Higher-order analysis of crack tip fields in elastic power-law hardening materials

A HIGHER-ORDER asymptotic analysis of a stationary crack in an elastic power-law hardening material has been carried out for plane strain, Mode 1. The extent to which elasticity affects the near-tip fields is determined by the strain hardening exponent n. Five terms in the asymptotic series for the stresses have been derived for n = 3. However, only three amplitudes can be independently prescribed. These are K1, K2 and K5 corresponding to amplitudes of the first-, second- and fifth-order terms. Four terms in the asymptotic series have been obtained for n = 5, 7 and 10; in these cases, the independent amplitudes are K1, K2 and K4. It is found that appropriate choices of K2 and K4 can reproduce near-tip fields representative of a broad range of crack tip constraints in moderate and low hardening materials. Indeed, fields characterized by distinctly different stress triaxiality levels (established by finite element analysis) have been matched by the asymptotic series. The zone of dominance of the asymptotic series extends over distances of about 10 crack openings ahead of the crack tip encompassing length scales that are microstructurally significant. Furthermore, the higher-order terms collectively describe a spatially uniform hydrostatic stress field (of adjustable magnitude) ahead of the crack. Our results lend support to a suggestion that J and a measure of near-tip stress triaxiality can describe the full range of near-tip states.

Stress-distribution around a rigid line in dissimilar media

The elastic plane problem of a rigid line inclusion between two dissimilar media was considered. By solving the Riemann-Hilbert problem, the closed-form solution was obtained and the stress distribution around the rigid line was investigated. It was found that the modulus of the singular behavior of the stress remains proportional to the inverse square root of the distance from the rigid line end, but the stresses possess a pronounced oscillatory character as in the case of an interfacial crack tip.

Orthotropy rescaling and implications for fracture in composites

For most practically important plane elasticity problems of orthotropic materials, stresses depend on elastic constants through two nondimensional combinations. A spatial rescaling has been found to reduce the orthotropic problems to equivalent problems in materials with cubic symmetry. The latter, under favorable conditions, may be approximated by isotropic materials. Consequently, solutions for orthotropic materials can be constructed approximately from isotropic material solutions or rigorously from cubic ones. The concept is developed to gain insight into the interplay between anisotropy and finite geometry. The inherent simplicity of the solutions allows a variety of technical problems to be addressed efficiently. Included are stress concentration related cracking, effective contraction of orthotropic material specimens, crack deflection onto easy fracture planes, and surface flaw induced delamination.

Crack deflection at an interface between dissimilar elastic-materials

A crack intersecting an interface between two dissimilar materials may advance by either penetrating through the interface or deflecting into the interface. The competition between deflection and penetration can be assessed by comparison of two ratios: (i) the ratio of the energy release rates for interface cracking and crack penetration; and (ii) the ratio of interface to material fracture energies. Residual stresses caused by thermal expansion misfit can influence the energy release rates of both the deflected and penetrating crack. This paper analyses the role of residual stresses. The results reveal that expansion misfit can be profoundly important in systems with planar interfaces (such as layered materials, thin film structures, etc.), but generally can be expected to be of little significance in fiber composites. This paper corrects an earlier result for the ratio of the energy release rate for the doubly deflected crack to that for the penetrating crack in the absence of residual stress.

The motion and the core structure of a geostrophic vortex - one-time scale inner solution and the motion of the vortex

By means of the matched asymptotic expansion method with one-time scale analysis we have shown that the inviscid geostrophic vortex solution represents our leading solution away from the vortex. Near the vortex there is a viscous core structure, with the length scale O(a). In the core the viscous stresses (or turbulent stresses) are important, the variations of the velocity and the equivalent height are finite and dependent of time. It also has been shown that the leading inner solutions of the core structure are the same for two different time scales of S/(ghoo)1/2 and S/a (ghoo)1/2. Within the accuracy of O(a) the velocity of a geostrophic vortex center is equal to the velocity of the local background flow, where the vortex is located, in the absence of the vortex. Some numerical examples demonstrate the contributions of these results.

