Decreasing Strain Rate Research Articles

Creep at low stresses in aluminium (Harper-Dorn) and in an austenitic stainless steel with a stress exponent of 1

Creep tests at very low stresses are often terminated before the stationary stage is reached, which makes it essential to use a model for primary creep to assess the results. Such a model was developed in a recent paper by the author. The model is applied to creep at very low stresses where dislocation creep is the controlling mechanism. Two cases are investigated. i) Aluminium at very high temperatures. This is usually referred to as Harper-Dorn creep. ii) The austenitic stainless steel 316H at 700ºC. Most aluminium data for the considered case can be modelled assuming stationary conditions, but some data has to be represented with the primary creep model giving stress exponents down to 1. Contrary to the case for aluminium, the data for 316H at low stresses are very far from stationary conditions. The model results give in agreement with observations a stress exponent of 1 and stress strain curves consistent with the ϕ (phi) model, i.e. an exponentially decreasing strain rate with increasing time. The consistency with the ϕ model verifies that dislocation creep is the controlling mechanism in spite of the fact that the Coble model gives a higher strain rate for diffusion creep.

Hot compression behavior of Mg–Zn–Y–Mn–Ti magnesium alloy enhanced by lamellar LPSO phase and spherical W phase

The hot compression experiments of the solution-treated Mg93.5Zn2.5Y2.5Mn1Ti0.5 alloy were carried out using a Gleeble-1500D thermal simulator under the conditions of a temperature of 350∼500 °C, a strain rate of 0.001–1 s−1 and a strain of 0.9. According to the stress-strain curve, the characteristics of flow stress were analyzed. Moreover, the constitutive equation of flow stress, the kinetic model of dynamic recrystallization, and the processing map were established. The results show that the flow stress of the alloy decreases as the deformation temperature increases or the strain rate decreases. The constitutive equation of flow stress can be expressed as a hyperbolic sine function: ε˙=4.27115×1019[sinh(0.01153σ)]8.493×exp(2.856×105/RT). With the increase of the deformation temperature or the decrease of the strain rate, the volume fraction and grain size of dynamic recrystallization of the alloy increase continuously. Its dynamic recrystallization volume fraction can be expressed by the Avrami equation as: XDRX=1−exp[−2.05((ε−εc)/ε∗)1.42]. The instability region of the alloy increases with the increase of strain. The first instability region is (350–410 °C, 0.12–1 s−1), the second one is (450–500 °C, 0.001–1 s−1), and the optimum domain for the hot processing of this alloy is (380–450 °C, 0.001–0.01 s−1).

Evolution of Grain Structure and Dynamic Precipitation during Hot Deformation in a Medium-Strength Al-Zn-Mg-Er-Zr Aluminum Alloy.

The hot deformation behavior of Al-Zn-Mg-Er-Zr alloy was investigated through an isothermal compression experiment at a strain rate ranging from 0.01 to 10 s-1 and temperature ranging from 350 to 500 °C. The constitutive equation of thermal deformation characteristics based on strain was established, and the microstructure (including grain, substructure and dynamic precipitation) under different deformation conditions was analyzed. It is shown that the steady-state flow stress can be described using the hyperbolic sinusoidal constitutive equation with a deformation activation energy of 160.03 kJ/mol. Two kinds of second phases exist in the deformed alloy; one is the η phase, whose size and quantity changes according to the deformation parameters, and the other is spherical Al3(Er, Zr) particles with good thermal stability. Both kinds of particles pin the dislocation. However, with a decrease in strain rate or increase in temperature, η phases coarsen and their density decreases, and their dislocation locking ability is weakened. However, the size of Al3(Er, Zr) particles does not change with the variation in deformation conditions. So, at higher deformation temperatures, Al3(Er, Zr) particles still pin dislocations and thus refine the subgrain and enhance the strength. Compared with the η phase, Al3(Er, Zr) particles are superior for dislocation locking during hot deformation. A strain rate ranging from 0.1 to 1 s-1 and a deformation temperature ranging from 450 to 500 °C form the safest hot working domain in the processing map.

