晶体塑性有限元 Crystal Plasticity Finite Element Method
The crystal deformation is a complex process, which is not only related to macroscopic factors
such as loading method, loading rate, deformation, et al., but also related to factors such as
crystal orientation, grain morphology, interaction between grains, and activation of the
deformation mechanism. Therefore, it is necessary to combine the crystal deformation with the
mechanical response of its microstructure and the deformation mechanism effectively.In 1982,
Peirce and other scholars combined finite element numerical simulation with crystal plasticity
theory, and proposed the crystal plasticity finite element method(CPFEM) for the first time.
This method not only considers the actual orientation in polycrystalline materials, but also
considers the different crystal structure types and slip mechanisms in plastic deformation of
multiphase materials.Compared
with the traditional finite element simulation, it can reflect the deformation mechanism
of the crystal material, and be closer to the realistic plastic deformation process via CPFEM.
This simulation method has been proved to play an important role in the modeling and prediction
of texture evolution of polycrystalline metals, and the reliability of crystal plasticity theory
is verified.
晶体材料的变形是一个复杂的过程，除了与加载方式、速率、变形量等宏观因素有关，还与晶体取向、晶粒形貌、晶粒间相互作用以及变形机制开动等因素有关。因此，需要将晶体材料的变形与微观组织力学响应及变形机制有效地结合在一起进行研究。1982年Peirce等学者将有限元数值模拟技术和晶体塑性理论相结合，首次提出了晶体塑性有限元（CPFEM）。该方法不仅考虑了多晶材料中晶体的实际取向，还可以考虑多相材料不同的晶体结构类型和塑性变形滑移机制。与传统的有限元模拟相比，考虑了晶体塑性的数值模拟更能体现晶体材料变形机制，比较接近现实的塑性变形过程。该模拟方法已被证明对多晶金属的建模和预测织构演变发挥了重要作用，并验证了晶体塑性理论的可靠性。
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晶体塑性有限元
文献1（2020）：Crystal Plasticity Finite Element Method for Slip Systems Evolution Analysis of α/β
Duplex Titanium Alloys during Quasi-Static Tensile
Testing（准静态拉伸试验中α/β双相钛合金滑移系演化分析的晶体塑性有限元法）
The model was developed from an EBSD image. The local area selected was 16.5 μm × 10.1 μm
(see Figure 2a). The area consisted of 12 grains, including seven α-phase grains and five
β-phase grains. The grains were numbered (i.e., ①, ② , ③ , and so on) and the excel file
including crystal structure,
centroid position, Euler angles (φ1, Φ, φ2) was output by channel5
software. Based on the RGB
values
of the image pixels, a 2D finite element model was developed. However, the 2D model used the
plane
strain or plane stress assumption, which may affect the accuracy of the simulation. Therefore, a
unit
thickness finite element model was established with 8-node 3D hexahedron solid elements, using
the microstructure-based finite element model construction software developed by our group
(see Figure 2b), so it is called a 2.5D finite element model, which can reduce the
calculation time
and well reflect the actual situation. Each grain was considered as a single crystal, with a
uniform crystallographic orientation, and its Euler angle was determined by centroid result.
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Figure 2. Process of developing the crystal plasticity finite element simulation
method (CPFEM): (a)
the Electron Backscatter Diffraction (EBSD) inverse pole figure (IPF) mapping, (b) 2.5D finite
element
model, (c) boundary condition, (d) displacement-time curve.
Generally, a resolved shear stress is determined from the full Schmid tensors unless the stress
state is uniaxial, what is unlikely for a local stress state. In this study, we analyze the
major principal stress to verify the assumption and prove the influence of grain interactions on
the SFs quantitatively For example, when the macro strain reached 0.7%， the prismatic slip
systems of grain No. 3 and 11
were activated, while the SF of（0110 ）[2110] in
grain No. 3 was 0. 136 and the SF
of（0110）[2110] in
grain No. 11 was 0. 321. It was found that the（0110 ）[2110] in grain No. 3 should not be the
primary ip system. Therefore, as shown in Figure 12a, the macro deformation direction was
parallel to X axis, and the direction of major principal stress δ1 deviated from the
X-axis
and
the deviation angle was e
（ignoring the deviation angle between the direction of δ1 and Z-axis）， which was used
to fit
with the Euler angle and recalculate the SFs. As shown in Figure 12b, the e of grain No. 3
was
30° and the e of grain No. 11 was close to 0°. After recalculation, the SF of（0110）[2110] in
grain
No. 3 was 0.333， which meant that the（0110
）[2110] slip system was easily activated
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Figure 12. (a) Schematic diagram of major principal stress; (b) ε = 0.7%; (c) ε =
2.4%; (d) ε = 7.8%
effective strain increment fields in the local and the direction of major principal stress.
