r7.02.09 Weibull model identification

Summary

Here we address the problem of identifying the parameters of the WEIBULL model on a test sample representative of the fracture behavior of a brittle material (typically, ferritic steel at low temperature). The linear regression method and the maximum likelihood method are the two methods used. The principle and associated resolution methods are detailed, based in both cases on an iterative process. Finally, their extension is shown in the case where one of the two parameters of this model (the cleavage stress) depends on the temperature.

Table of contents

• 1. 1 Introduction
• 2. 2 Reminders
  • 2.1. 2.1 The WEIBULL model
  • 2.2. 2.2 Parameter identification
• 3. 3 Linear regression method
  • 3.1. 3.1.1 Principle
  • 3.2. 3.1.2 Resolution
• 4. 4 Maximum likelihood method
  • 4.1. 4.1 Principle
  • 4.2. 4.2 Resolution
• 5. 5 Dependence of parameters with temperature
  • 5.1. 5.1 Linear regression
  • 5.2. 5.2 Maximum likelihood
• 6. 6 Conclusion
• 7. 7 Bibliography
• 8. Description of document versions