Characterization of grain-boundary configuration and fracture surface roughness by fractal geometry and creep-rupture properties of metallic materials

Grain-boundary configuration in heat-treated specimens and fracture surface roughness in creep-ruptured specimens of several kinds of metallic material were quantitatively evaluated on the basis of fractal geometry. Correlations between the fractal dimension of grain boundary, that of fracture surface profile, the creep-rupture properties and the fracture mechanisms of the alloys are discussed. In heat-resistant alloys, the fractal dimension of a nominally serrated grain boundary was always larger than that of a straight grain boundary in the same alloy. The relative importance of the ruggedness of grain boundaries was estimated by the fractal dimension difference between these two grain boundaries. There was a quantitative relationship between the increase of the fractal dimension of the grain boundary and the improvement of rupture ductility and rupture strength owing to grain-boundary serration in the alloy. A similar correlation was also found between the increase in the fractal dimension of the fracture surface profile and the improvement of the creep-rupture properties, since in some cases the fractal dimension of the fracture surface profile was correlated with that of the grain boundary. Both grain boundary and fracture surface profile were assumed to exhibit a fractal nature between one grain boundary length (upper bound) and an interatomic spacing (lower bound). In carbon steels with ferrite-pearlite structure, according to the increase in pearlite volume fraction, the rupture ductility decreased and the fracture mechanism changed from transgranular fracture in pure iron and low-carbon steels to intergranular fracture at ferrite-pearlite grain boundaries in medium-carbon steels, and further to intergranular fracture at pearlite grain boundaries in high-carbon steels. The correspondence between the fractal dimension of the grain boundary and that of the fracture surface was confirmed in ruptured specimens of ferrite-pearlite steels when the grain boundary was the fracture path.     

Fractal nature and quantitative evaluation of microstructures in metallic materials

The fractal nature of microstructures was investigated using metallic materials containing second-phase particles, grain-boundary reaction (GBR) nodules or creep voids. The area fraction of the precipitates or the creep voids in the specimens was correlated with the scale of the analysis. The microstructures of these specimens exhibited a fractal nature between the lower and the upper critical scales, and could be regarded as the aggregate of the unit pattern with the size of the upper critical scale. The fractal dimension of a given microstructure was generally larger in specimens containing a larger area fraction of the second phase. The lower critical scale was close to the average size of second-phase particles or GBR nodules or the size of a large creep void. The upper critical scale, above which the area fraction of the precipitates or the creep voids did not show a scale dependence, was generally much larger than the average size and the average spacing of the precipitates, but it was almost the same as or a fair degree smaller than the grain size in specimens containing the second-phase particles or the GBR nodules. In the creep-ruptured specimens, the upper critical scale was much larger than the initial grain size and the grain size at rupture. The true area fraction of the second phase or the creep voids corresponding to the upper critical scale was also obtained.     

Fractal dimension of the grain boundary fracture in creep-fracture of cobalt-based heat resistant alloys

The effects of grain boundary configuration and creep conditions on the fractal dimension of the grain boundary fracture (D _f) were investigated using commercial cobalt-based heat resistant alloys, namely, HS-21 and L-605 alloys. Creep-rupture experiments were carried out under the initial creep stresses of 19.6–176 MPa in the temperature range from 1089–1422 K in air. The value of D _f was larger in specimens with serrated grain boundaries than in those with straight grain boundaries in the HS-21 alloy under the same creep condition, and the difference in the value of D _f between these specimens was large in the scale range of the analysis which was less than about one grain boundary length. However, there was almost no difference in the value of D _f between the specimens with serrated grain boundaries and those with straight grain boundaries in the L-605 alloy, because there was no obvious difference in the microstructure between these specimens. The value of D _f increased with decreasing creep stress in the scale range of the fractal analysis larger than about one grain boundary length in both HS-21 and L-605 alloys, while the stress dependence of D _f was larger in the HS-21 alloy. The stress dependence of D _f was explained by the stress dependence on the number of grain boundary microcracks linked to the fracture surface. The value of D _f estimated in the scale range smaller than about one grain boundary length showed essentially no stress dependence in both L-605 and HS-21 alloys.     

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.     

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. This revised version was published online in November 2006 with corrections to the Cover Date.     

