Yield Point Return Research Articles

Activation energy calculations for discontinuous yielding in Inconel 718SPF

The kinetics of yield point return and of dynamic strain aging (DSA) were investigated for a commercial heat of Inconel 718SPF. During uniaxial tensile tests, the alloy exhibited serrated flow on the load–elongation curves at intermediate temperatures. Types A, B and C serrations were observed depending upon the test temperature and strain rate. For type A and B serrations, apparent activation energies ranging from 97 to 133 kJ mol −1 were measured, which suggests that type A and B serrated flow results from the diffusion of an interstitial solute, most likely carbon. For type C serrations, apparent activation energies in the range ∼210 to ∼272 kJ mol −1 were measured, which suggests that type C serrations arise from the diffusion of a substitutional solute, most likely Cr. Yield points induced during strain aging under stress experiments increased with a t n relationship, where the exponent n ranged from 0.3 to 0.5 before reaching a plateau. This suggests that the yield points were a combined result of bulk lattice diffusion and dislocation pipe diffusion of solutes. The apparent activation energies, ranging from 42 to 50 kJ mol −1, are consistent with prior observations, but cannot be explained by any classic models for static strain aging. It is suggested that the yield points result from the reorientation of carbon-vacancy pairs in the strain fields of dislocations.

Kinetics of static strain aging in polycrystalline NiAl-based alloys

The kinetics of yield point return have been studied in two NiAl-based alloys as a function of aging time at temperatures between 300 and 700 K. The results indicate that the upper yield stress increment, Delta sigma(sub u) (i.e., stress difference between the upper yield point and the final flow stress achieved during prestraining), in conventional purity (CP-NiAl) and in high purity carbon-doped (NiAl-C) material first increased with a t(exp 2/3) relationship before reaching a plateau. This behavior suggests that a Cottrell locking mechanism is the cause for yield points in NiAl. In addition, positive y-axis intercepts were observed in plots of Delta sigma(sub u) versus t(exp 2/3) suggesting the operation of a Snoek mechanism. Analysis according to the Cottrell Bilby model of atmosphere formation around dislocations yields an activation energy for yield point return in the range 70 to 76 kJ/mol which is comparable to the activation energy for diffusion of interstitial impurities in bcc metals. It is, thus, concluded that the kinetics of static strain aging in NiAl are controlled by the locking of dislocations by Cottrell atmospheres of carbon atoms around dislocations.

Application of a model for strain aging under stress to niobium

A simple model is proposed to rationalize yield point return curves obtained when specimens of a b.c.c. metal-interstitial atom solid solution are strain aged under stress. Several basic assumptions are involved. First that the solute is mobile enough to diffuse to the dislocations and strain age them during the period that they wait in front of obstacles to their motion for thermal activation (Sleeswyk's hypothesis). Second, the solute is not mobile enough to be dragged with the dislocations as they advance between obstacles. Third, the stress increment due to the strain aging of the dislocations is additive to the stress of the basic rate controlling mechanism. Fourth, in agreement with experimental observations, the strain again follows conventional static strain aging kinetics involving both Shoeck-Seeger (Snoek) reordering of the solute in the stress fields of the dislocations and the long range Cottrell-Bilby drift of the solute to form dislocation atmospheres. Tests of the model using niobium-oxygen data, taken from the literature, demonstrate that it is able to account, within the experimental error, for the effects of both temperature and prestrain on the strain aging under stress kinetics curves.

The Snoek-köster relaxation transient period in cold-worked niobium

The so-called S-K peak observed in internal friction experiments on cold-worked b.c.c. metals has been studied through relaxation tests in order to lengthen the measurable relaxation times and to lower the temperatures. We could then show the existence of a transient period during which the relaxation time τ SK increases in a very large proportion while the relaxation strength remains constant. The results agree qualitatively with Schoeck's theory and with an aging due to the migration of interstitials towards the dislocations. But the study of the aging kinetics together with that of yield point return conveys the idea that the dislocation mechanism is more complex and can be compared to that leading to the γ peak.

The initial development of a yield point due to carbon in nickel 200 during static strain aging

A model is proposed for the development of the first stage of the yield point return in Nickel 200. It is assumed that immediately after straining and unloading, vacancies cre-ated during deformation become trapped by interstitial carbon atoms. The carbon-va-cancy pairs thus formed then reorient quickly in the stress fields of nearby dislocations thus reducing the dislocation line energy so that dislocation pinning occurs. This model is based on a hypothesis proposed by Rose and Glover in 1966 for austenitic stainless steel.

Snoek Rearrangement and Long-Range Diffusion during Strain-Ageing in Iron

AbstractThe strain-ageing kinetics of annealed (870°C/1143 K) and quenched (700°C/973 K) single crystals and quenched (700°C/973 K) polycrystalline specimens of Ferrovac-E iron were studied over the temperature range −10°C (263 K) to 70°C (343 K) employing the yield-point return technique. Snoek rearrangement of interstitials about dislocations was deduced from the results as the first stage of the strain-ageing process. The completion time required for Snoek rearrangement corresponds to the time required for a single jump of an interstitial carbon or nitrogen atom. The ageing process obeys a t2/3 relationship. Only minute amounts of interstitials are required: no drastic difference could therefore be observed between quenched and annealed specimens. The activation energy is in the range 14·1±2·3 to 14·9±0·5 kcal/mol (59·0±9·6 to 62·4± 2·1 kJ/mol). The first value is based on Arrhenius' equation, the second on Hartley's analysis using 45 separate experimental determinations. The second state of strain-age...

