Effect of prestrain on fatigue crack propagation in mild steel containing non-metallic inclusions

The effect of tensile prestrain on fatigue crack propagation behaviour of commercial mild steel with significant amount of stringer inclusions has been studied. In prestrained materials the usual stable stage II crack growth region is preceded by a phase wherein a retardation in crack growth rate occurs. No such behaviour is observed in annealed material. The amount of retardation is found to increase with increase in prestrain. A mechanism for the observed retardation in crack growth rate is also presented.

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.

Effects of Ultrafast Solvation on the Rate of Adiabatic Outer-Sphere Electron Transfer Reactions

Recent studies have demonstrated that solvation dynamics in many common dipolar liquids contain an initial, ultrafast Gaussian component which may contribute even more than 60% to the total solvation energy. It is also known that adiabatic electron transfer reactions often probe the high-frequency components of the relevant solvent friction (Hynes, J. T. J. Phys. Chem. 1986, 90, 3701). In this paper, we present a theoretical study of the effects of the ultrafast solvent polar modes on the adiabatic electron transfer reactions by using the formalism of Hynes. Calculations have been carried out for a model system and also for water and acetonitrile. It is found that, in general, the ultrafast modes can greatly enhance the rate of electron transfer, even by more than an order of magnitude, over the rate obtained by using only the slow overdamped modes usually considered. For water, this acceleration of the rate can be attributed to the high-frequency intermolecular vibrational and librational modes. For a weakly adiabatic reaction, the rate is virtually indistinguishable from the rate predicted by the Marcus transition state theory. Another important result is that even in this case of ultrafast underdamped solvation, energy diffusion appears to be efficient so that electron transfer reaction in water is controlled essentially by the barrier crossing dynamics. This is because the reactant well frequency is-directly proportional to the rate of the initial Gaussian decay of the solvation time correlation function. As a result, the value of the friction at the reactant well frequency rarely falls below the value required for the Kramers turnover except when the polarizability of the water molecules may be neglected. On the other hand, in acetonitrile, the rate of electron transfer reaction is found to be controlled by the energy diffusion dynamics, although a significant contribution to the rate comes also from the barrier crossing rate. Therefore, the present study calls for a need to understand the relaxation of the high-frequency modes in dipolar liquids.

Role of elasto-plastic analysis under cyclic loading in fatigue crack growth studies

Linear Elastic Fracture Mechanics (LEFM) has been widely used in the past for fatigue crack growth studies, but this is acceptable only in situations which are within small scale yielding (SSY). In many practical structural components, conditions of SSY could be violated and one has to look for fracture criteria based on elasto-plastic analysis. Crack closure phenomenon, one of the most striking discoveries based on inelastic deformations during crack growth, has significant effect on fatigue crack growth rate. Numerical simulation of this phenomenon is computationally intensive and involved but has been successfully implemented. Stress intensity factors and strain energy release rates lose their meaning, J-integral (or its incremental) values are applicable only in specific situations, whereas alternate path independent integrals have been proposed in the literature for use with elasto-plastic fracture mechanics (EPFM) based criteria. This paper presents certain salient features of two independent finite element (numerical) studies of relevance to fatigue crack growth, where elasto-plastic analysis becomes significant. These problems can only be handled in the current day computational environment, and would have been only a dream just a few years ago.

Fatigue crack growth under an eqivalent falstaff spectrum

Optical fractography was used to estimate growth of small cracks at notches under programmed FALSTAFF loading in an Al-Cu alloy. Crack sizes as low as 25 microns and growth rates over two orders of magnitude could be resolved using this technique. Randomized MiniFALSTAFF load sequence was modified into a programmed load equivalent with major loads either preceding or following marker loads. Crack growth rate under programmed FALSTAFF spectrum as estimated by optical fractography conformed to compliance based estimates on a SE(T) specimen. Long crack growth rates under programmed and randomized MiniFALSTAFF spectrum were essentially similar. Spectrum load fatigue crack growth was studied in central hole coupons under notch inelastic conditions. Scatter in growth rates for small notch cracks was found to be of the same magnitude as that of long cracks. Multiple fatigue cracks are observed at the notch root, and they appear to influence each other.

