Complete determination of the stress tensor in a field using brittle coatings

Brittle coatings are used today, almost exclusively, to determine the directions of the principal stresses at a point located on the surface of a loaded body. This is a strange paradox of history, because no other method can give more complete information about the stress tensor in a whole field. This is so, event if it is also true that the precision of the determinations of some of the components of the tensor may not be as high as that generally obtained using other methods.This paper has the following objectives: (1) to show the application of the brittle-coating method to the determination of very complicated stress distributions like those which develop in thin-walled pressure vessels manufactured using circumferential and longitudinal weldings, (2) to show that the use of brittle coatings is the most practical method to solve some of these problems when boundary conditions are not well known, (3) to show that the method can, in certain cases (when the two principal stresses have the same sign), give the complete determination of the tensor in large parts of the field of complex stress distributions, and that it is the only method that can obtain that amount of information in one experiment, (4) to show how in other cases (when the two principal stresses are of opposite sign) that information can be obtained in two experiments, (5) to show the possibility of using the method to study yielding problems, (6) to review some of the advantages and limiations of the method and (7) to recommend an organized effort to find new materials which may permit the method to become popular again, without exhibiting some of the serious limitations that have significantly restricted its use. Some of the deficiencies in the present state of knowledge are described.     

Modeling the influence of the coating deposition technology on the contact interaction characteristics

For a multilayer elastic half-space, we consider an axisymmetric loading model taking into account damage on the interface between the layers. The influence of intermediate layers arising in various coating technologies on the contact and internal stresses occurring in the coating and the substrate under elastic indentation conditions is studied for relatively rigid and nonrigid coatings.     

Limit analysis of multi-layered plates. Part II: Shear effects

In the first part of this work [Dallot, J., Sab, K., 2007. Limit analysis of multi-layered plates. Part I: the homogenized Love-Kirchhoff model. J. Mech. Phys. Solids, in press, doi:10.1016/j.jmps.2007.05.005], the limit analysis of a multi-layered plastic plate submitted to out-of-plane loads was studied. The authors have shown that a homogeneous equivalent Love-Kirchhoff plate can be substituted for the heterogeneous multi-layered plate, as the slenderness (length-to-thickness) ratio goes to infinity. In fact, the out-of-plane shear stresses are shown to become asymptotically negligible when compared to in-plane stresses, as the slenderness ratio goes to infinity. Actually, failure of thick multi-layered structures often occurs by shearing in the core layers and sliding at the interfaces between the layers. Both shearing and sliding are caused by the out-of-plane shear stresses. The purpose of the present paper is to build an enhanced Multi-particular Model for Multi-layered Material (M4) taking into account shear stress effects. In this model, each layer is seen as a Reissner-Mindlin plate interacting with its neighboring layers through interfaces. The proposed model is asymptotically consistent with the homogenized Love-Kirchhoff model described in the first part of the work, as the slenderness ratio goes to infinity. Kinematic and static methods for the determination of the limit load of a thick multi-layered plate which is submitted to out-of-plane distributed forces are described. The special case of multi-layered plates under cylindrical bending conditions is studied. These conditions lead to simplifications which often allow for the analytical resolution of the Love-Kirchhoff and the M4 limit analysis problems. The benefit of the proposed M4 model is demonstrated on an example. A comparison between the heterogeneous 3D model, the Love-Kirchhoff model and the M4 model is performed on a three-layer sandwich plate under cylindrical bending conditions. Finite element calculations are used to solve the 3D problem, while both the Love-Kirchhoff and the M4 problems are analytically solved. It is shown that, when the contrast between the core and the skins strengths is high, the Love-Kirchhoff model fails to capture the plastic collapse modes that cause the ruin of the sandwich plate. These modes are well captured by the M4 model which predicts limit loads that are very consistent with the limit loads predicted by the heterogeneous 3D model (the relative error is found to be smaller than 1%).     

