# Applicability of the Modified Ritchie-Knott-Rice Failure Criterion to Examine the Feasibility of Miniaturized Charpy Type SE(B) Specimens

Authors: Toshiyuki Meshii; Teruhiro Yamaguchi; Yuma Higashino
Journal: Advances in Materials Science and Engineering
 (2016)

---

## Abstract

This paper examined whether the modified Ritchie-Knott-Rice (RKR) failure criterion can be applied to examine the feasibility of miniaturized Charpy type SE(B) specimens of thickness-to-width ratioB/W=1. The modified RKR failure criterion considered in this paper is the (4δt,σ22c) criterion which predicts the onset of cleavage fracture when the midplane crack-opening stress measured at a distance equal to four times the crack-tip opening displacement, denoted as σ22d, exceeds a critical stress σ22c. Specimens with B values of 25, 10, 3, and 2 mm (denoted as 25t, 10t, 3t, and 2t specimens, resp.) manufactured with 0.55% carbon steel were tested at 20°C. The results showed that the modified RKR criterion could appropriately predict the occurrence of cleavage fracture accompanied by negligibly small stable crack extension (denoted as KJc fracture) naturally for the 25t and 10t specimens. The modified RKR criterion could also predict that KJc fracture does not occur for the 2t specimen. The σ22c obtained from specimens for the 25t and 10t specimens exhibited only a small difference, indicating that the Jc obtained from the 10t specimens can be used to predict the Jc that will be obtained with the 25t specimens.


