# Integrated Numerical-Experimental Assessment of the Effect of the AZ31B Anisotropic Behaviour in Extended-Surface Treatments by Laser Shock Processing

^{*}

## Abstract

**:**

## 1. Introduction

^{−7}·s

^{−1}) [16].

^{−1}, in which the effect of the specimen temperature in results is also documented [19,20]. Jäger et al. [21] developed quasi static tensile behaviour experiments of hot rolled Mg AZ31 alloys up to 673 K. Biaxial tests were performed at room temperature to study the mechanical formability and elongation to failure [22]. Most of the researchers oriented these studies to understand the high-complexity physics involved in the different slip modes presented, twinning and detwinning in alternative paths, dislocations reorientation and the influence of grain size and texture in the mechanical properties in different loading orientations.

## 2. Materials and Methods

#### 2.1. Material Description

#### 2.2. Methodology

#### 2.2.1. Anisotropic Hardening Formulation based on Hill’s Yield Surface to Model Alternative Loading Paths Presented in LSP

#### 2.2.2. Model Calibration Based on the Anisotropic Stress-Strain Curves of Mg AZ31B Alloy

#### 2.2.3. Experimental Determination of the Spatial Pressure Pulse Profiles

^{2}. The material’s reflectivity was calculated with the aid of Wu and Shin model [41,42], which is set as an input parameter to the HELIOS code. The in-time pressure profile is represented in Figure 6.

## 3. Results

#### 3.1. Experimental Characterization of the Residual Stresses for Different Input Parameters

^{2}(Figure 9 shows a schematic representation):

^{2}, and an Equivalent Local Overlapping Factor, ELOF [44], of 4. The peening direction (PD) is set coincident with the transverse direction, TD.

^{2}, and an Equivalent Local Overlapping Factor, ELOF, of 4. The peening direction (PD) is set coincident with the rolling direction, RD.

^{2}, and an Equivalent Local Overlapping Factor, ELOF, of 7. The peening direction (PD) is set coincident with the transverse direction, TD.

^{2}, and an Equivalent Local Overlapping Factor, ELOF, of 7. The peening direction (PD) is set coincident with the rolling direction, RD.

#### 3.2. Realistic Modelling Results for Extended Surface High-Coverage LSP Treatments

^{2}up to 1 mm depth, which represents a similar volume than the one removed by means of the hole drilling method. Figure 12, Figure 13, Figure 14 and Figure 15 show a comparison between analytical predictions and experimental results for strategies (1), (2), (3) and (4) respectively. Table 4 shows a comparison between experimental results and the analytical predictions obtained by means of the anisotropic model. ${\left({d}_{max}\right)}_{i}$ is the depth at which the maximum peak compressive residual stress is presented. $min{\left({S}_{min}\right)}_{i}$ represents the peak compressive residual stress. $i=isot$ and $i=anisot$ corresponds to the analytical predictions of isotropic and anisotropic models respectively, and $i=exp$ to the experimental results.

^{2}(strategies (3) and (4)), experimental evidence shows that the residual stresses tend to saturate. Reasonably good agreement is obtained by means of the anisotropic model for strategy (3) while an overestimation of the compressive residual stresses is predicted for configuration (4). This is not surprising since the model is conceived for low-density treatments, which are the most suitable ones for the present alloy.

## 4. Discussion

## 5. Conclusions

^{2}). This effect cannot be computed properly by isotropic models. Therefore, the anisotropic hardening model is required for this purpose.

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 1.**Stress–strain curves in rolled Mg AZ31B alloy at different strain rates adapted from [19].

**Figure 9.**(

**a**) Schematic representation of treatments (1) and (3) (PD = TD); (

**b**) Schematic representation of treatments (2) and (4) (PD = RD).

**Figure 10.**(

**a**) Experimental residual stresses for EOD = 225 pp/cm

^{2}, PD = TD. (

**b**) Experimental residual stresses for EOD = 225 pp/cm

^{2}, PD = RD.

**Figure 11.**(

**a**) Experimental residual stresses for EOD = 400 pp/cm

^{2}, PD = TD; (

**b**) Experimental residual stresses for EOD = 400 pp/cm

^{2}, PD = RD.

