Near- threshold fatigue crack growth in copper and alpha- brass: Grain- size and environmental effects

The fatigue propagation rates and fatigue threshold ( ΔK _th) values were studied (R = 0.1 and frequency = 20 Hz) on copper and 70-30 α-brass of two different grain sizes in laboratory air and dry argon. With decreasing grain size, the threshold increased in copper, while it decreased in α-brass. These results suggest that in copper, crack tip plasticity considerations were more important in determining the threshold values than crack closure effects. Dry argon increased ΔK _th slightly in copper and more significantly in α-brass. A transition from completely transgranular to partially intergranular and back to completely transgranular cracking was observed with decreasing crack growth rates in both materials and environments. The growth rates for which intergranular cracking was obtained were found to be consistent with a hydrogen embrittlement mechanism, associated with adsorption of water molecules and dislocation transport of hydrogen.     

The growth of small fatigue cracks in A286 steel

Fatigue crack propagation in high-strength A286 steel was studied by comparing crack growth rates determined from: (1) conventional long-crack propagation tests, (2) closure-free long-crack tests at constant K_max, and (3) small-crack propagation tests. Small-crack growth rates were measured by following the growth of surface cracks in samples cycled from near-zero stress to 0.5 or 0.8σ_y. While most of the surface cracks became dormant shortly after nucleation, some grew into long cracks, and some of these propagated at cyclic stress intensities below the long-crack threshold, ΔK_th (or ΔK _th ^eff , the threshold cyclic stress intensity after crack closure effects have been removed). Surface cracks grew more rapidly than long cracks at the same ΔKor ΔK_eff. The small-crack effect disappeared when the crack-tip plastic zone size became greater than the grain size. The results show that the absence of crack closure is only one of several factors that influence short-crack growth in A286 steel. Both peak stress and microstructural effects are important. Microstructural effects are apparently responsible for subthreshold crack growth; the cracks that grow at ΔK < ΔK _th ^eff form and grow in statistically weak regions of the microstructure.     

Effects of temper level on the dependence of fatigue crack growth threshold and crack closure on the prior austenitic grain size

An attempt has been made to systematically investigate the effects of microstructural parameters, such as the prior austenite grain size (PAGS), in influencing the resistance to fatigue crack growth (FCG) in the near-threshold region under three different temper levels in a quenched and tempered high-strength steel. By austenitizing at various temperatures, the PAGS was varied from about 0.7 to 96 μm. The microstructures with these grain sizes were tempered at 200 °C, 400 °C, and 530 °C and tested for fatigue thresholds and crack closure. It has been found that, in general, three different trends in the dependence of both the total threshold stress intensity range, ΔK _th , and the intrinsic threshold stress intensity range, ΔK _{eff, th} , on the PAGS are observable. By considering in detail the factors such as cyclic stress-strain behavior, environmental effects on FCG, and embrittlement during tempering, the present observations could be rationalized. The strong dependence of ΔK _th and ΔK _{eff, th} on PAGS in microstructures tempered at 530 °C has been primarily attributed to cyclic softening and thereby the strong interaction of the crack tip deformation field with the grain boundary. On the other hand, a less strong dependence of ΔK _th and ΔK _{eff, th} on PAGS is suggested to be caused by the cyclic hardening behavior of lightly tempered microstructures occurring in 200 °C temper. In both microstructures, crack closure influenced near-threshold FCG (NTFCG) to a significant extent, and its magnitude was large at large grain sizes. Microstructures tempered at the intermediate temperatures failed to show a systematic variation of ΔK_th and ΔK_{eff, th} with PAGS. The mechanisms of intergranular fracture vary between grain sizes in this temper. A transition from “microstructure-sensitive” to “microstructure-insensitive” crack growth has been found to occur when the zone of cyclic deformation at the crack tip becomes more or less equal to PAGS. Detailed observations on fracture morphology and crack paths corroborate the grain size effects on fatigue thresholds and crack closure. K.S. RAVICHANDRAN, formerly Research Scholar, Department of Metallurgy, Indian Institute of Science     

