# Probability Assessment of the Mechanical and Low-Cycle Properties of Structural Steels and Aluminium

^{*}

## Abstract

**:**

_{pr}; relative yield strength, σ

_{0.2}; and ultimate tensile stress, σ

_{u}) and strain properties (proportional limit strain, e

_{pr}; percent area reduction, ψ; and percent area reduction at failure, ψ

_{u}). When selecting the key mechanical properties provided in the specifications, an error may be made due to the failure to account for a series of random factors that determine the distribution of properties. The majority of research papers dealing with statistical descriptions of the low-cycle strain properties do not look deeper into the distribution of mechanical properties and the diagram parameters of strain characteristics. This paper provides a description of the distribution patterns of mechanical properties, statistical parameters, and low-cycle fatigue curves. Log-normal distribution generated the lowest values for the coefficient of variation of one of the key statistical indicators, suggesting that log-normal distribution is superior to normal or Weibull distribution in this respect. The distribution of low-cycle strain parameters exceeded the distribution of mechanical properties considerably. Minimum coefficients of variation of the parameters were generated at normal distribution. The statistical analysis showed the lower distribution of the durability parameters compared to the distribution of parameters of the strain diagrams. The findings of the paper enable a revision of the durability and life of the structural elements of in-service facilities subject to elastoplastic loading by assessing the distribution of mechanical characteristics and low-cycle strain parameters as well as the permissible distribution limits.

## 1. Introduction

## 2. Materials and Methods

## 3. Identification of the Key Mechanical Properties and Correlations between Them

_{u}show the largest asymmetry. The coefficient of variation V is one of the key statistical indicators. Its lowest values were obtained using the log-normal distribution. Hence, this distribution may be considered superior to normal or Weibull distribution. It should be noted that the values of both the coefficient of variation and other mechanical properties were similar in the Weibull and normal distribution. The lowest values obtained were those of the ultimate tensile stress σ

_{u}and cyclic stress S

_{k}of k semicycle. The abscissa axis of Figure 5 presents the coefficient of variation of Weibull and normal distribution laws and the ordinate axis—the coefficient of variation of log—normal distribution law.

_{1}depended on the sample size and materials investigated, namely, steel 15Cr2MoVa—1.41; steel C45—1.40; and aluminium alloy D16T1—1.43 [28].

_{0.2}; ultimate tensile stress, σ

_{u}; and relative percent area reduction, ψ. These properties are usually provided in the reference sources.

_{0.2}, σ

_{u}, and ψ) is given in Figure 6, which suggests that the values of the standard properties do not correspond to the experimental and normalised data. High probability is characteristic of the reference properties of the relative yield strength (σ

_{0.2}) of the materials investigated: steel 15Cr2MoVa—74%; steel C45—62%; and aluminium alloy D16T1—90%. Meanwhile, the values of probability of the normalised mechanical properties σ

_{0.2}are considerably lower: steel 15Cr2MoVa—12%; steel C45—7.5%; and aluminium alloy D16T1—8%. Similar results were obtained for the stress (σ

_{u}) indicated in the ultimate strength standards for steel 15Cr2MoVa. The values of reference stress σ

_{u}of steel C45 and aluminium alloy D16T1 corresponded to a probability lower than 1%. Normalised σ

_{u}mechanical properties were: steel 15Cr2MoVa-25%; steel C45—105%; and aluminium alloy D16T1—8%.

_{pr}, σ

_{0.2}, σ

_{u}, S

_{k}, ψ, and ψ

_{u}of the key mechanical properties.

_{u}were seen for steel 15Cr2MoVa and C45. A comparison of the values of mechanical properties σ

_{pr}and σ

_{u}of the same materials showed that, for steel 15Cr2MoVa, the value of the proportionality limits σ

_{pr}of the K coefficient was 26% higher than the ultimate strength σ

_{u}value. This was 35% for steel C45 and 16% for aluminium alloy D16T1. This was related to the considerable distribution of the properties of the proportionality limit. The diagrams of K–s and K–V in Figure 7 show the curves of the materials and mechanical properties investigated, described by the following equations [27].

