# Structural Materials Durability Statistical Assessment Taking into Account Threshold Sensitivity

^{1}

^{2}

^{*}

## Abstract

**:**

_{0}) and top (N

_{k}) of the statistical distribution of the mechanical structural characteristics. For the structural materials alloyed steel 15Cr2MoVA, steel C45 and aluminium alloy D16T1, the statistical distribution of proportional limit, yield strength, ultimate tensile strength, reduction in area, cyclic stress was estimated, as well as the following statistical parameters: mathematical mean, average square deviation, dispersion, asymmetry, variation coefficient, and excess. Purpose: to determine whether the limits of the sensitivity of the statistical distribution of the mechanical characteristics have been computed using the maximum likelihood method. Value: there is a certain upward and downward flattening of the probability curves in the statistical distribution curves of the fatigue test results. This implies that the chosen law of the distribution of random variables has an effect on the appearance of errors. These errors are unacceptable given the importance of accurately determining the reliability and durability of transport means, shipbuilding, machinery, and other important structures. Our results could potentially explain why sensitive limits cannot be applied to the statistical distribution of the mechanical characteristics of structural materials.

## 1. Introduction

- Are there threshold sensitivity measures for statistical distribution in the analysis of mechanical properties of materials?
- Have threshold sensitivity measures for the statistical distribution been used in the statistical processing of low-cycle fatigue tests?
- Can threshold sensitivity measures for the statistical distribution be applied successfully to processing of the results of the tests of mechanical properties of materials?

_{0}(bottom) and N

_{k}(top) for statistical distribution of mechanical properties, (ii) generation of the statistical distribution curves for mechanical parameters, and (iii) verification of the influence of the statistical distribution curves on the statistical distribution parameters of mechanical properties of a structural materials.

## 2. Materials and Methods

#### 2.1. Experiment and Materials

#### 2.2. Review of Sensitivity Calculation Methods

_{0}) is found. This method, however, provides only an approximate threshold sensitivity value.

_{0}value is found, the difference between the end members of rank order for random measure X″ = lg (N – N

_{0}) is determined. The R interval is broken down into 9–15 equal parts, and the number of values is determined for each interval. Then, the values of the three initial h

_{1}, h

_{2}, h

_{3}and third central moment of distribution m

_{3}are determined:

_{0}value is picked, and the calculations are repeated. If m

_{3}> 0, N

_{0}value is increased in the following approximation; if not—reduced. Finally, the sensitivity threshold value is selected, at which the third central moment of random value X″ = lg (N – N

_{0}) becomes equal to zero is selected finally. To speed up the calculation process, it is recommended to create a distribution graph within coordinate system N

_{0}− m

_{3}.

_{p}corresponding by given probability measure P. Normalized random measure:

_{0}selected properly, the difference between the sums of mean square deviations of random measures X″ = lg (N – N

_{0}) and the sums of mean square deviations of the random normalized measure calculated according to Formula (5) will be minimal:

_{0}is calculated based on the equation under the system of three Equation (7):

#### 2.3. Application of Sensitivity Threshold to Statistical Calculations of High-Cycle Fatigue

_{i}has been noted. The probability of failure duration points marked in the coordinate system comprises the upward bent curves. Meanwhile, in the case of the theoretical normal distribution, the points are expected to form straight lines.

_{0}) to statistical calculations has led to reduction in the deviation from the theoretical normal distribution, and the experimental points in the coordinate system P – lg(N

_{i}– N

_{0}) have comprised straight lines. Value N

_{0}is referred to as the lower sensitivity threshold of the statistical distribution corresponding to the minimum number of cycles, at which the material is still likely to fail.

- the scattering of the experimental points has been reduced;
- the statistical distribution curves have become closer to being straight;
- the coefficient of skewness has approached zero, which is characteristic of the normal and logarithmic-normal random measure distribution laws;
- the use of a small number of specimens for the tests results in the errors of calculation of the sensitivity threshold.

