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.     

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.     

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.     

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.     

Creep rupture strength and grain-boundary sliding in austenitic 21 Cr-4Ni-9Mn steels with serrated grain boundaries

The effect of grain-boundary strengthening on the creep-rupture strength by modification of the grain-boundary configuration is studied using austenitic 21 Cr-4Ni-9Mn steel in the temperature range from 600 to 1000° C in air. Grain-boundary sliding is also examined on a steel with serrated grain boundaries during creep at 700° C. The improvement of creep-rupture strength by the strengthening of grain boundaries is observed at high temperatures above 600° C. The 1000 h rupture strength of steels with serrated grain boundaries is considerably higher than that of steels with straight grain boundaries, especially at 700 and 800° C. The strengthening by serrated grain boundaries is effective in retarding both the crack initiation and the crack propagation at 700° C, while it does not improve the life to crack initiation at 900° C. Grain-boundary sliding is considerably inhibited by the strengthening of grain boundaries at 700° C. The amount of it in steels with serrated grain boundaries is less than about one-third of that of steels with straight grain boundaries at the same creep strain. The stress dependence of grain-boundary sliding rate in the steady-state regime is also examined from the steels with these two types of grain-boundary configuration.     

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 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.     

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.     

The fractal dimension of grain-boundary fracture in high-temperature creep of heat-resistant alloys

The fractal dimension of the grain-boundary fracture in high-temperature creep was estimated by the vertical section method on several creep-ruptured specimens of the cobalt-nickel- and iron-based heat-resistant alloys. Grain-boundary microcracks linked to the fracture surface were also taken into account in the present analysis by the box-counting method. In the specimens containing many grain-boundary microcracks linked to the fracture surface, the fractal dimension of the grain-boundary fracture was larger in the scale range of more than about one grain-boundary length than in the scale range less than this length. Thus, there was a cross-over in the fractal dimension of the grain-boundary fracture at about one grain-boundary length in these specimens. In the specimens containing much fewer microcracks, there was no clear cross-over in the fractal dimension of the grain-boundary fracture with regard to the scale of the analysis, irrespective of creep-ductility and grain-boundary configuration of the specimens. The fractal dimension of the grain-boundary fracture was generally larger in specimens with serrated grain boundaries than in specimens with straight grain boundaries in these heat-resistant alloys, because the fractal dimension of the grain boundary and the number of the grain-boundary microcracks were larger in the former specimen. The fractal dimension of the grain-boundary fracture did not tend to converge to unity when the scale of the analysis approached the specimen size. The inclusion of near-specimen size data with regard to the scale of the analysis did not affect the fractal dimension of the grain-boundary fracture in these alloys. Thus, the grain-boundary fracture in the creep-ruptured specimens exhibited a fractal nature, at least in the scale range below specimen size, although there was a cross-over in the fractal dimension of the grain-boundary fracture in specimens containing a large number of grain-boundary microcracks.     

INITIATION AND GROWTH OF SMALL CRACKS IN DIRECTIONALLY SOLIDIFIED MAR-M247 UNDER CREEP-FATIGUE PART II: EFFECT OF ANGLE NETWEEN STRESS AXIS AND SOLIDIFICATION DIRECTION

This paper deals with the effect of anisotropy on fracture processes of a directionally solidified superalloy, Mar-M247, under a push–pull creep-fatigue condition at high-temperature. Three kinds of specimen were cut from a cast plate such that their axes possess angles of 0°, 45° and 90° with respect to the 〈001〉 orientation that is aligned parallel to the solidification direction (also to the grain boundaries and primary dendrite axis); these specimens being denoted the 0° specimen, the 45° specimen, and the 90° specimen, respectively. The tests were conducted at 1273  K (1000 °C) in air under equal magnitudes of the range of a Δ J -related parameter, Δ W _c , which represents the driving force for crack growth in creep-fatigue. Although the grain boundaries are macroscopically parallel to the solidification direction, they are wavy or serrated microscopically. Small cracks nucleate along parts of the grain boundaries perpendicular to the stress axis in all specimens. The 90° specimen has the shortest crack initiation life and the 0° specimen has the longest. In the 90° and 45° specimens, intergranular cracks continue to nucleate and a main crack is formed along the grain boundary due to the frequent coalescence of small cracks. In the 0° specimen, cracks grow into the grain, and transgranular cracks coalesce along the primary dendrite or grain boundary. The 0° specimen exhibits the slowest crack growth rate and the 90° specimen the fastest. These differences in the initiation and growth behaviour of small cracks cause the longest failure life in the 0° specimen and the shortest in the 90° specimen.     