Variability of sif and cod of stochastic structural systems

Stochastic structural systems having a stochastic distribution of material properties and stochastic external loadings in space are analysed when a crack of deterministic size is present. The material properties and external loadings are considered to constitute independent, two-dimensional, univariate, real, homogeneous stochastic fields. The stochastic fields are characterized by their means, variances, autocorrelation functions or the equivalent power spectral density functions, and scale fluctuations. The Young's modulus and Poisson's ratio are treated to be stochastic quantities. The external loading is treated to be a stochastic field in space. The energy release rate is derived using the method of virtual crack extension. The deterministic relationship is derived to represent the sensitivities of energy release rate with respect to both virtual crack extension and real system parameter fluctuations. Taylor series expansion is used and truncation is made to the first order. This leads to the determination of second-order properties of the output quantities to the first order. Using the linear perturbations about the mean values of the output quantities, the statistical information about the energy release rates, SIF and crack opening displacements are obtained. Both plane stress and plane strain cases are considered. The general expressions for the SIF in all the three fracture modes are derived and a more detailed analysis is conducted for a mode I situation. A numerical example is given.

Isomerization dynamics in viscous liquids: Microscopic investigation of the coupling and decoupling of the rate to and from solvent viscosity and dependence on the intermolecular potential

A detailed investigation of viscosity dependence of the isomerization rate is carried out for continuous potentials by using a fully microscopic, self-consistent mode-coupling theory calculation of both the friction on the reactant and the viscosity of the medium. In this calculation we avoid approximating the short time response by the Enskog limit, which overestimates the friction at high frequencies. The isomerization rate is obtained by using the Grote-Hynes formula. The viscosity dependence of the rate has been investigated for a large number of thermodynamic state points. Since the activated barrier crossing dynamics probes the high-frequency frictional response of the liquid, the barrier crossing rate is found to be sensitive to the nature of the reactant-solvent interaction potential. When the solute-solvent interaction is modeled by a 6-12 Lennard-Jones potential, we find that over a large variation of viscosity (eta), the rate (k) can indeed be fitted very well to a fractional viscosity dependence: (k similar to eta(-alpha)), with the exponent alpha in the range 1 greater than or equal to alpha >0. The calculated values of the exponent appear to be in very good agreement with many experimental results. In particular, the theory, for the first time, explains the experimentally observed high value of alpha even at the barrier frequency, omega(b). similar or equal to 9 X 10(12) s(-1) for the isomerization reaction of 2-(2'-propenyl)anthracene in liquid eta-alkanes. The present study can also explain the reason for the very low value of vb observed in another study for the isomerization reaction of trans-stilbene in liquid n-alkanes. For omega(b) greater than or equal to 2.0 X 10(13) s(-1), we obtain alpha similar or equal to 0, which implies that the barrier crossing rate becomes identical to the transition-state theory predictions. A careful analysis of isomerization reaction dynamics involving large amplitude motion suggests that the barrier crossing dynamics itself may become irrelevant in highly viscous liquids and the rate might again be coupled directly to the viscosity. This crossover is predicted to be strongly temperature dependent and could be studied by changing the solvent viscosity by the application of pressure. (C) 1999 American Institute of Physics. [S0021-9606(9950514-X].

