# On the Surface Residual Stress Measurement in Magnesium Alloys Using X-Ray Diffraction

^{*}

## Abstract

**:**

## 1. Introduction

^{2}ψ method is the most common XRD method for residual stress measurement, and standardized approaches using this method are well-established [1]. The XRD method has been used to measure residual stress in Mg alloys in several studies. These studies use the sin

^{2}ψ method for stress measurement and layer removal to evaluate residual stress distribution through the depth. For the residual stress induced by shot peening process, Zhang and Lindemann [2], Liu et al. [3], Liu et al. [4], Zinn and Scholtes [5], and Bagherifard et al. [6] evaluated the residual stress distribution due to the shot peening of AZ80, Mg–10Gd–3Y, ZK60, AZ31, and AZ31B, respectively. All reported a compressive residual stress in the sub-surface layer of the shot peened samples. Other studies measured the residual stresses from welding Mg alloys at different distances from the weld centerline: friction stir welding of AZ31 [7], friction stir welding of ZK60 [8], tubular laser welding of AZ31 [9], butt joint welding of AZ31B and 304L steel alloy by hybrid laser-TIG [10], and laser beam welding of AZ31B [11]. The residual stress in the longitudinal and transverse directions of AZ91 welded by a CO

_{2}laser as well as the in-depth distribution of residual stress using the layer removal method were studied by Kouadri and Barrallier [12]. Other researchers have measured the residual stresses induced in manufacturing various materials due to machining of AZ31B [13], due to dry and cryogenic machining of AZ31B on the surface and sub-surface in circumferential and axial directions [14], due to equal-channel angular pressing of AZ31 [15], and due to the extrusion of AZ31B [16]. A few studies have considered surface treatment processes such as cold spray [17,18,19] and laser shock peening [20].

## 2. Material, Experiments and Methods

#### 2.1. Material

^{3}, 45 GPa, and 0.29, respectively [22].

#### 2.2. Texture Measurement

#### 2.3. Shot Peening

#### 2.4. X-Ray Diffraction

^{−1}for the X and Y axis, respectively. Oscillating the sample also has the benefit of measuring the residual stress based on the stress distribution at different locations. In this case, the results would be the average residual stress in the X-ray exposed area. The area detector captures a part of the Debye ring. In this paper, 20° from the Debye rings ($\gamma $ = −80° to −100°) were used for stress measurements. This range was divided into 30 sub-regions, and the diffraction angle in each sub-region was calculated using the sliding gravity method. All 30 diffraction angles were involved in residual stress measurements. A sensitivity analysis was performed to confirm the evaluation method and parameters. According to Bragg’s law, the lattice spacing, d, is related to the diffraction angle, so any change in the d shifts the diffraction angle to the left or right. The diffraction angle (2θ) shifts can be used to calculate residual stress. In general, to obtain the stress tensor at a point, there are six independent unknown stresses. Thus, to evaluate the residual stress components, the sample should be tested in different orientations to find all the stress values. Different angles and orientations of the sample in XRD are illustrated schematically in Figure 1.

#### 2.5. Layer Removal for Through-Depth Measurement

#### 2.6. Stress Correction Methods

^{2}/gr for the Cu-Kα beam) [30]. Respectively, 50% and 90% of the exposed X-rays were diffracted from the surface up to 36.2 μm and 126.2 μm through the depth. These penetration depths for steel alloys, in which the mass attenuation coefficient is 299.7 cm

^{2}/gr [30], are 1.1 and 3.7 μm for 50% and 90% X-ray diffraction, respectively. As such, for steel alloys, the observed stress can be considered as a surface (actual) stress, but in Mg alloys, the stress correction factor should be applied to compensate for the volume of element exposed to the ray. Consequently, by measuring the stresses before and after electro-polishing layer removal and knowing the depth of the removed layer, the actual residual stress at the surface can be evaluated. Figure 2 shows the concept of the diffraction of X-rays from different locations through the depth, suggesting that the observed residual stress would be the weighted average of residual stress at different locations through the depth. In this figure, $\omega $ and $2\theta $ represent the incident angle and diffraction angle, respectively. This figure schematically shows that 50% and 90% of X-rays are diffracted up to 36.2 and 126.2 μm below the surface, respectively, and 10% of beams will penetrate deeper.

