A numerical investigation of ductile fracture initiation in a high-strength low-alloy steel

In this work, static and drop-weight impact experiments, which have been conducted using three-point bend fracture specimens of a high-strength low-alloy steel, are analysed by performing finite-element simulations. The Gurson constitutive model that accounts for the ductile failure mechanisms of microvoid nucleation, growth and is employed within the framework of a finite deformation plasticity theory. Two populations of second-phase particles are considered, including large inclusions which initiate voids at an early stage and small particles which require large strains to nucleate voids. The most important objective of the work is to assess quantitatively the effects of material inertia, strain rate sensitivity and local adiabatic temperature rise (due to conversion of plastic work into heat) on dynamic ductile crack initiation. This is accomplished by comparing the evolution histories of void volume fraction near the notch tip in the static analysis with the dynamic analyses. The results indicate that increased strain hardening caused by strain rate sensitivity, which becomes important under dynamic loading, plays a benign role in considerably slowing down the void growth rate near the notch tip. This is partially opposed by thermal softening caused by adiabatic heating near the notch tip.

High-temperature low-cycle fatigue behavior of a NIMONIC PE-16 superalloy—Correlation with deformation and fracture

Low-cycle fatigue (LCF) responses of NIMONIC PE-16 for various prior microstructures and strain amplitudes have been evaluated and the fatigue behavior has been explained in terms of the operative deformation mechanisms. Total strain-controlled LCF tests were performed at 923 K on samples possessing three different prior microstructures: alloy A in solution-annealed condition (free of γ′ and carbides), alloy B with double aging treatment (spherical γ′ of 18-nm diameter and M23C6), and alloy C with another double aging treatment (γ′ of size 35 nm, MC and M23C6). All three microstructures exhibited an intial cyclic hardening followed by a period of gradual softening at 923 K. Coffin-Manson plots describing the plastic strain amplitudevs number of reversals to failure showed that alloy A had maximum fatigue life while C showed the least. Alloy B exhibited a two-slope behavior in the Coffin-Manson plot over the strain amplitudes investigated. This has been ascribed to the change in the degree of homogeneity of deformation at high and low strain amplitudes. Transmission electron microscopic studies were carried out to characterize the various deformation mechanisms and precipitation reactions occurring during fatigue testign. Fresh precipitation of fine γ′ was confirmed by the development of “mottled contrast” in alloy C. Evidence for the shearing of the ordered γ′ precipitates was revealed by the presence of superdislocations in alloy C. Repeated shearing during cyclic loading led to the reduction in the size of the γ′ and consequent softening. Coarser γ′ precipitates were associated with Orowan loops. The observed fatigue behavior has been rationalized based on the micromechanisms stated above and on the degree of homogenization of slip assessed by slipband spacing measurements on tested samples.

Electrochemical phase formation involving multicomponents: hemispherical overlap models for varied nucleation and growth conditions

The phenomenological theory of hemispherical growth in the context of phase formation with more than one component is presented. The model discusses in a unified manner both instantaneous and progressive nucleation (at the substrate) as well as arbitrary growth rates (e.g. constant and diffusion controlled growth rates). A generalized version of Avrami ansatz (a mean field description) is used to tackle the ''overlap'' aspects arising from the growing multicentres of the many components involved, observing that the nucleation is confined to the substrate plane only. The time evolution of the total extent of macrogrowth as well as those of the individual components are discussed explicitly for the case of two phases. The asymptotic expressions for macrogrowth are derived. Such analysis depicts a saturation limit (i.e. the maximum extent of growth possible) for the slower growing component and its dependence on the kinetic parameters which, in the electrochemical context, can be controlled through potential. The significance of this model in the context of multicomponent alloy deposition and possible future directions for further development are pointed out.

