Statistical Properties of Low-Cycle Fatigue Data of Type 316L Stainless Steel

Sae-Hee Oh; Seon-Jin Kim

doi:10.26748/KSOE.2025.023

J. Ocean Eng. Technol. > Volume 39(3); 2025 > Article

Oh and Kim: Statistical Properties of Low-Cycle Fatigue Data of Type 316L Stainless Steel

Original Research Article

J. Ocean Eng. Technol. June 2025; 39(3): 308-316.

Available online: June 25, 2025

DOI: https://doi.org/10.26748/KSOE.2025.023

Statistical Properties of Low-Cycle Fatigue Data of Type 316L Stainless Steel

Sae-Hee Oh^1,²

and Seon-Jin Kim³

¹Graduate Student, Department of Mechanical Design Engineering, Graduate School, Pukyong National University, Busan, Korea

²Associate Professor, Department of Mechanical System, Ulsan Campus, Korea Polytechnics, Ulasn, Korea

³Professor, School of Mechanical Engineering, Pukyong National University, Busan, Korea

Corresponding author Seon-Jin Kim: +82-51-629-6163, sjkim@pknu.ac.kr

Received May 13, 2025 Revised May 28, 2025 Accepted May 28, 2025

Open access / Under a Creative Commons License

Keywords: Type 316L stainless steel, low-cycle fatigue, statistical properties, fatigue life, coefficient of variation

Abstract

It is well recognized that scatter exists in experimental low-cycle fatigue (LCF) data obtained under a constant-strain amplitude loading condition. The objective of this study is to investigate the statistical variability of LCF data of hot-rolled 316L stainless steel at room temperature (RT). Strain-controlled LCF tests were performed at RT. A triangular waveform was used for fatigue testing with a constant strain rate of 4 × 10⁻³/s and strain amplitude of ± 0.4. RT LCF specimens exhibited remarkable softening behavior followed by initial cyclic hardening. The coefficient of variation (COV) for LCF property data, such as tensile stress, compressive stress, stress range, and elastic modulus in the 1^st and half-life cycles, was 0.7%–6.2%. However, the COV of fatigue life was 20%. Additionally, the fatigue life followed a two-parameter Weibull distribution. The estimated shape and scale parameters were 6.12 and 8471 cycles, respectively. It was found that fatigue life had greater scatter than other LCF property data.

1. Introduction

Type 316L austenitic stainless steel is a promising material for various industrial applications, ranging from the marine industry to the nuclear power industry, because of its excellent mechanical properties and high corrosion resistance (Hong et al., 2007; Unigovski et al., 2009; Pham et al., 2011; Pelegatti et al., 2021). Owing to its excellent manufacturability and weldability, it has been widely used in the broad temperature range from cryogenic to high temperatures and under various operating conditions (Nam et al., 2003; Xie et al., 2019; Chen et al., 2022; Yin et al., 2023).