_{0}, but also the upper sensitivity threshold N

_{k}. Value N

_{k}is usually higher than N

_{0}by several grades. Where random measure X″ = lg (N

_{i}– N

_{0}) satisfies the logarithmic-normal law of statistical distribution, and N

_{k}is higher than N

_{0}by several grades, then random measure:

_{0}—lower, N

_{k}—upper) for these random values may also be determined under the maximum likelihood method. The maximum likelihood method was proposed by A. Fisher [48] and could be used to identify the lower N

_{0}and upper N

_{k}—values of sensitivity thresholds.

_{0}, N

_{k}then the maximum likelihood function, at its maximum point, shall be maximal L = maximum. In this case, we receive the following:

_{0}and N

_{k}has resulted in four equations with four unknowns:

_{0}and N

_{k}are used. This means that the sensitivity thresholds are the key approximations of the maximum likelihood function. The Least Squares Method has been chosen for greater accuracy compared to the graphical methods; moreover, the Least Squares Method requires performing fewer calculations compared to the Distribution Symmetry Improvement Method.

#### 2.4. Description of the Mathematical Model Function and Algorithms

_{0}, the approximation method has been used. Whereas arithmetic mean $\overline{X}$ and average square deviation σ of the distribution function is impossible to identify unless lower N

_{0}and upper N

_{k}sensitivity thresholds have been identified, the latter shall be calculated at first. The approximation method has been used only for the identification of the lower sensitivity threshold N

_{0}of the statistical distribution.

_{0}and N

_{k}of statistical distribution, a special algorithm has been used and a special Matlab application capable of performing the functions listed below has been designed:

- Calculation of lower sensitivity threshold N
_{0}of statistical distribution under approximation method following the selection of lower sensitivity threshold N_{k}of statistical distribution. - Provides values of Equation (8) for possible solutions of N
_{0}and N_{k}. - Calculates new random measure ${X}^{\u2034}=\frac{{N}_{i}-{N}_{0}}{{N}_{k}-{N}_{i}}$ for each mechanical property.
- Calculates failure probability P for each specimen.
- Calculates statistical parameters $\overline{X}$, σ, σ
^{2}, S, V, and E_{x}of the distribution for mechanical properties of the analysed structural materials.

_{0}shall not exceed the lowest value of the rank order of a mechanical property generated during the tests, and upper sensitivity threshold N

_{k}shall not be lower than the highest value of the rank order of a mechanical property generated during the tests. If not, the calculations made by the application will fail, as random size $\mathrm{ln}\frac{{N}_{i}-{N}_{0}}{{N}_{k}-{N}_{i}}$, in this case, will be a logarithm of a negative number.

_{0}is approached gradually, as lower sensitivity threshold N

_{0}of mechanical properties may occur in the first approximation cycle. Afterward, the calculation of Equation (19) and verification of the results obtained are provided in the algorithm. Where the resulting value is greater than or equal to zero, the verification of whether Equation (19) equals zero is performed. If so, the following equation is calculated, and the respective sensitivity thresholds are generated. In case the condition verified is not equal to zero at the initial sensitivity threshold, another approximation cycle is launched, the calculation is repeated, and verification is performed. At the increase in the lower sensitivity threshold, the interval reduces naturally, and the sought value of lower sensitivity threshold N

_{0}approaches the true value. When solution Equation (19) becomes negative, the MATLAB program returns to the last value of lower sensitivity threshold N

_{0}. Further in the process of calculation, the solution of Equation (19) is found using sensitivity thresholds N

_{0}and N

_{k}. Then, the condition showing that upper sensitivity threshold N

_{k}is the final one is subject to verification. If it is not final, subsequent upper sensitivity threshold N

_{k}is picked from array N

_{k}, and the program is repeated from the start. If the upper sensitivity threshold N

_{k}is final (eleventh, in this case), the calculations are completed. Then, the condition showing that upper sensitivity threshold N

_{k}is the final one is subject to verification. If it is not final, subsequent upper sensitivity threshold N

_{k}is picked from array N

_{k}, and the program is repeated from the start. If the upper sensitivity threshold N

_{k}is final (eleventh, in this case), the calculations are completed.

