Grain boundary sliding in the presence of grain boundary precipitates during transient creep

A constitutive rate equation for grain boundary sliding (GBS), in the presence of grain boundary precipitates, is developed. Langdon’s GBS model is modified by incorporating physically de-fined back stresses opposing dislocation glide and climb and by modifying the grain size de-pendence of creep rate. The rate equation accurately predicts the stress dependence of minimum creep rate and change in activation energy occurring as a result of changing the grain boundary precipitate distribution in complex Ni-base superalloys. The rate equation, along with the math-ematical formulations for internal stresses, is used to derive a transient creep model, where the transient is regarded as the combination of primary and secondary stages of creep in constant load creep tests. The transient creep model predicts that the transient creep strain is dependent on stress and independent of test temperature. It is predicted that a true steady-state creep will only be observed after an infinitely long time. However, tertiary creep mechanisms are expected to intervene and lead to an acceleration in creep rate long before the onset of a true steady state. The model accurately predicts the strain vs time relationships for transient creep in IN738LC Ni-base superalloy, containing different grain boundary carbide distributions, over a range of temperatures.     

Critical Assessment of Short-Term Stress-Relaxation Studies for the Prediction of Creep Properties of P91 Steel

An attempt has been made to interrelate the predicted creep-rupture properties using stress relaxation tests (SRT) with those obtained from uniaxial monotonic creep tests in P91 steel. Stress-relaxation tests were performed at specified total strain levels of 1.3 and 2.5% for fixed duration of 24 h at 873 K. The results from SRT have been used to predict the rupture life using Monkman–Grant relation and Gill–Goldhoff correlation for the steel. Further, the observed stress-relaxation behaviour has been described appropriately using an analytical model with suitable parameter values related to activation volume and activation energy.     

Simulation of the Forming Behaviour of a Boron Modified P91 Ferritic Steel

The forming behaviour at high temperature of a modified 9%Cr‐1%Mo (P91) ferritic steel containing B and Ti for elevated temperature service was investigated. The microstructure of the as‐received material is mainly martensite at room temperature, but special etching revealed prior austenite grains of about 25 μm in size. Torsion tests were conducted at temperatures in the range 850 to 1250 °C to simulate the hot rolling process under comparable conditions of temperature, strain rate and strain. The deformation data obtained from these tests were correlated with the Garofalo equation with a stress exponent of 4.6 and an activation energy of 315 kJ/mol. This equation was used to predict the formability behaviour for the rolling process and also to determine the maximum forming efficiency and stability of the steel. A temperature of 1200 °C is recommended to conduct the forming process.     

Interpretation of high-temperature creep of type 304 stainless steel

The elevated-temperature creep behavior of Type 304 stainless steel is examined in terms of the measured effective and internal stresses. Results show that the mean effective stress is related to the applied stress by a power law of the form σ^* = α(σ)^β, where the constants α and β are functions of temperature. The dependence of creep rate on applied stress follows a power law, and the stress exponent is dependent on temperature. The latter behavior arises from the variation in the mean effective stress with applied stress and temperature. The creep rates are also described as a function of effective stress. The dislocation velocity-stress exponent obtained from stresschange tests is higher than the effective stress exponent evaluated from creep data. The dependence of creep rate on temperature at various values of effective stress yields a total activation energy of approximately the same magnitude as self-diffusion.     

Creep of an AISI 310 type stainless steel and its numerical simulation using the Öström-Lagneborg creep model

The creep behaviour of an AISI 310 type stainless steel was determined under constant load (stress range 80–320 MPa) at a temperature of 700°C. The stress exponent, n, monotonically increased with the applied stress from a value of 2.8 to 16. The activation energy for creep, Q_c, measured at 170, 200 and 230 MPa over the temperature range 650–800°C, is 341 kJ/mol. An activation energy of this magnitude indicates that the alloying elements in this steel are involved in the recovery climb process of the dislocation network. A simple and practical simulation was made of the experimental creep results by using the Öström-Lagneborg creep model, and the results are compared to other independent models and experimental results. A good fit between the experimental results and the calculated strain-time curves can be obtained by adjustment of model parameters to out material. The applicability of the Öström-Lagneborg theory to the creep involving subgrain structure formation is evaluated in light of the elastic theories for subgrain boundaries and recent experimental findings. By considering only forest dislocations not incorporated in subgrain boundaries and introducing a subgrain structure function S_g(t), the Öström-Lagneborg model is able to simulate the creep behaviour where a subgrain structure is formed during the creep test. Further refinement of the theory is suggested whereby an assessment is made of the dislocation network coarsening kinetics.     