_{a}values (Table 7) showed that the error Δ

_{a}of determination of the mean value of a random measure had a considerable effect on the number of statistical tests.

_{a}of determination of the mean value of a random measure (equal to 0.01–0.05) showed that the increase in Δ

_{a}to 0.05 led to a 10-fold to 30-fold reduction in the number of specimens. In the same manner, the number of specimens was also affected by the reliability of normal distribution γ. The increase in its value from 0.05 to 0.1 led to a 1.5-fold increase in the number of specimens.

_{k}= constant), the effect was minor and depended on the level of loading. It could be observed in Figure 8 that loading with controlled stress (S

_{k}= constant) was difficult to implement on the absolute coordinates. For steel 15Cr2MoVa, with the load being up to 400 MPa, the strain e varied from 0.2% to 0.4%. Moreover, strain e varied from 0.2% to 4.5%, where loading reached 450 MPa and strain e varied from 0.2% to 11.5%. Where the loading level reached 500 MPa, strain e varied from 0.2% to ∞.

## 4. Statistical Assessment of Low-Cycle Fatigue Curves

_{k}= constant) on the cyclic plastic strain e

_{0}[35,36]:

_{1p}< m and C

_{1p}< ψ. Constants α

_{1p}and C

_{1p}may be determined using the mechanical properties of materials:

_{c}(Figure 9 and Figure 10). The relative values $\overline{{e}_{0}}$ of plastic strain were obtained by dividing the absolute strain values by the proportional limit strain e

_{pr}of the materials.

_{1p}and C

_{1p}with a small number of cycles. With the number of cycles N > 400, the experimental 99% probability curve corresponded to the 50% theoretical curve (Figure 9a). The theoretical curves calculated under the PNAE rules (Figure 9c) fell between the experimental curves. In all the calculations, the resulting arrangement was the reverse. The 99% experimental curve corresponded to the 1% theoretical curve, etc. It could be assumed that this resulted from the dependence of constant α

_{1p}on the relative percent area reduction ψ. According to Table 8, the ratio of proportional limit strain e

_{pr}99% to 1% values was 5.3:1 and for the relative percent area reduction it was 1.2:1. Moreover, the proportional limit strain e

_{pr}values were sensitive to variations in chemical composition, thermal processing technologies, surface hardening, loading conditions, and other factors of the material.

_{k}= constant) in Figure 10a suggests that, in all cases, the resulting curve slope was similar. The theoretically calculated curves were lower than the experimental ones; however, in this case, the probability arrangement of the curves was not the reverse. The 99% to 1% durability curve ratio is 7.1:1 at the relative strain amplitude $\overline{{e}_{0}}$ = 4% calculated by Equation (11), 7.6:1 according to Equation (12), and 10.3:1 according to Equation (12). In this case, with the relative strain amplitude $\overline{{e}_{0}}$ = 2%, the ratios of the durability curves were 8.4:1, 11.7:1, and 5.3:1. Figure 10c suggests that the calculation under the PNAE rules, Equation (15), had the best correspondence with the experimental results.

_{k}= constant) are presented in Figure 11. A comparison of the 99% and 1% probability curves in Figure 11a showed the clear dependence of the low-cycle durability on the strain level. The conducted analysis suggested that the 99% to 1% durability curve ratio was 37:1, where the strain amplitude e

_{0}= 0.3%, and 24:1 where the strain amplitude e

_{0}= 0.18%. The slope of the theoretical curves increased with the increase in the low-cycle failure probability. This could be related to the percent area reduction ψ distribution (Table 3). The $\overline{{e}_{0}}$ distribution band became narrower when relative coordinates were used. The 99% to 1% durability curve ratio was 3.3:1 when the strain amplitude $\overline{{e}_{0}}$ = 4 and 2.7:1 when the strain amplitude $\overline{{e}_{0}}$ = 3. The slope angles were smaller in the relative coordinate curves. Figure 11b presents a comparison of the experimental and theoretical curves. The experimental and theoretical results differed considerably, with the theoretical curves being in the elasticity zone.

