# Advantageous Description of Short Fatigue Crack Growth Rates in Austenitic Stainless Steels with Distinct Properties

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Materials

#### 2.2. Low Cycle Fatigue Tests

_{t}= 1.14 using the FEM software ANSYS 19.2 (Ansys, Inc., Canonsburg, PA, USA), depicted in Figure 2b. The value is small enough to have only a minor impact on the crack nucleation in other locations of the gauge length but high enough to initiate the primary crack in the investigated area of the shallow notch. The specimen gauge length was mechanically and electrolytically polished to remove any residual deformation and to avoid preparation-induced martensite occurrence from specimen fabrication. Moreover, the high quality of specimen surface facilitates the observation of the crack growth using optical microscopy (OM). A solution of nitric acid, perchloric acid and ethanol in the volume ratio 1.5:5:100 was used as the electrolyte for both materials. It is important to note that in the case of 304L steel, a small pre-crack of semi-elliptical shape in the center of the shallow notch was prepared using focus ion beam (FIB) technique by a field emission gun scanning electron microscope (SEM) TESCAN LYRA 3 XMU (Tescan Orsay holding, Brno, Czech Republic). Pre-crack surface length in the range of 100–150 μm and the depth of approximately 100 μm. Any martensite induced by FIB beam wasn’t observed.

_{ε}= −1) strain-controlled cycling under constant strain rate $\dot{\epsilon}$ = 0.005 s

^{−1}and constant total strain amplitude ε

_{a}regime. The cyclic tests for cyclic stress–strain curve determination were performed in total strain amplitude range of 0.25–1% and 0.3–1% for Sanicro 25 and 304L, respectively. Interrupted cyclic test dedicated to short crack growth characterization were performed in total strain amplitude range of 0.25–0.7% and 0.4–0.7% for Sanicro 25 and 304L, respectively.

#### 2.3. Cyclic Stress–Strain Response

#### 2.4. Short Crack Growth Measurement

#### 2.5. Fractography

## 3. Results and Discussion

#### 3.1. Optimization of the Fatigue Crack Front Shape during Crack Propagation

Young’s Modulus E [GPa] | Poisson’s Ratio υ | Proof Yield Strength R_{p0.2} [MPa] | Ultimate Tensile Strength R_{m} [MPa] | Elongation at Break [%] | |
---|---|---|---|---|---|

Sanicro 25 [32] | 185 | 0.3 | 375 | 787 | 49 |

304L | 201 | 0.3 | 236 | 651 | 83 |

_{I}was calculated as described above. The values of stress intensity factor as a function of the distance between X point and Y point at the crack front were fitted by a linear function, as presented in Figure 9. According to a slope of the linear function, three options may occur: (i) the slope is negative, whereas the ratio a/b increases due to increasing a; (ii) the slope is positive and the ratio a/b increases due to decreasing a; (iii) the slope is equal to zero, when the crack shape is optimized. Next step follows this procedure, only when the value of the axis b is higher. This loop was repeated until reaching the limit for physically short cracks of a = 2 mm, adopted from [38], which is also correspond to the maximum of experimentally captured crack length.

_{I}and that they were constant between the points X and Y, see Figure 10. The difference was only in calculation time for the elasto-plastic analysis which was longer by one order of magnitude. Therefore, to save the calculation time, the elastic analysis was performed for the crack front shape optimization and the elasto-plastic simulations were used just for the validation of the final crack shape.

#### 3.2. Description of Short Fatigue Crack Growth Rate Based on J-Integral

_{I}is the Mode I stress intensity factor, J is the J-integral and J

_{el}and J

_{pl}are its elastic and plastic part. The identity E* = E is valid for plane stress conditions and E* = E/(1 − ν

^{2}) for plain strain conditions.

_{a,pl}/J

_{a}. The fraction increases with increasing total strain amplitude in the case of Sanicro 25 (see Figure 16a). However, the SIMT in front of the crack tip, typical for 304L and other metastable austenitic stainless steels, results in significant cyclic hardening. As a consequence, the elastic and plastic parts of the J-integral do not increase in the same rate with increasing total strain amplitude. Therefore, the ratio J

_{a,pl}/J

_{a}slightly decreases, as presented in Figure 16b. However, the plastic part of J-integral is dominant for all total strain amplitudes and therefore, it was used for the description of short fatigue crack growth as it has been recommended [15,16,28].

