# Mechanical Behavior of Austenitic Steel under Multi-Axial Cyclic Loading

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## Abstract

**:**

## 1. Introduction

## 2. Material Characterization

#### 2.1. Specimen Preparation and Setup of EBSD

#### 2.2. Microstructure Analysis Using EBSD

#### 2.3. Fatigue Test

## 3. Micromechanical Model

#### 3.1. Representative Volume Element

#### 3.2. Material Model

#### 3.2.1. J2/Von Mises Plasticity

#### 3.2.2. Crystal Plasticity

## 4. Results and Discussion

#### 4.1. J2 Plasticity

#### 4.2. Crystal Plasticity

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclature

Variable | Description |

$\mathbf{\sigma}$, ${\sigma}_{ij}$ | Cauchy stress |

$\mathbf{S}$ | Second Piola Kirchhoff stress |

$\mathbf{E}$, ${E}_{ij}$ | Green-Lagrange strain |

${\mathbf{\u03f5}}_{\mathrm{pl}},{\u03f5}_{\mathrm{eq}}$ | Plastic strain tensor, equivalent plastic strain |

${\u03f5}_{\mathrm{eng}}$ | Engineering strain |

${\dot{\gamma}}^{\alpha}$ | Shear rate of dislocation on slip system $\alpha $ |

${\dot{\gamma}}_{0}$ | Initial shear rate |

${\tau}^{\alpha}$ | Resolved shear stress for slip system $\alpha $ |

${\tau}_{0}$ | Initial guess for the slip resistance |

$\{{\sigma}_{m},Q,b\}$ | Isotropic hardening material parameter for J2 plasticity model |

$\{{C}_{i},{g}_{i}\}$ | Chaboche kinematic hardening material parameter for J2 plasticity model |

$\{{\tau}_{c}^{f},{h}_{0},{p}_{2}\}$ | Isotropic hardening parameters for CP model |

$\{\eta ,\mathsf{\mu},m\}$ | Onho-Wang Kinematic hardening parameters for CP model |

$Y,G$ | Young’s modulus and shear modulus |

${\u03f5}_{eq}$ | Equivalent strain |

$\mathbb{C}$ | Stiffness tensor |

$\mathbf{F}$ | Deformation gradient |

${\mathbf{F}}^{\mathrm{e}}$ | Elastic deformation gradient |

${\mathbf{F}}^{\mathrm{p}}$ | Plastic deformation gradient |

$\mathbf{I}$ | Unit tensor |

q | Crystallographic orientation |

${w}_{i}$ | Weight of ${i}^{th}$ crystallographic orientation |

f | Orientation distribution function from experimental data |

$\widehat{f}$ | Orientation distribution function from reduced discrete orientations |

${\psi}_{\Omega}$ | Kernel density function with half-width $\Omega $ |

R | Ratio of maximum and minimum strains in cyclic hysteresis loop |

$\theta $ | Amplitude of torsional cyclic deformation |

## Appendix A. Parametric Study of CPFE Parameters

**Figure A1.**Effect of CP kinematic hardening parameters $\eta $ and $\mu $ on the stress–strain hysteresis loop and the axial creep behavior.

**Figure A2.**Effect of the kinematic hardening parameter m on the axial creep behavior and the mean stress relaxation during HPTF loading.