## 5. Conclusions

_{pr}, σ

_{0.2}, σ

_{u}, S

_{k}, ψ, and ψ

_{u}) of the materials, coefficient values with minimal variation were found to have been obtained under log-normal distribution. In the case of under loading with controlled strain, the coefficient of variation did not depend on the loading level. An increase in the sample size with loading under controlled strain and controlled stress led to a better correspondence of the statistical series with a normal distribution.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

b | tabular parameter |

c | tabular parameter |

c_{0} | the normalised value of the random measure |

D | dispersion |

e | monotonous strain (%) |

e_{0} | cyclic elastoplastic strain (%) |

e_{k} | cyclic strain of k semicycle (%) |

e_{p} | cyclic plastic strain (%) |

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

e_{y} | cyclic elastic strain (%) |

$\overline{e}$ | normalised cyclic strain (%) |

${\overline{e}}_{0}$ | normalised to proportional limit elastoplastic strain (%) |

K | the ratio of maximum and minimum of the mechanical properties |

k_{b} | tabular parameter |

k_{1} | statistical data density quantile |

m | constant |

m^{3} | the third central moment of distribution |

m_{i} | number of results in the i-th interval |

n | the total number of the results obtained for particular characteristics |

n_{a} | minimum statistical quantity of samples |

n_{int} | quantity of statistical intervals |

N_{c} | number of load cycles until crack initiation |

N_{f} | number of cycles till the cracks propagated to complete fracture |

P | probability |

P_{i} | the density of statistical data |

s | standard deviation |

S | skewness |

S_{k} | cyclic stress of k semicycle (MPa) |

t_{γ}_{1} | Student’s t-distribution |

t_{1-γ/2} | quantile of normal distribution |

x_{i} | random variable |

x_{int} | width of the bins (statistical intervals) |

x_{max} | maximum values of material mechanical properties in the bins (statistical intervals) |

x_{min} | minimum values of material mechanical properties in the bins (statistical intervals) |

${x}_{p}^{L}$ | the lower endpoint of the confidence intervals |

${x}_{p}^{U}$ | the upper endpoint of the confidence intervals |

$\overline{x}$ | sample mean |

V | coefficient of variation |

q_{b} | tabular parameter |

Greek symbols | |

γ | reliability of normal distribution |

Δ_{a} | the error of determination of the mean value of the random variable |

ψ | percent area reduction (%) |

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

µ | arithmetic mean |

σ | monotonic stress (MPa) |

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

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

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

$\overline{\sigma}$ | normalised to proportional limit cyclic stress (MPa) |

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**Figure 1.**Shape and dimensions of the specimens for: (

**a**) low-cycle fatigue tension-compression experiments; (

**b**) monotonous tensile experiments.

**Figure 2.**Histograms of mechanical properties of steel 15Cr2MoVa (1—σ

_{pr}; 2—σ

_{0.2}; 3—σ

_{u}; 4—S

_{k}; 5—ψ; and 6—ψ

_{u}).

**Figure 3.**Histograms of mechanical properties of steel C45 (1—σ

_{pr}; 2—σ

_{u}; 3—S

_{k}; 4—ψ; and 5—ψ

_{u}).

**Figure 4.**Histograms of mechanical properties of aluminium alloy D16T1 (1—σ

_{pr}; 2—σ

_{0.2}; 3—σ

_{u}; 4—S

_{k}; 5—ψ; and 6—ψ

_{u}).

