A method for developing the true stress-strain relationship for structural steels based on tension coupon tests

Predicting the uniaxial stress-stress response of ductile metals like structural steel can provide valuable insight into a broad range of engineering problems. Despite a wide body of research covering more than a century, the approach and guidance related to developing the true stress-strain relationship for ductile metals—specifically structural steels—continues to change and evolve. In particular, guidance related to accurate prediction of the onset of necking and post-necking response remains a topic of ongoing research and capturing these effects remains a challenge to researchers and engineers.

The research presented in this dissertation was undertaken to extend the body of knowledge in this area. Particular emphasis is placed on developing a true stress-strain relationship for structural steels that is capable of capturing the onset of necking and post-necking behavior up to fracture. In addition, as standard tension coupon load-deformation data are often the only available information from which to develop such a model, the processes and guidance presented in this dissertation require only that input information. Therefore, advanced experimental approaches and measurement techniques are not required to leverage the guidance presented herein. This path was chosen in the hopes of providing guidance that would be broadly applicable to a wide range of problems, industries, research, and practicing professionals.

This dissertation proposes a method for developing a true stress-strain relationship for structural steels that can be directly used in predictive finite element analysis (FEA) models using three-dimensional (3D) solid elements. The result of this research indicate that such a model should be able to reproduce the experimental results of the tension test quite accurately, providing validation and verification of the assumed material definition. Additionally, three derivative rules are presented. These rules were distilled from existing research and provide simple guidelines for capturing necking, maintaining computational stability and uniqueness, and prohibiting post-necking cold-drawing behavior. The rules are incorporated into the recommended process for developing the true stress-strain relationship for structural steels; however, they are also presented separately so they can easily be incorporated into alternate methods for defining such a constitutive relationship.

Finally, while this research has furthered the understanding of the true stress-strain relationship of structural steels, particularly in predicting necking and post-necking behavior, there is still considerable room for additional research on this topic. For example, automation, incorporating error minimizing techniques, and adding local and material-level and microstructural phenomena (e.g., void formation, growth and coalescence) each offer great potential for extending and improving the recommendations presented in this dissertation. Thus, while this effort has intentionally maintained a limited focus, it is the authors hope that it serves others as one more small step toward accurate prediction of the load-deformation behavior of structural steels and other ductile metals.