analisi statistica del metodo staircase e analisi delle prove di fatica in controllo di deformazione

In materials science, fatigue is a process which causes premature failure or damage of a component subjected to repeated loading and unloading. Fatigue life is defined as the number of stress cycles that a specimen sustains before failure of a specified nature occurs (not necessarily a break). For some material there is a theoretical value for stress amplitude below which the material will not fail for any number of cycles, called a fatigue limit or fatigue strength. Engineers use two methods to determine the fatigue life of a material: the stress-life method and the strain-life method. In high cycle fatigue situations, where stress is low and deformation is primarily elastic, materials performance is commonly characterized by an S-N curve, where S is the stress applied and N is the number of cycles to failure. When the stress is high enough, plastic deformation occurs. In this case a description in terms of stress is less useful and the strain offers a simpler and more accurate description. Then, in low cycle fatigue situations, materials performance is characterized by a Coffin-Manson curve. Instead the method to calculate fatigue limit is called staircase method. The staircase method is a quantal response test, indeed it does not consider the number of cycles to failure, but test are handled in a ¿pass/fail¿ manner. The objective of fatigue strength testing is to determine the appropriate stress level for which an acceptable proportion of specimens survive. In Chapter 1 we will study the linear regression model, which is used for modelling the relationship between two generic variables, and the confidence interval. This chapter will help us to go through the statistical analysis of fatigue data. Chapter 2 briefly shows the stress-life approach, which was the first fatigue analysis method to be developed. It is mainly used for long life applications where stresses and strains are elastic. In Chapter 3 we will study the staircase method, in particular the Dixon and Mood estimators. We will analyze the effects of test parameters (sample size, starting level and step size) using numerical simulation. Moreover we will compare this method with other estimators for both the mean and the standard deviation. Chapter 4 covers the strain-life approach. It is used when the strain is no longer totally elastic, but has a plastic component. Short fatigue lives generally occur under this conditions. We will compare different methods to analyze the fatigue data. This dissertation comes as a result of a internship of C.R.F. (¿Centro Ricerche Fiat¿ - Orbassano (TO)). The C.R.F. was interested in a statistical analysis of data coming from fatigue tests, and they provided us different sets of data obtained by experiments done in their laboratory fatigue. One of the purposes of this stage is to realize a new more flexible Matlab program in order to substitute the currently used Statfat for the statistical analysis of fatigue data obatained from stress-life method. We worked on two sides. In the first part we completed and tested an algorithm on load-controlled test. In the second part we realized new Matlab programs for the staircase simulation and for the statistical analysis of fatigue data obatained from strain-life method. The most significant programs are reported in Appendix A (for the staircase simulation) and in Appendix B (for the strain-life method).