Molecular dynamic simulation of crack propagation in nanocrystalline Ni containing different shapes and types of second phases

In order to investigate the crack propagation in the nanocrystalline Ni containing different types of impurities (Ag, Au, Cu, Pd), several molecular dynamics simulations were carried out using the embedded atom method (EAM). The crack was assumed in a (1 1 1)[1 0 0] system with 10,400 atoms. The impurities were considered in two different shapes of short and long cylinder. The impurities were introduced near the crack tip. To analyze the failure behavior, the strain energy density (G) and strain energy distributions near the crack tip were obtained and studied. The results show that when the shape of impurity is short cylinder, the rate of releasing energy during the crack propagation did not depend on the type of impurity. As for the long cylindrical impurity, palladium exhibited the maximum effect on G.     

Diffraction characterization of microstructure scale fatigue crack growth in a modern Al–Zn–Mg–Cu alloy

SEM-based electron backscattered diffraction (EBSD) measurements characterize constituent-particle nucleated fatigue crack path relative to local grain orientation and crack wake defect distribution for Al–Zn–Mg–Cu alloy 7050-T7451 stressed in moist air. Crack propagation is primarily transgranular; consisting of facets parallel to {1 0 0}, {1 1 0} and high-index planes with no evidence of {1 1 1} slip-based cracking; and is also inter-subgranular involving pre-existing or fatigue process zone generated subgrain boundaries. Dislocation substructure develops close to the fatigue crack surface due to dynamic recovery of crack tip cyclic plasticity. Crack growth through subgrain structure explains the broad occurrence of crack features without a low-index orientation and is justified based on trapped-hydrogen embrittlement. A failure criterion for environmental fatigue modeling must capture a failure mechanism based on: (a) formation of localized defect structure from cumulative cyclic plasticity (perhaps H sensitive), and (b) subsequent embrittlement due to interaction of H trapped at this defect structure with microstructure-sensitive local tensile stresses normal to this weakened interface. Crack interaction with subgrain (and grain) boundaries produces local deflections and branches that arrest over a short distance. Such features should cause a distribution of microstructure-sensitive growth rates.     

Molecular dynamic modelling of fatigue crack growth in aluminium using LEFM boundary conditions

A molecular dynamic (MD) model of a crack in pure aluminium has been developed with isotropic Linear Elastic Fracture Mechanics (LEFMs) boundary displacements that simulates the fatigue crack growth process. The model consists of a cylindrical region filled with atoms around a crack tip and subject to boundary displacements that change due to cyclic loading. A sinusoidal load that produced a $K_{\max }=1.0\text{MPa}\sqrt{\text{m}}$ was applied to produce fatigue crack growth using three different atomic potentials for aluminium at T = 20 K, and a range of different K_min. Each run consisted of the application of fifteen or more loading cycles. In some cases, the crack tip was seen to advance in each cycle typical of fatigue, however, growth was smooth and continuous during the entire cycle with contraction occurring during the unloading phase of the cycle. The model contained 3 × 10⁶ atoms and had a diameter and width of 20 nm. This width was just large enough for fragments of sessile dislocations to form and couple with the glissile dislocations emitted from the crack tip, resulting in work hardening about the crack tip. The model was oriented for cracking on the {1 1 0} plane in the 〈1 0 0〉 direction. Crack advance was observed to be due to a combination of dislocation emission and atomic separation.     

Atomic diffusion in the Fe [0 0 1] ∑ = 5 (3 1 0) and (2 1 0) symmetric tilt grain boundary

Both the formation and diffusion activation energies of single vacancy migrating intra-layer and inter-layer near the Fe [0 0 1] Σ = 5 (3 1 0) and (2 1 0) symmetric tilt grain boundaries have been calculated by using the MAEAM and a MD method. From energy minimization, the vacancy concentration in the second layer is higher than the one in the other layers for both (3 1 0) and (2 1 0) STGBs. By the diffusion activation energies of the vacancies migrating intra-layer and inter-layer, the vacancies located from the first to the eighth layers of (3 1 0) STGB as well as the ones located from the first to the tenth layers of (2 1 0) STGB are favorably migrated to the second layer. Thus there is a vacancy aggregation tendency to the second layer near the grain boundary. For the vacancy migrating intra-layer and inter-layer, the influences of the grain boundary are respectively as far as to the fifth and eighth layers for (3 1 0) STGB as well as to the sixth and tenth layers for (2 1 0) STGB.     