## Appendix B. Elastic Constants Estimation

## Appendix C. Material Parameter Optimization Algorithm

## References

- Thomann, U.I.; Uggowitzer, P.J. Wear-corrosion behavior of biocompatible austenitic stainless steels. Wear
**2000**, 239, 48–58. [Google Scholar] [CrossRef] - Uggowitzer, P.J.; Magdowski, R.; Speidel, M.O. Nickel free high nitrogen austenitic steels. ISIJ Int.
**1996**, 36, 901–908. [Google Scholar] [CrossRef] - Williams, D. Tissue-biomaterial interactions. J. Mater. Sci.
**1987**, 22, 3421–3445. [Google Scholar] [CrossRef] - Fini, M.; Giavaresi, G.; Giardino, R.; Lenger, H.; Bernauer, J.; Rimondini, L.; Torricelli, P.; Borsari, V.; Chiusoli, L.; Chiesa, R.; et al. A new austenitic stainless steel with a negligible amount of nickel: An in vitro study in view of its clinical application in osteoporotic bone. J. Biomed. Mater. Res. Part B Appl. Biomater.
**2004**, 71, 30–37. [Google Scholar] [CrossRef] [PubMed] - Montanaro, L.; Cervellati, M.; Campoccia, D.; Prati, C.; Breschi, L.; Arciola, C.R. No genotoxicity of a new nickel-free stainless steel. Int. J. Artif. Organs
**2005**, 28, 58–65. [Google Scholar] [CrossRef] [PubMed] - Torricelli, P.; Fini, M.; Borsari, V.; Lenger, H.; Bernauer, J.; Tschon, M.; Bonazzi, V.; Giardino, R. Biomaterials in orthopedic surgery: Effects of a nickel-reduced stainless steel on in vitro proliferation and activation of human osteoblasts. Int. J. Artif. Organs
**2003**, 26, 952–957. [Google Scholar] [CrossRef] - Niinomi, M.; Nakai, M.; Hieda, J. Development of new metallic alloys for biomedical applications. Acta Biomater.
**2012**, 8, 3888–3903. [Google Scholar] [CrossRef] - Salahinejad, E.; Hadianfard, M.J.; Ghaffari, M.; Mashhadi, S.B.; Okyay, A.K. Fabrication of nanostructured medical-grade stainless steel by mechanical alloying and subsequent liquid-phase sintering. Metall. Mater. Trans. A
**2012**, 43, 2994–2998. [Google Scholar] [CrossRef] - Carreno-Morelli, E.; Zinn, M.; Rodriguez-Arbaizar, M.; Bassas, M. Nickel-free P558 stainless steel processed from metal powder–PHA biopolymer feedstocks. Eur. Cells Mater.
**2016**, 32, 32. [Google Scholar] - Fini, M.; Aldini, N.N.; Torricelli, P.; Giavaresi, G.; Borsari, V.; Lenger, H.; Bernauer, J.; Giardino, R.; Chiesa, R.; Cigada, A. A new austenitic stainless steel with negligible nickel content: An in vitro and in vivo comparative investigation. Biomaterials
**2003**, 24, 4929–4939. [Google Scholar] [CrossRef] - Ngeru, T.; Kurtulan, D.; Karkar, A.; Hanke, S. Mechanical Behaviour and Failure Mode of High Interstitially Alloyed Austenite under Combined Compression and Cyclic Torsion. Metals
**2022**, 12, 157. [Google Scholar] [CrossRef] - Cruzado, A.; LLorca, J.; Segurado, J. Modeling cyclic deformation of inconel 718 superalloy by means of crystal plasticity and computational homogenization. Int. J. Solids Struct.
**2017**, 122, 148–161. [Google Scholar] [CrossRef] - Kowalewski, Z.; Szymczak, T.; Maciejewski, J. Material effects during monotonic-cyclic loading. Int. J. Solids Struct.
**2014**, 51, 740–753. [Google Scholar] [CrossRef] - Hennessey, C.; Castelluccio, G.M.; McDowell, D.L. Sensitivity of polycrystal plasticity to slip system kinematic hardening laws for Al 7075-T6. Mater. Sci. Eng. A
**2017**, 687, 241–248. [Google Scholar] [CrossRef] - Mróz, Z.; Maciejewski, J. Constitutive modeling of cyclic deformation of metals under strain controlled axial extension and cyclic torsion. Acta Mech.
**2018**, 229, 475–496. [Google Scholar] [CrossRef] - Armstrong, P.J.; Frederick, C.O. A Mathematical Representation of the Multiaxial Bauschinger Effect; Berkeley Nuclear Laboratories: Berkeley, CA, USA, 1966; Volume 731. [Google Scholar]
- Lemaitre, J.; Chaboche, J.L. Mechanics of Solid Materials; Cambridge University Press: Cambridge, UK, 1994. [Google Scholar]
- Ohno, N.; Wang, J.D. Kinematic hardening rules with critical state of dynamic recovery, part I: Formulation and basic features for ratchetting behavior. Int. J. Plast.
**1993**, 9, 375–390. [Google Scholar] [CrossRef] - Bari, S.; Hassan, T. Anatomy of coupled constitutive models for ratcheting simulation. Int. J. Plast.
**2000**, 16, 381–409. [Google Scholar] [CrossRef] - Schäfer, B.J.; Song, X.; Sonnweber-Ribic, P.; Hartmaier, A. Micromechanical modelling of the cyclic deformation behavior of martensitic SAE 4150—A comparison of different kinematic hardening models. Metals
**2019**, 9, 368. [Google Scholar] [CrossRef] - Sajjad, H.M.; Hanke, S.; Güler, S.; Fischer, A.; Hartmaier, A. Modelling cyclic behaviour of martensitic steel with J2 plasticity and crystal plasticity. Materials
**2019**, 12, 1767. [Google Scholar] [CrossRef] - Hielscher, R. Kernel density estimation on the rotation group and its application to crystallographic texture analysis. J. Multivar. Anal.
**2013**, 119, 119–143. [Google Scholar] [CrossRef] - Jin, Y.; Bernacki, M.; Rohrer, G.S.; Rollett, A.D.; Lin, B.; Bozzolo, N. Formation of annealing twins during recrystallization and grain growth in 304L austenitic stainless steel. In Materials Science Forum; Trans Tech Publications Ltd.: Baech, Switzerland, 2013; Volume 753, pp. 113–116. [Google Scholar]
- Ren, S.; Sun, Z.; Xu, Z.; Xin, R.; Yao, J.; Lv, D.; Chang, J. Effects of twins and precipitates at twin boundaries on Hall–Petch relation in high nitrogen stainless steel. J. Mater. Res.
