Question

how do you link the saturation curve to microscopic behavior (studying a droplet which gives the saturation curve) and how is young laplace equation used in this study?

Answer 1

SATURATION CURVE SHAPE

Each shot particle that indents the surface of an Almen strip causes a minute plastic expansion of that surface. This expansion induces a corresponding tiny increment of convex curvature into the strip. Because a peened strip has received a very large number of indenting particles we get a measurable curvature – expressed as the deviation from original flatness and termed “Almen Arc Height”. On initial exposure to a constant shot stream each shot particle can impose a similar increment of curvature. As a consequence the Almen arc height initially increases almost linearly with peening time. With further peening, the strip surface progressively work hardens so that the tiny increment of curvature attributable to each indenting particle is reduced. The rate of Almen height increase must therefore slow down. Eventually the incremental contributions become negligible. The slowing down and subsequent leveling-out are the reasons for the characteristic shape of Almen saturation curves. Shot streams with different indenting ability will give different ‘saturation curves’. With increase in shot velocity (and therefore of indenting ability) there is a corresponding increase in curve height, see fig.1. We should also note that the greater the shot flow the quicker will be the increase in arc height. That means that we can have different saturation curves without any difference in indentation ability. Consider next the problem: “How can we assign to each saturation curve a quantity that uniquely defines the indenting ability expressed by that curve?” To solve that problem we need to find a particular point of the curve that defines the curve. The standard solution is the so-called "ten percent rule”. This solution gives us: “The (first) point on the curve for which doubling the peening time increases the arc height by 10%”. For every saturation curve there is only one such point – shown as dots in fig.1. It should be emphasized that the saturation point is not a data point, it is a derived point. The saturation intensity is a defined high-curvature point of the saturation curve. There are alternative ‘characteristic points’. Mathematically-minded readers will note that the curve's curvature at the ‘saturation point’ is close to the ‘point of maximum curvature’. If we know the mathematical equation for the curve we can derive the point of maximum curvature by solving a relationship that includes the first and second derivatives of the curve’s equation. There are various specifications that detail the requirements for saturation curve measurements. All of these specify that several Almen strips must be exposed for different times to the same shot stream. The measured arc heights are then plotted against peening time. A curve must then be drawn so that the saturation intensity can be estimated. There are two alternatives: manual curve fitting and computer-based curve fitting. With the universal availability of computers and appropriate curve-fitting procedures the former technique should be ‘consigned to history’. SATURATION CURVE PREDICTION One advantage of computerized curve-fitting is that the curve’s equation has parameters that are directly related to saturation intensity and saturation time. Popular equations used for curvefitting are ‘two-parameter exponential’ and ‘two-parameter saturation growth’. These are: h = a(1 – exp(-b*t)) (1) and h = a*t/(b + t) (2) where h is arc height, t is peening time, a and b are the two parameters. For both equations the saturation intensity is a fixed proportion of parameter a, [9a/10 for equation (1) and 9a/11 for equation (2)]. Similarly the saturation time is a fixed proportion of parameter b, [2·303/b for equation (1) and 4·5*b for equation (2)]illustrates these relationships for equation (1). The similarity with fig.1 is not coincidental! The machine control settings that lead to every saturation curve produced by a particular peening shop should have been documented. Settings for a new job can therefore be based either directly on past records or on the superintendent’s wealth of experience (or both). Armed with a knowledge of the equation parameters we can plot an expected saturation curve immediately. The case study shown in the next column illustrates the approach used by the author for his laboratory peening facility. The primary factors that govern saturation curves, for a given shot charge, are shot velocity and shot stream flux. In this context, ‘flux’ is the number of shot particles crossing each unit area of the shot stream’s cross-section. Shot velocity is controlled by varying either air pressure or wheel speed. Shot stream flux is varied by means of some type of feed valve – such as a Magnavalve. There is, however, an inter-dependence of shot velocity and shot flux. That means that we cannot vary velocity and flux independently. There are several factors that contribute to the inter-dependence. The major factor is the efficiency of energy conversion. For an air-blast machine the compressed air is providing kinetic energy, some of which is translated into kinetic energy of the shot particles. The greater the shot flux, the lower is the air stream’s efficiency in accelerating the shot particles. Complex physics are involved!

60 1 50 으40 C 30 20 10 12 14 Local disorder index [Cs] -3000 03000 6000 9000 12,000 15,000 18,000 21,000 24,000 27,000 30,000 Dose (kGy)