---

## Body

## 1. Introduction

Test specimen size effects on the cleavage fracture toughnessJc of a material in the ductile-to-brittle transition temperature (DBTT) region are important when assessing aging steel structures and reactor pressure vessels. Large scatter in Jc has also been identified. A practical way to maintain conservatism in Jc used in a structural integrity assessment is to specify the test specimen type and thickness, as found in the IAEA recommendations for monitoring the degradation of irradiated nuclear reactor pressure vessels (RPVs) [1]. To understand and become able to convert Jc obtained with different specimen types and thicknesses, many studies have been performed in the past [2–10]. The cause of the test specimen size effect on Jc has usually been categorized into the planar size effect on Jc (i.e., different planar specimen configurations, including crack depth) and the test specimen thickness (TST) effect on Jc. The former has been assumed to result from constraint loss, and the latter results from statistical weakest link (SWL) size effects [2]. Here, this constraint loss is the loss in one-to-one correspondence between J and the crack-opening stress σ22 distribution (hereinafter denoted as J’s inability to characterize the crack-tip stress). Anderson et al. [5] gave theoretical background to the empirical TST effect on Jc, described as Jc∝TST-1/2, by assuming the SWL model. However, the fact that Jc has a nonnegligible lower bound value for large TST seemed to indicate that assuming the TST effect on the Jc effect is thoroughly due to the SWL size effect not being perfect.Thus, the authors have been working to explain the TST effect onJc based on J’s inability to characterize the crack-tip stress field [11–18]. The first work was to analyze and test whether there is “out-of-plane” stress σ33 difference between SE(B) specimens with identical planar specimen configuration but with different thicknesses (hereinafter denoted as nonproportional specimens) [11]. This was because the formerly mentioned theoretical work of Anderson et al. implicitly assumed the nonproportional specimens. SE(B) specimens of width W=25 mm and four thickness-to-width ratios B/W of 0.25, 0.5, 1, and 1.5 were considered. Fracture toughness tests results using 0.55% C steel JIS S55C showed that the empirical relationship Jc∝B-1/2 holds for B/W = 0.25~1 and that Jc is bounded for B/W=1 and 1.5. The difference in Jc, especially the bounding nature for large TST, clearly correlated with the difference in σ33 at the fracture load. The idea to explain the TST effect by using the difference in σ33 was supported by many researchers, such as [19–25].Our second work was to become able to transferJc’s between different TSTs. According to Chen et al. “… it is necessary to distinguish the concepts of the minimum toughness or the lower boundary of toughness values from that of the scatter band of toughness. The former is a definite parameter determined by the specimen geometry and yielding properties, and the latter is statistical behavior determined by the distribution of the weakest constituent” [26]; it was thought that the minimum toughness of a material, observed for a specific specimen and temperature, can be transferred by running an elastic-plastic finite element analysis (EP-FEA) with a given stress-strain relationship and a failure criterion. For this failure criterion, one of the modified Ritchie-Knott-Rice failure criterion, that is, the (4δt,σ22c) criterion [3], which predicts the onset of cleavage fracture when the crack-opening stress σ22, measured at a distance from the crack-tip equal to four times the crack-tip opening displacement (CTOD) δt (hereinafter denoted as σ22d), exceeds a critical value σ22c (Figure 1), was considered. The criterion successfully explained the TST effect on Jc observed for S55C steel nonproportional SE(B) specimens [13, 17] and RPV ASTM A533 Grade B class 1 steel (A533B) proportional SE(B) specimens (whose B/W ratio is held constant, though B is changed) [18]. The tests were conducted in the DBTT region. The specimen thickness ranged from 6.25 to 37.5 mm for S55C steel and from 8 to 254 mm for A533B steel. Although the Jc for the specimens exhibited a variation of 30.5 to 198 N/mm for S55C steel and 7 to 106 N/mm for A533B steel, the critical values for σ22c exhibited variations of only 5% and 4%, respectively. Another finding was that the stress level of σ22d is maintained as σ22c for increasing load. This finding suggested that the minimum J that satisfied σ22d=σ22c corresponds to the minimum Jc for a specific specimen [18], which seemed to be consistent with the formerly mentioned opinion of Chen et al. [26].Figure 1
( 4 δ t , σ 22 c ) failure criterion, which predicts the onset of cleavage fracture when the crack-opening stress σ22, measured at a distance from the crack-tip equal to four times the crack-tip opening displacement (CTOD) δt (hereinafter denoted as σ22d), exceeds a critical value σ22c [3, 13].This paper is an extension of our previous works to examine whether the(4δt,σ22c) failure criterion can be applied to examine the feasibility of miniaturized Charpy type SE(B) specimens, that is, (1) whether the criterion could predict the occurrence of cleavage fracture accompanied by negligibly small stable crack extension (hereinafter denoted as KJc fracture) and (2) whether σ22c is identical to that observed in full sized specimens in the case where KJc fracture occurred. SE(B) specimens of B/W=1 (Charpy type) with B of 25 (full size), 10, 3, and 2 (miniaturized sizes) mm were examined (hereinafter denoted as 25t, 10t, 3t, and 2t specimens, resp.). Additionally, 0.55% carbon steel JIS S55C at 20°C, which is in the DBTT region, was selected for material and test temperature. The results showed that the (4δt,σ22c) criterion could appropriately predict a KJc fracture naturally for the 25t and 10t specimens. The (4δt,σ22c) criterion could also predict that KJc fracture does not occur for the 2t specimen. The σ22c obtained from specimens for the 25t and 10t specimens exhibited only a small difference, indicating that the Jc obtained from the 10t specimens can be used to predict the Jc that will be obtained with the 25t specimens.


## 2. Outline of This Work and Material Selection

The outline of this work is summarized in Figure2. First, fracture toughness tests with the 25t specimens were conducted and fracture toughness Jc for this size was obtained. The critical stress σ22c was obtained by running EP-FEA. Then, EP-FEA for miniaturized-size specimens of 10t, 3t, and 2t were run, and the (4δt,σ22c) failure criterion was applied to predict whether these specimens will experience KJc fracture. For specimens for which KJc fracture was expected, Jc was predicted from the σ22c of the 25t specimen. Finally, fracture toughness tests were conducted to confirm the predictions.Figure 2
Prediction ofJc for the miniature specimens from the experiment using full-size specimens.Considering that the nominal tensile strengthσB0 to the nominal yield stress σYS0 ratio σB0/σYS0 for EURO RPVs and Japanese RPVs is equal to 1.3, 0.55% C steel JIS S55C, whose room temperature σB0/σYS0 is known to show a higher value of 1.8 was selected for examination and tested at 20°C. The material was quenched at 850°C and tempered at 650°C. Chemical contents were C: 0.55%, Si: 0.17%, Mn: 0.61%, P: 0.015%, S: 0.004%, Cu: 0.13%, Ni: 0.07%, and Cr: 0.08%, respectively. Charpy impact test results and a true stress-true strain curve are shown in Figure 3. These tests were conducted in accordance with JIS Z2242 [27] and Z2241 [28], respectively. Averaged nominal tensile properties were yield strength σYS0=394 MPa, tensile strength σB0=707 MPa, and elongation of 23.7%.Figure 3
Charpy impact test results and true stress-true strain curves of JIS S55C steel (20°C).
(a) (b)


