Effects of stress ratio on fatigue crack propagation properties of submicron-thick free-standing copper films

The dominant mechanics and mechanisms of fatigue crack propagation in ca. 500 nm thick free-standing copper films were evaluated at the submicron level using fatigue crack propagation experiments at three stress ratios, R = 0.1, 0.5 and 0.8. Fatigue cracking initiated at the notch root and propagated stably under cyclic loading. The fatigue crack propagation rate (da/dN) vs. stress intensity factor range (ΔK) relation was dependent on the stress ratio R;da/dN, increases with increasing R. Plots of da/dN vs. the maximum stress intensity factor (K_max) exhibited coincident features in the high-K_max region (K_max ? 4.5 MPa m^1/2) irrespective of R, indicating that K_max is the dominant factor in fatigue crack propagation. In this region, the fatigue crack propagated in tensile fracture mode irrespective of the R value. The region ahead of the fatigue crack tip is plastically stretched by tensile deformation, causing necking deformation in the thickness direction and consequent chisel-point fracture. In contrast, in the low-K_max region (K_max < 4.5 MPa m^1/2), the da/dN vs. K_max function assumes higher values with decreasing R; in this region, the fracture mechanism depends on R. At the higher R value (R = 0.8), the fatigue crack propagates in the tensile fracture mode similar to that in the high-K_max region. On the other hand, at the lower R values (R = 0.1 and 0.5), a characteristic mechanism of fatigue crack propagation appears: within several grains, intrusions/extrusions form ahead of the crack tip along the Σ3 twin boundaries, and the fatigue crack propagates preferentially through the intrusions/extrusions.     

Hold-time effect on the elevated-temperature crack growth behavior of solid-solution-strengthened superalloys

The fatigue crack growth behavior of two solid-solution-strengthened superalloys, Ni-based HAYNES^® 230 and HASTELLOY^® X, was studied at 816 and 927 °C in laboratory air. The fatigue crack growth tests were conducted following a baseline triangular waveform of 0.33 Hz. Various hold times were introduced at the maximum load to study the hold-time effect. Fracture mechanics parameters, K, C¹, C_t, and (C_t)_avg, were applied to correlate the crack growth rates at different temperatures for both HAYNES 230 and HASTELLOY X alloys. For both alloys, the fatigue cracking path was mainly transgranular at 816 and 927 °C. The cracking path became dominantly intergranular if the hold time increased to 2 min, indicating that the time-dependent creep damage mechanisms were in control. When the time-dependent damage dominated (temperature ⩾816 °C and hold time ⩾2 min), the crack growth rates can be correlated with C_t or (C_t)_avg parameters. The C_t and (C_t)_avg parameters were capable of consolidating data from different temperatures and different alloys.     

Elucidating the variables affecting accelerated fatigue crack growth of steels in hydrogen gas with low oxygen concentrations

The objective of this study was to quantify the effects of mechanical and environmental variables on oxygen-modified accelerated fatigue crack growth of steels in hydrogen gas. Experimental results show that in hydrogen gas containing up to 1000 v.p.p.m. oxygen fatigue crack growth rates for X52 line pipe steel are initially coincident with those measured in air or inert gas, but these rates abruptly accelerate above a critical ΔK level that depends on the oxygen concentration. In addition to the bulk gas oxygen concentration, the onset of hydrogen-accelerated crack growth is affected by the load cycle frequency and load ratio R. Hydrogen-accelerated fatigue crack growth is actuated when threshold levels of both the inert environment crack growth rate and K_max are exceeded. The inert environment crack growth rate dictates the creation of new crack tip surface area, which in turn determines the extent of crack tip oxygen coverage and associated hydrogen uptake, while K_max governs the activation of hydrogen-assisted fracture modes through its relationship to the crack tip stress field. The relationship between the inert environment crack growth rate and crack tip hydrogen uptake is established through the development of an analytical model, which is formulated based on the assumption that oxygen coverage can be quantified from the balance between the rates of new crack tip surface creation and diffusion-limited oxygen transport through the crack channel to this surface. Provided K_max exceeds the threshold value for stress-driven hydrogen embrittlement activation, this model shows that stimulation of hydrogen-accelerated crack growth depends on the interplay between the inert environment crack growth increment per cycle, load cycle frequency, R ratio and bulk gas oxygen concentration.     

