Stress-dependent Activation Energy Research Articles

Creep Rupture Assessment of New Heat-Resistant Sanicro 25 Steel Using Different Life Prediction Approaches

The paper deals with creep life and creep strength estimations of Sanicro 25 steel through various continuum damage models and modified extrapolation methods. Four different continuum damage models, i.e., modified K-R model, Dyson model, W-T model and modified W-T model considering the stress-dependent failure strain, were incorporated into numerical simulations using user subroutines so as to analyze the creep strain behavior and the creep rupture time. In the case of 700 °C, the predicted creep rupture lifetimes determined from modified K-R model, Dyson model, W-T model and modified W-T model all matched with the experimental data, where the modified W-T model provided the best prediction. However, at 750 °C, only the predictions using W-T model and modified K-R model matched with the experimental data. The Dyson model and modified W-T model underestimated the creep rupture lifetime. Besides the creep damage approaches, a modified extrapolation method developed by Wilshire (based on the stress-dependent creep activation energy) was also tested and verified to make predictions of creep lifetime under various stress conditions more easily than the creep damage models. A general comparison of the analyses made with different life prediction methods in Sanicro 25 steel was presented in this paper.

Atomistic prediction of the temperature- and loading-rate-dependent first pop-in load in nanoindentation

Nanoindentation has been used for a long time to investigate the mechanical properties of materials. A well-known displacement burst, the so-called “pop-in,” is usually observed during nanoindentation tests. In particular for the first pop-in has been well studied because it should be directly related to the fundamental mechanical strength of the local volume beneath the indenter. The first pop-in load measured for a defect-free local volume is corresponding to the onset load of homogeneous dislocation nucleation, while measured for a local volume with immobile defects is that of heterogeneous dislocation nucleation. The first pop-in is a thermally activated event under loading; thus, the pop-in load exhibits both temperature and loading-rate dependencies. Although theoretical studies have successfully explained the temperature and loading-rate dependencies, to the best of our knowledge, an atomistic prediction for specific materials which takes into account the stress state beneath the indenter has not yet been reported. In this study, we propose an atomistically informed multiscale (two-scale) modeling to predict the temperature and loading-rate dependencies of the first pop-in load for the homogeneous dislocation nucleation considering an atomistically estimated stress state beneath the indenter and stress-dependent activation energies of dislocation nucleation. Body-centered-cubic Fe and Ta are chosen as target metals, although the method is generally applicable to any ductile material. In addition to the homogeneous dislocation nucleation, we also developed a heterogeneous nucleation theory to explain the difference between the experimentally and atomistically obtained homogeneous nucleation pop-in loads.

Studying the Effect of Grain Size on Whisker Nucleation and Growth Kinetics Using Thermal Strain

To understand how and why Sn whiskers nucleate, measurements were performed in which the thermal expansion mismatch was used to induce strain in the samples. The current work focuses on the effect of grain size by studying samples with a thickness of 8 μm to compare with previous studies on 2.5 μm samples. The stress evolution during cycles of heating is determined by monitoring the resulting curvature in the sample. At the same time, the number of whisker nuclei are measured with optical microscopy which enables the relationship between film stress and nucleation rate to be quantified, where the stress relaxation kinetics depend on the grain size. The rate of stress relaxation is greater in the thick samples than the thin samples for the same heating cycle and the final stress after relaxation is smaller for the thicker samples. The whisker volume evolution was determined by using short sequences of heating and then measuring the size of different features after each interval in the scanning electron microscope. This enabled quantification of the relationship between film stress and whisker growth rate. The growth rate depends on the stress above the final stress, similar to our previous results for the thinner samples. The whisker nucleation kinetics in the 8 μm samples can also be explained with the same model used for the 2.5 μm samples. However, the stress-dependent activation energy is shifted to lower values.