Low-cycle fatigue (LCF) is one of the common loading conditions that structural members experience during use (Harlow, 2014). Understanding material properties that affect service performance, particularly cyclic deformation response behavior, is important for life design and structural integrity evaluation. In this regard, researchers have investigated the LCF of Type 316L austenitic stainless steel. Most of these studies were conducted over the temperature range of −196 to 700 °C in the uniaxial tension–compression loading mode (Vogt et al., 1991; Polak et al., 1994; Alaim et al., 1997; Srinivasan et al., 1999; Hong et al., 2003; Hong and Lee, 2004; Kang et al., 2010; Pham et al., 2011; Pham et al., 2013; Pham and Holdsworth, 2013; Hormozi et al., 2015; Xie et al., 2019; Pelegatti et al., 2021; Ha et al., 2022a; Ha et al., 2022b; Yin et al., 2023). Studies have also been conducted on LCF behavior in the multiaxial loading mode (Mazanova et al., 2017; Poczklan et al., 2023; Liang et al., 2025). Alaim et al. (1997) investigated the LCF behavior of Type 316L stainless steel in the temperature range of 20–600 °C. According to their results, the fatigue resistance significantly increased in the medium temperature range (200–500 °C) owing to dynamic strain aging, and the maximum fatigue life was observed at 300 °C. In this temperature range, secondary repeated hardening behavior occurred. Similarly, Hong et al. (2003) examined the impact of temperature on the LCF behavior of cold-worked 316L stainless steel and found that dynamic strain aging occurred in the temperature range of 300–600 °C. According to their research results, it is important to select appropriate life-prediction parameters because stress and strain significantly depend on temperature. Pham et al. (2013) and Pham and Holdsworth (2013) performed strain-controlled LCF experiments on AISI 316L stainless steel at room temperature (RT) and 300 °C and reported the complexity of the cyclic deformation behavior of the material. In other words, the cyclic hardening that occurs first is followed by cyclic softening and largely concludes with the stabilized response stage. Of course, such cyclic deformation behavior generally depends on the strain amplitude, even under a constant temperature and strain rate (Ha et al., 2022a; Oh and Kim, 2024). The cyclic deformation behavior of polycrystal materials is known to be complex for materials whose dislocations tend to occur in a planar manner under cyclic loading (Sauzay, 2008; Pham et al., 2013). In addition, the research results of Pham et al. (2013) and Pham and Holdsworth (2013) provided a basis for the development of physically based constitutive modeling that accurately represents the complex cyclic deformation responses of materials. They examined the role of microstructural conditions in crack initiation. Moreover, Xie et al. (2019) identified the cyclic hardening–cyclic softening behavior of Type 316L stainless steel through LCF experiments at RT and 650 °C and employed damage-coupled cyclic elastic–viscoplastic constitutive modeling to predict the behavior of the material. Furthermore, many researchers have studied the LCF behavior of Type 316L stainless steel. In most previous studies, the maximum temperature was 650 °C, and there are no experimental results for the LCF behavior at 700 °C, which is the design temperature of large-capacity high-temperature thermal energy storage system. Thus, strain-controlled LCF experiments of Type 316L stainless steel were performed at a high temperature of 700 °C, and fatigue life was evaluated using fatigue behavior and the Coffin–Manson–Basquin model (Ha et al., 2022a). Additionally, LCF experiments of the Type 316L stainless steel collected from two heats were performed at a high temperature of 700 °C to obtain experimental data and related design parameters (Ha et al., 2022b). In most of the aforementioned studies, the LCF characteristics were evaluated, analyzed, and modeled using the average values of one or more experimental data under constant-LCF load test conditions.

However, it is widely known that scatter (or variability) inevitably exists in LCF behavior and fatigue life (Kandil and Dyson, 1993a; Kandil and Dyson, 1993b; Dyson, 1995; Rao et al., 1996; Schijve, 2008; Schmitz et al., 2013; Zhao et al., 2000). Therefore, researchers have examined the statistical aspect of LCF behavior and fatigue life (Dyson, 1995; Sekhar et al., 2021; Bazaras and Lukosevicius, 2022). Understanding the statistical variability of LCF property data is crucial for ensuring the reliability and safety of structural members subjected to cyclic loading. However, there are few studies that systematically examined the statistical variability of LCF property data for hot-rolled Type 316L stainless steel (Oh and Kim, 2024). Oh and Kim (2024) carefully conducted LCF tests in the air at a high temperature of 700 °C and under constant strain amplitude and strain rate conditions for hot-rolled Type 31L stainless steel to investigate the cyclic deformation behavior and the statistical properties of LCF property data at a high temperature. No study has investigated the statistical variability of the LCF property data for the target material of this study at RT.

As such, in the present study, fully reversed continuous strain-controlled LCF tests were carefully conducted in the air at RT and under constant strain rate and strain amplitude loading conditions using 10 specimens to understand the statistical variability of the LCF property data of hot-rolled Type 316L stainless steel at a high temperature and RT. In addition, the cyclic deformation behavior and statistical variability of LCF property data at RT were investigated.