Elevated-temperature fatigue crack growth

The fatigue crack growth behavior of MAR-M200 single crystals was examined at 982 °C. Using tubular specimens, fatigue crack growth rates were determined as functions of crystallographic orientation and the stress state by varying the applied shear stress range-to-normal stress range ratio. Neither crystallographic orientation nor stress state was found to have a significant effect on crack growth rate when correlated with an effective ΔK which accounted for mixed-mode loading and elastic anisotropy. For both uniaxial and multiaxial fatigue, crack growth generally occurred normal to the principal stress direction and in a direction along which ΔK _II vanished. Consequently, the effective ΔK was reduced to ΔK_I and the rate of propagation was controlled by ΔK _I only. The through-thickness fatigue cracks were generally noncrystallographic with fracture surfaces exhibiting striations in the [010], [011], and [111] crystals, but striation-covered ridges in the [211] specimen. These fracture modes are contrasted to crystallographic cracking along slip bands observed at ambient temperature. The difference in cracking behavior at 25 and 982 °C is explained on the basis of the propensity for homogeneous, multiple slip at the crack tip at 982 °C. The overall fracture mechanism is discussed in conjunction with Koss and Chan’s coplanar slip model.     

The influence of aqueous environments on low δK and high ΔK fatigue crack propagation behavior in low carbon structural steels

The influence of aqueous environments on fatigue crack propagation behavior was investigated for two types of structural steel (SB42 and HT80) in pure and 3 pct NaCl water under freely corroding conditions. In the intermediate to high ΔK region, fatigue crack propagation rates were higher in both aqueous environments and in 1 atm hydrogen than in air for both types of steel, and the acceleration effect increased power functionally with decreasing frequency from 5 to 0.0005 Hz. Such a crack growth acceleration property was explained by the mechanism of cyclically induced hydrogen embrittlement, as shown by the brittle striations formed on the fracture surfaces. On the other hand, in the lower ΔK region, both aqueous environments inversely suppressed crack growth and enhanced the threshold stress intensity factor range ΔK _th just above the ΔK _th in air, while only in aerated 3 pct NaCl water was the crack observed to grow even under the condition below the ΔK _th in air, not showing the threshold. Probable mechanisms for such fairly complex environmental effects were also suggested.     

The effect of tempering temperature on near- threshold fatigue crack behavior in quenched and tempered 4140 steel

Fatigue crack growth in compact tension samples of high purity 4140 steel quenched and tempered to various strength levels was investigated. Tempering temperatures of 200, 400, 550, and 700 °C produced yield strengths from 1600 to 875 MPa, respectively. Crack propagation and crack closure were monitored inK-decreasing tests performed underR = 0.05 loading conditions in laboratory air. Results indicated that as the yield strength increased the crack growth rate increased at a given ΔK and ΔK_th decreased. Threshold values varied from 2.8 MPa m^1/2 (200 °C temper) to 9.5 MPa m_1/2 (700 °C temper). Cracks in the 200 °C tempered samples grew by an intergranular mechanism following prior austenite grain boundaries probably caused by hydrogen embrittlement or tempered martensite embrittlement. Tempering above 200 °C produced transgranular fatigue crack growth. The level of crack closure increased with tempering temperature and with crack propagation in a given tempered condition. Crack closure was caused by a combination of plasticity-induced and oxide-induced mechanisms. The use of an effective stress intensity range based on crack closure consolidated the fatigue crack growth curves and the threshold values for all tempering temperatures except 200 °C. Formerly Graduate Research Assistant, Department of Materials Science and Engineering, Stanford University, Stanford, CA. Formerly Professor, Department of Materials Science and Engineering, Stanford University, Stanford, CA.     

Near-threshold fatigue crack growth in 8090 Al-Li alloy

Near-threshold fatigue crack growth was studied in 8090-T8771 Al-Li alloy tested in moist laboratory air. The testing was conducted using (1) the ASTM E-647 load-shedding procedure, (2) a power-law load-shedding procedure, and (3) a constant-amplitude (CA) loading procedure. Crack closure in the three procedures was analyzed. In reconciling fatigue crack growth rates (FCGRs) with different crack closure levels under identical testing parameters, the conventional ΔK _eff (=K _max —K _op) fails to correlate the test data and the modified ΔK eff (=K _max - _χK_op, where χ is the shielding factor, defined by an energy approach) is proven to be the true crack driving force. A parallel slip-rupture model is proposed to describe the mechanism of near-threshold fatigue crack growth in this alloy. The model explains the mode transition from crystallographic slip band cracking (SBC) to subgrain boundary cracking (SGC)/brittle fracture (BF) in terms of a microstructure-environment synergy. The transition is related to the material’s short-transverse grain size.     

