Field under indenter

A complication is that the deformation field under an indenter is not homogeneous. It is characterized by local glide bands that form the rosette patterns mentioned earlier (Figure 2.2).This makes the process exceedingly difficult to accurately model using either analytic, or numerical computations. 

It can be easily shown that compressive uniaxial or biaxial stress results in the upshift of the Raman band to higher wavenumbers, whereas tensile stress decreases the Raman frequency in these cases [47]. However, in the complex stress field under the indenter, further complicated by the volumetric changes during possible phase transformations and the breakdown of constitutive equations due to macro- and microcracking, determination of the strain tensor components becomes a challenging task and the simplifying analytical models already discussed here need to be used. 

Given the variety of cracking mechanisms, both the stress field under load and the residual stress field are clearly very complex [101]. Difficulties of stress analysis have led to some inconsistency in the formulae derived to calculate indentation toughness. Rather than review the large number of published equations [102-107], a... 

From the morphology of the fibrous structure of the deformed polymer one concludes that the dominant deformation modes of the drawn polymer under the stress field of the indenter involve ... 

In textbooks, plastic deformation is often described as a two-dimensional process. However, it is intrinsically three-dimensional, and cannot be adequately described in terms of two-dimensions. Hardness indentation is a case in point. For many years this process was described in terms of two-dimensional slip-line fields (Tabor, 1951). This approach, developed by Hill (1950) and others, indicated that the hardness number should be about three times the yield stress. Various shortcomings of this theory were discussed by Shaw (1973). He showed that the experimental flow pattern under a spherical indenter bears little resemblance to the prediction of slip-line theory. He attributes this discrepancy to the neglect of elastic strains in slip-line theory. However, the cause of the discrepancy has a different source as will be discussed here. Slip-lines arise from deformation-softening which is related to the principal mechanism of dislocation multiplication a three-dimensional process. The plastic zone determined by Shaw, and his colleagues is determined by strain-hardening. This is a good example of the confusion that results from inadequate understanding of the physics of a process such as plasticity. 

The fiber modulus and matrix shear modulus are also required for the analysis. The fiber s coordinates are recorded directly from the stage controllers to the computer. The operator begins the test from the keyboard. The x and y stages move the fiber end to a position directly under the debonder tip the z stage then moves the sample surface to within 4 yum of the tip. The z-stage approach is slowed down to 0.04 jan/step at a rate of 6 steps/s. The balance readout is monitored, at a load of 2 g the loading is stopped, and the fiber end returned to the field of view of the camera. The location of the indent is noted and corrections are made, if necessary, to center the point of contact. Loading is then continued from 4 g in approximately 1 g increments. Debond is determined to have occurred when an interfacial crack is visible for 90-120° on the fiber perimeter. The load at which this occurs is used to calculate the interfacial shear stress at debond. 

Fig. 17 Contact mechanics analysis of Herztian cracks within brittle materials.a Schematic description of a Hertzian cone crack induced under normal indentation by a rigid sphere, b Reduced plot of JC-field as function of cone crack length and for increasing loads pf < p// < pm during sphere-on-flat normal indentation of brittle materials. Arrowed segments denote stage of stable ring crack extension from Cf to cc (initiation), then unstable to ci at P = P,n (cone-crack pop-in) (From [67]). Branches (1) and (3) correspond to unstable crack propagation (dK/dc > 0), branches (2) and (4) to stable crack propagation (dK/dc < 0)...

Cook suggests that water entry under the load imposed by the indenter is similar to water entry under the load imposed by the abrasive particle. As the abrasive particle moves across the surface, a strain field develops in the glass surface due to the load and velocity of the particle, with compressive strain in front of the particle and tensile strain behind the particle. In front of the particle, hydrostatic pressure leads to water entry into the oxide as the abrasive pushes water into the surface. However, diffusion of water into the oxide is inhibited by the compressive strain occurring in front of the particle. The diffusion coefficient of water decreases exponentially with compressive strain and increases exponentially with tensile strain. The difference between the traveling indenter (i.e., the abrasive particle) and the static indenter (i.e., the Knoop indenter) is the tensile strain that occurs in back of the traveling indenter leads to accelerated diffusion of water into the oxide. Thus, one of the functions of the abrasive particle is to pump water into the oxide surface. Water enters the oxide under the influence of the hydrostatic pressure in front of the particle and diffuses further into die oxide in back of the particle. The depth to which water diffuses into the oxide is a function of abrasive particle... 

