Grain Boundary Cracks Research Articles

Effects of the creep deformation on the fractal dimension of the grain boundaries in an austenite steel

The change in the fractal dimension of the grain boundaries during creep was investigated using an austenitic SUS304 steel at 973 K. The fractal dimension of the grain-boundary surface profile (the fractal dimension of the grain boundaries, D, 1 < D < 2) in the plane parallel to the tensile direction (in the parallel direction) and in the transverse direction, was examined on specimens deformed up to rupture (about 0.30 creep strain). Grain boundaries became serrated and the fractal dimension of the grain boundaries increased with increasing creep strain, because the density of slip lines which formed ledges and steps on grain boundaries increased as the creep strain increased. The increase in the fractal dimension due to creep deformation was slightly larger under the higher stress (118 MPa) than under the lower stress (98 MPa), while the increase of the fractal dimension with strain was a little larger in the specimens tensile-strained at room temperature (293 K) than in the crept specimens. These results were explained by the grain-boundary sliding and the diffusional recovery near grain boundaries, which lowered the increase of the fractal dimension with the creep strain. The fractal dimension of the grain boundaries in the parallel direction was slightly larger than that in the transverse direction in both creep at 973 K and tensile deformation at room temperature, especially at the large strains. This could be correlated with the shape change of the grains by creep or plastic deformation. Grain-boundary cracks were principally initiated at grain-boundary triple junctions in creep, but ledges, steps and carbide precipitates on serrated grain boundaries were not preferential nucleation sites for the cracks.

Grain boundary cracking in fatigued bicrystals

Compact tension (CT) shaped copper bicrystals containing the Σ3(111), Σ9(221), Σ41(338) or random [110] tilt boundaries either perpendicular or parallel to the tensile axis (TA) were tested to examine the effect of grain boundary (GB) structure on fatigue crack initiation and propagation. With both types of bicrystals, the GB resistance to intergranular cracking increases with the decrease in the Σ value. The effect of air on fatigue crack propagation is found to be of primary importance. It is shown that the GB is not necessarily a preferential site for crack propagation in vacuum. A crack introduced intergranularly in air may assume a stransgranular mode of growth in vacuum. The initial GB structure greatly affects the susceptibility of GBs to corrosion in air and this determines their resistance to crack growth. The relative importance of slip band cracking as compared to GB cracking in vacuum is examined. The dominant mechanism of fracture is seen to be determined by two factors: the GB structure in the non-equilibrium state and the geometry of slip with respect to GB orientation.

Statistical characteristics for the type and length of deformation-induced cracks in columnar-grain ice

AbstractObservations are reported on cracks formed during compressive, unidirectional, constant-strain-rate deformation of columnar-grain ice. The axis of hexagonal crystallographic symmetry of each grain tended to be in the plane perpendicular to the long direction of the grains and to have a random orientation in that plane. For stress applied perpendicular to the long direction of the grains, the deformation was practically two-dimensional. It was found that the relative proportion of grain-boundary cracks increased with increasing strain rate, decreasing temperature and, for strain rate greater than 7 × 10−5 s−1, with decreasing grain-size. Almost all the grain-boundary cracks had at least one edge at a triple point. For each test, the grain-boundary and transcrystalline crack lengths tended to have a log-normal distribution. The logarithmic mean crack length (LMCL) decreased with increasing strain rate, decreasing grain-size and decreasing temperature and tended to a constant value of 0.75 mm at 10°C. For grain-size of 3 mm or greater, the LMCL had a maximum at a strain rate of 10−5 to 10−6 S−1 at −10°C. The LMCLs and the relative proportion of grain-boundary cracks tended to be normally distributed for given load conditions.

