An extensive 3D dislocation dynamics investigation of stage-I fatigue crack propagation

Stage-I fatigue crack propagation is investigated using 3D discrete dislocation dynamics (DD) simulations. Slip-based propagation mechanisms and the role of the pre-existing slip band on the crack path are emphasized. Stage-I crack growth is found to be compatible with successive decohesion of the persistent slip band/matrix interface rather than a mere effect of plastic irreversibility. Corresponding crack tip slip displacement magnitude and the associated crack growth rate are evaluated quantitatively at various tip distances from the grain boundary. This shows that grain boundaries systematically amplify slip dispersion ahead of the crack tip and consequently, slow down the stage-I crack growth rate. The results help in developing an original crack propagation model, accounting for the boundary effects relevant to polycrystals. The crack growth trend is then evaluated from calculations of the energy changes due to crack length increments. It is shown that the crack necessarily propagates by increments smaller than 10 nm.     

Effect of surface treatment for steel adherends on static and fatigue crack growth of epoxy adhesives

The fracture toughness of unmodified, glass-bead-reinforced and CNBR-modified epoxy adhesives under mode I loading is not improved by acid surface treatment of steel adherends since cohesive failure always occurs for all adhesives with or without acid surface treatment. On the other hand, the fatigue crack growth resistance greatly increases due to acid surface treatment of steel adherends. Especially, the threshold dramatically increases. The crack grows cohesively at all stages of crack velocity for DCB specimens treated with acids while it grows at the interface between the adherend and the adhesive layer for the specimens whose polished surface of adherends is only decreased with solvent. An optical microscope observation revealed that adherend surfaces treated with acids were rougher than ones without acid treatment, although XPS examination for the surfaces did not show significant difference in their chemical elements among the specimens with and without acid treatment.     

Stage-I fatigue crack studies in order to validate the dislocation-free zone model of fracture for bulk materials

Stage-I fatigue cracks are commonly described by the model of Bilby, Cottrell and Swinden (BCS model). However, since several experimental investigations have shown a dislocation-free zone (DFZ) in front of crack-tips, it is necessary to validate the new DFZ model and to examine the deviations to the BCS model. Therefore, the dislocation density distribution is derived from height profiles of slip lines in front of stage-I fatigue cracks in CMSX4® single crystals measured by contact-mode atomic force microscopy. This is possible, because the cracks are initiated at notches milled by focused ion beam technique directly on slip planes with a high Schmid factor. Consequently, the directions of the Burgers vectors are well known; it is possible to calculate the dislocation density distributions from the height profiles. The measured distributions are compared to the calculated distribution function of the DFZ model proposed by Chang et al. The additionally measured microscopic friction stress of the dislocations is then used to calculate the influence of grain boundaries on the dislocation density distribution in front of stage-I cracks. The calculation is done by the extended DFZ model of Shiue et al. and compared with the measured distribution function in polycrystalline specimens. Finally, the crack-tip sliding displacement as a measure for the crack propagation rate is compared for the DFZ model and the BCS model with the experimentally revealed values. The important result: the often used BCS model does not reflect the experimental measurements. On the contrary, the DFZ model reflects the measurements at stage-I cracks qualitatively and quantitatively.     

Fracture mechanics of propagating 3-D fatigue cracks with parametric dislocations

Abstract

Propagation of 3-D fatigue cracks is analyzed using a discrete dislocation representation of the crack opening displacement. Three dimensional cracks are represented with Volterra dislocation loops in equilibrium with the applied external load. The stress intensity factor (SIF) is calculated using the Peach–Koehler (PK) force acting on the crack tip dislocation loop. Loading mode decomposition of the SIF is achieved by selection of Burgers vector components to correspond to each fracture mode in the PK force calculations. The interaction between 3-D cracks and free surfaces is taken into account through application of the superposition principle. A boundary integral solution of an elasticity problem in a finite domain is superposed onto the elastic field solution of the discrete dislocation method in an infinite medium. The numerical accuracy of the SIF is ascertained by comparison with known analytical solution of a 3-D crack problem in pure mode I, and for mixed-mode loading. Finally, fatigue crack growth simulations are performed with the Paris law, showing that 3-D cracks do not propagate in a self-similar shape, but they re-configure as a result of their interaction with external boundaries. A specific numerical example of fatigue crack growth is presented to demonstrate the utility of the developed method for studies of 3-D crack growth during fatigue.     

From monoscale to multiscale modeling of fatigue crack growth: Stress and energy density factor

The formalism of the earlier fatigue crack growth models is retained to account for multiscaling of the fatigue process that involves the creation of macrocracks from the accumulation of micro damage.The effects of at least two scales,say micro to macro,must be accounted for.The same data can thus be reinterpreted by the invariancy of the transitional stress intensity factors such that the microcracking and macrocracking data would lie on a straight line.The threshold associated with the sigmoid curve disappears.Scale segmentation is shown to be a necessity for addressing multiscale energy dissipative processes such as fatigue and creep.Path independency and energy release rate are monoscale criteria that can lead to unphysical results,violating the first principles.Application of monoscale failure or fracture criteria to nanomaterials is taking toll at the expense of manufacturing super strength and light materials and structural components.This brief view is offered in the spirit of much needed additional research for the reinforcement of materials by creating nanoscale interfaces with sustainable time in service.The step by step consideraton at the different scales may offer a better understanding of the test data and their limitations with reference to space and time.     