## 3. Results and Discussion

_{0}and upper N

_{k}sensitivity thresholds have been determined (Table 4) for statistical distribution under the calculation methodology discussed in the above paragraph.

_{pr}, yield strength σ

_{y}, strength limit σ

_{u}, failure resistance S

_{k}, percent area reduction ψ, and percent area reduction at failure ψ

_{u}. Scattering of mechanical properties is determined by: production process factors which determine the metal structure; specimen production process; the test method selected. In statistical investigation of the distribution of mechanical properties, the following three distribution laws are the most common: normal, logarithmic-normal, and Weibull’s. The best distribution of the sum of a fairly large number of independent random values is known to be achieved under the normal law. Hence, the normal distribution law is applied in most papers dealing with statistical investigation. To learn about the variation of statistical characteristics, in particular, the coefficient of skewness, under each distribution law by using the sensitivity threshold measure, all three distribution laws have been applied in the present paper. The following statistical characteristics have been calculated under the normal and logarithmic-normal distribution laws: arithmetic mean, mean square deviation, scattering, the third central moment, coefficient of skewness, and coefficient of variation. Under the methodology provided in reference [38], similar characteristics have been calculated for the Weibull’s distribution. These statistical characteristics have been calculated for two random measures X′ = lgX and X″ = lg(Ni – N

_{0}). The results are provided in Table 5.

_{0}and N

_{k}, for the statistical distribution of the mechanical properties, statistical parameters of the statistical distribution of all mechanical characteristics—statistical distribution skewness S, coefficient of variation V, as well as the kurtosis

**E**—have been observed to develop fairly high values different from zero. This indicates that sensitivity thresholds N

_{x}_{0}and N

_{k}affect agreement of statistical distribution to the logarithmic—normal law instead of supporting the agreement.

_{0}. and N

_{k}already calculated, statistical distribution curves for all the analyzed mechanical properties (σ

_{pr}, σ

_{y}, σ

_{u}, S

_{k}, ψ, ψ

_{u}) of the material have been developed within the coordinates $P-{X}^{\u2034}=\frac{{N}_{i}-{N}_{0}}{{N}_{k}-{N}_{i}}$. The statistical distribution curves are presented in Figure 5 and Figure 6 for steel 15Cr2MoVA, Figure 7 for steel C45 and Figure 8 for aluminum alloy D16T1.

_{pr}, σ

_{y}, σ

_{u}, S

_{k}) for steel 15Cr2MoVA have demonstrated fairly satisfactory conformity to the normal distribution law, good absorption into the straight line within the mean failure probability range, and fit into the 95% probability interval (Figure 5).

_{u}of this type of steel also develop similar characteristics (Figure 6). However, they show a downward or upward bend at low and high probability values, developing the form discussed in the references. Statistical distribution curves for the mechanical properties of steel C45 have demonstrated a similar behaviour (Figure 7). They are fairly good at maintaining the sequence of strength properties (σ

_{pr}, σ

_{y}, σ

_{u}, S

_{k}). Meanwhile, they overlap in the case of steel 15Cr2MoVA.

_{pr}, σ

_{y}, σ

_{u}, S

_{k}) of the analysed structural material steels 15Cr2MoVA, C45, D16T without taking into account the sensitivity thresholds. These statistical distribution curves show a good approximation to the straight-line in the range of low, average, and high probabilities of strength. It could be concluded that sensitivity thresholds N

_{0}and N

_{k}are not characteristic of mechanical properties. The same has been demonstrated by the statistical numeric parameters of the statistical distribution of mechanical properties (skewness S, coefficient of variation V, and kurtosis E

_{x}).

