 alloy is ∼ 20–64% lower than that for the as-cast one. This is reflected in significant reduction in the minimum creep strain rate from 10−4 s−1 for as-cast to 10−5 s−1 for TMPed Ti-5553 alloy. Dislocation creep mechanism is found to be active for both the alloys since creep exponent for both the as-cast and TMPed Ti-5553 alloys exceed the value of 2. Discontinuous semi-circular micro-shear bands are noted to form around the indents for the as-cast Ti5553 alloy. The kernel average misorientation map for this alloy reveals a lower degree of misorientation and a more homogeneous distribution of plastic strain. In contrary, the TMPed Ti-5553 alloy exhibits higher misorientation around the indent impression, thereby indicating towards the restriction of dislocation movement against α/β laths and hence positively influencing the creep behavior. Overall, the study highlights the important role of TMP in enhancing the creep resistance of Ti-5553 alloy for industrial applications.

A Calibration Approach for Accelerated Creep Testing for Electron Beam Melted Ti-6Al-4V Using the Wilshire–Cano–Stewart Model

Abstract This study outlines a model calibration approach for an accelerated creep test called the dynamic negative stepped test (DNST) to enable the rapid screening of creep-resistant materials. In DNST, stress is stepped decreased based on the attainment of a sufficient minimum-creep-strain-rate (MCSR) at each stress level. Steps are repeated, torturing the material, until rupture occurs. The DNST is advantageous as a screening test for new alloys. Alloys and heats with superior creep resistance will be able to survive longer and with greater ductility than those with poor creep resistance. The calibration of a constitutive model to DNST data furnishes predictions of the conventional creep response being between 65 h and 6685 h from the relatively short (<130 h) DNST Data. In this study, DNSTs are performed on electron beam melted (EBM) Ti-6Al-4V at 650 °C with stepping through 150, 75, 60, and 50 MPa. Six build orientations are tested including 0 deg, 30 deg, 45 deg, 60 deg, 90 deg, and V (vertical) direction. The Wilshire–Cano–Stewart (WCS) model is employed to calibrate the experimental data. A systematic calibration approach is adopted. Each step is calibrated numerically. A unique set of minimum-creep-strain-rate (MCSR) and stress-rupture (SR) related material constants, i.e., the Wilshire and Sinh constants are obtained for each build direction. A nonhomogenous objective function is used to numerically optimize the strain trajectory and damage trajectory constants. To find the best-fit curve, the strain trajectory constants, and damage trajectory constants are numerically refined for each step. The WCS model shows a near-perfect prediction of the DNST data. Based on the calibrated constants, conventional creep curves are generated in order to determine which build orientations are likely to exhibit poor, moderate, and superior creep resistance. Predictions of MCSR and SR curves over a wide stress range are estimated outside the experimental range to investigate the extrapolation pedigree of the approach. This will allow the material designers to have more confidence in DNST-generated test data for predicting long-term creep response and structural lifetime.

Creep property and microstructural evolution of laser powder bed fused binary Al–10Ce alloy

Aluminum–Cerium (Al–Ce) based alloys have shown promise as cost-efficient high temperature creep-resistant aluminum alloy. These alloys are also highly printable with laser powder bed fusion (LPBF) additive manufacturing. This study investigates the creep property of a near eutectic binary Al–10Ce (wt. %) alloy manufactured by LPBF and its microstructural evolution during creep. The as-built alloy exhibited columnar grain structure with a weak cube texture and its microstructure consisted of fine eutectic Al + Al11Ce3. Compressive creep tests with incremental stresses were performed perpendicular to the build direction at temperatures ranging from 275 to 400 °C. The stress exponent was approximately 1 in the low stress regime and 5–7 in the high stress regime, corresponding to diffusion and dislocation creep, respectively. The average activation energy was approximately 229 kJ/mol·K in the temperature between 275 and 375 °C. After creep deformation, the melt pool boundary faded and the eutectic Al11Ce3 intermetallics slightly coarsened. The grain structure remained relatively stable and the grain boundary became more pronounced. By comparing the minimum creep strain rate to other alloys, it was found that LPBF Al–10Ce is more creep resistant than similar cast binary Al–Ce counterpart, some ternary Al–Ce alloys and LPBF AlSi10Mg alloy. This benchmark results on the creep property of LPBF binary eutectic Al–Ce alloy provide insights to future development of creep-resistant Al–Ce alloys.