As pointed out above, the semicrystalline polymer can be considered as a two-phase composite of amorphous regions sandwiched between hard crystalline lamellae (Fig. 4.2(a)). Crystal lamellae ( c) are normally 10-25 nm thick and have transverse dimensions of 0.1-1 pm while the amorphous layer thickness, a, is 5-10 nm. As mentioned in the previous section, melt-crystallized polymers generally exhibit a spherulitic morphology in which ribbon-like lamellae are arranged radially in the polycrystalline aggregate (Bassett, 1981). Since the indentation process involves plastic yielding under the stress field of the indenter, microhardness is correlated to the modes of deformation of the semicrystalline polymers (see Chapter 2). These... 

The brazed Joints were mounted in epoxy, ground, polished, and examined using Field Emission Scanning Electron Microscopy (FESEM) (model Hitachi 4700) coupled with energy dispersive x-ray spectroscopy (EDS). Microhardness scans were made with a Knoop indenter across the joint interfaces on a Struers Duramin-A300 machine under a load of 200 g and loading time of 10 s. Multiple (4 to 6) hardness scans were made across each joint to check the reproducibility. 

A scratch test is an alternative to the conventional wear test to evaluate the tribological properties of polymers [75,100]. This test involves a high friction induced by a hard indenter which is pressed onto the material under load during the sliding process [51,150]. Briscoe et al. have provided a useful review about the most important theoretical models that have been developed in the field of scratching [179]. 

Figure 12.31 The slip-line field for a deep symmetrical notch (a) is identical to that for the frictionless punch indenting a plate under conditions of plane strain (b). (Reproduced with permission from Cottrell, The Mechanical Properties of Matter, Wiley, New York, 1964)...

Fig. 17 Contact mechanics analysis of Herztian cracks within brittle materials.a Schematic description of a Hertzian cone crack induced under normal indentation by a rigid sphere, b Reduced plot of iC-field as function of cone crack length and for increasing loads pf p// p/// (tuj-ing sphere-on-flat normal indentation of brittle materials. Arrowed seg-...

The work hardening demonstrated by the slider experiments clearly shows the effect of dislocation mobility on this rock-salt-structure material, and it is not unexpected to find much evidence for a load hardness effect with a range of n values at room temperature depending on plane and direction this is shown in Table 4.3. Dislocation mobility under the influence of the stress fields found in indentation hardening also manifests itself as an indentation creep effect as shown in Figure 4.11. 

From the above example it can be seen that a complex system needing careful analysis is present in each case, but the underlying fact is that the type of dislocation and their interactions are intimately concerned with the stress-strain field imposed by the geometry of the indenter. The implication of this is that hardness anisotropy is an obvious manifestation of dislocation interactions and indenter facet geometry. Simplified interpretations of this have been sought, of which the Brookes Resolved Shear Stress model, given in Section 3.6.1, is an important development. 

Highly concentrated stress field seems to be realized under an indentation. In the case of TZP, stress-induced transformation from tetragonal into monoclinic phase can be predicted to occur under the indentation. Raman spectroscopy by using a focused ultraviolet laser with a diameter of Ijim was carried out at the bottom of an indentation to confirm the phase transformation. 

Figure 3. Schematic view of sample setup in Vickers indentation test under applied electric field.

Figure 5. Uncracked and cracked Knoop indentations in the BK 7 borosilicate crown glass at 19.6 N. Indentations should be spaced further apart for most testing purposes in order to avoid interference, (a) is a bright field and (b) dark field optical microscope illumination. The dark field photo reveals that some localized cracking occurs under the left indentations, but the extent of cracking is dramatically different. The cracked indentation is 7 pjn longer.

The impact impression of the shot was observed under an optical microscope. After the macro-indentation test, a part of specimen surrounding the indentation was cut out, embedded in epoxy-resin, sectioned and had the sectional face ground and polished with abrasive (Buehler s Colloidal Silica). The surface was observed under the optical microscope in the bright field and through the differential interference, a scanning electron microscope (SEM Hitachi s-4000), and an electron probe surface analyzer (EPSA Elionix ERA8000). 

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