Effect of microstructure on the upper and lower limits of material toughness in elastic-plastic fracture

The objective of this study is to provide some quantitative relations linking the two bounds of fracture toughness, the lower (K_ini) and the upper (K_ss), with certain microstructural parameters, such as relative inclusion volume, grain size, average microvoid spacing, average radius of an activated inclusion, number of inclusions contained within the process zone associated with a quasi-static crack, etc. Two limits of material behavior, brittle and ductile, are discussed. Both limits are derived from a single mathematical model which employs the D-BCS concept of ‘line plasticity’ as developed for a stationary crack, but extends its range of validity onto a moving crack situation. Only the quasi-static limit of motion is considered.     

Optimizing settings by accounting for uncontrollable material and environmental variables

Process settings that work well for one batch may not work for another due to variation in the uncontrollable variables that characterize environmental and raw material properties, for example. This paper presents an optimization methodology to identify settings for a particular batch based on information about uncontrollable variables in the batch. Also, the methodology predicts whether the batch is likely to produce a successful output or if it should be scrapped. The batch process we consider, that is common in industries such as pharmaceuticals, petroleum, and food processing, is characterized by many, highly correlated input variables. Input variables include those that can be set, such as temperatures and flow rates, as well as the uncontrollable variables. A nonlinear mathematical program identifies the optimal process settings when the distribution of the uncontrollable variables is known. When the distribution is unknown, the optimal process settings are obtained by combining sequential sampling and a robust optimization procedure that takes into account the variability in the sample estimates. The work here is motivated by our research in multivariate process control for batch extrusion processes. We demonstrate the proposed methodology using an extrusion simulation.     

Finite-element simulation of interfacial crack propagation: Methods and tools for the complete failure process under large scale yielding

Interface crack propagation is described with an advanced finite element model on the basis of a non-linear material law with large plastic deformation and a global energy release rate criterion. The simulation covers the whole failure process in one model, starting from small loads, development of a large plastic zone, onset of cracking and crack propagation until complete rupture.The model implements an elastic-plastic material law including hardening. Numerical stability and reliability strongly depend on the correct implementation of the material law. The central part is the realization of a moving crack. Due to the discrete nature of a finite element model, the crack can only propagate in finite steps resulting in sudden changes of boundary conditions. Smoothing these changes is essential for numerical stability and reasonable computation time.Simulated crack propagation bases on a criterion to decide between further increase of load or further advance of crack. A global energy release criterion is used here and was found to be independent of the specific discretisation.     

Integrated approach for prediction of stability limits for machining with large volumes of material removal

High-speed machining of thin-walled structures is widely used in the aeronautical industry. Higher spindle speed and machining feed rate, combined with a greater depth of cut, increases the removal rate and with it, productivity. The combination of higher spindle speed and depth of cut makes instabilities (chatter) a far more significant concern. Chatter causes reduced surface quality and accelerated tool wear. Since chatter is so prevalent, traditional cutting parameters and processes are frequently rendered ineffective and inaccurate. For the machine tool to reach its full utility, the chatter vibrations must be identified and avoided. In order to avoid chatter and implement optimum cutting parameters, the machine tool including all components and the work piece must be dynamically mapped to identify vibration characteristics. The aim of the presented work is to develop a model for the prediction of stability limits as a function of process parameters. The model consists of experimentally measured vibration properties of the spindle-tool, and finite element calculations of the work piece in (three) different stages of the process. Commercial software packages used for integration into the model prove to accomplish demands for functionality and performance. A reference geometry that is typical for an aircraft detail is used for evaluation of the prediction methodology. In order to validate the model, the stability limits predicted by the use of numerical simulation are compared with the results based on the experimental work.     

Crack tip parameters for large scale yielding and low constraint configurations

This article introduces a quasi-deformation plasticity theory which takes account of nonproportional loading by means of an orthotropic yield surface. The analysis is used to extend fracture mechanics concepts beyond the normal limits of J-integral theory. A simple correction for crack tip stresses is derived from the quasi-deformation assumption. This correction indicates that the degree of crack tip triaxiality is related to the relationship between the J-integral and the crack tip opening displacement (CTOD). Predictions of crack tip stress fields agree well with published finite element results.The simple correction for crack tip fields is used in conjunction with micromechanical failure models for cleavage and microvoid coalescence to predict fracture toughness in large scale yielding. These analyses indicate that cleavage toughness is very sensitive to losses in triaxiality. Predictions for a center cracked panel, for instance, indicate that the effective driving force for cleavage may be significantly less than the apparent driving force. Resistance to crack initiation by microvoid coalesence is affected by constraint but it is not nearly as sensitive as cleavage resistance.