Statistical characteristics for the type and length of deformation-induced cracks in columnar-grain ice

AbstractObservations are reported on cracks formed during compressive, unidirectional, constant-strain-rate deformation of columnar-grain ice. The axis of hexagonal crystallographic symmetry of each grain tended to be in the plane perpendicular to the long direction of the grains and to have a random orientation in that plane. For stress applied perpendicular to the long direction of the grains, the deformation was practically two-dimensional. It was found that the relative proportion of grain-boundary cracks increased with increasing strain rate, decreasing temperature and, for strain rate greater than 7 × 10−5s−1, with decreasing grain-size. Almost all the grain-boundary cracks had at least one edge at a triple point. For each test, the grain-boundary and transcrystalline crack lengths tended to have a log-normal distribution. The logarithmic mean crack length (LMCL) decreased with increasing strain rate, decreasing grain-size and decreasing temperature and tended to a constant value of 0.75 mm at 10°C. For grain-size of 3 mm or greater, the LMCL had a maximum at a strain rate of 10−5to 10−6S−1at −10°C. The LMCLs and the relative proportion of grain-boundary cracks tended to be normally distributed for given load conditions.

Scaling exponent of grain-boundary sliding in creep deformation of polycrystalline materials

Grain-boundary sliding is an important deformation process in the high-temperature creep of materials [1]. It is known that grain-boundary sliding also plays an important role in the initiation and growth of grain-boundary cracks and voids which lead to grain-boundary fracture. In the previous study [2], the size distribution of large grain-boundary cracks was examined using crept specimens with different grain-boundary con®gurations, namely, the specimen with serrated grain boundaries (Dgb ˆ 1:241, where Dgb is the fractal dimension of the grain-boundary surface pro®le in the two-dimensional section (1 , Dgb , 2)) and the specimen with straight grain boundaries (Dgb ˆ 1:056) in the cobalt-based HS-21 alloy. The results indicated that the cumulative number, N (c), of the grain-boundary cracks with size larger than c can be correlated to the crack size, c, by a power-law equation, N (c) / cya9, where a9 is considered to be the fractal dimension of the size distribution of the cracks. The value of a9 for these specimens, which was in the range from about 0.66 to 2.0, was correlated to the relative ease of the crack growth. The value of a9 was larger in the specimens with serrated grain boundaries, in which the growth rate of creep cracks was lower. The present author and co-workers [3, 4] experimentally con®rmed that, in heat-resistant alloys, serrated grain boundaries are generally effective in retarding grain-boundary sliding which results in the nucleation and growth of a grain-boundary crack. The amount of grain-boundary sliding in specimens depends not only on the orientation of sliding grain boundaries [3, 5] but also on the grain-boundary con®guration [3, 4, 6] and on the grain-boundary character (coincidence boundary or random boundary) [6], although the average amount of the sliding increases with increasing creep strain [1, 3±5]. However, it is not clear whether the local variation in the amount of grain-boundary sliding is also ®tted to a power-law equation. In seismology, for example, there is a similar power-law relationship between the cumulative number of earthquakes and the magnitude of earthquakes: the Gutenberg±Richter [7] equation. In this study, the boundary-to-boundary variation of the grain-boundary sliding was examined on the crept specimens of the heat-resistant alloys. In analogy to the seismic study, a discussion was made on the local variation in the grainboundary sliding in the specimens. Gutenberg and Richter [7] found that the number, N (M), of earthquakes whose magnitude is greater than M can be ®tted to the following power-law equation: log [N (M)] ˆ a‡ b(8y M) (1)

Size distribution of large grain-boundary cracks in the creep-ruptured specimens of a cobalt-based alloy

Size distribution of large grain-boundary cracks in the creep-ruptured specimens of a cobalt-based alloy

The creep-rupture properties and the initiation and growth of the grain-boundary cracks in the cobalt-base HS-21 alloy

The effect of the grain-boundary microstructures on the creep-rupture properties and the initiation and growth of the grain-boundary cracks was investigated using four kinds of specimen of various grain-boundary microstructures in the cobalt-base HS-21 alloy at 1089 K in air. Both the rupture strength and the creep ductility increased with increasing mean value of the fractal dimension of the grain boundaries, Dgb. The strain to crack initiation was largest in the specimen of the highest value (1.241), while the strain was much the same in the specimens of the Dgb value less than 1.162. This was explained by the local variation in the grain-boundary microstructures in these specimens. The mean value of the fractal dimension of the grain-boundary fracture, Df, was close to the value of Dgb, although the value of Df was a little higher than that of Dgb in the specimens of the lower Dgb values. The fracture appearance changed from a brittle grain-boundary fracture to a ductile one with increasing values of Dgb and Df. The crack-growth rate is the surface-notched specimens decreased with increasing value of Dgb. The threshold stress intensity factor for crack growth was higher in the specimens with the higher Dgb values.

