A three-dimensional model of diffusion-controlled sintering

A three-dimensional diffusional model is used to describe sintering of powder compacts composed of monosized corundum particles. The sintering process is thought of as consisting of four stages. The duration of each stage and the corresponding shrinkage and porosity are evaluated. The results agree reasonably well with experimental data on the sintering of corundum ceramics.     

A model kinetics for nucleation and diffusion-controlled growth of immiscible alloys

A system of mean field rate equations is employed for describing the kinetics of solid-solid phase separation within the immiscibility gap of binary alloys. The system allows us to study the time evolution of both supersaturation and diffusion length of the components in the metastable phase. It is shown that in the case of simultaneous nucleation the system of differential equations leads to a simple formula for the characteristic time of the transformation in terms of material parameters and initial supersaturation. The nucleation rate is computed on the basis of the classical nucleation theory and the alloy is assumed to behave as a regular solution. It turns out that for low values of the initial supersaturation the nucleation process can be considered as simultaneous. It is also found that thermally activated nucleation takes place for supersaturation values lower than about 0.21. The assumption of a concentration-independent diffusion coefficient and the effect of nucleus curvature on interface composition have been analyzed and discussed.     

A mathematical model for wet-chemical diffusion-controlled mask etching through a circular hole

Asymptotic solutions are presented for diffusion-controlled wet-chemical etching through a round hole in a mask. The three-dimensional diffusion field is assumed to be axisymmetric and fully developed. Two time regimes are considered. The first applies when the etched depth is small in comparison with the width of the mask opening. In the second, the depth of etching is much greater than the width of the mask opening. Explicit solutions are found for the shape of the etched surface as a function of the physical parameters. Among other things it is found that, as long as the etched pits are shallow, etching through small apertures is faster than through larger ones. The opposite is true for deep pits.     

Contributions of internal hydrogen and room-temperature creep to the abnormal fatigue cracking of Ti6246 at high Kmax

This study aims at explaining the absence of a threshold for crack propagation in an /β titanium alloy during cyclic tests performed with constant K_max and increasing K_min, if K_max is higher than 60–70% of K_Ic. Tensile, creep as well as fatigue crack growth tests are performed on specimens with various hydrogen content. SIMS analyses of hydrogen content around the tip of a crack developed in the abnormal regime are made. Solute hydrogen is shown to segregate at the crack tip and to enhance room-temperature creep, strain localisation and decohesion along /β interfaces.     

Statistical model of the transverse ply cracking in cross-ply laminates by strength and fracture toughness based failure criteria

Cross-ply laminate subjected to tensile loading provides a relatively well understood and widely used model system for studying progressive cracking of the transverse ply. This test allows to identify material strength and/or toughness characteristics as well as to establish relation between damage level and the composite stiffness reduction. The transverse ply cracking is an inherently stochastic process due to the random variability of local material properties of the plies. The variability affects both crack initiation (governed by the local strength) and propagation (governed by the local fracture toughness). The primary aim of the present study is elucidation of the relative importance of these phenomena in the fragmentation process at different transverse and longitudinal ply thickness ratios. The effect of the random crack distribution on the mechanical properties reduction of the laminate is also considered. Transverse ply cracking in glass fiber/epoxy cross-ply laminates of the lay-ups [0₂/90₂]_s, [0/90₂]_s, and [0/90₄]_s is studied. Several specimens of each lay-up were subjected to uniaxial quasistatic tension to obtain crack density as a function of applied strain. Crack spacing distributions at the edge of the specimen also were determined at a predefined applied strain. Statistical model of the cracking process is derived, calibrated using crack density vs. strain data, and verified against the measured crack spacing distributions.     

A progressive fracture model for carbon nanotubes

An atomistic-based progressive fracture model for simulating the mechanical performance of carbon nanotubes by taking into account initial topological and vacancy defects is proposed. The concept of the model is based on the assumption that carbon nanotubes, when loaded, behave like space-frame structures. The finite element method is used to analyze the nanotube structure and the modified Morse interatomic potential to simulate the non-linear force field of the C–C bonds. The model has been applied to defected single-walled zigzag, armchair and chiral nanotubes subjected to axial tension. The defects considered were: 10% weakening of a single bond and one missing atom at the middle of the nanotube. The predicted fracture evolution, failure stresses and failure strains of the nanotubes correlate very well with molecular mechanics simulations from the literature.     

