Crack initiation and propagation under thermal fatigue of ...
Microstructure-sensitive Fatigue Initiation Behaviour: A ...
1
I-Form is an SFI Research Centre funded under the Science Foundation Ireland Research Centres Programme and co-funded under the European Regional Development Fund. Microstructure-sensitive Fatigue Initiation Behaviour: A Crystal Plasticity Finite Element Modelling Study Y. Tu 1,2,3 , S.B. Leen 1,2,3,4,5 N. M. Harrison 1,2,3,4,5 1 Mechanical Engineering, National University of Ireland Galway, Ireland 2 I-Form Advanced Manufacturing Research Centre, Ireland 3 Ryan Institute for Environmental, Marine and Energy Research, NUI Galway, Ireland 4 IComp Irish Composites Centre, Ireland 5 Centre for Marine and Renewable Energy Ireland (MaREI), Galway, Ireland . Introduction The microstructure of any metal component is determined by the manufacturing process conditions. In turn, the mechanical behaviour of the part is strongly influenced by the microstructure. A crystal plasticity finite element (CPFE) framework is developed here to study the relationship between microstructure and fatigue crack initiation behaviour. This work involves developing a process for turning a full experimental electron backscattered diffraction (EBSD) grain map into the finite element model that is suitable for the analysis of mechanical fatigue performance. In recent years, major advances in microstructural imaging, including electron backscatter diffraction (EBSD) have enabled accurate visual characterisation of grain structures and their orientation [2,3]. In parallel, advances in computational modelling methodologies, including crystal plasticity finite element (CPFE) modelling have permitted advanced microstructural mechanical characterisation [4]. This project links both advances to develop a novel technique for incorporating real grain structures and texture into CPFE-based prediction of cyclic plasticity and fatigue crack initiation (FCI). Objectives Develop an optimum methodology to rapidly and accurately construct image- based computational microstructural models. Compare complete image-based CPFE modelling to current Voronoi tessellation and partial image-based strategies (grain structure with random texture). Conduct microstructure-sensitive case studies for cyclic plasticity and FCI, with particular focus on grain size and texture. Results The microstructure morphology was processed in a series of image-cleaning steps, The orientation of the grains was mapped using custom-written software. The resulting 576 μm x 476 μm CPFE models were subjected to 12 cycles of strain-controlled cyclic loading for strain-ranges of ±0.5%, ±0.8%, ±1.0% and ±1.2%, with periodic boundary conditions. A user material (UMAT) subroutine was employed with the general-purpose, non-linear finite element software ABAQUS [7,8]. The UMAT includes isotropic and non-linear kinematic hardening. The results are compared to the experimental test data in Fig. 4[9]. Figure 6. (a) Schematic direction for fcc crystal;[5] (b)[1,1,1] texture; (c) [0,0,1] texture. (d) Comparison between random orientation(no texture) and texture (b) (c). Conclusion & Discussion 1. A method is presented for converting EBSD images of microstructural data into CPFE models, including grain morphology, size and texture data. 2. This method gives improved fidelity for microstructure modelling and reduces uncertainty, compared Voronoi tessellation or partial-image based methods. 3. A Hall-Petch effect has been implemented to represent the effect of average grain size on critical resolved shear stress and hence on fatigue. 4. The effect of different textures on tensile response has been demonstrated. Tensile (axial) stress decreases with increasing alignment of material texture to load direction. References 1. A.A. Antonysamy, J. Meyer, P.B. Prangnell, Materials Characterization, 84 (2013) 153-168. 2. Leyens, C., et al., Titanium and titanium alloys : fundamentals and applications. 2003, Wiley. 3. Soran Birosca, 2017. Process-Structure-Property Relationships in Metals, MDPI AG - Multidisciplinary Digital Publishing Institute. 4. Roters et al., 2010. Crystal plasticity finite element methods in materials science and engineering, Wiley. 5. Texture Analysis with MTEX - Free and Open Source Software Toolbox, F. Bachmann, R. Hielscher, H. Schaeben: Solid State Phenomena, 160 (2010) 63-68 6. A Groeber, Michael & A Jackson, Michael. (2014). DREAM.3D: A Digital Representation Environment for the Analysis of Microstructure in 3D. Integrating Materials and Manufacturing Innovation. 3. 5. 10.1186/2193-9772-3-5. 7. Huang Y. A User-material subroutine incorporating single crystal plasticity in the ABAQUS finite element program. Mech Report 178. Division of Applied Science Harvard University; 1991. 8. Ashton, P.J., A.M. Harte, and S.B. Leen, Statistical grain size effects in fretting crack initiation. Tribology International, 108 (2017) 75-86. 