Contribution of snoek rearrangement to strain aging

Using the yield point return technique the strain aging kinetics of annealed Ferrovac E iron (0.01% C, 0.0002% N) has been studied in the temperature range of 0° to 100° C. Aging was performed while the specimen was subjected to tensile stress. A two-stage aging process was observed at and below 31°C. The first stage attributed to Snoek-Schoeck-Seeger rearrangement of interstitials about dislocations was investigated in detail. For this stage the following has been found: (a) a t 2 3 relationship is obeyed, (b) the yield point return data agree with interstitial jump time, (c) the maximum value of the yield stress increment is a constant of 0.7 ± 0.1 kg/mm 2 and is independent of time and temperature, (d) positive intercepts at zero aging time are observed, and (e) there is close agreement between the activation energies determined by Hartley analysis (14.5 kcal/mole) and Arrhenius equation (15.5 kcal/mole). The second stage is ascribed to conventional interstitial bulk diffusion.

Oxygen dependence of strain-ageing in niobium

The effect of oxygen content on the strain-ageing behaviour of electron-beam-refined niobium has been studied, using both yield point return and internal friction measurements. The strain-ageing index, given by Δσ y = Δσ f + 2k y d −1 2 has been found to be proportional to the amount of oxygen migrating from free solid solution. The dislocation locking parameter k y attains a “saturation” value, which increases with increasing initial oxygen content, but is smaller than that for the annealed material. The results indicate that the smaller value of k y is primarily due to the increased density of dislocations in the strain-aged material. Δσ f , the increase in flow stress, commences to grow only after the k y parameter is almost saturated, and is associated with oxygen atoms which migrate to dislocations beyond the saturation of Cottrell atmospheres.

Strain-ageing in tantalum

A selfconsistent theory of the rise in flow stress with ageing after straining and of the yield point return is developed and applied to experimental results on unalloyed tantalum. It is shown that the initial rise in yield stress obeys the relation: Δσ \\ ̄ gs = K 1 × K 2t 2 3 where Δσ is the difference between, and δ the arithmetic average of the yield stress after ageing and the stress at which the prestrain was terminated, K 1 and K 2 are constants for a given set of test conditions and t is the ageing time. The constant K 2 is proportional to D 2 3 , D being the diffusivity of the pinning element. This equation is derived employing the concepts of thermally activated flow and by assuming that the only function of the pinning element is to reduce the length of mobile dislocation line produced by prestrain; the concept of breakaway is not invoked. The theory developed applies only to the early stages of ageing denned by the conditions that: 1. (a) dislocations produced by prestrain act as “yielding nuclei” for yielding after flow, 2. (b) the rate of segregation of impurities to dislocations is given by an equation of the form (1−q) = exp{−αt 2 3 } , where q is the concentration of impurities on a dislocation and 3. (c) the internal stress field within the metal is not significantly affected by ageing. Under these conditions it is also demonstrated that the rate of yield point return should follow an Arrhenius relationship. The theory is applied to strain-ageing studies of unalloyed tantalum and it is shown that the initial rise in flow stress and yield point return are controlled by the diffusion of oxygen to dislocations.

The mechanism of strain-ageing in commercially pure niobium

The strain-ageing process in commercially pure niobium has been studied using both yield point return and internal friction measurements. After a 6 % pre-strain specimens were aged at temperatures ranging from 100° to 165° C for periods of up to 160 hours. The yield point return results show that the strain-ageing process obeys a t 2 3 law up to about 65 % completion of the ageing process. The activation energy has been found to be 25 800 ± 1000 cal/mol, which is in good agreement with the reported activation energy for the diffusion of oxygen in niobium (26 600 cal/mol). The internal friction results offer complementary information to the yield point return measurements, and show that while oxygen diffuses to dislocations during the early stages of strain-ageing it subsequently returns into solid solution after more extensive ageing. The most likely explanation of this effect is that oxygen atoms are replaced at the dislocations by carbon atoms. An attempt has been made to calculate the dislocation density and dislocation atmosphere density for the fully strain-aged condition at 155° C.

Dislocation pinning effects in unalloyed molybdenum

The rate of yield point return and modulus defect recovery was studied in powder metallurgical and arccast molybdenum, respectively. The activation energy for yield point return is 25,100 ± 2700 cal/mol. This is believed to be due to pinning of deformation-produced free dislocations by oxygen or nitrogen atoms. A calculation of the number of impurity atoms per unit length of dislocation line necessary to cause yield point return implies that this pinning is effected by the formation of microprecipitates. Possible mechanisms consistent with this idea which exhibit kinetics similar to the Cottrell-Bilby “atmosphere” theory are discussed. Recovery of the modulus defect during the latter stages of aging may be controlled by the diffusion of the slowest pinning defect. Adopting this interpretation, the activation energy for diffusion of the slowest defect calculated from a treatment based on the Granato-Hikata-Lücke theory of point defect pinning is 44,300 ± 8000 cal/mol. It is suggested that this defect is carbon.

Effect of hydrogen on dislocation locking in niobium

The strain-aging tendencies of as-received commercial purity arc-melted Nb and hydrogenated Nb from the same heat were investigated using yield point return and dynamic modulus measurements to study the aging process. Comparison of activation energies for strain aging with those for interstitial diffusion revealed that hydrogen could be responsible for dislocation locking in niobium. In order to obtain a measure of the degree of dislocation locking as a function of hydrogen content, the lower yield stress of electron beam melted Nb (both as-received and hydrogen-charged) was measured, as a function of grain diameter, using a constant strain rate and test temperature. In the equation, σ y = σ i + k y d − built1 2 , the parameter σ i was found to be relatively insensitive to hydrogen content, and the parameter, k y , a measure of the locking strength, was found to increase with increasing hydrogen content.