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Résumé L'article introduit la théorie de la plasticité sous déformations virtuelles qui prend en compte une mise en charge non proportionnelle au moyen d'une surface d'écoulement plastique orthotrope.On utilise l'analyse par l'exclusion des concepts de mécanique de rupture au delà des limites normales de la théorie de l'intégrale J. Par l'hypothèse des déformations virtuelles, on déduit une correction simple pour les contraintes à l'extrémité de la fissure. Cette correction indique que le degré de triaxialité à l'extrémité de la fissure] est lié à la relation entre l'intégrale J et le CTOD. Les prévisions sur les champs de contraintes à l'extrémité de la fissure sont en bon accord avec les résultats par éléments finis qui sont publiés.La correction simple pour des champs à l'extrémité d'une fissure est utilisée dans des modèles de rupture à l'échelle microscopique pour le clivage et la coalescence de micro-lacunes, en vue de prédire la ténacité à la rupture lors d'un écoulement plastique à grande échelle.De telles analyses indiquent que la ténacité par rapport au clivage est très sensible à des pertes de triaxialité. Ainsi, par exemple, les prédictions relatives à un panneau fissuré en son centre, indiquent que la force entraînant effectivement le clivage peut être significativement moindre qu'il n'appert.La résistance à l'amorcage d'une fissure sous l'effet d'une coalescence de micro-lacunes est affectée par le bridage, mais elle n'y est pas aussi sensible que la résistance au clivage.

     

The effects of functionally graded material structure on wear resistance and toughness of repaired weldments

To perform a long lasting, crack-free repair welding on ultrahigh strength steels, the filler metal must be chosen and applied properly. Avoiding several short-term repairs or replacements, the repaired weldment should reveal comparative characteristics such as wear resistance, toughness and hardness to base metal. In the present study, a novel functionally graded material have been introduced to obtain enhanced wear resistance and hardness at surface as well as improved fracture toughness at fusion line of repaired weldments. A comparative study of wear resistance of repaired weld metals has been carried out by pin-on-disk apparatus at 5 N normal load and 0.14 ms⁻¹ sliding speed. Fracture toughness of weld metal was also evaluated by charpy absorbed fracture energy tests and scanning electron microscopy fractograghs. The results show that by employing functionally graded layers, toughness was enhanced significantly while retaining the surface wear resistance.     

Genuinely resultant shell finite elements accounting for geometric and material non-linearity

A general theoretical framework is presented for the fully non-linear analysis of shells by the finite element method. The governing equations are derived exclusively in terms of resulting quantities through a logical and straightforward descent from three-dimensional continuum mechanics without appealing to simplifying assumptions (hence the name genuinely resultant). As a result, the underlying theory is statically and geometrically exact, and it naturally includes small strain and finite strain problems of thin as well as thick shells. The underlying mathematical structure and the variational formulation of the theory are examined. This appears to be crucial for the development of computational procedures employing the Newton-Kantorovich linearization process and the Galerkin type discretization method. The treatment of finite rotations through an arbitrary parametrization of the rotation group and the interpolation procedure of SO(3)-valued functions underlying the construction of finite element basis are other issues studied in this paper. A numerical analysis is presented in order to assess the effectiveness of the proposed formulation. Small strain problems as well as finite strain deformation of rubber-like shells undergoing finite rotations are considered. Special attention is devoted to the assessment of the relevance of the drilling degree-of-freedom and highly non-uniform through-the-thickness deformation in the case of shells made of incompressible material.     