## 3. Fracture Toughness Tests and EP-FEA for 25t SE(B) Specimen to Obtain the Critical Stressσ22c of (4δt,σ22c) Failure Criterion

### 3.1. Fracture Toughness Tests for 25t SE(B) Specimen

The fracture toughness tests for the 25t SE(B) specimen were conducted in accordance with ASTM E1921 [29]. The dimensions of the SE(B) specimen are shown in Figure 4. The length L and the support span S of the specimen were designed to satisfy L/W≥4.5 and S/W=4.0 and were fabricated as L/W=4.52 and S/W=4.0, where width W=25 mm.Figure 4
Dimensions of the 25t SE(B) specimen.Fatigue precrack was inserted using loads corresponding toKmax=22 and 19 MPam1/2 for the 1st and final stages, respectively, which satisfied the requirement from the standard of Kmax≤25 and 20 MPam1/2. For each discrete step, the reduction in Pmax for any of these steps was 15%, which satisfied the suggestion from the standard that the reduction in Pmax for any of these steps be no greater than 20%. A maximum force Pmax and a minimum force Pmin with a ratio of R=Pmin/Pmax=0.1 were applied at a loading frequency of 10 Hz.During the fracture toughness test, the loading rate was controlled to be in a specified range from 0.1 to 2.0 MPam1/2/s to comply with the standard, resulting in a range from 1.21 to 1.71 MPam1/2/s. Test temperature requirements are to hold the temperature constant at 20±3°C for longer than 30B/25 minutes, where the specimen thickness B is 25 mm, resulting in 20±1°C for 45 minutes. Six test results satisfying the ASTM E1921 requirements were considered for examination. The results clearly showed KJc fracture.Fracture toughness data are summarized in Table1. The variable Kc in the table is the stress intensity factor calculated from the fracture load Pc and the measured crack depth-to-width ratio a/W. KJc in the table is the fracture toughness in terms of stress intensity factor, calculated as KJc=[JcE/(1-ν2)]1/2, where E=206 GPa is Young’s modulus and ν=0.3 is Poisson’s ratio used for this conversion. μ and Σ in the table denote the mean and standard deviation of each parameter. M=(W-a)σYS0/Jc≥30 is a requirement of the standard placed on the ligament size, where a is the crack length. Although not listed, negligible stable crack extension was measured using SEM observations.Table 1
Fracture toughness test results of S55C steel with 25t SE(B) specimen tested at 20°C. Here,μ and Σ in the table denote the mean and standard deviation of each parameter.
Specimen id 1 2 3 4 5 6 μ Σ 2Σ/μ% a / W 0.50 0.50 0.50 0.50 0.49 0.50 0.50 0.00 P c (kN) 23.1 22.7 22.4 24.1 23.6 22.4 23.1 0.629 K c (MPam1/2) 62.7 60.5 59.8 65.4 61.8 59.6 61.6 2.01 J c (N/mm) 46.8 35.9 33.5 61.1 52.0 37.8 44.5 9.81 K J c (MPam1/2) 103 90.1 87.1 118 108 92.4 99.8 10.9 21.8 M 105 137 147 80.6 96.6 130 116 23.7In Table1, the standard deviation Σ of a/W was 0.00, meaning that the potential Jc scatter due to crack depth difference was minimized. The mean μ of KJc was 99.8 MPam1/2. Therefore, the master curve reference temperature T0 in ASTM E1921 was approximately equal to the test temperature of 20°C. The standard deviation to average ratio of 2Σ/μ=21.8% for these data was sufficiently small compared with the ASTM E1921 prediction of 2Σ/μ=56(1-20/μ)% = 45%. The minimum M was 80.6, which satisfied the ASTM E1921 requirement of M≥30.


