Strength-differential effect

In the plasticity of disordered solids the critical shear resistance fc at yield in eompression and that in tension tt are substantially different, with the ratio tq/tt being referred to as the strength-differential-effect (S-D) ratio. In comparison with the critical shear resistanee is in simple shear, the S-D effect results in the ordering of resistances as tt < Ts < ic. The phenomenon is well known in glassy polymers (see e.g. Argon et al. (1968)) and in amorphous metals (see e.g., Donovan (1989) and references therein). The discussion of the S-D effect in the yielding of noncrystalline solids has been extensive and dates back to the well-known unsymmet-rical yield criteria of Coulomb (1773) and Mohr (1900) for soils and granular media (for an overview of these see Anand and Gu (2000)). 

In subsequent sections the Eshelby theory of shear transformations is broadened by incorporation of strain-induced dilatancy into an interaction-energy component of the transformation free energy to account for interaction of the transformation strains with mean normal stresses, to obtain specific results for the differences among shear, tension, and compression flow and strength-differential effects. 

The strength-differential effect and the multi-axial yield condition... 

The strength-differential effect is defined as the ratio f sD given by the difference between the resistance in compression and the corresponding resistance in tension (as scalar quantities) divided by the resistance in simple shear,... 

The strength-differential effect is also reflected prominently in the multi-axial yield criteria which translate the multi-axial stress driving forces for yield into an equivalent uniaxial state of extension (tension) or simple shear <7se that is most relevant to the mechanisms governing plastic flow. In a more mechanistieally relevant statement for polymers, the multi-axial yield criterion of von Mises defines a uniaxial equivalent stress Oe (or a o-se) as... 

Homo-PS is known to be brittle in tension at room temperature in unmodified form, as Fig. 13.3 demonstrates. It has a compressive yield strength of around 103 MPa that, with a substantial strength-differential effect, translates into a tensile yield strength of 73 MPa, and undergoes plastic flow if its brittleness can be suppressed. Experimental evidence, such as that in Fig. 13.3, shows that homo-PS undergoes brittle behavior initiated from surface flaws, and that elimination of these is impractical, primarily because, even if that could be achieved, crazes could still be initiated at free surfaces, as is discussed in Chapter 11, and craze matter breaks down from either extrinsic or intrinsic imperfections in craze matter at stress levels of around 40 MPa at 293 K. 

Table 8.2 resumes the strains and stresses along the principal directions that were derived from the proposed analytical framework for the SPIF of polymers. It can be concluded that where the strength-differential effect is null, the distribution of strains and stresses for the SPIF of metals (Silva et ah, 2008a) results. 

In contrast to metals where formability in SPIF is mainly influenced by the thickness of the sheet t, the radius of the forming tool and the ductility of the material, polymers may also show dependency on the initial value of the drawing angle, y/ and to the strength-differential effect, p. All of these dependencies will be analysed in the following sections of the chapter. 

Triaxiality ratio as a function of sheet thickness t caicuiated from the theoreticai framework the strength differential effect p= 0 for facilitating representation... 

Triaxiality ratio <7 as a fnnction of sheet thickness t calculated from the theoretical framework the strength differential effect... 

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