Cyclic-deformation behavior of notched mild-steel plates in plane stress

Notched rectangular SAE 1015 mild-steel plates were subjected to controlled cyclic nominal stresses or strains in a closed-loop servo-controlled fatigue-testing machine. Resistance strain gages were used to measure strains at the notch roots. These strains showed that large mean strains and strain ranges prevailed at these notches, though nominal strains were fully reversed and small. Inelastic stress- and strain-concentration factors calculated at various cycles were used to check the accuracy of the Neuber relation between these concentration factors and elastic stress-concentration factor. Limitations of this relation and characteristic notch-strain behavior mentioned above are discussed with reference to the peculiarities of the stress-strain relationships of this material.     

The Saint-Venant problem of plane bar under an axial force

I.PrefaceAsweknow,theSaint-Venanttheoryisawell-knownanduniversallyacceptedtheory.Butasoneofthegeneraltheoriesofelasticmechanics,itisnotprovedperfectely,althoughitistestedbyexperiments.Infact,onlyforthesimplestproblemofelasticity,itisnoteasytofindanalytics…     

Finite element analysis of localization in FCC polycrystalline sheets under plane stress tension

Localization phenomena in thin sheets subjected to plane stress tension are investigated. The sheet is modelled as a polycrystalline aggregate, and a finite element analysis based on rate-dependent crystal plasticity is developed to simulate large strain behaviour. Accordingly, each material point in the specimen is considered to be a polycrystalline aggregate consisting of a large number of FCC grains. The Taylor model of crystal plasticity theory is assumed. This analysis accounts for initial textures as well as texture evolution during large plastic deformations. The numerical analysis incorporates certain parallel computing features. Simulations have been carried out for an aluminum sheet alloy, and the effects of various parameters on the formation and prediction of localized deformation (in the form of necking and/or in-plane shear bands) are examined.     

A new concept of path-independent integrals for plane elasticity

A general method to construct path-independent integrals in the framework of plane elasticity is presented. The proposed path-independent integrals are valid not only for the case of a single straight crack, but also for the case of any number of collinear cracks. The integrands of these integrals are classified in three classes, which satisfy some well-defined restrictions. Therefore, it is possible to construct a large number of new path-independent integrals. As an illustration some of them are derived and are applied to the theoretical computation of the stress intensity factor in five particular cases of cracked elastic plates.

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Resumé On présente une méthode générale de construction d'intégrales indépendantes du contour dans l'élasticité plane. Les intégrales independantes du contour, proposées dans cet article, sont valables non seulement dans le cas d'une seule fissure mais aussi dans le cas d'un nombre arbitraire de fissures collineaires. Les intégrands de cas intégrales sont classifiés en trois classes, qui satisfont des restrictions bien-definies. De cette façon, il est possible de construire un nombre important de nouvelles integrales indépendentes du contour. Afin d'illustrer la méthode, un certain nombre d'intégrales est appliqué pour un calcul théorique du facteur d'intensité des contraintes de cinq cas des plaques fissurées.

     

Strain analysis of nonlocal viscoelastic Kelvin bar in tension

Based on viscoelastic Kelvin model and nonlocal relationship of strain and stress, a nonlocal constitutive relationship of viscoelasticity is obtained and the strain response of a bar in tension is studied. By transforming governing equation of the strain analysis into Volterra integration form and by choosing a symmetric exponential form of kernel function and adapting Neumann series, the closed-form solution of strain field of the bar is obtained. The creep process of the bar is presented. When time approaches infinite, the strain of bar is equal to the one of nonlocal elasticity.     