T91钢的高温塑性变形及动态再结晶行为

采用Gleeble-1500热模拟试验机进行了T91钢的压缩试验,研究了变形温度为1100~1250℃、应变速率为0.01~1 s-1时该钢的变形行为,分析了流变应力与应变速率和变形温度之间的关系,计算了高温变形时应力指数和变形激活能,并采用Zener-Hollomon参数法构建该钢高温塑性变形的本构关系,绘制了动态再结晶图和热加工图.结果表明:在试验变形条件范围内,其真应力-真应变曲线呈双峰特征;钢中发生了明显的动态再结晶,且再结晶类型属于连续动态再结晶.T91钢的热变形激活能为484 kJ.mol-1,利用加工图确定了热变形的流变失稳区,结合力学性能,可以优先选择的变形温度为1200~1 250℃,应变速率不高于0.1 s-1.      

Constitutive Equation for AISI4140 Steel Applicable to a Wide Range of Strain Rates at Elevated Temperatures

This paper presents a method to determine a constitutive equation of AISI4140 steel when it deforms at a wide range of strain rates (0.05~1900s⁻¹) under high temperatures. The fundamental idea considered here is that the dependency of flow stress upon strain rate and temperature is described by the power law model of the Arrhenius equation. Strengthening coefficient and work hardening exponent are introduced to take a simplified treatment to the flow stress behaviour characteristics without losing accuracy of the model. The validity of the proposed constitutive equation has been examined using results obtained from the hot compression test (GLEEBLE^® 3500C) and Split Hopkinson‐Pressure Bar test at high temperature. Results revealed the proposed constitutive equation could predict flow stress‐strain curve of the steel with an acceptable amount of error at the ranges of strain rates.     

Stress‐Temperature‐Transformation and Deformation‐Temperature‐Transformation Diagrams for an Austenitic CrMnNi as‐cast Steel

Stress‐Temperature‐Transformation (STT) and Deformation‐Temperature‐Transformation (DTT) diagrams are well‐suited to characterize the TRIP (transformation‐induced plasticity) and TWIP (twinning‐induced plasticity) effect in steels. The triggering stresses for the deformation‐induced microstructure transformation processes, the characteristic temperatures, the yield stress and the strength of the steel are plotted in the STT diagram as functions of temperature. The elongation values of the austenite, the strain‐induced twins and martensite formations are shown in the DTT diagram. The microstructure evolution of a novel austenitic Cr‐Mn‐Ni (16%Cr, 6% Mn, 6% Ni) as‐cast steel during deformation was investigated at various temperatures using static tensile tests, optical microscopy and the magnetic scale for the detection of ferromagnetic phase fraction. At the temperatures above 250 °C the steel only deforms by glide deformation of the austenite. Strain‐induced twinning replaces the glide deformation at temperatures below 250 °C with increasing strain. Below 100 °C, the strain‐induced martensite formation becomes more pronounced. The kinetics of the α'‐martensite formation is described according to stress and deformation temperatures. The STT and DTT diagrams, enhanced with the kinetics of the martensite formation, are presented in this paper.     

Steady state creep behaviour of silicon carbide particulate reinforced aluminium composites

The roles of volume fraction and size of reinfrecement on the steady state creep behaviour of pure aluminium matrix-silicon carbide particulate composites have been studied in the temperature range 623–723 K. The observed apparent stress exponents are higher than 15 and apparent activation energy is 249 kJ mol⁻¹. By considering the existence of a threshold stress, the data for 1.7 μm particulate reinforced composites with different volume fraction can be rationalized according to the substructure invariant model. The effective stress-strain rate behaviour of composites with 10 vol.% of coarser particulates (14.5 and 45.9 μm), however, agree with the stress dependent substructure model. The present analysis is validated by constructing a new type of “dislocation creep mechanism map”. The observed threshold stress varies with the volume fraction of reinforcement and is independent of particulate sizes and test temperatures. It is suggested that a model based on applied stress independent load transfer is required to explain the origin of such a threshold stress.     