_{Z}, of the diffracted beam intensity from the surface to the depth z, I

_{Z}, to the total impinged intensity, I

_{T}is calculated using Equation (2),

#### 2.7. Grazing-Incidence X-Ray Diffraction Method (GIXD)

#### 2.8. Error Calculation

#### 2.9. Hole Drilling

## 3. Results and Discussion

## 4. Conclusions and Further Remarks

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Evans, W.P. Residual Stress Measurement by X-Ray Diffraction. Soc. Automot. Eng. SAE HS784
**2003**, 74–79. [Google Scholar] - Zhang, P.; Lindemann, J. Influence of shot peening on high cycle fatigue properties of the high-strength wrought magnesium alloy AZ80. Scr. Mater.
**2005**, 52, 485–490. [Google Scholar] [CrossRef] - Liu, W.C.; Dong, J.; Zhang, P.; Korsunsky, A.M.; Song, X.; Ding, W.J. Improvement of fatigue properties by shot peening for Mg-10Gd-3Y alloys under different conditions. Mater. Sci. Eng. A
**2011**, 528, 5935–5944. [Google Scholar] [CrossRef] - Liu, W.C.; Dong, J.; Zheng, X.W.; Zhang, P.; Ding, W.J. Influence of shot peening on notched fatigue properties of magnesium alloy ZK60. Mater. Sci. Technol.
**2011**, 27, 201–207. [Google Scholar] [CrossRef] - Zinn, W.; Scholtes, B. Mechanical surface treatments of lightweight materials—Effects on fatigue strength and near-surface microstructures. J. Mater. Eng. Perform
**1999**, 8, 145–151. [Google Scholar] [CrossRef] - Bagherifard, S.; Hickey, D.J.; Fintová, S.; Pastorek, F.; Fernandez-Pariente, I.; Bandini, M.; Webster, T.J.; Guagliano, M. Effects of nanofeatures induced by severe shot peening (SSP) on mechanical, corrosion and cytocompatibility properties of magnesium alloy AZ31. Acta Biomater.
**2018**, 66, 93–108. [Google Scholar] [CrossRef][Green Version] - Commin, L.; Dumont, M.; Masse, J.E.; Barrallier, L. Friction stir welding of AZ31 magnesium alloy rolled sheets: Influence of processing parameters. Acta Mater.
**2009**, 57, 326–334. [Google Scholar] [CrossRef][Green Version] - da Silva, E.P.; Oliveira, V.B.; Pereira, V.F.; Maluf, O.; Buzolin, R.H.; Pinto, H.C. Microstructure and Residual Stresses in a Friction Stir Welded Butt Joint of as-cast ZK60 Alloy Containing Rare Earths. Mater. Res.
**2017**, 20, 775–779. [Google Scholar] [CrossRef][Green Version] - Nitschke-Pagel, T.; Dilger, K. Residual Stress Condition of Tubular Laser Welds of an AZ31 Magnesium Alloy. Mater. Res. Proc.
**2016**, 2, 277–282. [Google Scholar] [CrossRef][Green Version] - Zeng, Z.; Li, X.; Miao, Y.; Wu, G.; Zhao, Z. Numerical and experiment analysis of residual stress on magnesium alloy and steel butt joint by hybrid laser-TIG welding. Comput. Mater. Sci.
**2011**, 50, 1763–1769. [Google Scholar] [CrossRef] - Coelho, R.S.; Kostka, A.; Pinto, H.; Riekehr, S.; Koçak, M.; Pyzalla, A.R. Microstructure and mechanical properties of magnesium alloy AZ31B laser beam welds. Mater. Sci. Eng. A
**2008**, 485, 20–30. [Google Scholar] [CrossRef] - Kouadri, A.; Barrallier, L. Study of mechanical properties of AZ91 magnesium alloy welded by laser process taking into account the anisotropy microhardness and residual stresses by X-ray diffraction. Metall. Mater. Trans. A
**2011**, 42, 1815–1826. [Google Scholar] [CrossRef][Green Version] - Outeiro, J.C.; Batista, A.C.; Marques, M.J. Residual Stresses Induced by Dry and Cryogenic Cooling during Machining of AZ31B Magnesium Alloy. Adv Mater. Res.
