Influence of the hydrogen on fracture of polycrystalline metal Presented by: Junaid Afzal Presented to : Prof. Dr. Alexander Hartmaier Micromechanical and Macroscopic Modeling ICAMS| RUB

Contents Introduction Numerical Implementation Fortran Code layout Influence of the hydrogen on fracture of polycrystalline Metal Contents Introduction Numerical Implementation Fortran Code layout Results ICAMS| RUB | 22 April 2016 Micromechanical and Macroscopic Modeling ICAMS| RUB

Influence of the hydrogen on fracture of polycrystalline Metal Introduction Diffusion-mechanically coupled-theory which accounts for diffusion of hydrogen in material (Steel). Internal hydrogen embrittlement (IHE) and Environment hydrogen embrittlement (HEE). Numerical implementation of the theory in a Finite Element Program (ABAQUS) . Modeling : 2D Polycrystalline model with Simulation results from an analysis of hydrogen transport near a plastically-blunting crack-tip. Micromechanical and Macroscopic Modeling ICAMS| RUB | 22 April 2016 ICAMS| RUB

Hydrogen transport model Influence of the hydrogen on fracture of polycrystalline Metal Hydrogen transport model The hydrogen transport model (HTM) is capable of studying the effective hydrogen transport by distinguishing between lattice hydrogen and trapped hydrogen. There are two ways to implement HTM : a) Hydrogen concentration as boundary condition b) Chemical Potential as degree of freedom. We carried out our HTM by using Chemical Potential as degree of freedom, as it enable to study the lattice distortion implicitly. Chemical potential of lattice hydrogen and trapped hydrogen Trap equilibrium constant ICAMS| RUB | 22 April 2016 Micromechanical and Macroscopic Modeling ICAMS| RUB

Hydrogen transport model Influence of the hydrogen on fracture of polycrystalline Metal Hydrogen transport model Trapped concentration in equilibrium can be expressed as a function of the lattice concentration NL describes the number of locations that can be occupied by hydrogen atoms, for example tetrahedral or octahedral sites . In alpha –iron hydrogen uses tetrahedral sites at room temperature, therefore β is 6 . Number of trapping sites NT describes the number of locations to which hydrogen atoms can be bond with a larger binding energy than to lattice sites. ICAMS| RUB | 22 April 2016 Micromechanical and Macroscopic Modeling ICAMS| RUB

Constitutive formulation Influence of the hydrogen on fracture of polycrystalline Metal Constitutive formulation HTM considering plastic deformation, hydrostatic stresses, hydrogen diffusion and trapping is based on Krom [1]. H resides either on the lattice sites (CL ) or in trapping sites (CT ) assuming equilibrium Mass conservation requires the total H concentration, the sum of lattice (CL) and trapped (CT ) hydrogen, in volume V to be equal to the flux through surface S : The hydrogen diffusion flux J is defined by the chemical potential μ gradient, the driving force for diffusion ϑ = T ICAMS| RUB | 22 April 2016 Micromechanical and Macroscopic Modeling ICAMS| RUB

Constitutive formulation Influence of the hydrogen on fracture of polycrystalline Metal Constitutive formulation The chemical potential under external stress for constant temperature is Assuming that lattice hydrogen cause only lattice distortion lead to We use divergence theorem instead of the J give as : ICAMS| RUB | 22 April 2016 Micromechanical and Macroscopic Modeling ICAMS| RUB

Constitutive formulation Influence of the hydrogen on fracture of polycrystalline Metal Constitutive formulation The final implementation hydrogen transport model follows Elastic Deformation Plastic Deformation Diffusion equation ICAMS| RUB | 22 April 2016 Micromechanical and Macroscopic Modeling ICAMS| RUB

Numerical Implementation Hydrogen Diffusion and Fracture in steel Numerical Implementation Implementation: The Model implementation is carried in Abaqus subroutine UMATHT using hydrogen lattice concentration as degree of freedom. There are two ways of implementation: With the help of pressure gradient , which determine within Abaqus. The implementation of the pressure gradient is not straightforward as need for pressure gradient. The pressure gradient is determined explicitly based on the previous time increment which require external access on the result files. The other implementation are based on Chemical Potential as degree of freedom, which enable us to consider the driving force by lattice distortion implicitly.   ICAMS| RUB | 22 April 2015 Micromechanical and Macroscopic Modeling ICAMS| RUB