Hydrogen-induced cleavage fracture of Fe3Al-based intermetallics

Hydrogen-induced fracture of ductile Fe3Al-based intermetallics was studied through mechanical testing, fracture surface observation, andin situ transmission electron microscopy (TEM) tests of tensile specimens. Mechanical properties of ordinary ductile X-80 pipeline steel (low-alloy steel) were tested and compared with Fe3Al intermetallics. Elongations of the Fe3Al alloy decreased from 14 to 10 pct, with increases in the strain rate from 10−6 to 10−3/s. The elongation reduction of Fe3Al was caused by the hydrogen-induced fracture. There was no elongation reduction when the testing was done in mineral oil. Non-necking occurred near the fracture section, and the fracture surfaces mainly consist of cleavage and partial intergranular morphologies. Elongation near the fracture surface of the Fe3Al intermetallics was about 14 pct, which is the same as the total elongation. For the pipeline steel, however, an elongation near the fracture cross section was greater than 130 pct, which was much higher than its total elongation of 17 pct.In situ TEM observation on a tensile test sample showed crack propagation accompanied by dislocation plasticity. When the Fe3Al was precharged cathodically, the crack tip was sharp. Its radius was much less than that obtained without hydrogen charging. The crack propagated along the grain boundary for the charged specimens, but penetrated the grain boundary for the specimen without hydrogen charging. Effects of hydrogen on plastic deformation and grain-boundary cracking are discussed in this article.

Effect of ambient air on fatigue crack propagation in copper compact tension bicrystals

The effect of environment on fatigue crack propagation in copper compact tension (CT) bicrystals was examined. The role of the initial grain boundary (GB) structure is analyzed for bicrystals having Σ9 and Σ41 grain boundaries. It is shown that the GB is not necessarily a preferential site for crack propagation in vacuum. A crack introduced intergranularly in air may change its mode of growth to transgranular in vacuum. The relative importance of GB cracking compared with persistent slip band (PSB) cracking in vacuum is examined. The dominant mechanism of fracture is determined by two factors: the GB structure and the geometry of slip with respect to the GB orientation.

Near‐Surface Deformation in an Alumina–Silicon Carbide‐Whisker Composite due to Surface Machining

Deformation due to two different surface‐machining conditions—grinding (126 μm diamond) and polishing (3 μm diamond)—in an uniaxial hot‐pressed Al2O3–30%‐SiC‐whisker composite has been investigated. A Warren–Averbach analysis of grazing incidence X‐ray diffractometry data shows that the deformation is localized to the very top surface zone. The cell size and the root mean square of the strain show a gradient in the deformed layer. Transmission electron microscopy studies, in cross‐sectional view, also show a near‐surface deformation zone containing dislocations, twins, and cracks. This is seen for both machining procedures, but the depth of the zone and the degree of deformation, in terms of dislocation density and number of cracks, is much higher in the roughly ground specimen than in the polished one. For comparison, a monolithic Al2O3 sample also has been studied after grinding. The deformation zone is very similar to the Al2O3–SiC sample with the same grinding condition, but cracks and dislocations are present at a slightly larger depth. The deformation depth for the polished Al2O3–SiC sample is ∼50 nm. In the ground Al2O3–SiC sample, the deformation depth is 1–1.5 μm and corresponds to the grain size. The deformation zone in the ground monolithic Al2O3 sample is 1.5–2 μm deep. The observed grain‐boundary cracks are almost parallel to the surface and may originate from nonaccommodated plastic flow between grains.

