Anisotropy hardening

The referential formulation is translated into an equivalent current spatial description in terms of the Cauchy stress tensor and Almansi strain tensor, which have components relative to the current spatial configuration. The spatial constitutive equations take a form similar to the referential equations, but the moduli and elastic limit functions depend on the deformation, showing effects that have misleadingly been called strain-induced hardening and anisotropy. Since the components of spatial tensors change with relative rigid rotation between the coordinate frame and the material, it is relatively difficult to construct specific constitutive functions to represent particular materials. 

The deformation may be viewed as composed of a pure stretch followed by a rigid rotation. Stress and strain tensors may be defined whose components are referred to an intermediate stretched but unrotated spatial configuration. The referential formulation may be translated into an unrotated spatial description by using the equations relating the unrotated stress and strain tensors to their referential counterparts. Again, the unrotated spatial constitutive equations take a form similar to their referential and current spatial counterparts. The unrotated moduli and elastic limit functions depend on the stretch and exhibit so-called strain-induced hardening and anisotropy, but without the effects of rotation. 

It has already been noted that the unrotated moduli and elastie limit funetions are related to their referential eounterparts through U, and exhibit so-ealled strain-indueed hardening and anisotropy. For some purposes, this may not be desirable. Sinee s, and by similar arguments k, are themselves... 

In this ease the spatial moduli will ehange with the rotation R, but will not exhibit strain indueed hardening and anisotropy. 

The present review shows how the microhardness technique can be used to elucidate the dependence of a variety of local deformational processes upon polymer texture and morphology. Microhardness is a rather elusive quantity, that is really a combination of other mechanical properties. It is most suitably defined in terms of the pyramid indentation test. Hardness is primarily taken as a measure of the irreversible deformation mechanisms which characterize a polymeric material, though it also involves elastic and time dependent effects which depend on microstructural details. In isotropic lamellar polymers a hardness depression from ideal values, due to the finite crystal thickness, occurs. The interlamellar non-crystalline layer introduces an additional weak component which contributes further to a lowering of the hardness value. Annealing effects and chemical etching are shown to produce, on the contrary, a significant hardening of the material. The prevalent mechanisms for plastic deformation are proposed. Anisotropy behaviour for several oriented materials is critically discussed. 

Fig. 2.11. Schematic of a stress-strain curve illustrating the anisotropy of work hardening (adapted...

Material Young s modulus, E GPa 10 psi Yield strength MPa ksi Tensile strength MPa ksi Uniform elongation (%) Total elongation (%) Strain hardening exponent in) Average normal anisotropy (r, ) Planar anisotropy (Ar) Strain rate sensitivity (m)... 

Table 3.1-13 Typical values of strain-hardening exponent n and degree of anisotropy r for some aluminium-base materials based on data from various sources [1.9] n.a. - not available...

The work in reference (16), demonstrating the hardening effect of radiation, introduces a note of caution in ascribing the same type of hardness anisotropy to crystals having the same slip systems, because there is reported data for all, even nonceramic, rock-salt materials NaCl and KCl, which show the hard direction on (001) to be [100], not [110]. These anomalous data emerge from very soft crystals, NaCl (1.91 GPa) and KCl (0.92 GPa), which do have IIOKIIO) slip systems some attempt at interpretation is made in Section 3.6.1. 

Half penny crack, 156, l 9, 260 Hall-Petch relationship, 120 in MgO, 265 Hardening constant, 141 Hardening in glass, 194 Hardness absolute, 72 anisotropy, 65, 262, 293 and applied load, 7, 119-124, 251, 255, 281... 

Whiskers (Cont.) hardness (Cont.) of MgO, 265 of SiC, 261 Work of adhesion, 28 Work of elastic recovery of indent, 48 Work hardening, 45-46, 103, 106 of aluminium, 46, 262 and anisotropy peaks. 111, 115-116 caused by soft slider, 266 of crystals, 72 depth of, 45-46, 267 and diverging slip systems, 116 equation for, 266 of magnesia, 46, 265-267 and plastic zone anisotropy, 111 of SiC, 111... 

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