Theory of high temperature intercrystalline fracture under static or fatigue loads,with or without irradiation damage

Hull and Rimmer’s theory of high temperature creep fracture by grain boundary void growth and Skelton’s theory of high temperature fatigue fracture have been extended. The present theory includes the effect on void growth of volume diffusion and of vacancy generation by irradiation damage or plastic deformation within the grain interiors. The growth rate of cylindrical as well as spherical voids is calculated. We find that the presence of volume diffusion or of vacancy generation within the grain does not increase very much the growth rate of spherical voids but under certain conditions the growth rate of cylindrical voids is increased markedly. Unlike Skelton, we find that vacancy production within the grains does not decrease the critical radius for the growth of a grain boundary void in push-pull fatigue. (Likewise intra-granular vacancy production does not decrease the critical radius of grain boundary voids in creep.) Since in push-pull fatigue void growth is observed in the case of radii smaller than the critical value it is concluded that the stress concentrations that are produced by grain boundary sliding (according to the theory of Raj, Ashby, and Gifkins) are responsible for this growth. Whether voids aided by stress concentrations can continue to grow beyond a certain size depends critically upon the “roughness” of the grain boundary. It is strongly recommended that grain boundary internal friction peak studies be carried out in connection with void growth and high temperature fracture experiments. In particular, grain boundary voids are more likely to grow in push-pull fatigue (or in creep) if the value of the grain boundary sliding activation energy is close to that of volume self diffusion rather than if the sliding activation energy is close to the grain boundary self diffusion activation energy.     

Diffusion and deformation controlled creep crack growth

A mechanism for creep crack growth is proposed by which the crack grows by formation of grain boundary cavities ahead of the crack tip. Two cases are considered; firstly, when cavity growth is diffusion controlled and secondly, where growth is deformation controlled. The resultant crack growth rates predicted by these theoretical models are compared with experimental data.     

Mechanisms of creep crack growth in 1 wt% antimony-copper: Implications for fracture parameters

A copper alloy with 1% (by weight) antimony was used as a model material and tested at 400°C to study the mechanisms of creep crack growth. At this temperature, the creep deformation in this material was dominated by secondary and tertiary creep. The expression for estimating C_t (a crack tip parameter for creep conditions) in a compact type specimen used for testing was modified to include tertiary creep deformation. Extensive damage characterization was conducted on tested creep crack growth specimens using optical metallography and scanning electron microscopy. The following observations were derived from the test results. The creep crack growth rates correlated with C_t only when intense cavitation damage was restricted to a region approximately 1.3 mm in size near the crack tip and no crack branching occurred. It was observed that the average diameter, areal density, and percent of grain boundary area cavitated decreased as function of distance from the crack tip. From these results it is argued that simultaneous nucleation and growth of cavities occur on grain boundary facets during the creep crack growth process. Percent grain boundary area cavitated is proposed as the most reasonable measure of creep damage. The critical amount of damage for crack extension appears to depend on the magnitude of the C_t parameter.     

Creep crack growth behavior of several structural alloys

Creep crack growth behavior of several high temperature alloys, Inconel 600, Inconel 625, Inconel X-750, Hastelloy X, Nimonic PE-16, Incoloy 800, and Haynes 25 (HS-25) was examined at 540, 650, 760, and 870 °C. Crack growth rates were analyzed in terms of both linear elastic stress intensity factor and J*-integral parameter. Among the alloys Inconel 600 and Hastelloy X did not show any observable crack growth. Instead, they deformed at a rapid rate resulting in severe blunting of the crack tip. The other alloys, Inconel 625, Inconel X-750, Incoloy 800, HS-25, and PE-16 showed crack growth at one or two temperatures and deformed continuously at other temperatures. Crack growth rates of the above alloys in terms ofJ* parameter were compared with the growth rates of other alloys published in the literature. Alloys such as Inconel X-750, Alloy 718, and IN-100 show very high growth rates as a result of their sensitivity to an air environment. Based on detailed fracture surface analysis, it is proposed that creep crack growth occurs by the nucleation and growth of wedge-type cracks at triple point junctions due to grain boundary sliding or by the formation and growth of cavities at the boundaries. Crack growth in the above alloys occurs only in some critical range of strain rates or temperatures. Since the service conditions for these alloys usually fall within this critical range, knowledge and understanding of creep crack growth behavior of the structural alloys are important.     

