Harper-dorn creep in al,pb, and sn

High-temperature creep has been studied in lead and tin in the stress range of 10⁻⁶ to 10⁻⁴G over a range of temperatures near the melting point. A composite plot of dimensionless parameter^•/_γkT/DGb vsτ/G revealed a transition from a high stress region (with slope ∼4.9 for lead and ∼6.6 for tin) to a low stress region (with slope ∼1 for both metals), at stresses of ∼2 × 10^-5G for lead and ∼10⁻⁵G for tin. The creep behavior in the low stress region is identical to that attributed to creep of the Harper-Dorn type. In addition, earlier work on aluminum in the low stress region is confirmed using polycrystalline as well as single crystal samples. Formerly Graduate Student, University of California, Berkeley, Calif. 94720 Formerly Research Associate, Department of Materials Science, University of Calif., Berkeley, Calif.     

Evolution of dislocation structure in martensitic steels: the subgrain size as a sensor for creep strain and residual creep life

The results on the evolution of the dislocation structure in martensitic CrMoV-steels published by two research groups are shown to be consistent: The steady state dislocation spacings vary in inverse proportion to shear modulus normalized stress, the subgrains grow with strain at a rate which is determined by the initial subgrain size w₀, the steady state subgrain size w_∞ and the strain rate, independent of the composition of the material. At constant stress and temperature the strain ? and the subgrain size w are uniquely related by ? = ?_wln[log(w₀ / w_∞)/log(w / w_∞)] with ?_w = 0.12. Thus w can be used as a sensor for strain and, if the relation between strain and time is known, for the residual creep life.     

The influence of polycrystal grain size upon the creep ductility of copper

A study of the relationship between grain size and creep ductility has been made on OFHC copper when the fracture process involves intergranular cavitation. Tests have been carried out at a constant nominal strain-rate at 10^?2 hr^?1 at temperatures of 350°, 425°, and 500°C. At all temperatures a peak in the grain size vs ductility plots is obtained at (approximately) 30 μm for 350°C, 60 μm for 435°C, and 150μm for 500°C. The work involved a metallographic study of the fracture process and it is deduced that the final stage of fracture (cavity linkage) controls ductility, rather than either the rate of nucleation or individual growth of cavities. At coarse grain sizes and low temperature the crack length seems to be critical and increasing grain size decreases ductility. At fine grain sizes and high temperature, failure is by a ductile void-sheet process and the volume fraction of cavities is controlling so that decreasing grain size decreases ductility.     

Transient behavior of diffusion-induced creep and creep rupture

Steady state solutions to three types of diffusion problems: creep, grain boundary sliding and intergranular crack growth, have been published in the literature. This paper considers, in detail, the events which occur between the time when the external stress is applied and the time when the steady state is eventually reached. The time constant of the transient has been calculated. It is shown how the grain boundary tractions change with time from the initial “elastic” configuration (when sliding has been elastically accommodated) to the steady state “diffusional” configuration (when the sliding rate is diffusionally accommodated). This requires infusion of excess grain boundary dislocations; the distribution of these dislocations is calculated. The results are applied to problems of diffusional creep, grain boundary sliding and intergranular crack growth.     

Transient behavior of diffusion-induced creep and creep rupture

Steady state solutions to three types of diffusion problems: creep, grain boundary sliding and intergranular crack growth, have been published in the literature. This paper considers, in detail, the events which occur between the time when the external stress is applied and the time when the steady state is eventually reached. The time constant of the transient has been calculated. It is shown how the grain boundary tractions change with time from the initial “elastic” configuration (when sliding has been elastically accommodated) to the steady state “diffusional” configuration (when the sliding rate is diffusionally accommodated). This requires infusion of excess grain boundary dislocations; the distribution of these dislocations is calculated. The results are applied to problems of diffusional creep, grain boundary sliding and intergranular crack growth.     

The tertiary creep and necking of creep damaging solids

Tertiary creep and necking of bars composed of creep damaging material are investigated subject to the condition of constant applied load. The creep-damage constitutive model employed in the study is based on the concept of constrained cavity growth which characterizes the phenomenon of grain boundary cavitation in polycrystalline metals under creep conditions. For a perfect bar, tertiary creep arises from the interaction of cavitation with the geometrical effect of uniform thinning of the area cross section. Two coupled differential equations governing the evolution of the axial strain and area cross section are obtained and solved for the case of linear strain dependent nucleation. Necking is analyzed by considering the deformation of an initially imperfect bar modelled as a series of disk elements. The governing equations are integrated in these elements subject to the approximation that stresses and strains remain uniform throughout the deformation. Results indicate that the mechanism of cavitation can significantly affect the creep response of both the perfect and imperfect bars.     