### 3.2. EP-FEA for 25t SE(B) Specimen

The FE model used for the elastic-plastic analysis of the SE(B) specimen is shown in Figure5. In this study, the FE models were fundamentally generated based on the FE model described in the work by Gao and Dodds Jr. [30], so that total element number of 31,990 and node number of 139,816 do not change for specimen size. Using symmetry conditions, one-quarter of an SE(B) specimen containing a straight crack was analyzed, with appropriate constraints imposed on the symmetry planes, as illustrated in Figure 5. An initial blunted notch with a radius of ρ = 4.305 μm was inserted at the crack-tip and “spiderweb” radius of Rs=5.75 mm was selected to fully cover the high stress region for the 25t specimen. For all cases, 20-node isoparametric three-dimensional solid elements with reduced (2 × 2 × 2) Gauss integration were employed. A load line displacement VLL was applied for each EP-FEA. In the EP-FEA, the applied load P was measured as the total reaction force on the supported nodes. The J simulated by the EP-FEA, denoted as JFEA, was evaluated using a load-versus-crack-mouth opening displacement diagram (P-Vg diagram), in accordance with ASTM E1921 [29]. CTOD was measured at node A in Figure 5 [31].Figure 5
FE model for the SE(B) specimen.
(a)
Global mesh (b)
Detail of crack-tip meshThe mechanical properties of the test specimens are a Young’s modulusE of 206 GPa and a Poisson’s ratio ν of 0.3. The FEA material behavior was assumed to be governed by the J2 incremental theory of plasticity, the isotropic hardening rule, and the Prandtl-Reuss flow rule. Two total true stress-strain curves, shown in Figure 3(b), were averaged and used in the EP-FEA. WARP3D [32] was used as the FEA solver.First, to validate the EP-FEA results, the EP-FEAP-Vg diagram for the 25t specimen was compared with the experimental results in Figure 6. The open rectangles represent the EP-FEA results.Figure 6
Comparison of theP-Vg diagrams of the 25t SE(B) specimen: EP-FEA results shown with open rectangles show good agreement with the experimental results (S55C, 20°C).As shown in Figure6, the path of the EP-FEA P-Vg diagram showed good agreement with the experimental results. Therefore, the EP-FEA result was considered to be valid and proceeded to obtain the critical stress σ22c.The relationship betweenσ22d (i.e., crack-opening stress measured at a distance from the crack-tip equal to 4δt on x1-axis at the specimen midplane) and JFEA for each load step was summarized in Figure 7. The stars in the figure indicate the fracture toughness values (Jc’s) obtained from the experiments.Figure 7
The relationship betweenσ22d and JFEA of the 25t SE(B) specimen (S55C, 20°C): fracture always occurred after σ22d reached σ22c=3.82σYS0.From this figure, it is revealed that fracture always occurred afterσ22d reached 3.82σYS0; thus, this value was determined as the critical value σ22c of the (4δt,σ22c) criterion. If the criterion is applicable to miniaturized specimens, fracture is predicted when σ22d for these miniaturized specimens reaches the identical critical value of 3.82σYS0.


