Date of Award


Publication Type

Doctoral Thesis

Degree Name



Mechanical, Automotive, and Materials Engineering


Cellular Automata, Dual phase steels, Fracture mechanism, Plasticity, Rate-dependent hardening, Rousselier damage model


Green, Daniel




Advanced high strength steels (AHSS), such as dual phase (DP) and transformation induced plasticity (TRIP) steels, o er high ductility, formability, and strength, as well as high strength-to-weight ratio and improved crash resistance. Dual phase steels belong to a family of high strength grades which consist of martensite, responsible for strengthening, distributed in a ductile ferrite matrix which accommodates the deformation throughout the forming process. It has been shown that the predominant damage mechanism and failure in DP steels depends on the ferrite and martensite grain sizes and their morphology, and can range from a mixture of brittle and ductile rupture to completely ductile rupture in a quasi-static uniaxial tension test. In this study, a hybrid nite element cellular automata model, initially proposed by Anton Shterenlikht (2003), was developed to evaluate the forming behaviour and predict the onset of instability and damage evolution in a dual phase steel. In this model, the nite element constitutive model is used to represent macro-level strain gradients and a damage variable, and two di erent cell arrays are designed to represent the ductile and brittle fracture modes in meso-scale. In the FE part of the model, a modi ed Rousselier ductile damage model is developed to account for nucleation, growth and coalescence of voids. Also, several rate-dependent hardening models were developed and evaluated to describe the work hardening ow curve of DP600. Based on statistical analysis and simulation results, a modi ed Johnson-Cook (JC) model and a multiplicative combination of the Voce-modi ed JC functions were found to be the most accurate hardening models. The developed models were then implemented in a user-de ned material subroutine (VUMAT) for ABAQUS/Explicit nite element simulation software to simulate uniaxial tension tests at strain rates ranging from 0.001s-1to 1000s-1, Marciniak tests, and electrohydraulic free-forming (EHFF). The modi ed Rousselier model could successfully predict the dynamic behaviour, the onset of instability and damage progress in DP600 tensile test specimens. Also, the forming limit curve (FLC) as well as the nal damage geometry in DP600 Marciniak specimens was successfully predicted and compared with experiments. A hybrid FE+CA model was utilized to predict the major fracture mode of DP600 and DP780 sheet specimens under di erent deformation conditions. This hybrid model is able to predict quasi-cleavage fracture in ultra- ne and coarse-grained DP600 and DP780 at low and high strain rates. The numerical results showed the capabilities of the proposed model to predict that higher martensite volume fraction, greater ferrite grain sizes and higher strain rates promote the brittle fracture mechanism whereas ner grain sizes and higher temperature alter the dominant fracture mechanism to ductile mode.