Probabilistic creep with the Wilshire–Cano–Stewart model

AbstractCreep behavior is susceptible to uncertainty. Replicated creep data for steel can exhibit logarithm decades of uncertainty, which necessitates the development of probabilistic creep models for reliability‐based design. The deterministic Wilshire–Cano–Stewart (WCS) model is transformed into a probabilistic creep deformation, damage, and rupture prediction model via injecting the uncertainty of test conditions, pre‐existing damage, and material constants. The WCS model is calibrated to replicated quintuplicate creep data from a “single heat” of 304 stainless steel. The Markov chain Monte Carlo (MCMC) method with the Metropolis–Hastings (MH) algorithm is employed to introduce the sources of uncertainties into the model via calibrated probability distribution functions (pdfs). The probabilistic predictions encapsulate most of the experimental outliers across isostresses‐isotherms. Interpolative and extrapolative assessments reveal that minimum‐creep‐strain‐rate (MCSR) and stress rupture (SR) predictions are consistent across isotherms. The WCS probabilistic model captures the range of creep behavior of a single heat of material using short‐term data.

Using tube specimen to investigate the creep behavior of FeCrAl fuel cladding tubes

Fuel cladding tubes of nuclear power plants are operated at high temperatures. Creep behavior is therefore a crucial factor during the design and safety assessment of fuel cladding tubes. In this study, small punch creep tests (SPCTs) were conducted for tube specimens to examine the creep behavior of FeCrAl fuel cladding tubes. According to Chakrabarty’s membrane stretching theory and finite element simulation results, specimen shape had a negligible influence on the equivalent uniaxial creep stress and minimum creep strain rate. Therefore, the calculation equations of equivalent uniaxial creep stress and creep strain of plate specimens were directly used for tube specimens. When the lower die round radius was 0.2 mm, its effect on the calculated creep stress was within 5%, and it was negligible for the calculated minimum creep strain rate. The power law creep model of the FeCrAl fuel cladding tube was obtained based on the test results of SPCT using tube specimens.

High Temperature Strength Property and Creep-Fatigue Life Prediction of a Temper Bead Welded CrMo Casting Steel

Cr-Mo casting steels are widely used as casings and valves in thermal power plants. Creep fatigue damage gradually proceeds in these high-temperature components during operation resulting in creep voids and micro crack initiation in which repair welding is considered to be applied for life extension. In this study, a temper bead welded joint of Cr-Mo casting steel as well as fine and coarse grain simulated materials were prepared. Creep and fatigue, creep-fatigue tests were performed using specimens taken from base and weld metals of the welded joint, the simulated materials and cross welded specimens. Material constants of creep deformation and cyclic stress-strain properties for constituted materials of the welded joint were obtained from the creep and fatigue tests. Minimum creep strain rate of the base metal at the same stress was the highest than that of other materials. Plastic deformation resistance is higher in the order of the base metal, fine grain, coarse and weld metal. Creep-fatigue life of the welded joint, which failed at the base metal 2mm away from the boundary between the base metal and fine grain, was shorter than that of the uniform base metal specimen indicating that the temper bead welding may reduce the creep-fatigue life. Finite element analysis of the cross welded specimen showed that elastic-plastic and creep strains accumulated at the base metal near the boundary are higher than those at other regions causing life reduction and failure at the base metal. The creep-fatigue life prediction by using the analysis results indicated that the nonlinear damage accumulation model gave more accurate life prediction results than the time fraction and ductility exhaustion rules.