Deformation behavior of a two-phase Mo–Si–B alloy

Mo–Si–B alloys are being considered as possible candidates for high-temperature applications beyond the capabilities of Ni-based superalloys. In this paper, the high-temperature (1000–1400 °C) compression response over a range of quasi-static strain rates, as well as the monotonic and cyclic crack growth behaviors (as a function of temperature from 20 °C to 1400 °C) of a two-phase Mo–Si–B alloy containing a Mo solid solution matrix (Mo(Si,B)) with ∼38 vol% of the T2 phase (Mo₅SiB₂) is discussed. Analysis of the compression results confirmed that deformation in the temperature–strain-rate space evaluated is matrix-dominated, yielding an activation energy of ∼415–445 kJ/mol. Fracture toughness of the Mo–Si–B alloy varies from ∼8 MPa√m at room temperature to ∼25 MPa√m at 1400 °C, the increase in toughness with temperature being steepest between 1200 °C and 1400 °C. S–N response at room temperature is shallow whereas at 1200 °C, a definitive fatigue response is observed. Fatigue crack growth studies using R = 0.1 confirm the Paris slope for the two alloys to be high at room temperature (∼20–30) but decreases with increasing temperature to ∼3 at 1400 °C. The crack growth rate (da/dN) for a fixed value of ΔK in the Paris regime in the 900–1400 °C range, increases with increasing temperature.     

Fatigue crack growth behavior of a Zr58.5Cu15.6Ni12.8Al10.3Nb2.8 bulk metallic glass-forming alloy

Fatigue crack growth behavior was studied for a Zr_58.5Cu_15.6Ni_12.8Al_10.3Nb_2.8 bulk metallic glass in ambient air, demonstrating a fatigue threshold of ΔK_TH = 1.4 MPa√m and a Paris law exponent of 1.7. A nearly stress intensity-independent crack growth regime occurred at 2.5 × 10^?8 m cycle^–1, suggesting an environmental influence of ambient air on the fatigue crack growth, as has been observed for Zr–Ti–Ni–Cu–Be bulk metallic glasses. However, this environmental fatigue effect was shifted to 25× higher growth rates due to the different chemistry.     

An experimental investigation of crack initiation in thin sheets of nitinol

An experimental investigation into the fracture properties of 160-μm-thick edge-cracked specimens of austenitic nickel–titanium (nitinol) under uniaxial tension is presented. Using the in situ optical technique of digital image correlation (DIC), strain fields directly relating to phase boundary nucleation and propagation of fracture samples were observed for the first time. The shape and size of the saturation and transformation zones as a function of loading near the crack tip were examined. An average plane strain crack initiation fracture toughness (K_C) of 51.4 ± 3.6 MPa $\sqrt{m}$ for fine grained polycrystalline nitinol sheets at room temperature was measured. The extent and nature of the phase transformation obtained from DIC, combined with the relatively high value of K_C, underscores the importance of crack tip shielding in the fracture of shape memory alloys.     

Near-threshold propagation of mode II and mode III fatigue cracks in ferrite and austenite

The near-threshold behavior of mode II and mode III long fatigue cracks in ferritic (ARMCO iron) and austenitic (X5CrNi18-10) steel were experimentally studied using various samples specially prepared to obtain the effective threshold values ΔK_IIeff,th and ΔK_IIIeff,th. In both investigated materials, the effective thresholds for mode III were ～1.7 times higher than those for mode II. Three-dimensional topological data obtained by the examination of fracture surfaces using stereophotogrammetry were utilized to identify crack growth micromechanisms. In austenite, mode I branching of both the mode II and mode III cracks started at the very onset of crack growth. On the other hand, all cracks in ferrite propagated in crystallographically assisted local mixed mode I + II + III with mode II dominance. These experimental results can be understood in terms of crack growth micromechanisms according to a deformation model in ferrite and a decohesion model in austenite. The dissimilarity of growth mechanisms in ferrite and austenite may be attributed to a different number of available slip systems in body-centered cubic and face-centered cubic metals.     