Strain analysis of nonlocal viscoelastic Kelvin bar in tension

Based on viscoelastic Kelvin.model and：nonlocal relationship of strain and stress, a nonlocal constitutive relationshila of viscoelasticity is obtained and the strain response of a bar in tension is studied, By transforming governing equation of the strain analysis into Volterra integration form and by choosing a symmetric exponential form of kernel function and adapting Neumann series, the closed-form s.olution of strain field of the bar is obtained.： The creep process of the bar is presented： When time approaches infinite, the strain of bar is equal to the one of nonlocal elasticity     

平面梁杆结构几何非线性分析的一种简便方法

本文提出了一种新的几何非线性分析方法，适用于结点位移任意大，单元刚体转角任意大、单元局部弯曲比较小的平面梁杆结构。文中的刚度矩阵和附加荷载列阵都是以显式形式给出的，可直接应用。     

Chevron notched short bar testing of high toughness steels

Chevron notched short bar tests offer a simple, inexpensive method of fracture toughness measurement for both quality control and analytical purposes. They also provide data for thinner specimens than current techniques allow.This report describes an investigation into the applicability of this technique to medium strength, high toughness steel, which cannot easily be tested using plane strain fracture toughness methods. The results show that while the test procedure provides an accurate ranking of these steels in order of toughness, it systematically overestimates the values obtained from alternative test methods. In addition, current plasticity correction analyses are inadequate.     

Approximate elastic–plastic analysis of a notched bar under tensile and torsional fatigue

An approximate model is presented for estimating elastic–plastic stresses and strains in a notched bar subjected to synchronous non-proportional tensile and torsional cyclic loading. To begin with, it is applied to a multiaxial synchronous proportional loading system. A detailed FE analysis is performed for an axisymmetric bar of circular cross-section with a circumferential notch. The accuracy of the proposed approximate model is first established. The elastic–plastic material property is described by the von Mises yield criterion and a linear kinematic hardening rule. The comparison of the FE results with those estimated by the proposed approximate model shows good agreement for all loading cases investigated.     

A new method of stress analysis in photoelasticity

A new method of stress analysis in photoelasticity has been developed in this paper. Only the orders of isochromatic fringes and boundary conditions in three sections are adopted to analyse the stress components in these sections. The method requires minimum known data and can quickly analyse stress components. It reduces computational programs.     

A re-examination of stresses in a tension bar with symmetrical U-shaped grooves

Experimental Mechanics - A two-dimensional photoelastic study was made of stress-concentration factors and stress distributions in a statically loaded tension bar with symmetrical U-shaped grooves....     

拉压杆件有限元最佳应力点问题

以拉压杆件单元为例,对三种载荷作用下的位移和应变利用等参元计算,对等参元量佳应力计算点问题进行了分析。     

Failure analysis of unidirectional fiber composites under combined axial tension and shear

A method of analysis is proposed for investigating the mechanics of failure of unidirectional, fiber composite materials subjected to axial tension and shear. The mechanisms of failure are assumed to result from the interaction of the applied shear stress and local matrix shear stress concentrations which arise as a result of the scattered fiber breaks that occur throughout the material. Two modes of failure are identified. One is associated with the unstable growth of shear failure regions in the matrix. The other is primarily a tensile failure mode which is influenced by the applied shear. The analysis predicts that a variety of shear-tensile stress failure surfaces are possible, depending on material properties. The results suggest that radical changes in the shape of failure surfaces can occur as the result of environmental effects. This has significant implications for reliability.     

Interlaminar edge stress analysis of composite cross-ply flat specimens

Summary Interlaminar stresses in composite flat specimens are analysed by a method previously presented, apt to compute inertial and elastic properties of anisotropic beam. This method is based on the Virtual Work Principle (V. W.P.), and develops a finite element displacement formulation, extending the De Saint Vénant approach to anisotropic beams. In the present paper symmetric four cross ply flat laminates under uniaxial extension are considered, and the important role of the resin layer between two fibre plies is pointed out by means of a detailed stress analysis of interlaminar regions. Through the use of increasingly refined meshes the possible existence of singularities in the stress trend at the free edge is examined. The results obtained are shown to be in good accordance with those already available in the literature; furthermore the modellization of the interlaminar layer shifts the possible presence of a free edge singularity to the fibre ply/interlamina interface, showing on the contrary a non singular trend in stress field inside the interlaminar ply. This is important especially in view of the fact that, through this approach, natural boundary conditions are enforced at convergence by the V.W.P., without any a priori assumption.

