Threshold Stress Intensity Factor Kth Research Articles

A phase field model for elastic-gradient-plastic solids undergoing hydrogen embrittlement

We present a gradient-based theoretical framework for predicting hydrogen assisted fracture in elastic-plastic solids. The novelty of the model lies in the combination of: (i) stress-assisted diffusion of solute species, (ii) strain gradient plasticity, and (iii) a hydrogen-sensitive phase field fracture formulation, inspired by first principles calculations. The theoretical model is numerically implemented using a mixed finite element formulation and several boundary value problems are addressed to gain physical insight and showcase model predictions. The results reveal the critical role of plastic strain gradients in rationalising decohesion-based arguments and capturing the transition to brittle fracture observed in hydrogen-rich environments. Large crack tip stresses are predicted, which in turn raise the hydrogen concentration and reduce the fracture energy. The computation of the steady state fracture toughness as a function of the cohesive strength shows that cleavage fracture can be predicted in otherwise ductile metals using sensible values for the material parameters and the hydrogen concentration. In addition, we compute crack growth resistance curves in a wide variety of scenarios and demonstrate that the model can appropriately capture the sensitivity to: the plastic length scales, the fracture length scale, the loading rate and the hydrogen concentration. Model predictions are also compared with fracture experiments on a modern ultra-high strength steel, AerMet100. A promising agreement is observed with experimental measurements of threshold stress intensity factor Kth over a wide range of applied potentials.

Microscopic Mechanism of Hydrogen Embrittlement in Fatigue and Fracture

The microscope mechanism of hydrogen embrittlement (HE) is overviewed from the viewpoint of Mechanics-Microstructure-Environment Interactions. The plastic deformation (Mechanics) at crack tip for low strength steel is controlled by hydrogen concentration (Environment) to crack tip, eventually resulting in very strong time dependent phenomenon in static fracture and fatigue crack growth. Various typical phenomena in low strength steels which can be understood from the viewpoint of Mechanics-Environment Interactions will be presented. Fracture and fatigue of high strength steels (Microstructure) are strongly influenced by hydrogen. Especially, fatigue crack growth is remarkably accelerated by hydrogen-induced deformation twins. The HE phenomemon of the high-strength steels was applied to a newly inclusion rating method. Hydrogen trapped by nonmetalliec inclusions causes the elimination of fatigue limit at very high cycle fatigue. The values of threshold stress intensity factor KTH in hydrogen for small cracks are much smaller than those for long cracks measured by the standard WOL or CT specimens, which are eventually unconservative for the design of hydrogen components. This phenomenon is similar to the small crack problem in fatigue.

Corrosion Fracture of Structural Metallic Materials: Effect of Electrochemical Conditions in Crack

Abstract: The work is a compressed review based on the summarised results and the original approach for study of corrosion crack growth, taking into account local electrochemical conditions in the crack tip, which was developed at the Karpenko Physico‐Mechanical Institute of NASU. The model scheme of the pre‐fracture zone in the corrosion crack tip, which can be defined by the local values of pH of solution, electrode potential of metalEand stress intensity factorKIis proposed. For its realisation, the special method and testing equipment for corrosion crack growth study and local electrochemical measurements in the crack were developed. The variation of the electrochemical conditions in corrosion cracks was studied, and it has been found that some stabilised levels of the pH andEvalues can be achieved in the tip of a non‐propagating and a propagating crack under static and cyclic loading during of exposure time. On this ground, the method for forecasting of the threshold stress intensity factorKISCCunder stress corrosion cracking was proposed using these characteristic values of pH andE. This method was also adopted for the determination of the threshold stress intensity factorKthunder corrosion fatigue. The special method for determining corrosion fatigue crack growth rate diagrams based on consideration of extreme electrochemical conditions in the crack tip was developed. It has been proven that such diagrams reflect the extreme influence of the environmental factor on corrosion fracture of material, and they may be recommended as the base for the remaining lifetime calculation of the structural elements exploited under environmental conditions.

FATIGUE CRACK GROWTH BEHAVIOUR AND FRACTURE RESISTANCE IN CERAMICS

AbstractFatigue crack growth and the fracture resistance curve (R‐curve) were investigated in a polycrystalline alumina (AD90) and a silicon carbide whisker‐reinforced alumina composite (Al2O3‐SiCw) at room temperature in air using a combined loading technique for stabilizing crack growth, and a surface film technique for monitoring crack length. Fatigue crack growth was evaluated successfully with those experimental techniques. Load shedding tests were performed until the crack became dormant, in order to determine the threshold stress intensity factor Kth. Subsequently, the specimens were used for quasi‐static crack growth tests under a monotonic loading condition. The R‐curves were determined in this experiment; however, fracture resistance did not increase markedly with crack growth. Detailed observations of the crack growth behaviour revealed that the flat R‐curve was attributed to the shielding effect of the fatigue crack tip wake. Thus, the fatigue precrack introduced by the load shedding test was not regarded as an ideal crack for determining the R‐curve. Fractographic observations were performed to investigate the mechanistic difference between fatigue and quasi‐static crack growth. It was found that the cyclic loading produced fretting damage in the wake region and it reduced the shielding effect of the fatigue cracks. Based on the experimental results, the relationship between the fatigue crack growth and the R‐curve is discussed as is the significance of Kth as a material parameter.