Effect of 316L Stainless Steel Fabrication on Oxidation Resistance, Surface Morphology, and Hot Tensile Behavior

Samples based on 316L stainless steel were prepared by conventional manufacturing process (CM) and laser powder bed fusion (L-PBF). Surface morphology changes under air oxidation in the temperature range 600-900 °C were carried out. Tensile tests were carried out in the temperature range of 700-900 °C for strain rates between 0.001 and 0.1 s−1. The materials showed good oxidation resistance up to 700 °C. The CM and L-PBF material had a high mass gain instability and similar microstructures developed under high temperatures were found in both alloys. Increased temperature increases Cr concertation in the L-PBF material up to 40 at.% at 800 °C and a rich Fe based oxide is formed at 900 °C. Slightly thicker oxide scales were formed in the CM than in the L-PBF material.The hot tensile tests reveal that a fast work hardening occurs for all hot tensile tested samples up to a strain of approximately 0.025. Low temperatures and high strain rates within the investigated range promote a second work hardening regime, while a plateau in the flow stress is observed at high temperatures and low strain rates. The highest yield stress and peak stress values are reached at 700 °C. The yield stress is nearly independent of the strain rate at 700 °C. It decreases with a decrease in strain rate for 800 and 900 °C, and it decreases with an increase in temperature. The elongation till fracture varies from 10 to 22%, and it is strongly influenced by defects inherent of the L-PBF process.

Revealing the deformation behavior and microstructure evolution in Mg-12Y–1Al alloy during hot compression

In this study, the hot uniaxial compression of the heat-treated Mg-12Y–1Al alloy containing long-period stacking ordered (LPSO) phase was conducted by a Gleeble-3500 simulator. Compressive mechanical properties at elevated temperatures and the effects of deformation temperature (300–450 ℃) and strain rate (0.001–1 s−1) on the hot deformation behavior of the alloy were systematically investigated. Combining with an optical microscope (OM), electron backscatter diffraction (EBSD), and in-grain misorientation axes (IGMA) analysis, the microstructure and texture evolution, dislocation slip, and dynamic recrystallization (DRX) mechanism of the alloy was studied in detail. The results showed that the flow stress decreased with the increase in temperature and the decrease in strain rate. At a strain rate of 1 s−1, the compressive strength at 300 ℃ and 350 ℃ was basically the same. After deformation, the morphology of Al2Y had almost no change, while the LPSO underwent apparent kinking deformation. The increase in temperature was conducive to DRX. The DRX mechanism of the alloy mainly included discontinuous dynamic recrystallization (DDRX) and continuous dynamic recrystallization (CDRX), and DDRX was dominant. The dense lamellar LPSO at the grain boundary was detrimental to the occurrence of DDRX. In addition, the deformed microstructure presented a typical [0001]//CD (compression direction) texture. With the increase in temperature, the texture intensity decreased progressively due to the activation of multiple slip systems and the increased DRX fraction. At a strain rate of 0.01 s−1, when the temperature increased to 450 ℃, the number of deformed grains dominated by pyramidal Ⅱ<c+a> slip increased substantially.

Hot deformation behavior and dynamic recrystallization mechanism of Ti2ZrTa0.75 refractory complex concentrated alloy

Hot-deformation behavior and dynamic recrystallization (DRX) mechanism of Ti2ZrTa0.75 refractory complex concentrated alloy were systematically studied via uniaxial compression tests at various deformation temperatures from 800 °C to 1100 °C and different strain rates from 10−3 s−1 to 1 s−1. Stress-strain curves showed an increase in flow stress with decreasing deformation temperature and/or increasing strain rate, and there was continuous strain softening after the peak stress. Microstructure analysis based on electron backscattering diffraction (EBSD) indicated that deformation bands occurred in the hot deformation microstructure with a strain rate of 1 s−1, which is the appropriate location for DRX. Microstructure analysis revealed that DRX occurred during the hot deformation process and DRX fraction and grain size increase with increasing deformation temperature and/or decreasing strain rate. The grain boundary bulging nucleation mechanism and necklace-like structure of DRX grains demonstrate a typical discontinuous dynamic recrystallization (DDRX) process. Cumulative misorientation analysis of the initial grain interior and new grains formed without relying on the initial grain boundaries proved the occurrence of continuous dynamic recrystallization (CDRX).