2. Materials and Experimental Method

2.1 Materials

The material used in this study was a 25-mm-thick hot-rolled Type 316L stainless-steel plate of the same heat (No. 17SD62158) from company D in Korea. It was subjected to water cooling at 1040 °C after solution annealing treatment. Its microstructure is presented in Fig. 1. As shown, the stainless steel plate exhibited a typical single-phase coarse equiaxed austenitic microstructure, and annealing twins were observed. The average grain size calculated through the American Society for Testing and Materials (ASTM) intercept method (ASTM, 2021) was approximately 107 μm (ASTM grain size number, G = 3.5).

The chemical composition and mechanical properties of the material used in this study are presented in Tables 1 and 2. As shown, the content of each element in Table 1 meets the chemical composition requirement range of ASME/BPVC-SEC II-A-1 (ASME/BPVC, 2003). In addition, the content of each element presented in RCC-MRx III Tome 2 (AFCEN, 2018) is stricter compared than the ASME range, as indicated by the table. In particular, the content ranges of Cr and Ni, which affect corrosivity, manufacturability, and weldability, are more strictly restricted. For the Type 316L stainless steel used in this study, Ni and Mo slightly exceeded the RCC-MRx chemical composition requirements, but values at similar levels were observed.

2.2 Specimens and Experimental Method

For fatigue tests, button head-type cylindrical specimens were prepared from the material plate of the same heat. For the specimens, cutting was performed so that the rolling direction coincided with the loading direction. Fig. 2 shows the shape and dimensions of the cylindrical fatigue specimens used in this study. The shape and dimensions were precisely fabricated in accordance with the ASTM E606 standard (ASTM, 2021). The surfaces of all the specimens were polished so that the parallel section’s average roughness, i.e., the arithmetic average roughness and 10-point mean roughness, were 0.05 and ≤0.35 μm, respectively, to minimize the effect of surface roughness on the dispersion of fatigue property data.

Table 3 presents the conditions of the LCF testing at RT conducted in this study. Fully reversed continuous strain-controlled LCF tests were conducted in accordance with the ASTM E606/E606M standard (ASTM, 2021) for 10 specimens (K_OH10, K_OH11, K_OH12, K_OH13, K_OH14, K_OH15, K_OH16, K_OH18, K_OH19, and K_OH21) in the air at RT and under constant strain amplitude (±0.4%) and strain rate (4×10⁻³/s (0.4%/s)) conditions. MTS’s servo-hydraulic dynamic fatigue testing machine with a maximum load of 100 kN (MTS 370.10) was used. In addition, MTS’s 632.26F-40 model with a gauge length of 12 mm was used as the extensometer for strain control and data acquisition. In this study, the fatigue life was defined as the number of loading cycles at which the stress level decreased by 20%, as reported by Wright et al. (2013).

2.3 Analysis Method

Measurands must be defined to examine the statistical variability of LCF property data at RT, which is the purpose of this study. Although there are many parameters used in strain-controlled LCF testing (Kandil, 2000), in this study, however, 12 measurands were evaluated, as shown in Table 4. Various factors affect the dispersion of these measurands (Kandil, 2000). To consider the variability of fatigue property data due to material inhomogeneity, the experiments in this study were designed to minimize the impact of measurements (e.g., specimen diameter, specimen surface roughness, fatigue load control precision, environment, axial alignment, and experimenters’ techniques) on uncertainty.

