Concentrations stress concentration coefficient

This equation indicates that under isothermal conditions in instances where AHa < U0, w < y, and the polymer will experience ductile failure. Recognizing that the brittle stress concentration coefficient y is nearly constant (4), the requirements for brittle amorphous polymers, whose Affa > UQ and w > y, to fail in a ductile fashion are to minimize (AH — U0)/[Pg.130]

Coefficient a is related to stress concentration. Coefficients c and d are related to the adhesion of the polymer matrix to filler. In an experiment involving different sizes of calcium carbonate in poly(vinyl acetate), small and medium particles had a much larger values of coefficients c and d than did large particles. This is in agreement with an experiment which shows that large particles decrease the mechanical properties of composites. 

As shown in figure 10, the effect of coal 2 adopting face overlapping each other completely without coal pillar on protective layer of coal 1 was in area of 75 m away outside the face. And the maximum compression ratio was 0.15%, the maximum stress concentration coefficient was approximately 1.2 Protected layer was released by expansion within the range 5 75 m of inner side of the protective layer face the expansion ratio was approximately 0.8%, the stress was about 9% of stress in virgin rock mass. Expansion releasing state of the protected layer in the middle of the two... 

Where, Oy is vertical stress K is stress concentration coefficient y is average bulk density of overlying strata H is occurrence depth t is attenuation coefficient M is roof thickness y, is roof bulk density x is width of limit equilibrium. 

The stress concentration coefficient and the tensile stress area are two important indexes of surrounding rock stress field for tunnel stability... 

According to the theory of elasticity, the stress concentration coefficient near circular hole is equal to 3 in fact the real stress near the hole is approximately one. So, the circular hole might be considered as the standard stress concentrator. 

MPa the elastic modulus of the SiC whisker E = 400 GPa, and Poisson s ratio Vf = 0.16 the interfacial layer of the material is isotropic, Poisson s ratio is 0.2, and interfacial elastic modulus is E. The elastic-plastic modulus is calculated by using a different interfacial modulus E value. The exterior stress Oq is set at 0.85 MPa, and the influence of different interfacial bonding states on stress concentration coefficient, interfacial shear stress, and axial stress of whisker end face is simulated. Figure 4.12 is the stress concentration coefficient... 

Figure 4.12 Stress concentration coefficient distribution of the whisker end face with different interface elastic moduli.

The stress concentration coefficient of sharp triangle crack is expressed as follows [30] ... 

Let us consider in conclusion the physical significance of stable crack fractal dimension in PASF samples. As it has been shown in Ref [12], the stress concentration coefficient Kg of triangular crack is given by the Eq. (5.10). In Fig. 8.6 the relation between parameters and for PASF sample (solvent - chloroform) is adduced, fi om which linear reduction follows at growth. Thus, the dimension for stable crack has the simple physical significance - it is the value, reciprocal to stress concentration level at crack tip. 

FIGURE 8.6 The dependence of stress concentration coefficient of stable crack on its fractal dimension D for PAST [8],... 

Many subtleties associated with ED, for instance, accompanying thermodynamic cooling issues, failure processes, and effects of localized stresses, are discussed in detail in the extensive review on this topic by Briscoe et al. Other workers have observed similar fracture effects arising from rapid temperature increases while maintaining pressure the connection with ED is via Henry s law linking dissolved gas concentration and solubility coefficient, and the fact that solubility coefficient decreases (in an Arrhenius fashion, as it happens) for readily condensable (i.e., less volatile) gases when temperature increases. 

It should be stressed that the pH value of an actual buffer solution prepared by mixing quantities of the weak acid or base and its conjugate base or acid based on the calculated ratio will likely be different from what was calculated. The reason for this is the use of approximations in the calculations. For example, the molar concentration expressions found in Equations (5.23) to (5.30), e.g., [H+], are approximations. To be thermodynamically correct, the activity of the chemical should be used rather than the concentration. Activity is directly proportional to concentration, the activity coefficient being the proportionality constant ... 

C Partial volume Capacity Concentration Compliance Stress-optical coefficient... 

The photoelastic behavior of nonionized PAAm network and ionized P(AAm/MNa) network prepared by the copolymerization of AAm with MNa ( MNa = 0.05) was investigated in water-acetone mixtures [31]. For a pure PAAm network, the dependences of all photoelastic functions (see Eqs. (15) and (16)), i.e. modulus G, strain-optical function A and stress-optical coefficient C, on the acetone concentration in the mixtures are continuous (Fig. 17). At ac = 54 vol %, the ionized network undergoes a transition which gives rise to jumpwise change in G, A and C also the refractive index of the gel n8 changes discontinuously. While in the collapsed state the optical functions A and C are negative, in the expanded state they are positive. 

A final piece of evidence against both finite extensibility and internal viscosity is provided by flow birefringence studies. One would expect each to produce variations in the stress optical coefficient with shear rate, beginning near the onset of shear rate dependence in the viscosity (307). Experimentally, the stress-optical coefficient remains constant well beyond the onset of shear rate dependence in r for all ranges of polymer concentration (18,340). 

At the end of this section two tables are presented. The purpose of these tables is to show that, for matching solvents, the main predictions of the theory are fairly well obeyed, viz. that the stress-optical coefficient is independent of molecular weight and concentration. On the other hand, an influence of the solvent is clearly noticed. This means that, according to eq. (2.24), the anisotropy (ax — o ) of the random link is influenced by the solvent molecules. This has first been stated by Frisman, Dadi-vanyan and Dyuzhev (66) (see also Section 5.1.2). 

Table 2.2, which shows results for some polyolefines, indicates for these polymers a similar insensitivity of the stress-optical coefficinet to molecular weight and concentration as Table 2.1 for polystyrene. A typical solvent effect is noticed for all the three types of polyolefins, viz. that the stress-optical coefficient in decalin is considerably smaller than that in aromatic solvents. This effect was discovered by Garmonova (71). 

In Tsvetkov s review (7) stress-optical coefficients are given in terms of (% — otg) for a great number of different polymers. All these results were obtained on dilute solutions. The figures given in Tables 2.1 and 2.2 were selected from the literature as they yield the extraordinary possibility to compare stress-optical coefficients in a great concentration range up to the melts of the bulk polymers. 

However, as soon as a finite contribution of the form effect is contained in the value of Maxwell constant, the said conditions are no longer superfluous. In fact, the form effect is highly concentration dependent in the range of low concentrations (138, 63), and has a shear rate dependence different from that of intrinsic birefringence and viscosity. In other words, due to the presence of the form effect, the ratio of Maxwell constant and intrinsic viscosity can no longer be interpreted as twice the stress-optical coefficient in the sense of Chapter 2. 

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