Constitutive modeling for elevated temperature flow behavior of a novel Cr-Si alloyed hot stamping steel

The flow behavior of a novel Cr-Si alloyed hot stamping steel (Cr-Si steel) at elevated temperature was investigated via isothermal compression tests on a Gleeble-3500 thermomechanical simulator with a temperature range of 600 ∼ 900 °C and a strain rate range of 0.1 ∼ 10 s−1. Subsequently, the Arrhenius-type constitutive model, comprising strain compensation, was established in accordance with the friction and adiabatic heating corrected stress-strain curves. Furthermore, the predictability and prediction accuracy of the constitutive model were verified. The results reveal that at a constant strain rate, the flow stress of the Cr-Si steel initially increases as the strain increases before tending to stabilize, owning to the combined effects of work hardening and dynamic recovery. The peak flow stresses decrease as the temperatures increase and the strain rates decrease. The constitutive model can accurately predict the elevated temperature constitutive relationship of the Cr-Si steel during the hot stamping process.

Low strain rate yield characteristics and failure modes of solid composite propellant

Solid motor propellant grain is in low strain rate creep state under long-term storage condition. To analyze the yield characteristics and failure modes of HTPB (hydroxyl-terminated polybutadiene) propellant under different strain rate conditions, the constant speed tensile test of 2.38 × 10−5 s−1～2.38 × 10−2 s−1, 12-week long-term relaxation test and 4-week long-term creep test were carried out. The dynamic yield function of elastic-viscoplastic model was proposed, and the function parameters were fitted and verified by experimental data. The results show that the mechanical properties of the propellant show obvious rate dependence under lower strain rate, and the breaking strength and maximum elongation decrease significantly with the decrease of strain rate. The propellant starts to yield after strain reaching 15.0%, and the meso-structure enters an unstable state. The matrix and particle interface dewetting gradually becomes serious, developing into large particle shedding and matrix tearing, and finally causing macroscopic failure. The dynamic yield function can well describe the relationship between the dynamic yield strength, viscoplastic strain rate and static yield strength. The static yield strength of the propellant was analyzed and obtained as 0.06 MPa. The obtained yield strain and static yield strength can support the establishment of structural integrity failure criteria for long-term storage solid rocket motor.

Dynamic fracture characteristics of nanocrystalline Al containing He bubbles

This Letter reports the individual and combined effects of He bubbles and grain boundaries on the spallation of aluminum at different strain rates. Molecular dynamics simulations show that both He bubbles and grain boundaries reduce the spall strength, with the effect of He bubbles being reduced by about 50% when a grain boundary is present. Furthermore, it is found that He bubbles inhibit void nucleation and growth, while grain boundaries determine the location and mechanism of void or He bubble nucleation and growth, leading to a more rapid reduction in the spall strength of polycrystals than single crystals as the strain rate decreases. Additionally, a linear relationship is found between the spall strength of polycrystalline Al and the fraction of He atoms when He concentration is below 0.4 at.%.

Effects of strain rate and internal hydrogen on tensile properties of Al-10%Mg alloys

Strain rate dependences on tensile properties of the Al-10%Mg alloys containing high (5000H) and low (5000L) internal hydrogen were investigated. The total and uniform elongations increased with decreasing strain rate although the changes of tensile and yield strengths were small in 5000L. On the other hand, the total and uniform elongations also increased with decreasing strain rate whereas the tensile strength slightly increased and yield strength were almost constant in 5000H. The total and uniform elongations of 5000L at low strain rate were high in comparison with those of 5000H. A lot of cracks were observed at the particles consisting of Al-Mg-Mn in both 5000H and 5000L after tensile test. A lot of acoustic emission events (counts) were detected during plastic deformation in 5000H in comparison with those in 5000L. The low total and uniform elongations of 5000H at low strain rate might be attributed to the promotions of void and crack initiation, growth and propagation owing to the acceleration of cracking of particles due to the internal hydrogen which is introduced during casting process.