3. Results and Discussion

3.1 Cyclic Deformation Response Behavior

Fig. 3 shows the cyclic deformation response behavior of the material at RT for the K-OH10 specimen as an example. Fig. 3(a) shows the relationship between the number of cycles and the peak/valley stresses, while Fig. 3(b) shows the relationship between the number of cycles and the stress amplitude. Under the experimental conditions of this study, the cyclic deformation response behavior of Type 316L stainless steel can be clearly distinguished into three regions, as shown in Fig. 3. In the first region, cyclic hardening with increasing stress occurs for the initial dozens of cycles (approximately N = 20 to 30) (Stage 1). In the second region, cyclic softening with slowly decreasing stress occurs as the number of cycles increases (Stage 2). This region represents most of the LCF life. Finally, in the third region, the occurrence and propagation of microcracks lead to accelerated softening, resulting in failure (Stage 3). These patterns were observed for all the specimens used in this study. Such cyclic deformation response behavior is consistent with the experimental results of Pham and Holdsworth (2013) and Xie et al. (2019) at RT and a strain amplitude of ±0.4%. Compared with the cyclic deformation response behavior at 700 °C from previous study (Oh and Kim, 2024), however, there was a significant difference in cyclic deformation behavior at RT and a high temperature. In other words, at a high temperature, a region with initial cyclic hardening (Stage 1), a subsequent saturation region that represents most of the life (Stage 2), and a region that reached failure owing to the accelerated softening caused by the propagation of microcracks (Stage 3) were observed. This is because the mechanical behavior of the material causes different fatigue mechanisms at various temperatures (Kang et al., 2010; Pham et al., 2013; Xie et al., 2019).

3.2 Statistical Properties of Measurands

Fig. 4 shows the stress amplitude for 10 specimens obtained from the LCF tests of this study as a function of the number of cycles. Each specimen had different stress amplitudes even at the same number of cycles, and there was also variability in the fatigue life. As mentioned in Section 2.3, there are various measurands for LCF tests, but the statistical properties of the 12 fatigue property data presented in Table 4 were examined in this study.

3.2.1 Statistical properties of fatigue life

Fig. 5 shows the inter-specimen scatter of the fatigue life (N_f ) for the 10 LCF specimens (K_OH10 to K_OH21) under the experimental conditions of this study. Clearly, there was variability in the fatigue life even in the strain-controlled LCF experiment under the same conditions. The statistical properties for the fatigue life in the experiment are presented in Table 5. The coefficient of variation (COV) of the fatigue life at RT is 0.1932, which is approximately 20%. It is approximately 10% higher than the COV of the fatigue life at a high temperature of 700 °C from the authors’ previous study (Oh and Kim, 2024). This appears to be because the potential inhomogeneity decreased at the high temperature owing to material averaging.

Fatigue life can be treated as a random variable that reflects the potential uncertainty caused by the inhomogeneity of the material. The Weibull distribution is widely used to evaluate the variability of fatigue life (Mohd et al., 2012). In this study, the following two-parameter Weibull distribution function was also used to evaluate the variability of LCF life.

(1)

F(Nf)=1-exp[-(Nfβ)α]

Here, F (N_f ) is the probability distribution function of the two-parameter Weibull distribution, and N_f is the fatigue life, i.e., the number of cycles to failure. α and β are the shape parameter and scale parameter, respectively.

Fig. 6 shows the LCF life of Type 316L stainless steel at RT acquired in this study, plotted on Weibull probability paper by obtaining the probability (unreliability) of each rank assessed via the median rank method. In addition, the parameters of the two-parameter Weibull distribution were obtained using the Weibull++6 software based on the maximum likelihood method. The straight line in Fig. 6 is drawn using the maximum likelihood method. The probability distribution of the LCF life of Type 316L stainless steel obtained under the experimental conditions of this study can be expressed as follows. In other words, 6.12 and 8471 were obtained for α and β, respectively. This indicated that the fatigue life of the material at RT followed the two-parameter Weibull probability distribution well.

(2)

F(Nf)=1-exp[-(Nf8471)6.12]

3.2.2 Statistical properties of measurands at 1st cycle

Fig. 7 shows an example (K_OH10 specimen) of the hysteresis loop for the 1^st cycle. In the figure, the definitions of the measurands obtained from the 1^st cycle, i.e., tensile stress σ1T, compressive stress σ1C, stress range Δσ₁, and elastic modulus E₀, can be seen. Table 6 presents the experimental results of the measurands for 10 specimens obtained from the 1^st cycle. In addition, the statistical analysis results for the measurands are summarized in Table 7. According to the experimental results, the statistical variability of the LCF property data at the 1^st cycle is very low, as the COV is approximately 2% or less. In particular, the COV of the elastic modulus E₀ is 0.72%, which is approximately twice as low as the COVs of other measurands. In other words, the repeatability of the measurands at the 1^st cycle was excellent.