**2018**, 33, 1764–1772. [Google Scholar] [CrossRef] - Mainprice, D.; Hielscher, R.; Schaeben, H. Calculating anisotropic physical properties from texture data using the MTEX open-source package. Geol. Soc.
**2011**, 360, 175–192. [Google Scholar] [CrossRef] - Buhagiar, J.; Qian, L.; Dong, H. Surface property enhancement of Ni-free medical grade austenitic stainless steel by low-temperature plasma carburising. Surf. Coatings Technol.
**2010**, 205, 388–395. [Google Scholar] [CrossRef] - Heidari, L.; Tangestani, A.; Hadianfard, M.; Vashaee, D.; Tayebi, L. Effect of fabrication method on the structure and properties of a nanostructured nickel-free stainless steel. Adv. Powder Technol.
**2020**, 31, 3408–3419. [Google Scholar] [CrossRef] - Castelluccio, G.M.; McDowell, D.L. Effect of annealing twins on crack initiation under high cycle fatigue conditions. J. Mater. Sci.
**2013**, 48, 2376–2387. [Google Scholar] [CrossRef] - Pande, C.S.; Rath, B.; Imam, M. Effect of annealing twins on Hall–Petch relation in polycrystalline materials. Mater. Sci. Eng. A
**2004**, 367, 171–175. [Google Scholar] [CrossRef] - Biswas, A.; Vajragupta, N.; Hielscher, R.; Hartmaier, A. Optimized reconstruction of the crystallographic orientation density function based on a reduced set of orientations. J. Appl. Crystallogr.
**2020**, 53, 178–187. [Google Scholar] [CrossRef] [PubMed] - Biswas, A.; Prasad, M.R.; Vajragupta, N.; ul Hassan, H.; Brenne, F.; Niendorf, T.; Hartmaier, A. Influence of microstructural features on the strain hardening behavior of additively manufactured metallic components. Adv. Eng. Mater.
**2019**, 21, 1900275. [Google Scholar] [CrossRef] - Smith, M. ABAQUS/Standard User’s Manual; Version 6.14; Dassault Systèmes Simulia Corp: Johnston, RI, USA, 2014. [Google Scholar]
- de Borst, R.; Crisfield, M.A.; Remmers, J.J.C.; Verhoosel, C.V. Non-Linear Finite Element Analysis of Solids and Structures; Wiley: Chichester, UK, 2012. [Google Scholar]
- Roters, F.; Eisenlohr, P.; Hantcherli, L.; Tjahjanto, D.D.; Bieler, T.R.; Raabe, D. Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: Theory, experiments, applications. Acta Mater.
**2010**, 58, 1152–1211. [Google Scholar] [CrossRef] - McDowell, D. Stress state dependence of cyclic ratchetting behavior of two rail steels. Int. J. Plast.
**1995**, 11, 397–421. [Google Scholar] [CrossRef] - de Castro e Sousa, A.; Suzuki, Y.; Lignos, D. Consistency in solving the inverse problem of the Voce-Chaboche constitutive model for plastic straining. J. Eng. Mech.
**2020**, 146, 04020097. [Google Scholar] [CrossRef] - Vrh, M.; Halilovič, M.; Štok, B. The evolution of effective elastic properties of a cold formed stainless steel sheet. Exp. Mech.
**2011**, 51, 677–695. [Google Scholar] [CrossRef] - ul Hassan, H.; Maqbool, F.; Güner, A.; Hartmaier, A.; Ben Khalifa, N.; Tekkaya, A.E. Springback prediction and reduction in deep drawing under influence of unloading modulus degradation. Int. J. Mater. Form.
**2016**, 9, 619–633. [Google Scholar] [CrossRef] - Wilshire, B.; Willis, M. Mechanisms of strain accumulation and damage development during creep of prestrained 316 stainless steels. Metall. Mater. Trans. A
**2004**, 35, 563–571. [Google Scholar] [CrossRef] - Stout, M.; Martin, P.; Helling, D.; Canova, G. Multiaxial yield behavior of 1100 aluminum following various magnitudes of prestrain. Int. J. Plast.
**1985**, 1, 163–174. [Google Scholar] [CrossRef] - Schneider, A.; Kiener, D.; Yakacki, C.; Maier, H.; Gruber, P.; Tamura, N.; Kunz, M.; Minor, A.; Frick, C. Influence of bulk pre-straining on the size effect in nickel compression pillars. Mater. Sci. Eng. A
**2013**, 559, 147–158. [Google Scholar] [CrossRef] - Kresse, G.; Hafner, J. Ab initio molecular dynamics for open-shell transition metals. Phys. Rev. B
**1993**, 48, 13115–13118. [Google Scholar] [CrossRef] [PubMed] - Kresse, G.; Furthmüller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B
**1996**, 54, 11169–11186. [Google Scholar] [CrossRef] - Kresse, G.; Joubert, D. From ultrasoft pseudopotentials to the projector augmented-wave method. Phys. Rev. B
**1999**, 59, 1758–1775. [Google Scholar] [CrossRef] - Blöchl, P.E. Projector augmented-wave method. Phys. Rev. B
**1994**, 50, 17953–17979. [Google Scholar] [CrossRef] - Perdew, J.P.; Burke, K.; Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett.
**1996**, 77, 3865–3868. [Google Scholar] [CrossRef] [PubMed][Green Version] - Pack, J.D.; Monkhorst, H.J. Special points for Brillouin-zone integrations. Phys. Rev. B
**1977**, 16, 1748–1749. [Google Scholar] [CrossRef] - Gao, F.; Han, L. Implementing the Nelder-Mead simplex algorithm with adaptive parameters. Comput. Optim. Appl.
**2012**, 51, 259–277. [Google Scholar] [CrossRef]

