Hold-time effects on high temperature fatigue crack growth in Udimet 700

Crack growth behaviour under creep-fatigue conditions in Udimet 700 has been studied, and the crack growth data were analysed in terms of the stress intensity factor as well as theJ-integral parameter. Crack growth behaviour is shown to depend on the initial stress intensity level and the duration of hold-time at the peak load. For stress intensities that are lower than the threshold stress intensity for creep crack growth, the crack growth rate decreases with increase in hold time even on a cycle basis, da/dN, to the extent that complete crack arrest could occur at prolonged hold times. This beneficial creep-fatigue interaction is attributed to the stress relaxation due to creep. For stress intensities greater than the threshold stress intensity for creep crack growth, the growth rate on a cycle basis increases with increase in hold time. For the conditions where there is no crack arrest, the crack growth appears to be essentially cycle-dependent in the low stress intensity range and time-dependent in the high stress intensity range. Both the stress intensity factor and theJ-integral are shown to be valid only in a limited range of loads and hold-times where crack growth rate increases continuously.     

A fracture mechanics analysis of fatigue crack growth data for various materials

A large amount of previously published fatigue crack growth data obtained from 10 in. wide centre-cracked sheet specimens of various materials has been re-analysed in terms of the range of stress intensity factor (ΔK) and the results presented as master curves of crack growth rate against ΔK. In addition, data obtained previously from fatigue tests on edge-cracked plate specimens concerning the minimum cyclic stress that would just not cause a crack of a given length to grow have been similarly analysed.     

A fracture mechanics analysis of fatigue crack growth in a complex cross section

This paper describes research conducted to determine the fatigue crack growth behavior of corner cracks which occur in a beam with a complex “double-T” shaped cross section. Particular objectives were to determine the changes in crack shape as they grow from one leg of the double-T cross section into the wider portion of the specimen, and to determine whether crack growth could be delayed or arrested in this area. Since it is difficult, if not impossible, to obtain details of crack growth inside metal specimens, it was decided to test transparent polymer models which allow in situ photographs of the crack plane. Fatigue crack growth rates measured at various positions along the crack front were used to compute cyclic stress intensity factors from the baseline fatigue crack growth behavior of the test material. The results of these experiments do indicate that cracks may be delayed once they sever one leg of the double-T cross section, although crack arrest may be compromised if a second crack develops in the opposing leg.     

A synergistic fracture mechanics approach to fatigue life evaluation

A technique for modeling synergistic effects in fatigue crack propagation (FCP) is presented. First, a mission (load/temperature history) is segregated into elemental damage events. A simple three parameter model is then used to describe these events. The model coefficients are seen to be interrelated linear functions of FCP rate controlling variables such as frequency, temperature, stress ratio (σ_min/σ_max), dwell, overload ratio ($\text{P}{}_{\mathrm{overload}}$/$\text{P}{}_{\max }$) and cycles between overload. Finally, integrating event-by-event crack advance gives the expected component crack propagation life under mission cycling. Results of this procedure applied to gas turbine disk materials IN100 and Waspaloy are discussed to examine the accuracy of the model.     

Four lectures on fatigue crack growth: I. Fatigue crack growth and fracture mechanics

Aspects of the technical meaning of fatigue considerations in practice are indicated. The fatigue life is subdivided into a crack nucleation period and a crack propagation period. The significance of recognizing these periods for practical problems is illustrated by several examples. The similarity approach for correlating fatigue data is introduced. The meaning of the stress intensity factor for fatigue crack growth is discussed.     

