Brittle shear stresses, ductile

DIF values vary for different stress types in both concrete and steel for several reasons. Flexural response is ductile and DIF values are permitted which reflect actual strain rates. Shear stresses in concrete produce brittle failures and thus require a degree of conservatism to be applied to the selection of a DIF. Additionally, test data for dynamic shear response of concrete materials is not as well established as compressive strength. Strain rates for tension and compression in steel and concrete members are lower than for flexure and thus DIF values are necessarily lower. 

On the other hand a brittle solid may be made ductile by applying hydrostatic pressure. Let us consider a brittle solid, which fails at a tensile stress cr. If a hydrostatic pressure p is applied, the tensile stress necessary for failure is p + a. Associated with this tensile stress is a shear stress equal to Vz(p + cr). If the critical shear stress is less than this, the material will flow in a ductile manner before the tensile stress is large enough to produce brittle failure. 

Ductile Failure of Brittle Polymers under Compressive Shear Stresses... 

The brittle film cracking with plastic deformation of the ductile substrate at the interface has been described by using the shear lag model. " This model, which was proposed in the analysis of the fragmentation of fiber composites," " develops a relation for the critical stress producing the steady-state cracking of the film. It assumes that the interfacial shear stress, on the one hand, is activated at each crack tip along the characteristic slip length r, and, on the... 

Now that three separate values for the failure torque have been found for this shaft, the logical question Is which (If any) of the answers Is correct. The answer to this question depends very strongly on the nature of the material Investigated. For very brittle materials (e.g., cast unplastlclzed polystyrene), experiments have shown that the maximum principal stress criterion gives quite reasonable results. For ductile materials such as molded nylon, experimental evidence Indicates that either the maximum shear stress or octahedral shear stress criterion Is more appropriate. 

The obtainable increase in the tensile strength depends on both the plastic and the reinforcing fiber. Craze formation is caused by shear stress peaks at the fiber-plastic interface. Consequently, plastics with ductile deformation behavior lead to better mechanical properties than brittle plastics glass-fiber-reinforced polyamides exhibit the larger increase in tensile strength when compared with glass-fiber-reinforced epoxides. 

Most ceramics are brittle at low and medium temperatures, and can be deformed plastically above the brittle-to-ductile transition temperature. The critical resolved shear stress (CRSS) then decreases rapidly with increasing temperature. In many cases there is a linear relationship between 1( (CRSS) and temperature, as first shown by Castaing for semiconductor crystals [17]. Examples are shown in Figures 9.1-9.4. For MgO in Figure 9.1 [5], the relationship is well obeyed for both easy slip on the... 

Adhesives, as all plastics, are viscoelastic materials combining characteristics of both solid materials like metals and viscose substrates like liquids. Typically, the adhesive shear stress vs. shear strain curve is non-linear. This behaviour is characteristic especially for thermoplastic adhesives and modified thermosetting adhesives. Thermosetting adhesives are, by their basic nature, more brittle than thermoplastic adhesives but, as discussed earlier, are often modified for more ductile material behaviour. 

Shear fracture (microscopically ductile fracture) occurs by plastic deformation with slip in the direction of planes of maximum shear stress (see sections 3.3.2 and 6.2.5). Therefore, it occurs only in ductile materials. In most cases, shear fracture is associated with large macroscopic deformations, as, for example, in a tensile test. However, if this is prevented by the component geometry, the component may fail macroscopically brittle, but still with a shear fracture. This may happen if there are notches or cracks in the material (see chapters 4 and 5). 

In this context, literature [90] states that at room temperature, acetoxypropyl cellulose exhibits both chiral nematic phases—the lyotropic and the termotropic one. When subjected to specific conditions of shear flow, the cellulose derivative cholesteric liquid crystal suffers transformations, such as cholesteric helix and cholesteric-to-nematic transition. The films prepared from anisotropic solutions of termotropic acetoxypropyl cellulose in an isotropic solvent exhibit anisotropic mechanical properties, generated by the molecular orientation of the solution under shear stress. Thus, liquid crystalline solutions give rise to films with anisotropic mechanical properties the films are brittle when stretched parallel to the shear direction and ductile when stretched perpendicular to it. 

The deformation or ploughing modes can also be well described for plastic and possibly even brittle fracture systems using modem numerical techniques. As with the elastomeric systems the models basically include geometric terms, such as 6, some load and various parameters such as an interface shear stress but more importantly a relatively accessible bulk deformation or dissipation property of the material. For the case of elastomers, an appropriate viscoelastic loss tangent is sufficient and for a ductile polymer some pressure dependent yield stress. There are many examples in the literature where good correlations have been obtained between a bulk mechanical test and a frictional response. Properly, it has been seen as the domain of others, perhaps polymer scientists, to seek to provide interrelationships between molecular structure and deformation dynamics and the consequent bulk material responses. 

In order to work efficiently, the mechanical properties of the layer should be tailored. A thin residual layer reduces the shear stress needed to induce failure, while the use of a brittle polymer allows for a cleaner failure of the layer and, consequently, smoother surface and sidewalls of the final transferred structures than if a ductile polymer is used. The quality of the process depends as well on mold design molds with sharp edges induce failure of the residual layer in a specific location, while molds where protrusions edges are not sharp lead to nonspecific layer failure and, consequently, patterned features with rough edges [31]. 

Materials fracture in either a brittle or a ductile fashion. In brittle fracture, the design criterion is the maximum normal strain and fracture will occur on a plane normal to that of maximum normal strain. Ductile fracture involves shear, the design criterion is then maximum shear stress, and fracture occurs on a plane of maximum shear strain. 

Fig. 2.15 Cylinder in pure torsion, a element free body stress state, b brittle behavior with helicoidally failure, c and d ductile failure activated by either longitudinal or transverse shearing stress...

It is also desirable to know the magnitudes of shear and normal stresses individually since some adhesives are weak in shear loading (ductile adhesives) while others are weak in normal stress loading (brittle adhesives). 

For joints with ductile adhesives, the failure load is given by the load that causes adhesive global yielding along the overlap. This criterion works reasonably well provided the failure shear strain of the adhesive is more than 20%. However, for brittle adhesives, this methodology is not applicable (da Silva et al. 2008). For joints with a brittle adhesive, the Volkersen s model can be used (da Silva et al. 2009b) and the failure occurs when the maximum shear stress at the ends of the overlap exceeds the shear strength of the adhesive. Alternatively, the finite element method can be used. 

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