Ductilisation of tungsten (W) through cold-rolling: R-curve behaviour

Here we show that cold-rolling of tungsten (W) decreases the stable crack growth onset temperature. Furthermore, we show that stable crack growth is accompanied by crack bridging, which in turn is triggered by dislocation activity. The entire stable crack growth regime shows ductile intergranular fracture.Our ductilisation approach is the modification of microstructure through cold-rolling. In this work, we assess two different microstructures obtained from (i) cold-rolled and (ii) severely cold-rolled tungsten plates. From these plates, single-edge cracked-plate tension (SECT) specimens were cut and tested in the L-T direction. Crack growth resistance (R) curves were obtained using the direct-current-potential-drop method (DCPM). The experiments show the following results: cold-rolled plates are brittle at room temperature (RT), but show stable crack growth at 250 °C (523 K) and a fracture toughness, K_IQ, of about 100 MPa(m)^1/2 at a crack extension, Δa, of 0.6 mm. Severely cold-rolled tungsten plates show stable crack growth at RT and a fracture toughness, K_IQ, of 100 MPa(m)^1/2 at a crack extension, Δa, of 0.3 mm. Scanning electron microscopy (SEM) analyses of the stable crack growth region show intergranular fracture with microductile character.The question of why cold-rolling causes the stable crack growth onset temperature to decrease (or in other words, why cold-rolling causes the brittle-to-ductile transition (BDT) temperature to decrease) is discussed against the background of (i) intrinsic and extrinsic size effects, (ii) crystallographic texture, (iii) impurities and (iv) the role of dislocations. Our results suggest that the spacing between the dislocation nucleation sites (high angle grain boundaries (HAGBs) act as dislocation source) is the most important parameter responsible for the decrease of the stable crack growth onset temperature.     

Modeling dendrite growth in undercooled concentrated multi-component alloys

Most theoretical work on dendrite growth has focused on dilute binary alloys, while most industrial alloys are concentrated multi-component systems. By incorporating the local non-equilibrium effects both at the interface and in the bulk liquid, the thermodynamic database and diffusional interaction, a model was developed for dendrite growth in undercooled concentrated multi-component alloys. An experimental study of dendrite growth in undercooled Ni–18 at.% Cu–18 at.% Co melts was carried out and the measured interface velocities (V) were well predicted by the present model over the whole undercooling range (ΔT = 30–313 K). During dendrite growth the partition coefficients change non-monotonically due to interaction between the species and changes in the dendrite tip radius. Interaction between the species also leads to a lower interface velocity and larger ΔT and V as the ΔT–V relation plateaus. The previous definition of constitutional undercooling, i.e. the sum of the contributions of each solute, is not applicable to concentrated multi-component alloys. The controlling mechanisms during dendrite growth are discussed with respect to the results of the calculations.     

Microstructure,martensitic transformation and anomalies in c′-softening in Co–Ni–Al ferromagnetic shape memory alloys

The morphology, microstructure and elastic softening in single crystals of Co–Ni–Al ferromagnetic shape memory alloy were studied to clarify the conditions for martenstic transformation in this alloy. We used two-phase (β matrix + γ particles) samples with different heat treatments, as-cast and annealed at temperatures from 1523 to 1623 K, and a sample of pure β (B2) phase. A complete set of elastic coefficients at room temperature and the temperature dependence of the softest shear coefficient (c′) of the Co₃₈Ni₃₃Al₂₉ austenite was measured by a combination of pulse echo and resonant ultrasound spectroscopy in the range 208–398 K. All examined materials exhibit anomalous c′-softening for the whole temperature range except the interval 258– 328 K, in which a change in the slope appears. However, only annealed samples transformed to martensite. The change in the slope is ascribed to (i) magnetoelastic softening with the absence of a sharp Curie point; (ii) structural stiffening that prevents the martensitic transition in both the as-cast and single-phase alloys. No signature of the premartensite phenomenon was found.     