Constraint loss under dynamic loading in rate independent plastic solids

The objectives of this paper are to examine the loss of crack tip constraint in dynamically loaded fracture specimens and to assess whether it can lead to enhancement in the fracture toughness at high loading rates which has been observed in several experimental studies. To this end, 2-D plane strain finite element analyses of single edge notched (tension) specimen and three point bend specimen subjected to time varying loads are performed. The material is assumed to obey the small strain J(2) flow theory of plasticity with rate independent behaviour. The results demonstrate that a valid J-Q field exists under dynamic loading irrespective of the crack length and specimen geometry. Further, the constraint parameter Q becomes strongly negative at high loading rates, particularly in deeply cracked specimens. The variation of dynamic fracture toughness K-dc with stress intensity rate K for cleavage cracking is predicted using a simple critical stress criterion. It is found that inertia-driven constraint loss can substantially enhance K-dc for (K) over dot > 10(5) MPa rootm/s.

Influence of temperature and strain rate on the flow stress of an FeAl alloy

The deformation behavior of an FeAl alloy processed by hot extrusion of water atomized powder has been investigated. Compression tests are performed in the temperature range 1073–1423 K and in the strain rate range 0.001–100 s−1 up to a true plastic strain of 0.5. The flow stress has been found to be strongly dependent on temperature as well as strain rate. The stress exponent in the power law rate equation is estimated to be in the range 7.0–4.0, decreasing with temperature. The activation energy for plastic flow in the range 1073–1373 K varies from 430 kJ mol−1 at low stresses to 340 kJ mol−1 at high stresses. However, it is fairly independent of strain rate and strain. The activation area has similarly shown a stress dependence and lies in the range 160–45b2. At 1423 K and at strain rates lower than 0.1 s−1 a strain rate sensitivity of 0.3 is observed with an associated activation energy of 375 kJ mol−1. The plastic flow in the entire range of temperature and strain rate investigated appears to be controlled by a diffusion mechanism. The results have revealed that it is possible to process the alloy by superplastic forming in the range 1373–1423 K at strain rates lower than 0.1 s−1.

The effect of T-stress on plane strain dynamic crack growth in elastic-plastic materials

In this paper, the effects of T -stress on steady, dynamic crack growth in an elastic-plastic material are examined using a modified boundary layer formulation. The analyses are carried out under mode I, plane strain conditions by employing a special finite element procedure based on moving crack tip coordinates. The material is assumed to obey the J (2) flow theory of plasticity with isotropic power law hardening. The results show that the crack opening profile as well as the opening stress at a finite distance from the tip are strongly affected by the magnitude and sign of the T -stress at any given crack speed. Further, it is found that the fracture toughness predicted by the analyses enhances significantly with negative T -stress for both ductile and cleavage mode of crack growth.

Impact of Energy Expenditure Rate Constraints on the performance of Multihop Wireless Mesh Networks

In this article we study the problem of joint congestion control, routing and MAC layer scheduling in multi-hop wireless mesh network, where the nodes in the network are subjected to maximum energy expenditure rates. We model link contention in the wireless network using the contention graph and we model energy expenditure rate constraint of nodes using the energy expenditure rate matrix. We formulate the problem as an aggregate utility maximization problem and apply duality theory in order to decompose the problem into two sub-problems namely, network layer routing and congestion control problem and MAC layer scheduling problem. The source adjusts its rate based on the cost of the least cost path to the destination where the cost of the path includes not only the prices of the links in it but also the prices associated with the nodes on the path. The MAC layer scheduling of the links is carried out based on the prices of the links. We study the e�ects of energy expenditure rate constraints of the nodes on the optimal throughput of the network.

Effect of strain rate and temperature on the plastic deformation behaviour of a bulk metallic glass composite