## 4. Conclusions

_{0}and N

_{k}for the statistical distribution, the following conclusions could be drawn:

- Analysis of the graphical representation of the distribution in the probabilistic plot shows that the distribution curves for the random variable X″ are more skewed due to the higher variance. The lower part of the distribution curves for size X′ is more downward skewed. This slightly contradicts the statements in the references that, using a sensitivity threshold, the plots of the statistical distributions must be very close to straight lines. This flattening of the curves can be explained by the value of the sensitivity threshold being very close in value to the first members of the X′ variation series. As a result, the first components of X″ are closer to zero, which causes the curves to flatten.
- Application of the sensitivity threshold measure has led to decrease in the coefficient of skewness down to zero; however, the results have not corresponded to the hypothetical straight-line, unlike expected. This demonstrates that, application of the sensitivity threshold would be unreasonable.
- In the calculation of the statistical characteristics of the Weibull distribution, the coefficient of skewness S
_{k}for the variable measures X′ and X″, the difference between the values is small. This suggests that the Weibull’s distribution is not characteristic of measure X′. - The minimum number of elements of rank order, which still allows a reliable calculation of the sensitivity threshold measure N
_{0}, was different for each material and did not depend directly on the initial number of elements. - Sensitivity thresholds N
_{0}and N_{k}cannot be used for the description of the statistical distribution of mechanical characteristics skewness, coefficient of variation, and kurtosis develop values that are fairly distant from zero, supporting the fact that the statistical distribution moves further from the norm rather than approximating it. - During analysis of the statistical distribution curves for mechanical properties, it has been observed that the application of sensitivity thresholds N
_{0}and N_{k}within the ranges of the average probabilities of statistical distribution has led to a fairly good straight line approximation of the curves, while the curves tend to bend downward and upward in the case of low and high probability values and develop the primal form. - The estimated values of the random variable X‴ (the approximate part of the straight line) belong to the range of 40–60% probability values, allowing 50% acceptance probability values of the random variables to perform further low cycle fatigue calculations.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclature

b | slope of the straight line corresponding to mean square deviation σ; |

e_{pr} | proportional limit strain (%); |

${\overline{e}}_{0}$ | strain of initial (0 semi-cycle) loading normalized to proportional limit strain (%); |

E_{x} | kurtosis; |

F(N) | distribution function; |

F′(N) | distribution function derivative; |

i = 1 … ni | specimen ranks in the rank order; |

h_{1}, h_{2}, h_{3} | initial moments of distribution; |

L | likelihood function; |

m_{3} | the third central moment of statistical distribution; |

n | number of specimens; |

n_{i} | number of values within the j–th interval j = 1...e, e—number of intervals |

N | number of cycles; |

N_{0} | number of cycles bottom threshold sensitivity value; |

N_{f} | number of cycles to failure; |

N_{k} | number of cycles top threshold sensitivity value; |

P | probability; |

Q | sums of mean square deviations; |

R | variation interval; |

S | skewness; |

S_{k} | cyclic stress of k semi-cycle (MPa); |

V | coefficient of variation; |

x | variable; |

x_{j} | j–th interval mean value; |

$\overline{X}$ | arithmetic mean; |

X′, X″, X‴ | random measure value; |

z | normal distribution quantile; |

z_{p} | normalized random measure; |

Greek symbols | |

ψ | percent area reduction (%); |

ψ_{u} | percent area reduction at failure (%) |

σ | statistical distribution standard deviation; |

σ^{2} | dispersion; |

σ_{pr} | proportional limit stress (MPa); |

σ_{y} | yield strength (MPa); |

σ_{ys} | elastic limit or yield strength, the stress at which 0.2% plastic strain occurs (MPa); |

σ_{u} | ultimate tensile stress (MPa); |

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**Figure 1.**Equipment for tensile testing experiment (

**a**), shape and dimension of the specimens for: (

**b**) low—cycle fatigue tension-compression experiments, (

**c**) monotonous tensile experiments (Units in mm).

**Figure 2.**Low cycle fatigue durability curves under strain-controlled loading: 1—aluminium alloy D16T, 2—alloyed steel 15Cr2MoVA, 3—structural steel C45.