Film-Induced Brittle Intergranular Cracking of Silver-Gold Alloys

Abstract Dealloying of a binary noble alloy produces a porous layer rich in the more noble element. Application of a tensile load initiates a brittle intergranular (IG) crack in the dealloyed layer that advances into the unattacked material. This study showed that the crack penetration depth (Cd) is proportional to the thickness of the dealloyed layer (t). For a given value of t, the grain-boundary crack penetration distance was shown to decrease as the dealloying potential increased. The dependence of Cd on t and the dealloying potential, as opposed to the applied potential at the time of fracture, supported the film-induced cleavage model.

Thermal expansion of grain-boundary cracked aluminium titanate ceramics

The relation between thermal expansion coefficient and grain-boundary crack volume of aluminium titanate ceramics has been calculated based on the thermal expansion data of a single crystal. The calculation began with the drawing of a frequency distribution curve of the thermal expansion coefficient for a single grain. Using the single-grain distribution curve, a distribution curve of an average coefficient for two adjacent grains was derived. The thermal expansion with a partially grain-boundary cracked body was calculated in relation to the amount of cracked boundary from the average distribution curves. The expected relation between crack volume and thermal expansion was close to that of the experimental data.

Measurement of crack volume due to thermal expansion anisotropy in aluminium titanate ceramics

Grain-boundary crack onset and crack volume at room temperature resulting from thermal expansion anisotropy in aluminium titanate ceramics were studied by dilatometry. Investigation revealed that specimens with low bulk density have a smaller temperature difference between sintering and crack-onset temperature than those of the specimens with high density and the same grain size. The fracture surface energy of aluminium titanate on the grain-boundary cracking in the present study was about 22 J m−2; the grain-boundary crack volume is proportional to (grain size)0.5.

Structure, chemistry, and stress corrosion cracking of grain boundaries in alloys 600 and 690

The microstructure in six commercial batches of alloys 600 and 690 has been investigated using scanning electron microscopy (SEM), analytical transmission electron microscopy (ATEM), atom probe field ion microscopy (APFIM), and secondary ion mass spectroscopy (SIMS). The materials were also tested with respect to their resistance to intergranular stress corrosion cracking (IGSCC) in high-purity water at 365 °. Applied microanalytical techniques allowed direct measurement of carbon concentration in the matrix together with determination of grain boundary micro structure and microchemistry in all material conditions. The distribution of oxygen near a crack in material tested with respect to IGSCC was also investigated. The role of carbon and chromium and intergranular precipitates on IGSCC is discussed.

Effects of simultaneous boron and nitrogen implantation on microhardness and fatigue properties of Fe-13cr-15ni alloys

Eight complex austenitic stainless steel alloys based on the composition Fe-13Cr-15Ni-2Mo-2Mn-0.2Ti-0.8Si-0.06C were implanted simultaneously with 400-keV B+ and 550-keV N+ ions and were investigated for changes in fatigue properties and surface microhardness. The nearsurface hardness of all eight alloys improved, but the fatigue life of each decreased. These findings were contrary to those obtained in an earlier study using four simple Fe-13Cr-15Ni alloys, where the dual implantation improved fatigue life by up to 250 pct. While unimplanted specimens failed by slip-band crack initiation, it was hypothesized that the dual implantation suppressed slip to the extent that fewer slip-band cracks were initiated and these were subjected to accelerated crack propagation. In addition, grain-boundary cracking was promoted, yielding a lower fatigue life. Support for this hypothesis was obtained by a study of single crystals of Fe-15Cr-15Ni, which were also implanted with B+ and N+. The dual implantation caused a lower fatigue life due to concentration of slip along a few slip bands to relieve applied stress. Evidence of grain-boundary cracking was obtained using the four simple alloys, which were subjected to triple ion implantation with B+, N+, and C+. The triple implantation decreased the fatigue life of the alloys and caused accelerated growth of fewer slip bands and grain-boundary cracking due to suppression of surface slip bands. This study thus shows the existence of an optimum level of strengthening when multiple ion implantation is used to improve the fatigue properties of alloys.