Analysis of high temperature fatigue crack growth behavior

High temperature fatigue crack growth has been examined in the light of the new concepts developed by the authors. We observe that the high temperature crack growth behavior can be explained using the two intrinsic parameters ΔK and K_max, without invoking crack closure concepts. The two-parameter requirement implies that two driving forces are required simultaneously to cause fatigue cracks to grow. This results in two thresholds that must be exceeded to initiate the growth. Of the two, the cyclic threshold part is related to the cyclic plasticity, while the static threshold is related to the breaking of the crack tip bonds. It is experimentally observed that the latter is relatively more sensitive to temperature, crack tip environment and slip mode. With increasing test temperature, the cycle-dependent damage process becomes more time-dependent, with the effect that crack growth is dominated by K_max. Thus, in all such fracture processes, whether it is an overload fracture or subcritical crack growth involving stress corrosion, sustained load, creep, fatigue or combinations thereof, K_max (or an equivalent non-linear parameter such as J_max) remains as one essential driving force contributing to the final material separation. Under fatigue conditions, cyclic amplitude ΔK (or an equivalent non-linear parameter like ΔJ) becomes the second necessary driving force needed to induce the characteristic cyclic damage for crack growth. Cyclic damage then reduces the role of K_max required for crack growth at the expense of ΔK.     

Review of the fracture mechanics approach to creep crack growth in structural alloys

The application of the fracture mechanics approach to time-dependent high temperature crack growth has been reviewed. Available data on several structural alloys indicate that depending on the environmental sensitivity and creep ductility of the material, creep crack growth can be characterized by either linear elastic parameter, K, non-linear elastic-plastic parameter, J^*-integral, or reference stress, σ_ref. In particular for materials that are significantly sensitive to environment, K can adequately characterize the growth rate, and for materials that are significantly creep ductile, σ_ref can be used to predict creep life of a cracked body. Finally, for materials that are relatively ductile and wherein crack growth occurs predominantly by a deformation process, J^* integral appears to be the characterizing parameter for the growth rate. Data for several materials indicate that under steady state crack growth conditions, there may be a unique growth rate-J^* relation independent of temperature and material. This would have a profound impact in terms of the utility of fracture mechanics approach to predict creep crack growth rate and needs to be examined further. Conditions under which K, J^* or σ_ref is applicable are discussed in detail.     

Application of fracture mechanics to creep crack growth

International Journal of Fracture -     

Fracture mechanics approach to fatigue crack initiation from deep notches

Fracture mechanics approach is applied to fatigue crack initiation at the tips of deep, blunt notches including those with very small notch-tip radius. The theoretical relations between the stress intensity range ΔK_ρ and the notch-tip radius ρ for a fixed life for crack initiation were derived based on the models of dislocation-dipole accumulation and blocked slip-band. Those are approximated by a simpler equation: $\text{ΔK}{}_{\mathrm{\rho }}\text{ΔK}{}_{\mathrm{o}}\text{= (1 + ρ/ρ0)}\text{1}\text{2}$ where ΔK₀ and ρ0 are material constants which are related to the fatigue strength of smooth specimens Δρ0 as $\text{Δρ0 =}\text{2ΔK}{}_0\text{(πρ0)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$. The results of experiments done with bluntly notched compact tension specimens of a structural low-carbon steel agree with the above relation between $\text{ΔK}{}_{\mathrm{gr}}\text{ΔK}{}_{\mathrm{o}}$ and ρ/ρ_o. The method to predict ΔK_o, ρ_o and Δρ_o from the fatigue data of cracked and smooth specimens is proposed.     

The application of fracture mechanics to creep crack growth

A review is made of creep cracking test results analysed using various parameters such as the stress intensity factor, net section stress, crack opening displacement and deformation energy rate. Theoretical predictions of creep crack growth rate on the basis of creep laws are discussed. Creep crack growth due to vacancy diffusion and condensation is considered. Analytical treatments are reviewed. A new solution is presented.     

A unified approach to damage accumulation and fatigue crack growth

An approach is proposed to the theory of fatigue cracks propagation based on the following postulate: a growing crack at least once in a cycle becomes a nonequilibrium one (in the Griffith's sense) under the condition that the resistance to crack growth is calculated with an account of damage accumulated at the crack tip during the loading history. The theory is used for nonuniaxial stress states including jumplike growth, stops, kinking and branching phenomena. The general structure of differential equations is discussed for the averaged crack growth rate under nonuniaxial loading.     