Fracture surface topography and fracture mechanism in austenitic SUS316 steel plates fatigued by repeated bending

Fatigue experiments were carried out using the austenitic SUS316 steel plates (the average grain diameter is about 1.3 × 10⁻⁵ m) by repeated bending. The three-dimensional fatigue fracture surfaces were then reconstructed using stereo pairs of scanning electron micrographs by the stereo matching method. Striations were observed on the stage II fatigue fracture surface, while fine slip steps were found on the stage I fatigue fracture surface. The averaged value of the fractal dimension of stage I fracture surface was about 2.2 and was almost the same as that of stage II fracture surface when the fractal dimension was measured in the length scale range smaller than about one grain-boundary length (about 8 × 10⁻⁶ m). This may be attributed to the fact that both fracture surfaces were formed by the same mechanism, namely, slipping-off. According to the two-dimensional fractal analysis, both stage I and stage II fatigue fracture surfaces did not exhibit anisotropy in the length scale range of the fractal analysis smaller than about one grain-boundary length in the SUS316 steel. The fractal dimension of the fatigue fracture surface increased with decreasing the magnification of images when the maximum length scale of the fractal analysis was extended to the size of analyzed area. Magnification dependence of the fractal dimension was associated with large steps and ledges, which were not “typical” fractals.     

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.     

Improvement of creep-rupture properties of wrought cobalt-based HS-21 alloys at high temperatures

The improvement of creep-rupture properties by serrated grain boundaries is investigated using wrought cobalt-based HS-21 alloys in the temperature range 816 to 1038° C (1500 to 1900°F). Serrated grain-boundaries are produced in the early stage of the grain-boundary reaction (GBR) by a heat treatment. Specimens with serrated grain boundaries have superior creep-rupture properties compared with those with normal straight grain boundaries. The rupture lives of specimens with serrated grain boundaries are more than twice as long as those of specimens with straight grain boundaries. The rupture elongation is considerably improved by serrated grain boundaries especially at lower temperatures. A ductile grain-boundary fracture is observed in specimens with serrated grain boundaries, while brittle grain boundary facets prevail in specimens with straight grain boundaries.     

Effects of serrated grain boundaries on the crack growth in austenitic heat-resisting steels during high-temperature creep

The effect of serrated grain boundaries on creep crack growth is investigated using an austenitic 21Cr-4Ni-9Mn steel principally at 700° C. The relationship between the microstructure of specimens and the crack growth behaviour is discussed. The creep crack growth rate in the specimens with a surface notch is relatively reduced by serrated grain boundaries especially in the early stage of crack growth. The life of crack propagation in the specimens with serrated grain boundaries is longer compared with that of the specimens with straight grain boundaries. It is confirmed in the surface crack growth of smooth round bar specimens crept at 700° C that serrated grain boundaries are effective in retarding the growth of a grain-boundary crack less than about 4×10^–4 m long, and that this effect decreases with increasing crack length. It is suggested that crack deflection due to serrated grain boundaries caused a decrease in the stress intensity factor of the grain-boundary crack and resulted in a decrease of the crack growth rate in the steel. The crack arrest at the deflection points and the circumvention of crack path on the serrated grain-boundaries may also contribute to the retardation of the grain-boundary crack growth during creep. Further, it is deduced from the experimental results on the notched specimens that the creep fracture is caused by the linkage of the main crack to many microcracks and voids on the grain-boundary at 900°C.     

Effects of high-temperature ageing on the creep-rupture properties of cobalt-base L-605 alloys

