Embrittlement observed in Cr–Mo turbine bolts after service

The present paper describes a study aimed at investigating the extent of service related embrittlement suffered by a series of Cr–Mo steel turbine bolts after over 200,000 h at 450°C. A small section of material was removed from a non-critical location of all the 51 bolts. From this section, the chemical composition, average hardness and average prior austenite grain size were measured. The toughness of the bolts was measured by Charpy impact testing and/or Auger electron spectroscopy. From the various parameters investigated, it was established that grain size and phosphorus level were the only factors which consistently identified whether a bolt was embrittled or non-embrittled. Indeed it was established that bolt embrittlement could be predicted using the simple product of microstructure grain size d (μm's) and bulk phosphorus content. Finally, it was observed that bolt embrittlement could be predicted using the simple product of microstructure grain size and bulk phosphorus level and that such a trend indicated the importance of grain boundary area available for service induced phosphorus segregation.     

Near threshold fatigue behaviour of flake graphite cast irons microstructures

This paper describes the influence of material toughness degradation, through reversed temper embrittlement (RTE) and mean stress on the near threshold fatigue crack growth characteristics of a CrMoV turbine bolting steel at ambient and elevated temperatures. It was established at ambient temperatures that strong effects of R-ratio and material condition (toughness) were observed on near threshold fatigue crack growth characteristics. At elevated temperatures it was shown that for the non-embrittled material that only under low R-ratio conditions did increased temperature increase the level of threshold stress intensity ΔK_th, by some 20%. In the case of embrittled material, increasing the temperature increased ΔK_th levels by around 30% and decreased near threshold growth rates by an order of magnitude at low to intermediate R-ratio levels.The effects of R-ratio on ΔK_th for all material and mechanical testing conditions could be simply expressed by the difference between ΔK_th at R = O and a constant B multiplied by R.Quantitative fractographic observations indicated that, generally, the incidence of intergranular failure prevalent in embrittled and non-embrittled steels exhibited a maximum at some specific ΔK level. Also in embrittled steels large effects of environmental assisted crack (EAC) growth were observed at near threshold fatigue crack growth rates. It was suggested that this was the result of the much reduced material cohesive strength which was caused by the presence of both impurity and hydrogen atoms.     

Predicting the Hall–Petch effect in fcc metals using non-local crystal plasticity

Many conventional continuum approaches to solid mechanics do not address the size sensitivity of deformation to microstructural features like grain boundaries, and are therefore unable to capture much of the experimentally observed behavior of polycrystal deformation. We propose a non-local crystal plasticity model, in which the geometrically necessary dislocation (GND) density is calculated using a non-local integral approach. The model is based on augmented F^eF^p kinematics, which account for the initial microstructure (primarily grain boundaries) present in the polycrystal. With the augmented kinematics, the initial GND and the evolving GND state are determined in a consistent manner. The expanded kinematics and the non-local crystal plasticity model are used to simulate the tensile behavior in copper polycrystals with different grain sizes ranging from 14 μm to 244 μm. The simulation results show a grain size dependence on the polycrystal’s yield strength, which are in good agreement with the experimental data.     

Electrochemical monitoring of aging embrittlement of steel for gas-cooled reactor pressure boundary components

The nondestructive testing technique is applied to evaluate the temper embrittlement of normalized and tempered steel; it is based on the anodic polarization behavior in calcium nitrate solution. The steel specimen is aged at a stress of 210 MPa at 450°C for up to 8800 h in order to examine the effect of applied stress on the enhancement of intergranular segregation of phosphorus. The secondary peak observed in the polarization curve for the material aged under stress was compared with that for the non-stressed. It can be quantified with the degree of intergranular segregation of phosphorus. The data suggest that the enhancement of phosphorus segregation due to the applied stress is only recognized after 3000 h of aging. This effect diminishes with increasing aging time.     

Limit and shakedown analysis under hydrogen embrittlement condition

A modified shakedown theorem and its solving technique are presented to involve hydrogen embrittlement of steel into limit and shakedown analysis. Firstly, the shakedown theorem for hydrogen embrittled material is derived from a limited kinematic hardening shakedown theorem and hydrogen enhanced localized plasticity mechanism of hydrogen embrittlement. In the presented theorem, hydrogen’s effect is taken into account by the synergistic action of both strength reduction and stress redistribution. Secondly, a novel solving technique is developed based on the basis reduction method, in which the complicated constraints in the resulting nonlinear mathematical programming are released. At last, three numerical examples are carried out to verify the performance of the proposed method and to reveal hydrogen’s effect on the limit and shakedown load of structure. The numerical results are discussed and compared with those from literatures, which proves the accuracy and high efficiency of the introduced solving technique. It is concluded that the proposed theorem can predict the limit and shakedown load of hydrogen embrittled structure reasonably.     