9. Sweeney, Caoimhe et al., 2015. Strain-gradient modelling of grain size effects on fatigue of CoCr stents. Acta Materialia, 78 (2014) 341-353 Figure 1. Process-Structure-Property Interdependency Figure 4. (a) Inverse pole figure; (b) CPFE model; (c) CPFE-test comparison for different strain ranges and (d) comparison of predicted and measured FCI life. Figure 5. (a) Statistical size effect study; (b) Average grain size effect study. Texture in microstructure is common for samples manufactured by forging, rolling and additive manufacturing. The effect on mechanical behavior of texture direction was predicted here using the generated texture strength in the CPFE model. a c Methodology EBSD-based CPFE model dx = FdX = ∙ = ሶ =න 0 ሶ = ∆ : Gradient tensor dx ,dX: Configuration vectors L: Spatial velocity gradient s : Slip direction m: Slip plane normal : Slip plane. p: Accumulated effective slip : Crack initiation cycles Hot-rolled biomedical grade CoCr alloy[9] Figure 2 Overview of the image based CPFE model construction method EBSD Data Morphology Extraction Boundary conditions Loading definition & Material model Orientation dependent Grain property MATLAB tool MTEX [5] Commercial Software [6] Custom MATLAB script Python code [8] Ti6Al4V PBF Microstructure [1] Powder Bed Fusion Mechanical Property Microstructure Visual reconstruction Scatter of fatigue life is a key source of uncertainty in engineering fatigue design. Microstructure-induced statistical size effects are a potential source of scatter. We investigate this here for the CoCr alloy, by varying the number of grains in the RVE. A 15% reduction in life is predicted for 44% increase in number of grains. A Hall-Petch effect was implemented for average grain size effect on critical resolved shear stress. a b d (a) (b) (c) (d) 315 grains 377 grains 561 grains 0 5000 10000 15000 20000 25000 30000 0 10 20 30 N i Grain size ( mm) Pcyc Wcyc b
Transcript of Microstructure-sensitive Fatigue Initiation Behaviour: A ...
I-Form is an SFI Research Centre funded under the Science Foundation Ireland Research Centres Programme and
co-funded under the European Regional Development Fund.
Microstructure-sensitive Fatigue Initiation Behaviour: A Crystal Plasticity Finite Element Modelling Study
Y. Tu1,2,3, S.B. Leen1,2,3,4,5 N. M. Harrison1,2,3,4,51 Mechanical Engineering, National University of Ireland Galway, Ireland
2 I-Form Advanced Manufacturing Research Centre, Ireland3 Ryan Institute for Environmental, Marine and Energy Research, NUI Galway, Ireland
4 IComp Irish Composites Centre, Ireland5 Centre for Marine and Renewable Energy Ireland (MaREI), Galway, Ireland
.
IntroductionThe microstructure of any metal component is determined by the manufacturing
process conditions. In turn, the mechanical behaviour of the part is strongly
influenced by the microstructure. A crystal plasticity finite element (CPFE)
framework is developed here to study the relationship between microstructure
and fatigue crack initiation behaviour. This work involves developing a process for
turning a full experimental electron backscattered diffraction (EBSD) grain map
into the finite element model that is suitable for the analysis of mechanical fatigue
performance.
In recent years, major advances in microstructural imaging, including electron
backscatter diffraction (EBSD) have enabled accurate visual characterisation of
grain structures and their orientation [2,3]. In parallel, advances in computational
modelling methodologies, including crystal plasticity finite element (CPFE)
modelling have permitted advanced microstructural mechanical characterisation
[4]. This project links both advances to develop a novel technique for
incorporating real grain structures and texture into CPFE-based prediction of cyclic
plasticity and fatigue crack initiation (FCI).
Objectives Develop an optimum methodology to rapidly and accurately construct image-
based computational microstructural models.
Compare complete image-based CPFE modelling to current Voronoi
tessellation and partial image-based strategies (grain structure with random
texture).
Conduct microstructure-sensitive case studies for cyclic plasticity and FCI,
with particular focus on grain size and texture.
ResultsThe microstructure morphology was processed in a series of image-cleaning steps, The
orientation of the grains was mapped using custom-written software. The resulting 576 µm
x 476 µm CPFE models were subjected to 12 cycles of strain-controlled cyclic loading for
strain-ranges of ±0.5%, ±0.8%, ±1.0% and ±1.2%, with periodic boundary conditions. A
user material (UMAT) subroutine was employed with the general-purpose, non-linear finite
element software ABAQUS [7,8]. The UMAT includes isotropic and non-linear kinematic
hardening. The results are compared to the experimental test data in Fig. 4[9].
