A theory of diffusion controlled intergranular creep crack growth

A theory of intergranular creep crack growth in brittle materials has been developed. The mechanism of crack propagation is removal of atoms from the crack tip by stress induced grain boundary diffusion and their deposition at the grain boundary. The width of the crack is assumed to be constant during crack propagation. Any possible plastic deformation at the crack tip has been neglected. The stress relaxation ahead of the crack tip which arises due to the non-uniform deposition of material onto the grain boundary is calculated and the diffusion process governed by this relaxed stress studied. Thus the theory is analogous to those developed previously for the growth of r-type voids in grain boundaries. Both the steady state and the transient were considered. It was found that the rate of crack growth at any moment was determined by the nominal stress intensity factor K. A minimum stress intensity, K_min' exists below which no crack growth can take place. Conversely there is a maximum limiting rate of crack growth determined by the maximum surface diffusion rate. For K > K_min the steady state is always reached quickly and the length of the transient period t_tr is proportional to K⁻⁶. For K > K_min the rate of crack growth is proportional to K⁴. A comparison with experimental measurements on brittle ½Cr-½Mo-¼V steels show good agreement between the theory and experiment.     

Cavitation damage and creep crack growth

The effect has been investigated of prior damage on the creep crack propagation characteristics of 0.5 pct Cr, 0.5 pct Mo, 0.25 pct V steel at 823 K. On a macroscopic basis, the parametersK ₁ andC ^* both appear to correlate withda/dt although the parameterC ^* is unable to distinguish between virgin and damaged specimens. Rupture lives in the predamaged specimens are reduced by up to 60 pct when compared to virgin samples. Microscopically, it is found that the nature of the cavitation damage suggests that surface and grain boundary diffusion processes may have a minimal part to play, crack growth being controlled by the growth of cavities which is in turn controlled by the deformation of the surrounding matrix. A number of microscopic models are compared with the experimental data and it is suggested that a model which gives the best correlation with results is one proposed on the basis of matrix deformation. Formerly of the Department of Metallurgy, Manchester University Formerly of the Department of Metallurgy, Manchester University     

A theoretical model for creep crack growth

A theory of creep crack growth has been developed with the presumption that the crack growth occurs by the diffusion of vacancies along the grain boundaries. This is consistent with many experimental results that show that creep fracture is generally of intergranular type and the activation energies for crack growth rates fall within the range of grain boundary diffusion energies. The theory is based on the concept that creep crack growth results from a balance of two competing processes-the diffusion of point defects that contributes to the growth and the creep deformation process that retards the growth and causes even its arrest. The present analysis shows that crack growth via grain boundary diffusion occurs within some temperature range. The upper limiting temperature is determined by the bulk diffusion process which disperses the vacancies, that are diffusing to the crack tip, to the plastic zone ahead of the crack front. The lower temperature limit is set by the fact that the grain boundary diffusion rates decrease with the decrease in temperature and thus large stress intensities approaching the fracture toughness value are required to accomplish crack growth by the grain boundary diffusion. Outside these limits creep crack growth occurs via deformation which is significantly slower than growth by the grain boundary diffusion process. The importance of the present analysis rests on the fact that service conditions for many high temperature structural materials fall within the regime wherein creep crack growth occurs via grain boundary diffusion.     

Quasi-steady-state creep crack growth in a 3.5NiCrMoV steel

Creep crack growth rate ( ) is usually characterized in terms of macroscopic load parameters, such as C*, C _t and C(t), through the constant load test. However, load parameters are continuously changing during the test, and so is . Here, by conducting constant C _t and constant tests, quasi-steady-state crack growth was obtained where remained almost constant. Results indicate the ∼[C _t ]^0.76 correlation, which differ from the ∼[C _t ]^0.96 correlation of the constant load test. Discrepancies can be ascribed to the inclusion of the stage II data, which showed no correlation between and C _p in the constant load analysis. Finally, the crack growth rate was well predicted using the Monkmam-Grant analysis in creep crack growth.     

Study of creep crack growth in 2618 and 8009 aluminum alloys

Creep crack growth (CCG) has been investigated in an 8009 (Al-Fe-V-S) P/M alloy at 175 °, 250 °, and 316 ° and in a 2618 ingot alloy at 150 °, 175 °, and 200 °. Under sustained load, subcritical crack growth is observed at stress intensity levels lower thanK _ic ; for 2618, at 200 °, crack growth is observed at stress intensities more than 40 pct lower thanK _ic . Alloys 8009 and 2618 exhibit creep brittle behavior,i.e., very limited creep deformation, during CCG. The CCG rates do not correlate with CCG parameters C* and C but correlate with the stress intensity factor,K, and theJ integral. Generally, crack growth rates increase with increasing temperature. Micromechanisms of CCG have been studied with regard to microstructural deg-radation, environmental attack, and creep damage. Although theoretical estimation indicates that CCG resistance decreases with second-phase coarsening, such coarsening has not been observed at the crack tip. Also, no evidence is found for hydrogen- or oxygen-induced crack growth in comparing test results in moist air and in vacuum. Creep deformation and cavitation ahead of crack tip are responsible for observed time-dependent crack growth. Based on the cavitation damage in the elastic field, a micromechanical model is proposed which semiquantitatively explains the correlations between the creep crack growth rate and stress intensity factor,K.     

