Microstresses

In a polyphase material, when there is a large difference in thermal expansion coefficients among the different phases, microstresses develop during 

Variation of thermal expansion coefficients of two composites. The circles represent the experimental values. (From W. D. Kingery, /. Am. Ceram. Soc., 40,351,1957.) 

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Electrodeposits are usually in a state of internal stress. Two types of stress are recognised. First order, or macro-stress, is manifest when the deposit as a whole would, when released from the substrate, either contract (tensile stress) or expand (compressive stress) (Fig. 12.12). Second order or microstress, occurs when individual grains or localities in the metal are stressed, but the signs and directions of the micro-stresses cancel on the larger scale. The effects of first order stress are easily observed by a variety of techniques. 

Cantrell, J. H. and Qian, M. (1991). Microstress contrast in scanning electron acoustic microscopy of ceramics. In Review of progress in quantitative nondestructive evaluation, Vol. 10 (ed. D. O. Thompson and D. E. Chimenti). Plenum Press, New York. [17]... 

Each constituent suffers actions of three kinds the prescribed actions at a distance, represented by the densities of body force bi, microforce 7., and heating A the contact actions, represented by the stress 7), the microstress St and the heating flux q% the internal microactions... 

We notice that stress tensors are not a priori symmetric for (16) and that c)J. symmetric tensors. Further, the 3rd order microstress tensor Ss is normally related to boundary micro tractions, even if, in some cases, it could express weakly non-local internal effects % is interpreted as an externally controlled pore pressure (s includes interactive forces between the gross and fine structures. 

As well as producing these broadly beneficial effects, thermal microstresses can also degrade the strength of composites. The tensile components of stress can help in crack initiation. In a composite with a uniform distribution of particles, the tensile components act only over distances comparable with... 

Todd, R.I., Morsi, K. and Derby, B. Neutron diffraction measurements of thermal residual microstresses in ceramic particle reinforced alumina , Brit. Ceram. Proc. 57 (1997) 87-101. 

Invention Significance Cutaneous microstresses generated by prolonged... 

Let denote the in-plane microstresses in the damaged layer (i.e. stresses averaged across... 

Substitution of Eqs. (9) into Eqs. (8) and subsequent differentiation with respect to lead to the equilibrium equations in terms of microstresses and microstrains (i.e. strains averaged across the layer thickness). To exclude the latter, constitutive equations for the damaged layer and the outer sublaminate, equations of the global equilibrium of the laminate as well as generalised plane strain conditions are employed. Finally, a system of coupled second order non-homogeneous ordinary differential equations is obtained... 

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... 

Microstresses arise inside the material as a result of the unequal thermal expansion coefficients of the glass and of the crystals. This phenomenon is characteristic of polyphase ceramics. In porcelains, the stresses arise in particular at the boundary between large quartz crystals and glass. Their formation is also contributed to by the modification inversion of quartz. The stresses sometimes bring about formation of microscopically visible cracks inside the quartz grains or around them. The structure of porcelain thus contains weak points which enhance the development of fracture on loading. 

The facts mentioned above indicate that one of the ways to increase the mechanical strength of porcelain is to change the glassy phase composition in order to increase its thermal expansion coefficient, and thus reduce the microstress at the boundary with quartz. Practical experience shows that the same effect is obtained just by reducing the quartz grain size the small quartz grain size suppresses the adverse effects of microstresses at the boundaries. 

The differences in thermal expansion coefficients of the individual phases and also their anisotropies result in non-uniform shrinkage on cooling. Tf this non-uniform shrinkage cannot be met by deformation, stresses arise restricted to short distances (microstresse.s). This phenomenon is characteristic for ceramics and influences their mechanical properties. High tensile stresses may even result in the formation of ciacks visible under the microscope, for example iji fireclay or porcelain. These cracks arc usually situated at phase boundaries. 

Xu S, Merrill RT (1989) Microstress and microcoercivity in multidomain grains. J Geophys Res 94 10627-10636... 

Because the nonuniform strain due to residual microstress is the major cause of line broadening, we usually find that the broad diffraction lines characteristic of cold-worked metal partially sharpen during recovery. When recrystallization occurs, the lines attain their maximum sharpness. During grain growth, the lines become increasingly spotty as the grain size increases. 

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]. 

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. 

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." ... 

These are sometimes improperly referred to as microstresses. Clearly, the diffraction signal can only be sensitive to displacements. The transposition from the determination of a displacement field to the evaluation of a state of stress requires information on the elastic and plastic characteristics of the materials in question. This goes, of course, beyond the scope of this book. 

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... 

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