Figure 6. (a) Schematic direction for fcc crystal;[5] (b)[1,1,1] texture; (c) [0,0,1] texture. (d) Comparison
between random orientation(no texture) and texture (b) (c).
Conclusion & Discussion1. A method is presented for converting EBSD images of microstructural data into CPFE
models, including grain morphology, size and texture data.
2. This method gives improved fidelity for microstructure modelling and reduces
uncertainty, compared Voronoi tessellation or partial-image based methods.
3. A Hall-Petch effect has been implemented to represent the effect of average grain
size on critical resolved shear stress and hence on fatigue.
4. The effect of different textures on tensile response has been demonstrated. Tensile
(axial) stress decreases with increasing alignment of material texture to load direction.
References1. A.A. Antonysamy, J. Meyer, P.B. Prangnell, Materials Characterization, 84 (2013) 153-168.
2. Leyens, C., et al., Titanium and titanium alloys : fundamentals and applications. 2003, Wiley.
3. Soran Birosca, 2017. Process-Structure-Property Relationships in Metals, MDPI AG - Multidisciplinary Digital Publishing Institute.
4. Roters et al., 2010. Crystal plasticity finite element methods in materials science and engineering, Wiley.
5. Texture Analysis with MTEX - Free and Open Source Software Toolbox, F. Bachmann, R. Hielscher, H. Schaeben: Solid State Phenomena, 160 (2010) 63-68
6. A Groeber, Michael & A Jackson, Michael. (2014). DREAM.3D: A Digital Representation Environment for the Analysis of Microstructure in 3D. Integrating Materials and Manufacturing
Innovation. 3. 5. 10.1186/2193-9772-3-5.
7. Huang Y. A User-material subroutine incorporating single crystal plasticity in the ABAQUS finite element program. Mech Report 178. Division of Applied Science Harvard University; 1991.
8. Ashton, P.J., A.M. Harte, and S.B. Leen, Statistical grain size effects in fretting crack initiation. Tribology International, 108 (2017) 75-86.
9. Sweeney, Caoimhe et al., 2015. Strain-gradient modelling of grain size effects on fatigue of CoCr stents. Acta Materialia, 78 (2014) 341-353
Figure 1. Process-Structure-Property Interdependency
Figure 4. (a) Inverse pole figure; (b) CPFE model; (c) CPFE-test comparison for different strain ranges
and (d) comparison of predicted and measured FCI life.
Figure 5. (a) Statistical size effect study; (b) Average grain size effect study.
Texture in microstructure is common for samples manufactured by forging, rolling and
additive manufacturing. The effect on mechanical behavior of texture direction was
predicted here using the generated texture strength in the CPFE model.
a c
Methodology
EBSD-based
CPFE model
dx = FdX𝑭 = 𝑭𝑒 ∙ 𝑭𝑝
𝑳𝑝 =
𝛼
ሶ𝛾𝛼𝒔𝛼𝒎𝛼
𝑝 = න0
𝑡
ሶ𝑝𝑑𝑡
𝑁𝑖 =𝑝𝑐𝑟𝑖𝑡∆𝑝
𝑭 : Gradient tensordx ,dX: Configuration vectorsL: Spatial velocity gradients : Slip directionm: Slip plane normal𝛼: Slip plane.p: Accumulated effective slip𝑁𝑖: Crack initiation cycles
Hot-rolled biomedical grade CoCr alloy[9]
Figure 2 Overview of the image based CPFE model construction method
EBSD
Data
Morphology
Extraction
Boundary conditions
Loading definition &
Material model
Orientation dependent
Grain property
MATLAB tool
MTEX [5]
Commercial
Software [6]
Custom
MATLAB
script
Python code [8]
Ti6Al4VPBF
Microstructure[1]
Powder Bed Fusion
Mechanical PropertyMicrostructure
Visual
reconstruction
Scatter of fatigue life is a key source of uncertainty in engineering fatigue design.
Microstructure-induced statistical size effects are a potential source of scatter. We
investigate this here for the CoCr alloy, by varying the number of grains in the RVE. A 15%
reduction in life is predicted for 44% increase in number of grains. A Hall-Petch effect was
implemented for average grain size effect on critical resolved shear stress.
a
b d
(a) (b) (c) (d)
315 grains
377 grains
561 grains
0
5000
10000
15000
20000
25000
30000
0 10 20 30
N i
Grain size ( mm)
Pcyc
Wcyc
b