Influence of small-scale turbulence on internal flamelet structure

Direct numerical simulation data obtained from a highly turbulent (Kolmogorov length scale is less than a laminar flame thickness by a factor of about 20) lean hydrogen–air complex chemistry flame are processed, with the focus of the study being placed on flame and flow characteristics conditioned to instantaneous local values cFx,t of the fuel-based combustion progress variable. By analyzing such conditioned quantities, the following two trends are documented. On the one hand, magnitudes of fluctuations of various local flame characteristics decrease with increasing the combustion progress variable, thus implying that the influence of small-scale (when compared to the laminar flame thickness) turbulence on internal flamelet structure is reduced as the flow advance from unburned reactants to combustion products. On the other hand, neither local turbulence characteristics (conditioned rms velocities, total strain, and enstrophy) nor local characteristics of flame–turbulence interaction (flame strain rate) decrease substantially from the reactant side to the product side. To reconcile these two apparently inconsistent trends, the former is hypothesized to be caused by the following purely kinematic mechanism: residence time of turbulence within a large part of a local flamelet is significantly shortened due to combustion-induced acceleration of the local flow in the direction normal to the flamelet. This residence-time reduction with increasing cF is especially strong in the preheat zone (cF&amp;lt;0.3) and the residence time is very short for 0.3&amp;lt;cF&amp;lt;0.8. Therefore, small-scale turbulence penetrating the latter zone is unable to significantly perturb its local structure. Finally, numerical results that indirectly support this hypothesis are discussed.

Arrhenius constitutive model and dynamic recrystallization behavior of 18CrNiMo7-6 steel

In order to analyze the thermal deformation and dynamic recrystallization behavior of 18CrNiMo7-6 steel, the isothermal compression tests are carried out on Gleeble-3500 thermal simulator machine at deformation temperatures 973.15 K–1273.15 K with strain rates 0.001 s−1–1 s−1. Based on the true stress σ0.3, the Arrhenius constitutive models are constructed by using characterization parameters and physical base parameters, and the determination coefficients between the predicted values of the two models and the measured values are 0.98378 and 0.97613, respectively. The constitutive models of characterization parameters and physical base parameters considering strain effect are also constructed, and a comparative analysis is made. The results show that the predicted values of the characterization parameters constitutive model is closer to the measured values in the low strain region. After reaching the peak strain, the predicted values of the two constitutive models are close to the measured values, and both have high prediction accuracy. The dynamic recrystallization models are established to characterize the recrystallization behavior. The recrystallization activation energy of 18CrNiMo7-6 steel is 169.6793 kJ mol−1, the ratio of critical strain to peak strain is about 0.47074, and the ratio of critical stress to peak stress is about 0.94059. The activation energy of 50% dynamic recrystallization is 29.9844 kJ mol−1. The dynamic recrystallized grain size increases with increasing deformation temperature or decreasing strain rate, and the activation energy of grain growth is −49.9237 kJ mol−1.

Preparation and mechanism of copper ultra-fine grain strip by ultrasonic vibration extrusion cutting-model, FEM and experiment

Ultra-fine grain materials are widely used due to their superior material properties. In presented work, ultrasonic vibration extrusion cutting (UVEC) is put forward to prepare ultra-fine grain strip. UVEC induces material to produce strain and strain rate far exceeding that of ordinary severe plastic deformation process. The mathematical model and finite element simulation model of physical field parameters was established. UVEC test platform was set up to verify each other with previous model. Relationship and mechanism among processing parameters, physical field parameters and microstructure changes were analyzed, mechanism of grain refinement in UVEC was revealed. The results show that the grain size can be refined to ultra-fine grain size by UVEC method. With the increase of tool rake angle, the strip equivalent strain/equivalent strain rate decrease gradually, and the grain refinement weakens gradually. Besides UVEC, ordinary turning (OT) and ordinary extrusion cutting (OEC) tests are also carried out. The average grain size of UVEC-strip (0.75 μm) is about 3/4 that of OEC-strip (1.03 μm). The passivation layer depth of OT-strip (38 μm), OEC-strip (58 μm) and UVEC-strip (75 μm) increases gradually.

Evaluating the influence of deformation variables on dynamic recrystallization behavior using a crystal plasticity model

The present study is an attempt to model dynamic recrystallization (DRX) in a single phase metal using a mean field crystal plasticity (MFCP) based approach. A new empirical equation is proposed to model nucleation, in which the nucleation rate is a function of microstructure and plasticity descriptors that are known to affect DRX behavior, such as the temperature, strain rate, grain fineness and stored energy. Grains undergo nucleation when their dislocation density exceeds a threshold value. Subsequently, new grains grow based on the difference in stored deformation energy with respect to the average value over all grains. The MFCP-DRX model is able to correctly predict trends for the flow stress, dislocation density evolution, grain size evolution and kinetics across a range of temperatures and strain rates for uniaxial compression. Transition of the flow stress from single to multiple peaks is observed with increasing temperature and decreasing strain rate, thus comparing well against known DRX trends. The evolutions of crystallographic texture during DRX in uniaxial compression and plane strain compression are compared against experimental observations. A sensitivity analysis is conducted to understand the effect of variables on nucleation and growth. The competition between nucleation and growth dominated deformation in different strain regimes is analyzed in detail across various temperatures and strain rates.