Correlation Analysis of Established Creep Failure Models through Computational Modelling for SS-304 Material

To maintain safety and reliability in power plants, creep-life prediction models have received much attention over the years. This article was designed to focus on the conditions when a material structure is exposed to extremely high temperatures and pressures with the help of finite element analysis. A direct comparison of the feasibility of different models’ fitness and suitability in predicting creep damage was presented in this article by simulating the damage evolution of a uniaxial SS-304 specimen under a pre-defined load, using established constitutive creep models. Comparative assessments of minimum creep strain rate, creep deformation, and stress rupture were demonstrated using the Norton–Bailey (NB), Kachanov–Rabotnov (KR), Theta projection (TP), and sine-hyperbolic (SH) models while standardizing them with the Omega model. The FE results of a dog-bone specimen, while implementing the models, were compared with the actual creep experiment results to check for the models’ reliability and validation. Subsequently, sensitivity studies of the established creep models were conducted using the statistical tools RSM and ANOVA, with an analysis of how the parameters for operation, design, and material dependency came into effect. Thus, quantitative and qualitative correlation analyses of the FE creep response for these five established models were conducted together, resulting in finalizing the selection of the most suitable model, the sine-hyperbolic model, for the SS-304 material under the defined boundary conditions. The 0.84 R2 value of the sine-hyperbolic model proved the model’s selection for predicting the creep response of stainless steel 304. The method can be applied to select a suitable creep damage model as per the feasibility of the operating conditions.

Tensile creep behavior of HfNbTaTiZr refractory high entropy alloy at elevated temperatures

Tensile creep, which is one of the most important deformation modes for high temperature applications, is rarely reported for refractory high entropy alloys (RHEAs). In the present study, the optical floating zone (OFZ) technique was used to fabricate HfNbTaTiZr with grain size larger than 1 mm on average; tensile creep tests under vacuum at 1100-1250°C and stepwise loading of 5–30 MPa were conducted. The stress exponents and creep activation energies were determined to be 2.5–2.8 and 273 ± 15 kJ mol–1, respectively. The stress exponents determined have suggested solute drag creep behavior, and deformation was governed by a/2<111> type dislocations. To elucidate the effect of alloying constituents on solute drag creep, intrinsic diffusion coefficients of all elements were determined by simulation, and theoretical minimum creep strain rates were compared with those of experimental values. Analysis suggests that creep rate of HfNbTaTiZr appears to be controlled by Ta, which possesses the lowest intrinsic diffusivity and contributes the most to drag dislocations. To our knowledge, this work is the first to report tensile creep deformation mechanism of HfNbTaTiZr, especially up to 1250°C.

Application of a modified hyperbolic sine creep rate equation to correlate uniaxial creep data vs. stress and temperature for creep resistant low chrome steel alloys

ABSTRACT Modified hyperbolic sine minimum creep rate equations were used to correlate uniaxial minimum creep strain rate data of 1/2Cr-1/2Mo-1/4 V and Grade 22 steel alloys and to correlate creep life data of Grade 22 steel when coupled with the Monkman-Grant equation. Hyperbolic sine equations were selected because of their physical basis in dislocation creep and numerical stability. Both equations provided very good fits to minimum strain rate data over a wide range of temperatures and stresses. Reasonable correlations of a large Grade 22 creep life data set were obtained with goodness of fit nearly equivalent to those obtained with the Larson-Miller and Wilshire equations, and with more conservative predictions of long-term creep strength. However, all these equations provided a poor fit to the entire data set when only short-term data (tr < 5,000 h) were correlated, and they predicted lower long-term creep rupture strengths vs. the full data set correlations.

An initial study on the impression creep behaviour of stir-cast GNP reinforced AA6061 composite (AMMC)

Impression creep testing technique is used to screen out creep behaviour of materials as it is relatively faster method, requires small volume of the specimen, and is relatively material non-invasive technique when compared to conventional uniaxial tensile creep test method. This technique also possesses the benefit of maintaining constant stress throughout the experiment because a flat cylindrical indenter is used to apply load on the specimen. Owing to commercial unavailability of the materials under development such as metal matrix composites (MMC), the impression creep testing approach for such materials becomes a best method. In present work, creep behaviour of stir-cast graphene nanoplatelets (GNP) reinforced AA6061 composite (AMMC) is studied by using impression creep tests. The AMMC was prepared by adding GNPs in AA6061 through stir casting process by melting the alloy up to 1073 K. The impression creep experimentation included stress levels of 140 MPa, 170 MPa, and 200 MPa at a temperature of 573 K, 603 K and 633 K. The tests were conducted at constant stress by varying the temperature and vice-versa in vacuum. Two distinct regions i.e., primary and secondary/steady-state were observed and minimum creep strain rate was obtained in steady-state region. Tertiary region was absent, since the load/stress applied was compressive. During the experiment, depth of indentation of 0.03 mm to 0.14 mm was produced in the specimen. The microstructure of the composite has been analyzed using optical microscope and scanning electron microscope (SEM) to correlate with impression creep behaviour of the studied materials.

