Modem approaches to microstructural analysis of fatigue in metallic materials consider the density and the total length per unit area of propagating surface microcracks as useful indicators of fatigue damage. Such parameters, when observed on a carbon steel studied in a previous paper, have a dispersion similar to that of fatigue life and they are linearly correlated with fatigue endurance.The aim of this paper is to extend the research on fatigue damage in the already studied carbon steel and to examine the scatter of crack propagation rate together with the evolution of surface cracks during fatigue life. The final aim of this work is to study how these two factors are correlated with fatigue life distribution in order to evaluate the effectiveness of damage detection methods.Keywords-Fatigue crack density; Total crack length; Surface microcracks; Scatter of fatigue damage. INTRODUCI'IONModem approaches to the microstructural analysis of fatigue in metallic materials showed that surface microcracking and crack length distribution can be taken as indicators of fatigue damage.The first studies on this topic were [ 1-33, where the evolution of the crack population during fatigue life in carbon steels was studied. In particular Goto reported that in carbon steels there is a continuous formation of microcracks during the entire fatigue life and that consequently the shape of crack length distribution remains almost constant. Hyspeky and Stmadel [4], in carrying on the same type of experiments on a stainless steel, showed that the number of cracks is not directly related to the application of cyclic loads. In fact they observed that, after a given average crack length, the coalescence mechanisms overcame the formation of new microfractures and that the crack length distribution significantly changed during fatigue life.In accordance to these different cracking mechanisms two damage parameters were proposed the crack density [S-81 and the total length per unit area [9]. The latter has the advantage of a direct relationship to the endurance also for materials that have a prevailing coalescence mechanism (e.g. stainless steels). Moreover it has to be noticed that in the above mentioned studies neither the scatter of these indicators was analysed nor a standard measurement method was applied (the referenced authors examined different surface portions at different magnifications).On that basis we examined the correlation between fatigue endurance and final microcrack distributions [lo], working on a carbon steel with a peculiar life scatter [ 111. The analysis, which differed from those carried out by other authors who had focused their attention on small surface areas, consisted in the examination of the entire surface of the broken specimens at low magnifications ( x 30). The result was that both the crack density and the total length per unit area at the end of fatigue life were linearly correlated to the number of cycles to failure. Moreover no evident relationship with the shape of the crack length distribution was n...

Experimental determination of the fatigue endurance (S-N) curve of either a given material or a machine element imposes the choices of sample size and of stress levels to be tested. Since referenced recommendations do not apply when the data include run-outs or have variable scatter, this paper studies the confidence of fatigue tests, taking into account the effect of sample size and of a statistical model. In this research, a great number of rotary bending fatigue tests were carried out, using a heat treated carbon steel with relevant scatter of fatigue lives. The statistical analysis allowed one to obtain confidence limits of the S-N diagram estimates and to propose some criteria for a better formulation of test schedules. NOMENCLATURE K, = standard normal (100 + y)/2 percentile L = sample log-likelihood n = sample size N =cycles to failure S, = ultimate tensile strength S,, S, , = monotonic and cyclic yield strength S, = fatigue limit (rotating bending) -S = applied stress log S = sample log-stress average of tested levels XI, X,, X,, X,, =parameters of the statistical models considered y = log-life F= sample average of log-lives p =mean of the normal distribution of log-lives Q = standard deviation of the normal distribution y = confidence level

Using the three-dimensional photoelastic method a quantitative analysis was carried out on the tension trends in the proximal third of a normal human femur in a stationary weight-bearing situation on two legs. The results obtained show that in this loading situation the maximum stress values (both for tension and compression) are in the area just below the subtrochanteric zone; while going up along the borders of the diaphysis, the tension trends do not vary appreciably. Moreover, the state of the stresses is not constant but varies slightly along the thickness of the bone. The neutral axis is considerably displaced towards the tensile area. A comparison between the stress tension trends in two different static loading situations (one-leg and two-leg support) was carried out. It was found that the maximum tensile stress value in the one-leg position was about 24 times greater than that in the two-leg position and the maximum compression stress value was about 14 times greater than in the two-leg situation.

Comparative critical examination of methods suitable for studying stress in bones have shown that the three-dimensional photoelastic method is one of the most reliable. Described herein is the method for obtaining, by fusion, full-scale models in epoxy resin, that are exactly equivalent to external shape of the prototypes.This technique offers the advantages of being applicable without variation to any bone segment and of enabling a large number of additional resin castings to be made from the same mould. Hence it is possible to produce a very large number of copies of the same bone segment that will be suitable for comparative studies of different load situations.As an example, quantitative data expressing both surface and internal tension trends in the proximal third of a normal human femur are given.It is well known that a bone exposed to mechanical stress becomes elastically deformed and develops corresponding internal tensions which, influencing its biodynamics, improve the bone structure, making it mechanically better suited for the stresses applied. The internal structure of bones thus is in direct relation to the mechanical stresses exerted on them.The correlation between mechanical requirements and bone structure, with particular reference to the arrangement and orientation of cancellous bone trabecules, has been known since early in the last century. Ward (1838) was the first to provide detailed description of cancellous bone in the femoral neck, by identifying the three main trabecular systems; furthermore, comparing the construction of femur epiphysis to that of a crane, he identified a zone subjected to compression along the medial cortical bone and a zone of tension along the lateral cortical bone. These results were later confirmed by Wyman (1857). Humphry (1858) observed that in the femoral neck the main trabecular systems cross each other at right angles, and that the trabeculae are arranged perpendicularly in relation to the articular surface of the femur head. In 1867 von Meyer published, according to data of Culmann (1866), his theory regarding cancellous bone architecture, with a definition of trabecular trajectories arranged along the principal stress lines.On the basis of Meyer's and Culmann's data, the close relationship between the function and architecture of cancellous bone was demonstrated by Wolff (1892), and developed and confirmed by Roux (1893) in his theory of functional adaptation.More recently the now undisputed link between shape, structure, and mechanical function of bone has been verified in a series of studies which have used more sophisticated and accurate methods of investigation. Among these, the most reliable are: finite elements (theoretical calculation method), electric strain gauges, brittle coatings, holographic interferometry, and photoelasticity methods (all experimental methods).The finite elements method applied to bones (Zinkiewicz,

No abstract