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 ΔKth and ΔKeff, 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.

Assessment of conditional moment closure models of turbulent autoignition using DNS data

A systematic assessment of the submodels of conditional moment closure (CMC) formalism for the autoignition problem is carried out using direct numerical simulation (DNS) data. An initially non-premixed, n-heptane/air system, subjected to a three-dimensional, homogeneous, isotropic, and decaying turbulence, is considered. Two kinetic schemes, (1) a one-step and (2) a reduced four-step reaction mechanism, are considered for chemistry An alternative formulation is developed for closure of the mean chemical source term , based on the condition that the instantaneous fluctuation of excess temperature is small. With this model, it is shown that the CMC equations describe the autoignition process all the way up to near the equilibrium limit. The effect of second-order terms (namely, conditional variance of temperature excess sigma(2) and conditional correlations of species q(ij)) in modeling is examined. Comparison with DNS data shows that sigma(2) has little effect on the predicted conditional mean temperature evolution, if the average conditional scalar dissipation rate is properly modeled. Using DNS data, a correction factor is introduced in the modeling of nonlinear terms to include the effect of species fluctuations. Computations including such a correction factor show that the species conditional correlations q(ij) have little effect on model predictions with a one-step reaction, but those q(ij) involving intermediate species are found to be crucial when four-step reduced kinetics is considered. The "most reactive mixture fraction" is found to vary with time when a four-step kinetics is considered. First-order CMC results are found to be qualitatively wrong if the conditional mean scalar dissipation rate is not modeled properly. The autoignition delay time predicted by the CMC model compares excellently with DNS results and shows a trend similar to experimental data over a range of initial temperatures.

Universal crack closure integral for SIF estimation

Numerical analysis of cracked structures often involves numerical estimation of stress intensity factors (SIFs) at a crack tip/front. A newly developed formulation called universal crack closure integral (UCCI) for the evaluation of potential energy release rates (PERRs) and the corresponding SIFs is presented in this paper. Unlike the existing element dedicated forms of crack closure integrals (MCCI, VCCI) with application limited to finite element analysis, this new numerical SIF/PERR estimation technique is independent of the basic stress analysis procedure, making it universally applicable. The second merit of this procedure is that it avoids the generally error-producing zones close to the crack tip/front singularity. The UCCI procedure, based on Irwin's original CCI, is formulated and explored using a simple 2D problem of a straight crack in an infinite sheet. It is then applied to some three-dimensional crack geometries with the stresses and displacements obtained from a boundary element program.

Fuzzy optimization model for water quality management of a river system - Closure

A fuzzy waste-load allocation model, FWLAM, is developed for water quality management of a river system using fuzzy multiple-objective optimization. An important feature of this model is its capability to incorporate the aspirations and conflicting objectives of the pollution control agency and dischargers. The vagueness associated with specifying the water quality criteria and fraction removal levels is modeled in a fuzzy framework. The goals related to the pollution control agency and dischargers are expressed as fuzzy sets. The membership functions of these fuzzy sets are considered to represent the variation of satisfaction levels of the pollution control agency and dischargers in attaining their respective goals. Two formulations—namely, the MAX-MIN and MAX-BIAS formulations—are proposed for FWLAM. The MAX-MIN formulation maximizes the minimum satisfaction level in the system. The MAX-BIAS formulation maximizes a bias measure, giving a solution that favors the dischargers. Maximization of the bias measure attempts to keep the satisfaction levels of the dischargers away from the minimum satisfaction level and that of the pollution control agency close to the minimum satisfaction level. Most of the conventional water quality management models use waste treatment cost curves that are uncertain and nonlinear. Unlike such models, FWLAM avoids the use of cost curves. Further, the model provides the flexibility for the pollution control agency and dischargers to specify their aspirations independently.

Numerical prediction of load-displacement behaviors of adhesively bonded joints at different extension rates and temperatures

The present work focuses on simulation of nonlinear mechanical behaviors of adhesively bonded DLS (double lap shear) joints for variable extension rates and temperatures using the implicit ABAQUS solver. Load-displacement curves of DLS joints at nine combinations of extension rates and environmental temperatures are initially obtained by conducting tensile tests in a UTM. The joint specimens are made from dual phase (DP) steel coupons bonded with a rubber-toughened adhesive. It is shown that the shell-solid model of a DLS joint, in which substrates are modeled with shell elements and adhesive with solid elements, can effectively predict the mechanical behavior of the joint. Exponent Drucker-Prager or Von Mises yield criterion together with nonlinear isotropic hardening is used for the simulation of DLS joint tests. It has been found that at a low temperature (-20 degrees C), both Von Mises and exponent Drucker-Prager criteria give close prediction of experimental load-extension curves. However. at a high temperature (82 degrees C), Von Mises condition tends to yield a perceptibly softer joint behavior, while the corresponding response obtained using exponent Drucker-Prager criterion is much closer to the experimental load-displacement curve.

Certain Aspects Related To Computation By Modified Crack Closure Integral(MCCI)

This paper presents the proper computational approach for the estimation of strain energy release rates by modified crack closure integral (MCCI). In particular, in the estimation of consistent nodal force vectors used in the MCCI expressions for quarter-point singular elements (wherein all the nodal force vectors participate in computation of strain energy release rates by MCCI). The numerical example of a centre crack tension specimen under uniform loading is presented to illustrate the approach.