Crossover dynamics at large metastability in gas-liquid nucleation

We have developed an alternate description of dynamics of nucleation in terms of an extended set of order parameters. The order parameters consist of an ordered set of kth largest clusters, ordered such that k = 1 is the largest cluster in the system, k = 2 is the second largest cluster, and so on. We have derived an analytic expression for the free energy for the kth largest cluster, which is in excellent agreement with the simulated results. At large supersaturation, the free energy barrier for the growth of the kth largest cluster disappears and the nucleation becomes barrierless. The major success of this extended theoretical formalism is that it can clearly explain the observed change in mechanism at large metastability P. Bhimalapuram et al., Phys. Rev. Lett. 98, 206104 (2007)] and the associated dynamical crossover. The classical nucleation theory cannot explain this crossover. The crossover from activated to barrierless nucleation is found to occur at a supersaturation where multiple clusters cross the critical size. We attribute the crossover as the onset of the kinetic spinodal. We have derived an expression for the rate of nucleation in the barrierless regime by modeling growth as diffusion on the free energy surface of the largest cluster. The model reproduces the slower increase in the rate of growth as a function of supersaturation, as observed in experiments.

Inherent structures of phase-separating binary mixtures: Nucleation, spinodal decomposition, and pattern formation

An energy landscape view of phase separation and nonideality in binary mixtures is developed by exploring their potential energy landscape (PEL) as functions of temperature and composition. We employ molecular dynamics simulations to study a model that promotes structure breaking in the solute-solvent parent binary liquid, at low temperatures. The PEL of the system captures the potential energy distribution of the inherent structures (IS) of the system and is obtained by removing the kinetic energy (including that of intermolecular vibrations). The broader distribution of the inherent structure energy for structure breaking liquid than that of the structure making liquid demonstrates the larger role of entropy in stabilizing the parent liquid of the structure breaking type of binary mixtures. At high temperature, although the parent structure of the structure breaking binary mixture is homogenous, the corresponding inherent structure is found to be always phase separated, with a density pattern that exhibits marked correlation with the energy of its inherent structure. Over a broad range of intermediate inherent structure energy, bicontinuous phase separation prevails with interpenetrating stripes as signatures of spinodal decomposition. At low inherent structure energy, the structure is largely phase separated with one interface where as at high inherent structure energy we find nucleation type growth. Interestingly, at low temperature, the average inherent structure energy (< EIS >) exhibits a drop with temperature which signals the onset of crystallization in one of the phases while the other remains in the liquid state. The nonideal composition dependence of viscosity is anticorrelated with average inherent structure energy.

An experimental approach for non-destructive evaluation of fatigue damage in CFRP composites

Study of fatigue phenomenon in composites requires a dynamic tool which can detect and identify different failure mechanisms involved. The tool should also be capable of monitoring the cumulative damage progression on-line. Acoustic Emission Technique has been utilized in the experimental investigations on unidirectional carbon fiber reinforced plastic (CFRP) composite specimens subjected to tension-tension fatigue. Amplitude as well as frequency distribution of Acoustic Emission (AE) signals have been studied to detect and characterize different failure mechanisms. For a quantitative measure of degradation of the material with fatigue load cycles, reduction in stiffness of the specimen has been measured intermittently. Ultrasonic imaging could give the information on the changes in the interior status of the material at different stages of fatigue life.

Asymptotic and finite element analyses of mode III dynamic crack growth at a ductile-brittle interface

In this work, dynamic crack growth along a ductile-brittle interface under anti-plane strain conditions is studied. The ductile solid is taken to obey the J(2) flow theory of plasticity with linear isotropic strain hardening, while the substrate is assumed to exhibit linear elastic behavior. Firstly, the asymptotic near-tip stress and velocity fields are derived. These fields are assumed to be variable-separable with a power singularity in the radial coordinate centered at the crack tip. The effects of crack speed, strain hardening of the ductile phase and mismatch in elastic moduli of the two phases on the singularity exponent and the angular functions are studied. Secondly, full-field finite element analyses of the problem under small-scale yielding conditions are performed. The validity of the asymptotic fields and their range of dominance are determined by comparing them with the results of the full-field finite element analyses. Finally, theoretical predictions are made of the variations of the dynamic fracture toughness with crack velocity. The influence of the bi-material parameters on the above variation is investigated.

