Sampath Purushothaman

Role of back stress in the creep behavior of particle strengthened alloys

Abstract Based on the analysis of recent creep data on a γ strengthened wrought nickel-base superalloy, an oxide dispersion strengthened (ODS) nickel-base solid solution alloy, and an ODS nickel-base superalloy, it is concluded that creep in such particle strengthened systems can be mechanistically described through an effective stress dependence that includes a back stress consistent with the alloy microstructure. The back stress in the ODS solid solution alloy is on the order of the stress needed for the Orowan bypassing of the inert dispersoids by the mobile dislocations. The back stress in the ODS superalloy which combines both the inert dispersion strengthening and γ strengthening, is higher than that in the ODS solid solution primarily because of the higher yttria volume fraction in the ODS superalloy which leads to a higher Orowan critical stress. The back stress in the γ strengthened wrought superalloy at intermediate temperatures (760°C) appears to be on the order of the stress required to shear through the ordered γ precipitates and is expected to be on the order of the at-temperature flow stress of this alloy measured at creep strain rates. Coarsening of the γ precipitates in this alloy during elevated temperature (982°) creep leads to a lower back stress which is consistent with the stress required for the observed Orowan bypassing of the coarsened γ particles by the mobile dislocations. The effect of test environment on the creep of this alloy is found to be through the back stress which is higher in air than in vacuum, due perhaps to surface oxide strengthening of this reasonably coarse grained alloy. Expressions relating the apparent creep parameters (activation energy and stress exponent) to the true creep parameters through back stress, elastic modulus and their temperature dependence are also derived. It is shown that the high apparent creep parameters characteristic of some of these strengthened alloys can be corrected down to true creep parameters whose magnitudes can perhaps be accounted for by creep rate controlled by recover processes.

The role of the alloy matrix in the creep behavior of particle-strengthened alloys

Abstract The more obvious strengthening microstructural features in heat-resistant super-alloys are oxide dispersoids and/or γ′ precipitates. An interesting problem is the role that the strength of the alloy matrix plays in the creep resistance of these alloys. We sought an answer to this problem through the evaluation of experimental data on a host of oxide-dispersion- and/or precipitation-strengthened nickel-based alloys with various levels of matrix solid solution strengthening and through a generalized expression for creep rates which separates the matrix contributions from the particle contributions to the resisting stress and creep strength of these alloys. It is concluded that the major role of the alloy matrix in the creep behavior of these alloys is in determining the apparent stress dependence of the creep rates. Specifically, the stronger the matrix through solid solution strengthening, the less applied stress sensitive is the creep rate of the alloy. The implications of these findings with respect to alloy design for better creep resistance in multiphase alloys are also discussed.

A theory for creep crack growth

The paper derives an analytical expression for creep crack growth rate based on a model in which the higher and concentrated stresses ahead of the crack tip enhance creep deformation, thus progressively causing stress rupture and continuous crack advance. The equation derived for creep crack growth rate is expressed in terms of a geometrical factor in the stress intensity expression and in terms of the crack tip radius whose lower limit estimate is the fracture mechanics crack-tip opening displacement. The functional features of the derived creep crack growth rate equation can be compared with those of a pertinent empirical equation. The analytical expression provides some guidelines for alloy and microstructure design.

Slow Crystallographic Fatigue Crack Growth in a Nickel-Base Alloy

Fatigue crack propagation rates at very low cyclic stress intensity levels (1 to 3 MNm-372) have been measured in cube-oriented, planar slip nickel-base superalloy monocrystals using a high frequency (20 kHz) resonant fatigue testing technique. It is found that crack propagation is entirely along the crystallographic slip planes and the crack growth rate does not drop off into a threshold behavior but follows a power law with a power law exponent close to 4, which is similar to the functional dependency observed at higher cyclic stress intensity levels in similar superalloys. The observed behaviors are discussed with respect to a new theory on threshold and the effects of strong crystallographic constraints on crack propagation behavior.