The composites consisting of amorphous matrix reinforced with crystalline dendrites offer extraordinary combinations of strength, stiffness, and toughness and can be processed in bulk. Hence, they have been receiving intense research interest, with a primary focus to study their mechanical properties. In this paper, the temperature and strain rate effects on the uniaxial compression response of a tailored bulk metallic glass (BMG) composite has been investigated. Experimental results show that at temperatures ranging between ambient to 500 K and at all strain rates; the onset of plastic deformation in the composite is controlled by that in the dendrites. As the temperature is increased to the glass transition temperature of the matrix and beyond, flow in the amorphous matrix occurs readily and hence it dictates the composite's response. The role of the constituent phases in controlling the deformation mechanism of the composite has been verified by assessing the strain rate sensitivity and the activation volume for deformation. The composite is rate sensitive at room temperature with values of strain rate sensitivity and activation volume being similar to that of the dendrites. At test temperatures near to the glass transition temperature, the composite however becomes rate-insensitive corresponding to that of the matrix phase. At low strain rates, serrated flow akin to that of dynamic strain ageing in crystalline alloys was observed and the serration magnitude decreases with increasing temperature. Initiation of the shear bands at the dendrite/matrix interface and propagation of them through the matrix ligaments until their arrest at another interface is the responsible mechanism for this. (C) 2011 Elsevier B.V. All rights reserved.

Fatigue crack growth due to overloads in plain concrete using scaling laws

Scaling laws are represented in power law form and can be utilized to extract the characteristic properties of a new phenomenon with the help of self-similar solutions. In this work, an attempt has been made to propose a scaling law analytically, for plain concrete when subjected to variable amplitude loading. Due to the application of overload on concrete structures, acceleration in the crack growth process takes place. A closed form expression has been developed to capture the acceleration in crack growth rate in conjunction with the principles of dimensional analysis and self-similarity. The proposed model accounts for parameters such as, the tensile strength, fracture toughness, overload effect and the structural size. Knowing the governed and the governing parameters of the physical problem and by using the concepts of self-similarity, a relationship is obtained between the different parameters involved. The predicted results are compared with experimental crack growth data for variable amplitude loading and are found to capture the overload effect with sufficient accuracy. Through a sensitivity analysis, fracture toughness is found to be the most dominant parameter in accelerating the crack length due to application of overload.

On the sphere decoding complexity of high-rate multigroup decodable STBCs in asymmetric MIMO systems

A space-time block code (STBC) is said to be multigroup decodable if the information symbols encoded by it can be partitioned into two or more groups such that each group of symbols can be maximum-likelihood (ML) decoded independently of the other symbol groups. In this paper, we show that the upper triangular matrix encountered during the sphere decoding of a linear dispersion STBC can be rank-deficient even when the rate of the code is less than the minimum of the number of transmit and receive antennas. We then show that all known families of high-rate (rate greater than 1) multigroup decodable codes have rank-deficient matrix even when the rate is less than the number of transmit and receive antennas, and this rank-deficiency problem arises only in asymmetric MIMO systems when the number of receive antennas is strictly less than the number of transmit antennas. Unlike the codes with full-rank matrix, the complexity of the sphere decoding-based ML decoder for STBCs with rank-deficient matrix is polynomial in the constellation size, and hence is high. We derive the ML sphere decoding complexity of most of the known high-rate multigroup decodable codes, and show that for each code, the complexity is a decreasing function of the number of receive antennas.

Analysis of fatigue crack growth in reinforced concrete beams

Mechanical behavior of reinforced concrete members is influenced by the action of unknown crack bridging reactions of rebars. Under cyclic loading, due to progressive growth of cracks, this bridging action contributes to the overall strength, stiffness and hysteretic behavior of the member. In this work, fatigue behavior of reinforced concrete beams are studied using a crack propagation law, developed using dimensional analysis for plain concrete with the effect of reinforcement being simulated through constraint exerted on the crack opening. The parameters considered in the model are fracture toughness, crack length, loading ratio and structural size. A numerical procedure is followed to compute fatigue life of RC beams and the dissipated energy in the steel reinforcement due to the shake down phenomenon under cyclic loading. Through a sensitivity study, it is concluded that the structural size is the most sensitive parameter in the fatigue crack propagation phenomenon. Furthermore, the residual moment carrying capacity of an RC member is determined as a function of crack extension by including the bond-slip mechanism.