Effect of oxidation on creep data: Part 2 – A procedure for assessing the effect of oxidation on constant-stress or constant-load creep curves using the Theta-projection concept

Abstract

A procedure based on Theta-methodology coupled with the knowledge of oxidation kinetics is envisaged for quantitatively assessing the effect of oxidation on creep curves. The procedure is based on the generation of a series of real constant-stress creep curves, at different stress and temperature levels, in inert atmosphere, where the effects due to oxidation are kept to a minimum level. Stress enhancement factors due to the effect of area reduction on specimen cross-section with plastic deformation and oxidation are defined for constant-stress or constant-load creep testing. These factors can be used in the integration of the strain-rate equation related to the 4θ - parameter analysis, to derive constant-stress or constant-load curves in air using either the strain hardening or time hardening theories. Although systematic constant-stress creep data in vacuum are not yet available to test the methodology effectively, a preliminary simulation is done to demonstrate how the model works, to check its performance and the possibilities of analysis.     

Limit case analysis of the “stable indenter velocity” method for obtaining creep stress exponents from constant load indentation creep tests

This study concerns a commonly-used procedure for evaluating the steady state creep stress exponent, \(n\), from indentation data. The procedure involves monitoring the indenter displacement history under constant load and making the assumption that, once its velocity has stabilised, the system is in a quasi-steady state, with stage II creep dominating the behaviour. The stress and strain fields under the indenter are represented by “equivalent stress” and “equivalent strain rate” values. The estimate of \(n\) is then obtained as the gradient of a plot of the logarithm of the equivalent strain rate against the logarithm of the equivalent stress. Concerns have, however, been expressed about the reliability of this procedure, and indeed it has already been shown to be fundamentally flawed. In the present paper, it is demonstrated, using a very simple analysis, that, for a genuinely stable velocity, the procedure always leads to the same, constant value for \(n\) (either 1.0 or 0.5, depending on whether the tip shape is spherical or self-similar). This occurs irrespective of the value of the measured velocity, or indeed of any creep characteristic of the material. It is now clear that previously-measured values of \(n\), obtained using this procedure, have varied in a more or less random fashion, depending on the functional form chosen to represent the displacement–time history and the experimental variables (tip shape and size, penetration depth, etc.), with little or no sensitivity to the true value of \(n\).     

Impression creep of the rare-earth doped Sn–2%Bi lead-free solder alloy

Creep behavior of the Sn–2Bi–RE alloys containing 0.1, 0.25 and 0.5 wt% rare earth (RE) elements was studied by impression testing and compared to that of the Sn–2Bi alloy. The tests were carried out under constant punching stress in the range 70–190 MPa and at temperatures in the range 298–370 K. Results showed that for all loads and temperatures, Sn–2Bi–0.25RE had the lowest creep rate, and thus the highest creep resistance among all materials tested. This was attributed to the formation of Sn–Bi, Sn–RE, and Sn–Bi–RE intermetallic particles which act as both strengthening agent and grain refiner in the RE-containing Sn–2Bi alloy. RE contents higher than 0.25 wt%, resulted in a lower creep resistance due to the formation of the same intermetallics but with much higher Bi content. This consumes the Bi content of the matrix and reduces the corresponding solid solution hardening, resulting in a lower creep resistance of the material. The stress exponents in the range 8–10.5, 8.4–11.5, 8.8–12.3, 8.4–11.6 and average activation energies of 64.5, 65.1, 67.4 and 68.0 kJ mol^?1 were obtained for Sn–2Bi, Sn–2Bi–0.1RE, Sn–2Bi–0.25RE, and Sn–2Bi–0.5RE, respectively. Although these activation energies are close to the activation energy of lattice self diffusion for β-Sn, the relatively high stress exponents of about 8–12 suggests that creep mechanisms associated with dislocation movement such as dislocation creep are prevailing.     

Crack growth behaviour of P92 steel under creep and creep–fatigue conditions

Abstract

High temperature creep and creep–fatigue crack growth tests were carried out on standard compact specimens machined from ASME P92 steel pipe. The effects of various loading conditions on crack growth behaviours were investigated. Crack initiation time was found to decrease with the increasing initial stress intensity factor under creep condition and further to decrease by the introduction of fatigue condition. For creep test, the crack growth rate can be well characterised by the facture mechanics parameter C*. For creep–fatigue test, the crack growth behaviour is dominated by the cycle dependent fatigue process when the hold time is shorter, but it becomes dominated by the time dependent creep process when the hold time becomes longer.     

Computation of the relaxation and creep functions of elastomers from harmonic shear modulus

The purpose of this paper is to compute the relaxation and creep functions from the data of shear complex modulus, G ^∗(iν). The experimental data are available in the frequency window ν∈[ν_min,ν_max] in terms of the storage G′(ν) and loss G″(ν) moduli. The loss factor h( n) = \fracG"( n)G￠(n)\eta( \nu) = \frac{G'( \nu )}{G'(\nu )} is asymmetrical function. Therefore, a five-parameter fractional derivative model is used to predict the complex shear modulus, G ^∗(iν). The corresponding relaxation spectrum is evaluated numerically because the analytical solution does not exist. Thereby, the fractional model is approximated by a generalized Maxwell model and its rheological parameters (G _k ,τ _k ,N) are determined leading to the discrete relaxation spectrum G(t) valid in time interval corresponding to the frequency window of the input experimental data. Based on the deterministic approach, the creep compliance J(t) is computed on inversing the relaxation function G(t).     

