Stress defined

The distance from the crack tip, along the X-axis, at which the von Mises equivalent stress falls below the yield stress, defines the size of the plastic zone, r. For the plane stress case of unconstrained yielding, which corresponds to the free surface of the specimen in Figure 4, this gives... 

The results of uniaxial stress-strain experiments are often analyzed in terms of the reduced stress defined by... 

The allowable stresses defined in (a), (b), and (c) below shall be used in design calculations unless modified by other provisions of this Code. The material performance factor, Mp as shown in Mandatory Appendix IX, Tables IX-5B and IX-5C, shall be used in Chapter IP-3. 

There are many types of deformation and forces that can be applied to material. One of the foundations of viscoelastic theory is the Boltzmann Superposition Principle. This principle is based on the assumption that the effects of a series of applied stresses acting on a sample results in a strain which is related to the sum of the stresses. The same argument applies to the application of a strain. For example we could apply an instantaneous stress to a body and maintain that stress constant. For a viscoelastic material the strain will increase with time. The ratio of the strain to the stress defines the compliance of the body ... 

Although the magnitude of the stresses defining the LVE region of behav ior is important, it is not intuitive to the average person. What does a stress of 20 Pa feel like Strains are perhaps more accessible. If we were to consider... 

Normal Stresses in Shear Flow. The tendency of polymer molecules to curl-up while they are being stretched in shear flow results in normal stresses in the fluid. For example, shear flows exhibit a deviatoric stress defined by... 

Each cell must not overcome the determined operating voltage which allows the system to reach the application lifetime requirement. To fix the voltage, which may be applied on each cell, it is necessary to consider the derating law presented before in this chapter. Moreover, it is often necessary to consider the voltage distribution of the different application stresses defined in the customer specification to optimize the storage system size. 

Shear yielding in polymers has much in common with ductility in metals. In polymers, the yielding may be localised into shear bands, which are regions of high shear strain less than 1 m in thickness or the yield zones may be much more diffuse " Under a general state of stress, defined by the three principal stresses Gi, 02 and 03, the condition for yielding is given by a modified von Mises crite-rion l ... 

Yield Behavior of Powders The yield behavior of a powder depends on the existing state of consolidation within the powder bed when it is caused to flow or yield under a given state of stress, defined by the acting normal and shear stresses. The consolidation state controls the current bed voidage or porosity. Figure 21-34 illustrates a times series of shears occurring for the BCR116 hmestone standard for a rotary shear cell. For each shear step, torque is applied... 

The scientific community has been discussing for quite some time now the relationship between oxidative stress, defined as the imbalance between oxidant and antioxidants [45], and the health-disease status. An impressive amount of information available in the literature deals with the effects of the classic antioxidants, ascorbic acid, a-tocopherol, and jS-carotene in a huge series of pathophysiological situations in experimental animals and humans. Concerning the effects of the classic antioxidants on mitochondrial function in situations of oxidative stress, the information is not so vast and most of the time it is not conclusive. However, substantial progress has been made in the description of the mitochondrial alterations in neurodegenerative diseases and in the a-tocopherol effects,both as prevention and as treatment [46]. We will briefly review some reports related to vitamin E and mitochondrial dysfunction in oxidative metaboHc disorders and in the neurodegenerative Alzheimer s and Parkinson s diseases. 

Reynolds number Re = DWp/p, Ratio of inertial to viscous stress defines turbulent, transitional, and laminar-flow regimes a correlating parameter for flow-sensitive terms in mixing... 

Results for polystyrene (1 ) indicate that the bands start to occur at a tensile yield stress defined (1 ) as the point at which stress is no longer proportional to strain. For our spec imen, tl onset of oscillation occurs at a stress of 3.9 x 10 dynes/cm, and it tensile yield stress as defined above is... 

Yield stress defined by the conditions y = 0 Critical stress defined by the conditions y(t) = 0... 

The surface forces are those applied by the external stresses defined through Eq. (2.2.12), where... 

Viscosity (q) - The proportionality factor between sheer rate and sheer stress, defined through the equation f = n A(dvldx), where F is the tangential force required to move a planar surface of area A at velocity v relative to a parallel surface separated from the first by a distance x. Sometimes called dynamic or absolute viscosity. The term kinematic viscosity (symbol v) is defined as q divided by the mass density. 

In any given system, there is some stress, defined as the critical stress, below which dispersion cannot occur. However, when the shear stress is just slightly larger than the critical stress, only agglomerates with a favorable initial orientation become dispersed. 

The stress defined by Equation (6) represents the interaction between surfaces due to the macromolecules in solution. To obtain the total stress, contrioutions of long range colloidal forces between the oilayers themselves must be added to (Tp. For phospholipid oilayers, the added stress can be expressed as the sum of a strong exponential repulsion due to hydration forces, a weak power law attraction for the van der Waals force, and exponential repulsion due to electric double layer forces (1-2),... 

The simplest model is the statistical theory of rubber-like elasticity, also called the affine model or neo-Hookean in the solids mechanics community. It predicts the nonlinear behavior at high strains of a rubber in uniaxial extension with Fq. (1), where ctn is the nominal stress defined as F/Aq, with F the tensile force and Aq the initial cross-section of the adhesive layer, A is the extension ratio, and G is the shear modulus. 

Note that, with this model, the reduced stress defined by Eq. (3) depends on the deformation X, whereas it did not for the simple affine model. 

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