Linear and Nonlinear Algorithms for Stress Separation in Photoelasticity

An experimental-numerical hybrid method for the stress separation in photoelasticity is proposed in this study. In the proposed method, boundary conditions for a local finite element model, that is, tractions along boundaries are inversely determined from photoelastic fringes. Two algorithms are proposed for determining the boundary condition. One is a linear algorithm in which the tractions are obtained by the method of linear least-squares from both principal stress difference and principal direction. Another is the nonlinear algorithm in which the tractions are determined only from the principal stress difference. After determining the boundary conditions for the local finite element model, the stresses can be obtained by finite element direct analysis. The effectiveness is demonstrated by applying the proposed method to a perforated plate under tension and contact problems. Results show that the boundary conditions of the local finite element model can be determined from the photoelastic fringes and then the individual stresses can be obtained by the proposed method. Furthermore, the stresses can be evaluated even if the boundary condition is complicated such as at the contact surface. It is expected that the proposed method can be powerful tool for stress analysis.     

Deformable spherical devices to measure stresses within field soils

The design, calibration and use of two deformable spherical stress transducers are described. They are suitable for detecting principal stresses in deforming media such as soil and have major advantages over many rigid transducers previously used in such situations. One of the transducers is a water-filled rubber ball (WFRB) sensitive to hydrostatic and deviator stresses, the other is a mastic ball which deforms plastically and is sensitive to only deviator stresses. When the two devices are used at similar depths under a surface load, e.g. a wheel, the combined measurements of internal pressure of the WFRB and axial deformation of the mastic ball can be used to derive values for first and third principal stresses (assuming second and third principal stresses are equal). Calibration of the transducers at different temperatures is described.

Field measurements made with the transducer under loaded wheels are compared with predicted values of first principal stresses using equations developed by Söhne. Close correspondence between predicted and measured values was observed, when the existing soil strength conditions were taken into account.

The transducers promise to be useful in the measurement of stresses in field soils.     

Computer simulation of the interaction between a wheel and a corrugated rail

The paper discusses the problems of modelling and simulation of the wheel/rail contact in the case when geometrical irregularities of the rail are taken into account. The iterative method for determining the geometrical relationship between the profile of a rigid rail and the trajectory of the centre of a rigid wheel is presented. The computer code that implements this method is a part of the computer model of the wheel/rail system. The model allows the case when the wheel loses contact with the rail and afterwards hits the rail. Simulation analysis is focused on the question as to whether the wheel bouncing off and on the rail may occur under normal operation conditions. The other question is how this bouncing influences the pressure forces between the wheel and the rail, and how it influences the stress distribution within the contact zone.     

Characterization of random microstructural stresses and fracture estimation

In this paper, the analytical approach to quantitative characterization of random microstructural residual stress field in brittle elastic materials is presented. The analysis consists of two parts. First, we expound the basic features of random microstructural stresses and show how the eigenstrain approach (of “classical” micromechanics) can be extended to the situations where randomness of the initial eigenstrains has to be taken into account. The second part of the paper deals with the effects of random microstresses on crack growth phenomena. The stress intensity induced by random dilatant transformation eigenstrains and by thermally-induced random microstresses are treated in detail, including numerical and graphical illustrations of specific crack problems.     

Local stress singularities in mixed axisymmetric problems of the bending of circular cylinders

A method of analyzing the near-edge stress state in mixed problems of the deformation of an isotropic cylindrical body is proposed. The method is based on the expansion of the solution of three-dimensional problems of elasticity into a series of Lurie–Vorovich homogeneous basis functions. An asymptotic analysis is performed to find the principal part of the solution of the infinite systems of linear algebraic systems to which the problems are reduced. The type of the stress singularity at the edge of the cylinder is the same as in the mixed problems for a quarter plane. Kummer’s convergence acceleration method is used. The obtained results are validated by testing the boundary conditions and by comparing with results obtained by other authors     

Mechanics of formation and rupture of human aneurysm

The mechanical response of the human arterial wall under the combined loading of inflation, axial extension, and torsion is examined within the framework of the large deformation hyper-elastic theory. The probability of the aneurysm formation is explained with the instability theory of structure, and the probability of its rupture is explained with the strength theory of material. Taking account of the residual stress and the smooth muscle activities, a two layer thick-walled circular cylindrical tube model with fiber-reinforced composite-based incompressible anisotropic hyper-elastic materials is employed to model the mechanical behavior of the arterial wall. The deformation curves and the stress distributions of the arterial wall are given under normal and abnormal conditions. The results of the deformation and the structure instability analysis show that the model can describe the uniform inflation deformation of the arterial wall under normal conditions, as well as formation and growth of an aneurysm under abnormal conditions such as the decreased stiffness of the elastic and collagen fibers. From the analysis of the stresses and the material strength, the rupture of an aneurysm may also be described by this model if the wall stress is larger than its strength.     