Gas-liquid nucleation at large metastability: unusual features and a new formalism

Nucleation at large metastability is still largely an unsolved problem, even though it is a problem of tremendous current interest, with wide-ranging practical value, from atmospheric research to materials science. It is now well accepted that the classical nucleation theory (CNT) fails to provide a qualitative picture and gives incorrect quantitative values for such quantities as activation-free energy barrier and supersaturation dependence of nucleation rate, especially at large metastability. In this paper, we present an alternative formalism to treat nucleation at large supersaturation by introducing an extended set of order parameters in terms of the kth largest liquid-like clusters, where k = 1 is the largest cluster in the system, k = 2 is the second largest cluster and so on. At low supersaturation, the size of the largest liquid-like cluster acts as a suitable order parameter. At large supersaturation, the free energy barrier for the largest liquid-like cluster disappears. We identify this supersaturation as the one at the onset of kinetic spinodal. The kinetic spinodal is system-size-dependent. Beyond kinetic spinodal many clusters grow simultaneously and competitively and hence the nucleation and growth become collective. In order to describe collective growth, we need to consider the full set of order parameters. We derive an analytic expression for the free energy of formation of the kth largest cluster. The expression predicts that, at large metastability (beyond kinetic spinodal), the barrier of growth for several largest liquid-like clusters disappears, and all these clusters grow simultaneously. The approach to the critical size occurs by barrierless diffusion in the cluster size space. The expression for the rate of barrier crossing predicts weaker supersaturation dependence than what is predicted by CNT at large metastability. Such a crossover behavior has indeed been observed in recent experiments (but eluded an explanation till now). In order to understand the large numerical discrepancy between simulation predictions and experimental results, we carried out a study of the dependence on the range of intermolecular interactions of both the surface tension of an equilibrium planar gas-liquid interface and the free energy barrier of nucleation. Both are found to depend significantly on the range of interaction for the Lennard-Jones potential, both in two and three dimensions. The value of surface tension and also the free energy difference between the gas and the liquid phase increase significantly and converge only when the range of interaction is extended beyond 6-7 molecular diameters. We find, with the full range of interaction potential, that the surface tension shows only a weak dependence on supersaturation, so the reason for the breakdown of CNT (with simulated values of surface tension and free energy gap) cannot be attributed to the supersaturation dependence of surface tension. This remains an unsettled issue at present because of the use of the value of surface tension obtained at coexistence.

Low cycle fatigue behaviour of a nitrogen modified 316L stainless steel at 823 K

Strain controlled low cycle fatigue tests on solution annealed nitrogen modified 316L stainless steel have been conducted in air at 823 K to ascertain the influence of strain rate and strain amplitude. Effect of strain rate was examined from 3x10(-5) s(-1) to 3 x 10(-2) at a fixed strain amplitude of +/- 0.6%. The influence of strain amplitude was evaluated between +/- 0.25 % and +/- 1.0% at a constant strain rate of 3x10(-3) s(-1). The cyclic stress response at all testing conditions is characterized by an initial hardening followed by saturation. Serrated flow, a characteristic feature of dynamic strain ageing (DSA) was seen at strain rates lower than 3x10(-3) s(-1). Fatigue life was found to decrease with decrease in strain rate. The reduction in fatigue resistance is attributed mainly to the detrimental effects associated with DSA.

