# Heterogeneous Deformation and Microstructure of TWIP Steel under Damage and Fracture

Authors: Fuyuan Dong; Mingxu Zhang; Junfeng Hou
Journal: Journal of Nanomaterials
 (2022)

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## Abstract

Materials have always been a research hotspot in the chemical industry. With the continuous development of technology, the iteration of materials research has become faster and faster. Steel has strong toughness and tensile strength, and it is widely used in construction and other fields. However, one problem that cannot be avoided is the fracture of steel. The purpose of this paper is to analyze the damage and fracture of TWIP steel. In this paper, a microstructure characterization calculation method based on TWIP is proposed, which can effectively analyze the fracture surface, and for the performance of TWIP steel, this paper uses two different TWIP steels for comparative analysis. The results of this paper show that the HDI hardening rate of 22Mn0.6C TWIP steel is higher than that of 22Mn0.6C3Al TWIP steel.


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## Body

## 1. Introduction

Twin-induced plasticity steel, also known as TWIP, is a new second-generation high-strength transportation steel developed in China. TWIP steel has attracted extensive attention in the automotive and other industries due to its comprehensive mechanical properties such as high strength, high plasticity, and high strain hardening ability. TWIP steel is usually a relatively stable single-phase austenite structure under the condition of no external load at room temperature. When plastic deformation occurs under the applied load, due to the formation of deformation twins, it will extend without necking, resulting in relatively excellent mechanical properties.As one of the high-strength steels for automobiles, TWIP steel enjoys high strength, high plasticity, and high strain hardenability, as well as high energy absorption and excellent formability. The good comprehensive mechanical properties of TWIP steel show considerable development potential in the exploration of a new generation of automotive lightweight technology, which has attracted extensive attention in the steel and automotive industries. However, TWIP steel is prone to hydrogen-induced cracking, which is intergranular brittle fracture behavior under low stress. The occurrence of this dangerous brittle fracture makes the service safety of TWIP steel face an unprecedented challenge, which not only restricts its development but also becomes a bottleneck for its wide application. Therefore, it is necessary to conduct microscopic research on TWIP steel.The innovations of this paper are as follows: this paper takes 22Mn0.6C and 22Mn0.6C3Al TWIP steels as the research objects; based on the stress distribution relationship, through the loading-unloading-reloading tensile test, the evolution of the stress induced by heterogeneous deformation in the material is quantitatively investigated. The study found that the heterogeneous deformation-induced stress of the two steels increased with the increase of strain, and the contribution of deformation twins to the heterogeneous deformation-induced stress in TWIP steel was limited. Further microstructural analysis also confirmed that deformation twins hinder the geometrically necessary dislocation density more weakly than grain boundaries, so the heterogeneous deformation around the deformation twins is smaller.


## 2. Related Work

At present, universities and enterprises at home and abroad have developed various TWIP steels with different compositions and have conducted in-depth research on their processing technology, microstructure, and mechanical properties. The plastic deformation of TWIP steel involves a variety of deformation mechanisms (dislocation slip, deformation twinning, and martensitic transformation), and there are complex coupling effects between different mechanisms, so the source of its excellent mechanical properties has been controversial. Peng et al. believe that stacking fault dynamics is rarely covered by scholars. So they investigated new physical insights into the dynamics of stacking faults in TWIP steels [1]. In order to overcome the relative sheet formability problem of TWIP steel, Kim et al. used TWIP core three-layer construction steel plate to produce a mild steel sheath cladding. In order to optimize the design of layer structure materials, they theoretically and experimentally studied the strain hardening exponent n and strain rate sensitivity m of the laminate [2]. Mohammadzadeh studied the nanocrystals of TWIP steel. He conducted experiments on the structure of microscopic molecules. He believes that the current technology is sufficient to analyze the atomic level, so it is necessary to conduct microscopic steel fracture surface analysis. This is confirmed by the experimental results of TWIP microcrystals with a stress dependence [3]. Hu et al.’s research is more microscopic. They aim to use SEM to analyze the microstructure changes of TWIP steel. Their experimental results prove this, but their experiments lack the necessary data support; there are not many types of steel studied without self-preparation [4]. According to Peng and Zhang’s study, by controlling the volume fraction of the TWIP core area, the TWIP core steel sheet covers a wide range of yield and tensile strength and ductility levels required for automotive steel sheets, thus providing a new application for multifunctional automotive steel sheets [5]. Wang et al.’s experiments found that nanotwins were also observed in single-pass and double-pass samples as a result of secondary twinning [6]. Unfortunately, there is still no clear conclusion on the evaluation and method research of hydrogen-induced cracking of TWIP steel and on how to effectively improve the resistance to hydrogen-induced cracking and the fracture mechanism at home and abroad.


## 3. TWIP Steel and Fracture Nonuniform Deformation

### 3.1. Deformation Mechanism of TWIP Steel

#### 3.1.1. The Stacking Fault Energy of TWIP Steel

The calculation of stacking fault energy (SFE) is very important for the research of TWIP steel, and it can provide many references for the composition design, alloying element control, and service conditions (such as temperature) of TWIP steel [7, 8]. The calculation of stacking fault energy is mainly based on dislocation theory, and the slip plane and twin plane of austenitic steel with face-centered cubic structure are {1,1,1}. The total dislocation can be decomposed into two incomplete dislocations, the region between the two incomplete dislocations is called stacking fault, and the energy change caused by dislocation is called stacking fault energy. Stacking faults are formed by the expansion of incomplete dislocations under the action of shear stress, and the stacking fault energy is the work done to overcome the elastic interaction of dislocations. The stacking fault energy is an important factor affecting the deformation mechanism of austenitic steel, but there is no perfect and unified method for the calculation of stacking fault energy. The stacking fault energy results obtained by different methods may vary greatly. There are three commonly used calculation methods for stacking fault energy in TWIP steel alloy systems: based on the method of measuring incomplete dislocation distances by transmission electron microscopy (TEM), the method of measuring stacking fault probability based on X-ray diffraction (XRD), and the calculation of stacking fault energy based on thermodynamic models [9, 10].Mn is the most important alloying element in TWIP steel. Mn has two functions: (1) Mn expands the austenite phase region and increases the austenite stability. (2) Mn affects the stacking fault energy of alloy elements, but the relationship between Mn content and stacking fault energy is nonlinear, as shown in Table1. Thermodynamic models also confirmed this nonlinear relationship.Table 1
Effects of different Mn contents on stacking fault energy of austenitic steels.
Component partLayer fault energy (mJ/m2)Fe-16Mn26±3.1Fe-18Mn22±2.6Fe-20Mn18±2.2Fe-22Mn15±1Fe-22Mn-3Al-3Si15±3Fe-25Mn-3Al-3Si21±3Fe-28Mn-3Al-3Si38.8±5