Stress concentration around several holes in structural elements

Conclusions Our analysis of specific numerical results for nonclassical problems has thus established two conclusions.1. The stresses do not increase monotonically as the holes are brought closer together (in the case of problems for shells under static loading and for plates under dynamic loading).2. For several holes in the case of problems for plates under dynamic loading, the maxima of the stress concentration factors can occur in the interior of the main region rather than at the edges of the holes, depending on the frequency and form of the applied load.These conclusions do not apply to classical problems (the planar problem under static loading) and must therefore be taken into account when stress concentrations are created.Because of space limitations, the concluding part of this article was not included in the EPMESC'92 Conference Proceedings and is therefore published here in its entirety.This is the complete text of a paper that was presented by the author at the EPMESC'92 International Conference in Talien, China, June 30-August 2, 1992, but was not published in its entirely in the Conference Proceedings.S. P. Timoshenko Institute of Mechanics, Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 30, No. 4, pp. 6–13, April, 1994.     

Micromechanical analysis of failure in thin protective coatings

The integrity of protective coatings is the subject of this investigation. Specifically, we concentrate on the case of thermo-protective coatings, so-called thermal barrier coatings, aiming at development of methodology for service life estimation of the coated components under thermal loading. At the current phase of the development, we establish relationships between various thermal loading patterns and failure driving parameters at different failure stages by developing an analytical–computational model of the process. The analysis addresses a typical failure development pattern consisting of a system of multiple surface cracks leading to and branching along or near the interface between the coating and the base material. The process is driven by thermal stresses. The developed model is applicable to thin coatings and provides insight into the processes taking place during failure development and the effect of the details of the applied thermal loading.The methods developed in the course of this investigation may be applied to the analysis of environmental effects on protective coatings and to investigations of failure development in layered composite systems under general loading conditions.     

EVOLUTION OF VOIDS IN DUCTILE POROUS MATERIALS AT HIGH STRAIN RATE

In the present work,a dynamic damage model in ductile materials underthe application of dynamic general stresses loading is presented.The evolution equationof ductile voids has the closed form,in which work-hardening,the change of surfaceenergy of voids,rate-dependent,inertial effects are taken into account.Theexpressions of critical stresses for the growth and compaction of voids are directlyobtained from the evolution equations of voids.From the expressions,the resultobtained by Carroll and Holt,as a special example,is given.Numerical analysis ofthe model indicates that the growth of voids is sensitive to the strain rates.The voidsgrow quickly as the increase of strain rates.It is also shown that the influence of theinertial effects on the void growth is great at high loading rates.It appears to resist thegrowth of voids.In addition,a dynamic collapse model of ductile voids is alsoproposed,which can be applied to study the problems of compaction in powder andother materials.     

On local buckling of thin shells

A class of problems is considered where the buckling initially starts only in a part of the shell—locally. The stability analysis is focused on the zone of initial buckling. This leads to radical simplification. First the basic hypothesis and stability equations are formulated. Closed-form stability criteria asymptotically exact for very thin shells are discussed. This gives sufficient conditions for the local character of buckling and for the adequacy of the asymptotic approximation. The analysis taking into account the variation of stresses and shape inside the buckling zone results in a check of stability by hand calculations or by simple coding of a desk-top computer. The adequacy of the simplest representation of the stress and strain variation in the buckling zone is tested.     

On the boundary conditions of the geometrically nonlinear Kirchhoff–Love shell theory

The present paper addresses the problem of establishing the boundary conditions of a geometrically nonlinear thin shell model, especially the kinematic ones. Our model is consistently derived from general 3D continuum mechanics statements. Generalized cross-sectional strains and stresses are based on the deformation gradient and the first Piola–Kirchhoff stress tensor. Since only the bending deformation is included in this model, no special technique needs to be adopted in order to avoid shear-locking. The theory is derived in such a way that any material model can be considered as a constitutive relation, once the zero transverse normal stress assumption is properly taken into account.     