**Figure 2.**(

**top left**) IPF-Z plot of one of the EBSD data sets, (

**bottom left**) corresponding IPF key, (

**top right**) pole figure contour plot of the ODF estimated by combining all EBSD data sets (i.e., ≈19,000 grains), (

**bottom right**) the grain equivalent diameter histogram.

**Figure 3.**Figure showing the dimensions and surface finish for (

**a**) HPTF specimen, (

**b**) uniaxial fatigue specimen, and (

**c**) HPTF loading of the specimen, indicating the constant axial force and the cyclic torsional angles.

**Figure 4.**(

**left**) Experimental stress–strain hysteresis loops recorded for uniaxial fatigue after the saturation of the mean stress and (

**right**) axial creep for the HPTF loading cases given in the legend, where $\theta $ is the amplitude of the cyclic torsion loading, and R is the ratio of the minimum vs. maximum torsion angle.

**Figure 5.**(

**top left**) Graphical representation of the used RVE with 512 cubic grains and 8 finite elements per grain, (

**bottom left**) grains are colored according to their orientation and the corresponding IPF key. Contour plots of the ODF pole figures from the orientation set obtained by combining all the EBSD data sets of about 19,000 grains (

**top right**) and 512 discrete orientations in the RVE (

**bottom right**).

**Figure 6.**(

**left**) Stress–Strain hysteresis loop and (

**right**) reduction of the maximum stress in uniaxial fatigue tests with a strain amplitude of ${E}_{33}=0.55\%$ and an amplitude ratio of $R=-1$.