Recent progress on the modelling of the minimum creep strain rate and the creep cavitation damage and fracture

ABSTRACT Modelling of the long-term creep damage and lifetime is very challenging due to their strong stress level dependence. Aiming at developing a set of creep damage constitutive equations suitable for long-term service, research was carried out in modelling of the minimum creep strain rate, creep cavitation damage and rupture, and the coupling between creep cavitation damage and creep deformation. Firstly, based on the stress driven concept, the cavity nucleation model and cavity growth model were calibrated together using cavity histogram. Then, a simple analytical equation was derived to model creep cavitation damage. Furthermore, the creep cavitation damage model offered the theoretical background and supports for the stress-based extrapolation method and time-based extrapolation method. Two case studies were carried to explore the opportunities. This paper summarizes some of the progresses. This paper contributes to the generic methodology as well as the specific knowledge to the topic area.

Accelerated Creep Test Qualification of Creep-Resistance Using the Wilshire–Cano–Stewart Constitutive Model and Stepped Isostress Method

Abstract In this study, a qualification of accelerated creep-resistance of Inconel 718 is assessed using the novel Wilshire–Cano–Stewart (WCS) model and the stepped isostress method (SSM) and predictions are made to conventional creep data. Conventional creep testing is a long-term continuous process; in fact, the ASME B&amp;PV III requires that 10,000+ h of experiments must be conducted to each heat for materials employed in boilers and/or pressure vessel components. This process is costly and not feasible for rapid development of new materials. As an alternative, accelerated creep testing techniques have been developed to reduce the time needed to characterize the creep resistance of materials. Most techniques are based upon the time-temperature-stress superposition principle that predicts minimum-creep-strain-rate (MCSR) and stress-rupture behaviors but lack the ability to predict creep deformation and consider deformation mechanisms that occur for experiments of longer duration. The SSM has been developed, which enables the prediction of creep deformation response as well as reduce the time needed for qualification of materials. The SSM approach has been successful for polymer, polymeric composites, and recently has been introduced for metals. In this study, the WCS constitutive model, calibrated to SSM test data, qualifies the creep resistance of Inconel 718 at 750 °C and predictions are compared to conventional creep testing data. The WCS model has proven to make long-term predictions for stress-rupture, MCSR, creep deformation, and damage in metallic materials. The SSM varies stress levels after time interval adding damage to the material, which can be tracked by the WCS model. The SSM data is calibrated into the model and the WCS model generates realistic predictions of stress-rupture, MSCR, damage, and creep deformation. The calibrated material constants are used to generate predictions of stress-rupture and are postaudit validated using the National Institute of Material Science database. Similarly, the MCSR predictions are compared from previous studies. Finally, the creep deformation predictions are compared with real data and is determined that the results are well in between the expected boundaries. Material characterization and mechanical properties can be determined at a faster rate and with a more cost-effective method. This is beneficial for multiple applications such as in additive manufacturing, composites, spacecraft, and industrial gas turbines.

Numerical Prediction of Creep Rupture Life of Ex-Service and As-Received Grade 91 Steel at 873 K

Infallible creep rupture life prediction of high temperature steel needs long hours of robust testing over a domain of stress and temperature. A substantial amount of effort has been made to develop alternative methods to reduce the time and cost of testing. This study presents a finite element analysis coupled with a ductility based damage model to predict creep rupture time under the influence of multiaxial stress state of ex-service and as-received Grade 91 steel at 873 K. Three notched bar samples with different acuity ratios of 2.28, 3.0 and 4.56 are modelled in commercial Finite Element (FE) software, ABAQUS v6.14 in order to induce different stress state levels at notch throat area and investigate its effect on rupture time. The strain-based ductility exhaustion damage approach is employed to quantify the damage state. The multiaxial ductility of the material that is required to determine the damage state is estimated using triaxiality-ductility Cock and Ashby relation. Further reduction of the ductility due to the different creep mechanisms over a short and long time is also accounted for in the prediction. To simulate the different material conditions: ex-service and as-received material, different creep coefficients (A) have been assigned in the numerical modelling. In the case of ex-service material, using mean best fit data of minimum creep strain rate gives a good life prediction, while for new material, the lower bound creep coefficient should be employed to yield a comparable result with experimental data. It is also notable that ex-service material deforms faster than as-received material at the same stress level. Moreover, higher acuity provokes damage to concentrate on the small area around the notch, which initiates higher rupture life expectancy. It also found out that, the stress triaxiality and the equivalent creep strain influence the location of damage initiation around the notch area.