Threshold crack growth behavior of shear and tensile cracks

Crack-face interference-free mode I and mode II crack-growth data was combined with smooth axial (λ = ε_xy/ε_xx = 0) and torsional (λ = ∞) endurance limit data to develop unified crack growth models that incorporate both shear and tensile cracking. The crack growth models incorporated growth from a slip band (including short crack behavior) size crack until the final failure of a long crack, and the ability to switch between crack growth on shear planes to growth on tensile planes. The models successfully predicted smooth specimen crack-face interference-free fatigue lives and gave reasonable estimates of the smooth specimen endurance limits of crack-face interference free tubular tests run at intermediate strain ratios (λ = 3/4, 3/2, and 3). The series of Kitigawa–Takahashi (threshold fatigue) diagrams developed from the models help illustrate the competition between shear and tensile cracking at the fatigue limit under crack-face interference-free crack growth.     

Short cracks initiated in Al 6013-T6 with the focused ion beam (FIB)-technology

The fatigue crack growth behaviour of short corner cracks in the Aluminium alloy Al 6013-T6 was investigated. The aim was to determine the crack growth rates of small corner cracks at a stress ratio of R = 0.1, R = 0.7 and R = 0.8 and to find a possible way to predict these crack growth rates from fatigue crack growth curves determined for long cracks. Corner cracks were introduced into short crack specimens, similar to M(T) – specimens, at one side of a hole (Ø = 4.8 mm) by cyclic compression (R = 20). The precracks were smaller than 100 μm (notch + precrack). A completely new method was used to cut very small notches (10–50 μm) into the specimens with a focussed ion beam. The results of the fatigue crack growth tests with short corner cracks were compared with the long fatigue crack growth test data. The short cracks grew at ΔK-values below the threshold for long cracks at the same stress ratio. They also grew faster than long cracks at the same ΔK-values and the same stress ratios. A model was created on the basis of constant K_max-tests with long cracks that gives a good and conservative estimation of the short crack growth rates.     

Molecular dynamics study of vacancy migration in Al

The embedded atom method (EAM) potential developed for Al was used to study self-diffusion. The vacancy formation and migration energies were obtained both from molecular static calculations at T = 0 and molecular dynamics (MD) calculations near the melting temperature. Applying pure dilatation at T = 900 K, we also obtained the vacancy migration volume. The obtained results are compared with available experimental data.     

Crack initiation in VHCF regime on forged titanium alloy under tensile and torsion loading modes

This paper is focused on the VHCF behavior of aeronautical titanium alloy under tensile and torsion fatigue loadings. Tensile tests were carried out with two different stress ratios: R = −1 and R = 0.1. Both surface and subsurface crack initiations were observed. In the case of subsurface crack initiation several fatigue life controlling mechanisms of crack initiation were found under fully-reversed loading conditions: initiation from (1) strong defects; (2) ‘macro-zone’ borders; (3) quasi-smooth facets and (4) smooth facets. Tests with stress ratio R = 0.1, have shown that initiation from the borders of ‘macro-zones’ becomes the dominant crack initiation mechanism in presence of positive mean stress. Like for the tensile results, surface and subsurface crack initiations were observed under ultrasonic torsion in spite of the maximum shear stress location on the specimen surface. But the real reason for the subsurface crack initiation under torsion was not found.     

Crack Tip Opening Displacement in atomistic modeling of fracture of silicon

We analyze the fracture of single crystal silicon simulated by atomistic modeling with ReaxFF first principles based reactive force field. The simulations are performed at three temperatures: 500 K, 800 K and 1200 K, capturing both brittle and ductile behavior for the selected crystallographic orientation with (1 0 0) as the fracture plane. Three failure mechanisms are observed: bond breaking, amorphization and emission of dislocations. We demonstrate that the Crack Tip Opening Displacement (CTOD) gives a realistic estimate of the fracture toughness of brittle fracture, linking continuum mechanics fracture theory with the direct crack tip atomistic approach. We discuss the physics based mechanisms of failure in silicon in view of the CTOD measurements.     

Localized microtwin formation and failure during out-of-phase thermomechanical fatigue of a single crystal nickel-based superalloy

The deformation and damage mechanisms of a single crystal nickel-based superalloy CMSX-4 have been investigated under out-of-phase thermomechanical fatigue (OP TMF) condition. The deformation was highly localized to the area near the crack tip, where multiple groups of parallel twin plates on {1 1 1} planes formed during the high temperature-compressive half cycle. The atomistic a/6 〈1 1 2〉 twinning shear-based approach is presented which explains the origin of twinning. The localized twins provided a preferential path for crack propagation. OP TMF deformation was dominated by partial dislocation movement with {1 1 1}〈1 1 2〉 slip system, resulting in the formation and propagation of deformation twins.     