A modified θ projection model for constant load creep curves-II. Application of creep life prediction

To minimize the deviation of the predicted creep curves obtained under constant load conditions by the original θ projection model, a new modified version that can be expressed by $\epsilon ={\theta }_1\left(1-e^{-{\theta }_{2}t}\right)+{\theta }_3\left(e^{{\theta }_4{e}^{{\theta }_5\epsilon }t}-1\right)$, was derived and experimentally validated in our last study. In the present study, the predictive capability of the modified θ projection model was investigated by comparing the simulated and experimentally determined creep curves of K465 and DZ125 superalloys over a range of temperatures and stresses. Furthermore, the linear relationship between creep temperature and initial stress was extended to the 5-parameter model. The results indicated that the modified model could be used as a creep life prediction method, as it described the creep curve shape and resulted in predictions that fall within a specified error interval. Meanwhile, this modified model provides a more accurate way of describing creep curves under constant load conditions. The limitations and future direction of the modified model were also discussed. In addition, this modified θ projection model shows great potential for the evaluation and assessment of the service safety of structural materials used in components governed by creep deformation.     

Effect of σ-Phase on the creep properties of Cr25Ni20 stainless steel

It is concluded from above that effect of σ-phase on creep properties depends on particle size and distribution. Fine σ-phase particles dispersively precipitated along grain boundaries and within grains increase creep resistance and rupture strength, having general characteristics of dispersion hardening.     

A modified θ projection model for constant load creep curves-I. Introduction of the model

Estimating long-term creep deformation and life of materials is an effective way to ensure the service safety and to reduce the cost of long-term integrity evaluation of high temperature structural materials. Since the 1980s, the θ projection model has been widely used for predicting creep lives due to its ability to capture the characteristic transitions observed in creep curves obtained under constant true stress conditions. However, the creep rupture behavior under constant load or engineering stress conditions cannot be simulated accurately using this model because of the different stress states. In this paper, creep curves obtained under constant load conditions were analyzed using a modified θ projection model by considering the increase in true stress with creep deformation during the creep tests. This model is expressed as $\epsilon ={\theta }_1\left(1?{\text{e}}^{?{\theta }_{2}t}\right)+{\theta }_3\left(e^{{\theta }_4{e}^{{\theta }_5\epsilon }t}?1\right)$, and was validated using the creep curves of K465 and DZ125 superalloys tested at a range of temperatures and engineering stresses. Moreover, it was shown that the predictive capability of the modified θ projection model was significantly improved over the original one, as it reduces the prediction uncertainty from a range of 10% to 20% to below 5%. Meanwhile, it was shown that the model can be reasonably used for predicting constant stress creep conditions, when appropriate parameters are used. The prediction performance of the modified model will be discussed in another paper. The results of this study show great potential for the evaluation and assessment of the service safety of structural materials used in applications where designs are limited by creep deformation.     

Effect of cyclic loading on subsequent creep behaviour and its implications in creep–fatigue life assessment

Abstract

Evaluation of creep–fatigue failure is essential in design and fitness evaluation of high-temperature components in power generation plants. Cyclic deformation may alter the creep properties of the material and taking cyclic effects into account may improve the accuracy of creep–fatigue failure life prediction. To evaluate such a possibility, creep tests were conducted on 316FR and modified 9Cr–1Mo steel specimens subjected to prior cyclic loading; their creep deformation and rupture behaviours were compared with those of as-received materials. It was found that creep rupture life and elongation generally decreased following cyclic loading in both materials. In particular, the rupture elongation of 316FR in long-term creep conditions drastically decreases as a result of being cyclically deformed at a large strain range. Use of creep rupture properties after cyclic deformation, instead of those of as-received material, in strain-based and energy-based life estimation approaches brought about a clear improvement of creep–fatigue life prediction.     

Transition in the creep failure mode of an alloy 800H weld at 850°C

Creep tests were conducted in air and helium on Alloy 800H welded with a high strength filler. Shorter tenn tests produced ductile parent metal failures, but long-tenn samples (>5000 h) failed near the weld with low ductility. Crack distributions suggested that this transition arose because restraint of the parent by the more creep-resistant weld caused triaxial tensile stresses to develop near the weld. At short times, these reduced local creep rates in the parent so that fracture occurred away from the weld. However, given sufficient time, restraint promoted diffusion-assisted cavitation near the weld. Implications for other weldments are discussed.     

