The process of ductile damage and subsequent crack growth and of cleavage in ferritic steels occur in steps whose controlling microstructural features are quite different. Useful models of these can, therefore, be attempted by associating the mechanisms of ductile damage or cleavage with an appropriate, microstructurally controlled, cell size. Furthermore, the cell size for ductile damage is typically too large to be used for the crack-tip finite elements that are required for accurate resolution of the large strain gradients in the continuum field that represents the deformation there prior to significant damage development. What is required is a finite-element code that allows (at least potentially) the presence of cells of more than one size.
These considerations have led to mesh-independent damage mechanics modeling, and a model of the ductile-to-brittle transition that has appropriate cell sizes for each failure mechanism. The complexity of these refined models demands very large computational times for technically interesting problems. Accordingly, our predictions of the outcome of engineering tests have used a compromise single-size cell model chosen to balance the conflicting requirements for each failure process. The paper describes the proving of this, and its use in predicting two of the large-scale spinning cylinder tests.
The work illustrates the potential conflict that may arise between the detailed accuracy required for rigorous physical representation and the pragmatism needed to capture the essentials of application-driven research programs. The paper ends with a discussion of the possible relations between these approaches and their areas of effectiveness.