Fatigue and creep crack growth in oxide dispersion strengthened INCONEL MA-754

The influence of temperature, orientation, and environment on fatigue and creep crack growth behavior in oxide dispersion strengthened INCONEL MA-754 was examined. With an increase in temperature, crack growth rates increase due largely to an increasing creep contribution. Environment also may influence crack growth behavior, its effect depending on orientation. Orientation has a marked effect on crack growth because of the propensity for creep void formation along particle stringers in the microstructure, which form in the processing. The rate of crack growth can be enhanced if the aligned voids are parallel to the main crack or retarded if these voids are normal to the direction of the crack. In the transverse-longitudinal (T-L) orimation crack growth is faster on a time basis in creep than in fatigue; the reverse of this is true in the longitudinal-transverse (L-T) orientation. Predicted fatigue crack growth rates based on a cumulative damage model agree with experimentally determined growth rates.     

An intergranular creep crack growth model based on grain boundary sliding

An intergranular crack growth model is developed to describe the effect of microstructural features such as grain size, grain boundary precipitates, and serrated grain boundaries on creep crack growth under grain boundary sliding (GBS) conditions. The model considers quantitatively that several deformation mechanisms contribute to the stress redistribution ahead of the crack tip through a stress relaxation process. The crack tip region is divided into three zones: (a) the intragranular-deformation-controlled stress relaxation zone, (b) the GBS-controlled stress relaxation zone, and (c) the elastic region. Intergranular creep crack growth is considered to occur as a result of the GBS-controlled process in all cases. The derived creep crack growth model shows a complex dependence of the creep crack growth rate (CCGR) on fracture mechanics quantities, such as C(t) (the path-independent energy integral with its steady-state value as C*) and K (the stress intensity factor). For creep-brittle materials, the model predicts that the CCGR depends on K to the power of 2 and this is verified experimentally; however, when environmental effects contribute to the crack growth process, the power exponent will increase. A semiempirical factor is introduced to account for the effects of oxidation on CCGR.     

Creep deformation and crack growth behavior of a single-crystal nickel-base superalloy

Uniaxial creep deformation and crack growth data are presented on the single-crystal nickel-base superalloy SC16, which is a candidate material for industrial gas turbine applications. All testing was performed at 900 °C. The uniaxial experiments were conducted with the loading direction aligned approximately along the [001] crystallographic axis of the material. Under these conditions, a small primary region followed by mainly tertiary creep was obtained, and failure initiated from cracks at interdendritic pores. The crack growth experiments were performed on single-edge notch tension specimens and compact tension test pieces containing deep side grooves to examine state-of-stress effects. A selection of crystallographic orientations was also examined. Little effect of stress state and orientation was obtained. It has been found that the creep crack growth characteristics of the alloy can be predicted satisfactorily from a model of the accumulation of damage at a crack tip using the creep fracture mechanics parameter C* and assuming plane stress conditions. This article is based on a presentation made at the “High Temperature Fracture Mechanisms in Advanced Materials” symposium, as a part of the 1994 Fall meeting of TMS, October 2-6, 1994, in Rosemont, Illinois, under the auspices of the ASM/SMD Flow and Fracture Committee.     

Diffusion controlled precipitate growth in ternary systems: II

The author’s initial treatment of diffusion controlled precipitate growth in isothermal ternary systems is generalized to account for ternary diffusional interaction. The analysis is applicable to the growth of planar surfaces, circular cylinders, and spheres in an effectively infinite matrix. It is assumed that one independent component diffuses at least an order of magnitude faster than the other. The resultant growth rate expressions have a surprisingly simple form from which kinetic and thermodynamic implications are easily extracted. Because of its relevance to austenite decomposition reactions in alloy steels, the limit in which one independent component diffuses many orders of magnitude faster than the other is examined in detail. It is demonstrated that in this limit, the present essentially kinetic analysis is completely consistent with thermodynamic concepts proposed by Hillert.     

Influence of cyclic to mean load ratio on creep/fatigue crack growth

Crack growth data under combined creep and fatigue loading conditions are presented on a nickel base superalloy and a brittle and ductile low alloy steel. The main variables that have been examined are minimum to maximum load ratioR and frequency. It is shown that at high frequencies transgranular fatigue failure dominates and at low frequencies time dependent mechanisms govern. Where fatigue processes control, it is demonstrated that crack growth/cycle can be described by the Paris law and that the influence ofR ratio can be accounted for by crack closure caused by fracture surface roughness, oxidation, and creep and plastic strain developed at the crack tip. At the low frequencies where time dependent processes dominate, it is shown that crack growth can be characterized satisfactorily in terms of the creep fracture mechanics parameterC * using a model of crack extension based on ductility exhaustion in a creep damage zone at the crack tip. This model leads to enhanced resistance to creep/fatigue crack growth with increase in material creep ductility. This paper is based on a presentation made in the symposium “Crack Propagation under Creep and Creep-Fatigue” presented at the TMS/AIME fall meeting in Orlando, FL, in October 1986, under the auspices of the ASM Flow and Fracture Committee.     