Effects of high-temperature ageing on the creep-rupture properties of cobalt-base L-605 alloys were investigated at 1089 and 1311 K in air. The specimens with serrated grain boundaries and those with normal straight grain boundaries were aged for 1080ksec at 1273 or 1323 K to cause the matrix precipitates of tungsten-rich b c c phase and M₆C carbide. The creep-rupture strength of both specimens were improved by the high-temperature ageing. The rupture strength at 1311 K was the highest in the specimens with serrated grain boundaries aged at 1273 K, while the specimens with straight grain boundaries aged at 1273 K of the highest matrix hardness had the highest rupture strength at 1089 K. The high-temperature ageing did not decrease the rupture ductility of specimens. The ruptured specimens with serrated grain boundaries exhibited a ductile grain-boundary fracture surface which consisted of dimple patterns and steps, regardless of whether high-temperature ageing was carried out. The fracture mode of the specimens with straight grain boundaries was changed from the brittle grainboundary fracture to the ductile one similar to that of the specimens with serrated grain boundaries by high-temperature ageing, since large grain-boundary precipitates which gave nucleation sites of dimples were formed during the ageing. The grain-boundary cracks initiated in the early stage of creep (transient creep regime) in both non-aged and aged specimens of L-605 alloys in creep at 1089 and 1311 K, although the time to crack initiation is shorter in the specimens with straight grain boundaries than in those with serrated grain boundaries. Thus, the period of crack growth and linkage occupied most of the rupture life. The strengthening mechanisms of the aged specimens were also discussed.     

Fractal dimension of grain boundary in CuAu alloys refined by platinum addition

Irregularity of the grain boundaries in CuAu alloys refined by platinum addition was estimated by fractal analysis. The fractal dimension increased with decreasing the grain size, which introduced by platinum addition. The grain refinement produced more complexity in microstructure.     

Grain boundary crystallography in two Fe-C-P alloys

Abstract

Misorientation, grain growth and brittle fracture were investigated in two iron - carbon alloys containing 0.06 wt-% phosphorus (0.06P) and 0.12 wt-% phosphorus (0.12P) after selected heat treatment schedules. A 'fracture surface serial sectioning' technique was devised and combined with misorientation measurements to reconstruct specimens after fracture. Anomalous grain growth occurred in the 0.06P specimen only, after 1000°C annealing. This was attributed to the inhomogeneous distribution of phosphorus at the interfaces. No evidence was found for the direct influence of misorientation angle distributions or coincidence site lattice distributions on anomalous grain growth. The proportion of Σ3s increased greatly after annealing at 1000°C, attributed to the twinning that developed in the austenite range. There was strong evidence that Σ3s were in general more resistant to brittle fracture than were random boundaries. It is suggested that alloys of this type could be 'grain boundary engineered' to improve fracture resistance.     

Creep-rupture properties and grain-boundary sliding in wrought cobalt-base HS-21 alloys at high temperatures

The effects of serrated grain boundaries on the creep-rupture properties of wrought cobaltbase HS-21 alloys were investigated at 1311 and 1422 K. The amount of grain-boundary sliding and the initiation and growth of grain-boundary cracks were also examined during creep at 1311 K. Specimens with serrated grain boundaries exhibited longer rupture life and larger rupture ductility than those with straight grain boundaries, but these specimens had almost the same rupture life and rupture ductility under lower stresses at 1422 K, because serrated grain boundaries were also formed in specimens with originally straight grain boundaries. The average amount of grain-boundary sliding during creep at 1311 K increased with time (or with creep strain), but was almost the same in both specimens with serrated grain boundaries and those with straight grain boundaries at the same creep strain. Grain-boundary cracks or voids initiated in the early stage of creep in those specimens at 1311 K. Therefore, the strengthening by serrated grain boundaries at high temperatures above about 1311 K was attributed to the retardation of growth and linkage of grain-boundary cracks and voids.     

全层状TiAl基合金断裂中晶界的双重作用

通过SEM原位拉抻技术和双晶体压缩实验研究了全片层TiAI基合金晶界断裂行为。研究表明,在全层状组织的断裂行为中,晶界具有双重作用。一方面,微裂纹首先萌发于晶界区,其扩展方式取决于晶界两侧片层的取向。另一方面,不同类型的晶界对裂纹扩展的阻力不同,因而对全层状TiAI基合金韧性的作用不同,纵向晶界有助于断裂韧性的提高,而横向晶界对合金韧性不利。     

Effect of grain size on cavitation in superplastic Zn-Al eutectoid

The effect of initial grain size on cavitation during superplastic deformation in two commercially available Zn-Al eutectoid alloys has been studied using metallography and precision density measurements. Cavitation was found to be minimal for initial grain sizes below about 5 m. Superplastic deformation caused grain growth in both alloys under all testing conditions, and when the grain size exceeded about 8 m a significant level of cavitation was produced. The grain size and extent of cavitation increased with increasing strain along the specimen gauge length, with cavities concentrated in regions adjacent to the fracture tip. Although never very large, the cross-sectional area at fracture increased with increasing levels of cavitation. It was concluded that cavitation in Zn-Al eutectoid results from incomplete accommodation of grain-boundary sliding when excessive grain growth leads to restricted grain-boundary diffusion and/or to restricted grain-boundary migration.     

