Residual curvature measurement

To predict the residual stress distributions in sprayed FGM, in-situ curvature measurement is necessary because the values of quenching stress are difficult to... 

To circumvent the drawbacks of the sin2 P-technique including the problem of a non-linearity of the modulus of elasticity, attempts have been made to apply other tests to obtain estimates of the residual stresses. The curvature measurement is probably one of the most widely used method for determining residual stress and involves measuring the bending of the coated sample in response to both quenching and thermal stresses. From the measured radius of curvature, the stress can be calculated according to the Stoney equation (Stoney, 1909) as... 

There are several ways to test the linearity of a calibration line one can devise theory-based tests, or use common sense. The latter approach is suggested here because if only a few calibration points are available on which to rest one s judgement, a graph of the residuals will reveal a trend, if any is present, while numerical tests need to be adjusted to have the proper sensitivity. It is advisable to add two horizontal lines offset by the measure of repeatability accepted for the method unless the apparent curvature is such that points near the middle, respectively the end of the x-range are clearly outside this reproducibility band, no action need to be taken. 

Interpretation The model can only be improved upon if the residual standard deviation remains significantly larger (F-test ) than the experimental repeatability (standard deviation over many repeat measurements under constant conditions, which usually implies within a short period of time ). Goodness of fit can also be judged by glancing along the horizontal (residual = 0) and looking for systematic curvature. 

In a parallel experiment, the extent of the reaction a is measured using the partial heat to a particular time divided by the total heat of the isotherm plus the residual heat of a subsequent 10°/min ramp. Figures 5 and 6 show the observed relationship of In a and In t to a. As expected for a similar degree of advancement a, the ionic mobility a increases with temperature. Similarly for the same value of a, the dipolar mobility increases. An increase in dipolar mobility corresponds to a shorter relaxation time. Thus t decreases as temperature increases. Somewhat unexpected, both In a and In t exhibit a nearly linear dependence on a. Curvature in the In a and In t versus a plot is most pronounced for small values of a and at the highest temperature. There is no evidence of a break in the In <7 or In T dependence on a which would indicate gel. 

Fig. 8.9. Stress fields at the end of a trench etched in a 15f

In the fictive gray system the value of Tc would be on the upper curve in Figure 6 with a value between the values of both parent compounds. However, in the real pseudoquaternary system YxLui xNi2B2C, Tc has a considerably lower value than expected from a linear interpolation, i.e. the gray system. As shown in Figure 60 the concentration dependence of Tc is non-monotonic with a minimum near x = 0.5. A similar behavior was found also for other quantities characterizing the electronic state of the system as the upper critical field H 2 and the parameter a [from Hc2(T) = H 2( 1 - T/Tc)1+ ] which is a measure for the positive curvature of Hc2(T), the residual resistance ratio RRR = pn(300 K)/pn(Tc), where pn(T) is the normal-state resistivity, and the two parameters kn and describing the field... 

Residual stresses may be measured from the radius of curvature (ROC) of the warpage that occurs on a substrate when the adhesive is cured on that substrate. The bending stress, 5b, is inversely proportional to the radius of curvature, R, and directly proportional to the modulus, E, and the thickness, /j, of the adhesive according to ... 

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