**Figure 3.**Statistical distribution curves for mechanical properties of steel 15Cr2MoVA: random value X′ (straight lines) and random value X″ (dashed lines); 1—σ

_{y}, 2—σ

_{pr}, 3—σ

_{u}, 4—S

_{k}.

**Figure 4.**Statistical distribution curves for mechanical properties of steel 15Cr2MoVA: random value X′ (straight lines) and random value X″ (dashed lines); 1—ψ, 2—ψ

_{u}.

**Figure 5.**Statistical distribution curves for the mechanical properties of steel 15Cr2MoVA with identified sensitivity thresholds N

_{0}and N

_{k}(1—σ

_{y}, 2—σ

_{pr}, 3—σ

_{u}, 4—S

_{k}).

**Figure 6.**Statistical distribution curves for the mechanical properties of steel 15Cr2MoVA with identified sensitivity thresholds N

_{0}and N

_{k}(1—ψ, 2—ψ

_{u}).

**Figure 7.**Statistical distribution curves for the mechanical properties of steel C45 with identified sensitivity thresholds N

_{0}and N

_{k}(1—σ

_{y}, 2—σ

_{pr}, 3—σ

_{u}, 4—S

_{k}).

**Figure 8.**Statistical distribution curves for the mechanical properties of steel D16T with identified sensitivity thresholds N

_{0}and N

_{k}(1—σ

_{y}, 2—σ

_{pr}, 3—σ

_{u}, 4—S

_{k}).

**Figure 9.**Statistical distribution curves for the mechanical properties of steel 15Cr2MoVA without adjusting for the sensitivity thresholds N

_{0}and N

_{k}(1—σ

_{y}, 2—σ

_{pr}, 3—σ

_{u}, 4—S

_{k}).

**Figure 10.**Statistical distribution curves for the mechanical properties of steel C45 without adjusting for the sensitivity thresholds N

_{0}and N

_{k}(1—σ

_{y}, 2—σ

_{pr}, 3—σ

_{u}, 4—S

_{k}).

**Figure 11.**Statistical distribution curves for the mechanical properties of steel D16T without adjusting for the sensitivity thresholds N

_{0}and N

_{k}(1—σ

_{y}, 2—σ

_{pr}, 3—σ

_{u}, 4—S

_{k}).

Material | C | Si | Mn | Cr | Ni | Mo | V | S | P | Mg | Cu | Al |
---|---|---|---|---|---|---|---|---|---|---|---|---|

% | ||||||||||||

15Cr2MoVA (GOST 5632-2014) | 0.18 | 0.27 | 0.43 | 2.7 | 0.17 | 0.67 | 0.30 | 0.019 | 0.013 | - | - | - |

C45 (GOST 1050-2013) | 0.46 | 0.28 | 0.63 | 0.18 | 0.22 | - | - | 0.038 | 0.035 | - | - | - |

D16T1 (GOST 4784-97) | - | - | 0.70 | - | - | - | - | - | - | 1.6 | 4.5 | 9.32 |

Material | e_{pr} | σ_{pr} | σ_{ys} | σ_{u} | S_{k} | ψ |
---|---|---|---|---|---|---|

% | MPa | % | ||||

15Cr2MoVA (GOST 5632-2014) | 0.200 | 280 | 400 | 580 | 1560 | 80 |

C45 (GOST 1050-2013) | 0.260 | 340 | 340 | 800 | 1150 | 39 |

D16T1 (GOST 4784-97) | 0.600 | 290 | 350 | 680 | 780 | 14 |

**Table 3.**Low cycle testing programme under strain-controlled loading (${\overline{e}}_{0}$ = constant).

Material | $\mathbf{Loading}\mathbf{Level},{\overline{\mathit{e}}}_{0}$ | Number of Specimens, pcs. |
---|---|---|