Relationship between Fracture Toughness and Fractal Dimension of Fracture Surface of Steel

The relationship between fracture toughness and fractal dimension of fracture surface was analysed based on a united fractal model of microscopic fracture modes. It was indicated that fracture toughness is a multivariant function of yield strength, microstructural length, fractal dimension of fracture surface and volume fraction of inclusions, other than a monovariant function of fractal dimension of fracture surface. This new fractal model of fracture toughness was verified to fit well with a set of experimental data of a ultrahigh strength steel with equal microstructure and grain size but different volume fraction of inclusion.     

Analysis of the fractal dimension of grain boundaries of AA7050 aluminum alloys and its relationship to fracture toughness

Quantitative analysis of the grain boundaries in partially recrystallized microstructures of heat-treated 7050 aluminum alloys has been performed. Fractal dimensions of the extracted grain boundaries were calculated by box-counting method. Five different types of tear-tested materials rolled in different processes each at two orientations of 0° and 90° were studied. Efforts were made to connect the fractal dimensions of grain boundaries in the crack propagation direction to the fracture toughness (unit propagation energy, UPE, in tear test). The results show that there is a linear correlation between UPE and the fractal dimensions of the grain boundaries along the crack propagation direction for both 0° and 90° samples. The dependence corresponds well with the observation of transition from intergranular fracture to transgranular fracture with the increase of UPE. Quantitative analysis has also been performed on the micrographs to estimate the degree of recrystallization and the grain size in crack growth direction. No correlation between the fraction of recrystallized grains and the UPE could be detected.     

Investigation on the Static Fatigue Mechanism and Effect of Specimen Thickness on the Static Fatigue Lifetime in WC–Co Cemented Carbides

The static fatigue mechanism and effect of specimen thickness on static fatigue lifetime for four WC–Co cemented carbides were studied with different binder contents and carbide grain sizes. Static fatigue tests under three-point bend loading were conducted on different sized specimens. The fracture surfaces of rupture specimens were examined by scanning electron microscopy to investigate the static fatigue micromechanisms. Experimental results show that microcracks nucleate from defects or inhomogeneities and the connection of microcracks produces a main crack. The main crack propagates rapidly, resulting in the fracture of specimens. The extension of static fatigue lifetime with the increase of specimen thickness is due to the decrease of plastic zone size near the crack tip and relevant energy change during the crack growth. The effect of specimen thickness on static fatigue lifetime is much greater for cemented carbides with larger WC grain size or higher cobalt content, which is attributed to operative toughening mechanisms.     

Fractal dimensions for fatigue fracture surfaces performed on micro- and meso-scale levels

A methodology was developed to use digital photograph fracture for calculating the integral fractal dimension and spectrum fractal dimensions for two perpendicular directions. The fractal dimension value, which was discovered by the variation of the pixel size up until the fractal dimension became unchangeable, i.e., where d _\min,d _\max are the borders of the scale level used. The effectiveness of the methodology performed showed the basis of the fracture surface analyses for Al-based alloys BS L65 and 2024 T351 (analogous to Al alloy D16T), specimens of which were tested by pull-push with imitation fretting corrosion damage of the sur- face and with four-point bending after the laser peening, respectively.     

Fractal dimensions for fatigue fracture surfaces performed on micro- and meso-scale levels

A methodology was developed to use digital photograph fracture for calculating the integral fractal dimension and spectrum fractal dimensions for two perpendicular directions. The fractal dimension value, which was discovered by the variation of the pixel size up until the fractal dimension became unchangeable, i.e., where d _\min,d _\max are the borders of the scale level used. The effectiveness of the methodology performed showed the basis of the fracture surface analyses for Al-based alloys BS L65 and 2024 T351 (analogous to Al alloy D16T), specimens of which were tested by pull-push with imitation fretting corrosion damage of the sur- face and with four-point bending after the laser peening, respectively.