Failure surface parabolic

Figure 24. Parabolic failure surfaces coaxial to the hydrostatic axis...

FORM usually works well when the failure surface has only one minimal distance point and the function is nearly linear in the MPP neighborhood. However, for increasingly nonlinear failure surface the probability of failure estimated by FORM becomes increasingly inaccurate (and possibly unreasonable) (Melchers 1999). To address such non linearity SORM incorporates some curvature in the limit state approximation through a parabolic approximation to the failure surface (Breitung 1984). 

To determine adhesive failure, it was necessary to apply appropriate algorithms to the data For quantitative analysis data were imported to a spreadsheet, smoothed to remove noise from the LVDTs, and then sorted to remove edge effects. Because there was considerable warp in all specimens due to the durability test, a parabolic function was fit to this distortion and subtracted from the raw data to produce a flat bondline. The data were again sorted (in ascending order) to produce a cumulative frequency distribution of surface irregularities (wood failure). Conceptually, a thickness tolerance could then be specified to define the bondline region as well as a depth tolerance for shallow wood failure. The relative population of data within these regions represented the percent e of adhesive, shallow, and deep wood failure. 

Complex rate laws are usually observed for alloys where different oxides are simultaneously formed on the surface leading to changes in the oxidation rate. For example, if at the beginning a more or less nonprotec-tive oxide scale is formed which is undergrown by a protective partial layer then the oxidation rate will initially be higher than later in the oxidation period in other words, sub-parabolic behavior will be measured. Complex rate laws will also follow when gas phase transport through pores or cracks in the scales is involved. This case, however, is not a protective situation and actually represents at least partial failure of a protective scale. 

---