Generalized theory of fatigue crack propagation: Part II — Derivation of threshold and Paris regime crack growth rates

Abstract Expressions for the growth rate of fatigue cracks by the continuous advance of the crack front normal to itself, as well as by the discontinuous ledge-controlled processes, are derived in the presence and absence of strong crystallographic constraints on crack front motion. With no crystallographic constraints, the functional trends found are consistent with the Paris law and the sharply ΔK eff- dependent threshold regime behaviors commonly observed in ductile materials. In the case where strong crystallographic constraints may be operating at all ΔK eff levels, the fatigue crack growth rates derived, based on crack advance rate controlled by the lateral motion of pre-existing ledges on the cusporiented and crystallographic crack front, are proportional to ΔK eff 4 at all ΔK eff levels.

Generalized theory of fatigue crack propagation: Part I — derivation of thresholds

Abstract An energetic analysis of the fatigue crack propagation process has been carried out and it was found that there is a critical effective stress intensity range, ΔK°eff, below which it is energetically unfavorable for a crack front to move continuously normal to itself. It is proposed instead that, below this critical ΔK°eff, the crack front can advance through the lateral motion of ledge-like perturbations on its front in the manner of the low driving force motion of interphase and grain boundaries in phase transformations. Expressions for this critical stress intensity range are derived for noncrystallographic crack fronts and crack fronts suspected to be strongly constrained by crystallographic factors. The magnitudes of these critical stress intensities are discussed with regard to experimentally observed threshold stress intensity ranges.

Understanding the Larson-Miller parameter

The Larson-Miller (L-M) method of extrapolating stress rupture and creep results is based on the contention that the absolute temperature-compensated time function should have a unique value for a given material. This value should depend only on the applied stress level. The L-M method has been found satisfactory in the case of many steels and superalloys. The derivation of the L-M relation is discussed, taking into account a power law creep relationship considered by Dorn (1965) and Barrett et al. (1964), a correlation expression reported by Garofalo et al. (1961), and relations concerning the constant C. Attention is given to a verification of the validity of the considered derivation with the aid of suitable materials.

Kinetics of environmental fatigue crack growth in a nickel-copper alloy: Part II. In hydrogen

A systematic matrix of fatigue crack growth rate data in a hydrogen environment has been generated in a nickel-copper alloy and compared with the base line data in the milder oxygen and vacuum environments described in the preceding paper. It is found that crack growth in the hydrogen environment is characterized by high values of the Paris equation exponent and faster crack propagation rates as compared to those in the milder environments. Fractographic examination shows that brittle inter granular separation occurs superimposed on an otherwise ductile crack mode in the hydrogen tests. Quantitative fractographic analysis of the hydrogen affected fracture surfaces indicates that the percentage of intergranular failure (area fraction) is a uniquely related function of the mean stress intensity rather than the maximum stress intensity level of fatigue loading. This dependence is discussed in terms of dislocation sweep-in transport of hydrogen deep into the plastic zone during fatigue cycling.

Kinetics of environmental fatigue crack growth in nickel-copper alloy: Part I. In vacuum and oxygen

Fatigue crack growth rates have been determined in a nickel-copper alloy in the mild test environments of vacuum and oxygen. It is found that the fatigue crack growth mode in both vacuum and oxygen is ductile and the growth rate is sensibly independent of the maximum stress intensity levels and stress intensity ratio. The growth rate is found to be lower in vacuum than in oxygen, and the growth rate dependency on the cyclic stress intensity range is more pronounced in vacuum than in oxygen. These differences in behavior may be consistent with differences in crack closure behavior for the two environments.

Effects of aging and plane strain constraint on the ductility of an aluminum alloy

Abstract Deformation and fracture behavior under uniaxial loading and under plane strain were investigated for Al 2024 alloy in the underaged, peak-aged and overaged conditions. It was found that the plane strain ductility is always lower than the corresponding uniaxial tensile ductility for all the three aging conditions, the maximum plane strain sensitivity being associated with the overaged condition. On the basis of fractographic analysis, it is suggested that this is most probably a consequence of enhanced void initiation, growth and coalescence processes which are promoted by overaging-induced incoherent precipitates and the large hydrostatic tensile component associated with plane strain constraint.