Static and fatigue failure behavior of carbon-fiber reinforced epoxy composite-materials with edge notch

A study of carbon fiber reinforced epoxy composite material with 0° ply or ±45°ply(unnotched or with edge notch) was carried out under static tensile and tension-tensioncyclic loading testing. Static and fatigue behaviour and damage failure modes in unnotched/notched specimens plied in different manners were analysed and compared with each other.A variety of techniques (acoustic emission, two types of strain extensometer, high speed pho-tography, optical microscopy, scanning electron microscope, etc.) were used to examine thedamage of the laminates. Experimental results show that when these carbon/epoxy laminateswith edge notch normal to the direction of the load are axially loaded in static or fatiguetension, the crack does not propagate along the length of notch but is in the interface (fiberdirection). The notch has no substantial effect on the stresses at the unnotched portion. Thedamage failure mechanism is discussed.

Mixed-mode fracture mechanisms near the fatigue threshold of aisi-316 stainless-steel

Near threshold, mixed mode (I and II), fatigue crack growth occurs mainly by two mechanisms, coplanar (or shear) mode and branch (or tensile) mode. For a constant ratio of ΔK_I/ΔK_II the shear mode growth shows a self-arrest character and it would only start again when ΔK_I and ΔK_II are increased. Both shear crack growth and the early stages of tensile crack growth, are of a crystallographic nature; the fatigue crack proceeds along slip planes or grain boundaries. The appearance of the fracture surfaces suggest that the mechanism of crack extension is by developing slip band microcracks which join up to form a macrocrack. This process is thought to be assisted by the nature of the plastic deformation within the reversed plastic zone where high back stresses are set up by dislocation pile-ups against grain boundaries. The interaction of the crack tip stress field with that of the dislocation pile-ups leads to the formation of slip band microcracks and subsequent crack extension. The change from shear mode to tensile mode growth probably occurs when the maximum tensile stress and the microcrack density in the maximum tensile plane direction attain critical values.

波浪作用下海床的有效应力分析

波浪作用下海床的稳定性分析是海洋工程地质评价的重要内容。海床的稳定性可通过计算分析其随时间变化的有效应力场来评估。本文建议了一个周期荷载作用下土体的本构模型，并用于计算波浪作用下海床的应力与变形。采用Biot固理论和有限单元法，分析了海床的动态应力场与孔隙水压力场。波浪作用下两种渗系数时有效应力的动态变化过程结果对比，反映了渗透消散作用对海床有效应力变化的影响。

热喷涂构件中残余应力的理论分析

本文发展一种新的分析涂层结构（平板、梁）热残余应力的模型，可以研究骤冷过程（Quenching）和冷却过程（Cooling）在涂层结构内引发的残余应力分布。与以往模型相比，其优势在于：它可以考虑源于喷涂过程的涂层孔隙率、温度梯度等因素对于涂层和基底内残余应力的影响。其中孔隙率和温度分布由计算机模拟涂层沉积过程得到。另外，当基底的材料和几何参数被固定时，我们分析了诸如涂层的理想模量、厚度、热膨胀系数等参数，对于涂层结构中最终残余应力分布的改变机理。

激光辐照热障涂层中平面应变问题的热弹性变分分析

针对激光辐照热障涂层材料的平面应变问题,提出热障涂层热弹性分析的基本方程,对定常温度场给出级数形式解析解,并用最小余能原理和变分法分析了结构的热弹性应力场,研究了最大应力和界面应力的分布特征,并就一些物理参数的影响进行了讨论.结果表明,热障涂层的主要破坏因素为表面拉伸应力,界面应力相对较小,但在自由边界有集中现象,剥落应力大于剪切应力,是导致涂层破坏的重要原因.涂层厚度增加会改变厚度方向上的应力分布,界面应力向中心集中.