Effect of grain size on slow fatigue crack propagation and plastic deformation near crack tip

Fatigue crack growth and its threshold are investigated at a stress ratio of 0.5 for the three-point bend specimen made of Austenitic stainless steel. The effect of grain size on the crack tip plastic deformation is investigated. The results show that the threshold value Δk_th increases linearly with the square root of grain size d and the growth rate is slower for materials with larger grain size. The plastic zone size and ratio for different grain sizes are different at the threshold. The maximum stress intensity factor is k_max and σ_ys is the yield strength. At the same time, the characteristics of the plastic deformation development is discontinuous and anti-symmetric as the growth rate is increased from 2·10^—8 to 10⁻⁷ mm/cycle.A dimensionless relation of the form for collating fatigue crack starting growth data is proposed in which Δk_th represents the stress intensity factor range at the threshold. Based on experimental results, this relation attains the value of 0.6 for a fatigue crack to start growth in the Austenitic stainless steel investigated in this work. Metallurgical examinations were also carried out to show a transgranular shear mode of cyclic cleavage and plastic shear.     

Fatigue crack growth studies in rail steels and associated weld metal

Fatigue crack growth studies in rail steels and associated weld metal have shown that (a) deformed rail steel exhibited fatigue crack growth rates that are slightly faster than undeformed rail steel and (b) weld metal growth data are appreciably faster than rail steel growth results and exhibit growth rate plateaux that reside above the upper bound reported for rail steel fatigue crack growth.In rail steel microstructures at low ΔK levels fatigue crack extension occurred by a ductile striated growth mechanism. However at K_max values approaching 40 MPa √m transgranular cleavage facets initially formed and their incidence increased with K_max until final fast fracture. The average cleavage facet size agreed well with pearlite nodule dimensions of 60–100 μm.The weld metal microstructure was much coarser than the rail steel and contained highly directional columnar grain growth. At all ΔK levels the dominant fracture mode was transgranular cleavage containing small isolated regions of ductile striated fatigue crack growth. The cleavage facet size varied from 150 to 600 μm; such a large variation was explained by the fact that in general crack extension tended to occur in association with the proeutectoid ferrite phase.     

Particle dispersion in a single-sided backward-facing step flow

The paper describes the particle dispersion in a single-sided backward-facing step flow. Particles of well-known sizes in the diameter range from 1 to 70 μm were suspended in an air flow and the particle motion over a step was measured by mean of a laser-Doppler anemometer. Thus, the local and integral flow quantities, i.e. the mean and turbulent velocity data could be measured precisely. In the experiments, monodispersed particle size distributions were used to exclude particle size related information ambiguity, known as triggering effects or size bias. The results of this study show qualitatively and quantitatively the difference in time-averaged particle dynamics for selected particle sizes in a backward-facing step flow. The experiments show, for different sizes, the changes in the particle velocity field in comparison with the velocity field of the continuous phase deduced from the 1 μm particles, and also imply the strong influences which different particle sizes have on flow data evaluation when size effects are not taken into account with particle-related optical measuring techniques.     

Role of grain boundary energetics on the maximum strength of nanocrystalline Nickel

Numerical simulations are used to investigate the competing grain boundary and dislocation mediated deformation mechanisms in nanocrystalline Ni with grain sizes in the range 4-32 nm. We present a 3D phase field model that tracks the evolution of individual dislocations and grain boundaries. Our model shows that the transition from Hall-Petch to inverse Hall-Petch as the grain size is reduced cannot be characterized only by the grain size, but it is also affected by the grain boundary energetics. We find that the grain size corresponding to the maximum yield stress (the transition from Hall-Petch strengthening with decreasing grain size to inverse Hall-Petch) decreases with increasing grain boundary energy. Interestingly, we find that for grain boundaries with high cohesive energy the Hall-Petch maximum is not observed for grains in the range 4-32 nm.     