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Sommario Si analizzano gli sforzi interlaminari di bordo in provini piani di materiale composito. Il metodo utilizzato si basa sul Principio dei Lavori Virtuali e sviluppa una formulazione ad elementi flniti, estendendo approccio di De Saint Vénant alle travi anisotrope. Si prendono in considerazione laminati piani simmetrici cross-ply a quattro strati sottoposti a estensione uniassiale e si mette in rilievo importante ruolo svolto dal sottile strato interlaminare di resina posto tra due stati di flbra. L'eventuale esistenza di singolarità nell'andamento degli sforzi al bordo libero viene esaminata attraverso I'uso di schematizzazioni via via più dettagliate. I risultati sembrano indicare la presenza di tali singolarità solo all'interno dello strato interlaminare limitatamente alla zona di interfaccia con lo strato di fibre a 90°. Infine si mostra come i risultati ottenuti siano in buon accordo con quelli ricavati da altri autori.

     

Fracture and stability of notched thin-walled bodies in tension (survey)

Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Prikladnaya Mekhanika, Vol. 26, No. 11, pp. 3–24, November, 1990.     

A new holographic interferometer for stress analysis

In holographic interferometry with a photoelastic model, two families of fringes are generated simultaneously when the model is stressed. One family represents the isochromatic-fringe pattern normally associated with photoelasticity which yields the difference between the principal stresses. The other family represents the isopachic-fringe pattern associated with interferometry which yields the sum of the principal stresses. From these complementary patterns, the magnitudes of the principal stresses can readily be determined throughout the field of observation. Unfortunately, these fringe patterns are not completely independent but interact in such a way as to make interpretation difficult in critical regions of the model. A new system has been developed which readily permits simultaneous acquisition of these fringe patterns without their undesirable mutual interaction, as well as providing increased sensitivity. This new interferometer uses a double-pass object beam and an optical rotator to eliminate the isochromatic-fringe pattern and its effect from the isopachic interferogram. Such a system has considerable value in experimental mechanics for applications to both static and dynamic model studies and to materials investigation.     

A new boundary element approach of modeling singular stress fields of plane V-notch problems

In this paper, a new boundary element (BE) approach is proposed to determine the singular stress field in plane V-notch structures. The method is based on an asymptotic expansion of the stresses in a small region around a notch tip and application of the conventional BE in the remaining region of the structure. The evaluation of stress singularities at a notch tip is transformed into an eigenvalue problem of ordinary differential equations that is solved by the interpolating matrix method in order to obtain singularity orders (degrees) and associated eigen-functions of the V-notch. The combination of the eigen-analysis for the small region and the conventional BE analysis for the remaining part of the structure results in both the singular stress field near the notch tip and the notch stress intensity factors (SIFs).Examples are given for V-notch plates made of isotropic materials. Comparisons and parametric studies on stresses and notch SIFs are carried out for various V-notch plates. The studies show that the new approach is accurate and effective in simulating singular stress fields in V-notch/crack structures.     

Hybrid experimental-numerical concept of residual stress analysis in laser weldments

The concept, methodology and instrumentation for hybrid experimental-numerical residual stress analysis in a laser weldment are presented. Grating interferometry and digital speckle photography are applied as complementary experimental methods for the determination of the initial model of residual strains and of the material properties at the various zones of a laser weldment. These data inserted into a finite element model enable one to analyze the formation of the residual stress state of the object, which is compared and modified by means of experimental data in a closed iterative loop. This full hybrid approach is tested successfully on a laser-welded steel specimen in uniaxial tensile tests.