Thermal Activation Analysis for Higher-Temperature Deformation of Gamma-Iron

Recent extension of Zerilli–Armstrong (Z–A) constitutive relations to higher temperature is assessed using yield strength measurements on 0.09 C steel covering the initial deformation behaviors of metastable and stable γ-iron phases. Descriptions of temperature dependence of yield stress; stress-dependent activation energy; and, activation area agree with the Z–A formulation. The relatively weaker thermal dependence of fcc strain hardening compared to a stronger thermal dependence of yield stress for bcc metals is pointed out.

Effect of minor Gd addition on the microstructure and creep behavior of a cast Al–15Mg2Si in situ composite

The influence of 0.5 wt% Gd addition on the microstructure and creep behavior of a cast Al–15Mg2Si composite was studied by means of compression tests under different constant stresses in the range of 50–250 MPa, corresponding to the modulus-compensated stress levels of 0.002 ≤ σ/G ≤ 0.011, in the temperature range of 473–563 K. Analysis of the data showed that for all loads and temperatures, the Al–15Mg2Si–0.5Gd composite had lower creep rates, and therefore, higher creep resistances than the base composite. This is ascribed to the morphological modification of the primary Mg2Si particles, refinement of the eutectic structure, significant reduction in the size and volume fraction of the primary Mg2Si particles, and the formation of the fine thermally stable MgGd intermetallic phase at the grain boundary areas. Based on the obtained stress exponents of 4.6–5.9 and stress-dependent activation energies, which are close to that of the lattice self-diffusion in pure aluminum, it can be proposed that the dominant creep mechanism in the present composites is stress-assisted dislocation climb controlled by lattice self-diffusion.

Cross-slip in face-centered cubic metals: a general Escaig stress-dependent activation energy line tension model

Cross-slip is a dislocation mechanism by which screw dislocations can change their glide plane. This thermally activated mechanism is an important mechanism in plasticity and understanding the energy barrier for cross-slip is essential to construct reliable cross-slip rules in dislocation models. In this work, we employ a line tension model for cross-slip of screw dislocations in face-centred cubic (FCC) metals in order to calculate the energy barrier under Escaig stresses. The analysis shows that the activation energy is proportional to the stacking fault energy, the unstressed dissociation width and a typical length for cross-slip along the dislocation line. Linearisation of the interaction forces between the partial dislocations yields that this typical length is related to the dislocation length that bows towards constriction during cross-slip. We show that the application of Escaig stresses on both the primary and the cross-slip planes varies the typical length for cross-slip and we propose a stress-dependent closed form expression for the activation energy for cross-slip in a large range of stresses. This analysis results in a stress-dependent activation volume, corresponding to the typical volume surrounding the stressed dislocation at constriction. The expression proposed here is shown to be in agreement with previous models, and to capture qualitatively the essentials found in atomistic simulations. The activation energy function can be easily implemented in dislocation dynamics simulations, owing to its simplicity and universality.

Quantifying the Effect of Stress on Sn Whisker Nucleation Kinetics

Although Sn whiskers have been studied extensively, there is still a need to understand the driving forces behind whisker nucleation and growth. Many studies point to the role of stress, but confirming this requires a quantitative comparison between controlled stress and the resulting whisker evolution. Recent experimental studies applied stress to a Sn layer via thermal cycling and simultaneously monitored the evolution of the temperature, stress and number of nuclei. In this work, we analyze these nucleation kinetics in terms of classical nucleation theory to relate the observed behavior to underlying mechanisms including a stress dependent activation energy and a temperature and stress-dependent whisker growth rate. Non-linear least squares fitting of the data taken at different temperatures and strain rates to the model shows that the results can be understood in terms of stress decreasing the barrier for whisker nucleation.