**Figure 7.**(

**top left**) FE model used to simulate HTPF loading with a J2 plasticity model and resulting axial creep strain (${E}_{33}$) of simulation and experiment vs. cycle number. The axial pressure amounted to ${\sigma}_{33}=250$ MPa and three different combinations of amplitude ratios R and cyclic torsion amplitudes $\theta $ are shown: (

**a**) $R=-1,\phantom{\rule{0.166667em}{0ex}}\theta =7.{5}^{\circ}$, (

**b**) $R=0,\phantom{\rule{0.166667em}{0ex}}\theta ={10}^{\circ}$, and (

**c**) $R=0,\phantom{\rule{0.166667em}{0ex}}\theta ={15}^{\circ}$.

**Figure 8.**Contour plot of the axial stress in MPa (

**top**) and the axial plastic strain (

**bottom**) along a cut through the J2 model.

**Figure 9.**To mimic HPTF loading conditions on the length scale of the RVE used for CPFEM simulations, the distortions of a small volume element close to the surface of the cylindrical FE model, representing the gauge section of the HPTF specimens, are applied as boundary conditions to the RVE.

**Figure 10.**Comparison of saturated HPTF stress–strain hysteresis loops between simulation and experiment; the constant axial pressure amounts to ${\sigma}_{33}=250$ MPa in all cases and cyclic shear loading ${E}_{13}$ is applied to mimic the cyclic torsion in the experiment. (

**a**) The result of calibration for HPTF loading with $R=-1,\phantom{\rule{4pt}{0ex}}\theta =7.{5}^{\circ},\phantom{\rule{4pt}{0ex}}{E}_{13}=0.02$. The two subfigures in the bottom represent predictions of the model for (

**b**) $R=0,\phantom{\rule{4pt}{0ex}}\theta ={10}^{\circ},\phantom{\rule{4pt}{0ex}}{E}_{13}=0.028$, and (

**c**) $R=0,\phantom{\rule{4pt}{0ex}}\theta ={15}^{\circ},\phantom{\rule{4pt}{0ex}}{E}_{13}=0.04$.

**Figure 11.**Comparison of maximum and minimum stress obtained in experiment and simulation during torsional cycles with (

**a**) $R=-1,\phantom{\rule{4pt}{0ex}}\theta =7.{5}^{\circ}$, comparison of cyclic softening behavior for the loading cases (

**b**) $R=0,\phantom{\rule{4pt}{0ex}}\theta ={10}^{\circ}$, and (

**c**) $R=0,\phantom{\rule{4pt}{0ex}}\theta ={15}^{\circ}$.

**Figure 12.**Axial creep strain (${E}_{33}$) vs. the number of cycles obtained from HPTF simulations with the CPFE model and from experiment for a constant axial pressure of ${\sigma}_{33}=250$ MPa and cyclic torsional loading: (

**a**) $R=-1,\phantom{\rule{4pt}{0ex}}\theta =7.{5}^{\circ}$) used for calibration, (

**b**) $R=0,\phantom{\rule{4pt}{0ex}}\theta ={10}^{\circ}$, and (

**c**) $R=0,\phantom{\rule{4pt}{0ex}}\theta ={15}^{\circ}$. Cases (

**b**,

**c**) represent predictions of the model.

**Figure 13.**Comparison of experimental and simulated stress–strain hysteresis loops (

**a**) for uniaxial fatigue with the strain amplitude ${E}_{33}=0.55\%$ and (

**b**) under HPTF loading with ($R=-1$, $\theta =7.{5}^{\circ}$, ${E}_{13}=0.02$). The material parameters for set 1 (Table 5) were obtained using an inverse analysis of the HPTF experiments, whereas the parameters of set 2 (Table 6) were fitted to uniaxial experiments.

**Figure 14.**Comparison of the hysteresis loops in the regime where the stress amplitude is constant for the uniaxial fatigue experiment (${E}_{33}=0.55\%,\phantom{\rule{4pt}{0ex}}R=-1$) and the HPTF loading case ($\theta =7.{5}^{\circ},\phantom{\rule{4pt}{0ex}}R=-1$), where $\theta $ and ${E}_{33}$ are the amplitudes of the cyclic deformation. The values of all stresses in the plot are normalized with the corresponding stiffness parameters, i.e., Young’s Modulus $Y=185.2$ GPa for uniaxial fatigue and shear modulus $G=76.506$ GPa for the torsional loading during HPTF.

C | Si | Mn | P | S | Cr | Ni | Mo | Cu | V | Nb | N |
---|---|---|---|---|---|---|---|---|---|---|---|

$0.19$ | $0.41$ | $12.20$ | $0.01$ | $0.00$ | $17.15$ | $0.02$ | $2.89$ | $0.02$ | $0.01$ | $0.03$ | $0.54$ |

**Table 2.**Details of uniaxial fatigue and high pressure torsion fatigue (HPTF) experiments. Axial stress and strain components are denoted by indices “33”.

