1. 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

2. 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

3. 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

4. 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

5. 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

6. 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

7. 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

8. 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

9. 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

10. 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

11. 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

12. 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

13. 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

14. 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

15. 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

16. 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

17. 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
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18. Mises Stress at initial step
Hydrogen Diffusion and Fracture in steel
Mises Stress at initial step
Micromechanical and Macroscopic Modeling
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19. Counter plot of Mises Stress
Hydrogen Diffusion and Fracture in steel
Counter plot of Mises Stress
Micromechanical and Macroscopic Modeling
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20. Mises Stress at initial step
Hydrogen Diffusion and Fracture in steel
Mises Stress at initial step
Micromechanical and Macroscopic Modeling
ICAMS| RUB

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