Time-dependent deformation in an enhanced SiC/SiC composite

Time-dependent deformation in an enhanced SiC/SiC composite has been studied under constant load at high temperatures of 1200 °C, 1300 °C, and 1400 °C. Creep damage evolution was evaluated by a Young’s-modulus change of partial unloading and microscopic observation. The addition of the glassy phase in the matrix is very effective for protecting the composite from oxidation. The transient creep is dominant in creep life at all the temperatures. An empirical equation is proposed to describe creep behavior of the composite. It is found that creep activation energy increases with creep time at stresses lower than matrix cracking stress, but the activation energy remains constant at stresses higher than the matrix cracking stress. The creep strain rate of the composite is considered to be controlled by creep of fibers based on examining the time, strain, stress, and temperature dependencies of creep strain rates.     

Constant substructure creep of aluminum following stress reductions

A series of stress reduction experiments was conducted on high purity polycrystalline aluminum. Initial stresses of 8.27, 10.3 and 12.4 MPa at 573 K and 3.44 MPa at 673 K were used, and stress reductions were made during steady state creep at approximately 22% true strain. For each initial stress, the constant substructure strain rates are characterized by an exponential dependence of rate on the reduced stress. These data are consistent with an exponential form of the kinetic law for flow within subgrain interiors, which is based on the theory of obstacle-controlled dislocation glide. In addition, the experimentally determined slopes for each set of constant substructure strain rate-vs-reduced stress data vary approximately as the inverse of the initial stress. This finding suggests that the strength of the microstructure scales with the initial applied stress. Finally, it is proposed that the activation energy for dislocation glide can be determined from a combination of constant structure and steady state creep data. The results of this analysis suggest that the thermal activation process may be controlled by lattice self-diffusion.     

Impression Creep Behavior of an Mg–Zn–RE Alloy at Elevated Temperatures

Mg–Zn–RE alloys are promising candidates for automotive and aerospace applications as, among magnesium alloys, they have better corrosion and creep resistance abilities at elevated temperatures. This study evaluates the high-temperature creep behavior of ZE41 magnesium alloy, belonging to the Mg–Zn–RE family, using impression test. Impression tests were performed under a constant temperature and stress with a flat-ended cylindrical punch. Power law and Eyring relationships were used to analyze the creep mechanism. By applying the power-law relationship, it was found that the creep exponent decreased from 7.5 to 4 in the temperature range of 493 K to 593 K. Activation energy increased from 78.5 to 107.1 kJ/mol in the applied stress range of 350 to 500 MPa (normalized stress: 0.024 ≤ σ_imp/G ≥ 0.034). Using the Eyring relationship, a single activation energy of 25 kJ/mol for the entire stress and temperature range was obtained. Based on the creep exponent and activation energy, it is proposed that pipe-diffusion-controlled dislocation climb is the dominant mechanism, but grain boundary sliding also contributes at higher stresses.

     

Viscoelastic Analysis of Constant Creep Tests on Silicate-Grouted Sands at Low Stress Levels

This paper presents the mechanical properties of silicate-grouted sands subjected to creep loadings at low stress levels. Uniaxial compressive tests were performed in order to determine the stress levels of constant creep tests. The uniaxial compressive strength rapidly increased with time over the first 7 days of curing and then approached a constant level. A series of creep tests were performed for three stress levels and viscoelastic theory was employed to assess the creep behavior. During the loading process elastic, plastic, and viscoelastic strains existed together. The recoverable portions contained elastic and time-dependent viscoelastic strains, and both were approximately linear. Test results showed that the magnitude of the instantaneous recoverable strains was independent of the unloading time. A constitutive model to predict the permanent deformation was developed.     

Effect of Impurity Tin on the Creep Properties of a P91 Heat-Resistant Steel

The creep properties of P91 steel specimens undoped and doped with 0.058 wt pct tin, which was normalized from 1328 K (1055 °C) and tempered at 1033 K (760 °C), were examined under different engineering stresses (150 to 210 MPa) and temperatures [873 K to 923 K (600 °C to 650 °C)]. The creep behavior followed the temperature-compensated power law and Monkman–Grant equations. In the temperature-compensated power law equation, the apparent activation energy and stress exponent for creep were approximately 541 kJ/mol and 12 for the undoped steel and 527 kJ/mol and 11 for the Sn-doped one, respectively. In the Monkman–Grant relation, the values of constants m and C were around 1.062 and 0.0672 for the undoped steel, and 1.012 and 0.0650 for the Sn-doped one, respectively. The 100 MPa stress creep lifetime at 873 K (600 °C) was estimated as 100641 hours for the undoped steel and 35290 hours for the Sn-doped steel, respectively. These indicated that Sn substantially deteriorated the creep properties of the steel. It was found that grain or subgrain boundary segregation of Sn could promote the nucleation of cavities or microcracks, thereby leading to the deterioration of the steel creep properties.     