A viscoplastic constitutive model for dynamic fracture

The use of a viscoplastic approach to dynamic fracture prediction is proposed with the aim of producing a model which is applicable to ductile situations. A numerical (finite-element) approach is adopted with specially developed joint elements being used to simulate behaviour within the fracture-process zone. Results are presented for an expanding edge-crack problem. Experimental results are used to calibrate the numerical model by determining the material-specimen parameters under dynamic-fracturing conditions. Detailed results are presented for both LEFM and nonlinear fracture-mechanics approaches.     

A continuum phase field model for fracture

A phase field model based on a regularized version of the variational formulation of brittle fracture is introduced. The influences of the regularization parameter that controls the interface width between broken and undamaged material and of the mobility constant of the evolution equation are studied in finite element simulations. A generalized Eshelby tensor is derived and analyzed for mode I loading in order to evaluate the energy release rate of the diffuse phase field cracks. The numerical implementation is performed with finite elements and an implicit time integration scheme. The configurational forces are computed in a postprocessing step after the coupled problem of mechanical balance equations and the evolution equation is solved. Some of the numerical results are compared to analytical results from classical Griffith theory.     

A micro-continuum model for the creep behavior of complex nanocrystalline materials

A nanocrystalline material which has an average grain size of less than 100 nm is characterized with a significant portion of atoms residing in the grain boundaries or in the grain-boundary affected zone (GBAZ), while nanocrystalline materials with a more complex structure may contain additional strengthening nanoparticles or nano pores. In this article we develop a micro-continuum model to capture the creep response of such a complex nanocrystalline system. We make use of the concept of a three-phase composite with the GBAZ serving as the matrix, and grain interiors and dispresed particles (or voids) as two distinct types of inclusions. Both the grain interior and the GB zone are capable of undergoing the rate-dependent plastic deformation, but the strengthening nanoparticles or pores are taken to deform only elastically. During deformation the porosity will continue to evolve; its evolution is also addressed. In addition, the effect of temperature on the overall creep response is also accounted for. Several important features of creep characteristics in light of grain size, and nanoparticle and nanopore concentrations, are illustrated, and it is also demonstrated that the calculated results are in reasonable agreement with available experimental data.     

A state-based peridynamic model for quantitative fracture analysis

A new state-based peridynamic model is proposed to quantitatively analyze fracture behavior (crack initiation and propagation) of materials. In this model, the general relationship of the critical stretch and the critical energy release rate is for the first time obtained for the state-based peridynamic model of linear elastic brittle materials, and the released energy density is defined to quantitatively track the energy released during crack propagation. The three-dimensional (3D) and two-dimensional (2D) (for both plane stress and plane strain) cases are all considered. As illustrations, the compact tension and double cantilever beam tests are analyzed using the proposed model, which is capable of successfully capturing fracture behaviors (e.g., crack path and concentration of strain energy density) of the considered fracture tests. The characteristic parameters (i.e., critical load, critical energy release rate, etc.) are calculated and compared with available experimental and numerical data in the literature to demonstrate validity of the proposed model.     

A phase-field model for fracture in piezoelectric ceramics

A phase-field model is presented for modeling the fracture of piezoelectric ceramics. The implementation of several different crack face boundary conditions, including conducting, permeable, and insulating or impermeable, as well as energetically consistent is described. The approach to the latter involves a finite deformation framework for piezoelectricity. In addition, a new function that governs material degradation is proposed to eliminate the presence of high phase-field values in the vicinity of large electric fields. The new function is found to lead to improved brittle material behavior as well. Results are presented that demonstrate the capability of the model to capture complicated phenemona that arise in piezoelectric fracture, including crack retardation, acceleration, and turning.     

A fracture mechanics model for fatigue in concrete

A theoretical model based on fracture mechanics is developed. The tensile failure of plain concrete during both monotonic and cyclic loading conditions can be described. The results of a numerical study utilizing the model are compared with experimental results.     

Effects of creep ductility and notch constraint on creep fracture behavior in notched bar specimens

The creep rupture life of U-type notched specimens and smooth specimens has been calculated based on the ductility exhaustion damage model using stress-dependent creep ductility. Effects of creep ductility and notch constraint on creep fracture behaviour in notched bar specimens have been investigated. The results show that the U-type notch exhibits notch strengthening effect under a wide range of stress level and notch constraint condition (notch acuity) for creep ductile materials. The lower equivalent stress in notched specimens plays main role for reducing creep damage and increasing rupture life. The rupture life of notched specimens of creep brittle materials (with lower creep ductility) decreases with the increase in stress level and notch constraint. With increasing creep ductility and decreasing notch constraint, the degree of the notch strengthening effect increases. In creep life designs and assessments of high-temperature components containing notches, the material creep ductility, notch constraint and stress levels need to be fully considered.     