#### 3.3. Residual Fatigue Lifetime Estimation

_{a,pl}is the amplitude of plastic part of J-integral and C

_{Jp}and m

_{Jp}are material characteristics obtained by experimental measurements listed in Table 4 and Table 5. The mentioned importance of the effect of plasticity corresponds well with the Polák model [9]. The model suggests that the fatigue lifetime is controlled by the plastic strain amplitude upon constant total strain amplitude loading. Based on this fact, the following model of short fatigue crack propagation rate was proposed:

_{g}is the crack growth coefficient corresponding to the relative increment of the crack length in one cycle. The coefficient k

_{g}mainly depends on the applied plastic strain amplitude using a power law:

## 4. Conclusions

_{a, pl}for plotting of the crack growth rate results.

_{pl}were determined by 3D finite element modeling of the cracked specimens considering the cyclic stress–strain curves of the materials. The numerical model was also used for the simulation of the crack front shape evolution during crack growth. It helped to verify the relationship between the measured crack length at the specimen surface and the true in-depth crack length during the experiments. The resulting crack front shapes were in agreement with those measured post mortem at fracture surfaces.

_{pl}relationships for the materials as well as to the Polák model parameters (related to the Manson–Coffin law parameters), the residual fatigue life of individual specimens was calculated for the same initial short crack lengths. The results were in good agreement with the measured number of cycles to failure. It should be noted that such a result is not so self-evident, since each specimen was loaded by different strain amplitude, which may cause problems in some other approaches.

_{a, pl}for the two tested steels fell onto the same so-called “master curve”, which was previously measured for various other steels with different properties (such as 316L, Eurofer 97 and duplex 2025). This is a reasonable result, since the plastic part of the J-integral corresponds well to the physical mechanism of crack propagation given by cyclic plastic deformation in the crack tip area. It means that it is possible to use the “master curve” advantageously to predict roughly the fatigue life by considering the short crack propagation rates without necessity for any other experimental data.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Overview of the specimen geometry: (

**a**) The specimen with a shallow notch in the middle of the gauge length. (

**b**) The gauge length segment of the finite element model used for the estimation of theoretical stress concentration factor of the notch (Y axis is the loading direction). Stress distribution under monotonic loading.

**Figure 4.**Crack growth at the surface of Sanicro 25 cycled at ε

_{a}= 2.5 × 10

^{−3}. Crack propagation is shown in two stages of cycling: (

**a**) at N = 25,000 cycles where A, B, C depicts independently initiated cracks; (

**b**) N

_{f}= 37,500 cycles where underwent coalescence of cracks is evident. The estimation of projected surface crack length is outlined.

**Figure 5.**Crack growth at the surface of 304L cycled at ε

_{a}= 4 × 10

^{−3}. Crack propagation is shown in two stages of cycling: (

**a**) at N

_{P1}= 12,000 cycles and (

**b**) at N

_{P2}= 15,100 cycles.

**Figure 6.**Detail of the crack tip vicinity: (

**a**) Sanicro 25—distinct planar character of cyclic plastic deformation; (

**b**) 304L—slip plane markings accompanied with significant surface roughness indicating the occurrence of the strain-induced martensitic transformation (SIMT) within crack plastic zone.

**Figure 10.**Change of elastoplastic J-integral for selected crack lengths in 304L in the case of cyclic test with total strain amplitude ε

_{a}= 0.4%.

**Figure 12.**Fracture surface of Sanicro 25 cycled at ε

_{a}= 0.7%. Three developed cracks are denoted by numbers 1, 2 and 3. Cracks 1 and 3 were used for the comparison of numerically predicted crack front shapes with real crack front shapes, shown in the insets.

**Figure 13.**Fracture surface of 304L cycled at ε

_{a}= 0.4%. Two developed cracks are notable and denoted by numbers 4 and 5. The shapes of both cracks 4 and 5 were used for comparison with numerically predicted crack front shapes.

**Figure 14.**Amplitude of J-integral and amplitude of plastic part of J-integral vs. crack length a for 304L in the case of cyclic test at total strain amplitude ε

_{a}= 0.4%. The data is fitted by the polynomial function, which can be used for the calculation of J-integral (or the plastic part of J-integral) for any particular crack length within the interval from 0.1–2.4 mm.