Fatigue crack propagation in aluminum-base copper alloys

Fatigue crack propagation ratesda/dN in binary Al alloys with 3.6 wt pct Cu and 6.3 wt pct Cu and commercial 2024 aged at 21°C were compared with 99.95⁺ wt pct aluminum. Omitting an anomalous region at lowΔK, the extrapolated rates for “pure” aluminum are more than 100 times greater than those in the three alloys at the same ΔK. The data for the alloys fit into a single scatter band of a factor of three. It was suggested thatda/dN varies inversely with the square of the strength of the alloy but that another parameter related to the fatigue crack propagation energy per unit area is also important. Theda/dN vs ΔK curves were determined for 3.6 wt pct Cu single crystals aged seven days at 21°C which containGP zones and two and seven days at 160°C which contain mixtures ofθ′ andθ′’. No systematic variation of (da/dN _Δ with crystallographic orientation was discerned, but the naturally aged specimen had a strong orientation dependence on crack initiation. At low ΔK 21°C aged specimens gave the lowestda/dN while at high ΔK the warm aged specimens gave the lower values ofda/dN. Measurement ofda/dN vs ΔK curves were conducted on specimens of 3.6 wt pct Cu with 1 mm equiaxed grains aged for various times at 130°C, 160°C, and 190°C. All warm aged specimens experienced brittle intergranular fracture at sufficiently high ΔK. The transition ΔK where intergranular fracture first appears is inversely proportional to the aging temperature. The change of fracture mode from intra to intergranular occurs gradually over a broad range of ΔK which shifts to lower ΔK with increase in aging temperature. This research was supportd by U.S. Air Force Office of Scientific Research, Office of Aerospace REsearch, Grant No. AF-AFOSR-73-2431.     

The fatigue crack growth behavior of electron-beam welded a286 superalloy

Fatigue crack growth curves(Δa/ΔN =f(K _max )) were measured with 2.5 mm thick sheets of electron beam welded iron base superalloy A286. Fatigue testing frequency was 21 kHz,R = −1 (mean stress zero) and the environment was noncorrosive silicone oil at 20 °C. Two series of samples with different welding conditions were tested. One series was welded perfectly, whereas the second contained microcracks within the weld and the heat affected zone. It was shown that the crack growth rate in the base metal is slower than in the weld. The threshold stress intensity factorK _th of the base metal is 14 MNm^-3/2 and that of the weld, 10 MNm ^-3/2 . However, at higherK _max values, the crack grows more rapidly in the weld than in the base metal; for example, the crack growth rate is 16 times higher at K_max = 20 MNm ^-3/2 . Microcracks introduced by an imperfect welding process do not influence the fatigue cracking behavior in the threshold regime; atK ^max = 15 MNm^-3/2, however, the crack growth rates differ by an order of magnitude. Fractographic examination shows considerable differences in the fracture appearance of weld, heat affected zone, and base material. Weld and base metal display ductile fracture surfaces and the heat affected zone is characterized by crystallographic fracture facets.     

Initiation and growth of small fatigue cracks in a Ni-base superalloy

This article reports research on the initiation and growth of small fatigue cracks in a nickel-base superalloy (produced commercially by INCO as INCOLOY* 908) at 298 and 77 K. The experimental samples were square-bar specimens with polished surfaces, loaded in fourpoint bending. The crack initiation sites, crack growth rates, and microstructural crack paths were determined, as was the large-crack growth behavior, both at constant load ratio (R) and at constant maximum stress intensity (K _max). Small surface cracks initiated predominantly at (Nb,Ti)_xC_y, inclusion particles, and, less frequently, at grain boundaries. Small cracks grew predominantly along {111} planes in individual grains and were perturbed or arrested at grain boundaries. For values of ΔK above the large-crack threshold, ΔK _th, the average rate of smallcrack growth was reasonably close to that of large cracks tested under closure-free conditions. However, short-crack growth rates varied widely, reflecting the local heterogeneity of the microstructure. The threshold cyclic stress (Δσ_th) and the threshold cyclic stress intensity (ΔKσ_th) for small surface cracks were measured as functions of the crack size, 2c. The results suggest that a combination of the fatigue endurance limit and the threshold stress intensity for closure-free growth of large cracks can be used to define a fatigue-safe load regime. formerly with Lawrence Berkeley Laboratory     