Effects of grain boundary- and triple junction-character on intergranular fatigue crack nucleation in polycrystalline aluminum

The effects of grain boundary- and triple junction-character on intergranular fatigue crack nucleation were studied in coarse-grained polycrystalline aluminum specimens whose grain boundary microstructures were analyzed by SEM-EBSD/OIM technique. Fatigue crack nucleation occurred mainly along grain boundaries and depended strongly on both the grain boundary character and grain boundary configuration with respect to the persistent slip bands. However, it was little dependent on the geometrical arrangements between the grain boundary plane and the stress axis. Particularly, random boundaries become preferential sites for fatigue crack nucleation. The fatigue cracks were also observed at CSL boundaries when the grain-boundary trace on the specimen surface was parallel to persistent slip bands. On the other hand, no intergranular fatigue cracks were observed at low-angle boundaries. The fatigue cracks were observed at triple junctions as well as grain boundaries. Their nucleation considerably occurred at triple junctions where random boundaries were interconnected. The grain boundary engineering for improvement in fatigue property was discussed on the basis of the results of the structure-dependent intergranular and triple junction fatigue crack nucleation.     

Fatigue-crack propagation in modified 300-grade maraging steel

Fatigue-crack-propagation studies were performed on an 18Ni (300-grade) maraging steel at room temperature in dry and humid argon environments (atmospheric pressure) to examine the effect of moisture on the rate of fatigue-crack propagation and on the fracture path through the microstructure. The results showed that the rate of fatigue-crack propagation was increased by about 30 per cent by moisture in the argon.

Fractographic analyses showed that the crack path in the dry-argon atmosphere was transgranular. In the humid-argon atmosphere, the crack path was predominantly transgranular with respect to prior austenitegrain boundaries, but appeared to be partly intergranular with respect to subboundaries. The fracture surfaces of the specimens were covered with fatigue striations regardless of the testing environment, an indication that the mechanism of crack growth was similar in both environments, even though the fracture surfaces of the specimens fatigued in dry argon were rougher. Therefore, although moisture in the argon environment accelerated crack growth by about 30 per cent, it apparently did not change the mechanism of crack growth. Evidently the effect of moisture in the environment is to promote striation-type crack growth along paths such as subboundaries. A comparison of fractographic results with those of previous work on hydrogen-accelerated fatigue-crack growth in 250-grade maraging steel indicates that in 300-grade maraging steel the increased rate of fatigue-crack growth in the humid environment is not hydrogen-induced.     

Wedge crack nucleation in Type 316 stainless steel

Type 316 austenitic steel has been heat-treated to produce a range of grain sizes and then creep-tested at 625° C at various stresses so as to examine the nucleation and the factors which effect the nucleation of grain-boundary triple point or wedge cracks. An internal marker technique was used to evaluate the extent of the grain-boundary sliding in relation to the total creep strain. Triple point crack nucleation occurred over the entire range of grain sizes and stresses examined when the product of the stress and grain-boundary displacement reached a critical value; the effective surface energy for grain boundary fracture, estimated using an expression derived by Stroh, was in approximate agreement with the surface free energy value indicating that only limited relaxation occurred by plastic deformation. The first cracks were observed to form along grain boundary facets perpendicular to the applied stress direction and with the sliding grain boundaries at high angles (60 to 80°) to the crack growth direction. Subsequent cracking occurred under conditions which deviated slightly from this initial condition, and the increase in crack density with strain was expressed in terms of geometrical factors which take account of the orientation effects.     

Conditions of invariance of corrosion crack resistance characteristics

Conclusions It has been established that for a number of materials the condition of invariance of fracture toughness depends not only upon the type of material but also upon its structure.For a high-strength steel with a martensitic structure the kinetics of subcritical crack growth and also the parameter K_Iscc are sensitive to the original austenitic grain size. Heat treatment for coarse grains has a favorable influence on the corrosion crack resistance of such a steel. The creation in coarse-grained steel of serrated austenitic grain boundaries leads to an additional increase in resistance to corrosion crack growth.The generally accepted criterion of invariance of fracture toughness Eq. (1) is unsuitable as a condition guaranteeing no change in corrosion crack resistance parameters. The value of the coefficient A_c in Eq. (2), which characterizes the condition of obtaining the parameter K_Iscc independent of sample thickness, is determined by the structure of the material and for the systems considered is more than 500.Corrosion cracks in steel with a martensitic structure may have a complex morphology dependent upon the subcritical crack growth mechanism, the size of the austenitic grains, and the form of their boundaries. In contrast to fine-grained and overheated steel, for which intergranular subcritical crack growth is characteristic, in steel with serrated grain boundaries the subcritical crack growth mechanism is more complex. It was also observed that in the center layers of thick samples there is primarily transgranular failure replaced by intergranular at the transition to the surface layers.To determine the effective stress intensity factor at the tip of a corrosion crack with a complex trajectory, a method based on determining the pliability of a sample with a crack propagating in a curved trajectory was found to be effective.Translated from Fiziko-Khimicheskaya Mekhanika Materialov, Vol. 17, No. 3, pp. 24–33, May–June, 1981.     