### 3.2. Interface of Metal Materials

The interface of metal structural materials has a great influence on its performance, and the interface characteristics of materials usually play a dual role. For the improvement of material mechanical properties (such as fine grain strengthening), the interface generally plays a more positive role; however, from the perspective of material failure, the interface often becomes the initiation site of failure damage, but this cannot be generalized. For austenite-based metal materials, there are usually grain boundaries inside the material, and the types of grain boundaries are different. If a phase transformation occurs, there are also phase boundaries. In addition, from the perspective of material failure, the fracture surface (fracture) of the material is also an extremely important interface, which can be used as the direct evidence of failure [11–13].


#### 3.2.1. Fracture Surface (Fracture)

The fracture surface, which is often referred to as the fracture, is the matching surface formed after the material breaks during the test or service process and is one of the most important evidences for the failure analysis of engineering materials. The fracture records the irreversible deformation of the material before fracture under the coupling action of the applied load and the service environment and the whole process of crack initiation and propagation until the final fracture. At the same time, the fracture morphology is affected by factors such as stress state, environmental medium, and material properties [14–16]. Usually, the typical hydrogen embrittlement fracture is characterized by the intergranular fracture morphology, and the degree of convexity and concave of the fracture varies greatly with different hydrogen embrittlement susceptibilities. Therefore, to deeply understand the failure and fracture behavior of materials, it is necessary to quantitatively characterize the fracture. Through quantitative characterization, the correlation between the mechanical properties of materials and the failure mechanism can be directly established.


#### 3.2.2. Phase Interface

Usually, the interface existing between two solid phases with different crystal structures is called a phase boundary, such as the phase interface in duplex stainless steel. After the phase transformation, the interface between the new phase and the parent phase can also be formed; for example, theε/γ phase interface is formed after the ε martensitic transformation occurs in TWIP steel. The so-called different structures include materials with different qualities, either in the symmetry of the crystal structure or in the lattice parameters (such as the phase interface between α martensite and ferrite) or in the type of bonding, which will make the phase boundary have very complex structural characteristics [17]. If the two-phase interface is completely ordered and perfectly matched, the interface is called a coherent phase interface. If there are local dislocations at the interface through the relaxation process, the interface with relatively small elastic distortion in the local area is called a semicoherent phase interface. If the interface is completely disordered, it is an incoherent phase boundary.In general, phase interfaces with very strict coherent relationships are particularly rare. A typical coherent phase boundary is the interface between the face-centered cubic (FCC) phase and the dense hexagonal (HCP) phase after the cobalt phase transition. Since the two phases have the same close-packed properties, but have different stacking orders on both sides of the interface, it is a phase interface with lower energy. In the process of martensitic transformation or in the early stage of precipitation, some phase boundaries can also be regarded as coherent phase interfaces. At this time, the phase boundaries are phase interfaces with a certain orientation relationship, that is, a habitual relationship. Figure1 shows the geometry of a coherent interface.Figure 1
Geometry of the coherent interface.A semicoherent phase boundary is a particularly common type of phase boundary. Taking the interface formed by misfit dislocations in epitaxial growth as an example, for example, the two crystal structures have the same lattice, and the slight difference is only manifested in lattice parameters or the angle between lattices (<10%). If a coherent phase interface is to be formed, a large amount of distortion must be generated in the crystal, then by introducing misfit dislocations along the interface, the changes in lattice parameters or included angles can be coordinated, as shown in Figure2. This concentrates the distortion in the vicinity of the dislocation line, thereby relaxing the coherent elastic distortion of the crystal, which is consistent with the principle of minimum energy.Figure 2
Geometry of a semicoherent interface.


#### 3.2.3. Grain Boundary

Metal structural materials are usually polycrystalline, and the boundaries between different grains are grain boundaries. Compared with the coherent and incoherent phase interfaces, the lattice distortion of the grain interface is larger, so it has a greater impact on the mechanical behavior (fracture behavior, creep behavior, and corrosion behavior) of the material. Therefore, grain boundaries occupy a high enough position in the study of crystal defects [18, 19]. Generally, grain boundaries can be divided into small-angle grain boundaries and high-angle grain boundaries. The grain boundaries in materials such as TWIP steel are mainly composed of high-angle grain boundaries.The widely accepted model of high-angle grain boundary structure is the coincident position lattice model. If the two grains separated by the grain boundary are regarded as interpenetrating, some of their lattice points will be coincident, and these coincident lattice points will constitute a new lattice, that is, the coincidence position lattice (CSL). The coincident lattice has nothing to do with the crystal interface, but the orientation relationship of the crystal interface relative to the coincident lattice has a great influence on the interface structure. When the interface is the most densely packed surface of the coincident lattice, the interface has a relatively complete lattice matching degree, the mismatch is small, and the interface energy is also the lowest. Of course, it does not mean that any interface with an orientation relationship has a high density of coincident lattice points. Then if the reciprocal∑ of the coincidence lattice point density is used to represent the coincidence degree, for the face-centered cubic crystal, among the grain boundaries with the [110] direction as the rotation axis, the ones with higher coincidence degree have ∑3, ∑9, and ∑11 grain boundaries. These correspond to rotations of 70.5°, 39°, and 129.5° around the [110] axis, respectively. Figure 3 shows the geometry of the ∑3 grain boundary.Figure 3
Geometric structure of the grain boundary of lattice∑3 at the coincident position.