**2014**, 996, 658–663. [Google Scholar] [CrossRef][Green Version] - Pu, Z.; Outeiro, J.C.; Batista, A.C.; Dillon, O.W.; Puleo, D.A.; Jawahir, I.S. Enhanced surface integrity of AZ31B Mg alloy by cryogenic machining towards improved functional performance of machined components. Int. J. Mach. Tools Manuf.
**2012**, 56, 17–27. [Google Scholar] [CrossRef] - Hosaka, T.; Yoshihara, S.; Amanina, I.; Macdonald, B.J. Influence of Grain Refinement and Residual Stress on Corrosion Behavior of AZ31 Magnesium Alloy Processed by ECAP in RPMI-1640 Medium. Procedia Eng.
**2017**, 184, 432–441. [Google Scholar] [CrossRef] - Kalatehmollaei, E.; Mahmoudi-Asl, H.; Jahed, H. An asymmetric elastic-plastic analysis of the load-controlled rotating bending test and its application in the fatigue life estimation of wrought magnesium AZ31B. Int. J. Fatigue
**2014**, 64, 33–41. [Google Scholar] [CrossRef][Green Version] - Marzbanrad, B.; Jahed, H.; Toyserkani, E. On the evolution of substrate’s residual stress during cold spray process: A parametric study. Mater. Des.
**2018**, 138, 90–102. [Google Scholar] [CrossRef] - Shayegan, G.; Mahmoudi, H.; Ghelichi, R.; Villafuerte, J.; Wang, J.; Guagliano, M.; Jahed, H. Residual stress induced by cold spray coating of magnesium AZ31B extrusion. Mater. Des.
**2014**, 60, 72–84. [Google Scholar] [CrossRef] - Shaha, S.K.; Marzbanrad, B.; Jahed, H. Influence of Cold Spray on the Microstructure and Residual Stress of Resistance Spot Welded Steel-Mg. In TMS Annual Meeting & Exhibition 2018; Springer International Publishing: Cham, Switzerland, 2018; pp. 635–644. [Google Scholar]
- Zhang, Y.; You, J.; Lu, J.; Cui, C.; Jiang, Y.; Ren, X. Effects of laser shock processing on stress corrosion cracking susceptibility of AZ31B magnesium alloy. Surf. Coatings Technol.
**2010**, 204, 3947–3953. [Google Scholar] [CrossRef] - Behravesh, S.B.; Jahed, H.; Lambert, S. Fatigue characterization and modeling of AZ31B magnesium alloy. Int. J. Fatigue
**2014**, 64, 1–13. [Google Scholar] [CrossRef][Green Version] - Behravesh, S.B. Fatigue Characterization and Cyclic Plasticity Modeling of Magnesium Spot-Welds. Ph.D. Thesis, University of Waterloo, Waterloo, ON, Canada, 2013. [Google Scholar]
- Toscano, D.; Shaha, S.K.; Behravesh, B.; Jahed, H.; Williams, B. Effect of Forging on Microstructure, Texture, and Uniaxial Properties of Cast AZ31B Alloy. J. Mater. Eng. Perform
**2017**, 26, 3090–3103. [Google Scholar] [CrossRef] - Mos, Y.M.; Vermeulen, A.C.; Buisman, C.J.N.; Weijma, J. X-Ray Diffraction of Iron Containing Samples: The Importance of a Suitable Configuration. Geomicrobiol. J.
**2018**, 35, 511–517. [Google Scholar] [CrossRef][Green Version] - Bunaciu, A.A.; Udriştioiu, E.G.; Aboul-Enein, H.Y. X-Ray Diffraction: Instrumentation and Applications. Crit. Rev. Anal. Chem.
**2015**, 45, 289–299. [Google Scholar] [CrossRef] [PubMed] - Sharma, R.; Bisen, D.P.; Shukla, U.; Sharma, B.G. X-ray diffraction: A powerful method of characterizing nanomaterials. Recent Res. Sci. Technol.
**2012**, 4, 77–79. [Google Scholar] - Takakuwa, O.; Soyama, H. Optimizing the Conditions for Residual Stress Measurement Using a Two-Dimensional XRD Method with Specimen Oscillation. Adv. Mater. Phys. Chem.
**2013**, 3, 8–18. [Google Scholar] [CrossRef][Green Version] - He, B. Two-Dimensional X-Ray Diffraction, 2nd ed; John Wiley & Sons: Hoboken, NJ, USA, 2018. [Google Scholar]
- ASTM International. E1558-09. Standard Guide for Electrolytic Polishing of Metallographic Specimens, E1558-09. ASTM Int.