Corrosion Fatigue Crack Initiation in a Mode II Notch Specimen

The stress intensityK _II of a Mode II specimen was calculated using a finite element methodvia theJ integral. The site, direction, and the threshold value for crack initiation from the notch under cyclic Mode II loading in air, in water, and under dynamic charging with hydrogen were investigated. The results showed that the Mode II fatigue crack in a high strength steel initiated at or close to the site of the maximum principal stress, rather than at the site of the maximum shear stress, and the subsequent crack growth was oriented approximately normal to the direction of the maximum principal stress. The site and direction of crack initiation in water and under dynamic charging with hydrogen were similar but different from that in air. The threshold values for crack initiation in air, in water, and under dynamic charging were 28.8, 12.3, and 10.2 MPa m^1/2, respectively. The fracture surface of a corrosion fatigue crack in water and under dynamic charging consisted of intergranular facets at low ΔK _II values but of quasi-cleavage at higher ΔK _II values and were different from those in air.     

Influence of corrosive environments on near-threshold fatigue crack growth in 403 stainless steel

The near-threshold fatigue crack growth behavior of 403 stainless steel has been investigated in low O₂ steam (<1 ppm), high O₂ steam (40 ppm), and boiling water with various concentrations of NaCl and Na₂SO₄ at a test frequency of 160 Hz. High O₂ steam tends to increase the crack propagation rates in the threshold region, relative to low O₂ steam. Values of threshold stress intensity range, ΔK_th, slightly increase with an increase in the concentration of NaCl in the solution. During threshold crack growth, the percentage of intergranularity decreases with a decrease inAK. Varying pH from 5.0 to 10.0 in a 0.1 gm NaCl plus 1.0 gm Na₂SO₄ per 100 ml H₂O solution does not affect the rates of near-threshold crack propagation. However, increasing the hydrazine level from 30 to 10⁷ ppb in the same salt solution enhances the resistance to crack growth while reducing the percentage of intergranular fracture to nearly zero.     

On the mechanism of fatigue crack growth in silicon nitride

The mechanism of fatigue crack growth in silicon nitride under the experimental conditions utilized is found to be of a cyclic nature, as contrasted to a form of static fatigue observed in some other ceramic systems. Conventional methods of analysis of the rate of fatigue crack growth in terms of ΔK_eff are not applicable, because the results of the experimental portion of this investigation show that ΔK_eff can decrease as the rate of fatigue crack growth increases. A mechanism which involves the formation of microcracks caused by a wedge effect which develops during the unloading portion of a cycle is discussed and evaluated. The wedge effect results from crack closure, which arises due to the roughness of the intergranular fracture surface as well as to debris trapped between the opposing fracture surfaces. In the proposed mechanism, the extent of crack advance per cycle is limited because of the decrease in stress intensity factor with crack advance in a given cycle associated with the wedge effect. The quantitative results of a semiempirical analysis of tests carried out in either air or vacuum are in agreement with some unusual experimental trends.     

High frequency stage I corrosion fatigue of austenitic stainless steel (316L)

High frequency (123 Hz) fatigue crack propagation studies were conducted under rising ΔK conditions (R-ratio = 0.22) on single edge notch specimens of austenitic stainless steel (type 316L) that contained an annealed precrack. Tests were conducted in near neutral (pH 5.5) solutions of 1 M NaCl and 1 M NaCl + 0.01 M Na₂S₂O₃ under potentiostatically controlled conditions and in desiccated air. Attention was directed primarily to the near threshold behavior and the stage I (crystallographic) region of cracking. Good mixing between the crack solution and bulk solution was obtained and crack retardation and arrest effects, due to surface roughness induced closure, were minimized at high anodic potentials by electrochemical erosion. Thermodynamic considerations showed that hydrogen played no role in fatigue crack propagation. Analysis of the results in terms of the estimated effective cyclic stress intensity, ΔK _eff, showed a systematic effect of potential on the average crack growth increment per cycle,da/dN. Anodic dissolution processes were considered to make an insignificant contribution toda/dN. A model was proposed for stage I fatigue cracking based on the effect of oxide nucleation rate on restricted slip reversal. The essential features of the model were considered to be relevant to cracking in aqueous environments and in desiccated air.     