Type | R | Amplitude | Frequency | Axial Pressure |
---|---|---|---|---|

Uniaxial | −1 | ${E}_{33}=0.55\%$ | 2.5 Hz | - |

HPTF | −1 | $\theta =7.{5}^{\circ}$ | 2.5 Hz | ${\sigma}_{33}=250$ MPa |

HPTF | 0 | $\theta ={10}^{\circ}$ | 2.5 Hz | ${\sigma}_{33}=250$ MPa |

HPTF | 0 | $\theta ={15}^{\circ}$ | 2.5 Hz | ${\sigma}_{33}=250$ MPa |

**Table 3.**Ideal elastic stiffness parameters ${C}_{11}$, ${C}_{12}$, and ${C}_{44}$ obtained by DFT calculations, resulting homogenized Young’s modulus Y, and scaling factor $\lambda $.

${\mathit{C}}_{11}$ | ${\mathit{C}}_{12}$ | ${\mathit{C}}_{44}$ | Y | $\mathit{\lambda}$ |
---|---|---|---|---|

(GPa) | (GPa) | (GPa) | (GPa) | (-) |

$263.159$ | $122.644$ | $76.506$ | $185.184$ | $0.63$ |

${\mathit{C}}_{1}$ | ${\mathit{C}}_{2}$ | ${\mathit{g}}_{1}$ | ${\mathit{g}}_{2}$ | ${\mathit{\sigma}}^{\mathit{m}}$ | Q | b |
---|---|---|---|---|---|---|

(MPa) | (MPa) | (-) | (-) | (MPa) | (MPa) | (-) |

$\mathrm{43,106.44}$ | $4192.81$ | $513.95$ | $0.0$ | $545.82$ | $-300$ | $3.17$ |

$\mathit{\lambda}$ | ${\dot{\mathit{\gamma}}}_{0}$ | ${\mathit{p}}_{1}$ | ${\mathit{\tau}}_{0}$ | ${\mathit{\tau}}_{\mathit{c}}^{\mathit{f}}$ | ${\mathit{h}}_{0}$ | ${\mathit{p}}_{2}$ | $\mathit{\eta}$ | $\mathsf{\mu}$ | m |
---|---|---|---|---|---|---|---|---|---|

(-) | (1/s) | (-) | (MPa) | (MPa) | (MPa) | (-) | (MPa) | (-) | (-) |

$0.63$ | $0.001$ | 25 | 235 | $184.2$ | $-25.0$ | 2 | $\mathrm{16,888.0}$ | $125.0$ | $2.0$ |

**Table 6.**Re-calibrated CPFE model parameters for uniaxial fatigue loading (set 2). The remaining material parameters are unchanged with respect to set 1 and given Table 5.

$\mathit{\lambda}$ | ${\mathit{\tau}}_{0}$ | ${\mathit{\tau}}_{\mathit{c}}^{\mathit{f}}$ | ${\mathit{h}}_{0}$ |
---|---|---|---|

(-) | (MPa) | (MPa) | (MPa) |

$0.95$ | 188 | 92 | $-130.0$ |

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**MDPI and ACS Style**

Biswas, A.; Kurtulan, D.; Ngeru, T.; Azócar Guzmán, A.; Hanke, S.; Hartmaier, A. Mechanical Behavior of Austenitic Steel under Multi-Axial Cyclic Loading. *Materials* **2023**, *16*, 1367.
https://doi.org/10.3390/ma16041367

**AMA Style**

Biswas A, Kurtulan D, Ngeru T, Azócar Guzmán A, Hanke S, Hartmaier A. Mechanical Behavior of Austenitic Steel under Multi-Axial Cyclic Loading. *Materials*. 2023; 16(4):1367.
https://doi.org/10.3390/ma16041367

**Chicago/Turabian Style**

Biswas, Abhishek, Dzhem Kurtulan, Timothy Ngeru, Abril Azócar Guzmán, Stefanie Hanke, and Alexander Hartmaier. 2023. "Mechanical Behavior of Austenitic Steel under Multi-Axial Cyclic Loading" *Materials* 16, no. 4: 1367.
https://doi.org/10.3390/ma16041367