**2014**, 9, 1–13. [Google Scholar] [CrossRef] - Hubbell, J.H.; Seltzer, S.M. Tables of X-Ray Mass Attenuation Coefficients and Mass Energy-Absorption Coefficients (Version 1.4); National Institute of Standards and Technology: Gaithersburg, MD, USA, 2004. [Google Scholar]
- Azanza Ricardo, C.L.; D’Incau, M.; Scardi, P. Revision and extension of the standard laboratory technique for X-ray diffraction measurement of residual stress gradients. J. Appl. Crystallogr.
**2007**, 40, 675–683. [Google Scholar] [CrossRef] - Marciszko, M.; Baczmanski, A.; Wierzbanowski, K.; Wróbel, M.; Braham, C.; Chopart, J.-P.; Lodini, A.; Bonarski, J.; Tarkowski, L.; Zazi, N. Application of multireflection grazing incidence method for stress measurements in polished Al-Mg alloy and CrN coating. Appl. Surf. Sci.
**2013**, 266, 256–267. [Google Scholar] [CrossRef][Green Version] - Kania, B.; Indyka, P.; Tarkowski, L.; Beltowska-Lehman, E. X-ray diffraction grazing-incidence methods applied for gradient-free residual stress profile measurements in electrodeposited Ni coatings. J. Appl. Crystallogr.
**2015**, 48, 71–78. [Google Scholar] [CrossRef] - Klaus, M.; Genzel, C. X-ray residual stress analysis on multilayer systems: An approach for depth-resolved data evaluation. J. Appl. Crystallogr.
**2013**, 46, 1266–1276. [Google Scholar] [CrossRef] - Withers, P.J.; Preuss, M.; Webster, P.; Hughes, D.; Korsunsky, A.M. Residual strain measurement by synchrotron diffraction. Mater. Sci. Forum
**2002**, 1–12. [Google Scholar] [CrossRef] - He, B. Measurement of Residual Stresses in Thin Films by Two-Dimensional XRD. Mater. Sci. Forum
**2006**, 524–525, 613–618. [Google Scholar] [CrossRef] - Marciszko, M.; Baczmański, A.; Braham, C.; Wróbel, M.; Wroński, S.; Cios, G. Stress measurements by multi-reflection grazing-incidence X-ray diffraction method (MGIXD) using different radiation wavelengths and different incident angles. Acta Mater.
**2017**, 123, 157–166. [Google Scholar] [CrossRef] - Baczmanski, A.; Braham, C.; Seiler, W.; Shiraki, N. Multi-reflection method and grazing incidence geometry used for stress measurement by X-ray diffraction. Surf. Coat. Technol.
**2004**, 182, 43–54. [Google Scholar] [CrossRef] - Schajer, G.S. Measurement of Non-Uniform Residual Stresses Using the Hole-Drilling Method. Part II—Practical Application of the Integral Method. J. Eng. Mater. Technol.
**1988**, 110, 344–349. [Google Scholar] [CrossRef] - ASTM E 837:08. Standard Test Method for Determining Residual Stresses by the Hole-Drilling Strain-Gages. AIP Conf. Proc.
**2008**, 1, 1–17. [Google Scholar] [CrossRef] - Honeycombe, R. The Plastic Deformation of Metals; St. Martin’s Press: New York, NY, USA, 1975. [Google Scholar]
- Stouffer, D.; Dame, L. Inelastic Deformation of Metals: Models, Mechanical Properties, and Metallurgy; John Wiley & Sons: Hoboken, NJ, USA, 1996. [Google Scholar]
- Guo, Z. The Deformation and Processing of Structural Materials; Woodhead Pub Limited: Sawston, UK; Cambridge, UK, 2005. [Google Scholar]