Calculations of charge transfer in Nb–17Al and V–50Al alloys,using the Auger parameter

Conventional and high energy X-ray photoelectron spectroscopy (XPS) with Al K_α and Cr K_β radiation, respectively, were used to calculate the Auger parameters of the elements in the V–50 at% Al and Nb–17 at% Al alloys. The shifts of the Auger parameters of the elements of interest between unalloyed and alloyed conditions were used to calculate values of charge transfer occurring upon alloying. The results were related to thermodynamic predictions and the microstructures of the two alloys. The ordering tendency in the Nb–17 at% Al alloy, shown by thermodynamic modelling and the microstructural studies, was attributed to substantial electron transfer from Al to Nb. The small charge transfer from Al to V in the V–50 at% Al alloy was attributed to the lack of ordering in this alloy.     

Microstructure control and compressive strength of 10 mol% Ti-bearing Nb3Al/Nbss in-situ composites

10 mol% Ti-bearing Nb₃Al(δ)/Nb_ss(β) in-situ composites with fine and homogeneous microstructures have been successfully fabricated by heat treatment or thermo-mechanical processing of cast ingots. Homogenization treatment at an extremely high-temperature of 2173 K for 1 h, which produces a B2 single phase, plays an important role for obtaining homogeneous two-phase microstructures. δ-rich alloys annealed at 1473 K after homogenization form δ/β colonies with unidirectionally dispersed β filaments in δ grains. On the other hand, microstructures of δ-rich alloys isothermally forged and annealed become fine and equiaxed. Compression tests indicate that increase in volume content of β phase enables plastic deformation at lower temperatures, although it decreases yield strength at 1473 K. Nevertheless some of Nb–x mol%Al–10 mol%Ti alloys, e.g. Nb–13 mol%Al–10 mol%Ti including about 50 vol% β, possess superior strength in the range from room temperature to 1473 K, making them more applicable as a structural material than conventional Ni-based superalloys.     

The characterization of structure,thermal stability and magnetic properties of Fe–Co–B–Si–Nb bulk amorphous and nanocrystalline alloys

Recently bulk amorphous alloys have attracted great attention due to their excellent magnetic properties. The glass-forming ability of bulk amorphous alloys depends on the temperature difference (ΔT_x) between glass transition temperature (T_g) and crystallization temperature (T_x). The increase of ΔT_x causes a decrease of the critical cooling rate (V_c) and growth of the maximum casting thickness of bulk amorphous alloys. The aim of the present paper is to characterize the structure, the thermal stability and magnetic properties of Fe₃₆Co₃₆B₁₉Si₅Nb₄ bulk amorphous alloys using XRD, Mössbauer spectroscopy, DSC and VSM methods. Additionally the magnetic permeability μ_i (at force H ≈ 0.5 A/m and frequency f ≈ 1 kHz) and the intensity of disaccommodation of magnetic permeability Δμ/μ(t₁) (Δμ = μ(t₁ = 30 s) ? μ(t₂ = 1800 s)), have been measured, where μ is the initial magnetic permeability measured at time t after demagnetisation, the Curie temperature T_C and coercive force H_c of rods are also determined with the use of a magnetic balance and coercivemeter, respectively.Fe–Co–B–Si–Nb bulk amorphous alloys were produced by pressure die casting with the maximum diameters of 1 mm, 2 mm and 3 mm.The glass transition temperature (T_g) of studied amorphous alloys increases from 807 K for a rod with a diameter of 1 mm to 811 K concerning a sample with a diameter of 3 mm. The crystallization temperature (T_x) has the value of 838 K and 839 K for rods with the diameters of 1 mm and 3 mm, respectively. The supercooled liquid region (ΔT_x = T_x ? T_g) has the value of about 30 K. These values are presumed to be the origin for the achievement of a good glass-forming ability of the Fe–Co–B–Si–Nb bulk amorphous alloy. The investigated amorphous alloys in the form of rods have good soft magnetic properties (e.g. M_s = 1.18–1.24 T). The changes of crystallization temperatures and magnetic properties as a function of the diameter of the rods (time of solidification) have been stated.     