Dislocation cross-slip controlled creep in Zircaloy-4 at high stresses

Abstract Uniaxial creep tests were performed on Zircaloy-4 sheet in the temperature range of 500–600 °C at high stresses (>10−3E), to uncover the rate-controlling mechanism. A stress exponent of 9.3–11 and a stress-dependent activation energy in the range of 220–242 kJ/mol were obtained from the steady state creep data. TEM analyses revealed an extensive presence of hexagonal screw dislocation network on the basal planes indicating recovery of screw dislocations by cross-slip to be the dominant mechanism. The creep data was therefore analyzed in the light of Friedel׳s cross slip model for HCP metals according to which the stress-dependency of the activation energy determined from the creep data was written in the form, U = ( 150 ± 4 ) + ( 2236 ± 124 τ ) kJ / mol The constriction energy of screw dislocations of 150 kJ/mol is in agreement with the values reported in the literature for zirconium and other HCP metals. Further analysis of the yield strength and the activation volume data obtained from stress relaxation tests in the temperature range 500–600 °C favors cross-slip of screw dislocations as the rate controlling mechanism over the test conditions.

Stress-induced glass transitions

In 1995, Chudnovsky and coworkers (Zhou, Chudnovsky, Bosnyak, & Sehanobish, 1995) interpreted cold drawing in polymeric glasses as a dual glass transition, first from glass state to a liquid, and then, after drawing turned the glass into a non-isotropic oriented polymeric liquid, from oriented liquid to a new glass state. On the microscopic scale, a glass is a system with local arrangements of particles frozen. At the glass–liquid transition temperature, these arrangements become changeable at an observable time scale. Assuming that cold drawing is caused by slip-stick rearrangements in small clusters throughout the material, we investigate the relations of conventional glass transition to the onset of cold drawing; our theory is based on a generalization of Eyring’s ideas of stress-dependent rearrangement activation energies.

Core element effects on dislocation nucleation in 3C–SiC: Reaction pathway analysis

The nucleation of glide-set 90° partial dislocation from a sharp corner in 3C–SiC has been investigated by reaction pathway analysis. We focus on the core element effect and assert that both the stress-dependent activation energy and the athermal strain of C-core dislocation nucleation are higher than those of Si-core, while the gradient of the energy curve for C-core nucleation is lower than the Si-core counterpart, manifesting the greater thermal sensitivity of C-core dislocation. The results indicate that the nucleation of Si-core dislocation is more energy-favorable, while the C-core dislocation would nucleate with thermal assistance under high temperature, which explain the observation of core nature effects on dislocation performance in SiC by previous experiments. Estimation of dislocation nucleation behavior under high temperature has also been conducted. The free energy is obviously reduced at deposition temperature, implicating the much higher occurrence rate of dislocations with both C-core and Si-core during the crystal growth process. Moreover, from the viewpoint of different mobilities of boundary partial dislocations due to the core element effect, the distinct performances of stacking faults with Si-face and C-face exposure on the (001) surface during film deposition have been discussed, providing a reasonable explanation of our previous observation [1,2].

Creep properties of low-temperature sintered nano-silver lap shear joints

As a potential alternative to conventional solders and adhesive films, low-temperature sintered nano-silver paste, as a result of its high thermal and electrical conductivity (240Wm−1K−1 and 4.1×107Sm−1, respectively) and high melting temperature (961°C), can be used for connecting chips that require high temperature operation and high heat dissipation ability. In the present work, a number of creep tests were carried out to study the effect of stress and temperature on the creep behavior of low-temperature sintered nano-silver lap shear joints. The steady-state creep flow behavior of the joints was discussed. In general, the creep shear strain rate increased as the applied stress and ambient temperature increased. When the creep strain rate was described by the Arrhenius power-law model, we found that the stress exponent and activation energy were temperature dependent and stress dependent, respectively. A modified power-law model with a temperature-dependent stress exponent and stress-dependent activation energy was proposed to describe accurately the creep flow of the sintered lap shear joints.

Shuffle-glide dislocation transformation in Si

The transformation of dislocation cores from the shuffle to the glide set of {111} glide planes in Si is examined in this work. The transformation is thermally activated and is favored by a resolved shear stress which applies no force on the original perfect shuffle dislocation. A resolved shear stress driving dislocation motion in the glide plane is not observed to promote the transition. The stress-dependent activation energy for the described shuffle-glide transformation mechanism is evaluated using a statistical analysis. It is observed that the transformation is not associated with an intermediate metastable state, as has been previously suggested in the literature.