Correlation of grain-boundary precipitates parameters with fracture toughness in an Al–Cu–Mg–Ag alloy subjected to long-term thermal exposure

The effect of thermal exposure on grain-boundary precipitation in Al–Cu–Mg–Ag alloy was studied using quantitative transmission electron microscopy. Grain-boundary precipitate parameters, such as average size, number density and precipitate-free zone width, were measured. The effective diameter of precipitates, number of precipitates per grain-boundary area and area fraction of precipitates on the grain boundary were calculated. These data were applied to a grain-boundary fracture model to calculate grain-boundary fracture strain. The calculated fracture strains, in turn, were used to check the validity of two existing models of fracture toughness, which are based on grain-boundary nucleation of cracks and their propagation through precipitate-free zones. The fracture toughness model of Hornbogen and Graf closely agrees with the experimental results.     

THE GROWTH OF SMALL FATIGUE CRACKS IN A LOW CARBON STEEL; THE EFFECT OF MICROSTRUCTURE AND LIMITATIONS OF LINEAR ELASTIC FRACTURE MECHANICS

The growth characteristics of small fatigue cracks were studied under rotary bending in a low carbon steel prepared with two ferrite grain sizes of 24 and 84 μm, and were compared with the growth characteristics of large through cracks in fracture mechanics type specimens. The effect of microstructure on crack growth rates and the interaction in growth behaviour between two neighboring small cracks were examined experimentally, and also the critical crack lengths above which linear elastic fracture mechanics (LEFM) is applicable were evaluated for small crack growth and for fatigue crack thresholds. It is found that small cracks grow much faster than large ones and also show growth rate perturbations due to grain boundaries. It is indicated that the critical crack lengths for fatigue crack thresholds are significantly shorter than those for small crack growth.     

Cyclic stress effects on the grain boundary cracking in Al-Mg solid solution

The difference in the grain boundary deformation between statically and cyclically crept specimens of Al-Mg solid solution has been investigated at the temperature of 580 K and for the peak stress level of 15 to 20 M Pa. In statically crept specimens, the grain boundaries deform irregularly and no crack is formed either at the triple point or along the serrated boundaries. However, in cyclically crept specimens, where the stress frequency, stress amplitude and the ratio of on-load to off-load time are 3 cycles per minute, 90% of maximum peak stress and less than 1, respectively, the grain boundaries remain smooth and wedge-type cracks are formed at the triple points, which results in intercrystalline fracture. On the basis of the experimental observations it is believed that cyclic stressing enhances grain boundary sliding through an accelerated recovery with the help of mechanically generated excess vacancies during cycling. However, due to the constraints of the grain alignment, boundary sliding becomes very difficult and creates an intercrystalline fracture at a triple point. On the other hand, under static stress, since the grain boundary is serrated to decrease the stress concentration at a triple point, a crack hardly forms at the triple point.     

Roles of precipitates on corrosion fatigue crack growth of high-strength steels in corrosive environments

The effect of microstructures on resistance to corrosion fatigue cracking and fracture surface morphology for age-hardened steels were investigated in a 3.5% NaCl aqueous solution under a cathodic potential of –0.85 V (Ag/AgCl). The free corrosion was about –0.63 V (Ag/AgCl). The resistance to corrosion fatigue cracking of materials containing coherent precipitates in the matrix (underaged conditions) was less than that of materials containing incoherent precipitates (reheated conditions) at equal strength levels. Accelerated fatigue crack growth rates of the underaged material in the aqueous solution were followed by cracking along prior-austenite grain boundaries, due to hydrogen embrittlement, while the overaged material did not show accelerated fatigue crack growth rates and had fracture surfaces similar to those in air. The difference in the fracture surfaces of both materials in air and in the aqueous solution was considered to depend on the ease of diffusion of hydrogen to the prior-austenite grain boundaries. It is concluded that incoherent precipitates in the matrix made hydrogen accumulation at prior-austenite grain boundaries much slower than for coherent precipitates.     

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.     

LIMITATIONS OF LINEAR ELASTIC FRACTURE MECHANICS IN RESPECT OF SMALL FATIGUE CRACKS AND MICROSTRUCTURE

The growth characteristics of small fatigue cracks were investigated under rotary bending in a low alloy steel prepared with two prior austenite grain sizes of 15 μm (fine grain) and 91 μm (coarse grain). The influence of grain boundaries on crack growth rate and the crack aspect ratio was examined, and the critical crack length above which linear elastic fracture mechanics (LEFM) is applicable was evaluated for a growing small crack. When the surface crack length is shorter than three grain diameters (3d), crack growth rates decrease near the grain boundaries. Aspect ratios are also affected by the microstructure and thus vary widely. Cracks longer than 3d are not influenced by the microstructure, but they grow faster than would be expected based on LEFM until their lengths reach 3d+ 150 μm. This behaviour may be attributed to the difference in crack closure between small cracks and large cracks. If the contribution of crack closure to the growth of small cracks can be established experimentally or analytically, the critical crack length above which LEFM is applicable would be 3d. However, because it is difficult to evaluate crack closure, 3d+ 150 μm is considered to be the critical crack length for engineering applications.