Micro/macro-crack growth due to creep–fatigue dependency on time–temperature material behavior

The implicit character of micro-structural degradation is determined by specifying the time history of crack growth caused by creep–fatigue interaction at high temperature. A dual scale micro/macro-equivalent crack growth model is used to illustrate the underlying principle of multiscaling which can be applied equally well to nano/micro. A series of dual scale models can be connected to formulate triple or quadruple scale models. Temperature and time-dependent thermo-mechanical material properties are developed to dictate the design time history of creep–fatigue cracking that can serve as the master curve for health monitoring.In contrast to the conventional procedure of problem/solution approach by specifying the time- and temperature-dependent material properties as a priori, the desired solution is then defined for a class of anticipated loadings. A scheme for matching the loading history with the damage evolution is then obtained. The results depend on the initial crack size and the extent of creep in proportion to fatigue damage. The path dependent nature of damage is demonstrated by showing the range of the pertinent parameters that control the final destruction of the material. A possible scenario of 20 yr of life span for the 38Cr2Mo2VA ultra-high strength steel is used to develop the evolution of the micro-structural degradation. Three micro/macro-parameters μ^*, d^* and σ^* are used to exhibit the time-dependent variation of the material, geometry and load effects. They are necessary to reflect the scale transitory behavior of creep–fatigue damage. Once the algorithm is developed, the material can be tailor made to match the behavior. That is a different life span of the same material would alter the time behavior of μ^*, d^* and σ^* and hence the micro-structural degradation history. The one-to-one correspondence of the material micro-structure degradation history with that of damage by cracking is the essence of path dependency. Numerical results and graphs are obtained to demonstrate how the inherently implicit material micro-structure parameters can be evaluated from the uniaxial bulk material properties at the macroscopic scale.The combined behavior of creep and fatigue can be exhibited by specifying the parameter ξ with reference to the initial defect size a₀. Large ξ (0.90 and 0.85) gives critical crack size a_cr = 11–14 mm (at t < 20 yr) for a₀ about 1.3 mm. For small ξ (0.05 and 0.15), there results critical a_cr = 6–7 mm (at t < 20 yr) for a₀ about 0.7–0.8 mm. The initial crack is estimated to increase its length by an order of magnitude before triggering global to the instability. This also applies ξ ≈ 0.5 where creep interacts severely with fatigue. Fine tuning of a_cr and a₀ can be made to meet the condition oft = 20 yr.Trade off among load, material and geometric parameters are quantified such that the optimum conditions can be determined for the desired life qualified by the initial–final defect sizes. The scenario assumed in this work is indicative of the capability of the methodology. The initial–final defect sizes can be varied by re-designing the time–temperature material specifications. To reiterate, the uniqueness of solution requires the end result to match with the initial conditions for a given problem. This basic requirement has been accomplished by the dual scale micro/macro-crack growth model for creep and fatigue.     

Evaluation of fracture behavior of iron aluminides

Comparative fracture tests of three Fe-28%Al iron aluminides showed that alloys with Zr and C addition (FA-187) or with B, Zr, and C addition (FA-189) are extrinsically more susceptible to environmental embrittlement than the base ternary alloy (FA-186) under constant tensile loading condition. This may be caused by the variations of grain boundary morphology (i.e. changes of grain size and grain boundary cohesive strength) caused by the alloy addition. The effect of grain boundary size and cohesive strength are further investigated with reference to the susceptibility of hydrogen embrittlement. Finite element simulation of initial intergranular fracture of two iron aluminides (FA-186 and FA-189) are made. The computational scheme involves coupling the stress and mass diffusion analyses to determine crack-tip stress state and the crack tip hydrogen diffusion. Maximum strain failure criteria was adopted to simulate intergranular fracture. The numerical modeling results correlated well with the experimental data. The result further confirmed that the grain boundary morphology is important as it appears to control the intrinsic and extrinsic fracture behavior of iron aluminides.     

The Effect of Grain Size on Deformation and Failure of Ti<Subscript>2</Subscript>AlC MAX Phase under Thermo-Mechanical Loading

An experimental investigation was performed to analyze the effects of grain size on the quasi-static and dynamic behavior of Ti₂AlC. High-density Ti₂AlC samples of three different grain sizes were densified using Spark Plasma Sintering and Pressureless sintering. A servo-hydraulic testing machine equipped with a vertical split furnace, and SiC pushrods, was used for the quasi-static experiments. Also, a Split Hopkinson Pressure Bar (SHPB) apparatus and an induction coil heating system were used for the dynamic experiments. A series of experiments were conducted at temperatures ranging from 25 °C to 1100 °C for strain rates of 10^?4 s^?1 and 400 s^?1. The results show that under quasi-static loading the specimens experience a brittle failure for temperatures below Brittle to Plastic Transition Temperature (BPTT) of 900–1000 °C and large deformation at temperatures above the BPTT. During dynamic experiments, the specimens exhibited brittle failure, with the failure transitioning from catastrophic failure at lower temperatures to graceful failure (softening while bearing load) at higher temperatures, and with the propensity for graceful failure increasing with increasing grain size. The compressive strengths of different grain sizes at a given temperature can be related to the grain length by a Hall-Petch type relation.     