Heterogeneous nucleation of nanometre-sized Bi particles embedded in a Zn matrix

It is argued that the nanometric dispersion of Bi in a Zn matrix is an ideal model system for heterogeneous nucleation experiments. The classical theory of heterogeneous nucleation with a hemispherical cap model is applied to analyse the nucleation data. It is shown that, unlike the results of earlier experiments, the derived site density for catalytic nucleation and contact angle are realistic and strongly suggest the validity of the classical theory. The surface energy between the 0001 plane of Zn and the <10(1)over bar 2> plane of Bi, which constitute the epitaxial nucleation interface, is estimated to be 39 mJ m(-2).

Numerical simulations of fracture initiation in ductile solids under mode I, dynamic loading

In this paper, an overview of some recent computational studies by the authors on ductile crack initiation under mode I, dynamic loading is presented. In these studies, a large deformation finite element procedure is employed along with the viscoplastic version of the Gurson constitutive model that accounts for the micro-mechanical processes of void nucleation, growth and coalescence. A three-point bend fracture specimen subjected to impact, and a single edge notched specimen loaded by a tensile stress pulse are analysed. Several loading rates are simulated by varying the impact speed or the rise time and magnitude of the stress pulse. A simple model involving a semi-circular notch with a pre-nucleated circular hole situated ahead of it is considered. The growth of the hole and its interaction with the notch tip, which leads to plastic strain and porosity localization in the ligament connecting them, is simulated. The role of strain-rate dependence on ductile crack initiation at high loading rates, and the specimen geometry effect on the variation of dynamic fracture toughness with loading rate are Investigated.

Re-examination of crack opening model of interface fracture

The complex singularity associated with a crack at the interface between two dissimilar, isotropic and homogeneous materials leads to mathematical artefacts, such as stress oscillations and crack face interpenetrations in the vicinity of the crack tip. To avoid these unrealistic features, Sinclair (Sinclair GB. On the stress singularity at an interface crack. International Journal of Fracture 1980;16(2):111-9) assumed a finite crack opening angle (COA) such that the singularity lambda became real equal to 1/2. This paper extends the COA model by considering real singularities not necessarily equal to 1/2. When COA is 0 degrees: the interface crack singularity is complex with a real part equal to 1/2. On increasing COA, the imaginary part of the singularity decreases and becomes zero at a threshold value of COA; at this point, the singularity is a real, repeated value. A further increase in COA results in a pair of real singularities. Different crack opening configurations and material combinations are studied, and results presented for threshold COAs and associated values of singularity. Stress analyses for these three regimes: (a) complex, (b) real pair and (c) real repeated singularities, are reported. It is seen that additional complexities are present in the last case. Typical results for stress fields are also included for comparing with standard fields. (C) 1999 Elsevier Science Ltd. All rights reserved.

Energy released during arc crack propagation

The problem of circular arc cracks in a homogeneous medium is revisited. An unusual but simple method to calculate the energy change due to arc crack propagation along a circle is illustrated based on the earlier work of Sih and Liebowitz (1968). The limiting case of crack of angle 27pi is shown to correspond with the problem of a circular hole in a large plate under remote loading.

Low-pressure MOCVD of Al2O3 films using aluminium acetylacetonate as precursor: nucleation and growth

A study of the deposition of aluminium oxide films by low-pressure metalorganic chemical vapour deposition from the complex aluminium acetylacetonate, in the absence of an oxidant gas, has been carried out. Depositions on to Si(100), stainless steel, and TiN-coated cemented carbide are found to be smooth, shiny, and blackish. SIMS, XPS and TEM analyses reveal that films deposited at temperatures as low as 600 degreesC contain small crystallites Of kappa-Al2O3, embedded in an amorphous matrix rich in graphitic carbon. Optical and scanning electron microscopy reveal a surface morphology made up of spherulites that suggests that film growth might involve a melting process. A nucleation and growth mechanism, involving the congruent melting clusters of precursor molecules on the hot substrate surface, is therefore invoked to explain these observations. An effort has been made experimentally to verify this proposed mechanism. (C) 2002 Elsevier Science B.V. All rights reserved.