15Cr2MoVA | 1.8 | 40 |

3.0 | 80 | |

5.0 | 40 | |

C45 | 2.5 | 60 |

4.0 | 100 | |

6.0 | 60 | |

D16T1 | 1.0 | 20 |

1.5 | 80 | |

2.0 | 20 |

Mechanical Property | Material | N_{0} | N_{k} |
---|---|---|---|

σ_{pr}, MPa | 15Cr2MoVA C45 D16T1 | 184.0 | 410.0 |

206.0 | 510.0 | ||

201.8 | 390.0 | ||

σ_{y}, Mpa | 15Cr2MoVA C45 D16T1 | 276.4 | 550.0 |

206.0 | 510.0 | ||

245.6 | 440.0 | ||

σ_{u}, Mpa | 15Cr2MoVA VA 45 D16T1 | 445.1 | 700.0 |

594.8 | 1000.0 | ||

535.4 | 800.0 | ||

S_{k}, Mpa | 15Cr2MoVA C45 D16T1 | 1153.5 | 2110.0 |

874.0 | 1450.0 | ||

641.7 | 945.0 | ||

ψ, % | 15Cr2MoVA C45 D16T1 | 72.4 | 91.0 |

29.2 | 55.0 | ||

9.1 | 24.0 | ||

ψ_{u}, % | 15Cr2MoVA C45 D16T1 | 5.8 | 25.3 |

9.1 | 35.0 | ||

10.5 | 15.0 |

**Table 5.**Coefficients of skewness for mechanical properties under the statistical distribution laws.

Mechanical Property | Material | Distribution Law | |||||
---|---|---|---|---|---|---|---|

Normal | Logarithmic-Normal | Weibull’s | |||||

X′ | X″ | X′ | X″ | X′ | X″ | ||

σ_{pr}, MPa | 15Cr2MoVA C45 D16T1 | 0.07647 | 0.000038 | −0.3199 | −0.000411 | 0.07793 | 0.07793 |

0.41101 | 0.000127 | 0.05815 | −0.000137 | 0.416676 | 0.416682 | ||

−0.09905 | −0.000008 | −0.2426 | −0.000448 | −0.10158 | −0.010158 | ||

σ_{y}, Mpa | 15Cr2MoVA C45 D16T1 | 0.005413 | 0.000003 | −0.3164 | −0.000427 | 0.005516 | 0.005502 |

0.41101 | 0.000127 | 0.05815 | −0.000137 | 0.416676 | 0.416682 | ||

0.1197 | 0.000092 | −0.1258 | −0.000489 | 0.122715 | 0.122706 | ||

σ_{u}, Mpa | 15Cr2MoVA C45 D16T1 | −0.3332 | −0.000166 | −0.6145 | −0.000658 | −0.3396 | −0.3396 |

−0.322 | −0.000099 | −0.5682 | −0.000316 | −0.326442 | −0.32643 | ||

−0.1403 | −0.000108 | −0.3343 | −0.000743 | −0.143851 | −0.143855 | ||

S_{k}, Mpa | 15Cr2MoVA C45 D16T1 | 0.2425 | 0.000121 | −0.05469 | −0.000387 | 0.247175 | 0.247177 |

−0.1088 | −0.000034 | −0.307 | −0.000274 | −0.110319 | −0.110327 | ||

−0.06094 | −0.000047 | −0.2495 | −0.000671 | −0.062491 | −0.062505 | ||

ψ, % | 15Cr2MoVA C45 D16T1 | 1.096878 | 0.000547 | 0.901323 | −0.000013 | 1.436741 | 1.117773 |

0.224567 | 0.000069 | 0.021761 | −0.000081 | 0.227662 | 0.227669 | ||

0.528782 | 0.000407 | 0.161176 | −0.000074 | 0.542263 | 0.542267 | ||

ψ_{u}, % | 15Cr2MoVA C45 D16T1 | 2.37809 | 0.001186 | 0.916574 | 0.000106 | 2.638781 | 2.423339 |

1.445826 | 0.000446 | 0.24641 | 0.000011 | 2.219523 | 1.465758 | ||

0.071902 | 0.000055 | −0.177563 | −0.000287 | 0.246678 | 0.073743 |

**Table 6.**Statistical properties for mechanical properties of structural materials under the logarithmic-normal law taking into account sensitivity thresholds N

_{0}and N

_{k}.