The effect of time dependent void density on grain boundary creep fracture—i. continuous void coalescence

When voids in a creeping solid are non-uniformly distributed over a grain boundary facet void coalescence occurs simultaneously with void growth. The effect of such coalescence on subsequent grain boundary void growth can be analysed assuming a random (i.e. Poisson) initial void distribution. A simple relationship between the fraction of voids remaining on a grain boundary facet and their area fraction is found. This relationship is independent of the mechanism by which the voids grow. When voids grow by surface diffusion or by power-law creep very little effect of coalescence on the overall rate of damage accumulation is found. However, when void growth is controlled by grain boundary diffusion, the rate of void growth is decreased dramatically during coalescence, and effectively stops. Final fracture occurs by creep controlled void growth. The model predicts a non-linear stress dependence for this process, and an activation energy different from that for boundary diffusion alone. The model is compared with creep fracture data for pure metals implanted with water vapour bubbles. Good agreement with the model is found in two cases, while in a third case void growth appears to have been controlled by surface diffusion.     

Creep cavity growth from tritium-induced helium bubbles in nickel

The growth of grain boundary cavities in nickel under creep conditions was investigated. Growth could be studied unambiguously and without the complications of radiation damage due to a unique sample preparation technique making use of the tritium-to-helium’ decay reaction. Resultant helium bubbles served effectively as creep cavity nuclei, the growth of which led to premature intergranular fracture. Constant stress tension creep tests under argon were performed on helium embrittled samples, revealing information on the stress and temperature dependence of the creep-fracture process. The cavity spacing developed during primary creep by bubble migration and coalescence persisted to fracture. Bulk plastic deformation was strongly suppressed by a matrix bubble population which stabilized a finer subgrain network than is characteristic of virgin nickel. This enhanced creep resistance permitted observation of a stress region in which void growth was controlled by classical Hull-Rimmer grain boundary vacancy diffusion. At higher stresses a transition to plasticity control appeared to take place. These results are interpreted in terms of a coupled grain boundary diffusive/ matrix plasticity model. 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.     

Creep crack growth in alloy 718

Subcritical crack growth behavior in Alloy 718 was studied under creep conditions at 538, 649, and 760°C (1000, 1200, 1400°F) and crack growth rates were correlated using both linear and nonlinear elastic fracture mechanics. The results show that for a given stress intensity value crack growth rate increases significantly with increase in temperature from 538 to 649°C but either decreases or increases slightly with further increase in temperature to 760°C. On the basis of these results it is concluded that creep crack growth results from a balance of two competing processes, diffusion of point defects which contributes to crack growth, and creep deformation process that causes retardation of crack growth and even its arrest. Significance of these concepts in relation to enhancing the resistance of a given material to creep crack growth is discussed in detail.     

Quasi-static intergranular brittle fracture at 0.5 tm: A non-equilibrium segregation mechanism of sulphur embrittlement in stress-relief cracking of low-alloy steels

A theory of elastic-plastic-diffusive crack growth along grain boundaries is developed and compared with experimental observations of stress-relief cracking of low-alloy steels. Intergranular decohesion advances atomistically by coupled surface and grain-boundary diffusion, while the macroscopic plain-strain crack grows quasi-statistically by maintaining a deformation field in small-scale yielding. Near an advancing crack tip, a surface diffusion distance is found within which steady-state diffusion is driven by a sharp curvature, while a corresponding boundary diffusion distance is found within which diffusion plating overtakes elastic-plastic stretching to smooth out the stress concentration. Diffusional and elastic-plastic processes at an extending crack tip are thus coupled to each other and to the loading parameter at distance. Fast diffusants are predicted to accumulate near the crack tip on both surfaces and grain boundary, confirming a recent scanning Auger observation of sulphur segregation by Hippsley et al. Considerations of non-equilibrium interfacial energies and fracture work reveal the embrittling role of sulphur, both as a fast diffusant and as a strong surface segregant. Predictions of growth rates are in excellent agreement with the data of Shin and McMahon, over the entire range of stress intensity factor and temperature studied. Metallurgical factors promoting brittle stress-relief cracking in the heat-affected zones of welding of low-alloy steels, including sulfide distribution, hot yield strength, and notch sensitivity, are explained.     

Scanning electron microscope fractography of continuously cast high purity copper after high temperature creep

Fracture surfaces produced by high temperature creep were studied using the scanning electron microscope. The material investigated was continuously cast high purity copper containing a nodal impurity segregation structure at which grain boundary voids are formed during creep. The observed void shape suggests that vacancies are supplied mainly via grain boundaries, and also by enhanced diffusion via segregation nodes; the vacancies seem to originate mainly at internal sources. The known distribution of potential nucleation sites was used to study the efficiency of the segregation structure in nucleating voids under various test conditions. Within the range of conditions employed, three different fracture modes were observed in separate regions of the stress-temperature plane. The regions are sequentially denotedA, B, and C as the temperature is increased at a given stress; they shift to lower temperatures as the stress is increased. In regionA fracture is initiated by extensive cavitation along grain edges (line of junction of three grains); cavitation at the segregation structure seems to be of secondary importance. In regionB formation and growth to coalescence of voids at segregation nodes governs fracture; the change of growth mechanisms with test conditions is discussed. In region C fracture is controlled by plastic instability. A. RUKWIED,Physicist , formerly with Mechanical Properties Section, Metallurgy Division, Institute for Materials Research, National Bureau of Standards, U. S. Department of Commerce, Washington, D. C.     