Fatigue crack growth and damage characteristics of high-speed rail at low ambient temperature

Low temperature can be a significant problem affecting safety and maintenance of railway. In this study, the fatigue crack growth rate and rolling contact fatigue damage behaviors of high-speed rail material under different temperature conditions were investigated by a series of experiments. The results indicate that the stress and strength of rail material increase with the decrease of ambient temperature. The crack growth rate at 0 °C and − 20 °C is similar with that at 20 °C. While, when the temperature decreases to − 60 °C, the growth rate of crack increases sharply. The promotion of rail embrittlement at low temperature accompanied with the action of high stress causes the rapid failure and increase of surface crack length and subsurface crack damage. Meanwhile, three crack growth mechanism models at different temperatures can be inferred. The brittle fracture mode is increasingly apparent with the temperature decreasing.     

Insights into the structures,energies and electronic properties of nesquehonite surfaces by first-principles calculations

By using the first-principles calculations, the structure, energies and electronic properties of four commonly exposed surfaces for the nesquehonite crystal were investigated. The needle-like nesquehonite whisker is well developed with smooth side faces and irregular hexagonal end faces. Surface energy results indicate that the (1 0 1) surface is the most stable surface and corresponds to the side face. The density of dangling bond has a positive relationship with surface energy and the (1 0 1) surface has the least dangling bonds. In terms of relaxed surface energy, the order of relaxed surfaces is (1 0 1) < (2 0 0)-H < (3 0 1) < (2 0 0)-M < (0 0 4). During surface relaxation, the changes in the length of Mg-O bonds and hydrogen bonds contribute to generating a more stable surface with a lower surface energy. The PDOS (partial density of states) of these surfaces are mainly dominated by Mg and O atoms. A small peak value is found in the PDOS of (1 0 1) and (3 0 1) surfaces, which have less exposed Mg-O bonds. Electron transfer causes changes in the length of Mg-O bonds. A more active surface will obtain a larger value of transferred electrons during surface relaxation.     

Crack precursor size for natural rubber inferred from relaxing and non-relaxing fatigue experiments

Fatigue life prediction for a dumbbell cylindrical natural rubber component under uniaxial tensile loading conditions was performed based on the Thomas fatigue crack growth model for relaxing (R = 0) load cycles and the Mars–Fatemi model for non-relaxing (R > 0) load cycles. By using a self-written program, we proposed a new approach to establish the relation between the power law exponent F and the R ratio in the Mars–Fatemi model. The approach is based on rubber fatigue life (S–N) data rather than crack growth rate and tearing energy (da/dN–T) data, avoiding certain difficulties often encountered using the crack growth method. The results indicate that the relation between F and R is a quadratic or cubic function over the range 0 < R < 0.3. Finally, the quantitative effect of initial crack size on fatigue life was studied. We found that the inferred mean size of crack precursors in the rubber component is around 30–40 μm under both relaxing and non-relaxing loading conditions, and the fluctuation of fatigue life is due to the inhomogeneity of crack precursor size except the factors such as unavoidable variations in testing conditions and specimen variations. The good agreement of inferred crack precursor sizes from different R ratio loading conditions is a strong indication that the Mars–Fatemi model provides a proper accounting for the effects of strain crystallization, and it confirms yet again the understanding that nucleated cracks originate from similarly sized precursors in both relaxing and non-relaxing fatigue experiments.     

Evaluation of crack growth behavior and probabilistic S–N characteristics of carburized Cr–Mn–Si steel with multiple failure modes

The unexpected failures of case-hardened steels in long life regime have been a critical issue in modern engineering design. In this study, the failure behavior of a carburized Cr–Mn–Si steel under very high cycle fatigue (VHCF) was investigated, and a model for evaluating the probabilistic S–N curve associated with multiple failure modes was developed. Results show that the carburized Cr–Mn–Si steel exhibits three failure modes including the surface flaw-induced failure, the interior inclusion-induced failure without the fine granular area (FGA) and the interior inclusion-induced failure with the FGA. As the predominant failure mode in the VHCF regime, the interior failure process can be divided into four stages: (i) the small crack growth around the inclusion, (ii) the stable macroscopic crack growth outside the FGA, (iii) the unstable crack growth outside the fish-eye and (iv) the momentary fracture outside the final crack growth zone. The threshold values are successively evaluated to be 2.33 MPa m^1/2, 4.13 MPa m^1/2, 18.51 MPa m^1/2 and 29.26 MPa m^1/2. The distribution characteristics of the test data in transition failure region can be well characterized by the mixed two-parameter Weibull distribution function. The developed probabilistic S–N curve model is in good agreement with the test data with multiple failure modes. Although the result is somewhat conservative in the VHCF regime, it is acceptable for safety considerations.     