### 3.3. Microstructure Characterization Calculation Method

The phase content in the annealed samples was measured by XRD (Ultima IV), the target was a copper rake, the wavelength was 1.5406 A, the scanning speed was 20°/min, and the scanning range was 40°~100°. The normal tensile test is carried out at room temperature, and the gauge length of the sample is20×5×1.3 mm3. The size of the dynamic hydrogen charging slow strain rate tensile test specimen is the same as that of the normal tensile test specimen, and the tensile rates are 1×10−5S−1,5×10−6S−1,and1×10−6S−1, respectively. Using in situ electrochemical hydrogen charging, the hydrogen charging solution is 3%NaCl+3g/LNH4SCN, the hydrogen charging current density is 5 A/m2, and platinum wire is used as the counter electrode for electrochemical hydrogen charging. The test device is shown in Figure 4. All tensile tests were carried out on a microcomputer-controlled stress corrosion slow tensile testing machine model QB/LC-JL-159-2010. After dynamic hydrogen charging and stretching at a slow strain rate, the fracture morphology of the fractured specimens was observed with a field emission scanning electron microscope (electron microscope model) with a working voltage of 20 kV and a working distance of 12-13 mm. In this work, the loss of elongation is used to characterize the hydrogen embrittlement susceptibility; usually, the hydrogen embrittlement susceptibility (Elose) is calculated by the following formula:
(1)Elose=Ehair−EhHEhair×100%.Figure 4
Schematic diagram of the in situ electrochemical hydrogen charging slow strain rate stretching device.Among them,Ehair is the uniform elongation of stretching in air, and EhH is the uniform elongation of stretching under in-situ hydrogen charging.The fracture morphology under scanning electron microscope (SEM) usually enjoys a certain degree of undulating fracture surface, with obvious height difference (elevation) atμm scale. Obtaining accurate elevation data is extremely challenging using traditional surveying methods. SEM images are two-dimensional grayscale images, but the differences in different grayscales throughout the image provide an effective indirect method. White indicates the raised area, which represents the highest position (its value is 255). Gray indicates the position between them. Therefore, the gray value can be expressed by the following formula:
(2)Ax,y,G~Ax,y,H.Calculate the box counting dimension method and projection covering method, and preprocess and cut each original SEM image. The original SEM image is rectangular (768×1624 pixels), and six areas (upper left, upper middle, upper right, lower left, lower middle, and lower right) are cropped in such an image. For example, Figure 5 shows the upper right and lower left positions.Figure 5
Fracture diagram of digital image recognition technology processing.
(a)(b)(c)Based on the projection coverage algorithm, as shown in Figure6, it is proposed to calculate the fractal dimension Ds of a single surface area. The rough surface area Ak enclosed by the projected grids a,b,c,andd can be approximately expressed as
(3)Ak=S1+S2=p1p1−abp1−adp1−bd+p2p2−bcp2−cdp2−bd,p1=ab+ad+bd2,p2=bc+cd+bd2,ad=x1−x22+y1−y22+H1−H22,ATδ=∑NδAkδ.Figure 6
The schematic diagram of the projection coverage algorithm to calculate the fractal dimension of the fracture.After the above formula, it can be shown that the grid overlay projection algorithm is effective and can determine the fixed pixel value in the image, whereNδ is the total number of boxes. In this paper, the images are distributed in boxes of different sizes, which can be defined as a power law, and the formula is expressed as
(4)ATδ=∑NδAkδ~δ2−D.AT is the total rough area, and when δ⟶0, AT is close to the actual surface area.Generalized entropyHqδand generalized dimensionDqare defined as
(5)Hqδ=ln∑i=1Nhiq1−q,Dq=−limδ⟶0Hqδlnδ=τqq−1q=1,D1=hilnhilnδ.After calculation, we can find that there are many definitions that are not perfect, but as shown in Figure6, the multifractal spectrum can be expressed by the following formulas:
(6)fα=−limδ⟶0lnNαlnδ,αq=limδ⟶0lnhilnδ,where αq is the singularity exponent and fα is the multifractal spectral function. Nα represents the α integral value in α,α+dα. Through the legend transformation, fα and αq can be given as follows:
(7)αq=∂τq∂q,(8)fα=αqq−τq.According to the definition of functionτq, formulas (7) and (8) can be rewritten as
(9)αq=limδ⟶01lnδ∑iμilnhi,fα=limδ⟶01lnδ∑iμiμi.Among them,(10)μi=hiq∑ihiq.