**Figure 5.**Coefficients of variation of mechanical properties (x-axis—normal and Weibull; y-axis—log-normal): 1—σ

_{pr}; 2—σ

_{0.2}; 3—σ

_{u}; 4—S

_{k}; 5—ψ; and 6—ψ

_{u}.

**Figure 6.**Log-normal distribution curves of the proportionality, relative yield, and strength limits: (

**a**) steel 15Cr2MoVa; (

**b**) steel C45; (

**c**) aluminium alloy D16T1 (1—σ

_{pr}; 2—σ0.2; and 3—σ

_{u}); of the stress at failure (

**d**), continuous (

**e**), and percent area reduction at failure (

**f**), 1—steel 15Cr2MoVa; 2—steel C45; 3—aluminium alloy D16T1; —normalised values; —standard values.

**Figure 7.**Dependence of relative value K under the log-normal distribution law on mean square deviation s (

**a**) and coefficient of variation V (

**b**) (1—σ

_{pr}; 2—σ

_{0.2}; 3—σ

_{u}; 4—S

_{k}; 5—ψ; and 6—ψ

_{u}).

**Figure 8.**Strain diagrams. For steel 15Cr2MoVa: (

**a**) on the absolute coordinates σ–e; (

**b**) on the relative coordinates $\overline{\sigma}$–$\overline{e}$ (1 − P = 0.3125%; 2 − P = 99.6875%); steel C45: (

**c**) on the absolute coordinates σ–e; (

**d**) on the relative coordinates $\overline{\sigma}$–$\overline{e}$ (1 − P = 0.23%; 2 − P = 99.77%); for aluminium alloy D16TA: (

**e**) on the absolute coordinates σ–e; (

**f**) on the relative coordinates $\overline{\sigma}$–$\overline{e}$ (1 − P = 0.42%; 2 − P = 99.58%).

**Figure 9.**Experimental (dashed lines) and theoretical (straight lines) curves for 15Cr2MoVa steel under loading with controlled strain (1–7 = analytical probability, 1–99%; 8–14 = experimental probability, 1–99%): (

**a**) according to Coffin dependency (Equation (11)); (

**b**) according to Manson–Langer dependency (Equation (13)); (

**c**) according to PNAE rules (Equation (14)).

**Figure 10.**Comparison of the experimental (dashed lines) and theoretical (straight lines) curves for the C45 steel under loading with controlled strain (1–7 = analytical probability, 1–99%; 8–10 = experimental probability, 1–99%): (

**a**) according to the Coffin dependency (Equation (11)); (

**b**) according to the Manson–Langer dependency (Equation (13)); (

**c**) according to PNAE rules (Equation (14)).

**Figure 11.**Comparison of the theoretical and experimental curves for the D16T1 aluminium alloy under loading with controlled strain (1–7 = analytical probability, 1–99%, straight lines; 8–10 = experimental probability, 1–99%, dashed lines): (

**a**) absolute coordinates; (

**b**) relative coordinates of the theoretical curve according to the Coffin dependency (Equation (11)).

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_{0.2} | 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 |

Mechanical Property | Material | Normal | Log-Normal | Weibull | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

$\overline{\mathit{x}}$ | s | D | S | V | $\overline{\mathit{x}}$ | s | D | S | V | $\overline{\mathit{x}}$ | s | S | V | ||

σ_{pr}, MPa | 15Cr2MoVa | 287 | 42 | 1764 | 0.080 | 0.146 | 284 | 0.0649 | 0.0042 | −0.301 | 0.026 | 287 | 42 | 0.081 | 0.146 |

45 | 325 | 52 | 2704 | 0.410 | 0.160 | 321 | 0.0688 | 0.0047 | 0.074 | 0.027 | 325 | 52 | 0.419 | 0.159 | |

