# Identification of Hosford’s Yield Criterion Using Compression Tests

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## Abstract

**:**

## 1. Introduction

## 2. Methodology and Theory

#### 2.1. Methodology

#### 2.2. Theory

_{0}is the initial height of all specimens, R

_{0}is the initial radius of cylindrical specimens and the initial outer radius of ring specimens, r

_{0}is the initial inner radius of ring specimens, L

_{0}is the initial length of strips, and B is the width of strips. The value of B does not change in the course of deformation under plane strain conditions. The current height of all specimens is denoted as H. The dimensionless height is defined as

#### 2.2.1. Cylinder Compression

#### 2.2.2. Ring Compression

#### 2.2.3. Plane Strain Compression

## 3. Experimental Design

_{0}= 10 mm and H

_{0}= 20 mm, respectively. These specimens have small recesses on their end faces which retain the stearin during the compression. A pair of flat plates are used as a die. A schematic diagram of the specimens, a specimen image, and a schematic diagram of the process are presented in Figure 2.

_{0}= 12 mm, r

_{0}= 6 mm and H

_{0}= 8 mm, respectively. This nominal geometry is slightly modified to include recesses for retaining the stearin, similar to the Rastegaev specimens. A schematic diagram of the specimens, a specimen image, and a schematic diagram of the process are presented in Figure 3.

_{0}= 20 mm, H

_{0}= 20 mm, and B = 14 mm, respectively. The compression is performed using a plane strain die [31]. The width of the die channel is 14 mm (Figure 4). Similarly to the previous groups of specimens, the nominal geometry is slightly modified to retain the stearin during the compression. A drawing and photos of the billet are presented in Figure 5.

## 4. Experimental Results

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

h | dimensionless height |

k | ratio of the shear yield stress to the tensile yield stress |

n | constitutive parameter |

r | initial inner radius of ring specimens |

s | current cross-sectional area of the ring specimens |

t | time |

u_{r}, u_{z} | radial and axial velocities |

u_{x}, u_{z} | Cartesian velocity components |

w | plastic work |

B | width of strips |

F | force required to deform specimens |

H | current height of all specimens |

H_{0} | initial height of all specimens |

L | current length of strips |

L_{0} | initial length of strips |

R | current radius of cylindrical specimens |

R_{0} | initial radius of cylindrical specimens and initial outer radius of ring specimens |

V | velocity |

$\beta $ | dummy variable of integration |

${\xi}_{1}$, ${\xi}_{2}$, ${\xi}_{3}$ | principal strain rates |

${\xi}_{x}$,${\xi}_{z}$ | strain rate components in x and z directions |

${\sigma}_{1}$, ${\sigma}_{2}$, ${\sigma}_{3}$ | principal stresses |

${\sigma}_{Y}$ | yield stress in tension |

${\sigma}_{z}$ | axial stress |

${\tau}_{Y}$ | shear yield stress |

## Appendix A

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**Figure 2.**Schematic diagram of the specimens (

**a**), a specimen image (

**b**), and a schematic diagram of the process (

**c**).

**Figure 3.**Schematic diagram of the specimens (

**a**), a specimen image (

**b**), and a schematic diagram of the process (

**c**).

**Figure 4.**Die for plane strain compression [31].

**Figure 8.**Variation of σ

_{y}and τ

_{y}with the plastic work for cylinder and ring (

**a**), and prismatic specimens (

**b**).

Mass. % | C | Si | Mn | S | Cr | P | Al | Cu | Mo | Ni |
---|---|---|---|---|---|---|---|---|---|---|

C15E | 0.17 | 0.25 | 0.516 | 0.019 | 0.017 | 0.015 | 0.022 | 0.140 | 0.045 | 0.214 |

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**MDPI and ACS Style**

Alexandrov, S.; Vilotic, M.; Dacevic, N.; Li, Y.
Identification of Hosford’s Yield Criterion Using Compression Tests. *Metals* **2023**, *13*, 471.
https://doi.org/10.3390/met13030471

**AMA Style**

Alexandrov S, Vilotic M, Dacevic N, Li Y.
Identification of Hosford’s Yield Criterion Using Compression Tests. *Metals*. 2023; 13(3):471.
https://doi.org/10.3390/met13030471

**Chicago/Turabian Style**

Alexandrov, Sergei, Marko Vilotic, Nemanja Dacevic, and Yong Li.
2023. "Identification of Hosford’s Yield Criterion Using Compression Tests" *Metals* 13, no. 3: 471.
https://doi.org/10.3390/met13030471