Variability of large-crack fatigue-crack-growth thresholds in structural alloys

The fatigue threshold of large cracks is known to show substantial variations due to microstructural variability in structural alloys. The ΔK _th variations are dependent on the stress ratio (R); they are extremely large at low R ratios, e.g., R<0.5, but are drastically reduced at high R ratios (R>0.8). The origins of these large variations due to intrinsic and extrinsic mechanisms are examined by theoretical analyses. First, an intrinsic fatigue crack growth (FCG) threshold model is developed for structural alloys by considering the cyclic slip process at the crack tip. Second, the effects of extrinsic mechanisms such as residual plastic stretch, crack deflection, fracture-surface roughness, and oxide wedging are considered both individually and concurrently in order to delineate their relative contributions to threshold variability. The theoretical results indicate that the intrinsic threshold depends on the elastic properties, magnitude of the Burgers vector, yield stress, and Taylor factor (i.e., texture), but is independent of the R ratio or the maximum applied stress intensity factor, K _max. The large variability of ΔK _th at low R ratios and their corresponding dependence on K _max appear to arise from various crack closure mechanisms. Applications of the threshold models to structural alloys show good agreement between theory and experimental data from the literature for steels, Ti, Al, Ni, Cu, Nb, and Mo alloys.     

Influence of impurity segregation on temper em brittlement and on slow fatigue crack growth and threshold behavior in 300-M high strength steel

Interactions between hydrogen embrittlement and temper embrittlement have been examined in a study of fracture and low growth rate (near-threshold) fatigue crack propagation in 300-M high strength steel, tested in humid air. The steel was investigated in an unembrittled condition (oil quenched after tempering at 650°C) and temper embrittled condition (step-cooled after tempering at 650°C). Step-cooling resulted in a severe loss of toughness (approximately 50 pct reduction), without loss in strength, concurrent with a change in fracture mode from micr ovoid coalescence to inter granular. Using Auger spectroscopy analysis, the embrittlement was attributed to the cosegregation of alloying elements (Ni and Mn) and impurity elements (P and Si) to prior austenite grain boundaries. Prior temper embrittlement gave rise to a substantial reduction in resistance to fatigue crack propagation, particularly at lower stress intensities approaching the threshold for crack growth(x0394;K _o). At intermediate growth rates (10^-5 to 10^-3 mmJcycle), propagation rates in both unembrittled and embrittled material were largely similar, and only weakly dependent on the load ratio, consistent with the striation mechanism of growth observed. At near-threshold growth rates (<10⁻⁵ to 10⁻⁶ mmJcycle), embrittled material exhibited significantly higher growth rates, 30 pct reduction in threshold ΔK_o values and intergranular facets on fatigue fracture surfaces. Near-threshold propagation rates (and ΔK_o values) were also found to be strongly dependent on the load ratio. The results are discussed in terms of the combined influence of segregated impurity atoms (temper embrittlement) and hydrogen atoms, evolved from crack tip surface reactions with water vapor in the moist air environment (hydrogen embrittlement). The significance of crack closure concepts on this model is briefly described. ntmis]formerly with the Lawrence Berkeley Laboratory, University of California in Berkeley. Formerly with the Lawrence Berkeley Laboratery, University of California in Berkeley.     

The influence of interparticle spacing on cyclic deformation and fatigue crack propagation in an aluminum-4 Pct copper alloy

A high purity Al-4 pct Cu alloy has been overaged for two different times at 400°C giving interparticle spacings (λ) of about 0.53 and 1.37 μm. Cyclic plasticity of the alloy with the smaller interparticle spacing can be explained in terms of plastic deformation behavior controlled by the structure whereas that for the alloy with the larger interparticle spacing is controlled by the matrix. The fatigue lives of the weaker alloy (λ = 1.37 μm) may be accurately predicted using the models of Coffin-Manson and Tomkins, however, these models are not applicable to the stronger alloy (λ = 0.53 μm). It was found that the crack tip opening displacement at the threshold stress intensity range (ΔK_th) was equivalent to the interparticle spacing. ΔK_th is related to the cyclic yield stress, σ_cy and the interparticle spacing in the following manner: ΔK_th ≈ (2 Eλσ_cy)^1/2, whereE is the modulus of elasticity. In the present case, the term λσ_cy is constant, giving the impression that ΔK_th is independent of the mechanical properties and microstructure. At very low growth rates, however, the fatigue crack growth is independent of these parameters and also the method of cyclic deformation. A transition to higher crack growth rates occurs when the plastic zone size reaches approximately one-seventh of the specimen thickness, allowing a nonplanar crack front to be developed. The value of the stress intensity range (ΔK_T) at this transition was found to be dependent upon the interparticle spacing according to the relation: ΔK_Tλ = 9.6 Pa-m^3/2. Formerly Lecturer and Research Associate, Department of Mechanical Engineering, University of Waterloo     