Turbulence modulation by large ellipsoidal particles: concentration effects

We use laboratory measurements to study how suspended ellipsoidal particles affect the velocity statistics of a turbulent flow. The ellipsoids have size, time, and velocity scales corresponding to the inertial subrange of the turbulence and are nearly neutrally buoyant. These characteristics make them likely candidates for two-way interactions with the fluid (i.e., they influence the flow and are influenced by it). We vary the volume fraction of suspended ellipsoids and observe the effects on one- and two-point velocity statistics in the fluid phase. Measurements at two different heights indicate that particle buoyancy (0.5 % denser than the ambient fluid) significantly changes volume fraction. We see that particles’ effect on turbulent kinetic energy is a non-monotonic function of the volume fraction. We also find that particles’ presence causes a redistribution of velocity variance from large scales to small scales within the inertial subrange, i.e., the slope of power spectra is flatter than in the single-phase case.     

Folded graphene reinforced nanocomposites with superior strength and toughness: A molecular dynamics study

Toughness and strength are important material parameters in practical structural applications.However,it remains a great challenge to achieve high toughness and high strength simultaneously for most materials.Here,we report a folded graphene(FG) reinforced copper(Cu) nanocomposite that overcomes the long-standing conflicts between toughness and strength.Intensive molecular dynamics simulations show that the 10% pre-strain-induced four-wave-patterned FG(1.09 wt%) reinforced Cu nanocomposite exhib...     

The Brazilian test: a tool for measuring the toughness of a material and its brittle to ductile transition

Due to their brittleness, assembling of ceramics pieces is generally achieved through brazing but thermal stresses during cooling frequently induce cracking of the material used for brazing. In order to check if such damage is avoidable, it is necessary to characterize the brittle to ductile transition (BDT) of the material. Simple compression is not suited for crack studies, because of mixed loading (mode II + compressive mode I cracking). Another type of test, the cylinder splitting test, known as the Brazilian test, can be carried out by applying compressive forces on two opposite generatrix of a cylinder: this causes a uniform tensile stress on the plane containing the axis of the cylinder and the generatrix, leading to mode I cracking. The advantage of this test is to avoid expensive and random machining of brittle samples. This study shows that the Brazilian test is well adapted for the measurement of toughness and the characterization of the BDT of materials whose room temperature behaviour is brittle (silicides, intermetallics etc.).     

Nickel-alumina interfacial fracture toughness: experiments and analysis of residual stress effects

The purpose of the present work is to account for the influence of residual stresses on the measured fracture toughness of a representative metal-ceramic system and, in conjuction with a maximum hoop stress criterion, to explain the observed increase in toughness with increasing mixity of loading. For the sandwich specimen geometry adopted in the current study, a simple argument yields a critical layer thickness below which residual stress effects are expected to be minimized. The measured fracture toughness is found to be independent of thickness for thicknesses below this threshold. For such specimens a general result is demonstrated: compared to the same loading without residual stresses present, the effect of residual stresses is to decrease the magnitude of the phase angle of the stresses which develop along the interface. It is argued that when small-scale yielding conditions hold, both the mixity and the critical hoop stress corresponding to fracture should be reported at a length which falls within the -dominant region in the sample. In this manner, good quantitative agreement between theory and experiment is demonstrated.     

飞艇囊体薄膜材料的双向拉伸试验及结构仿真

飞艇囊体膜材的弹性常数是飞艇外形设计、结构分析、动力学分析的基础。本文根据正交异性平面应力模型假设,应用双向拉伸试验方法获得了飞艇囊体膜材HV130在不同载荷比条件下的经纬向弹性模量和泊松比。对飞艇囊体进行应力分析,得到囊体应力的理论解及环向应力和轴向应力的载荷比。根据飞艇囊体受力情况,选取对应的弹性常数,对飞艇进行不同压差条件下的静力学仿真分析。利用非接触应变测量系统测试不同压差条件下飞艇囊体的变形情况,验证了双向拉伸试验所得的弹性常数的准确性和仿真分析的可靠性。本文能为飞艇的外形设计和结构分析提供参考。      

Plane-strain propagation of a fluid-driven fracture during injection and shut-in: Asymptotics of large toughness