A meso-mechanical approach to time-dependent deformation and fracturing of partially saturated sandstone

In the present paper, we investigate how water acts to weaken rock in two complementary ways: mechanically through the generalized effective stress principle, and chemically through time-dependent rock-fluid reactions that allow subcritical crack growth. These processes, together with capillary suction and stress corrosion , were incorporated into a three-dimensional discrete element grain-based model to investigate both the time-independent and the time-dependent mechanical behavior of partially saturated sandstone at the mesoscale . The capillary parameters related to capillary suction and subcritical parameters related to stress corrosion in the model were calibrated to match the deformation behavior of partially saturated sandstone observed in laboratory. Following this calibration, numerical simulations of partially saturated sandstone with different levels of saturation were performed in uniaxial compression. The simulations show that both the peak strength and elastic modulus of the sandstone decrease as a function of increasing saturation and that the relationships between these properties can be expressed by negative exponential functions. The simulations are in good agreement with the experimental results. Second, the long-term brittle deformation of partially saturated sandstone with different levels of saturation under a constant stress level was modeled. The results show that time-to-failure during brittle creep decreases, and the initial strain and the minimum creep strain rate increases, as a function of increasing saturation, as also observed in laboratory. The simulations also highlight the formation of tensile cracks as the main deformation mechanism during brittle creep. Finally, brittle creep in partially saturated sandstone samples with different levels of saturation was studied under different stress levels. These simulations show that the minimum creep strain rate and the time-to-failure as a function of stress can be well described by exponential relations. We conclude that the proposed model permits a deeper understanding of time-independent and time-dependent deformation and failure of partially saturated sandstone at the mesoscale.

Investigation of modelling the minimum creep strain rate of P91 over a wide range of stress

ABSTRACT Four sets of experimental data of a minimum creep rate of P91 in different range of stress (from 1.1 to 350 MPa) were compiled for the calibration of the linear + power law and modified sine law. An investigation was conducted to examine the accuracy of both laws in different range of stress. It appears that modelling result of linear + power law fitted experimental data well in low and high stress level while modified sine law fits experimental data in all stress level. The predicted results from narrow ranges of stress indicates that linear power law requires data from both high and low stress levels to make a prediction, modified sine law could make prediction on a wider range of stress with data from a narrow range of stress. This conclusion could help research on predicting low stress level’s data with experimental data from high stress level.

Design of near α-Ti alloys using δ-parameter

In this study, to obtain a high solid-solution strengthening effect, new Ti alloys with bimodal structures were designed using the δ-parameter, which represents the average atomic radius misfit of the constituent elements used in high-entropy alloys. The δ-parameter calculated by the alloy composition was used to estimate the average solid-solution strengthening of the alloys. In particular, to clarify the effect of Zr and Sn in Ti alloys, Ti alloys were designed with different amounts of Zr and/or Sn using the δ-parameter. The compressive strength and creep behavior of the designed alloys were investigated to determine whether the δ-parameter is useful for designing strengthened alloys. The compressive strength of the designed alloys was comparable to or higher than that of the commercial TIMETAL834 alloy up to 650 °C. This indicates that the δ-parameter is a useful parameter for estimating the average solid-solution strengthening of the alloys. The compressive strengths of the designed alloys were approximately proportional to the 4/3 power of the δ−parameter. An increase in the strength by precipitation strengthening by α2-Ti3Al was also observed in the Sn-added alloys, whereas Ti3Al was not formed in the Sn-free alloys. Microstructural factors, such as the volume fraction of the equiaxed α phase and lamellar spacing in the bimodal microstructure, significantly contributed to the minimum creep strain rate, in addition to solid-solution and precipitation strengthening.