D16T1 | 292 | 40 | 1600 | −0.043 | 0.136 | 290 | 0.0609 | 0.0037 | −0.263 | 0.025 | 292 | 40 | −0.043 | 0.138 | |

σ_{0.2}, MPa | 15Cr2MoVa | 414 | 53 | 2809 | 0.002 | 0.128 | 410 | 0.0571 | 0.0032 | −0.299 | 0.022 | 414 | 53 | 0.002 | 0.129 |

45 | 325 | 52 | 2704 | 0.410 | 0.160 | 321 | 0.0688 | 0.0047 | 0.073 | 0.027 | 325 | 52 | 0.418 | 0.159 | |

D16T1 | 346 | 41 | 1681 | 0.011 | 0.118 | 343 | 0.0513 | 0.0026 | 0.117 | 0.020 | 346 | 41 | 0.023 | 0.117 | |

σ_{u}, MPa | 15Cr2MoVa | 602 | 42 | 1764 | −0.491 | 0.069 | 600 | 0.0315 | 0.0009 | −0.828 | 0.011 | 602 | 42 | −0.499 | 0.070 |

45 | 811 | 77 | 5929 | −0.033 | 0.095 | 806 | 0.0423 | 0.0018 | −0.558 | 0.015 | 811 | 77 | −0.340 | 0.095 | |

D16T1 | 677 | 41 | 1681 | −0.141 | 0.061 | 676 | 0.0267 | 0.0007 | −0.308 | 0.009 | 677 | 41 | −0.142 | 0.061 | |

S_{k}, MPa | 15Cr2MoVa | 1585 | 201 | 40,401 | 0.240 | 0.127 | 1571 | 0.0551 | 0.0030 | −0.033 | 0.017 | 1585 | 201 | 0.246 | 0.127 |

45 | 1154 | 100 | 10,000 | −0.110 | 0.087 | 1149 | 0.0381 | 0.0014 | −0.278 | 0.012 | 1154 | 100 | −0.112 | 0.087 | |

D16T1 | 793 | 52 | 2704 | −0.061 | 0.066 | 791 | 0.0287 | 0.0008 | −0.218 | 0.010 | 793 | 52 | −0.062 | 0.066 | |

ψ, % | 15Cr2MoVa | 80.12 | 2.41 | 5.86 | 1.451 | 0.030 | 80.03 | 0.0129 | 0.0002 | 1.186 | 0.007 | 79.60 | 2.42 | 1.478 | 0.032 |

45 | 41.05 | 5.18 | 26.86 | 0.225 | 0.126 | 40.68 | 0.0548 | 0.0029 | 0.045 | 0.034 | 41.05 | 5.18 | 0.228 | 0.126 | |

D16T1 | 14.59 | 2.58 | 6.64 | 0.529 | 0.177 | 14.36 | 0.0754 | 0.0057 | 0.168 | 0.065 | 14.59 | 2.58 | 0.542 | 0.177 | |

ψ _{u}, % | 15Cr2MoVa | 10.16 | 5.56 | 6.58 | 2.432 | 0.252 | 9.90 | 0.0945 | 0.0089 | 0.995 | 0.095 | 8.19 | 2.56 | 0.248 | 0.313 |

45 | 14.18 | 2.77 | 7.67 | 1.446 | 0.195 | 13.92 | 0.0807 | 0.0065 | 0.258 | 0.071 | 12.75 | 2.77 | 1.466 | 0.217 | |

D16T1 | 12.84 | 0.71 | 0.51 | 0.071 | 0.055 | 12.82 | 0.0241 | 0.0006 | −0.168 | 0.022 | 12.80 | 0.71 | 0.073 | 0.056 |

Material Property | p | 15Cr2MoVa | C45 | D16T1 | |||
---|---|---|---|---|---|---|---|

${\mathit{x}}_{\mathit{p}}^{\mathit{U}}$ | ${\mathit{x}}_{\mathit{p}}^{\mathit{L}}$ | ${\mathit{x}}_{\mathit{p}}^{\mathit{U}}$ | ${\mathit{x}}_{\mathit{p}}^{\mathit{L}}$ | ${\mathit{x}}_{\mathit{p}}^{\mathit{U}}$ | ${\mathit{x}}_{\mathit{p}}^{\mathit{L}}$ | ||