3.2.3 Statistical properties of measurands at half-life cycle

Fig. 8 shows an example (K_OH10 specimen) of the hysteresis loop for the half-life cycle. In the figure, the definitions of the measurands obtained from the half-life cycle, i.e., tensile stress σhT, compressive stress σhC, stress range Δσ, elastic strain range Δε_e, plastic strain range Δε_p, unloading elastic modulus E₁, and loading elastic modulus E₂, can be seen. Table 8 presents the experimental results of the measurands for 10 specimens obtained from the half-life cycle. The data indicate the inter-specimen scatter of the measurands of LCF properties. The statistical analysis results for the measurands are summarized in Table 9. The experimental results indicate that COV is approximately 3% for the statistical variability of the LCF property data at the half-life cycle, except for the elastic modulus. The COVs of the elastic modulus E₁ and E₂ at the half-life cycle were 6.2% and 3.9%, respectively, which were approximately twice the COVs of other LCF measurands. As shown in Table 9, the repeatability of the measurands at the half-life cycle was excellent.

3.3 Discussion of Experimental Results

The aforementioned results confirm that the scatter of the fatigue life of Type 316L stainless steel at RT exceeds that of other LCF property data. Meanwhile, the variability of the measurands of the LCF property data at RT examined in this study is summarized along with previous experimental results at a high temperature of 700 °C (Oh and Kim, 2024) in Fig. 9. As shown, the COVs of all the measurands of LCF properties, except for measurands 10 and 12, are approximately 3% at RT (black lines in the figure). This scatter exhibits almost the same degree of order as that of the static tensile strength, yield strength, and elastic modulus, indicating that the repeatability of LCF property data at RT is excellent, except for fatigue life. At a high temperature of 700 °C (red lines in the figure), the COVs of the measurands of LCF property data exhibited different results from those at RT. Specifically, the COVs of all the measurands at the high temperature exceeded those at RT, except for measurands 5, 6, 7, and 12. In particular, the COVs of the elastic modulus E₀ at the 1^st cycle and the elastic modulus E₁ and E₂ at the half-life cycle were significantly higher than those at RT. This is attributed to the uncertainty of strain measurement by the contact between the ceramic rod-type high-temperature extensometer and the specimens in the high-temperature LCF experiment, even though various factors affect uncertainty. Meanwhile, the COV of the LCF life of the material at RT was approximately 20%, which was approximately twice that (10%) at a high temperature of 700 °C (Oh and Kim, 2024). It was found that the variability of fatigue life can be evaluated using the two-parameter Weibull distribution.

Because the LCF life resulting from different heats, different manufacturing methods, or round-robin tests is likely to exhibit a higher COV (Dyson, 1995), more attention is required for design. It was also found that the COVs of LCF property data, including fatigue life, differ between RT and a high temperature. In particular, when the variability of the measurands of LCF properties at a high temperature is examined, it is necessary to consider the effects of uncertainty.

4. Conclusions

(1) The cyclic deformation response behavior of the target material at RT can be clearly divided into three regions. In the first region, cyclic hardening with increasing stress occurred for the initial dozens of cycles (Stage 1). In the second region, cyclic softening with slowly decreasing stress occurs as the number of cycles increases (Stage 2). Finally, in the third region, the occurrence and propagation of microcracks lead to accelerated softening, resulting in failure (Stage 3).
(2) The COV of the LCF life of the material at RT was 20%. Additionally, the fatigue life followed the two-parameter Weibull probability distribution well, and values of 6.12 and 8471 were obtained for α and β, respectively.
(3) The COVs of tensile stress, compressive stress, stress range, and elastic modulus at the 1^st cycle were <2%.
(4) The COVs of tensile stress, compressive stress, stress range, elastic strain range, and plastic strain range at the half-life cycle were ≤3%. The COVs of the elastic modulus E₁ and E₂ at the half-life cycle, however, were 6.2 and 3.9%, respectively, which were approximately twice those of other LCF measurands.
(5) It was found that the COVs of LCF property data, including fatigue life, differ between RT and a high temperature.