## 3.1. Deformation Mechanism of TWIP Steel

### 3.1.1. The Stacking Fault Energy of TWIP Steel

The calculation of stacking fault energy (SFE) is very important for the research of TWIP steel, and it can provide many references for the composition design, alloying element control, and service conditions (such as temperature) of TWIP steel [7, 8]. The calculation of stacking fault energy is mainly based on dislocation theory, and the slip plane and twin plane of austenitic steel with face-centered cubic structure are {1,1,1}. The total dislocation can be decomposed into two incomplete dislocations, the region between the two incomplete dislocations is called stacking fault, and the energy change caused by dislocation is called stacking fault energy. Stacking faults are formed by the expansion of incomplete dislocations under the action of shear stress, and the stacking fault energy is the work done to overcome the elastic interaction of dislocations. The stacking fault energy is an important factor affecting the deformation mechanism of austenitic steel, but there is no perfect and unified method for the calculation of stacking fault energy. The stacking fault energy results obtained by different methods may vary greatly. There are three commonly used calculation methods for stacking fault energy in TWIP steel alloy systems: based on the method of measuring incomplete dislocation distances by transmission electron microscopy (TEM), the method of measuring stacking fault probability based on X-ray diffraction (XRD), and the calculation of stacking fault energy based on thermodynamic models [9, 10].Mn is the most important alloying element in TWIP steel. Mn has two functions: (1) Mn expands the austenite phase region and increases the austenite stability. (2) Mn affects the stacking fault energy of alloy elements, but the relationship between Mn content and stacking fault energy is nonlinear, as shown in Table1. Thermodynamic models also confirmed this nonlinear relationship.Table 1
Effects of different Mn contents on stacking fault energy of austenitic steels.
Component partLayer fault energy (mJ/m2)Fe-16Mn26±3.1Fe-18Mn22±2.6Fe-20Mn18±2.2Fe-22Mn15±1Fe-22Mn-3Al-3Si15±3Fe-25Mn-3Al-3Si21±3Fe-28Mn-3Al-3Si38.8±5


## 3.1.1. The Stacking Fault Energy of TWIP Steel

The calculation of stacking fault energy (SFE) is very important for the research of TWIP steel, and it can provide many references for the composition design, alloying element control, and service conditions (such as temperature) of TWIP steel [7, 8]. The calculation of stacking fault energy is mainly based on dislocation theory, and the slip plane and twin plane of austenitic steel with face-centered cubic structure are {1,1,1}. The total dislocation can be decomposed into two incomplete dislocations, the region between the two incomplete dislocations is called stacking fault, and the energy change caused by dislocation is called stacking fault energy. Stacking faults are formed by the expansion of incomplete dislocations under the action of shear stress, and the stacking fault energy is the work done to overcome the elastic interaction of dislocations. The stacking fault energy is an important factor affecting the deformation mechanism of austenitic steel, but there is no perfect and unified method for the calculation of stacking fault energy. The stacking fault energy results obtained by different methods may vary greatly. There are three commonly used calculation methods for stacking fault energy in TWIP steel alloy systems: based on the method of measuring incomplete dislocation distances by transmission electron microscopy (TEM), the method of measuring stacking fault probability based on X-ray diffraction (XRD), and the calculation of stacking fault energy based on thermodynamic models [9, 10].Mn is the most important alloying element in TWIP steel. Mn has two functions: (1) Mn expands the austenite phase region and increases the austenite stability. (2) Mn affects the stacking fault energy of alloy elements, but the relationship between Mn content and stacking fault energy is nonlinear, as shown in Table1. Thermodynamic models also confirmed this nonlinear relationship.Table 1
Effects of different Mn contents on stacking fault energy of austenitic steels.
Component partLayer fault energy (mJ/m2)Fe-16Mn26±3.1Fe-18Mn22±2.6Fe-20Mn18±2.2Fe-22Mn15±1Fe-22Mn-3Al-3Si15±3Fe-25Mn-3Al-3Si21±3Fe-28Mn-3Al-3Si38.8±5


## 3.2. Interface of Metal Materials

The interface of metal structural materials has a great influence on its performance, and the interface characteristics of materials usually play a dual role. For the improvement of material mechanical properties (such as fine grain strengthening), the interface generally plays a more positive role; however, from the perspective of material failure, the interface often becomes the initiation site of failure damage, but this cannot be generalized. For austenite-based metal materials, there are usually grain boundaries inside the material, and the types of grain boundaries are different. If a phase transformation occurs, there are also phase boundaries. In addition, from the perspective of material failure, the fracture surface (fracture) of the material is also an extremely important interface, which can be used as the direct evidence of failure [11–13].


### 3.2.1. Fracture Surface (Fracture)

The fracture surface, which is often referred to as the fracture, is the matching surface formed after the material breaks during the test or service process and is one of the most important evidences for the failure analysis of engineering materials. The fracture records the irreversible deformation of the material before fracture under the coupling action of the applied load and the service environment and the whole process of crack initiation and propagation until the final fracture. At the same time, the fracture morphology is affected by factors such as stress state, environmental medium, and material properties [14–16]. Usually, the typical hydrogen embrittlement fracture is characterized by the intergranular fracture morphology, and the degree of convexity and concave of the fracture varies greatly with different hydrogen embrittlement susceptibilities. Therefore, to deeply understand the failure and fracture behavior of materials, it is necessary to quantitatively characterize the fracture. Through quantitative characterization, the correlation between the mechanical properties of materials and the failure mechanism can be directly established.


### 3.2.2. Phase Interface

Usually, the interface existing between two solid phases with different crystal structures is called a phase boundary, such as the phase interface in duplex stainless steel. After the phase transformation, the interface between the new phase and the parent phase can also be formed; for example, theε/γ phase interface is formed after the ε martensitic transformation occurs in TWIP steel. The so-called different structures include materials with different qualities, either in the symmetry of the crystal structure or in the lattice parameters (such as the phase interface between α martensite and ferrite) or in the type of bonding, which will make the phase boundary have very complex structural characteristics [17]. If the two-phase interface is completely ordered and perfectly matched, the interface is called a coherent phase interface. If there are local dislocations at the interface through the relaxation process, the interface with relatively small elastic distortion in the local area is called a semicoherent phase interface. If the interface is completely disordered, it is an incoherent phase boundary.In general, phase interfaces with very strict coherent relationships are particularly rare. A typical coherent phase boundary is the interface between the face-centered cubic (FCC) phase and the dense hexagonal (HCP) phase after the cobalt phase transition. Since the two phases have the same close-packed properties, but have different stacking orders on both sides of the interface, it is a phase interface with lower energy. In the process of martensitic transformation or in the early stage of precipitation, some phase boundaries can also be regarded as coherent phase interfaces. At this time, the phase boundaries are phase interfaces with a certain orientation relationship, that is, a habitual relationship. Figure1 shows the geometry of a coherent interface.Figure 1
Geometry of the coherent interface.A semicoherent phase boundary is a particularly common type of phase boundary. Taking the interface formed by misfit dislocations in epitaxial growth as an example, for example, the two crystal structures have the same lattice, and the slight difference is only manifested in lattice parameters or the angle between lattices (<10%). If a coherent phase interface is to be formed, a large amount of distortion must be generated in the crystal, then by introducing misfit dislocations along the interface, the changes in lattice parameters or included angles can be coordinated, as shown in Figure2. This concentrates the distortion in the vicinity of the dislocation line, thereby relaxing the coherent elastic distortion of the crystal, which is consistent with the principle of minimum energy.Figure 2
Geometry of a semicoherent interface.


