Stress state dimensionality

IV, INFLUENCE OF STRESS STATE DIMENSIONALITY ON REFRACTORY STRENGTH... 

Rather than a plane-stress state, a three-dimensional stress state is considered in the elasticity approach of Pipes and Pagano [4-12] to the problem of Section 4.6.1. The stress-strain relations for each orthotropic layer in principal material directions are... 

The macromechanical behavior of a lamina was quantitatively described in Chapter 2. The basic three-dimensional stress-strain relations for elastic anisotropic and orthotropic materials were examined. Subsequently, those relations were specialized for the plane-stress state normally found in a lamina. The plane-stress relations were then transformed in the plane of the lamina to enable treatment of composite laminates with different laminae at various angles. The various fundamental strengths of a lamina were identified, discussed, and subsequently used in biaxial strength criteria to predict the off-axis strength of a lamina. 

Consider the two-dimensional stresses on the faces of a cartesian control volume as illustrated in Fig. 2.25. The differential control-volume dimensions are dx and dy, with the dz = 1. Assuming differential dimensions and that the stress state is continuous and differentiable, the spatial variation in the stress state can be expressed in terms of first-order Taylor series expansions. 

Stress calculations are carried out by the finite element method. Here, the commercial finite method code ABAQUS (Hibbit, Karlsson, and Sorensen, Inc.) is used. Other codes such as MARC, ANSYS are also available. To calculate the stresses precisely, appropriate meshes and elements have to be used. 2D and shell meshes are not enough to figure out stress states of SOFC cells precisely, and thus 3D meshes is suitable for the stress calculation. Since the division of a model into individual tetrahedral sometimes faces difficulties of visualization and could easily lead to errors in numbering, eight-comered brick elements are convenient for the use. The element type used for the stress simulation here is three-dimensional solid elements of an 8-node linear brick. In the coupled calculation between the thermo-fluid calculation and the stress calculation a same mesh model have to be used. Consequently same discrete 3D meshes used for the thermo-fluid analysis are employed for the stress calculation. Using ABAQUS, the deformations and stresses in a material under a load are calculated. Besides this treatment, the initial and final conditions of models can be set as the boundary conditions and the structural change can thus be treated. 

From the residual coating strain, the residual coating stress can be calculated assuming a two-dimensional stress state in the thin coating. 

The numerical model we used was originally developed by Gill and Clyne [6] and has been modified to handle multi-layered deposits. It is a 1-dimensional model and consists of two parts thermal profile calculation and stress calculation. By regarding the torch motion as a fluctuation in the heat and mass flux onto a reference point on the substrate and assuming biaxial stress state, the program calculates both the through-thickness thermal profile and stress distribution during thermal spray as functions of time. 

Harting, M. (1998) A seminumerical method to determine the depth profile of the three dimensional residual stress state with X-ray diffraction. Acta Mater., 46 (4), 1427-1436. 

A horizontal circular tunnel is considered. It is assumed that the rock is initially saturated and the stress state is supposed to be isotropic. This assumption allows us to simplify the geometric configuration and to make an axisymmetrical mono-dimensional calculation as shown in figure 2. The initial values of stress and pressure are given by ... 

Thermomechanlcal Behavior. Requirements for optical performance Impose unprecedented requirements for dimensional stability of polymers used In hlgh-concentratlon reflectors. Requirements for mechanical compatibility are also strict for photovoltaic systems subjected to moisture and thermal stresses. Moisture, temperature, and UV, separately and In combination, can change the volume and thus the stress state of polymers. For example, temperature and humidity cycles alone do not cause surface micro-cracks In polycarbonate. However, In the presence of UV radiation, such cycles cause microcracks, while UV alone does not [32]. An understanding of these relationships Is essential to permit reliable design of equipment that uses polymers. 

With the effect of the cross-secti(Mial deformation, longitudinal, lateral, and shear stresses superpose, whereby a three-dimensional stress state is reached. 

The net plane distances dhki in ideal case show a linear distribution versus sin vf/, from which the residual stress state in the measured direction can be determined (Fig. 7). The residual stresses determined by this method are as a rule two-dimensional. 

Three-dimensional finite element analysis method can exactly reflect the comprehensive effect of complex stress state due to generating fold point and arching. 

The nanoferroics are known as low-dimensional objects of different morphology with dimensions from zero to three, i.e., quantum dots, nanoparticles, nanorods, thin films and bulk solids. As stated above, the properties of ferroelectric, ferromagnetic and ferroelastic materials are highly dependent on their dimensionality and symmetry of stressed state. In particular, above consideration shows that the phase transitions have the same nature in the particles, films and 3D polycrystals. 

The goal of the study Is to develop mathematical procedures by which existing design methodology for brittle fracture could accurately account for the Influence of protrusion Interference on fracture of cracks with realistic geometry under arbitrary stress states. To predict likelihood of fracture in the presence of protrusion Interference, a simulation will be developed. The simulation will be based on a three-dimensional model of cracks with realistic geometry under arbitrary stresses. 

B. Paul and L. Mirandy (1976), "An Improved Fracture Criterion for Three-Dimensional Stress States, /. Eng. Mater. Technol, Trans. ASME, 98,4, 159-63. 

The simplest theories of plasticity exclude time as a variable and ignore any feature of the behaviour that takes place below the yield point. In other words, we assume a rigid-plastic material whose stress-strain relationship in tension is shown in Figure 11.9. For stresses below the yield stress there is no deformation. Yield can be produced by a wide range of stress states and not just by simple tension. In general, therefore, it must be assumed that the yield condition depends on a function of the three-dimensional stress field. In a Cartesian axis set, this is defined by the six components of stress cr , ayy, a z, Oxy, Oy and However, the numerical values of these components depend on the orientation of the axis set, and it is crucial that the 3ueld criterion be independent of the observer s chosen viewpoint. It is therefore more straightforward to make use of the principal stresses, whose directions and values are determined uniquely by the nature of the stress field. If the material itself is such that its tendency to yield is independent of... 

We have already seen in Section 10.3.4 that yield can be modelled using the Eyring process. It provides a convincing representation of both the temperature-and strain rate dependence of the yield stress. However, the discussions of Chapter 10 were confined to one-dimensional states of stress, whereas we now appreciate that yield criteria are essentially functions of the three-dimensional stress state. Also, in view of the discussion in the previous section, it is of interest to explore its applicability to pressure dependence. Both pressure dependence and the extension of the Eyring process to general stress states are considered here. 

Hadingham PT (1983) The stress state in the human left ventricle. Adv Cardiovascular Phys 5 88-105 Heethaar RM, Pao YC, Ritman EL (1977) Computer aspects of three-dimensional finite-element analysis of stresses and strains in the intact heart. Comp and Biomed Res 10 291-295 Horowitz A, Perl M, Sideman S Minimization of fiber length changes and mechanical work in the heart muscle. Submitted for publication... 

For two dimensional problems we can consider two idealized states the plane strain state where s = Sxz = yi = and the plane stress state in which = Oxz = [Pg.52]

If the phase morphology is fine disperse, the particle distances are reduced and the stress state is changed to a one-dimensional stresses. If the dispersed phase has no intensive interactions with the matrix, than the PP matrix fibrillates between the drops. This mechanism leads to higher specimen deformability, thus higher maximum extension at break. 

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