Cohesion stress

K, stress intensity factor ctc cohesive stress G, energy release rate. 

The cohesive stress ac is assumed to be constant (Dugdale model) as in Eq. (7.5). Chan, Donald and Kramer [87] found a good agreement between the critical energy release rate GIC, as estimated by the Dugdale model and G)C as computed from the actual stress and displacement profiles in their experiments. 

The deformation zones were calculated for the polymers of Table 5.1 and Table 6.1 according to the Dugdale-Barenblatt-model. Yield stress ay from tensile tests was used instead of the cohesive stress ctc since a reasonable agreement of ay and ctc... 

This result indicates that the stress necessary to cause brittle fracture is lower, the longer the existing crack and the smaller the energy, P, expended in plastic deformation. The quantity Of represents the smallest tensile stress that would be able to propagate the crack of length 2 L. The term Of (tt L)°5 is generally denoted by the symbol K and is known as the stress-intensity factor (for a sharp elastic crack in an infinitely wide plate). Fracture occurs when the product of the nominal applied stress and the stress concentration factor of a flaw attains a value equal to that of the cohesive stress. 

In simple terms, a cohesive powder can be defined as a material where the adhesive forces between particles exceed the particle weight by at least an order of magnitude. In such systems, particles no longer flow independently rather, they move in chunks whose characteristic size depends on the intensity of the cohesive stresses. 

For a fixed coefficient of friction p. and a fixed dimensionless shear rate K, the measurement of the power consumption per unit volume of the moist powder mass is proportional to the cohesive stress Uc- Thus, if the granulating liquid is added to the powder mass at a constant rate, the power consumption profile describes in a first approximation the cohesive stress (Tc as a function of the relative saturation S of the void space between the particles (Fig. 5). 

In general, this Ck)ulomb yield criterion can be used to determine what stress will be required to cause a ceramic powder to flow or deform. All that is needed are the two characteristics of the ceramic powder the angle of friction, 8, and the cohesion stress, c, for each particular void fraction. With these data, the effective yield locus can be determined, from which the force required to deform the powder to a particular void fraction (or density) can be determined. This Coulomb yield criterion, however, gives no information on how fast the deformation will take place. To determine the velocity that occurs durii flow or deformation of a dry ceramic powder, we need to solve the equation of motion. The equation of motion requires a constitutive equation for the powder. The constitutive equation gives the shear and normal states of stress in terms of the time derivative of the displacement of the material. This information is unavailable for ceramic powders, and the measurements are particularly difficult [76, p. 93]. 

Cohesive stress, decohesion, craze, impact, adiabatic, polyethylene. 

The cohesive zone approach to fracture mechanics reduces the fracture resistance properties of a material to a traction-separation law. This Taw relates, o, the normal cohesive stress which resists the parallel separation of two internal planes which were initially very close together, to the current increase r] in their separation. The fracture resistance (and hence the fracture toughness K,.) is simply given by the area under the o,. ri) curve up to 6,.. The simplest form of traction separation law assumes 0 (77) to be constant up to a critical maximum separation 4. and this was developed analytically into a fracture model by Dugdale... 

However, the thermal decohesion time predicted for a craze layer which thickens at constant high rate still depends strongly on the cohesive stress. We now describe a method by which this parameter can be measured directly, and by which the impact lifetime of the craze can be measured and compared to the predictions of the model. 

The objective of this test method is to measure the cohesive stress and the time to failure of a crystalline polymer craze layer under rapid, uniform extension. The method is an impact variant of the Full Notch Creep test used by Fleissner [12], Duan and Williams [13], Pandya and Williams [14] and others. The specimen (Fig. 2), a square-section tensile bar, is injection moulded. At the mid-plane of the gauge length a sharp, deep circumferential notch reduces the cross-section to about one fifth of its original area. This notch plane is formed by a moulded-in, hardened steel washer. Specimens were injection moulded at 210°C into a warm (100°C) mould and air cooled to 40 C using a hold pressure of 45-50 bar. 

As far as the craze drawing lifetime (Fig. 4) was concerned, estimation was certainly rather more subjective. Nevertheless, two series of tests interpreted by two different experimenters produced similar results, their estimates were supported independently by their supervisor, and neither experimenter knew of the values which would be predicted by the model. For this material Af = 310k density, specific enthalpy and thermal conductivity were known as functions of temperature and the craze stress measured using full notch impact tests was in the range 20-30 MPa. Figure 5 compares the measured decohesion times to those predicted by the model, plotted as trend lines for two constant values of cohesive stress — 20 and 50 MPa — and two values of effective molecular weight (which has only a secondary effect). 

Electrostatic forces are dependent on the nature of the particles, in particular, on their conductivity. For non-conducting particles, high cohesive stresses in the range of 104 to 107 N/m2 have been reported. 

When the stress at the tip of the crack is equal to the cohesive stress calculated in Section S4.2.1, the bonds will break, so increasing the length of the crack and causing fracture to occur. Equating these values, we obtain... 

The cohesive zone stress can be extracted from experimental data. To determine the cohesive stresses, the J-integral as a function of crack opening displacement (COD) can be determined experimentally for a DCB specimen using the following relationship [175],... 

The COD can be obtained by measuring the crack opening displacement between two points (one above and one below) at the location of the crack tip in the unloaded state [176]. Fuchs and Major [177] described that cohesive stresses can be evaluated by taking the first derivative of J-integral with respect to COD (5) for Mode-I type failure. 

Electrostatic precipitation is a widely nsed process for removing polluting particles from gas streams, for example, in power station fines or in cement kilns. The effluent dust grains become charged as the gas flows between two electrodes, then deposit in a cake on the electrode snrface. This cake sticks to the electrode with a force that rises with the electric field bnt not simply proportional to the square of field strength as expected from the basic electrostatic equation for the cohesive stress a in a dielectric ... 

Note that instead of the shear stress, t, the stress, <7, is used in line with the notation in Fig. 8.5 for cohesive stress. Thus, re-expressing Eq. (8.21), gives ... 

Carloni C and Subramaniam K V (2010), Direct determination of cohesive stress transfer during debonding of ERP from concrete . Compos Struct, 93(1), 184—192. 

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