**Figure 1.**Sample orientation guide, defining different angles required for stress measurements with respect to the position of tube, sample and detector.

**Figure 2.**X-rays diffracting from different locations through the depth, 36.2 and 126.2 μm showing 50% and 90% ray diffraction, when using Cu-K

_{α}for $2\theta ={99.22}^{\xb0}$ in Mg substrate.

**Figure 3.**Stress correction factor due to redistribution of residual stress after layer removal and the parameters defined in Equation (7).

**Figure 5.**Observed (before proposed stress correction) residual stress on the peened AZ31B-H24 plate with steel shots; data points correspond to measurements after each layer removal.

**Figure 6.**Observed (before proposed stress correction) residual stress on as received AZ31B-H24 plate and after shot peening with steel and glass shots.

**Figure 7.**Corrected residual stress on the as-received AZ31B-H24 plate and after shot peening with steel and glass shots.

**Figure 8.**Residual stress distribution of the as-received, peened with steel shot, and peened with glass shot samples, as measured by the hole drilling method. Corrected residual stress measurements of XRD are added for comparison to show close agreement of the results.

**Figure 9.**Results of the grazing-incidence X-ray diffraction (GIXD) method on the shot peened sample using steel and glass shots, and comparison with corrected stress evaluated by XRD.

**Figure 10.**Cross-section of (

**a**) the as-received sample, (

**b**) peened using steel shots, and (

**c**) peened using glass shots, showing much higher roughness in the shot peened samples as compared to the as-received sample.

**Table 1.**Summary of studies on residual stress measurement of Mg alloys using X-ray diffraction (XRD).

Reference | Material | Process | Surface/In-Depth Measurement | X-Ray Source | Correction Applied |
---|---|---|---|---|---|

Zhang and Lindemann [2] | AZ80, Forged | Shot peening | In-depth | Cu-Kα | NA |

Liu et al. [3] | Mg–10Gd–3Y, Extrusion | Shot peening | In-depth | NA | NA |

Liu et al. [4] | ZK 60, Extrusion | Shot peening | In-depth | NA | NA |

Zinn and Scholtes [5] | AZ31, Rolled | Shot peening | In depth | NA | NA |

Bagherifard et al. [6] | AZ31, Rolled | Shot peening | In-depth | Cr-Kα | Yes |

Commin et al. [7] | AZ31, Rolled | Friction stir welding | Surface | Cr-Kα | NA |

Silva et al. [8] | ZK60, Cast | Friction stir welding | Surface | Co-Kα | NA |

Nitschke-Pagel and Dilger [9] | AZ31B | Tubular laser welding | Surface | Cu-Kα | NA |

Zeng et al. [10] | AZ31B, Rolled | Hybrid laser-TIG welding | Surface | NA | NA |

Coelho et al. [11] | AZ31B, Rolled | Laser beam welding | Surface | NA | NA |

Kouadri and Barrallier [12] | AZ91, Rolled | Laser beam welding | In-depth/Surface | Cr-Kα | NA |

Outeiro et al. [13] | AZ31B, Rolled | Machining | In-depth | Cr-Kα | NA |

Pu et al. [14] | AZ31B, Rolled | Machining | In-depth | Mn-Kα | NA |

Hosaka et al. [15] | AZ31B, Extrusion | Equal-channel angular pressing | Surface | NA | NA |

Kalatehmollaei et al. [16] | AZ31B, Extrusion | Machining | Surface | NA | NA |

Marzbanrad et al. [17] | AZ31B, Rolled | Cold spray | Surface | Cu-Kα | NA |

Shayegan et al. [18] | AZ31B, Extrusion | Cold spray | In-depth | Cr-Kα | Yes |

Shaha et al. [19] | Mg alloy | Resistance spot welding | In-depth | NA | NA |

Zhang et al. [20] | AZ31B, Rolled | Laser shock peening | In-depth | Cr-Kα | NA |

**Table 2.**Chemical composition of AZ31B rolled sheet [21].

Composition | Al | Zn | Mn | Mg |
---|---|---|---|---|

Weight% | 2.73 | 0.915 | 0.375 | Bal. |

**Table 3.**Different sample orientations [27].

ψ (°) | φ (°) |
---|---|

0 | 0 |

25 | 0, 45, 90, 135, 180, 225, 270, 315 |

50 | 0, 45, 90, 135, 180, 225, 270, 315 |

**Table 4.**Cu-Kα effective penetration depths for Mg alloys, corresponding to different incident angles, calculated from Equation (8).

ω (°) | z (μm) |
---|---|

5 | 7.7 |

10 | 14.3 |

15 | 19.8 |

25 | 28.3 |

35 | 33.8 |

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**MDPI and ACS Style**

Yazdanmehr, A.; Jahed, H.
On the Surface Residual Stress Measurement in Magnesium Alloys Using X-Ray Diffraction. *Materials* **2020**, *13*, 5190.
https://doi.org/10.3390/ma13225190

**AMA Style**

Yazdanmehr A, Jahed H.
On the Surface Residual Stress Measurement in Magnesium Alloys Using X-Ray Diffraction. *Materials*. 2020; 13(22):5190.
https://doi.org/10.3390/ma13225190

**Chicago/Turabian Style**

Yazdanmehr, Amir, and Hamid Jahed.
2020. "On the Surface Residual Stress Measurement in Magnesium Alloys Using X-Ray Diffraction" *Materials* 13, no. 22: 5190.
https://doi.org/10.3390/ma13225190