Structural and magnetic study of thin films based on anisotropic ternary alloys FeNiPt2

L1₀ ordered (Fe–Ni)₅₀Pt₅₀ alloy films with perpendicular magnetic anisotropy were successfully prepared by interdiffusing FePt(0 0 1) and NiPt(0 0 1) layers co-deposited on MgO(0 0 1) substrates by MBE. The [0 0 1] growth direction corresponds to the epitaxy of the alloy on the substrate and is the interesting growth orientation to get a perpendicular magnetization. The X-ray diffraction shows a high L1₀ chemical order (S = 0.7 ± 0.1). The easy magnetization direction is perpendicular for all samples. The MFM images display highly interconnected stripes corresponding to up and down orientations of the magnetization. Large uniaxial magnetic anisotropy (K_u = 9.10⁵ J/m³) and suitable magnetic transition temperature (T_C = 400 K) are obtained. The addition of Ni changes the spin–orbit interaction in the FePt compound system, hence causes a decrease of anisotropy, saturation magnetization and coercivity.     

Influence of texture on corrosion rate of AZ31 Mg alloy in 3.5 wt.% NaCl

In this study, AZ31 Mg alloys with different grain orientation were prepared to investigate the influence of texture on corrosion rate in 3.5 wt.% NaCl. Experimental results showed that texture had significant influence on the corrosion rate of AZ31 in 3.5% NaCl. The corrosion rate of AZ31 dramatically increased with the (0 0 0 1) texture intensity decreased and the (1 0 ?1 0)/(1 1 ?2 0) texture intensity increased. The corrosion rate reached a maximum at about 3 h immersion and subsequently decreased slightly due to the formation of a Mg(OH)₂ corrosion product layer. This study indicates that the corrosion rate of AZ31 Mg alloy in NaCl solution can be modified to some extend by controlling texture.     

Crack growth in discontinuous glass fibre reinforced polypropylene under dynamic and static loading conditions

Crack propagation in single edge notched tensile specimens of isotactic polypropylene reinforced with short E-glass fibres has been investigated under both fatigue and creep loading conditions. Fatigue crack propagation (FCP) experiments have been performed at three different frequencies (0.1, 1, 10 Hz) and at a mean applied tensile load of 1200 N. Isothermal creep crack propagation (CCP) tests have been conducted under a constant tensile applied load of 1200 N at various temperatures in the range from 32 to 60 °C. Analysis of FCP data allowed an estimation of the pure fatigue and pure creep components of the crack velocity under the adopted cyclic loading conditions. Crack growth at low frequencies (0.1 and 1 Hz) is mainly associated with a non-isothermal creep process. At higher frequency (10 Hz), the pure fatigue contribution appeared more pronounced. Finally, the comparison of FCP and CCP as a function of the mean applied stress intensity factor confirmed the major contribution of creep crack growth during FCP process at low frequencies.     

Growth,optical and microstructural properties of PbB4O7 plate crystals

Centimeter-sized optical quality plate-like PbB₄O₇ crystals have been grown by Czochralski method. The fundamental absorption edge has been found at 237 nm (corresponding bandgap 5.75 eV) with the distinct sideband protruding up to 300 nm. The crystals are well faceted with the (1 0 0), (0 1 0) and (1 0 1) planes, (1 0 0) surfaces being mostly developed. The etching in diluted nitric acid (5 wt.%) at the temperature of 90 °C have been used to reveal the defect structure and remove melt residuals. The (1 0 0) surface shows the presence of etching pits and twin boundaries. The Kikuchi line pattern and developed microrelief with the roughness of ∼8 nm have been observed by RHEED and AFM, respectively.     

Very high cycle fatigue of nitrided 18Ni maraging steel sheet

Thin sheets of nitrided 18Ni maraging steel are tested under cyclic tension (load ratio R = 0.1) in the very high cycle fatigue (VHCF) regime. The ultrasonic fatigue testing method with a cycling frequency of about 20 kHz has been further developed for these experiments. Sheet specimens with 0.35 mm thickness are mounted on a carrier specimen, they are pre-stressed and are forced to vibrate jointly. Between 10⁷ and 10⁹ cycles, fatigue cracks are initiated exclusively at internal TiN inclusions. The areas of the crack initiating inclusions projected perpendicular to the applied tensile stress are evaluated. The square root of inclusion areas, (area_INC)^1/2 lies between 2.5 μm and 5.3 μm. Considering inclusions as cracks, their stress intensity range is between ΔK_INC = 1.3 MPa m^1/2 and 2.4 MPa m^1/2. The sizes of crack initiating inclusions influence fatigue lifetimes. This is considered in a crack propagation model and by presenting lifetimes versus the stress amplitudes multiplied by (area_INC)^1/12. A mean lifetime of 10⁹ cycles is found at a stress amplitude of 22% of the tensile strength, which is comparable to other high strength steels tested under cyclic tension.