# Path Dependency of Plastic Deformation in Crystals: Work Hardening, Crystallographic Rotation and Dislocation Structure Evolution

^{*}

## Abstract

**:**

## 1. Introduction

## 2. The Research Progress of Studies on Metallic Single Crystals under Tension

#### 2.1. The Effects of the Crystal Rotation of Metallic Single Crystals on Strain Hardening

#### 2.2. The Effects of Dislocation Evolution on Strain Hardening under Tension

## 3. The Work Hardening Mechanism of Single Crystals That were Deformed by Shear

#### 3.1. Different Methods for Shear

#### 3.2. Research on Metallic Single Crystals under Microshear

#### 3.3. Investigations on the Path Dependency of Single Crystals That Were Deformed by Shear

#### 3.4. The Effects of Dislocation Evolution on the Work Hardening of a Single Crystal That Was Deformed by Shear

## 4. Concluding Remarks and Prospective Future Research

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**The stress–strain curves of single crystal nickel with an initial orientation of [001] (black line) and [111] (gray line), as obtained by the MD simulations [37].

**Figure 2.**(

**a**) The stress–strain curves of single crystal aluminum with initial orientations of [001], [111], [112], [101], [102] and [213], as obtained by the MD simulations [23]; (

**b**) the corresponding experimental stress–strain curves, as obtained from tensile straining tests using single crystal copper [14].

**Figure 3.**The theoretical rotation behavior of an FCC single crystal specimen under uniaxial tension [27]. The tensile axis starts from ${\mathrm{F}}_{0}$, rotates to ${\mathrm{F}}_{1}$ following the pathway of ${\mathrm{F}}_{0}\to {\mathrm{F}}_{1}\to \left[\overline{1}01\right]$ and then turns to $\left[\overline{1}12\right]$ along the edge of the orientation triangle.

**Figure 4.**(

**a**) An SEM image of the [110]-orientated single crystal nickel after tensile deformation; (

**b**) an EBSD inverse pole figure map of the right half of the fractured sample in (

**a**,

**c**) for the pole figures of single crystal nickel after tensile deformation; (

**d**) the pole figures of the [110]-oriented sample before testing [47].

**Figure 5.**The dislocation structures of a 99.99% aluminum alloy that was deformed by tension: (

**a**) the TA orientations of 100 of the grains examined; (

**b**–

**d**) the TEM diagrams of grains with type I, II and III structures, respectively [62].

**Figure 6.**The in situ TEM observations of dislocation boundary evolution and the cross-slip of dislocation when single crystal aluminum was deformed to work hardening stage III [65], (

**a**–

**d**) frames at the time of 2 min 20 s, 5min 10 s, 5 min 35 s and 5 min 50 s, showing the depletion of the cell’s volume from dislocations into the cell’s boundary by cross slip of dislocation, respectively.

**Figure 7.**The different ways to directly apply simple shear that have been proposed in the literature: (

**a**) a specimen with a double shear zone [74]; (

**b**) a double-notch specimen in compression mode [70,71] (SZ is the zone of shear); (

**c**) a double-notch tensile–shear specimen [75]; (

**d**) a tilted double-notch tensile–shear specimen [76,77].

**Figure 8.**(

**a**) A schematic of the shear plane and the shear direction of single crystal magnesium; (

**b**) the geometry of single crystal magnesium under microshear [90].

**Figure 9.**The mechanical results of a specimen (

**a**) under (111)[01$\overline{1}$] shear loading (single slip orientation); (

**b**) (111)[$\overline{2}$11] shear loading (double slip orientation); (

**c**) (100)[010] shear loading (multiple slip orientation) [89].

**Figure 10.**The TEM observations of dislocation tangles after tensile deformation along the [011] orientation when deformed by a strain of (

**a**) 0.06 and (

**b**) 0.12 and the TEM observations after simple shear deformation at 0.3 shear strain for (

**c**) 45° and (

**d**) 90° shear [97].

**Table 1.**The qualitative characteristics of strain hardening that were observed in the MD simulations [22].

Initial Axis | Initial Slip Symmetry | Does the Crystal Rotate? | Hardening Response | End Axis |
---|---|---|---|---|

[001] | Eightfold; holds | No | Parabolic | [001] |

[111] | Sixfold; holds | No | Parabolic | [111] |

[101] | Fourfold; breaks | Yes | Three-stage | [112] |

[112] | Twofold; holds | No | Parabolic | [112] |

[212] | Twofold; holds | Yes | Three-stage | [111] |

[102] | Twofold; breaks | Yes | Three-stage | [112] |

[213] | No symmetry | Yes | Three-stage | [112] |

[8 5 13] | No symmetry | Yes | Three-stage | [112] |

Slip Systems | Shear Directions and Planes | |||
---|---|---|---|---|

$\left(111\right)$$\left[11\overline{2}\right]$ | $(1\overline{1}$1)[110] | (001)[110] | $(1\overline{1}$2)[110] | |

$\left(111\right)[1\overline{1}$0] | 0 | 0 | 0 | 0 |

$\left(111\right)[10\overline{1}$] | 0.866 | 0.167 | 0.289 | 0.236 |

$\left(111\right)[01\overline{1}$] | 0.866 | 0.167 | 0.289 | 0.236 |

$(\overline{1}$11)[110] | 0.192 | 0.333 | 0.577 | 0 |

$(\overline{1}$11)[101] | 0.096 | 0.167 | 0.289 | 0 |

$\left(\overline{1}11\right)$$[01\overline{1}$] | 0.324 | 0.167 | 0.289 | 0 |

$(1\overline{1}$1)[110] | 0.192 | 1 | 0.577 | 0.942 |

$\left(1\overline{1}1\right)$$[10\overline{1}$] | 0.324 | 0.5 | 0.289 | 0.471 |

$(1\overline{1}$1)[011] | 0.096 | 0.5 | 0.289 | 0.471 |

$\left(11\overline{1}\right)$$[1\overline{1}0]$ | 0 | 0 | 0 | 0 |

$(11\overline{1}$)[101] | 0.096 | 0.167 | 0.289 | 0.236 |

$(11\overline{1}$)[011] | 0.096 | 0.167 | 0.289 | 0.236 |

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## Share and Cite

**MDPI and ACS Style**

Zhang, Z.-W.; Li, Z.; Liu, Y.; Wang, J.-T.
Path Dependency of Plastic Deformation in Crystals: Work Hardening, Crystallographic Rotation and Dislocation Structure Evolution. *Crystals* **2022**, *12*, 999.
https://doi.org/10.3390/cryst12070999

**AMA Style**

Zhang Z-W, Li Z, Liu Y, Wang J-T.
Path Dependency of Plastic Deformation in Crystals: Work Hardening, Crystallographic Rotation and Dislocation Structure Evolution. *Crystals*. 2022; 12(7):999.
https://doi.org/10.3390/cryst12070999

**Chicago/Turabian Style**

Zhang, Zhen-Wei, Zheng Li, Ying Liu, and Jing-Tao Wang.
2022. "Path Dependency of Plastic Deformation in Crystals: Work Hardening, Crystallographic Rotation and Dislocation Structure Evolution" *Crystals* 12, no. 7: 999.
https://doi.org/10.3390/cryst12070999