Heterogeneously randomized STZ model of metallic glasses: Softening and extreme value statistics during deformation

A nanoscale kinetic Monte Carlo (kMC) model is developed to study the deformation behavior of metallic glasses (MGs). The shear transformation zone (STZ) is adopted as our fundamental deformation unit and each nanoscale volume element (∼1nm voxel) in the MG is considered as a potential STZ that may undergo inelastic rearrangements sampled from a randomized catalog that varies from element to element, with stress-dependent activation energies. The inelastic transformation sampled out of spatially randomized catalogs (a key characteristic of glass) is then treated as an Eshelby’s inclusion and the induced elastic field is solved in the Fourier space using the spectral method. The distinct features of our model, compared to previous work, are the introduction of randomized event catalogs for different nanoscale volume elements, repeated operations within the same element, and a “generation-dependent” softening term to reflect the internal structural change after each deformation. Simulations of uniaxial tension show the important effect of softening on the formation of shear bands, with a size-independent thickness of 18nm. Statistical analysis of the accumulated strain at the ∼1nm voxel level is carried out and sample size effect on the extreme value statistics is discussed.

Anisotropy Behavior of Dislocation Nucleation from a Sharp Corner in Copper

By means of reaction pathway analysis, we have investigated the nucleation of 90° and 30° partial dislocation from a sharp corner in an f.c.c. crystal copper. The anisotropy aspects of dislocation nucleation revealed by the results have shown that the stress-dependent activation energy of 30° partial dislocation is approximately twice over the counterpart of 90° partial dislocation, and that the maximum inelastic displacement for the former is also higher. Moreover, the shape of the saddle-point configuration of 30° partial dislocation is similar to a half-ellipse whereas in the case of 90° partial dislocation it is more like a semi-circle, reflecting the different Peierls barriers influenced by the Burgers vectors. Further study of the surface reconstruction demonstrates that although the nucleation of 30° partial dislocation has been enhanced by surface reduction, it is still more energy-unfavorable than the 90° partial dislocation. These results suggest that the higher Peierls barrier is responsible for the larger activation energy of 30° partial dislocation nucleation.

Reaction pathway analysis for dislocation nucleation from a Ni surface step

Threshold strain required for a thermally activated dislocation nucleation from a Ni surface step has been measured using an atomistic-based reaction pathway analysis. We show that the saddle-point configuration and the stress-dependent activation energy are strongly influenced by the presence of a surface step. Our results provide insight into the previous experimental findings concerning the mechanism on a coherency loss at the Ni∕Cu(001) interface. We conclude that the coherency strain caused by a lattice mismatch between Ni and Cu does not yield a sufficient driving force for the dislocation nucleation.

A model based creep equation for 9Cr–1Mo–0·2V (P91 type) steel

The isothermal constant stress creep tests data for a 9Cr–1Mo–0·2V (P91 type) steel were submitted for a phenomenological analysis in order to obtain the relevant creep equation for such steel. Namely, the minimum creep strain rate of P91 type steel cannot be described by the simple Arrhenius type power law constitutive model. The incorporation of the threshold stress concept in the analysis of creep data leads to a modified power law, which satisfactorily describes the creep behaviour of the examined P91 steel. However, the threshold stress is not a good material parameter, as it often varies with temperature and/or applied stress. This adds uncertainty to the extrapolation of the creep rates into ranges where experimental data are not available. Besides the fact that the physical foundation for a threshold stress is questionable from a scientific point of view, this is a serious practical limitation of the modified power law creep equation. The second creep equation proposed in the present paper is the improved stress dependent energy barrier model. The improvement of the standard model is based on two assumptions: first, on the hypothesis that the application of a stress also affects the energy barrier to be overcome when a local region transitions from the initial to the final state, and second, by applying a simple power function of stress instead of a hyperbolic sin function in the model based equation. The obtained value of stress exponent, n=5·5, is too high for entirely climb controlled creep. The apparent activation energy of approximately 510 to 545 kJ mol−1, which is considerably higher than the activation energy for lattice diffusion, is the stress dependent activation energy of the slowest, dominant rate controlling process of the supposed multiple creep mechanisms.