Derivation of crack closure and crack growth rate data from effective-strain fatigue life data for fracture mechanics fatigue life predictions

This study deals with the behavior of short cracks growing out of notches. Three types of load histories are used: (a) a fully-reversed constant amplitude history; (b) a periodic compressive overload history consisting of repeated load blocks containing one fully-reversed constant amplitude yield–stress magnitude cycle (the overload) followed by a group of smaller constant amplitude cycles having the same maximum stress as the overload cycle; (c) and a service strain history. Procedures are presented for deriving crack closure data and crack growth rate vs effective stress intensity factor range data from data obtained by subjecting a small number of smooth laboratory specimens to simple periodic compressive overload tests to obtain closure-free strain-life data. These procedures are illustrated in an example in which fatigue life predictions are made for a service strain history applied to notched plate specimens. The fatigue life predictions based on the measured and the derived crack closure and crack growth rate data are in good agreement with the experimentally determined fatigue lives.     

A plastic flow-induced fracture theory for fatigue crack growth

A plastic flow-induced fracture theory for fatigue crack growth is presented. A new formulae for the fatigue stress intensity threshold and the fatigue crack growth rate law are derived by applying the principle of energy conservation in considering the fatigue crack growth process in the presence of local plastic flow ahead of the crack-tip. The present theory predicts not only the fatigue crack growth rate being just proportional to the rate of creation of dislocation at the crack-tip, but also the fatigue stress intensity threshold, which can be determined according to the applied fatigue stress amplitude and the characteristic size of microstructural fracture process ahead of the crack-tip, and can account for the fatigue crack growth characteristics at both low and high levels of applied fatigue stress intensity amplitude. All the results are universal and agree with the existing empirical results and experimental observations.     

A low-cycle fatigue approach to fatigue crack propagation

The damage accumulation hypothesis is used to derive a fatigue crack growth rate equation. The fatigue life of a volume element inside the plastic zone is evaluated by using low-cycle fatigue concepts. Crack growth rate is expressed as a function of cyclic material parameters and plastic zone characteristics. For a given material, crack growth increment, is predicted to be a fraction of the plastic zone size which can be expressed in terms of fracture mechanics parameters,K andJ. Hence, the proposed growth rate equation has a predictive capacity and is not limited to linear elastic conditions.     

Analytical prediction of short to long fatigue crack growth rate using small- and large-scale yielding fracture mechanics

Modifications are introduced to account for the differences in crack growth behavior of long and short cracks, that permit the use of the stress intensity factor. These modifications stem from the principles of fracture mechanics for small- and large-scale yielding. Short cracks can grow well below the long crack fatigue threshold range, because the short crack fatigue threshold range is smaller than that for long cracks as it is dependent on the stress level, and the plastic constraint factor. Analytical expressions are developed for these relationships, and for the fatigue crack growth rates in plane stress and plane strain, for short semi-elliptical cracks including those emanating from notches. Microstructural features are not considered. A linear approximation is used for the gradual transition from plane stress to plane strain. The model is formulated using only the readily available material properties. It is then validated using published experimental data for fatigue crack propagation rates for positive and negative stress ratios down to –2. There is reasonable agreement between the model predictions and the published experimental data for short cracks (from 0.1 to 2 mm) and long cracks.     

3D fracture mechanics investigation on surface fatigue crack propagation

Surface fatigue crack propagation is the typical failure mode of engineering structures. In this study, the experiment on surface fatigue crack propagation in 15MnVN steel plate is carried out, and the crack shape and propagation life are obtained. With the concept of ‘equivalent thickness’ brought into the latest three‐dimensional (3D) fracture mechanics theory, one closure model applicable to 3D fatigue crack is put forward. By using the above 3D crack‐closure model, the shape and propagation life of surface fatigue crack in 15MnVN plates are predicted. The simulative results show that the 3D fracture mechanics‐based closure model for 3D fatigue crack is effective.     