Effect of strain rate on the high-temperature low-cycle fatigue properties of a nimonic PE-16 superalloy

Strain-rate effects on the low-cycle fatigue (LCF) behavior of a NIMONIC PE-16 superalloy have been evaluated in the temperature range of 523 to 923 K. Total-strain-controlled fatigue tests were per-formed at a strain amplitude of +/-0.6 pct on samples possessing two different prior microstructures: microstructure A, in the solution-annealed condition (free of gamma' and carbides); and microstructure B, in a double-aged condition with gamma' of 18-nm diameter and M23C6 carbides. The cyclic stress response behavior of the alloy was found to depend on the prior microstructure, testing temperature, and strain rate. A softening regime was found to be associated with shearing of ordered gamma' that were either formed during testing or present in the prior microstructure. Various manifestations of dynamic strain aging (DSA) included negative strain rate-stress response, serrations on the stress-strain hysteresis loops, and increased work-hardening rate. The calculated activation energy matched well with that for self-diffusion of Al and Ti in the matrix. Fatigue life increased with an increase in strain rate from 3 x 10(-5) to 3 x 10(-3) s-1, but decreased with further increases in strain rate. At 723 and 823 K and low strain rates, DSA influenced the deformation and fracture behavior of the alloy. Dynamic strain aging increased the strain localization in planar slip bands, and impingement of these bands caused internal grain-boundary cracks and reduced fatigue life. However, at 923 K and low strain rates, fatigue crack initiation and propagation were accelerated by high-temperature oxidation, and the reduced fatigue life was attributed to oxidation-fatigue interaction. Fatigue life was maximum at the intermediate strain rates, where strain localization was lower. Strain localization as a function of strain rate and temperature was quantified by optical and scanning electron microscopy and correlated with fatigue life.

Effects of high-temperature ageing on the creep-rupture properties of high-tungsten cobalt-base superalloys

The effects of high-temperature ageing on creep-rupture properties were studied using cobalt-base superalloys containing about 14–20 wt% tungsten (W) at 1089 K (816 °C) and 1 311 K (1038 °C) in air. A high-temperature ageing for 1080 ks at 1273 K after solution treatment caused grain-boundary and matrix precipitates of W solid solution and carbide phases in these alloys, and grain boundaries were serrated especially in the alloys with higher W content. The high-temperature ageing largely improved the rupture life in the alloys with higher W content, particularly under lower stresses at 1089 K, whereas it caused the creep ductility to decrease a little in the alloy containing 20% W. The high-temperature ageing also improved the rupture life without decreasing creep ductility in these alloys under higher stresses at 1311 K. Under the same ageing conditions of 1080 ks at 1273 K, the initiation of grain-boundary cracks was retarded in the solution-treated and aged specimens, as well as in the aged specimens with serrated grain boundaries, for the alloys with higher W content at both 1089 and 1311 K. A large amount of grain-boundary serration also occurred in the non-aged specimens of the alloys with higher W content during creep at 1311 K, and contributed to the strengthening of the alloys. The solution-treated and aged specimen had almost the same rupture strength as the aged specimens with serrated grain boundaries in these cobalt-base alloys. The rupture strength of the solution-treated and aged specimens largely increased with increasing W content under the lower stresses at 1089 K and under the higher stresses at 1311 K. A ductile grain-boundary fracture surface, which was composed of dimples and grain-boundary ledges associated with grain-boundary precipitates, was observed in the solution-treated and aged specimens, as well as in the aged specimens with serrated grain boundaries at both 1089 and 1311 K. The fracture surface of the non-aged specimens was a brittle grain-boundary facet at 1089 K, but it became a ductile grain-boundary fracture surface, as serrated grain boundaries were formed owing to grain-boundary precipitates occurring during creep at 1311 K.

