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Numerical Modeling of Hydrogen Embrittlement A NUMERICAL MODELING OF HYDROGEN EMBRITTLEMENT A Dissertation Presented to The Graduate Faculty of The University of Akron In Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy Chuanshi Huang May, 2020 NUMERICAL MODELING OF HYDROGEN EMBRITTLEMENT Chuanshi Huang Dissertation Approved: Accepted: Advisor Department Chair Dr. Xiaosheng Gao Dr. Sergio Felicelli Committee Member Dean of the College Dr. Gregory Morscher Dr. Craig Menzemer Committee Member Dean of the Graduate School Dr. Yalin Dong Dr. Marnie Saunders Committee Member Date Dr. Gary L. Doll Committee Member Dr. Chien-Chung Chan ii ABSTRACT This dissertation developed a comprehensive numerical framework for the prediction of hydrogen embrittlement. The framework contains a numerical implementation of the hydrogen diffusion model, a study of hydrogen’s effect on ductile fracture under various stress states, a development of the phase field method for ductile and brittle fracture and the fracture mechanism transition from ductile to brittle caused by hydrogen, and a coupled numerical solution strategy that combines the phase field model with hydrogen diffusion model. The first part of this dissertation uses a unit cell model to study the effect of hydrogen enhanced localized plasticity (HELP) on ductile fracture. The void growth and coalescence of the unit cell is influenced by the initial uniformly hydrogen distribution. The hydrogen redistribution caused by the stress field and plastic strain is observed. The results show that hydrogen reduces the ductility of the material by accelerating void growth and coalescence, and the effect of hydrogen on ductile fracture is strongly influenced by the stress state experienced by the material, as characterized by the stress triaxiality and the Lode parameter. This dissertation presents a phase field model for simulating brittle and ductile fracture. The new developments include the introduction of a degradation function to the yield surface and the modification of the crack driving force function by including the plastic contribution. As the phase field value increases, the yield surface is degraded at the iii same rate as the elastic modulus is, which maintains the integrity of the elasto-plastic constitutive equations. Parameters in the modified crack driving force function include the critical energy release rate and a plastic adjustment factor, which is an exponential function of the plastic strain. The conjoint effect of the plastic adjustment function and the value of the critical energy release rate on the crack driving force reflects the competition between the brittle and ductile fracture mechanisms. A numerical algorithm is proposed to implement the plasticity model with phase field and to solve the coupled system equations monolithically. A strategy using the crack driving force increment to control the size of solution increment is shown to be computationally efficient to assure solution accuracy. Various numerical examples are carried out to demonstrate the capability of the proposed model and to illustrate the influences of model parameters on the simulation results. To modify the phase field model for the simulation of hydrogen embrittlement, a HEDE model is proposed account for hydrogen’s effect on the critical energy release rate, the hydrogen diffusion coefficient and the hydrogen trapping density function are modified as functions of the phase field value, the HELP model is considered in the material constitutive equations. iv ACKNOWLEDGEMENTS First, I would like to express my sincere appreciation to my advisor Dr. Xiaosheng Gao for his continuous support of my study and research. He always has been patient, motivative and inspiring. His guidance helped me throughout the years of my academic and industrial works at the University of Akron. His mentoring trained me to be a better engineer and researcher which with no doubt will continue benefit me in the future. Beside my advisor, I would like to thank the rest of my committee members: Dr. Chien-Chung Chan, Dr. Gary L. Doll, Dr. Gregory Morscher and Dr. Yalin Dong for their time to review my dissertation, and their insightful comments and questions. Additional thanks to Dr. Chang Ye who served as my committee member for my proposal. I also want to thank my colleagues and friends in the group: Dr. Jinyuan Zhai, Dr. Tuo Luo, Clayton Reakes, Chuan Zeng and Guanyue Rao for their helps and advises. they helped me a lot in my research and daily life during this period of time. v TABLE OF CONTENTS Page LIST OF TABLES ............................................................................................................. ix LIST OF FIGURES ............................................................................................................ x CHAPTER I. INTRODUCTION ........................................................................................................... 1 1.1 Hydrogen Embrittlement Understanding ................................................................. 1 1.2 Hydrogen transport and trapping ............................................................................. 2 1.3 Hydrogen enhanced localized plasticity................................................................... 3 1.4 Hydrogen enhanced decohesion ............................................................................... 5 1.5 Phase Field Method .................................................................................................. 7 1.6 Fracture mechanisms ................................................................................................ 8 1.7 Research objective ................................................................................................... 9 II. THE EFFECT OF HYDROGEN ON DUCTILE FRACTURE .................................. 12 2.1 Hydrogen Diffusion Formulation ........................................................................... 12 2.2 Unit cell model ....................................................................................................... 15 2.3 HELP effect under different stress triaxialities ...................................................... 19 vi 2.4 HELP effect under different Lode parameters ....................................................... 25 2.5 Summary and conclusions ..................................................................................... 30 III. PHASE FIELD MODELING FOR BRITTLE AND DUCTILE FRACTURE ......... 33 3.1 Geometrical phase field method for ductile fracture.............................................. 34 3.1.1 Phase field modeling ......................................................................................... 34 3.1.2 Degradation function ........................................................................................ 36 3.1.3 Free energy function ......................................................................................... 37 3.2 Plasticity Model and Numerical Algorithm ........................................................... 41 3.3 Finite Element Implementation .............................................................................. 46 3.4 Parameter Studies ................................................................................................... 49 3.4.1 Effect of the Increment Size ............................................................................. 49 3.4.2 Effect of the Critical Energy Release Rate ....................................................... 55 3.4.3 Effects of α ........................................................................................................ 58 3.4.4 Effect of the Yield Stress .................................................................................. 61 3.5 Additional Examples .............................................................................................. 62 3.5.1 Flat specimen without notch ............................................................................. 63 3.5.2 Compact tension specimens .............................................................................. 66 3.6 Summary and Conclusions ..................................................................................... 73 IV. PHASE FIELD MODELING OF HYDROGEN EMBRITTLEMENT ..................... 75 4.1 Hydrogen Transport Coupled with Displacement and Phase Field ....................... 75 vii 4.2 Hydrogen trapping ................................................................................................. 78 4.3 Hydrogen embrittlement modeling ........................................................................ 80 4.4 Yield function......................................................................................................... 81 4.5 Numerical implementation ..................................................................................... 81 4.6 Compact Tension Specimen ................................................................................... 84 4.6.1 Lattice Hydrogen Diffusion and Hydrogen Trapping ...................................... 84 4.6.2 Hydrogen Embrittlement Mechanisms ............................................................. 90 4.7 Double Notched Flat Specimen ............................................................................. 95 4.7.1 Lattice Hydrogen Diffusion and Hydrogen Trapping ...................................... 96 4.7.2 Hydrogen Embrittlement Mechanisms ............................................................. 97 4.8 Conclusions .........................................................................................................
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