### 3.2.3. Grain Boundary

Metal structural materials are usually polycrystalline, and the boundaries between different grains are grain boundaries. Compared with the coherent and incoherent phase interfaces, the lattice distortion of the grain interface is larger, so it has a greater impact on the mechanical behavior (fracture behavior, creep behavior, and corrosion behavior) of the material. Therefore, grain boundaries occupy a high enough position in the study of crystal defects [18, 19]. Generally, grain boundaries can be divided into small-angle grain boundaries and high-angle grain boundaries. The grain boundaries in materials such as TWIP steel are mainly composed of high-angle grain boundaries.The widely accepted model of high-angle grain boundary structure is the coincident position lattice model. If the two grains separated by the grain boundary are regarded as interpenetrating, some of their lattice points will be coincident, and these coincident lattice points will constitute a new lattice, that is, the coincidence position lattice (CSL). The coincident lattice has nothing to do with the crystal interface, but the orientation relationship of the crystal interface relative to the coincident lattice has a great influence on the interface structure. When the interface is the most densely packed surface of the coincident lattice, the interface has a relatively complete lattice matching degree, the mismatch is small, and the interface energy is also the lowest. Of course, it does not mean that any interface with an orientation relationship has a high density of coincident lattice points. Then if the reciprocal∑ of the coincidence lattice point density is used to represent the coincidence degree, for the face-centered cubic crystal, among the grain boundaries with the [110] direction as the rotation axis, the ones with higher coincidence degree have ∑3, ∑9, and ∑11 grain boundaries. These correspond to rotations of 70.5°, 39°, and 129.5° around the [110] axis, respectively. Figure 3 shows the geometry of the ∑3 grain boundary.Figure 3
Geometric structure of the grain boundary of lattice∑3 at the coincident position.


## 3.2.1. Fracture Surface (Fracture)

The fracture surface, which is often referred to as the fracture, is the matching surface formed after the material breaks during the test or service process and is one of the most important evidences for the failure analysis of engineering materials. The fracture records the irreversible deformation of the material before fracture under the coupling action of the applied load and the service environment and the whole process of crack initiation and propagation until the final fracture. At the same time, the fracture morphology is affected by factors such as stress state, environmental medium, and material properties [14–16]. Usually, the typical hydrogen embrittlement fracture is characterized by the intergranular fracture morphology, and the degree of convexity and concave of the fracture varies greatly with different hydrogen embrittlement susceptibilities. Therefore, to deeply understand the failure and fracture behavior of materials, it is necessary to quantitatively characterize the fracture. Through quantitative characterization, the correlation between the mechanical properties of materials and the failure mechanism can be directly established.


## 3.2.2. Phase Interface

Usually, the interface existing between two solid phases with different crystal structures is called a phase boundary, such as the phase interface in duplex stainless steel. After the phase transformation, the interface between the new phase and the parent phase can also be formed; for example, theε/γ phase interface is formed after the ε martensitic transformation occurs in TWIP steel. The so-called different structures include materials with different qualities, either in the symmetry of the crystal structure or in the lattice parameters (such as the phase interface between α martensite and ferrite) or in the type of bonding, which will make the phase boundary have very complex structural characteristics [17]. If the two-phase interface is completely ordered and perfectly matched, the interface is called a coherent phase interface. If there are local dislocations at the interface through the relaxation process, the interface with relatively small elastic distortion in the local area is called a semicoherent phase interface. If the interface is completely disordered, it is an incoherent phase boundary.In general, phase interfaces with very strict coherent relationships are particularly rare. A typical coherent phase boundary is the interface between the face-centered cubic (FCC) phase and the dense hexagonal (HCP) phase after the cobalt phase transition. Since the two phases have the same close-packed properties, but have different stacking orders on both sides of the interface, it is a phase interface with lower energy. In the process of martensitic transformation or in the early stage of precipitation, some phase boundaries can also be regarded as coherent phase interfaces. At this time, the phase boundaries are phase interfaces with a certain orientation relationship, that is, a habitual relationship. Figure1 shows the geometry of a coherent interface.Figure 1
Geometry of the coherent interface.A semicoherent phase boundary is a particularly common type of phase boundary. Taking the interface formed by misfit dislocations in epitaxial growth as an example, for example, the two crystal structures have the same lattice, and the slight difference is only manifested in lattice parameters or the angle between lattices (<10%). If a coherent phase interface is to be formed, a large amount of distortion must be generated in the crystal, then by introducing misfit dislocations along the interface, the changes in lattice parameters or included angles can be coordinated, as shown in Figure2. This concentrates the distortion in the vicinity of the dislocation line, thereby relaxing the coherent elastic distortion of the crystal, which is consistent with the principle of minimum energy.Figure 2
Geometry of a semicoherent interface.