Creep crack growth in the absence of grain boundary precipitates in UDIMET 520

The effects of grain size and environment on creep crack growth (CCG) in Ni-base superalloy, UDIMET 520, were studied through experiments at 540 °C. Specially designed solution and aging treatments were used to produce γ′ strengthened microstructures with different grain sizes but without any M₂₃C₆ grain boundary precipitates. Five grain sizes, which fall into three groups (i.e., small, medium, and large), were employed. The creep crack growth rates (CCGRs) in specimens with small grain sizes were approximately 2.5 times lower than those with medium and large grain sizes, as a result of crack branching and the presence of some undissolved primary MC carbides at the grain boundaries. Otherwise, the CCGRs were insensitive to the grain size. Fractographic observations on the fracture surfaces and metallographic examinations on the cross sections of the interrupted CCG specimen revealed intergranular microcracks and a faceted intergranular mode of fracture in both air and argon environments. The test results suggest that the formation and propagation of intergranular cracks by grain boundary sliding (GBS) is the main micromechanism responsible for CCG in both air and argon environments at the relatively low test temperature employed. Grain boundary oxidation attack in the air environment simply accelerates the crack growth process. The present results are in agreement with the theoretical predictions of the GBS-controlled CCG model previously developed by the authors. S. XU, formerly Graduate Student, Department of Engineering Physics and Materials Engineering, Ecole Polytechnique de Montreal A. K. KOUL, formerly Senior Research Officer, NRC, Ottawa     

Crack growth in a nearly fully-lamellar gamma TiAl alloy at 650 °C and 800 °C under constant load conditions

The crack growth behavior of a gamma titanium aluminide alloy, K5S, was investigated at 650 °C and 800 °C under constant load conditions in a nearly fully-lamellar microstructural form. Crack growth at both temperatures ensues at stress intensities (K) much higher than anticipated from the R curves. At 650 °C, creep crack extension occurs through the formation of microcracks (interlamellar (IL) separation) and their joining to the main crack tip through ligament fracture. This results in a mainly transgranular (TG) fracture with occasional IL separation. This process features a rapid initial crack growth but at decreasing growth rate, followed by a nearly no-growth stage. At 800 °C, crack extension is accompanied by extensive plastic deformation and consists of an initial rapid transition period and a subsequent steady state. For similar K’s, crack extension and growth rate are greater at 800 °C than at 650 °C, but even these are very slow processes for this alloy. The resistance to crack propagation at 650 °C is explained in terms of work hardening that arises during the extended primary creep deformation occurring ahead of the crack tip. Increased crack propagation at 800 °C is accredited to grain boundary and lamellar-interface weakening and extensive post primary creep damage in the plastic zone. The resulting fracture at 800 °C is mainly boundary fracture, which consists of IG fracture involving formation and coalescence of voids, and IL separation.     

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.     

Role of grain boundary segregation in diffusional creep

The high temperature deformation of polycrystalline materials by the stress directed flow of vacancies is now a well established creep mechanism which operates in two temperature regimes: high temperature, or Nabarro-Herring creep, in which lattice diffusion is rate determining, and low temperature, or Coble creep, in which grain boundary diffusion predominates. Basic studies have been conducted mostly with pure metals for which there exists in general a good correspondence between predicted and observed behavior. Multicomponent engineering alloys will normally experience, as part of their processing history or service lives, the segregation enrichment of interfaces such as grain boundaries by species present in solid solution. The aim of this paper is to evaluate the experimental information and to explore the manner in which this segregation affects the principal forms of diffusional creep. Cases of retarded Herring-Nabarro creep are analyzed in terms of the efficacy of grain boundaries as sources and sinks for vacancies: strongly bound segregant atoms at grain boundaries affect the mobility of defects and hence control the operation of vacancy sources. Recently, observations have been made on the effect of strongly segregating solutes on grain boundary diffusivity. Such behavior influences Coble creep rates, producing in general a retardation. Here we assess the magnitude of the effect induced by various surface active species on grain boundary diffusivity and consequently on Coble creep; predictions show that in general, small amounts of highly surface active impurities induce a remarkable inhibition of this form of creep.     