塑封硅器件中介电薄膜的温湿效应分析

随着铜互连以及low-k电介质在超大规模集成电路中地广泛使用，low-k电介质的机械完整性及其对互连可靠性变得更加重要。影响介电膜的机械完整性和互连可靠性的因素包括介电膜的工艺制程，芯片与封装材料的相互影响，以及环境温度和湿度的影响。本文研究集中于了解环境温度和湿度对塑封硅器件中介电薄膜的可靠性影响。采用快速温度和湿度实验条件，对塑封硅器件中介电薄膜受水分和温度损伤的敏感性进行了分析。运用商业有限元（FEA）分析软件，对水分在塑封材料和硅器件中的扩散过程进行了建模及仔细分析。并对硅器件周边密封圈的防水分扩散效力进行了研究。通过这一系列实验与分析，对塑封硅器件中介电薄膜的温湿效应有了完整地了解，并提出和建立了相关的物理模型和经验公式。运用这物理模型和经验公式可对在各种使用环境温度和湿度条件下，塑封硅器件中介电薄膜的可靠性进行评估及分析。     

Propagation of thin plastic zones in the vicinity of a normally separating crack

A problem of the development of a plastic zone in the vicinity of a physical cut in the plain strain and stress states is posed and solved on the basis of a discrete deformation model under the assumption of an ideal elastoplastic medium. The Tresca yield condition and the ultimate plasticity condition are used in studying the plane stress state. The dependence of the plastic zone length on the external load is compared with a similar dependence obtained on the basis of the Leonov-Panasyuk-Dugdale model. In contrast to the Leonov-Panasyuk-Dugdale model, the distributions of stresses and lengths of plastic zones in the plane strain and stress states are found to be substantially different if elastic compressibility and compressive-tensile stresses along the cut direction are taken into account.     

Torsion of cylindrical bodies with varying strain properties

We analyze the results of experimental studies of effective strain properties of damaged, porous, and other inhomogeneous materials and study the main laws of their behavior under strain. We consider the possible versions of constitutive relations taking account of the dependence of the properties of the media under study on the loading conditions or the strain conditions and the relations between the shear and bulk strains. Since the traditional statement of the torsion problems for bodies with such properties cannot be used, we analyze the strain consistency equations and the relations between the strains and displacements in cylindrical coordinates and obtain expressions for the displacements in an appropriate generalized form, which can be used not only for the torsion problems. We study how the distributions of displacements, strains, and stresses under torsion depend on the parameter characterizing the susceptibility of the material strain properties to variations in the stress state type. We show that, in the case of torsion of a cylinder of circular cross-section, there is no deplanation of the cross-section, just as in the classical solution, but the distributions of displacements, strains, and stresses significantly differ from the well-known solutions.     

高应变率下延性多孔介质中孔洞的动态演化

本文提出了一个新的材料延性动态损伤模型，模型中不但包括了率效应，同时还考虑了惯性效应，孔洞表面能变化和材料硬化对孔洞演化的影响。此外，在模型中同时考虑了体应力和偏应力对孔洞演化的作用，从孔洞演化方程地接到了孔洞增长和压缩应力临界表达式，Ｃａｒｒｏｌｌ和Ｈｏｌｔ结果作为该表达式的一个特例而得出，模型的数值分析得出以下结论：①延性孔洞的动太增长对率效应十分敏感，应变率越高，孔洞增长越快；②惯性效应在主     

Stress Analysis of Laminated Shells of Revolution with an Imperfect Interlayer Contact

An approach is proposed to solve problems on the contact interaction of layers in structurally inhomogeneous shells of revolution with allowance for both the normal and tangential stresses in the contact zones. A system of algebraic equations is constructed by using a method for solution of static problems for arbitrary shells of revolution. From this system, the contact zones and contact stresses are determined by the iteration method. The restricted behavior of the adhesion layer in cleavage and shear is taken into account. As an example, the stress state of a two-layer cylindrical shell under a concentrated load is determined