Conflict of Interest

No potential conflict of interest relevant to this article is reported.

Funding

This work was supported by a Research Grant of Pukyong National University (2025).

Fig. 1

Microstructure of the as-received hot-rolled Type 316L stainless steel plate used in this study (200×)

Fig. 2

Shape and dimension of the cylindrical fatigue testing specimen (unit: mm)

Fig. 3

Cyclic deformation response behavior at RT: (a) relationship between peak/valley stresses and number of cycles; (b) relationship between stress amplitude and number of cycles

Fig. 4

Variation in stress amplitude as a function of the number of cycles for 10 specimens

Fig. 5

Inter-specimen scatter of the fatigue life N_f at RT

Fig. 6

Two-parameter Weibull plot of the fatigue life at RT

Fig. 7

Definition of the measurands obtained at the 1^st cycle hysteresis loop (ex.: K_OH10 specimen)

Fig. 8

Definitions of the LCF measurands obtained at the half-life cycle hysteresis loop

Fig. 9

COVs of the measurands for LCF property data at RT and 700 °C

Table 1

Chemical composition of the Type 316L stainless steel plate (wt.%)

Element	Type 316L stainless steel plate

	ASME/BPVC¹⁾	RCC-MRx	in this work
C	≤0.030	≤0.030	0.020
Mn	≤2.00	1.60–2.00	1.01
Si	≤0.75	≤0.50	0.42
Cr	16.00–18.00	17.00–18.00	16.77
Ni	10.00–14.00	12.00–12.50	10.03
Mo	2.00–3.00	2.30–2.70	2.04
P	≤0.045	≤0.030	0.030
S	≤0.030	≤0.015	0.001
N	≤0.100	0.060–0.080	0.043
B	-	≤0.0020	-
Fe	Bal.	Bal.	Bal.

¹⁾ ASME/BPVC SECIIPart A

Table 2

Mechanical properties of Type 316L stainless steel plate at RT

Tensile properties	Room temperature (RT)
Yield strength¹⁾ (MPa)	276
Ultimate tensile strength (MPa)	592
Total elongation (%)	58
Elastic modulus (GPa)	203

¹⁾ 0.2% off-set yield strength

Table 3

Conditions of the LCF testing at RT

Testing parameter	Condition
Strain amplitude (%)	±0.4
Strain rate (/s)	4×10⁻³
RT Environments (°C)	25 in Air
Waveform	Triangular
Strain ratio, R −1	(tension–compression)
Drop in load¹⁾ (%)	20

¹⁾ LCF life criterion used in this study

Table 4

Measurands, along with their units and symbols

Measurands	Unit	Symbol
Fatigue life	Cycles	N_f
Tensile stress at 1^st cycle	MPa	σ1T
Compressive stress at 1^st cycle	MPa	σ1C
Stress range at 1^st cycle	MPa	Δσ₁
Elastic modulus at 1^st cycle	GPa	E₀
Tensile stress at half-life cycle	MPa	σhT
Compressive stress at half-life cycle	MPa	σhC
Stress range at half-life cycle	MPa	Δσ
Elastic strain range at half-life cycle	%	Δσ_e
Plastic strain range at half-life cycle	%	Δσ_p
Elastic modulus¹⁾ at half-life cycle	GPa	E₁, E₂

¹⁾ unloading (E₁ ) and loading (E₂)

Table 5

Estimated statistics of the fatigue life N_f

N	Mean	Standard error	Standard deviation	COV	Min. value	Median value	Max. value	95% CI¹⁾ of mean
10	7876	481	1522	0.1932	5416	7987	10588	6787–8964

¹⁾ Confidence interval (CI).