## 3.2.3. Grain Boundary

Metal structural materials are usually polycrystalline, and the boundaries between different grains are grain boundaries. Compared with the coherent and incoherent phase interfaces, the lattice distortion of the grain interface is larger, so it has a greater impact on the mechanical behavior (fracture behavior, creep behavior, and corrosion behavior) of the material. Therefore, grain boundaries occupy a high enough position in the study of crystal defects [18, 19]. Generally, grain boundaries can be divided into small-angle grain boundaries and high-angle grain boundaries. The grain boundaries in materials such as TWIP steel are mainly composed of high-angle grain boundaries.The widely accepted model of high-angle grain boundary structure is the coincident position lattice model. If the two grains separated by the grain boundary are regarded as interpenetrating, some of their lattice points will be coincident, and these coincident lattice points will constitute a new lattice, that is, the coincidence position lattice (CSL). The coincident lattice has nothing to do with the crystal interface, but the orientation relationship of the crystal interface relative to the coincident lattice has a great influence on the interface structure. When the interface is the most densely packed surface of the coincident lattice, the interface has a relatively complete lattice matching degree, the mismatch is small, and the interface energy is also the lowest. Of course, it does not mean that any interface with an orientation relationship has a high density of coincident lattice points. Then if the reciprocal∑ of the coincidence lattice point density is used to represent the coincidence degree, for the face-centered cubic crystal, among the grain boundaries with the [110] direction as the rotation axis, the ones with higher coincidence degree have ∑3, ∑9, and ∑11 grain boundaries. These correspond to rotations of 70.5°, 39°, and 129.5° around the [110] axis, respectively. Figure 3 shows the geometry of the ∑3 grain boundary.Figure 3
Geometric structure of the grain boundary of lattice∑3 at the coincident position.


## 3.3. Microstructure Characterization Calculation Method

The phase content in the annealed samples was measured by XRD (Ultima IV), the target was a copper rake, the wavelength was 1.5406 A, the scanning speed was 20°/min, and the scanning range was 40°~100°. The normal tensile test is carried out at room temperature, and the gauge length of the sample is20×5×1.3 mm3. The size of the dynamic hydrogen charging slow strain rate tensile test specimen is the same as that of the normal tensile test specimen, and the tensile rates are 1×10−5S−1,5×10−6S−1,and1×10−6S−1, respectively. Using in situ electrochemical hydrogen charging, the hydrogen charging solution is 3%NaCl+3g/LNH4SCN, the hydrogen charging current density is 5 A/m2, and platinum wire is used as the counter electrode for electrochemical hydrogen charging. The test device is shown in Figure 4. All tensile tests were carried out on a microcomputer-controlled stress corrosion slow tensile testing machine model QB/LC-JL-159-2010. After dynamic hydrogen charging and stretching at a slow strain rate, the fracture morphology of the fractured specimens was observed with a field emission scanning electron microscope (electron microscope model) with a working voltage of 20 kV and a working distance of 12-13 mm. In this work, the loss of elongation is used to characterize the hydrogen embrittlement susceptibility; usually, the hydrogen embrittlement susceptibility (Elose) is calculated by the following formula:
(1)Elose=Ehair−EhHEhair×100%.Figure 4
Schematic diagram of the in situ electrochemical hydrogen charging slow strain rate stretching device.Among them,Ehair is the uniform elongation of stretching in air, and EhH is the uniform elongation of stretching under in-situ hydrogen charging.The fracture morphology under scanning electron microscope (SEM) usually enjoys a certain degree of undulating fracture surface, with obvious height difference (elevation) atμm scale. Obtaining accurate elevation data is extremely challenging using traditional surveying methods. SEM images are two-dimensional grayscale images, but the differences in different grayscales throughout the image provide an effective indirect method. White indicates the raised area, which represents the highest position (its value is 255). Gray indicates the position between them. Therefore, the gray value can be expressed by the following formula:
(2)Ax,y,G~Ax,y,H.Calculate the box counting dimension method and projection covering method, and preprocess and cut each original SEM image. The original SEM image is rectangular (768×1624 pixels), and six areas (upper left, upper middle, upper right, lower left, lower middle, and lower right) are cropped in such an image. For example, Figure 5 shows the upper right and lower left positions.Figure 5
Fracture diagram of digital image recognition technology processing.
(a)(b)(c)Based on the projection coverage algorithm, as shown in Figure6, it is proposed to calculate the fractal dimension Ds of a single surface area. The rough surface area Ak enclosed by the projected grids a,b,c,andd can be approximately expressed as
(3)Ak=S1+S2=p1p1−abp1−adp1−bd+p2p2−bcp2−cdp2−bd,p1=ab+ad+bd2,p2=bc+cd+bd2,ad=x1−x22+y1−y22+H1−H22,ATδ=∑NδAkδ.Figure 6
The schematic diagram of the projection coverage algorithm to calculate the fractal dimension of the fracture.After the above formula, it can be shown that the grid overlay projection algorithm is effective and can determine the fixed pixel value in the image, whereNδ is the total number of boxes. In this paper, the images are distributed in boxes of different sizes, which can be defined as a power law, and the formula is expressed as
(4)ATδ=∑NδAkδ~δ2−D.AT is the total rough area, and when δ⟶0, AT is close to the actual surface area.Generalized entropyHqδand generalized dimensionDqare defined as
(5)Hqδ=ln∑i=1Nhiq1−q,Dq=−limδ⟶0Hqδlnδ=τqq−1q=1,D1=hilnhilnδ.After calculation, we can find that there are many definitions that are not perfect, but as shown in Figure6, the multifractal spectrum can be expressed by the following formulas:
(6)fα=−limδ⟶0lnNαlnδ,αq=limδ⟶0lnhilnδ,where αq is the singularity exponent and fα is the multifractal spectral function. Nα represents the α integral value in α,α+dα. Through the legend transformation, fα and αq can be given as follows:
(7)αq=∂τq∂q,(8)fα=αqq−τq.According to the definition of functionτq, formulas (7) and (8) can be rewritten as
(9)αq=limδ⟶01lnδ∑iμilnhi,fα=limδ⟶01lnδ∑iμiμi.Among them,(10)μi=hiq∑ihiq.