**Figure 15.**Short crack growth rate vs. J-integral amplitude under cycling with total strain amplitudes ε

_{a}: (

**a**) Sanicro 25, ε

_{a}= 0.25%–0.7%, (

**b**) 304L, ε

_{a}= 0.4%–0.7%.

**Figure 16.**Ratio between plastic part of J-integral and J-integral vs. crack length in (

**a**) Sanicro 25 and (

**b**) 304L.

**Figure 17.**Short crack growth rate vs. plastic part of J-integral amplitude under cycling with total strain amplitude ε

_{a}; (

**a**) Sanicro 25, ε

_{a}= 0.25–0.7%, (

**b**) 304L, ε

_{a}= 0.4–0.7%. All data points are fitted by a black curve.

**Figure 18.**Comparison of the short crack growth rate vs. J

_{a, pl}of Sanicro 25 and 304L steels with previously published data of Eurofer 97 steel [28], 316L steel [16] and duplex 2025 steel [15]. Experimental data of each material include all tested amplitudes merged together. These particular datasets were fitted by the master curve.

**Figure 19.**Comparison of experimentally measured and numerically modeled cyclic stress–strain curves of selected materials.

**Figure 20.**Total strain amplitude ε

_{a}vs. number of cycles required for the crack growth from the length of 0.1 mm to 0.5 mm in (

**a**) Sanicro 25, (

**b**) 304L.

C | Cr | Ni | W | Co | Cu | Mn | Nb | N | Si | Fe |
---|---|---|---|---|---|---|---|---|---|---|

0.1 | 22.5 | 25 | 3.6 | 1.5 | 3 | 0.5 | 0.5 | 0.23 | 0.2 | Bal. |

C | Cr | Ni | Mn | S | P | Si | Fe |
---|---|---|---|---|---|---|---|

0.023 | 18.12 | 8.18 | 1.79 | 0.003 | 0.04 | 0.17 | Bal. |

Sanicro 25 | ||||||||||

ε_{a} (%) | 0.25 | 0.32 | 0.35 | 0.5 | 0.6 | 0.7 | ||||

m_{Jp} | 0.60 | 0.79 | 0.66 | 0.61 | 1.07 | 0.90 | ||||

C_{Jp} | 4.23 × 10^{−7} | 2.13 × 10^{−7} | 4.22 × 10^{−7} | 7.72 × 10^{−7} | 0.65 × 10^{−7} | 2.06 × 10^{−7} | ||||

304L | ||||||||||

ε_{a} (%) | 0.4 | 0.5 | 0.6 | 0.7 | ||||||

m_{Jp} | 0.94 | 1.14 | 1.08 | 0.82 | ||||||

C_{Jp} | 1.57 × 10^{−7} | 0.79 × 10^{−7} | 1.54 × 10^{−7} | 9.23 × 10^{−7} |

C_{Jp} | m_{Jp} | k_{g0} | d | |
---|---|---|---|---|

Sanicro 25 | 1.59 × 10^{−7} | 0.867 | 0.544 | 1.393 |

304L | 9.78 × 10^{−8} | 1.087 | 4191 | 2.8 |

Master Curve | 1.05 × 10^{−7} | 1.072 |

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**MDPI and ACS Style**

Trávníček, L.; Kuběna, I.; Mazánová, V.; Vojtek, T.; Polák, J.; Hutař, P.; Šmíd, M.
Advantageous Description of Short Fatigue Crack Growth Rates in Austenitic Stainless Steels with Distinct Properties. *Metals* **2021**, *11*, 475.
https://doi.org/10.3390/met11030475

**AMA Style**

Trávníček L, Kuběna I, Mazánová V, Vojtek T, Polák J, Hutař P, Šmíd M.
Advantageous Description of Short Fatigue Crack Growth Rates in Austenitic Stainless Steels with Distinct Properties. *Metals*. 2021; 11(3):475.
https://doi.org/10.3390/met11030475

**Chicago/Turabian Style**

Trávníček, Lukáš, Ivo Kuběna, Veronika Mazánová, Tomáš Vojtek, Jaroslav Polák, Pavel Hutař, and Miroslav Šmíd.
2021. "Advantageous Description of Short Fatigue Crack Growth Rates in Austenitic Stainless Steels with Distinct Properties" *Metals* 11, no. 3: 475.
https://doi.org/10.3390/met11030475