Experimental and numerical study on the relationship between creep crack growth properties and fracture mechanisms

Evaluation of creep crack growth properties taking microscopic aspects into account is effective for developing more accurate life prediction of structural components. The present study investigated the relationship between creep crack growth properties and microscopic fracture aspects for austenitic alloy 800H and 316 stainless steel. The growth rate of wedge-type intergranular and transgranular creep crack could be characterized by creep ductility. Creep damages formed ahead of the void-type crack tip accelerated the crack growth rate. Based on these experimental results, a three-dimensional finite element method (FEM) code, which simulates creep crack growth, has been developed. The effect of creep ductility on da/dt vs C* relations could be simulated based on the critical strain criteria. The diffusion of vacancies toward crack tip would accelerate the crack growth under creep conditions. The change of vacancy concentration during creep was computed for a three-dimensional compact-type (CT) specimen model by solving the diffusive equation under multiaxial stress field. The experimental results that crack growth was accelerated by creep damages formed ahead of the crack tip could be successfully simulated.     

Fatigue crack tip deformation

The shape of a fatigue crack tip as influenced by an air or a vacuum environment has been investigated in two stainless steels and an aluminum alloy. Under plane strain conditions and at crack growth rates in the Paris region, the crack tip opening displacement (CTOD) is much larger in vacuum than in air, a circumstance attributed to strain localization in air due to the presence of moisture and the absence of strain localization in vacuum. In type 304 stainless steel, a strain-induced transformation from austenite to martensite occurs at the crack tip, and the extent of this strain-induced transformation in type 304 stainless steel is consistent with the degree of blunting taking place at the crack tip as influenced by the environment. In air, the extent of transformation is a function of the ΔK level, and as a result, the crack opening level is found to differ in a ΔK decreasing test as compared to aAK increasing test. Fatigue striations are observed in air but are absent in vacuum. It is proposed that the greater extent of blunting in vacuum is responsible for the absence of striations in vacuum.     

Constrained cavity growth models of longitudinal creep deformation of oxide dispersion strengthened alloys

Two models of constrained cavity growth are developed to describe the long-term longitudinal creep behavior of nickel based oxide dispersion strengthened (ODS) alloys. For both models the rupture time is taken as the time for a transverse grain boundary to cavitate fully. A diffusive cavity growth law is assumed to govern cavitation. The applicability of the respective models is determined by the particular grain morphology achieved by thermal-mechanical processing. The first model assumes that longitudinal grain boundaries are unable to slide; hence displacements due to cavitation must be matched by displacements due to dislocation creep in adjoining grains. This model predicts a low stress exponent at the transition from single crystal to cavitation creep behavior, and higher stress exponents at stresses below this transition. Good agreement is found between the model predictions and creep data for MA 754 at 1000 and 1093 °C. A second model considers a grain morphology wherein longitudinal grain boundaries are able to slide by means of deformation of pockets of fine grains. Cavitation of transverse grain boundaries is thus controlled by grain boundary sliding. This model predicts a stress exponent of 1 at low stresses, and serves as an upper bound for the creep rate when a duplex grain morphology is present. Model predictions are in good agreement with creep data for a heat of MA 754 with a duplex grain morphology. Formerly Graduate Research Assistant in the Department of Materials Science and Engineering at Stanford University     

Effect of environment on crack growth behavior in austenitic stainless steels under creep and fatigue conditions

Crack growth behavior at high temperatures under cyclic, static, and combined loads was studied in annealed and 20 pct cold-worked Type 316 and 20 pct cold-worked Type 304 austenitic stainless steels in air and vacuum. Under cyclic load, crack growth rates in annealed Type 316 steel are slightly lower in vacuum than in air, but this difference decreases with increase in crack growth rate. Most importantly, the effect of temperature on crack growth is present even in vacuum and arises mostly from the variation of elastic modulus with temperature. In the cold-worked Type 316 steel, the pronounced hold-time effects on fatigue crack growth in air reported in the literature persists even in vacuum. This implies that at high crack growth rates these hold-time effects arise mostly from creep-fatigue interaction rather than environment fatigue interaction. Environment has a negligible effect also on crack growth under static load. Thus, time dependent crack growth in these steels is due to creep processes. Crack growth behavior in annealed and cold-worked materials are compared and reasons for the enhanced time dependent crack growth in cold-worked material are discussed in detail.     

Diffusion controlled growth of lamellar eutectics and eutectoids in binary and ternary systems

The mathematical treatment of the steady state growth of lamellar eutectics and eutectoids in binary systems, as controlled by volume diffusion in the matrix or boundary diffusion, is extended to include compositional variations in the two growing phases. It is concluded that the effect of such variations on the growth rate is normally rather small.The effect of a ternary addition is treated for a number of combinations of volume diffusion and boundary diffusion of the alloying elements. Explicit expressions for the growth rate are obtained in all the cases thanks to the assumption that only the content of the ternary addition varies within the two growing phases.