CMC simulations of lifted turbulent jet flame in a vitiated coflow

Lifted turbulent jet diffusion flame is simulated using Conditional Moment Closure (CMC). Specifically, the burner configuration of Cabra et al. [R. Cabra, T. Myhrvold, J.Y. Chen. R.W. Dibble, A.N. Karpetis, R.S. Barlow, Proc. Combust. Inst. 29 (2002) 1881-1887] is chosen to investigate H-2/N-2 jet flame supported by a vitiated coflow of products of lean H-2/air combustion. A 2D, axisymmetric flow-model fully coupled with the scalar fields, is employed. A detailed chemical kinetic scheme is included, and first order CIVIC is applied. Simulations are carried out for different jet velocities and coflow temperatures (T-c) The predicted liftoff generally agrees with experimental data, as well as joint-PDF results. Profiles of mean scalar fluxes in the mixture fraction space, for T-c = 1025 and 1080 K reveal that (1) Inside the flame zone, the chemical term balances the molecular diffusion term, and hence the Structure is of a diffusion flamelet for both cases. (2) In the pre-flame zone, the structure depends on the coflow temperature: for the 1025 K case, the chemical term being small, the advective term balances the axial turbulent diffusion term. However, for the 1080 K case. the chemical term is large and balances the advective term, the axial turbulent diffusion term being small. It is concluded that, lift-off is controlled (a) by turbulent premixed flame propagation for low coflow temperature while (b) by autoignition for high coflow temperature. (C) 2009 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

Analysis of Raman bandwidths and bandshapes of glasses through their glass-transition temperatures

Raman bandwidths and bandshapes of some molecular and ionic glasses have been investigated through the glass-transition region. Widths of both polarised and depolarised bands exhibit step-like changes during the glass transition. Molecular and ionic glasses differ with respect to the magnitude and the nature of variations in bandwidths and reorientational times. An attempt has been made to understand the changes in bandwidths around the glass-transition temperature.

1H NMR study of [N(CH3)4]2ZnCI4 at high pressures and low temperatures

Wide-line proton NMR studies on polycrystalline tetramethylammonium tetrachlorozincate have been carried out at high hydrostatic pressures up to 15 kbar in the temperature range 77-300 K and at ambient pressure down to 4.2 K. A second-moment transition is observed to occur starting around 161 K, the temperature for the V-VI phase transition. This transition temperature is seen to have a negative pressure coefficient up to 2 kbar, beyond which it changes sign. At 77 K the second moment decreases to 4 kbar and then increases again as a function of pressure. The results are explained in terms of the dynamics of the N(CH3)4 groups.

The effect of crack closure on the grain size dependence of fatigue crack growth threshold

Recent studies (I-7) clearly indicate a strong dependence of fatigue threshold parameter, A K on grain size in several alloy systems. Attempts to explain these observations on the basis of crat~tortuosity (1,8), fracture surface roughness (5,9) and crack closure (6) appear to present a fairly clear picture of the mechanisms that cause a reduction in crack growth rates at threshold. In general, it has been shown that coarse grained microstructures exhibit higher fatigue threshold in low carbon steels (1,5) aluminium alloys (7) and titanium alloys (6). In spite of these observations, there exists (10-1#) considerable uncertainity about the manner in which the AK~L depends on prior austenitic grain size in quenched and tempered steels. Studies in quenched and tempered steels demonstrating both an increase (3,12,14) as well as a decrease (11,12) in AKth with an increase in prior austenitic grain size can be sought to illustrate this point. Occasionally , the absence of any sensitivity of AKth to the variations in prior austenitJc grain size has also been reported (11,13). While a few investigators (5-7) comfortably rationalised the grain size effects on AK~L on the basis of crack closure by a comparison in terms of the closure-free component of the thresho~Ifc~, AK -f such an approach has yet to be extended to high strength steels, An attempt has been made in t~et ,pthrg sent study to explai. n the effect of pri, or austeniti.c grain size on &Kth on the basis of crack closure measurements in a high strength steel.

A simple vibrating reed apparatus for use at low temperatures

The authors report the design and construction of a very simple vibrating reed apparatus with automatic frequency locking capability where the resonance frequency and the internal friction can be recorded continuously as a function of temperature. The apparatus is particularly suitable for studies down to liquid helium temperatures or below.

Analysis of randomly time varying systems by gaussian closure technique

The Gaussian probability closure technique is applied to study the random response of multidegree of freedom stochastically time varying systems under non-Gaussian excitations. Under the assumption that the response, the coefficient and the excitation processes are jointly Gaussian, deterministic equations are derived for the first two response moments. It is further shown that this technique leads to the best Gaussian estimate in a minimum mean square error sense. An example problem is solved which demonstrates the capability of this technique for handling non-linearity, stochastic system parameters and amplitude limited responses in a unified manner. Numerical results obtained through the Gaussian closure technique compare well with the exact solutions.

Automated estimation of fatigue crack length and closure/opening stress

An experimental technique is proposed for the estimation of crack length as well as crack closure/opening stress during fatigue crack growth. A specially designed, single cantilever, crack opening displacement gauge is used to monitor these variables during fatigue crack propagation testing. The technique was experimentally validated through electronfractography.

Highly Enhanced Thermopower in Two-Dimensional Electron Systems at Millikelvin Temperatures

We report experimental observation of an unexpectedly large thermopower in mesoscopic two-dimensional (2D) electron systems in GaAs/AlGaA heterostructures at sub-Kelvin temperatures and zero magnetic field. Unlike conventional nonmagnetic high-mobility 2D systems, the thermopower in our devices increases with decreasing temperature below 0.3 K, reaching values in excess of 100 mu V/K, thus exceeding the free electron estimate by more than 2 orders of magnitude. With support from a parallel study of the local density of states, we suggest such a phenomenon to be linked to intrinsic localized states and many-body spin correlations in the system.