Diamond stress curves

Figure 3.24. Reciprocal mean effective resolved shear stress curves for Knoop indentation calculated for (001) planes of diamond cubic crystals for the lll (lT0) slip systems.

Assuming that a diamond-pyramid hardness test creates a further nominal strain, on average, of 0.08, and that the hardness value is 3.0 times the true stress with this extra strain, construct the curve of nominal stress against nominal strain, and find ... 

Figure 7.4. Total, elastic, and viscous stress-strain curves for collagen fibers from rat tail tendon. The total stress-strain curve (open boxes) was obtained by collecting all the initial, instantaneous, force measurements at increasing time intervals and then dividing by the initial cross-sectional area. The elastic stress-strain curve (closed diamonds) was obtained by collecting all the force measurements at equilibrium and then dividing by the initial cross-sectional area. The viscous component curve (closed squares) was obtained as the difference between the total and the elastic stresses. Error bars represent one standard deviation of the mean.

Figure 7.7. Total, elastic, and viscous stress-strain curves for uncrosslinked self-assembled type I collagen fibers.Total (open squares), elastic (filled diamonds), and viscous (filled squares) stress-strain curves for self-assembled uncrosslinked collagen fibers obtained from incremental stress-strain measurements at a strain rate of 10%/min. The fibers were tested immediately after manufacture and were not aged at room temperature. Error bars represent one standard deviation of the mean value for total and viscous stress components. Standard deviations for the elastic stress components are similar to those shown for the total stress but are omitted to present a clearer plot. The straight line for the elastic stress-strain curve closely overlaps the line for the viscous stress-strain curve. Note that the viscous stress-strain curve is above the elastic curve suggesting that viscous sliding is the predominant energy absorbing mechanism for uncrosslinked collagen fibers.

Fig. 9 Changes in the crack initiation times and crack depths in an epoxy resin as a function of the amplitude of the imposed cyclic displacement, a Number of cycles to the initiation of the primary cracks at the edge of the contact zone, b Measured depths of the primary cracks at various number of cycles and displacement amplitudes. Circles 103 cycles, solid diamonds 5 x 103 cycles, squares 5 x 104 cycles, c Calculated values of the maximum tensile stress at the edge of the contact using Hamilton (gross slip condition) or Mindlin—Cattaneo (partial slip condition) theories. The two curves correspond to calculations using the initial (/x = 1.0) and the steady-state (/x = 1.5) values of the coefficient of friction. PSR Partial slip regime, MR mixed regime, GSR gross slip regime...

See, for example, the product literature for Perkin Elmer s Diamond TMA and PYRIS software. The TMA and the DMA can both be used for running simple mechanical tests like stress-strain curves, creep-recovery, heat set and stress relaxation. Other vendors have similar packages. 

Calculations were performed at 8 volumes for )8-tin and 9 volumes for the sh structure. At each volume two preliminary calculations were performed with different c/a ratios close to the minimum in energy. By linear extrapolation of the anisotropic part of the stress (cr -cr where z is in the c direction and x is in the a direction) it was possible to rapidly find the c/a ratio at which the anisotropic stress is zero. This is the desired equilibrium c/a ratio at which the crystal is in equilrium with an externally applied pressure. With only the linear extrapolation, the residual anisotropy in the stress was typically less than 2 kbars. Thus the true equilibrium structure for each phase was found at each volume. The total energies from calculations performed at the predicted minima are plotted in Fig. 4 together with a curve for diamond Si of comparable accuracy. 

The results from Eqs. (4.17) and (4.18) may be used to define domains of applicability of various stress limits. The interaction curves based on exact methods using Appendix B and those using Eq. (4.15) are shown in Figure 4.7 for the circular and diamond sections. The exact and the approximate solutions are not too different from each other. 

In summary, a planar interface causes the mean focal position to be significantly deeper that the usually quoted paraxial focal depth, and there is also a large spread in the axial illumination, resulting in a large depth of focus. When the system is coupled to a confocal collection aperture, the collection efficiency curves are relatively complex, with a generally rapid fall in the collection efficiency with focal depth. For a given (large) focal depth, there will be an optimum numerical aperture for efficient collection of Raman intensity. The results of this theory will be compared to measured spectra in Section III, which describes an experiment to map the stress distribution within the diamonds of a diamond anvil cell. 

The numerator on the left hand side (LHS) of Eq. 10.64 represents data and the right hand side (RHS) represents a mathematical representation of the data from which n and 8x(ti) can be found. The RHS can be plotted as parametric family of curves with respect to n as shown on Fig, 10,11 by the solid lines. The numerator on the LHS is known creep recovery data for a stress level in the linear range and is shown by square symbols in Fig. 10,11. The denominator represents the amount, 8 (11), the linear recovery data must be shifted downward on a log scale to match the curve with the proper exponent and is equivalent to the transient creep strain at ti for the same stress level in the linear range. The x symbol shows that the recovery data when shifted does not match the exponent n = 0,25. The diamond symbol shows that the recovery strain when shifted downward by the correct amount does fit the exponent n = 0,15. Thus the power law exponent is found as well as the transient creep strain, 8j.(ti), for the particular stress level used in the linear range. 

Therefore, materials harder than diamond can be synthesized by bond engineering through twining and interfacing and the curved diamond indentation tip can measure sample of harder than namre diamond because of the IHPR effect and the stress state difference between the tip and the testing sample. 

Fig. 10.4 Tensile modulus and toughness versus miring speed for 15 % PET/LCP blends. Filled circle tensile modulus open circle toughness (area under stress—strain curve) filled diamond tensile modulus for 100 % LCP...

Figure 2.3 shows deformation curves plotted in tensile strain versus tensile stress coordinates. The endpoints on the curves conform to the time of sample rupture with respective stress and strain. The elasticity modulus of the samples was calculated by the tangent of the angle of slope of the initial segments of the deformation curves. The deformation curves of filled SAN are characteristic of plastics with brittle failure. Nonfilled SAN exhibits considerable deformations. As seen in Figure 2.3 and Table 2.4, addition of up to 10% diamond carbon to SAN... 

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