Numerical Implementation Hydrogen Diffusion and Fracture in steel Numerical Implementation Computational Programing: The Model implementation is carried in Abaqus subroutine UMATHT in which chemical potential as degree of freedom in implement.   Calculating trapping concentration Start Trapping Model General, Diffusion and HTM Parameters Calculating Lattice concentration Calculating Yield Stresses as function of H End ICAMS| RUB | 22 April 2015 Micromechanical and Macroscopic Modeling ICAMS| RUB

Computational Programing: Hydrogen Diffusion and Fracture in steel Computational Programing: UMATHT based on Chemical Potential: The Model implementation is carried in Abaqus subroutine UMATHT in which chemical potential as degree of freedom in implement.   Start Import Trapping Model Global Module End States for Out put Input Parameter ie. T, Do,NL,NT, etc Calculating Diffusion Flux Call NT & Calculating occupancy trap Calculating Effective Diffusion and mobility Calculating CP (former internal energy) NL ICAMS| RUB | 22 April 2015 Micromechanical and Macroscopic Modeling ICAMS| RUB

Hydrogen Diffusion and Fracture in steel Fortran Coding Layout User defined field subroutine and Combination of All Subroutines Equation approach (for Cohesive) Python coding Nodes Data Trapping Model + UMATH T Subroutine & Calculation of CL & CT Trapping Model constants for use in subroutine to calculate concentration and can be easily accessed in UMATHT. Python : The main purpose of using this code to generate the node data of the specific node those share at the interface. This code help to identify the Node ID to used in Equation command. Node must have the as temperature has degree of freedom. Combination of UMATH & UDFLD Subroutines.   ICAMS| RUB | 22 April 2016 Micromechanical and Macroscopic Modeling ICAMS| RUB

HTM parameter Hydrogen Diffusion and Fracture in steel H-Model Values units T 300 K α 1.0 β 6.0 NL 2.11E-4 mol/mm3 NT 2.1E-08 Δ ET 32.0 kJ/mol Do 36.8 mm2/s Δ ED 26.0 VH 2000 mm3/mol VM 7116 ICAMS| RUB | 22 April 2015 Micromechanical and Macroscopic Modeling ICAMS| RUB

Material Parameter CZ Parameter Hydrogen Diffusion and Fracture in steel Material Parameter Elasticity Values units E 160,200,240…. GPa v 0.3 Plasticity Values units E 800,1200,1600…. MPa CZ Parameter Elasticity Values units K 200 GPa tn,s 550 MPa δf 0.001 mm ICAMS| RUB | 22 April 2015 Micromechanical and Macroscopic Modeling ICAMS| RUB

Mechanical Modelling The RVE was generated by New plugin for Abaqus Influence of the hydrogen on fracture of polycrystalline Metal Mechanical Modelling The RVE was generated by New plugin for Abaqus 2D Voronio tesslation ICAMS| RUB | 22 April 2016 Micromechanical and Macroscopic Modeling ICAMS| RUB

Meshing The RVE was generated by New plugin for Abaqus Influence of the hydrogen on fracture of polycrystalline Metal Meshing The RVE was generated by New plugin for Abaqus 2D Voronio tesslation ICAMS| RUB | 22 April 2016 Micromechanical and Macroscopic Modeling ICAMS| RUB

Implementation of Study Hydrogen Diffusion and Fracture in steel Implementation of Study Simple Grain Boundary Model (Cohesive Surface Based)   A qusi 2D polycrystalline with grain structure is simulated. Periodic Boundary conditions are implemented. With respect to hydrogen boundary condition i-e concentration of hydrogen on the lattice sites, two cases have been studies: Case 1 : Predefined Hydrogen atmosphere and preloaded sample. In this case , there was prior hydrogen in side the sample. The model is loaded and Hydrogen is then accumulated ahead of crack tip. Case 2 : Loading and Hydrogen diffusion at same time. In this case, there was no prior hydrogen inside the sample but the sample is loaded and then placed in hydrogen atmosphere Micromechanical and Macroscopic Modeling ICAMS| RUB

Mises Stress at initial step Hydrogen Diffusion and Fracture in steel Mises Stress at initial step   Micromechanical and Macroscopic Modeling ICAMS| RUB

Counter plot of Mises Stress Hydrogen Diffusion and Fracture in steel Counter plot of Mises Stress   Micromechanical and Macroscopic Modeling ICAMS| RUB

Mises Stress at initial step Hydrogen Diffusion and Fracture in steel Mises Stress at initial step   Micromechanical and Macroscopic Modeling ICAMS| RUB

S22 stresses along crack path Hydrogen Diffusion and Fracture in steel S22 stresses along crack path   Micromechanical and Macroscopic Modeling ICAMS| RUB