Creep crack growth in the absence of grain boundary precipitates in UDIMET 520

The effects of grain size and environment on creep crack growth (CCG) in Ni-base superalloy, UDIMET 520, were studied through experiments at 540 °C. Specially designed solution and aging treatments were used to produce γ′ strengthened microstructures with different grain sizes but without any M₂₃C₆ grain boundary precipitates. Five grain sizes, which fall into three groups (i.e., small, medium, and large), were employed. The creep crack growth rates (CCGRs) in specimens with small grain sizes were approximately 2.5 times lower than those with medium and large grain sizes, as a result of crack branching and the presence of some undissolved primary MC carbides at the grain boundaries. Otherwise, the CCGRs were insensitive to the grain size. Fractographic observations on the fracture surfaces and metallographic examinations on the cross sections of the interrupted CCG specimen revealed intergranular microcracks and a faceted intergranular mode of fracture in both air and argon environments. The test results suggest that the formation and propagation of intergranular cracks by grain boundary sliding (GBS) is the main micromechanism responsible for CCG in both air and argon environments at the relatively low test temperature employed. Grain boundary oxidation attack in the air environment simply accelerates the crack growth process. The present results are in agreement with the theoretical predictions of the GBS-controlled CCG model previously developed by the authors.     

Deformation and failure caused by grain boundary sliding and brittle cracking

A failure mechanism which entails grain boundary sliding and brittle crack extension along grain boundaries is analyzed. It is demonstrated that the crack growth, which occurs above a threshold stress, is dictated by the grain boundary viscosity, fracture energy, the grain facet length, and the boundary orientations vis-à-vis the applied stress. The time taken to form a stable facet-sized crack is derived, and shown to be non-linear in the applied stress. The creep strains that result from this mode of cracking are generally small and non-linear.     

板条马氏体钢变形与断裂过程的原位观察

 在备有拉伸装置的扫描电镜上,原位观察了低碳板条马氏体钢的变形和断裂过程。结果表明,板条马氏体的变形是以滑移方式进行的,位错沿滑移面的滑移受阻,在试样表面留下呈波纹状的变形带。在应力峰值前后,主裂纹开始起裂;在主裂纹扩展过程中,在主裂纹前面的薄弱区域如夹杂等会先起裂形成小裂纹或空洞,随应力加大相邻的微孔聚合、连接长大成新裂纹;在断裂过程中,裂纹在板条束界发生转折。尽管原奥氏体晶粒尺寸小的试样起裂载荷大,不同晶粒尺寸马氏体组织的变形和断裂过程没有本质差别。     

A model for creep based on the climb of dislocations at grain boundaries

A model for creep based on the climb of dislocations at grain boundaries is presented. It is shown that when a sliding interface or slip band intersects a grain boundary, a traction distribution is established on the boundary. The diffusional flow induced by these tractions results in a steady state creep process. This slip band model predicts an activation energy corresponding to grain boundary self diffusion, with a stress exponent and a grain size dependence which increase and decrease, respectively, as the applied stress increases. The theoretically determined creep rates are in good agreement with the data for metals and alloys which deform by grain boundary sliding and exhibit superplastic flow properties. Other models for creep controlled by grain boundary diffusion are briefly reviewed and compared with the present model. It is concluded that superplastic deformation involves both purely diffusional flow and dislocation motion.     

Grain boundary sliding and stress concentration during creep

Importance of grain boundary sliding to creep intergranular fracture is focussed. Previous metallographic and fractographic studies of creep intergranular fracture on metal bicrystals and polycrystals are briefly reviewed in order to show the close relationship between grain boundary sliding and fracture. Deformation ledge and migration irregularity are shown to be potential sites of stress concentration and crack nucleation on sliding grain boundaries without particles. The effect of grain boundary structure on creep intergranular fracture is discussed on the basis of the effect of grain boundary structure on sliding, the contribution of sliding to the overall creep deformation, and a sliding-fracture diagram. Recent observations of the effect of grain boundary structure on creep intergranular fracture on alpha iron-tin alloy polycrystals are shown. This paper is based on a presentation made at the symposium “The Role of Trace Elements and Interfaces in Creep Failure” held at the annual meeting of The Metallurgical Society of AIME, Dallas, Texas, February 14-18, 1982, under the sponsorship of The Mechanical Metallurgy Committee of TMS-AIME.     

High temperature deformation and fracture mechanisms in a dendritic Ni3Al alloy

The mechanisms that control high temperature deformation and rupture were studied in a Ni₃Al alloy that was thermo-mechanically treated to produce a non-porous dendritic grain structure. Comparisons of data corresponding to the dendritic grain morphology with that for the equiaxed grain structures indicate that the dendritic morphology results in significantly lower creep rates as well as substantially greater times to rupture. Comparison of the data with numerical calculations suggests that this difference in creep strength is due to an inherent resistance to grain boundary sliding by the dendritic grain structure. A constrained cavity growth model was adapted based on microstructural observations to account for cavitation within the dendritic microstructure. The success of the model indicates that rupture time is primarily determined by constrained cavity growth on isolated dendrite boundary segments.     

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.