Kinetics study on non-isothermal crystallization of the metallic Co43Fe20Ta5.5B31.5 glass

The crystallization kinetics of metallic Co₄₃Fe₂₀Ta_5.5B_31.5 glass has been studied by continuous heating differential scanning calorimetry. The DSC traces have been analyzed in terms of activation energy and kinetic model. It is found that all the DSC traces have a single exothermic peak which is asymmetrical, with a steeper leading edge and a long high temperature tail. The heating rate has a significant influence on the shape of the DSC curve, activation energy and transformation mechanism. The existence of a critical heating rate, β_crit = 20 K min⁻¹, is evident. The activation energy for crystallization are determined as 594.8 and 581.4 KJ mol⁻¹ for the heating rates β = 5–20 K min⁻¹, and 437.7 and 432 KJ mol⁻¹ for the heating rates β = 25–65 K min⁻¹, when using the Kissinger equation and the Ozawa equation, respectively. For the volume fraction crystallized, α, E_c dependence was obtained by the general Ozawa's isoconversional method. Using the Suriñach curve fitting procedure, the kinetics was specified. Namely, the crystallization begins with the Johnson–Mehl–Avrami nucleation-and-growth mode and the mode which has been well described by the normal grain growth kinetic law. These two modes are mutually independent. The proportion between the JMA-like and the NGG-like modes is related to the heating rate. The JMA kinetics is manifested as a rule in the early stages of the crystallization. The JMA exponent, n, initially being larger than 4 and continuously decreases to 1.5 along with the development of crystallization. The NGG-like mode dominates in the advanced stages of the transformation with the NGG exponent, m = 0.5 and is the major and principal kinetic characteristics for heating rate, β > 25 K min⁻¹.     

Effect of hydrogen on internal friction and elastic modulus in titanium alloys

The effect of hydrogen on the variation with temperature of internal friction (Q^?I) and elastic modulus (E) of a number of Ti-based alloys has been studied in the Hz and kHz frequency ranges. A relaxation peak of internal friction with a high degree of relaxation (Q^?I_max ～ 10^?1) and with a ΔE effect is observed in all hydrogen-doped samples at T ～ 600 K at ～1 kHz, and at T ～ 500 K at ～1 Hz. Such a peak is not present in samples without hydrogen. The activation energy W and the frequency factor v₀ of the observed relaxation are determined to be W ～ 1.55 eV, v₀ ～ 10¹⁷ s^?1. It is shown that the observed effects are connected with the mechanism of grain boundary relaxation, as the introduction of hydrogen into titanium alloys leads to the formation of fine-grained structures.     

Enhancing magnetocrystalline anisotropy of the Fe70Pd30 magnetic shape memory alloy by adding Cu

Fe–Pd–Cu thin films are of great interest for applications in magnetic shape memory microsystems due to their increased martensitic transformation temperature. Here we analyse the consequences of Cu addition to Fe–Pd on the binding energy and magnetic properties by a combination of thin film experiments and first-principles calculations. Strained epitaxial growth of Fe₇₀Pd_30-xCu_x with x = 0, 3, 7 is used to freeze intermediate stages during the martensitic transformation. This makes a large range of tetragonal distortion susceptible for analysis, ranging from body-centred cubic to beyond face-centred cubic (1.07 < c/a_bct < 1.57). We find that Cu enhances the quality of epitaxial growth, while spontaneous polarization and Curie temperature are reduced only moderately, in agreement with our calculations. Beyond c/a_bct > 1.41 the samples undergo structural relaxations through adaptive nanotwinning. Cu enhances the magnetocrystalline anisotropy constant K₁ at room temperature, which reaches a maximum of ?2.4 × 10⁵ J m^?3 around c/a_bct = 1.33. This value exceeds those of binary Fe₇₀Pd₃₀ and the prototype Ni–Mn–Ga magnetic shape memory system. Since K₁ represents the maximum driving energy for variant reorientation in magnetic shape memory systems, we conclude that Fe–Pd–Cu alloys offer a promising route towards microactuator applications with significantly improved work output.     