Fatigue of polycrystalline copper with different grain sizes and texture

Fatigue experiments of polycrystalline copper with different grain sizes and texture were conducted under tension–compression, torsion, and non-proportional loading. The grain sizes ranged from 10 μm to 2 mm. The stress–strain response was found to be a strong function of the grain size and texture. A plasticity-based critical plane multiaxial fatigue criterion was used to predict the fatigue lives of the polycrystalline copper. It was found that the criterion was able to correlate all the experimental results with one single set of material constants. This indicates that the fatigue failure of the material under consideration is dominated by the fatigue resistance of the grains with an insignificant influence of the grain boundaries on the fatigue of the polycrystalline material. It was found that the fatigue model with the material constants obtained from fatigue experiments can be applied to predict failure under monotonic torsion.     

Scale transition of a higher order plasticity model – A consistent homogenization theory from meso to macro

Standard plasticity models cannot capture the microstructural size effect associated with grain sizes, as well as structural size effects induced by external boundaries and overall gradients. Many higher-order plasticity models introduce a length scale parameter to resolve the latter limitation – microstructural influences are not explicitly account for. This paper adopts two distinct length scales in the formulation, i.e. an intrinsic length scale (l) governing micro-processes such as dislocation pile-up at internal boundaries, as well as the characteristic grain size (L), and aims to unravel the interaction between these two length scales and the characteristic specimen size (H) at the macro level. At the meso-scale, we adopt the strain gradient plasticity model developed in Gurtin (2004) [Gurtin, M.E., 2004. A gradient theory of small-deformation isotropic plasticity that accounts for the Burgers vector and for dissipation due to plastic spin. J. Mech. Phys. Solids 52, 2545–2568] which accounts for the direct influence of grain boundaries. Through a novel homogenization theory, the plasticity model is translated consistently from meso to macro. The two length scale parameters (l and L) manifest themselves naturally at the macro scale, hence capturing both types of size effects in an average sense. The resulting (macro) higher-order model is thermodynamically consistent to the meso model, and has the same structure as a micromorphic continuum. Finally, we consider a bending example for the two limiting cases – microhard and microfree conditions at grain boundaries – and illustrate the excellent match between the meso and homogenized solutions.     

Turbulent pipe flow of a drag-reducing rigid “rod-like” polymer solution

Fully developed turbulent pipe flow of an aqueous solution of a rigid “rod-like” polymer, scleroglucan, at concentrations of 0.005% (w/w) and 0.01% (w/w) has been investigated experimentally. Fanning friction factors were determined from pressure-drop measurements for the Newtonian solvent (water) and the polymer solutions and so levels of drag reduction for the latter. Mean axial velocity u and complete Reynolds normal stress data, i.e. u′, v′ and w′, were measured by means of a laser Doppler anemometer at three different Reynolds numbers for each fluid. The measurements indicate that the effectiveness of scleroglucan as a drag-reducing agent is only mildly dependent on Reynolds number. The turbulence structure essentially resembles that of flexible polymer solutions which also lead to low levels of drag reduction.     

Composite ceramics fabricated from “blotting paper” technology

The “blotting paper” technology is developed to fabriacte composite materials. It consists of heating the initial oxide of a given composition to a temperature interval where it decomposes intothe necessary solid oxide and a liquid infitrating a porous medium as the matrix. Laminated composites could be fabricated with relatively high critical temperature, T_c at which the material exhibits superconductive property.     

The effect of mixing particles of different size on the electrorheological response under steady shear flow

 The effect of mixing particles of different sizes on the electrorheological response of suspensions under steady shear flow was investigated. Two sizes, 15 μm and 50 μm, of monodisperse spherical sulfonated poly(styrene-co-divinylbenzene) particles were used. Several electrorheological fluids were made containing different proportions of small and large particles dispersed in silicone oil, but with constant overall particulate concentration. It was found that the mixed size system produced the highest electrorheological response under the shear rates used (10 s⁻¹ to 500 s⁻¹), which is the opposite trend to previous studies of bimodal systems with larger size ratios. Received: 21 December 2000 Accepted: 29 March 2001     

A Micromechanics Study of Lamellar TiAl

Microdeformation patterns of lamellar TiAl specimens with various grain sizes under uniaxial tension are mapped using the micro/nano experimental mechanics technique called SIEM (Speckle Interferometry w ith Electron Microscopy). The stress–strain relationships were obtained from deformations within decreasing areas ranging from mm² to μm². We found that the stress–strain relationship of the material depends on the size of strain measuring area in relation to the grain size. The stiffness at a grain boundary can be as large as 7–10 times more than that of the grain itself. From the data obtained so far, it seems that the traditional way of using PST (polysynthetically twinned) single crystal to predict polycrystalline behavior may not be appropriate.