Stress concentration strain analysis

Partially Plastic Thick-Walled Cylinders. As the internal pressure is increased above the yield pressure, P, plastic deformation penetrates the wad of the cylinder so that the inner layers are stressed plasticady while the outer ones remain elastic. A rigorous analysis of the stresses and strains in a partiady plastic thick-waded cylinder made of a material which work hardens is very compHcated. However, if it is assumed that the material yields at a constant value of the yield shear stress (Fig. 4a), that the elastic—plastic boundary is cylindrical and concentric with the bore of the cylinder (Fig. 4b), and that the axial stress is the mean of the tangential and radial stresses, then it may be shown (10) that the internal pressure, needed to take the boundary to any radius r such that is given by... 

Abstract When subjected to a mechanical loading, the solid phase of a saturated porous medium undergoes a dissolution due to strain-stress concentration effects along the fluid-solid interface. Through a micromechanical analysis, the mechanical affinity is shown to be the driving force of the local dissolution. For cracked porous media, the elastic free energy is a dominant component of this driving force. This allows to predict dissolution-induced creep in such materials. 

Determination of residual stress of a failed component is one of the most important steps in failure analysis. The determination of residual stress is useful when failed components experience stress concentration, overload, distortion or the formation of cracks in the absence of applied loads, subjected to corrosive environments as in stress corrosion, mechanical or thermal fatigue due to cyclic loading, or when faults in processing such as shot peening, grinding, milling and improper heat treatment such as stress relief, induction hardening, thermal strains, exposure temperature are involved. 

This is the response of the material to an osdUating stress or strain [1]. When a sample is constrained in, say, a cone and plate or concentric cylinder assembly, an oscillating strain at a given frequency a> (rad s ) (t = 2v r, where v is the frequency in cycles s or Hz) can be appHed to the sample. After an initial start-up period, a stress develops in response of the applied strain that is, it oscillates with the same frequency. The change of the sine waves of the stress and strain with time can be analysed to distinguish between elastic, viscous, and viscoelastic response. An analysis of the resulting sine waves can be used to obtain the various viscoelastic parameters, as discussed below. 

At larger stresses, beyond SSY, for which the plastic zone extends deeper into the undeformed ligament t = D - a as shown in Fig. 12.6(b), the stress and strain distributions at the crack tip inside the yield zone are now very significantly altered, such that the strongly attenuated stresses are accompanied by more concentrated crack-tip plastic strains. To deal with a family of such problems a form of non-linear crack-tip analysis was introduced independently by Hutchinson (1968) and by Rice and Rosengren (1968). This approach is referred to as the HRR crack-tip analysis. 

In a multiscale analysis, the localization relations, that is, stress and strain concentration tenors, bridge the microscopic and macroscopic mechanical fields. When the medium behaves elastically, these relations are exact [56]. The main difficulty arises when nonlinearity is introduced in the mechanical behavior of the subphases, such as inelastic deformation or damage [56,62], which is the case for SMPFs. In general, three approaches within the micromechanics framework are available to establish the localized relations in the presence of such nonlinear processes. 

Wake(37) and by Adams and Wake(5), and Kinloch(4) summarises the evolution of the approach of the many stress analysts. The most common shear test comprises the single lap shear joint embodied in BS 5350(10) and ASTM 01002-72(11) (Fig. 4.7(a)). With reference to Figs. 4.1(a) and 4.8 it can be seen that the resulting stress concentrations can be extremely large at the joint ends (points X and Y in Fig. 4.8(b)). The analysis of Volkersen(15) predicts that for identical adherends, the elastic shear stress concentration factor, for the adhesive due to adherend tensile strain is given by... 

The finite element (FE) technique is an approximate numerical method for solving differential equations. Within the field of adhesive technology, it is most commonly used to determine the state of stress and strain within a bonded joint. It can also be used to determine moisture diffusion, natural frequencies of vibration and other field problems. Although this article will concentrate on the stress analysis, the same concepts can be applied to these other applications of finite element analysis. The basis of any finite element method is the discretization of the (irregular) region of interest into a number of... 

The finite element analysis technique has been used very successfully to confirm the regions of concentrated stress and strain. In this technique, the bonded assembly is subdivided into small elements and the forces relevant to each element are computed using basic mathematical equations. This is very useful, particularly in the understanding of complex joint designs. 

Furthermore, the presence of defects in a crystal lattice may also alter the diffraction pattern Depending on the type and the concentration of the defects, systematic peak broadening, peak shifts as well as peak splitting may be observed, and stress and strain may also influence the diffractograms [20, 21]. Thus the detailed analysis of measured peak positions, their widths and intensities can be used for the identification of the defects existing in a particular sample. 

The work of Hohn previously described in which stresses were determine from strain measuremmts indicated that two critical stress groups exist (1) the stresses in an element of an elliptical dished head r ulting from internal pressure and the geometry of the hmd and (2) the stress concentrations in Ae neighborhood of the junction of the head and the shell. Huggenberger (115, 116) developed an analysis of the stresses in an element of an elliptical dieted head... 

Czamocki and Piekarski s) used a nonlinear elastic stress-strain law for three-dimensional failure analysis of a symmetric lap joint. Taking into account the variation of Poisson s ratio with strain within the adhesive, the authors concluded that the failure of the adhesive layer originates in the central plane of a joint (at the front edge). It was also observed that the joint width did not have any effect on the stress peaks in the central plane and that the application of a weaker but more flexible adhesive resulted in higher load-carrying capacity and lower stress concentrations in the adherends. 

In Additional to these tensile stresses, some random tensile stresses are introduced due to differential cooling strains which cannot be covered by analysis constructional stresses locked in, local stress concentration and thermal gradient stresses are some more to be considered while assessing the amount of reinforcement. 

Gere, J. M. 2004. Mechanics of Materials, 6th ed. London Brooks/Cole. Describes the fundamentals of mechanics of materials. Principal topics are analysis and design of structural members subjected to tension, compression, torsion, and bending as well as stress, strain, elastic behavior, inelastic behavior, and strain energy. Transformations of stress and strain, combined loadings, stress concentrations, deflections of beams, and stability of columns are also covered. Includes many problem sets with answers in the back. 

Pneumatic tyre structure mechanics were analysed using non-linear finite element analysis. The deformation and stress-strain of all the components under inflation pressure of the tyre were predicted and the effects of three different bead structures on tyre performance were studied. It was found that stress concentration was the main cause of bead burst, separation and wear and that the tendency of the tyre to undergo early damage increased with decrease in bead rigidity. The study showed that the finite element method was an effective means of optimising tyre structure. 7 refs. 

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