Property | Material | $\overline{\mathit{X}}$ | σ | D | S | V | E_{x} |
---|---|---|---|---|---|---|---|

σ_{pr}, MPa | 15Cr2MoVA | 0.0145 | 0.4154 | 0.1726 | −0.8310 | −2.0004 | 1.2513 |

C45 | 0.0109 | 0.4380 | 0.1918 | −1.0160 | −2.3199 | 1.8201 | |

D16T1 | 0.0193 | 0.4575 | 0.2093 | −0.1727 | −0.3776 | 0.2053 | |

σ_{y}, Mpa | 15Cr2MoVA | 0.0169 | 0.4411 | 0.1946 | 0.7756 | 1.7582 | 5.0906 |

C45 | 0.0109 | 0.4380 | 0.1918 | −1.0160 | −2.3199 | 1.8201 | |

D16T1 | 0.0199 | 0.4541 | 0.2062 | 0.4916 | 1.0824 | 0.6362 | |

σ_{u}, Mpa | 15Cr2MoVA | 0.0165 | 0.4332 | 0.1877 | 1.3853 | 3.1976 | 1.7565 |

C45 | 0.0117 | 0.4020 | 0.1616 | 0.0496 | 0.1233 | 0.5252 | |

D16T1 | 0.0192 | 0.3350 | 0.1122 | 0.2878 | 0.8591 | 4.6627 | |

S_{k}, Mpa | 115Cr2MoVA | 0.0159 | 0.5068 | 0.2568 | −0.1880 | −0.3709 | 2.0149 |

C45 | 0.0113 | 0.3651 | 0.1333 | −0.5566 | −1.5247 | 2.7141 | |

D16T1 | 0.0188 | 0.3666 | 0.1344 | −0.2374 | −0.6476 | 2.9361 | |

ψ, % | 15Cr2MoVA | 0.0137 | 0.3307 | 0.1093 | −1.1230 | −3.3962 | 6.4751 |

C45 | 0.0111 | 0.4228 | 0.1787 | −0.7040 | −1.6650 | 0.1065 | |

D16T1 | 0.0158 | 0.4902 | 0.2403 | −1.5768 | −3.2166 | 0.4385 | |

ψ_{u}, % | 15Cr2MoVA | 0.0134 | 0.7288 | 0.5312 | −1.1051 | −1.5163 | −0.7647 |

C45 | 0.0081 | 0.7878 | 0.6206 | −1.3378 | −1.6983 | −0.8945 | |

D16T1 | 0.0191 | 0.3477 | 0.1209 | 0.1802 | 0.5183 | 4.2422 |

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**MDPI and ACS Style**

Bazaras, Ž.; Lukoševičius, V.; Bazaraitė, E.
Structural Materials Durability Statistical Assessment Taking into Account Threshold Sensitivity. *Metals* **2022**, *12*, 175.
https://doi.org/10.3390/met12020175

**AMA Style**

Bazaras Ž, Lukoševičius V, Bazaraitė E.
Structural Materials Durability Statistical Assessment Taking into Account Threshold Sensitivity. *Metals*. 2022; 12(2):175.
https://doi.org/10.3390/met12020175

**Chicago/Turabian Style**

Bazaras, Žilvinas, Vaidas Lukoševičius, and Eglė Bazaraitė.
2022. "Structural Materials Durability Statistical Assessment Taking into Account Threshold Sensitivity" *Metals* 12, no. 2: 175.
https://doi.org/10.3390/met12020175