Microstructure change characteristic and fracture mechanism of Ti-47.5Al-2.5V-1.0Cr-0.2Zr alloy during high temperature tensile deformation

Changes in the microstructure characteristics and fracture mechanism of Ti-47.5Al-2.5 V-1.0Cr-0.2Zr alloy during tensile deformation were studied by high temperature tensile tests at 750–900 °C and strain rate of 10−5–10−3 s−1. The experimental results indicate that when the tensile temperature increases or the strain rate decreases, the number of small dimples in the tensile fracture structure increases, the proportion of cross-layer fracture decreases, the dimples have torn edges, and the plastic deformation resistance increases. The higher tensile temperature corresponds to a higher dynamic recrystallization (DRX) ratio, and the number of dislocations near the DRX structure is reduced, which shows that the rheological softening effect is significantly enhanced. A lower strain rate corresponds to a higher proportion of DRX and a smaller proportion of lamellar microstructure. Dislocation slip is the main deformation mode; stacking faults can be observed in DRX grains. The changes in the hot deformation microstructure directly reflect decrease of high temperature tensile strength in macroscopic flow behavior. Under the action of tensile stress, holes usually form at the lamellar grain boundary, and the aggregation of multiple micro-holes will merge and connect to form micro-cracks. Cracks are generated and propagated between layers, and the tendency of holes or cracks generated at lower deformation temperatures or higher strain rates is greater. When the stress concentration reaches a certain critical value, the specimen will eventually fracture.

Dynamic recrystallization behavior and processing maps of 5CrNiMoV steel during hot deformation

Hot deformation tests of 5CrNiMoV steel were performed at deformation temperatures of 700 to 870 °C and strain rates of 0.001 to 0.1 s−1 using the DIL 805D thermomechanical simulator. The critical strain and volume fraction models of Dynamic Recrystallization (DRX) were constructed based on the work hardening theory. The results showed that the critical strain of DRX decreases with increasing deformation temperature and decreasing strain rate, which implies that DRX occurs easily at higher temperatures and lower strain rates. The average DRX grain size model was established to predict grain size changes during hot deformation. Based on the hot processing maps that were constructed using the Dynamic Material Model (DMM) and microstructure observation, the optimum hot working parameters for 5CrNiMoV steel are a deformation temperature of 800 °C–870 °C, a strain rate of 0.001–0.05 s−1.

Pressure Solution Grain Boundary Sliding as a Large Strain Mechanism of Superplastic Flow in the Upper Crust

AbstractA mechanism accommodating large strain in superplastic flow with elongation of 100%–300%, is described for fine‐grained calcareous shales deformed at temperature of 200–335°C and depths of 5–8 km up to slate schists in the Oisans massif, Western Alps, France. Using electron microscopy techniques on thin sections parallel to the principal finite strain axes, we show that the shape ratios of the slightly elongated grains (1.4–1.6), mainly calcite and quartz, do not match the finite strains recorded by the markers of the deformation (truncated belemnites, folded veins) in the maximum elongation and shortening plane (ratio 6.7) or in the maximum and minimum elongations plane (ratio 2.4). Consequently, a grain boundary sliding mechanism is required to explain the measured large finite strains. The most soluble minerals (quartz, calcite, dolomite, and albite), which represent about 95% of the rock, accommodate deformation by pressure solution grain boundary sliding whereas the least soluble minerals (muscovite, chlorite, Fe‐Ti oxides) act as indenters or are passively reoriented. Pressure solution is especially efficient in polymineralic rocks. Soluble minerals, which have been healed together in veins or fossils, are much more resistant to deformation and act as rigid objects. Models with idealized tessellation of hexagonal grains and creep laws derived from pressure solution indentation experiments provide deformation maps. We discuss the main parameters of this ductile deformation in the upper crust (thermodynamic conditions, strain rate, stress, distance of mass transfer) and show possible drastic decrease of mass transfer efficiency with decrease of stress and strain rate.