Scatter of fatigue data owing to material microscopic effects

A common phenomenon of fatigue test data reported in the open literature such as S-N curves exhibits the scatter of points for a group of same specimens under the same loading condition.The reason is well known that the microstructure is different from specimen to specimen even in the same group.Specifically,a fatigue failure process is a multi-scale problem so that a fatigue failure model should have the ability to take the microscopic effect into account.A physically-based trans-scale crack model is established and the analytical solution is obtained by coupling the micro-and macro-scale.Obtained is the trans-scale stress intensity factor as well as the trans-scale strain energy density(SED)factor.By taking this trans-scale SEDF as a key controlling parameter for the fatigue crack propagation from micro-to macro-scale,a trans-scale fatigue crack growth model is proposed in this work which can reflect the microscopic effect and scale transition in a fatigue process.The fatigue test data of aluminum alloy LY12 plate specimens is chosen to check the model.Two S-N experimental curves for cyclic stress ratio R=0.02 and R=0.6 are selected.The scattering test data points and two S-N curves for both R=0.02 and R=0.6 are exactly re-produced by application of the proposed model.It is demonstrated that the proposed model is able to reflect the multiscaling effect in a fatigue process.The result also shows that the microscopic effect has a pronounced influence on the fatigue life of specimens.     

A model of a belt chamber cracking based on crack profiles calculations

Abstract

The problem of a Belt chamber matrix cracking is presented. The influence of crack surface quality on the effective values of near crack tip stress is discussed. It is shown that under working conditions of the vessel, the existing shear friction between upper and lower crack surfaces caused by crack surface roughness can prevent the crack surface sliding displacement. Therefore, the control variable for matrix cracking is the value of stress intensity factor K_I corresponding to normal node of loading only. The calculations are performed by finite element method within the range of linear elastic fracture mechanics.     

A model for crack formation during active solid pyrolysis of a char-forming solid: crack patterns; surface area generation; volatile mass efflux

A model is developed for the formation and propagation of cracks in a material sample that is heated at its top surface, pyrolyses, and then thermally degrades to form char. In this work the sample is heated uniformly over its entire top surface by a hypothetical flame (a heat source). The pyrolysis mechanism is described by a one-step overall reaction that is dependent nonlinearly on the temperature (Arrhenius form). Stresses develop in response to the thermal degradation of the material by means of a shrinkage strain caused by local mass loss during pyrolysis. When the principal stress exceeds a prescribed threshold value, the material forms a local crack. Cracks are found to generally originate at the surface in response to heating, but occasionally they form in the bulk, away from ever-changing material boundaries. The resulting cracks evolve and form patterns whose characteristics are described. Quantities examined in detail are: the crack spacing in the pyrolysis zone; the crack length evolution; the formation and nature of crack loops which are defined as individual cracks that have joined to form loops that are disconnected from the remaining material; the formation of enhanced pyrolysis area; and the impact of all of the former quantities on mass flux. It is determined that the mass flux from the sample can be greatly enhanced over its nominal (non-cracking) counterpart. The mass efflux profile qualitatively resembles those observed in Cone Calorimeter tests.     

A growth kinetics model of rate decomposition for Si1-xGex alloy based on dimer theory

According to the dimer theory on semiconductor surface and chemical vapor deposition(CVD) growth characteristics of Si1-xGex, two mechanisms of rate decomposition and discrete flow density are proposed. Based on these two mechanisms, the Grove theory and Fick’s first law, a CVD growth kinetics model of Si1-xGex alloy is established. In order to make the model more accurate, two growth control mechanisms of vapor transport and surface reaction are taken into account. The paper also considers the influence of the dimer structure on the growth rate. The results show that the model calculated value is consistent with the experimental values at different temperatures.     

A random covering interpretation for the phase transition of the random energy model

The random energy model is related to a random covering of the real line. The phase transition is interpreted as the passage from a regime where a family of random intervals covers the line (high temperature) to a noncovering regime (low temperature).     

A qualitative model for the growth mechanism of silver clusters in polymer solution

A simple and high-reproducible method for the synthesis of polymer-protected silver cluster of controlled size is described. UV-visible spectroscopy has been used for investigating the influence of the aging of the protective poly(vinylpyrrolidone) layer on the cluster growth rate at different reaction temperatures and poly(vinylpyrrolidone)/ethylene glycol weight ratios. The obtained results show that the aging time of the polymeric stabilizer solution plays a fundamental role in the reproducibility of the cluster growth process. A model for the metal cluster formation-grow process is also proposed. Received 18 July 2001 and Received in final form 3 October 2001     

锗硅/硅异质结材料的化学气相淀积生长动力学模型

基于化学气相淀积(CVD)的Grove理论和Fick第一定律,提出并建立了锗硅(SiGe)/硅(Si)异质结材料减压化学气相淀积(RPCVD)生长动力学模型.与以前锗硅/硅异质结材料生长动力学模型仅考虑表面反应控制不同,本模型同时考虑了表面反应和气相传输两种控制机理,并给出了两种控制机理极限情况下的模型.本模型不仅适用于低温锗硅/硅应变异质结材料生长的表征,也适用于表征高温锗硅/硅弛豫异质结材料生长的表征.将模型计算值与实验结果进行了对比,无论是625℃低温下的应变SiGe的生长,还是900℃高温下的弛豫 关键词： SiGe/Si异质结材料 化学气相淀积生长动力学模型 Grove理论 Fick第一定律     

A simple model for the growth kinetics of Fe2B iron boride on pure iron substrate

The present work evaluates the growth kinetics of Fe₂B iron boride forming on iron substrate by means of a diffusion model in the temperature range 1223-1323 K. The model takes into account the effect of the boride incubation time during the formation of Fe₂B phase. The parabolic growth constant at the (Fe₂B/Fe) interface and the mass gain generated by this treatment were estimated. Likewise a simple relationship was proposed to describe the variation of the parabolic growth constant as a function of both the temperature and the boron content in the Fe₂B phase. Furthermore, the simulation results show a good agreement with our experimental results.