Correlation of one-dimensional fatigue crack growth at cold-expanded holes using linear fracture mechanics and superposition

This work assesses the ability of linear elastic fracture mechanics (LEFM) with superposition to correlate the growth of one-dimensional fatigue cracks at cold-expanded open holes under constant amplitude loading. Care is taken in the work to accurately: control the test setup to ensure one-dimensional crack growth, determine residual stress in the coupons, measure crack growth, determine the fatigue crack growth rate (FCGR), compute stress intensity factors, and correlate fatigue crack growth rate with stress intensity factor range ΔK and stress ratio R. The work used long dog-bone coupons having a gage section 38.1 mm wide and a centrally located 7.09 mm diameter hole. The coupons were fabricated from 2.03 mm thick 7075-T6 sheet. The small coupon thickness and alignment of the loading fixture to eliminate bending resulted in one-dimensional crack growth. Residual stress due to cold expansion (CX) was measured using the contour method, as a function of position on the crack plane. Residual stress measurements gave typical results for the average residual stress field, with near-yield compression at the hole giving way to tension further out. Measurements on multiple coupons showed ±10% variability in residual stress. Crack growth behavior of multiple as-machined (AM) coupons (without CX) tested at R of 0.1 or 0.5 agreed with earlier results published in the literature. The scatter in lifetime, defined as the range of lifetime divided by the average lifetime, was less than 30% in the AM coupons. Crack growth behavior of multiple CX coupons tested at the same two applied stress ratios was consistent with predictions by linear superposition, where the predictions used a correlation for fatigue crack growth rate as a function of ΔK and R based on crack closure concepts and a piecewise log–log fit to FCGR versus ΔK_eff data from tests of non-residual stress bearing material and from the literature. Scatter in lifetime of CX coupons was 152% at R = 0.1 and 69% at R = 0.5. While the scatter in CX coupon lifetime is considerably greater than for AM coupons, it is found consistent with the observed 10% variability in residual stress. The work therefore demonstrates the ability of LEFM with superposition to accurately correlate the behavior of coupons with and without residual stresses.     