σ_{pr}, MPa | 0.01 | 277.9 | 277.4 | 313.4 | 312.8 | 284.5 | 283.9 |

0.50 | 284.4 | 283.8 | 321.4 | 320.8 | 290.1 | 289.6 | |

0.99 | 290.9 | 290.3 | 329.7 | 329.1 | 296.1 | 295.5 | |

σ_{0.2}, MPa | 0.01 | 403.4 | 402.7 | 313.4 | 312.8 | 338.9 | 338.4 |

0.50 | 410.5 | 409.8 | 321.4 | 320.8 | 343.7 | 343.3 | |

0.99 | 417.7 | 417.0 | 329.7 | 329.1 | 348.6 | 348.1 | |

σ_{u}, MPa | 0.01 | 596.7 | 596.4 | 798.3 | 797.7 | 673.3 | 673.0 |

0.50 | 600.4 | 599.6 | 806.2 | 805.4 | 676.2 | 675.6 | |

0.99 | 603.1 | 602.7 | 813.7 | 813.1 | 678.4 | 678.2 | |

S_{k}, MPa | 0.01 | 1546.9 | 1544.8 | 1140.2 | 1139.5 | 787.7 | 787.4 |

0.50 | 1572.3 | 1570.1 | 1149.1 | 1148.4 | 791.2 | 790.8 | |

0.99 | 1598.0 | 1595.8 | 1158.8 | 1157.4 | 794.7 | 794.4 | |

ψ, % | 0.01 | 79.96 | 79.94 | 40.05 | 40.01 | 13.95 | 13.91 |

0.50 | 80.04 | 80.02 | 40.70 | 40.66 | 14.38 | 14.34 | |

0.99 | 80.10 | 80.08 | 41.36 | 41.32 | 14.83 | 14.78 | |

ψ_{u}, % | 0.01 | 9.45 | 9.42 | 13.46 | 13.42 | 12.78 | 12.76 |

0.50 | 9.92 | 9.87 | 13.94 | 13.90 | 12.83 | 12.81 | |

0.99 | 10.41 | 10.36 | 14.44 | 14.39 | 12.87 | 12.85 |

Mechanical Properties | c_{0} | ||
---|---|---|---|

15Cr2MoVa | C45 | D16T1 | |

σ_{pr}, MPa | 228 | 253 | 235 |

σ_{0.2}, MPa | 339 | 253 | 288 |

σ_{u}, MPa | 542 | 703 | 618 |

S_{k}, MPa | 1302 | 1014 | 719 |

ψ, % | 76.72 | 33.79 | 10.90 |

ψ_{u}, % | 6.58 | 10.30 | 11.82 |

Material | σ_{pr} | σ_{0.2} | σ_{u} | S_{k} | ψ | ψ_{u} |
---|---|---|---|---|---|---|

MPA | % | |||||

15Cr2MoVa | 2.06 | 1.88 | 1.52 | 1.78 | 1.24 | 4.19 |

C45 | 2.41 | 2.41 | 1.57 | 1.62 | 1.71 | 3.09 |

D16T1 | 1.72 | 1.66 | 1.45 | 1.43 | 2.24 | 1.38 |

Mechanical Characteristic | Material | Δ_{a} | |||||
---|---|---|---|---|---|---|---|