A phase-field model for brittle fracture of anisotropic materials

In the present work, a phase field damage model is developed to address the numerical simulation of brittle fracture. This model successfully captures some important aspects of crack propagation, including crack branching and bifurcation. In addition, the proposed phase field model has been developed in the general framework of anisotropic elasticity. It can thus be used for the simulation of brittle fracture in polycrystalline materials, for which crack propagation is impacted by crystallographic orientation because of the anisotropic character of stiffness properties.     

A model for fracture of explosively driven metal shells

A model for fracture of explosively driven metal shells presented in this work is based on integrating three-dimensional axisymmetric arbitrary Lagrangian-Eulerian hydrocode analyses with analyses from a newly developed fragmentation computer code MOTT. The developed model was based on the Mott’s theory of break-up of cylindrical “ring-bombs”, in which the length of the average fragment is a function of the radius and the expansion velocity of the shell at the moment of break-up, and the mechanical properties of the metal. The validation of the MOTT code fragmentation model was accomplished using existing explosive fragmentation munition arena test data. After having established the crucial parameters of the model, a new explosive fragmentation munition was designed and optimized. Upon fabrication of the developed munition, the performance of the new charge was tested in a series of small-scale experiments including flash radiography, high-speed photography, and sawdust fragment recovery. The accuracy of the MOTT code predictions is excellent.     

A simple model for elastic fracture in thin films

A simple model for the cracking of thin films has been developed and investigated. The film is represented by a network of bonds and nodes which initially form a triangular lattice in which each node is at the junction of six bonds. The nodes are also attached to a rigid substrate by bonds which are not broken but have a relatively small force constant. Cracking is simulated by a sequence of thermally activated bond breaking events followed by mechanical relaxation. If the stretching force constant associated with the bonds in the surface layer is large, linear cracks propagate rapidly and, at a later stage, are connected by secondary cracks which become less and less linear as the strain in the surface layer is relaxed by the cracking process. Many of our simulations exhibit a distint “initiation” period in which the bond breaking rate is low, followed by a period of rapid crack propagation in which a large fraction of the surface strain energy is released. This period is then followed by a second period of relatively slow bond breaking. During the first period isolated defects are formed, followed by linear cracks in the second period. During the third period non-linear cracks connect the linear cracks, and structures which resemble shear bands are formed. Results for the effects of finite relaxation rates for the elastic network (visco-elastic effects) are also presented.     

A statistical model of cleavage fracture

The aim of the paper is to provide a sound theoretical basis to the statistics of cleavage fracture in three-dimensional cracked structures. The probability of critically sized carbide being present in a Fracture Initiation Zone ahead of the crack tip has been derived, and shown to have a two-parameter Weibull distribution, with a shape parameter that is proportional to the strain-hardening exponent of the material. In a three-dimensional structure the cracking of such critically sized, intergranular carbide is necessary, but may not be sufficient to precipitate brittle fracture; this is because intergranular carbide is randomly orientated within the crack-opening stress field, so its orientation must also be unfavourable. It has been hypothesised that in three-dimensional structures the actual probability of fracture will be an extreme from the necessary distribution, in which case a sample of fracture toughness observations will be described by a Gumbel distribution, called here the LED model. After discussing the minimum number of fracture toughness observations needed to fit the model, its strength of evidence is compared with those of other candidate models, including the Master Curve model, and the LED model is shown to be the best.     

Plasticity,fracture and friction in steady-state plate cutting

A closed form solution to the problem of steady-state wedge cutting through a ductile metal plate is presented. The considered problem is an idealization of a ship bottom raking process, i.e. a continuous cutting damage of a ship bottom by a hard knife-like rock in a grounding event A new kinematic model is proposed for the strain and displacement fields and it is demonstrated that the analysis is greatly simplified if the strain field is assumed to be dominated by plastic shear strains and moving hinge lines. Also, it is shown that the present shear model offers the basis for a convenient extension of the presented plate model to include more structural members as for example the stiffeners attached to a ship bottom plating. The fracture process is discussed and the model is formulated partly on the basis of the material fracture toughness. The effect of friction and the reaction force perpendicular to the direction of motion is derived theoretically in a consistent manner. The perpendicular reaction force is of paramount importance for predicting the structural damage of a ship hull because it governs the vertical ship motion and rock penetration which is strongly coupled with the horizontal resistance and thus with the damaged length. The derived expressions are discussed and compared with previously published experimental results and formulas.