Finite Element Study On the Closure of Thermal Microcracks In Feldspar/Quartz-Rocks-Ii. Intra-, Transgranular and Mixed Cracks

SUMMARY The formation of microcracks is studied in a planar composite material using the finite element method. Intraganular (IGC), transgranular (TGC) and mixed-type cracking is modelled in a system containing angular-cornered quartz (QTZ) grains surrounded by feldspar (FSP). Physical rock properties (elastic moduli, seismic velocity) show a gradual increase with increasing confining pressure due to the closure of cracks as expected from experiments only in the case of IGC. the collapse closure of grain-boundary cracks (GBC) and the TGC is documented by a jump in the pressure-dependent rock properties. Strictly parallel aligned flaws should be replaced by preferred oriented ones or by crack populations with different closing pressures to provide a gradual closure curve. the thermal microcracks investigated can be categorized with respect to their closure process quantified in terms of crack length, aperture and aspect ratio versus confining pressure. Major crack types (GBC I, IGC and TGC) close at pressures ranging from 30 to about 70MPa after cooling the composite by 400 °C. For mixed-type cracks (GBC & IGC), the GBC closes at 30MPa before the remaining IGC starts to shorten at 50 MPa. the friction coefficient μ along the re-closed GBC-planes is responsible for whether the IGC closes totally (μ= 0.1) or degenerates into a residual pore located at the grain boundary (μ≥ 0.3). For μ≥ 0.3 significant in situ porosity of QTZ/FSP-rich rocks may be found as deep as 10 km within the crust of the earth. Lowering the friction coefficient residual porosity can disappear at shallower depths (e.g. μ= 0.1 for the mixed type crack results in a closing pressure of 50 MPa corresponding to a depth of about 2 km).

Finite Element Study On the Closure of Thermal Microcracks In Feldspar/Quartz-Rocks-I. Grain-Boundary Cracks

SUMMARY The formation of microcracks is simulated in 2-D composites using the finite element method. the rock is modelled by a planar, periodic array of angular-cornered grains embedded in a matrix with different thermoelastic moduli. During cooling or unloading stress-concentration points arise at sharp corners inside the grain aggregate. Microcracking is simulated in a system containing quartz (QTZ) grains surrounded by feldspar (FSP). By investigating stress-intensity factors for different crack paths one can conclude that grain-boundary cracking (GBC) is most likely. Seismic velocities of the fractured composite are calculated from effective moduli. In a rock containing an array of parallel aligned GBC (1 mm length), the anisotropy turned out to be 29 per cent for P waves and 20 per cent for S waves. Crack-closure modelled by repressurizing the rock is substantially different for an aggregate with parallel oriented cracks (GBC I) than for a composite where most of the grain boundaries are broken (matrix containing totally separated grains, GBC II). the closing pressure of GBC I is finite and lies between 31 MPa (QTZ grains) and 41 MPa (FSP grains) after a temperature change of 400°C. the closing pressure of thermal cracks is largest in composites with very small inclusions and decreases for composites with larger grains. In case of small inclusions a collapse closure of GBC is evident, whereas in systems with larger grains a more gradual crack-closure dominates. the closure of GBC II is characterized by the occurrence of residual pores. the pores originate in the final stage of crack closure near sharp corners of the grains, where the former stress-concentration points after cooling were located. the phenomenon of residual pores may be a hint for interpreting fluid inclusions in rocks as a relic of the incomplete closure of cracks. From the results obtained in this study it can be concluded that significant in situ porosity of QTZ/FSP-rich rocks may be found at pressures as high as 300 MPa corresponding to a depth of about 10 km in the crust of the earth.

The effect of grain-size on the stress and velocity fields ahead of a crack in a material which deforms by Coble creep

The stress and velocity fields ahead of a grain-boundary crack in a material which deforms by Coble creep are investigated for a series of grain sizes using the numerical analysis technique established by Cocks [1–3]. The numerical results are compared with the linear viscous fields obtained by the boundary element method and the finite element method. It is demonstrated that a detailed knowledge of the micromechanical processes of material transport and deformation are required to determine the stress and displacement fields for the grains which immediately surround the crack tip. But the response of the surrounding material can be adequately described from a conventional linear viscous analysis of the problem.