This paper considers the problem of plane-strain fluid-driven fracture propagating in an impermeable elastic medium under condition of large toughness or, equivalently, of low fracturing fluid viscosity. We construct an explicit solution for a fracture propagating in the toughness-dominated regime when the energy dissipated in the viscous fluid flow inside the fracture is negligibly small compared to the energy expended in fracturing the solid medium. The next order corrections in viscosity to this limiting solution are then derived, allowing the range of problem parameters corresponding to the toughness-dominated regime to be established. The first-order small viscosity (large toughness) solution is shown to provide an excellent approximation of the solution for the crack length in the wide range of the viscosity parameter. Furthermore, this solution, when combined with the first-order small-toughness solution of Garagash and Detournay [Journal of Applied Mechanics, 2005], provides a simple analytical approximation of the crack length solution in practically the entire range of viscosity (toughness). It is also shown that the established method of asymptotic expansion in small parameter is equally applicable to study other small effects (e.g., fluid inertia) on the otherwise toughness-dominated solution. A solution for the fracture evolution during shut-in (i.e., after fluid injection rate is suddenly stopped) is also obtained. This solution, which corresponds to a slowing fracture evolving towards the toughness-dominated steady state, draws attention to the possibility of substantial fracture growth after fluid injection is ceased especially under conditions when the fracture propagation during injection phase is dominated by viscous dissipation.     

A study concerning material fracture toughness and some small punch test data for low alloy steels

The present study has demonstrated the existence of a significant relationship between the small punch energy and the biaxial strain at the point of failure. Furthermore, using published trends relating biaxial fracture strain and fracture material toughness, relationships concerning fracture toughness and small punch energy values were generated. It was shown that the predictions from certain such relationships exhibited good commonality with published real fracture toughness data. Furthermore, one study which related fracture toughness to non-metallic inclusion distribution was promising while other models based upon microstructural details and small scale fracture roughness factors were less successful. This study must be considered provisional in nature since it represents a first attempt at relating small punch data with material fracture toughness, and as such, contains a few assumptions which are somewhat tentative.     

Freezing of silver cluster and nanowire: A comparison study by molecular dynamics simulation

The crystallization of liquid Ag cluster and nanowire, about 2.3 nm in diameter, has been studied by molecular dynamics simulation at three different cooling rates (i.e., 2 × 10¹³ K/s, 2 × 10¹² K/s, 2 × 10¹¹ K/s). It is found that the structure of Ag cluster in the specified size changes from amorphous to crystalline directly during the cooling process, rather than follows the route of amorphous–icosahedra–crystalline. The Ag nanowire in the specified size also changes from amorphous to crystalline directly, rather than follows the route of amorphous–(multi-shelled)–crystalline. All the finial structures of Ag cluster and nanowire after relaxation are FCC despite the different cooling rates, which means that the FCC is the most stable structure. Furthermore, the crystallization temperature of Ag nanowire is higher than that of cluster at the same cooling rate, which suggests that the crystallization temperature is dimensional-dependent.     

Prediction of Joule-Thomson inversion curves for pure fluids and one mixture by molecular simulation

The predictive power of a set of molecular models, which have been adjusted to vapor-liquid equilibria only, is validated. For that purpose, Joule-Thomson inversion curves were determined by molecular simulation for 15 pure fluids, i.e. argon, methane, oxygen, nitrogen, carbon dioxide, ethylene, carbon monoxide, R11, R23, R41, R124, R125, R134a, R143a, R152a, and for air. Comparison of the simulation results with reference equations of state shows an excellent agreement.     

A mixed shell formulation accounting for thickness strains and finite strain 3d material models

A non‐linear quadrilateral shell element for the analysis of thin structures is presented. The Reissner–Mindlin theory with inextensible director vector is used to develop a three‐field variational formulation with independent displacements, stress resultants and shell strains. The interpolation of the independent shell strains consists of two parts. The first part corresponds to the interpolation of the stress resultants. Within the second part independent thickness strains are considered. This allows incorporation of arbitrary non‐linear 3d constitutive equations without further modifications. The developed mixed hybrid shell element possesses the correct rank and fulfills the in‐plane and bending patch test. The essential feature of the new element is the robustness in the equilibrium iterations. It allows very large load steps in comparison with other element formulations. We present results for finite strain elasticity, inelasticity, bifurcation and post‐buckling problems. Copyright © 2007 John Wiley & Sons, Ltd.