Data-driven prediction of the probability of creep–fatigue crack initiation in 316H stainless steel

Stainless steel components in advanced gas-cooled reactors (AGRs) are susceptible to creep–fatigue cracking at high temperatures. Quantifying the probability of creep–fatigue crack initiation requires probabilistic numerical simulations; these are complex and computationally intensive. Here, we present a data-driven approach to develop fast probabilistic surrogate models of creep–fatigue crack initiation in 316H stainless steel. We perform a set of Monte Carlo simulations based on the R5V2/3 high temperature assessment procedure and determine the sensitivity of the probability of crack initiation to loads and operating conditions. The data are used to train different supervised machine learning models considering Bayesian hyperparameter optimization. We discuss the relative performance of such models and show that a gradient tree boosting algorithm results in surrogate models with the highest accuracy.     

Steady-state creep of an alloy based on the intermetallic compound Ni3Al(γ′)

An investigation of the steady-state creep of a Ni₃Al.10 at% Fe alloy () has shown that two creep mechanisms were operative over the temperature range 530 to 930° C. The experimental data at low temperatures (below 680° C) were not consistent with any of the established creep theories. However, the experimental data were in good agreement with a proposed model for cross-slip from octahedral {111} planes on to cube {100} planes in Li₂ crystals. Above 680° C, the rate-controlling mechanism, which had an activation energy of 3.27eV atom^–1, is considered to be the removal/production of APBs during climb.     

Effect of primary α content on creep and creep crack growth behaviour of near α-Ti alloy

Abstract

The effect of primary α content on creep and creep crack growth behaviour of a near α-Ti alloy has been investigated at 600°C. The alloy was heat treated at different temperatures so as to obtain different volume fractions of equiaxed primary α in the range from 5 to 40%. Constant load creep tests were carried out at 600°C in the stress range 250–400 MPa until rupture of the specimens. Creep crack growth tests were carried out at 600°C and at an initial stress intensity level of 25 MPa m^1/2. Creep data reveal that minimum creep rate increases and time to rupture decreases with increase in primary α content indicating that higher primary α leads to creep weakening. On similar lines, maximum creep crack growth resistance is associated with the alloy with lowest primary α content (i.e. 5%). Microstructural and fractographic examination has revealed that creep fracture occurs by nucleation, growth and coalescence of microvoids nucleated at primary α/transformed β (matrix) interfaces. On the other hand, creep crack growth occurs by surface cracks nucleated by fracture of primary α particles as well as by growth and coalescence of microvoids nucleated at primary α/transformed β (matrix) interfaces in the interior of the specimen ahead of the crack tip.     

Effect of rare earth element additions on the impression creep of Sn–9Zn solder alloy

Creep behavior of the Sn–9Zn–RE alloys containing 0.1, 0.25 and 0.5 wt.% rare earth (RE) elements was studied by impression testing and compared to that of the eutectic Sn–9Zn alloy. The tests were carried out under constant punching stress in the range 40–135 MPa and at temperatures in the range 298–420 K. Results showed that for all loads and temperatures, Sn–9Zn–0.25RE had the lowest creep rate, and thus the highest creep resistance among all materials tested. This was attributed to the formation of Sn–RE second phase precipitates which act as the main strengthening agent in the RE-containing Sn–Zn alloys. RE contents higher than 0.25 wt.%, resulted in a lower creep resistance due to a reduction in the volume fraction of Zn-rich phase caused by the formation of Sn–Zn–RE intermetallics. The average stress exponents of 6.8, 6.9, 7.1, 6.8 and activation energies of 42.6, 40.6, 43.0 and 44.9 kJ mol⁻¹ were obtained for Sn–9Zn, Sn–9Zn–0.1RE, Sn–9Zn–0.25RE, and Sn–9Zn–0.5RE, respectively. These activation energies were close to 46 kJ mol⁻¹ for dislocation climb, assisted by vacancy diffusion through dislocation cores in the Sn. This, together with the stress exponents of about seven suggests that the operative creep mechanism is dislocation climb controlled by dislocation pipe diffusion.     

Inherited effects from artificial aging on the tensile creep behaviors of hot-rolled Mg–7.5wt%Y alloy

Journal of Materials Science - Herein, the impacts of inherited attributes from artificial aging treatment of the hot-rolled Mg–7.5wt%Y alloy’s tensile creep resistance were...     

Plasma-sprayed coatings for oxidation protection on creep of the Ti–6Al–4V alloy

Abstract

The titanium affinity for oxygen is one of the main factors that limit the application of its alloys as structural materials at high temperatures. The objective of this work was to estimate the influence of the plasma-sprayed coatings for oxidation protection on creep of the Ti–6Al–4V alloy, focusing on the determination of the experimental parameters related to the creep stages. Yttria (8 wt.%) stabilized zirconia (YSZ) with a CoNiCrAlY bond coat was air plasma sprayed on Ti–6Al–4V substrates. Constant load creep tests were conducted on the Ti–6Al–4V alloy in air for coated and uncoated samples and in a nitrogen atmosphere for uncoated samples at 600°C to evaluate the oxidation protection on creep of the Ti–6Al–4V alloy. The steady-state creep rate of the coated alloy is smaller than that of the uncoated alloy in air and nitrogen atmosphere. Results about the activation energies and the stress exponent values indicate that the primary and stationary creep, for all test conditions, was probably controlled by dislocation climb. The plasma-sprayed coatings increased the time to rupture and the strain at rupture is smaller than for uncoated samples tested in air.