Residual strains

The microstructure/property relationships observed in shock-recovered samples have been often tacitly assumed to result solely from the shock compression, duration, and rarefaction due to the imposed uniaxial-strain shock. Recent shock-recovery studies have, however, shown that the degree of residual strain in the sample significantly influences the measured struc-... 

Figure 6.8. Plot of the quasi-static reloaded yield stress of shock-loaded copper versus the natural logarithm of residual strain for a 10 GPa symmetric shock with 1 /is pulse duration.

G.T. Gray III, P.S. Follansbee, and C.E. Frantz, Effect of Residual Strain on the Substucture Development and Mechanical Response of Shock-Loaded Copper, Mater. Sci. Engrg. AIII (1989), 9. 

G.T. Gray III, The Effect of Residual Strain on Twinning in Shock-Loaded Copper, in Proc. 44th Annual Meeting of Electron Microscopy Soc. (edited by G.W. Bailey), San Francisco Press, 1986, 422 pp. 

For a linear viscoelastic material in which the strain recovery may be regarded as the reversal of creep then the material behaviour may be represented by Fig. 2.49. Thus the time-dependent residual strain, Sr(t), may be expressed as... 

From equation (2.63) and the definition of Fractional Recovery, Fr, the residual strain is given by... 

If there have been N cycles of creep and recovery the accumulated residual strain would be... 

Note also that the total accumulated strain after the load application for the (A + l)th time will be the creep strain for the load-on period ie edT) plus the residual strain r(0-... 

Example 2.16 Analysis of the creep curves given in Fig. 2.51 shows that they can be represented by an equation of the form e(t) = Aat" where the constants n = 0.083 and A = 0.0486. A component made from this material is subjected to a loading pattern in which a stress of 10.5 MN/m is applied for 1(X) hours and then completely removed. Estimate (a) the residual strain in the material 100 hours after the stress has been removed, (b) the total creep strain after the 5th loading cycle in which the stress has been applied for 100 hours and removed for 100 hours in each cycle and (c) the residual strain after KKX) cycles of the type described in (b). 

However, in the absence of a programmable calculator or computer the problem may be solved as follows. If the residual strain is calculated for, say 10 cycles then the value obtained is... 

Therefore after the 11th cycle the total creep time is 11x100=1.1x10 hours. If the total strain at this time is plotted on Fig. 2.51 then a straight line can be drawn through this point and the point edT), and this line may be extrapolated to any desired number of cycles. For the case in question the line must be extrapolated to (1001 x 1(X)) hours at which point the total strain may be obtained as 1.09%. Thus the accumulated residual strain after KXX) cycles would be 1.09 — 0.747 = 0.343% as calculated on the computer. 

In tests on a particular plastic it is found that when a stress of 10 MN/m is applied for 100 seconds and then completely removed, the strain at the instant of stress removal is 0.8% and 100 seconds later it is 0.058%. In a subsequent tests on the same material the stress of 10 MN/m is applied for 2400 seconds and completely removed for 7200 seconds and this sequence is repeated 10 times. Assuming that the creep curves for this material may be represented by an equation of the form (r) = At" where A and n are constants then determine the total accumulated residual strain in the material at the end of the 10th cycle. 

It appears that the observed breakdown must be explained in terms of the transient behavior of stress-induced defects even though the stresses are well within the nominal elastic range. In lithium niobate [77G06] and aluminum oxide [68G05] the extent of the breakdown appears to be strongly influenced by residual strains. In the vicinity of the threshold stress, dielectric relaxation associated with defects may have a significant effect on current observed in the short interval preceding breakdown. 

Fig. 7.2. X -ray diffraction line broadening studies in inorganic powders by Morosin and co-workers show evidence for large plastic deformation with residual strain characteristic of cold-worked metals [86M02].

In a comparison of shock-modified powder to powder subjected to other intense deformation, data on shock-modified TiC was compared to a well annealed TiC powder wet milled for many hours to similar values of residual strain. As depicted in Fig. 7.4 the anisotropies observed in residual strain and crystallite size in the two cases are quite different. The shock-modified powders show less anisotropy in strain and more anisotropy in crystallite size... 

Fig. 7.4. Residual strain and crystallite size are compared for TiC powders subjected to wet milling and shock modification. Significant differences are observed in the anisotropies of both features (after Morosin and co-workers [86M02]).

As in other shock-modified powders, the x-ray diffraction measurements showed large values of residual strain resulting from extensive plastic defor-... 

The crossed polarizer effects of both types are used in analysis work. The concentration of optically active organic materials is determined by the degree of rotation. In plastic processing the residual strains in molded materials as well as the degree of orientation of polymers is determined by the effect on polarized light. Crossed polarizers are used with special wave plates to control the amount of light that passes through an optical system. 

This photoelastic stress analysis is a technique for the nondestructive determination of stress and strain components at any point in a stressed product by viewing a transparent plastic product. If not transparent, a plastic coating is used such as certain epoxy, polycarbonate, or acrylic plastics. This test method measures residual strains using an automated electro-optical system. 

To solve the measurement problem and obtain quantitative results (retardation, magnitude of the residual strain, etc.), various techniques are used. An example is using a very simple device known as a wedge compensator (ASTM D 4093). It is placed between the... 

The relation between matter and ether was rendered clearer by Lord Kelvin s vortex-atom theory, which assumed that material atoms are vortex rings in the ether. The properties of electrical and magnetic systems have been included by regarding the atom as a structure of electrons, and an electron as a nucleus of permanent strain in the ether— a place at which the continuity of the medium has been broken and cemented together again without fitting the parts, so that there is a residual strain all round the place (Larmor). 

The mechanical concepts of stress are outlined in Fig. 1, with the axes reversed from that employed by mechanical engineers. The three salient features of a stress-strain response curve are shown in Fig. la. Initial increases in stress cause small strains but beyond a threshold, the yield stress, increasing stress causes ever increasing strains until the ultimate stress, at which point fracture occurs. The concept of the yield stress is more clearly realised when material is subjected to a stress and then relaxed to zero stress (Fig. Ih). In this case a strain is developed but is reversed perfectly - elastically - to zero strain at zero stress. In contrast, when the applied stress exceeds the yield stress (Fig. Ic) and the stress relaxes to zero, the strain does not return to zero. The material has irreversibly -plastically - extended. The extent of this plastic strain defines the residual strain. 

The response of productivity to stress (Fig. 5) has the same form as the strain response (Fig. 1) and emphasises the major concern of agriculture and ecology in defining and (usually) reducing the plastic residual strain, the permanent productivity reduction. 

The focus on productivity in growing systems requires a time component in the study of ecosystem responses. The response of productivity to stress must therefore be considered in three dimensions (Fig. 6). This figure illustrates the effects of a stress at any particular time on the classic sigmoid curve of growth (productivity). Positive production will occur only if the stress is less than the ultimate stress and the residual strain (permanent productivity reduction) will be seen as a lowering of the growth curve below the upper boundary (the z dimension in Fig. 6). 

---