## 4. Deformation and Microscopic Analysis of TWIP Steel under Damage Fracture

### 4.1. Thermomechanical Treatment Process

The 22Mn0.6C and 22Mn0.6C3Al TWIP steels used in the experiment were cast into ingots by vacuum smelting, and the weight of the ingots was 75 kg. Subsequently, the ingots were cut with risers, and samples were taken on the ingots, and the chemical composition of the steel was measured by emission spectroscopy as shown in Table2.Table 2
Element content (wt.%).
Steel22Mn0.6C22Mn0.6C3AlMn21.2621.45C0.550.58Al0.0032.86Si0.110.13S0.0060.005P0.0080.010FeMarginMarginThe chemical compositions of the TWIP steels used in this chapter are shown in Table2. For convenience, Fe-22Mn-0.6C and Fe-22Mn-0.6C-3Al are abbreviated as 22Mn0.6C and 22Mn0.6C3Al, respectively, in the remainder of this chapter. Figure 7 shows the schematic diagram of the thermodynamic processing of the two TWIP steels: first, the ingots of the two steels were homogenized and heat-treated in an argon atmosphere at 1423 K for 2 h. Subsequently, it is hot rolled to 3 mm thick plate in the temperature range of 1373 K to 1223 K. Then, using a twin-roll mill, the hot-rolled sheet was cold-rolled in multiple passes into a 1.5 mm sheet. Finally, the 22Mn0.6C and 22Mn0.6C3Al steels were recrystallized and annealed at 1123 k and 1173 k for 0.5 h, respectively, and then quickly quenched in water after being taken out to obtain initial materials with uniform equiaxed grains. Tensile specimens were taken from the initial sheet by wire cutting, with the long axis of the specimen parallel to the rolling direction of the sheet.Figure 7
Schematic diagram of thermodynamic processing of TWIP steel.In this paper, the loading-unloading-reloading method is used to measure HDI stress, and its principle is shown in Figure8. In the measurement method, first, the hysteresis loop is obtained through the loading-unloading-reloading process. Then, the unloading yield stress (σu) and the reloading yield stress (σr) are measured on the unloading and reloading curves, respectively, and finally the HDI stress (σHDI) is obtained:
(11)σHDI=σu+σr2.Figure 8
Load-unload-reload schematic.In addition, the effective stress (σeff) can also be obtained by subtracting the HDI stress from the total flow stress.


### 4.2. Initial Microstructure

Figure9 shows the frequency distribution of grain sizes of two TWIP steels and their log-normal distribution fitting curves. The average grain sizes obtained by statistics are 4.9 μm and 4.3 μm, respectively. The approximately equal grain size helps to elucidate the role of deformation twinning in heterogeneous deformation-induced strengthening.Figure 9
Grain size distribution.


### 4.3. Variation of HDI Stress

Figure10 shows the variation of HDI stress with true strain in both steels. Repeated load-unload-reload tensile tests were performed on two steels at strain levels of 0.01, 0.02, 0.03, 0.04, 0.06, 0.09, 0.11, 0.14, 0.17, 0.19, 0.21, 0.26, 0.31, and 0.34, as shown in Figure 10(a). Figure 10(b) shows the load-unload-reload curve at 0.14 true strain, and it can be seen that both steels have significant hysteresis loops. Figure 10(c) shows that the HDI stress increases with increasing strain, and the HDI stress of the two steels is approximately equal until 0.11 true strain. Thereafter, as the strain increases, the gap between HDI stresses becomes larger, and at 0.34 true strain, the HDI stress of 22Mn0.6C steel is 104 MPa larger than that of 22Mn0.6C3Al steel. Error bars for HDI stress values were obtained from three replicate experiments. The HDI stress values of the two steels were fitted using the power exponential relationship σb=σb0+Kεn, as shown in Figure 10(c). In the fitted curve, σb0, K, ε, and n represent the intrinsic strength, material strengthening coefficient, true strain, and strain hardening exponent, respectively. It can be seen that the empirical formula can fit the change of HDI stress value well, but its hidden physical meaning still needs to be further explored in the future. In 22Mn0.6C TWIP steel, σb0, K, and n are 149.8 MPa, 1250.2 MPa, and 0.875, respectively; in 22Mn0.6C3A1 TWIP steel, σb0, K, and n are 165.7 MPa, 877.0 MPa, and 0.733, respectively.Figure 10
HDI stress of TWIP steel specimen. Among them: (a) loading-unloading-reloading tensile curve; (b) is an enlarged view of the area marked by the dotted box in (a); (c) the relationship between HDI stress and strain.
(a)(b)(c)It can be seen from the stress-strain curve that the plastic loss of the three samples at a strain rate of1∗10−6S−1 is greater than that at a strain rate greater than 1∗10−5S−1. This indicates that the plastic loss increases with decreasing strain rate. At the strain rate of 1∗10−5S−1, the plastic loss of the three specimens (T0⟶T10⟶T30) gradually increased. However, at the strain rate of 1∗10−6S−1, the hydrogen embrittlement susceptibility of T0 specimen is greater than that of T10 and T30. The calculated results of the brittle sensitivity are shown in Table 3. The fitting results show that the HDI hardening rate of 22Mn0.6C TWIP steel is higher than that of 22Mn0.6C3Al TWIP steel.Table 3
Brittleness sensitivity (Eloss).
Sample1∗10−5S−11∗10−6S−1T064±1.5294±0.32T1074±0.6783±0.72T3078±0.7493±1.38