**Figure 12.**Experimental results vs. numerical predictions for strategy (1). (

**a**) Analytical isotropic model predictions. (

**b**) Anisotropic model predictions.

**Figure 13.**Experimental results vs. numerical predictions for strategy (2). (

**a**) Analytical isotropic model predictions. (

**b**) Anisotropic model predictions.

**Figure 14.**Experimental results vs. numerical predictions for strategy (3). (

**a**) Analytical isotropic model predictions. (

**b**) Anisotropic model predictions.

**Figure 15.**Experimental results vs. numerical predictions for strategy (4). (

**a**) Analytical isotropic model predictions; (

**b**) Anisotropic model predictions.

**Table 1.**Calibrated constants for the analytic predictions of compressive stress–strain curves (ND).

Parameter | Value |
---|---|

${\sigma}_{ND0}$ (MPa) | 178 |

$Q\text{}$(MPa) | 125 |

${b}_{0}\text{}$(–) | 19 |

$b$ (–) | 18 |

${\dot{\epsilon}}_{0}$ (s^{−1}) | 0.001 |

${\dot{\epsilon}}_{1}$ (s^{−1}) | 4300 |

Parameter | Value |
---|---|

${\sigma}_{D0}$ (MPa) | 60 |

${\sigma}_{RDmax}$ (MPa) | 426 |

${\sigma}_{TDmax}$ (MPa) | 463 |

${Q}_{D}$ (MPa) | 98 |

${Q}_{RD2}$ (MPa) | 720 |

${Q}_{TD2}$ (MPa) | 810 |

${Q}_{RDd}$ (MPa) | 280 |

${Q}_{TDd}$ (MPa) | 320 |

${b}_{D}\text{}$ (–) | 50 |

${b}_{De}$ (–) | 5 |

${b}_{RDd}$ (–) | 80 |

${b}_{TDd}$ (–) | 95 |

${\left(\mathsf{\Delta}{\epsilon}_{p}\right)}_{c}$ (–) | 0.059 |

Parameter | Value |
---|---|

${a}_{\mathsf{\varphi}}$ (–) | 1.9 |

${R}_{c}\text{}$(mm) | 0.8 |

$H\text{}$(–) | 1.3 |

Feature | (1) | (2) | (3) | (4) |
---|---|---|---|---|

$EOD$ (pp/cm^{2}) | 225 | 225 | 400 | 400 |

Peening direction (–) | TD | RD | TD | RD |

${\left({d}_{max}\right)}_{isot}$ (µm) | 250 | 250 | 299 | 299 |

${\left({d}_{max}\right)}_{anisot}$ (µm) | 197 | 297 | 297 | 300 |

${\left({d}_{max}\right)}_{exp}$ (µm) | 100 | 300 | 334 | 315 |

$min{\left({S}_{min}\right)}_{isot}$ (MPa) | −215 | −215 | −249 | −249 |

$min{\left({S}_{min}\right)}_{anisot}$ (MPa) | −130 | −213 | −199 | −268 |

$min{\left({S}_{min}\right)}_{exp}$ (MPa) | −136 | −178 | −174 | −181 |

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**MDPI and ACS Style**

Angulo, I.; Cordovilla, F.; García-Beltrán, Á.; Porro, J.A.; Díaz, M.; Ocaña, J.L. Integrated Numerical-Experimental Assessment of the Effect of the AZ31B Anisotropic Behaviour in Extended-Surface Treatments by Laser Shock Processing. *Metals* **2020**, *10*, 195.
https://doi.org/10.3390/met10020195

**AMA Style**

Angulo I, Cordovilla F, García-Beltrán Á, Porro JA, Díaz M, Ocaña JL. Integrated Numerical-Experimental Assessment of the Effect of the AZ31B Anisotropic Behaviour in Extended-Surface Treatments by Laser Shock Processing. *Metals*. 2020; 10(2):195.
https://doi.org/10.3390/met10020195

**Chicago/Turabian Style**

Angulo, Ignacio, Francisco Cordovilla, Ángel García-Beltrán, Juan A. Porro, Marcos Díaz, and José L. Ocaña. 2020. "Integrated Numerical-Experimental Assessment of the Effect of the AZ31B Anisotropic Behaviour in Extended-Surface Treatments by Laser Shock Processing" *Metals* 10, no. 2: 195.
https://doi.org/10.3390/met10020195