Fracture Mechanics Evaluation of Crack Growth and Strength in Gas-Pressure-Sintered Silicon Nitride.

Crack growth behavior was investigated under static and cyclic loads in gas-pressure-sintered silicon nitride (EC-141) using a combined loading technique for stabilizing crack growth and a surface film technique for monitoring crack length. Load shedding tests were performed on two speciments at the loading frequencies of 1 and 10 Hz to evaluate fatigue crack growth until the crack became dormant, in order to determine the threshold stress intensity factor Kth. Then, one of the specimens was used in a fatigue test without the combined loading technique, in which Kth values for different crack lengths were determined. The other specimen was used in the quasi-static test under a monotonic loading condition, in which the fracture resistance curve for the fatigue precrack was measured. The results were compared to those reported in the literature for the same material and for other silicon nitrides. Based on the crack growth characteristics, the fracture strength under various loading conditions involving static, cyclic and monotonic loads was discussed.

Fatigue crack growth in KhN60MVYu nickel alloy at temperatures of 293 and 11�K

1. The results show that when the temperature is reduced from 293 to 11°K the fatigue crack growth rate in Kh60MVYu nickel alloy decreases only insignificantly and only in the near-threshold region. Under the effect of vacuum the rate decreases to a considerably greater extent and in a wider range. 2. The threshold stress intensity factor Kth increases under the effect of both the medium and low temperature (11°K). 3. The size of the plastic zone at the crack tip is independent of the medium and decreases with decreasing temperature. 4. The size of the plastic zone at the point with the abscissa K* corresponds to 2h=3d, both for 293°K and 11°K. At this point the value m changes abruptly from m2=2 to m1=6.

Effect of test temperature on the cracking resistance of a vessel steel with various impurity content

1. The results show that at temperatures of 293 and 623 °K the fatigue crack growth rate in the 15Kh2MFAA and 15Kh2MFA steels coincides in the middle section of the KDFF. At the same time, the threshold stress intensity factor Kth for 15Kh2MFAA steel is higher than for 15Kh2MFA steel. The increase of the stress ratio from 0.1 to 0.7 reduces the fatigue crack growth rate in both steels. 2. The fracture toughness characteristics Kfc1, Kfck, KIc (KQ5%) of the 15Kh2MFAA and 15Kh2MFA steels increase with increase in test temperature and in the temperature range 250–623°K they reach the upper plateau. In the low-temperature range (>123°K) the characteristics Kfc1, Kfck, KIc converge but the distinctive lower plateau does not form. 3. In the low-temperature range (123–200°K) the cyclic nature of loading reduces the fracture toughness characteristics Kfc1, Kfck, and σfc1, σfck in comparison with the values of KIc and σcmax in static loading. 4. At temperatures below 150°K the fracture resistance in static loading of 15Kh2MFAA steel is lower than that of 15Kh2MFA steel, and in the temperature range 150–623°K it is higher than that of 15Kh2MFA steel. Below 243°K the fracture resistance in cyclic loading 15Kh2MFAA steel is higher than that of 15Kh2MFA steel, and in the temperature range 243–623°K it is lower than that of 15Kh2MFA steel.

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

Fatigue crack growth curves(Δa/ΔN =f(Kmax)) 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 factorKth of the base metal is 14 MNm-3/2 and that of the weld, 10 MNm-3/2. However, at higherKmax 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 Kmax = 20 MNm-3/2. Microcracks introduced by an imperfect welding process do not influence the fatigue cracking behavior in the threshold regime; atKmax = 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.

Crack opening displacement and the rate of fatigue crack growth

Using a direct proportionality between the rate of fatigue crack growth and crack opening displacement above a threshold, it is shown that fatigue crack growth data for a wide variety of different materials can be accurately described in terms of the mechanical properties and two material constants; the constant of proportionality A and the threshold stress intensity factorKth. Some 65 sets of data for tests atR ≅ 0 were analysed by computer and it is shown that the approach is valid to growth rates up to about 10−4 in./cycle, i.e. until the onset of crack propagation by dimple formation. It is found thatA can be related to the yield strain for crack growth in non-aggressive environments, and is increased by increasingly severe environments, whileKth is decreased. These changes provide a measure of the severity of the environment. Crack growth rate in non-aggressive environments is shown to be independent of the yield stress and proportional to the strain intensity factor above the threshold. The tabulation ofA andKth values as a function of material, environment and loading conditions provides a systematic engineering approach to estimating rates of fatigue crack growth and in determining the residual lifetimes of flawed structures.