Ternary Sm–Al–Ni bulk metallic glasses

The present paper is concerned with the formation of the ternary Sm-based Sm–Al–Ni bulk metallic glasses. Composition design is carried out using our e/a- and cluster-related criteria. Three bulk metallic glasses, Sm₅₄Al₂₃Ni₂₃, Sm₅₆Al₂₂Ni₂₂ and Sm₅₈Al₂₁Ni₂₁, are obtained by suction casting into rods with diameter of 3 mm. All of them share a constant e/a = 1.5 and fall along the e/a-constant composition line in the ternary composition diagram. The Sm₅₄Al₂₃Ni₂₃ BMG exhibits the best thermal stability and glass-forming ability, which is located at the intersecting point of the e/a-constant line and the Sm₇Ni₃–Al cluster line.     

Solidification behavior of γ′-Ni3Al-containing alloys in the Ni–Al–O system

The chemical activities of Al and Ni in γ′-Ni₃Al-containing alloys were measured using the multi-cell Knudsen effusion-cell mass spectrometry technique, over the composition range 8–32 at.% Al and temperature range T = 1400 to 1750 K. From these measurements a better understanding of the equilibrium solidification behavior of γ′-Ni₃Al-containing alloys in the Ni–Al–O system was established. Specifically, these measurements revealed that (i) γ′-Ni₃Al forms via the peritectiod reaction, γ + β (+Al₂O₃) = γ′ (+Al₂O₃), at 1633 ± 1 K; (ii) the {γ + β + Al₂O₃} phase field is stable over the temperature range 1633–1640 K; and (iii) equilibrium solidification occurs by the eutectic reaction, L (+Al₂O₃) = γ + β (+Al₂O₃), at 1640 ± 1 K and a liquid composition of 24.8 ± 0.2 at.% Al (at an unknown oxygen content). When projected onto the Ni–Al binary, this behavior is inconsistent with the current Ni–Al phase diagram and a new diagram is proposed. This new Ni–Al phase diagram explains a number of unusual steady-state solidification structures reported previously and provides a much simpler reaction scheme in the vicinity of the γ′-Ni₃Al phase field.     

Evolution of multivariant microstructures with anisotropic misfit: A phase field study

We study, in two dimensions, the effect of misfit anisotropy on microstructural evolution during precipitation of an ordered β phase from a disordered α matrix; these phases have, respectively, 2- and 6-fold rotation symmetries. Thus, precipitation produces three orientational variants of β phase particles, and they have an anisotropic (and crystallographically equivalent) misfit strain with the matrix. The anisotropy in misfit is characterized using a parameter t = ?_yy/?_xx, where ?_xx and ?_yy are the principal components of the misfit strain tensor. Our phase field simulations show that the morphology of β phase particles is significantly influenced by t, the level of misfit anisotropy. Particles are circular in systems with dilatational misfit (t = 1), elongated along the direction of lower principal misfit when 0 < t < 1 and elongated along the invariant direction when ?1 ? t ? 0. In the special case of a pure shear misfit strain (t = ?1), the microstructure exhibits star, wedge and checkerboard patterns; these microstructural features are in agreement with those in Ti–Al–Nb alloys.     

Synthesis of π-conjugated polymers possessing 1,3-butadiene-1,4-diyl units by reactions of regioregular organometallic polymer having titanacyclopentadiene moieties in the main chain

The synthesis and properties of π-conjugated polymers possessing phenylene-1,4-diyl and 1,3-butadiene-1,4-diyl alternating units in the main chain by reactions of a regioregular organometallic polymer having titanacyclopentadiene-2,5-diyl unit are described. The polymerization of 1,4-diethynyl-2,5-dioctyloxybenzene with a low-valent titanium complex, generated in situ from titanium(IV) isopropoxide and isopropyl magnesium chloride, was carried out at ?78 °C to ?50 °C for 12 h to give the regioregular organotitanium polymer. The diene-containing π-conjugated polymers were obtained by the reactions of the organotitanium polymer with electrophiles such as hydrochloric acid and iodine. For example, the reaction with hydrochloric acid gave a diene-containing polymer in a 61% yield whose M_n and M_w/M_n were estimated as 5700 and 1.61, respectively (by GPC). The π-conjugated character of the resulting polymer could be supported by its UV–vis spectrum. That is, the absorption maximum (λ_max) of the polymer was observable at 470 nm, which was bathochromically shifted by 115 nm compared to that of a model compound (1,4-bis(2-methoxyphenyl)-1,3-butadiene, λ_max = 355 nm).