Size-dependent elastic properties of Ni nanofilms by molecular dynamics simulation

Size-dependent elastic properties of Ni nanofilms are investigated by molecular dynamics ( MD) simulations with embedded atom method (EAM). The surface effects are considered by calculating the surface relaxation, surface energy, and surface stress. The Young's modulus and yield stress are obtained as functions of thickness and crystallographic orientation. It is shown that the surface relaxation has important effects on the the elastic properties at nanoscale. When the surface relaxation is outward, the Young's modulus decreases with the film thickness decreasing, and vice versa. The results also show that the yield stresses of the films increase with the films becoming thinner. With the thickness of the nanofilms decreasing, the surface effects on the elastic properties become dominant.

Growth of deformation twins in room-temperature rolled nanocrystalline nickel

Deformation twinning has been observed in room-temperature rolled nanocrystalline Ni. The growth of the deformation twins via the emission of partial dislocations from a grain boundary has been examined in detail. Partial dislocations on neighboring slip planes may migrate for different distances and then remain in the grain interior, leading to the formation of a steplike twin boundary TB . With continued twin growth, the TBs become gradually distorted and lose their coherent character due to accumulated high stresses. Moreover, we propose that microtwins may form near such TBs due to the emission of partial dislocations from the TB.

Shape effects on the yield stress and deformation of silicon nanowires: A molecular dynamics simulation

The tension and compression of single-crystalline silicon nanowires (SiNWs) with different cross-sectional shapes are studied systematically using molecular dynamics simulation. The shape effects on the yield stresses are characterized. For the same surface to volume ratio, the circular cross-sectional SiNWs are stronger than the square cross-sectional ones under tensile loading, but reverse happens in compressive loading. With the atoms colored by least-squares atomic local shear strain, the deformation processes reveal that the failure modes of incipient yielding are dependent on the loading directions. The SiNWs under tensile loading slip in {111} surfaces, while the compressive loading leads the SiNWs to slip in the {110} surfaces. The present results are expected to contribute to the design of the silicon devices in nanosystems.

Nonlinear Dynamic Responses of Tension Leg Platform with Slack-Taut Tether

The slack-taut state of tether is a particular Averse circumstance, which may influence the normal operation stale of tension leg platform (TLP). The dynamic responses of TLP with slack-taut tether are studied with consideration of several nonlinear factors introduced by large amplitude motions. The time histories of stresses of tethers of a typical TLP in slack-taut state are given. In addition, the sensitivities of slack to stiffness and mass are investigated by varying file stiffness of tether and mass of TLP. It is found that slack is sensitive to the mass of TLP. The critical culled surfaces (over which indicates the slack) for the increase of mass are obtained.

Work and energy equations and the principle of generalized effective stress for unsaturated soils

The effective stress principle has been efficiently applied to saturated soils in the soil mechanics and geotechnical engineering practice; however, its applicability to unsaturated soils is still under debate. The appropriate selection of stress state variables is essential for the construction of constitutive models for unsaturated soils. Owing to the complexity of unsaturated soils, it is difficult to determine the deformation and strength behaviors of unsaturated soils uniquely with the previous single-effective-stress variable theory and two-effective-stress-variable theory in all the situations. In this paper, based on the porous media theory, the specific expression of work is proposed, and the effective stress of unsaturated soils conjugated with the displacement of the soil skeleton is further derived. In the derived work and energy balance equations, the energy dissipation in unsaturated soils is taken into account. According to the derived work and energy balance equations, all of the three generalized stresses and the conjugated strains have effects on the deformation of unsaturated soils. For considering these effects, a principle of generalized effective stress to describe the behaviors of unsaturated soils is proposed. The proposed principle of generalized effective stress may reduce to the previous effective stress theory of single-stress variable or the two-stress variables under certain conditions. This principle provides a helpful reference for the development of constitutive models for unsaturated soils.