Effects of boron on the creep properties,phosphorus segregation behaviour,and stress relief cracking susceptibility of 1.5% Cr–0.5% Mo steels

The effects of 25 ppm boron and of 0.05% phosphorus on the creep behaviour at 550 °C and on the fracture temperature in the constant load fracture test were tested for a 1.5% Cr–0.5% Mo steel. B and P decrease the creep strength, the rupture elongation is increased by B. B and P lower stress relief cracking susceptibility, however, it is increased at low stress. In the B doped material the rate of P grain boundary segregation is accelerated and the level of equilibrium segregation is somewhat higher, the equilibrium segregation is somewhat lower in the bainitic than in the martensitic structure.     

Short‐term Creep Behavior of an X 37 Cr Mo V 5‐1 Hot‐work Tool Steel with almost Bainitic and fully Martensitic Microstructures

In this study two different heat treatments were conducted on an X 37 Cr Mo V 5‐1 hot‐work tool steel, resulting either in a tempered fully martensitic matrix or a matrix almost consisting of tempered bainite. Short‐term creep tests were performed at a high stress level of 800 MPa and at temperatures in the range from 450 °C to 500 °C. Creep specimens consisting of a tempered fully martensitic microstructure exhibited a three times longer creep‐to‐rupture time, than those consisting of a tempered almost bainitic microstructure. Microstructural investigations of creep specimens were performed by transmission electron microscopy. Results of these investigations revealed that due to a lower cooling rate, which is necessary to form bainite, the tempered bainitic microstructure consists of large former bainitic plates, whereas tempered martensite shows fine former martensitic laths. Tempered bainite also exhibits a higher number density of large M₃C, M₇C₃ and MC carbides than tempered martensite. Small M₂C carbides appear in both microstructures in the same quantity, however, nanometer‐sized MC carbides could only be found in tempered martensite. Thus poor short‐term creep behavior of the tempered almost bainitic microstructure can be explained by the lesser amount of strengthening relevant precipitates, a smaller size‐effect due to distance of bainitic interfaces as well as lower solid solution hardening.     

Hot Workability of as‐Cast High Manganese‐High Carbon Steels

In order to produce new high Mn‐high C austenitic steels (R_m>700 MPa), different tests and methods were used to determine a suitable window of process parameters. In‐situ melting hot tensile tests and hot compression tests were carried out to investigate the hot ductility, fracture characteristics and flow behaviour during continuous casting and hot deformation of 3 steels with Mn and C contents between 9‐23% and 0.6‐0.9%, respectively. The results show that these steels are susceptible to interdendritic fracture at high temperatures. Decreasing Mn content improves the reduction of area at high temperatures to 60% or more. Hot deformation loads for processing the investigated steels are not higher in comparison to the stainless steel 1.4301.     

New model describing creep of metallic materials under variable temperatures

A creep function using only three fitting parameters is presented hereafter. The function is derived from a more general physical - phe-nomenoiogical model representing metallic materials creep behaviour and describes all three stages of creep. The dependence of the fitting parameters upon the temperature are investigated and simple analytical relations are provided for that purpose. Those relations already incorporate the effect of stress. At the outcome, ten material constants are derived which are neither dependent on the stress nor on the temperature. On the basis of the derived constitutive relations a prediction is carried out for creep strain of three metallic materials and particularly steels, at different temperatures and under constant stress. The derived curves agree with the experiments, not only the ones carried out in the laboratory but also the ones taken from literature.     

Creep characteristics of single crystalline Ni3Al(Ta,B)

The creep characteristics, including the nature of the creep transient after a stress reduction and activation energy for creep of single crystalline Ni₃Al(Ta,B) in the temperature range 1083 to 1388 K, were investigated. An inverse type of creep transient is exhibited during stress reduction tests in the creep regime where the stress exponent is equal to 3.2. The activation energy for creep in this regime is equal to 340 kJ mol⁻¹. A normal type of creep transient is observed during stress reduction tests in the regime where the stress exponent is equal to 4.3. The activation energy for creep in this regime is equal to 530 kJ mol⁻¹. The different transient creep behavior and activation energies for creep observed in this investigation are consistent with the previous suggestion that then = 4.3 regime is associated with creep controlled by dislocation climb, whereas then = 3.2 regime is associated with a viscous dislocation glide process for Ni₃Al at high temperatures.