The improved power-law, stress-dependent, energy-barrier model of 9Cr–1Mo–0.2V steel using short-term creep data

The creep equation in the present paper is the improved stress-dependent energy-barrier model. The improvement over the standard model is based presumably on the assumption that the application of a stress also affects the energy barrier to be overcome when a local region transitions from the initial to the final state. The apparent activation energy of approximately 610–645 kJ mol−1 is the stress-dependent activation energy of the slowest, dominant rate-controlling process of the proposed multiple creep mechanisms.

Geometrical effect on dislocation nucleation at crystal surface nanostructures

Crystal surface nanostructures such as steps and trenches in microelectronic layer structures have been considered as stress concentrators that may facilitate dislocation nucleation. Quantitative characterization of the critical condition of this atomic scale process is of considerable interest for the development of high performance electronic devices. This paper addresses this issue using a multiscale approach based on the variational boundary integral formulation of the Peierls–Nabarro dislocation model. By representing the profiles of embryonic dislocations as the relative displacements between the two adjacent atomic layers along the slip planes, the critical conditions for dislocation nucleation are obtained by solving the stress dependent activation energies required to activate embryonic dislocations from their stable to unstable saddle point configurations. The geometrical effect of surface nanostructures such as steps and trenches on dislocation nucleation is ascertained quantitatively. Our results show that the atomic scale surface nanostructures can reduce the critical stress for dislocation nucleation by nearly an order of magnitude and the trench configurations are more prone to dislocation nucleation than the step configurations. Nucleation of versatile dislocations in multiple slip systems at crystal surfaces may be attributed surface nanostructures of a variety of geometries.

Critical conditions for dislocation nucleation at surface steps

Dislocation nucleation at a surface step is analyzed based on a general variational boundary integral formulation of the Peierls–Nabarro dislocation model. By modelling the surface step as part of the surface of a three-dimensional crack, the free surface effect is taken into account by transferring the half space problem into an equivalent one in the infinite medium. The profiles of embryonic dislocations, corresponding to the relative displacements between the two adjacent atomic layers along the slip planes, are then rigorously solved through the variational boundary integral method. The critical conditions for dislocation nucleation are determined by solving the stress-dependent activation energies required to activate the embryonic dislocations from their stable to unstable saddle-point configurations. In particular, the effect of the step geometry, such as the height of the step, the dip angle of the slip plane and the inclined angle of the step surface on dislocation nucleation, is quantitatively ascertained. The results show that the atomic-scale surface step can rapidly reduce the critical stress required for dislocation nucleation from the surface by nearly an order of magnitude. The decrease in critical stress as a function of the height of the step is more significant for slip planes with smaller dip angles and surface steps with smaller inclined angles.

Critical Conditions for Dislocation Nucleation from Surface Steps

AbstractThe critical conditions for dislocation nucleation from the surface steps of various geometries are analyzed based on the Peierls-Nabarro dislocation model. By modeling a surface step as part of a three- dimensional crack surface, the half space problem is transferred into an equivalent three dimensional crack problem in an infinite medium. The profiles of embryonic dislocations, corresponding to the relative displacements between the two adjacent atomic layers along slip planes, are then rigorously solved through the variational boundary integral method. The critical conditions for dislocation nucleation are determined by solving the stress dependent activation energies required to activate embryonic dislocations from their stable to unstable saddle point configurations. For a given slip plane, the effects of step geometry such as the step height and inclined angle on dislocation nucleation are analyzed in detail. The results show that the atomic scale steps may reduce the critical stress required for dislocation nucleation from the surface by several factors. Compared to previous analyses of this type of problem based on continuum elastic dislocation theory, the presented analysis eliminates the uncertain core cutoff parameter by allowing for the existence of an extended dislocation core as the embryonic dislocation evolves. Because of the serious limitation of direct atomic simulation for this type of problem, the presented methodology of incorporating atomic information into continuum approach appears to be particularly noteworthy for providing insights of energetics of the atomic processes involved in dislocation nucleation.