0.01 | 0.03 | 0.05 | |||||

γ | |||||||

0.05 | 0.10 | 0.05 | 0.10 | 0.05 | 0.10 | ||

σ_{pr}, MPa | 15Cr2MoVa | 819 | 573 | 47 | 33 | 33 | 23 |

C45 | 984 | 689 | 110 | 77 | 39 | 28 | |

D16T1 | 709 | 497 | 78 | 55 | 28 | 20 | |

σ_{0.2}, MPa | 15Cr2MoVa | 629 | 440 | 71 | 49 | 25 | 18 |

C45 | 984 | 689 | 110 | 77 | 39 | 28 | |

D16T1 | 535 | 375 | 59 | 41 | 21 | 15 | |

σ_{u}, MPa | 15Cr2MoVa | 182 | 128 | 20 | 14 | 7 | 5 |

C45 | 347 | 243 | 39 | 27 | 14 | 10 | |

D16T1 | 139 | 97 | 16 | 11 | 6 | 4 | |

S_{k}, MPa | 15Cr2MoVa | 619 | 434 | 69 | 48 | 25 | 17 |

C45 | 290 | 203 | 31 | 22 | 12 | 8 | |

D16T1 | 167 | 117 | 18 | 12 | 7 | 5 | |

ψ, % | 15Cr2MoVa | 35 | 25 | 4 | 3 | 1 | 1 |

C45 | 609 | 427 | 69 | 48 | 24 | 17 | |

D16T1 | 1203 | 842 | 133 | 93 | 48 | 34 | |

ψ_{u}, % | 15Cr2MoVa | 2440 | 1708 | 18,286 | 200 | 98 | 68 |

C45 | 1460 | 1022 | 162 | 114 | 58 | 41 | |

D16T1 | 116 | 81 | 14 | 10 | 5 | 3 |

Mechanical Property | Material | Probability, % | ||||||
---|---|---|---|---|---|---|---|---|

1 | 10 | 30 | 50 | 70 | 90 | 99 | ||

σ_{0.2}, MPa | 15Cr2MoVa | 300 | 340 | 370 | 400 | 430 | 475 | 535 |

C45 | 220 | 265 | 300 | 340 | 360 | 420 | 500 | |

D16T1 | 260 | 300 | 320 | 350 | 370 | 405 | 460 | |

σ_{u}, MPa | 15Cr2MoVa | 500 | 530 | 560 | 580 | 600 | 640 | 680 |

C45 | 620 | 700 | 750 | 800 | 850 | 900 | 1020 | |

D16T1 | 580 | 620 | 650 | 680 | 700 | 750 | 800 | |

ψ, % | 15Cr2MoVa | 74 | 76 | 79 | 80 | 82 | 85 | 90 |

C45 | 28 | 32 | 37 | 39 | 42 | 47 | 54 | |

D16T1 | 9.5 | 11.3 | 12.8 | 14.0 | 15.5 | 17.5 | 21.0 | |

e_{pr}, % | 15Cr2MoVa | 0090 | 0130 | 0170 | 0200 | 0245 | 0320 | 0475 |

C45 | 0140 | 0180 | 0225 | 0260 | 0300 | 0360 | 0480 | |

D16T1 | 0.46 | 0.52 | 0.56 | 0.60 | 0.64 | 0.70 | 0.78 |

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## Share and Cite

**MDPI and ACS Style**

Bazaras, Ž.; Lukoševičius, V.; Vilkauskas, A.; Česnavičius, R.
Probability Assessment of the Mechanical and Low-Cycle Properties of Structural Steels and Aluminium. *Metals* **2021**, *11*, 918.
https://doi.org/10.3390/met11060918

**AMA Style**

Bazaras Ž, Lukoševičius V, Vilkauskas A, Česnavičius R.
Probability Assessment of the Mechanical and Low-Cycle Properties of Structural Steels and Aluminium. *Metals*. 2021; 11(6):918.
https://doi.org/10.3390/met11060918

**Chicago/Turabian Style**

Bazaras, Žilvinas, Vaidas Lukoševičius, Andrius Vilkauskas, and Ramūnas Česnavičius.
2021. "Probability Assessment of the Mechanical and Low-Cycle Properties of Structural Steels and Aluminium" *Metals* 11, no. 6: 918.
https://doi.org/10.3390/met11060918