Multi-scale crystal plasticity finite element simulations of the microstructural evolution
and formation mechanism of adiabatic shear bands in dual-phase Ti20C alloy under complex
dynamic loading
Appl. Sci. 2020, 10(21), 7782
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文献2（2020）：Multi-scale crystal plasticity finite element simulations of the microstructural
evolution and formation mechanism of adiabatic shear bands in dual-phase Ti20C alloy under
complex dynamic loading（复合动态载荷作用下双相Ti20C合金绝热剪切带的微观组织演化及形成机理的多尺度晶体塑性有限元模拟）
A multi-scale CPFEM method is proposed for extracting load infor-mation from the macro model, and
then progressively applying thisinformation to the micro grain models. Firstly, microregion of
interest is selected from the interior of the ASB, anda set of the micro region boundaries is
established in LS-DYNA. Secondly, a model with the same size as the micro region of interest,and
a finer mesh method (than previously employed) is established. The region near theedge of Ti20C
sample was selected as the observation area, andSEM and EBSD measurements were performed after
the edge ofthe sample was bombarded uniformly with focused ion beam.
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Fig. 4. (a) Process of extracting load information from the macro to the micro
model and (b) phase distribution and grain orientation distribution based on the
grainmicrostructure.
The grain rotation and recrystallization in the ASB, as well as the plastic deformation and
softening mechanism of the grains are analyzed via CPFE simulation. In the simulation, the large
plastic deformation of the micro multiple-grain model under dynamic compression is reproduced..
As shown in Fig. 8(a), two α-phase
grains (Gα1, Gα2) and β -phase grain (Gβ1) are chosen as
research
objects. The elements at the centroids of the grains are referred
to as Eα1, Eα2, and Eβ1, respectively. The effective stress
history
of the centroid element is extracted (see Fig. 8(b)). As shown in
the figure, these elements all undergo yielding, and the effective
stress decreases with continued deformation, indicating that stress
softening has occurred in these elements during the plastic deformation process. The softening
effect is strong in Eα1 and relatively
weak in Eα2 and Eβ1. When εT = 0.198, the stress associated
with
α1 decreases to 472 MPa, i.e., 33.5 % of the peak value (1407 MPa).
However, the stress associated with Eα2 and Eβ1 (1045 MPa) corresponds to
71.6 % and 66.0 % of the
respective peak stresses.
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Fig.8. Simulation results of the micro model: (a) schematic showing the positions
of grains Gα1, Gα2, Gβ1, and the centroid elements
Eα2,
Eα2 , Eβ1; (b) effective stress historyof
the centroid elements.
Multi-scale crystal plasticity finite element simulations of the microstructural evolution
and formation mechanism of adiabatic shear bands in dual-phase Ti20C alloy under complex
dynamic loading
Journal of Materials Science & Technology 59 (2020) 138–148
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文献3（2020）：Experimental study and crystal plasticity finite element simulations of
nano-indentation-induced lattice rotation and the underlying mechanism in TC6 single
α-grain（通过实验和晶体塑性有限元模拟研究TC6α相单晶中纳米压痕诱导的晶格旋转及其潜在机理）
In order to study the orientation evolution after nano-indentation, the lattice orientation is
seldom determined from the surface of the sample, so it is necessary to conduct an in-depth
study on the sample at the selected indentation, as shown in Fig.7. In this work, the sample is
examined via SEM (see Fig.7(a)) and the selected symmetry axis across the indentation, and the
facets as well as the inner-edges of the indentation are indicated. The slice shown in Fig.7(b)
is cut by FIB along the symmetry axis, and prepared for subsequent orientation analysis such as
TEM and PED.
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Fig.7. (a) Morphology of the indentation, (b) slice cut by FIB.
The mapping relationship between the lattice orientations and the IPF colors can be obtained from
the IPF map, where the dictionary of Euler angles with the corresponding RGB values is
established. A virtual IPF map can then be obtained based on the simulated orientation
information and, the lattice orientation is illustrated. A high-resolution lattice orientation
map was successfully obtained through PED in the slice beneath the indentation despite the large
residual stress caused by severe plastic deformation of the sample, and the experimentally
determined IPF map and simulated IPF map are compared in Fig.8.
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Fig.8. IPF map of the slice after indentation: (a) simulation results along X,
(b) experimental results along X, (c) experimental results along Z and diffraction patterns
obtained from
different subgrains, (d) distributions of rotation angles and rotation axes.
Experimental study and crystal plasticity finite element simulations of
nano-indentation-induced lattice rotation and the underlying mechanism in TC6 single α-grain
Materials Science & Engineering A 746 (2019) 322–331
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