Macrostress

Impact and Erosion. Impact involves the rapid appHcation of a substantial load to a relatively small area. Most of the kinetic energy from the impacting object is transformed into strain energy for crack propagation. Impact can produce immediate failure if there is complete penetration of the impacted body or if the impact induces a macrostress in the piece, causing it to deflect and then crack catastrophically. Failure can also occur if erosion reduces the cross section and load-bearing capacity of the component, causes a loss of dimensional tolerance, or causes the loss of a protective coating. Detailed information on impact and erosion is available (49). 

This brought a bout a keen interest in other methods of intensification in processing. Lately, the directed effect of physical (mechanical) fields on molten polymers has become one such area. These effects, as demonstrated in many works published in the 1970s and in the 1980s, (see for examples [6-9]) result in altered parameters of micro- and macrostress of the system. Molding under conditions of directed physical fields, in particular, in the case of mechanical and acoustic vibration effects upon melts, is performed so that an additional stress superimposed on the polymer s main shear flow and the state of material is characterized by combined stress. 

For most metal-reinforced nanocomposites the thermal expansion coefficient of the metal phase will be larger than that of the matrix, reversing the expected stress fields compared to SiC-reinforced alumina. Thus while the tensile radial stresses surrounding occluded particles may induce transgranular cracking, the compressive hoop stresses may inhibit crack propagation if the particles are located at grain boundaries. Macrostresses in sub-micron Ni... 

Roytburd AL (1998) Thermodynamics of polydomain heterosfructures. I. Effect of macrostresses. J Appl Phys 83 228... 

The lamina macrostresses o , involved in Eq. (6), are obtained by averaging the microstresses, Eqs. (II), across the length of the representative segment as explicit functions of the relative crack density O "" and relative delamination area Djf... 

Thus, the lamina macrostresses, Eq. (12), and macrostrains, Eq. (13), are determined as explicit functions of the damage parameters. Consequently, first partial derivatives of IDEFs,... 

The correction is best determined on a specimen of fine powder, which is necessarily free of macrostress. The powder should have about the same composition as the material in which stress is to be measured in order that its diffraction line occur at about the same 26 position, because the correction (A20)o itself depends to some extent on 26. 

If the specimen has been plastically deformed in a particular way in the region examined by x-rays, the x-ray method does not indicate the true macrostress. (If the plastic deformation causing the residual stress is remote from the region examined, the accuracy of the x-ray method is not affected this condition exists,... 

When a specimen is stretched plastically a few percent and then unloaded, x-ray measurements show a line shift indicating residual compressive macrostress in the direction of prestrain. The effect is symmetrical after plastic compression, x-rays indicate residual tensile stress. It is not a surface effect, because x-ray measurements made after successive removal of surface layers show that the stress persists throughout the specimen. On the other hand, dissection measurements show that a true macrostress does not exist, and, in fact, none would be expected after uniform deformation. The stress indicated by x-rays is called pseudo-macrostress, pseudo because it is not a true macrostress causing strain on dissection and macro because it causes an x-ray line shift. Pseudo-macrostress is actually an unusual kind of microstress, in which the portions of the material that are in tension and in compression are unequal in volume. It has been discussed in various reviews [16.26-16.28]. 

The effect was first observed after uniaxial deformation, but such deformation is not restricted to pure tension and compression. Plastic bending, for example, causes true macrostress (Fig. 16-2), but the deformation mode is predominantly a tension or compression of layers parallel to the neutral axis of the beam. The longitudinal residual stress indicated by x-rays is therefore the sum of true macrostress and pseudo-macrostress, and the x-ray result will be numerically larger at either surface than the result obtained by dissection. 

Deformation by rolling or die drawing has a certain uniaxial character, but the forces on the material at the roll or die surface are inclined to the specimen axis. Macrostress is produced, superimposed on a complex system of microstresses the latter probably include a pseudo-macrostress. As a result, the x-ray method does not measure the true macrostress, but rather the sum of macrostress and some component of the microstress that causes an additional line shift. 

On the other hand, plastic deformation by grinding or shot peening produces maCrostresses that are accurately measurable by x-rays, as shown by excellent agreement between x-ray and dissection measurements. Figure 16-11 shows an example. Deformation by these processes appears to be multiaxial, rather than uniaxial, and pseudo-macrostress is accordingly absent. 

In summary, the x-ray method does not reveal the true macrostress in specimens that have been plastically deformed by tension, compression bending, rolling, or die drawing. It would be wrong to conclude, however, that the x-ray method is in error. Pseudo-macrostress is just as real as macrostress. X-rays indicate the sum of the two, dissection only the latter. 

When the sin / method (Sec. 16-4) is used, some specimens that have been plastically deformed in the region examined yield values of df that vary with sin in an oscillatory manner, rather than linearly [16.33, 16.34, 16.26]. These oscillations in di are not fully understood. They must be caused by a system of micro-stresses more complex than pseudo-macrostress, because pseudo-macrostress, like true macrostress, yields a linear variation of di with sin ij/. When oscillations occur, the standard two-exposure method of stress measurement (Sec. 16.4) can be seriously in error.)... 

Micro structural Properties Texture and Macrostress Effects... 

In Table 12.7 we see that r4 for the group 4/m differs by one term from r4 for the group 4lmmm. The extra-term in 4/m splits those reflections that are nonequivalent but coincident in the absence of the macrostress. The same is valid for the trigonal group 3. The anisotropic peak broadenings caused by microstress are also different for coincident but non-equivalent peaks." ... 

X3 = 5,54 = 55 = 56 = 0, one obtains (sh) = (3Ai + 82/2)3. There is no dependence of (sh) on the Miller indices for the Voigt and the Kroner model. For the Reuss model the dependence is similar to those from Equation (115) and Table 12.8 but with only one refinable parameter for all Laue groups, the macrostress 5, and very probably the refined value of 5 will be wrong. 

Microstructural Properties Texture and Macrostress Effects Equation (81) is replaced the following truncated WSODF ... 

As shown above, the ZrO/Ni composites examined by disk-bend testing are found to deform in a nonlinear manner, so that composition-dependent fracture strengths cannot be obtained directly from the stress-strain diagram in Fig. 3. Under the circumstances, we now make a micromechanical analysis to estimate actual stresses to be developed by plastic deformation of the ductile constituent on the basis of an established "mean-field" model [12]. In the following, the macrostress a) is related to the microstresses and (o) such... 

The in-plane macrostress o vs inplane macrostrain e curves computed with appropriate values of material constants are shown in Fig. 6. The corresponding in-plane and out-of-plane microstress components in the PSZ phase, and are... 

Fig. 6 In-plane macrostress vs in-plane macrostrain curves in equibiaxial tension, computed with (broken lines) and without (solid lines) taking account of residual stresses.

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