Aqueous environmental crack propagation in high-strength beta titanium alloys

The aqueous environment-assisted cracking (EAC) behavior of two peak-aged beta-titanium alloys was characterized with a fracture mechanics method. Beta-21S is susceptible to EAC under rising load in neutral 3.5 pct NaCl at 25 °C and −600 mV_SCE, as indicated by a reduced threshold for subcritical crack growth (K _TH ), an average crack growth rate of up to 10 μms, and intergranular fracture compared to microvoid rupture in air. In contrast, the initiation fracture toughness (K _ICi ) of Ti-15-3 in moist air is lower than that of Beta-21S at similar high σ_YS (1300 MPa) but is not degraded by chloride, and cracking is by transgranular microvoid formation. The intergranular EAC susceptibility of Beta-21S correlates with both α-colonies precipitated at β grain boundaries and intense slip localization; however, the causal factor is not defined. Data suggest that both features, and EAC, are promoted by prolonged solution treatment at high temperature. In a hydrogen environment embrittlement (HEE) scenario, crack-tip H could be transported by planar slip bands to strongly binding trap sites and stress/strain concentrations at α colony or β grain boundaries. The EAC in Beta-21S is eliminated by cathodic polarization (to −1000 mV_SCE), as well as by static loading for times that otherwise produce rising-load EAC. These beneficial effects could relate to reduced H production at the occluded crack tip during cathodic polarization and to increased crack-tip passive film stability or reduced dislocation transport during deformation at slow crack-tip strain rates. High-strength β-titanium alloys are resistant, but not intrinsically immune to chloride EAC, with processing condition possibly governing fracture. Formerly Graduate Research Associate, University of Virginia Formerly Graduate Research Associate, University of Virginia     

A transgranular fatigue crack growth model based on restricted slip reversibility

This article presents a transgranular fatigue crack growth model based on a restricted slip reversal process where the transgranular crack growth rate is related to the cyclic plastic strain range ahead of the crack tip. Upon applying deformation and fracture kinetics theories, a physically based constitutive law for fatigue crack growth rate is derived. In the absence of any environmental contributions to crack growth, the model takes the form of the Paris equation with a power law exponent of 3 at positiveR values. The model expresses the fatigue crack growth rate explicitly in terms of material properties, such as yield strength, work-hardening coefficient, microstructural quantities such as activation energy, activation volume, and work factor, as well as test constraints such asΔK andR. The absence of a fatigue threshold is predicted for test conditions where environment does not influence the crack growth process and the material microstructure remains stable. Formerly Graduate Student, Department of Mechanical Engineering, University of Ottawa.     

Effect of threshold stress intensity on fracture mode transitions for hydrogen-assisted cracking in AISI 4340 steel

Fracture mode transition in hydrogen-assisted cracking (HAC) of AISI 4340 steel has been studied from an equilibrium aspect at room temperature with 8.6-mm-thick double cantilever beam (DCB) specimens. The threshold stress intensity,K _th , necessary for the occurrence of HAC and the corresponding fracture surface morphology have been determined as a function of hydrogen pressure and yield strength. The K _th increases with decrease in hydrogen pressure at a given yield strength and also with decrease in yield strength at a given hydrogen pressure. AsK _th increases, the corresponding HAC fracture mode changes from the intergranular (IG) and quasi-cleavage (QC) modes to the microvoid coalescence (MVC) mode. The experimental results indicate that the critical hydrogen concentration for crack extension in the IG mode is higher than that for crack extension in the MVC mode. The fracture mode transition with varying hydrogen pressure and yield strength is discussed by simultaneously considering the micromechanisms for HAC and the hydrogen pressure and yield strength dependencies ofK _th .