## 4.1. Thermomechanical Treatment Process

The 22Mn0.6C and 22Mn0.6C3Al TWIP steels used in the experiment were cast into ingots by vacuum smelting, and the weight of the ingots was 75 kg. Subsequently, the ingots were cut with risers, and samples were taken on the ingots, and the chemical composition of the steel was measured by emission spectroscopy as shown in Table2.Table 2
Element content (wt.%).
Steel22Mn0.6C22Mn0.6C3AlMn21.2621.45C0.550.58Al0.0032.86Si0.110.13S0.0060.005P0.0080.010FeMarginMarginThe chemical compositions of the TWIP steels used in this chapter are shown in Table2. For convenience, Fe-22Mn-0.6C and Fe-22Mn-0.6C-3Al are abbreviated as 22Mn0.6C and 22Mn0.6C3Al, respectively, in the remainder of this chapter. Figure 7 shows the schematic diagram of the thermodynamic processing of the two TWIP steels: first, the ingots of the two steels were homogenized and heat-treated in an argon atmosphere at 1423 K for 2 h. Subsequently, it is hot rolled to 3 mm thick plate in the temperature range of 1373 K to 1223 K. Then, using a twin-roll mill, the hot-rolled sheet was cold-rolled in multiple passes into a 1.5 mm sheet. Finally, the 22Mn0.6C and 22Mn0.6C3Al steels were recrystallized and annealed at 1123 k and 1173 k for 0.5 h, respectively, and then quickly quenched in water after being taken out to obtain initial materials with uniform equiaxed grains. Tensile specimens were taken from the initial sheet by wire cutting, with the long axis of the specimen parallel to the rolling direction of the sheet.Figure 7
Schematic diagram of thermodynamic processing of TWIP steel.In this paper, the loading-unloading-reloading method is used to measure HDI stress, and its principle is shown in Figure8. In the measurement method, first, the hysteresis loop is obtained through the loading-unloading-reloading process. Then, the unloading yield stress (σu) and the reloading yield stress (σr) are measured on the unloading and reloading curves, respectively, and finally the HDI stress (σHDI) is obtained:
(11)σHDI=σu+σr2.Figure 8
Load-unload-reload schematic.In addition, the effective stress (σeff) can also be obtained by subtracting the HDI stress from the total flow stress.


## 4.2. Initial Microstructure

Figure9 shows the frequency distribution of grain sizes of two TWIP steels and their log-normal distribution fitting curves. The average grain sizes obtained by statistics are 4.9 μm and 4.3 μm, respectively. The approximately equal grain size helps to elucidate the role of deformation twinning in heterogeneous deformation-induced strengthening.Figure 9
Grain size distribution.


## 4.3. Variation of HDI Stress

Figure10 shows the variation of HDI stress with true strain in both steels. Repeated load-unload-reload tensile tests were performed on two steels at strain levels of 0.01, 0.02, 0.03, 0.04, 0.06, 0.09, 0.11, 0.14, 0.17, 0.19, 0.21, 0.26, 0.31, and 0.34, as shown in Figure 10(a). Figure 10(b) shows the load-unload-reload curve at 0.14 true strain, and it can be seen that both steels have significant hysteresis loops. Figure 10(c) shows that the HDI stress increases with increasing strain, and the HDI stress of the two steels is approximately equal until 0.11 true strain. Thereafter, as the strain increases, the gap between HDI stresses becomes larger, and at 0.34 true strain, the HDI stress of 22Mn0.6C steel is 104 MPa larger than that of 22Mn0.6C3Al steel. Error bars for HDI stress values were obtained from three replicate experiments. The HDI stress values of the two steels were fitted using the power exponential relationship σb=σb0+Kεn, as shown in Figure 10(c). In the fitted curve, σb0, K, ε, and n represent the intrinsic strength, material strengthening coefficient, true strain, and strain hardening exponent, respectively. It can be seen that the empirical formula can fit the change of HDI stress value well, but its hidden physical meaning still needs to be further explored in the future. In 22Mn0.6C TWIP steel, σb0, K, and n are 149.8 MPa, 1250.2 MPa, and 0.875, respectively; in 22Mn0.6C3A1 TWIP steel, σb0, K, and n are 165.7 MPa, 877.0 MPa, and 0.733, respectively.Figure 10
HDI stress of TWIP steel specimen. Among them: (a) loading-unloading-reloading tensile curve; (b) is an enlarged view of the area marked by the dotted box in (a); (c) the relationship between HDI stress and strain.
(a)(b)(c)It can be seen from the stress-strain curve that the plastic loss of the three samples at a strain rate of1∗10−6S−1 is greater than that at a strain rate greater than 1∗10−5S−1. This indicates that the plastic loss increases with decreasing strain rate. At the strain rate of 1∗10−5S−1, the plastic loss of the three specimens (T0⟶T10⟶T30) gradually increased. However, at the strain rate of 1∗10−6S−1, the hydrogen embrittlement susceptibility of T0 specimen is greater than that of T10 and T30. The calculated results of the brittle sensitivity are shown in Table 3. The fitting results show that the HDI hardening rate of 22Mn0.6C TWIP steel is higher than that of 22Mn0.6C3Al TWIP steel.Table 3
Brittleness sensitivity (Eloss).
Sample1∗10−5S−11∗10−6S−1T064±1.5294±0.32T1074±0.6783±0.72T3078±0.7493±1.38


## 5. Conclusions

Gradient substructure 22Mn0.6C TWIP steel was prepared by a simple pretorsion method, which combines high yield strength, tensile strength, and plasticity. Gradient substructure samples were found to have greater heterogeneous plastic deformation at the grain scale and at the specimen scale, which resulted in higher heterogeneous deformation-induced strengthening and hardening, compared to the homogeneous coarse-grained structure. More dislocations and deformation twins are formed inside the gradient substructure samples, which hinder the short-range motion of mobile dislocations, resulting in higher effective stress strengthening and hardening. Therefore, the excellent mechanical properties of the graded substructure TWIP steel originate from the synergistic contribution of its higher heterogeneous deformation-induced stress and short-range effective stress. The gradient substructure design strategy is a reasonable method to prepare high strength and high plasticity TWIP steel.



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*Source: 3650644-2022-05-20.xml*