Indentation stress

Indentation stress-strain curves for both graded ( ) and control (A) samples. 

Figure 8.88 Indentation stress-strain curve for polycrystalline alumina. (Adapted from Guiberteau et al., 1994, reproduced courtesy of The American Ceramic Society, Westerville, OH.)...

FIGURE 16.14 Indentation stress versus indentation strain. 

At the early stage of densification where P is high, plastic yielding can be the major densification mechanism. The plastic deformation between particles may be regarded as identical to that occurring in a hardness test using an indenter. Then, if the indentation stress a,- satisfies the yielding condition. 

In Fig. 5.6 the indentation pressure is plotted versus a/r. The Hertzian relation between the indentation stress, po, and the indentation strain, a/r, is linear (see, for example, [2]) and given by ... 

Fig. 5.6 Indentation stress-strain curves for base glass and glass-ceramics heat-treated at specified temperatures for 4 h. Data from experiments line fits fl om theoretical analysis [7]. With kind permission of Elsevier...

Field and Swain have studied elasto-plastic response on a number of brittle materials, including silicate glass, silicon single crystal and single crystalline sapphire, by the indentation with small micron sized spherical tipped indenters. The analysis of indentation stress-strain curve was performed from the indentation on... 

The loading and unloading elastic moduli, yield stress, yield strain and constants associated with power law fitting of the indentation stress-strain curves on the different GCs are summarized in Table 2. These values decrease with the elevation of HTT of GCs. 

Figure 3. Indentation stress strain relationships for glass ceramic. Dashed line shows the expected Hertzian elastic response. Experimental results are shown for the coarse (10p.m grain size), medium (5 pm) and fine (2 jm) microstructures. The larger the grains, the more deviation from the elastic response.

Finite element modelling on a macroscopic scale using the Tresca criterion matches the observed size and shape of the plastic zone and also the shape of the indentation stress-strain curves indicating that the physical characteristics of the microstructure determine its yield strength. The use of the Tresca criterion implies a zero coefficient of friction on the microstructural scale. The range of macroscopic yield stresses for the materials studied here is 750 MPa to 2000 MPa. 

A. C. Fischer Cripps and B. R. Lawn, Indentation stress strain curves for quasi ductile ceramics, Acta Mater. 44(2), 519 527 (1996). 

Solutions for simplified cases in which it is assumed that plane sections of the coating remain plane after indentation-induced compression, can be found in the book by Johnson [75]. Johnson s approach was subsequently extended by Jaffar [76]. An early work [24] assumed frictionless contact and used elastic continuum mechanics to estimate the stress distribution in layered materials. In this analysis, force and displacement continuity at the interfaces was satisfied exactly, while the surface displacement condition (profile of the indenter), was only approximated. These authors analyzed indentation stresses created by circular flat-ended and parabolic indenters numerically on both single and multilayer systems, with good results. 

This property may indicate the rubber like nature of the matrix the indenter stress is probably distributed to other parts of the shell and stored as elastic energy which is released when the indenter is raised. ... 

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