Elucidating the influence of temperature and strain rate on superplasticity and microstructure evolution of near-α TNW700 titanium alloy

The superplastic deformation and microstructure evolution of a new near-α TNW700 titanium alloy with short-term service temperature up to 700 °C were systematically investigated in the temperature range of 900–975 °C and strain rate range of 0.0005–0.01s−1. The results illustrate that TNW700 alloy has excellent superplasticity with elongation above 300% and m value above 0.41 at 900–950 °C, and the maximum elongation of 523% is obtained at 950°C-0.001s−1 due to the appropriate grain size and phase ratio. In addition, TNW700 alloy exhibits high temperature softening and strain rate hardening behaviors. The increase of β phase volume fraction induced by dynamic phase transformation is a crucial cause for flow softening, and this phenomenon is accelerated with increasing temperature and decreasing strain rate. The refinement of primary α grains and the inconspicuous growth of β grains at lower temperatures are favorable for grain boundary sliding and superplasticity enhance, whereas the overgrowth of β grains at 975 °C results in superplasticity absence. The decrease of dislocation density in primary α grains caused by strain partitioning, dynamic recovery (DRV) or dynamic recrystallization (DRX) is another important factor for high temperature softening; the increase of dislocation density and velocity, and the decrease of annihilation time contribute to strain rate hardening. The appearance of random texture indicates the activation of grain boundary sliding (GBS) and grain rotation. GBS is the overarching mechanism of superplastic deformation of TNW700 alloy, accompanied by grain rotation, dislocation movement, dynamic phase transformation and grain refinement or coarsening.

The influence of strain rate and annealing heat treatments on the corrosion and mechanical properties of WE43 and Zn7Ag biodegradable wires for application in soft tissue reconstructions

This study investigated the influence of annealing heat treatments on the microstructure, corrosion and mechanical behaviour of wires made from the Mg alloy WE43 and the Zn alloy Zn7Ag. The applied strain rate had little influence on the mechanical properties of WE43, whereas decreasing strain rate decreased the strength and increased the ductility of Zn7Ag attributed to creep. The annealing heat treatments had (i) a small influence on the corrosion rate of both WE43 and Zn7Ag wires, (ii) little influence on the mechanical properties of WE43, and (iii) had little influence on the strength of Zn7Ag but tended to decrease ductility and eliminated strain softening. WE43-FA immersed in Zahrina's interstitial fluid (ZIF) for 12 days had a yield strength that was decreased somewhat but fracture occurred much earlier causing a lower ductility and a lower ultimate tensile strength, attributed to notch sensitivity. Zn7Ag after 12 days and 20 days exposure to ZIF showed some reduction in the yield stress, and also early onset of fracture leading to a large decrease in ductility and some decrease in the ultimate tensile strength, also possibly attributed to notch sensitivity.

Morphological evolution and dissolution mechanisms of γ′ phase in a novel HIPed P/M superalloy in hot deformation process

Isothermal compressive tests of a new hot isostatic pressed (HIPed) powder metallurgy (P/M) superalloy are performed at diverse deformation amounts, strain rates, and elevated temperatures. The impacts of hot compression parameters on the morphological evolution and dissolution behavior of γ' phase are studied. Results show that the morphology of γ′ phase changes from the various initial shapes (irregular, split-off branch, dendrite, butterfly-like, and cauliflower) to spherical, due to the overlap of the γ'/γ interface energy and the coherent strain energy related to lattice misfit. Besides, the dislocation accumulation leads to the increased local stress and enhances the spheroidization behavior of γ' phase. Increasing temperature/true strain or decreasing strain rate, the dynamic dissolution behavior of γ' phase is obvious. It is because the dislocation/ vacancies-assisted element diffusion is rapid at high deformation temperatures/true strains, and the low strain rate can provide the enough time for element diffusion. The substantial dissolution of γ' phase at 1140 °C and 1170 °C is also related to the deformation temperature approaching and exceeding the γ' solvus temperature (1150 °C), respectively. Additionally, the decreased fraction of γ' phase is also related to the high γ'/γ interfacial energy. To quantitatively describe the dissolution behavior of γ′ phase, a dynamic dissolution kinetics model is proposed, and the correlation coefficient between the predicted and experimental values is 0.990. It indicates that the proposed model can precisely depict the dissolution behavior of γ′ phase. The findings in this work can provide the theoretical guidance to optimize deformation parameters, as well as control the morphology and fraction of γ′ phases.