Net stress

Fig. 14.5. An optical micrograph and stress maps in bovine femoral bone near a fracture. The map in (a) was acquired at zero applied stress and in (b) at critical stress for crack propagation. The net stress field was obtained by subtracting (a) from (b) and is shown in (c). Reprinted with permission from [48]...

Po on the face area jtR. Along the flank of the piston, the supporting pressure P(h) falls to zero at h = ho- We require that at any h along the flank, the cross-sectional area of the piston, jth2 sitrcy, bears a net stress less than the simple compression strength of the material, 5. The net stress is the total load on the cross section divided by its area, minus the support pressure P(h). The total load is the piston face load plus the piston flank load. 

Fig. 6.18 Schematic representation showing how a reduction in the bridging force by interface wear leads to matrix crack growth. The fibers carry the applied load across the matrix cracks, reduing the crack opening displacement and the net stress intensity (Klip) at the tip of matrix cracks. If the interfacial shear stress t decreases during fatigue, then the bridging stress p(x) decreases, leading to a reduction in Kp. This reduction increases Kfy, which can cause the further extension of a matrix crack.

From this analysis, the net stress is given by [26] the difference between the effective stress and the average stress ... 

Abstract The Canadian Nuclear Safety Commission (CNSC) used the finite element code FRACON to perform blind predictions of the FEBEX heater experiment. The FRACON code numerically solves the extended equations of Biot s poro-elasticity. The rock was assumed to be linearly elastic, however, the poro-elastic coefficients of variably saturated bentonite were expressed as functions of net stress and void ratio using the state surface equation obtained from suction-controlled oedometer tests. In this paper, we will summarize our approach and predictive results for the Thermo-Hydro-Mechanical response of the bentonite. It is shown that the model correctly predicts drying of the bentonite near the heaters and re-saturation near the rock interface. The evolution of temperature and the heater thermal output were reasonably well predicted by the model. The trends in the total stresses developed in the bentonite were also correctly predicted, however the absolute values were underestimated probably due to the neglect of pore pressure build-up in the rock mass. 

Ax represents the swelling of the EB at the interface with the site, o o" and a" denote respectively the net stress, the equivalent fluid stress and the total stress at the contact EB-canister. A negative stress is compressive. 

Table 2 gives the main mechanical results of those three calculations. As no displacement is allowed at the interface EB-canister, saturation phenomenon develops stresses. A compressive stress of about 32 MPa is supported at the contact between the EB and the canister. The clay skeleton is there submitted to a net stress of about 33 MPa. 

The discussion above suggests that a single suction field is not enough to interpret the behaviour of expansive materials with a marked bi-modal porosity distribution. Therefore, in addition to the net stress, two additional water potential fields are considered Sm and s, . Sm may be interpreted as a capillary potential, but the concept of water potential, linked to the physico-chemical mechanisms of water bounding to the clay minerals, is more appropriate for s. For the purposes of discussing the experimental behaviour observed it is convenient to work with two stress spaces which integrate the net stress field and the two independent water potential variables The space (Oq,SM) associated with the macrostructure and the space (ajj,s, ) associated with the microstructural level. (A reference zero air pressure will be considered, for simplicity). 

In partially saturated materials, most experimental data have shown that the plastic deformation is controlled by two independent force variables the net stress tensor, a =a + bpg, and capillary pressure (Alonso et al. 1990 Fredlund and Rahardjo 1993). However, for hard rocks, plastic deformation due to pure change of capillary pressure can be neglected. Based on experimental data from argillites (Chiarelli 2000), a quadratic function is used to describe plastic yielding surface ... 

Notched wide-plate tests on base metal and welded joints result in ductile fracture at room and low temperatures. The fracture strength (the maximum net stress at the notched section) for both cases was nearly equal and was higher than the 0.2% proof stress. 

This was consistent with a two phase microstructure where there are two contributions to the stress an elastic component and a viscous component [61]. The sign of the viscous stress changed sign on reversal of straining, and therefore relaxation of this stress during unloading produced an increase in the net stress. 

From this equation, it can also be shown that the thickness of the compression layer is theoretically 21% of the overall wall thickness. Therefore, 42% of the glass will be in compression and 58% will be in compensating tension. The net stress has to be zero so the beneficial surface compressive stress is balanced by the buried tensile stress. Also, due to the cylindrical symmetry of most glass containers, and their small wall thickness in relation to their diameter, the stress will be governed by the following summation rule ... 

It should be noted that the soil settlement depends on the net stress increases. Thus, unlike bearing stability, net bearing stresses should be used in the settlement analysis. However, often when footings are founded on relatively shallow depth, differences settlement estimated by using net and gross applied bearing stresses maybe small. 

If both stress fx and / are acting rimultaneousiy, the net unit elongation, 2, in the x direction will be (the subscript 2 refers to the net stress or stram for the biaxial loading condition) ... 

The normal stress difference, the net stress on the ends of the sample, is then... 

The first step to extend the stress-strain relationship to higher dimensions is to begin using vectors to represent stresses and strains in the x- and y-direaions (for example), and the net stress and strain due to linear superposition (Scheme 2). However, one must also consider that the direction in which the stress is acting (for greater than one dimension) is not necessarily in the same direction that the strain is being produced. Physically, this is observed in shear and in the Poisson s ratio. 

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