Numerical Simulation of Residual Stresses in Quenched Steel Bodies Using Subroutines to Represent TTT and CCT Diagrams

The objective of this work is to analyze residual strains and stresses and volumetric expansion due to phase transformations that occur during quenching of a steel body. Three different models are proposed, based on the finite element software ABAQUS ® and on the use of FORTRAN subroutines. The time-tempreature-transformation (TTT) or continuous-cooling-transformation (CCT) diagrams of SAE 4140 steel are represented differently in each model, depending on the transformed phases and correspondent volumetric expansion. In the first model, diagrams are intentionally simplified in order to consider only the austenite-martensite transformation. In the second model, the thermomechanical-phase transformation coupling is represented through the incorporation of the austenite-pearlite transformation into the TTT diagram used in the first model and considering that this transformation occurs for cooling rates lower than the limit for martensitic transformation. The third model is based on a subroutine that calculates all the microstructures resulting from quenching (ferrite, pearlite, bainite, and martensite), depending on cooling rate. This subroutine includes information from all the TTT and CCT diagrams of SAE 4140 into a FORTRAN code. Model testing was conducted based on the analysis of the quenching of a cylinder with diameter of 45 mm and based on the comparison with results presented in the literature. Significant differences are observed in the numerical results provided by each model, which, in some cases, also provided data with significant differences from literature.