The effect of sample size on the steady state creep characteristics of Ni-6 pct W

The effects of sample size and grain morphology on the steady state creep properties of Ni-6 pct W in the temperature range of 0.55T _m to 0.74T _m have been studied. It is shown that a decrease in sample thickness results in a corresponding decrease in the number of grains per thickness and gives rise to a decrease in the measured values of bothQ _creep andn when compared to existing data on thick samples with many grains per thickness. The observed effects of sample configuration on the creep properties are explained with a model for creep deformation which is based on the interaction of free surfaces with grain boundary sliding and grain deformation. Using this model, an expression for the stress and temperature dependence of the total steady state strain rate is obtained as a function of the grain matrix strain rate and the grain boundary sliding strain rate. The results of this model are shown to correlate well with the observed deformation characteristics of the thin samples and to explain the variations ofQ{creep} andn with sample morphology. Formerly Graduate Student, Department of Materials Science and Engineering, Stanford University     

Creep at low stresses: An evaluation of diffusion creep and Harper-Dorn creep as viable creep mechanisms

High-temperature creep experiments often reveal a transition at very low stresses to a region where the stress exponent is reduced to a value lying typically in the range of ∼1 to 2. This region is generally associated with the occurrence of a new creep mechanism, such as grain-boundary sliding, diffusion creep, and/or Harper-Dorn creep. Several recent reports have suggested that diffusion creep and Harper-Dorn creep may not be viable creep mechanisms. This article examines these two processes and demonstrates that there is good evidence supporting the occurrence of both creep mechanisms under at least some experimental conditions. This article is based on a presentation made in the workshop entitled “Mechanisms of Elevated Temperature Plasticity and Fracture,” which was held June 27–29, 2001, in San Diego, CA, concurrent with the 2001 Joint Applied Mechanics and Materials Summer Conference. The workshop was sponsored by Basic Energy Sciences of the United States Department of Energy.     

The effect of environment and grain size on the creep behavior of a ni-6 pct w solid solution

The effects of environment and grain size on the steady-state creep and creep rupture properties of a Ni-6 pct W solid solution are examined by testing in vacuum and commercial purity argon at 5000 psi and 900°C. The steady-state creep rate is found to decrease with increasing grain size at small grain sizes, both in vacuum and argon, owing to the effects of grain boundary sliding. At large grain sizes the creep rate is independent of grain size in vacuum and increases with grain size in argon. It is suggested that the increase in creep rate with increasing grain size is associated with fact that large-grained samples tested in argon do not reach steady-state before rupture occurs. Formerly Graduate Student, Stanford University, Stanford, Calif.     

Effect of initial gamma prime size on the elevated temperature creep properties of single crystal nickel base superalloys

The influence of initial γ′ size and shape on the high temperature creep properties of two single crystal nickel-base superalloys was investigated. The two alloys were chosen to represent different magnitudes of γ-γ′ lattice mismatch. A range of initial microstructures was produced by various quenching and aging treatments. Creep-rupture testing at 1000 °C was performed under stresses where γ′ directionally coarsens to form γ-γ′ lamellae in the early portion of the creep life. Both alloys exhibited a peak in creep resistance as a function of initial γ′ size. The peak corresponded to an initial microstructure consisting of cuboidal precipitates aligned along [001] directions. These aligned cuboidal γ′ particles directionally coarsened into a relatively perfect lamellar γ-γ′ structure in the early stages of creep, whereas the more irregularly shaped and distributed γ′ particles in both under and overaged material formed more irregular lamellae with more imperfections. The alloy with a lower magnitude of mismatch was less sensitive to initial γ′size and shape.     

Induced creep and creep/fatigue of a nickel-base superalloy at ambient temperatures

The stress controlled fatigue of Nimonic*115, a typical γ’-strengthened nickel-base superalloy, was studied at ambient temperature, using a trapezoidal wave form at 1 Hz, with stresses chosen to produce failure in the lO⁴ to lO⁴ cycle range. In tests with maximum stress greater than the proportional limit, most of the fatigue damage occurs within the first few test cycles. Much of this strain is accumulated under static load and is therefore identified as creep strain. Transmission electron microscopy shows that these creep strains occur in slip bands which disrupt the ordered γ’ precipitates. Strain is found to follow a logarithmic time dependence, which suggests a low activation energy mechanism.     

Effect of microstructure on creep and creep crack growth behaviour of titanium alloy

Creep and creep crack growth behaviour of a near α titanium alloy has been investigated at 600°C which is affected by primary α content. The alloy was heat treated at different temperatures so as to obtain different levels of equiaxed primary α in the range from 5 to 24 %. Constant load creep tests were carried out at 600°C in the stress range 250 to 400 MPa till rupture of the specimens. Creep crack growth tests were carried out at 600°C. Creep data reveals with increase in primary α content leads to creep weakening. On similar lines maximum creep crack growth resistance is associated with the alloy with lowest primary α content. Microstructural and fractographic examination has revealed that creep fracture occurs by nucleation, growth and coalescence of microvoids nucleated at primary β / 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 β / transformed β (matrix) interfaces in the interior of the specimen.