Table 6

Quantitative data of the measurands obtained at the 1^st cycle hysteresis loop

Spec. ID¹⁾	Tensile stress, σ1T (MPa)	Compressive stress, σ1C (MPa)	Stress range, Δσ₁ (MPa)	Elastic modulas, E₀ (GPa)
K_OH10	259	−272	531	194.6
K_OH11	260	−275	535	192.5
K_OH12	257	−276	533	194.6
K_OH13	254	−272	526	194.5
K_OH14	268	−277	545	195.5
K_OH15	260	−277	537	194.2
K_OH16	256	−278	534	196.3
K_OH18	259	−279	538	197.3
K_OH19	260	−279	539	194.1
K_OH21	252	−272	524	193.2

¹⁾ K_OH17 and K_OH20 speciemns’ data are rejected by cracking outside knife edge.

Table 7

Estimated statistics of the measurands obtained at the 1^st cycle hysteresis loop

Measurands	Mean	Standard Error	Standard Deviation	COV	Min. Value	Median Value	Max. Value	95% CI¹⁾ of mean
σ1T	258.5	1.37	4.33	0.0168	252.0	259.0	260.0	255.4–261.6
σ1C	−275.7	0.895	2.83	0.0103	−279.0	−276.5	−272.0	−277.7 to −273.7
Δσ₁	534.2	1.96	6.20	0.0116	524.0	534.5	545.0	529.8–538.6
E₀	194.7	0.444	1.40	0.0072	192.5	194.6	195.7	193.7–195.7

¹⁾ Confidence interval

Table 8

Quantitative data of the measurands obtained at the half-life cycle hysteresis loop

Spec. ID¹⁾	Tensile stress, σhT (MPa)	Compressive stress, σhC (MPa)	Stress range Δσ (MPa)	Elastic strain range, Δσ_e (%)	Plastic strain range, Δσ_p (%)	Unloading elastic modulas, E₁ (GPa)	Loading elastic modulas, E₂ (GPa)
K_OH10	265	−259	524	0.286	0.514	194.1	189.9
K_OH11	272	−266	538	0.289	0.511	199.3	203.3
K_OH12	263	−256	519	0.282	0.518	206.3	191.4
K_OH13	278	−273	551	0.290	0.510	222.9	209.3
K_OH14	257	−267	524	0.285	0.516	189.0	197.4
K_OH15	277	−267	544	0.292	0.508	213.0	193.0
K_OH16	274	−266	540	0.292	0.508	226.6	195.7
K_OH18	286	−280	566	0.310	0.490	193.8	212.4
K_OH19	267	−269	536	0.285	0.515	207.6	196.7
K_OH21	260	−273	533	0.283	0.517	215.9	205.9

¹⁾ K_OH17 and K_OH20 speciemns’ data are rejected by cracking outside knife edge.

Table 9

Estimated statistics of the measurands obtained at the half-life cycle hysteresis loop

Measurands	Mean	Standard error	Standard deviation	COV	Min. value	Median value	Max. value	95% CI¹⁾ of mean
σhT	269.9	2.87	9.07	0.0336	257.0	269.5	286.0	263.4–276.4
σhC	−276.7	2.18	6.90	0.0249	−280.0	−267.0	−256.0	−272.5 to −262.7
Δσ	537.5	4.44	14.03	0.0261	519.0	537.0	566.0	527.5–547.5
Δσ_e	0.28940	0.00255	0.00806	0.0279	0.28200	0.28750	0.31000	0.28364–0.29516
Δσ_p	0.51070	0.00257	0.00812	0.0159	0.49000	0.51250	0.51800	0.50489–0.51651
E₁	206.9	4.05	12.81	0.0619	189.0	206.9	226.6	197.7–216.0
E₂	199.5	2.46	7.78	0.0390	189.9	197.1	212.4	193.9–205.1

¹⁾ Confidence interval

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