The fracture mechanics of slow crack growth in polyethylene

The following theoretical equation was obtained for the rate of initiation fx- of slow crack growth in polyethylene:% MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbnL2yY9% 2CVzgDGmvyUnhitvMCPzgarmqr1ngBPrgitLxBI9gBaerbd9wDYLwz% YbItLDharuavP1wzZbItLDhis9wBH5garqqr1ngBPrgifHhDYfgasa% acOqpw0le9v8qqaqFD0xXdHaVhbbf9v8qqaqFr0xc9pk0xbba9q8Wq% Ffea0-yr0RYxir-Jbba9q8aq0-yq-He9q8qqQ8frFve9Fve9Ff0dme% aabaqaciGacaGaaeqabaWaaqaafaaakeaadaWfGaqaaiabes7aKbWc% beqaaiaac6caaaGccqGH9aqpdaWcaaqaaiabeo8aZnaaBaaaleaaca% WG5baabeaacaWGlbWaaWbaaWqabeaacaaI0aaaaSGaaiikaiaaigda% cqGHsislcqaHZoWzdaahaaadbeqaaiaaikdaaaWccaGGPaWaaWbaaW% qabeaacaaIYaaaaaGcbaGaeq4TdGMaamizaiaadweadaahaaWcbeqa% aiaaikdaaaGccqaHdpWCdaqhaaWcbaGaam4yaaqaaiaaikdaaaaaaa% aa!5AB3!\[\mathop \delta \limits^. = \frac{{\sigma _y K^4 (1 - \gamma ^2 )^2 }}{{\eta dE^2 \sigma _c^2 }}\] where = applied stress, K = stress intensity, = Poisson's ratio, E = Young's modulus, _c = stress to produce a craze, _y = yield point, d = primordial thickness of the craze and = the intrinsic viscosity of the fibrils of the craze. The dependence of % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbnL2yY9% 2CVzgDGmvyUnhitvMCPzgarmqr1ngBPrgitLxBI9gBaerbd9wDYLwz% YbItLDharuavP1wzZbItLDhis9wBH5garqqr1ngBPrgifHhDYfgasa% acOqpw0le9v8qqaqFD0xXdHaVhbbf9v8qqaqFr0xc9pk0xbba9q8Wq% Ffea0-yr0RYxir-Jbba9q8aq0-yq-He9q8qqQ8frFve9Fve9Ff0dme% aabaqaciGacaGaaeqabaWaaqaafaaakeaadaWfGaqaaiabes7aKbWc% beqaaiaac6caaaaaaa!4668!\[\mathop \delta \limits^. \] on K agrees with the experimental data. The experimental values of % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbnL2yY9% 2CVzgDGmvyUnhitvMCPzgarmqr1ngBPrgitLxBI9gBaerbd9wDYLwz% YbItLDharuavP1wzZbItLDhis9wBH5garqqr1ngBPrgifHhDYfgasa% acOqpw0le9v8qqaqFD0xXdHaVhbbf9v8qqaqFr0xc9pk0xbba9q8Wq% Ffea0-yr0RYxir-Jbba9q8aq0-yq-He9q8qqQ8frFve9Fve9Ff0dme% aabaqaciGacaGaaeqabaWaaqaafaaakeaadaWfGaqaaiabes7aKbWc% beqaaiaac6caaaaaaa!4668!\[\mathop \delta \limits^. \] vary by a factor of 10⁷ depending on the type of polyethylene. This large variation in % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbnL2yY9% 2CVzgDGmvyUnhitvMCPzgarmqr1ngBPrgitLxBI9gBaerbd9wDYLwz% YbItLDharuavP1wzZbItLDhis9wBH5garqqr1ngBPrgifHhDYfgasa% acOqpw0le9v8qqaqFD0xXdHaVhbbf9v8qqaqFr0xc9pk0xbba9q8Wq% Ffea0-yr0RYxir-Jbba9q8aq0-yq-He9q8qqQ8frFve9Fve9Ff0dme% aabaqaciGacaGaaeqabaWaaqaafaaakeaadaWfGaqaaiabes7aKbWc% beqaaiaac6caaaaaaa!4668!\[\mathop \delta \limits^. \]% MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbnL2yY9% 2CVzgDGmvyUnhitvMCPzgarmqr1ngBPrgitLxBI9gBaerbd9wDYLwz% YbItLDharuavP1wzZbItLDhis9wBH5garqqr1ngBPrgifHhDYfgasa% acOqpw0le9v8qqaqFD0xXdHaVhbbf9v8qqaqFr0xc9pk0xbba9q8Wq% Ffea0-yr0RYxir-Jbba9q8aq0-yq-He9q8qqQ8frFve9Fve9Ff0dme% aabaqaciGacaGaaeqabaWaaqaafaaakeaadaWfGaqaaiabes7aKbWc% beqaaiaac6caaaaaaa!4668!\[\mathop \delta \limits^. \] is directly related to intrinsic viscosity which evolved from the theory.     

Prediction of frequency effect in high temperature fatigue crack growth using damage factors

An earlier modification of the Paris law for the growth of deep cracks in the linear elastic fracture mechanics regime is extended to include a term enabling the prediction of cyclic crack growth rates at low frequencies. The relation requires (i) a reference growth law under continuous cycling at the appropriate elevated temperature and (ii) a specified, dimensionless degradation term, defined as D_c, the creep/oxidation damage per cycle, which increases as the applied frequency decreases or as the dwell time at peak load is prolonged. The relationship is validated against data from the previous analysis on low alloy ferritic and austenitic steels in the range 538–650°C and against further published results on Ni-based alloys at temperatures up to 700°C. It appears that for the former series oxidation is the dominant damaging mode, whereas a linear creep damaging mechanism is manifest in the Ni-based alloys. Moreover, levels of cyclic damage in terms of D_c are higher in the latter, ranging between 10^?3 and 5 × 10^?1 compared with 10^?4 to 5 × 10^?2 for the steels. A brief comparison is made with damage factors arising from the high strain fatigue deformation mode at elevated temperatures and other models for the prediction of frequency effects are discussed.