## 3.1. Fracture Toughness Tests for 25t SE(B) Specimen

The fracture toughness tests for the 25t SE(B) specimen were conducted in accordance with ASTM E1921 [29]. The dimensions of the SE(B) specimen are shown in Figure 4. The length L and the support span S of the specimen were designed to satisfy L/W≥4.5 and S/W=4.0 and were fabricated as L/W=4.52 and S/W=4.0, where width W=25 mm.Figure 4
Dimensions of the 25t SE(B) specimen.Fatigue precrack was inserted using loads corresponding toKmax=22 and 19 MPam1/2 for the 1st and final stages, respectively, which satisfied the requirement from the standard of Kmax≤25 and 20 MPam1/2. For each discrete step, the reduction in Pmax for any of these steps was 15%, which satisfied the suggestion from the standard that the reduction in Pmax for any of these steps be no greater than 20%. A maximum force Pmax and a minimum force Pmin with a ratio of R=Pmin/Pmax=0.1 were applied at a loading frequency of 10 Hz.During the fracture toughness test, the loading rate was controlled to be in a specified range from 0.1 to 2.0 MPam1/2/s to comply with the standard, resulting in a range from 1.21 to 1.71 MPam1/2/s. Test temperature requirements are to hold the temperature constant at 20±3°C for longer than 30B/25 minutes, where the specimen thickness B is 25 mm, resulting in 20±1°C for 45 minutes. Six test results satisfying the ASTM E1921 requirements were considered for examination. The results clearly showed KJc fracture.Fracture toughness data are summarized in Table1. The variable Kc in the table is the stress intensity factor calculated from the fracture load Pc and the measured crack depth-to-width ratio a/W. KJc in the table is the fracture toughness in terms of stress intensity factor, calculated as KJc=[JcE/(1-ν2)]1/2, where E=206 GPa is Young’s modulus and ν=0.3 is Poisson’s ratio used for this conversion. μ and Σ in the table denote the mean and standard deviation of each parameter. M=(W-a)σYS0/Jc≥30 is a requirement of the standard placed on the ligament size, where a is the crack length. Although not listed, negligible stable crack extension was measured using SEM observations.Table 1
Fracture toughness test results of S55C steel with 25t SE(B) specimen tested at 20°C. Here,μ and Σ in the table denote the mean and standard deviation of each parameter.
Specimen id 1 2 3 4 5 6 μ Σ 2Σ/μ% a / W 0.50 0.50 0.50 0.50 0.49 0.50 0.50 0.00 P c (kN) 23.1 22.7 22.4 24.1 23.6 22.4 23.1 0.629 K c (MPam1/2) 62.7 60.5 59.8 65.4 61.8 59.6 61.6 2.01 J c (N/mm) 46.8 35.9 33.5 61.1 52.0 37.8 44.5 9.81 K J c (MPam1/2) 103 90.1 87.1 118 108 92.4 99.8 10.9 21.8 M 105 137 147 80.6 96.6 130 116 23.7In Table1, the standard deviation Σ of a/W was 0.00, meaning that the potential Jc scatter due to crack depth difference was minimized. The mean μ of KJc was 99.8 MPam1/2. Therefore, the master curve reference temperature T0 in ASTM E1921 was approximately equal to the test temperature of 20°C. The standard deviation to average ratio of 2Σ/μ=21.8% for these data was sufficiently small compared with the ASTM E1921 prediction of 2Σ/μ=56(1-20/μ)% = 45%. The minimum M was 80.6, which satisfied the ASTM E1921 requirement of M≥30.


## 3.2. EP-FEA for 25t SE(B) Specimen

The FE model used for the elastic-plastic analysis of the SE(B) specimen is shown in Figure5. In this study, the FE models were fundamentally generated based on the FE model described in the work by Gao and Dodds Jr. [30], so that total element number of 31,990 and node number of 139,816 do not change for specimen size. Using symmetry conditions, one-quarter of an SE(B) specimen containing a straight crack was analyzed, with appropriate constraints imposed on the symmetry planes, as illustrated in Figure 5. An initial blunted notch with a radius of ρ = 4.305 μm was inserted at the crack-tip and “spiderweb” radius of Rs=5.75 mm was selected to fully cover the high stress region for the 25t specimen. For all cases, 20-node isoparametric three-dimensional solid elements with reduced (2 × 2 × 2) Gauss integration were employed. A load line displacement VLL was applied for each EP-FEA. In the EP-FEA, the applied load P was measured as the total reaction force on the supported nodes. The J simulated by the EP-FEA, denoted as JFEA, was evaluated using a load-versus-crack-mouth opening displacement diagram (P-Vg diagram), in accordance with ASTM E1921 [29]. CTOD was measured at node A in Figure 5 [31].Figure 5
FE model for the SE(B) specimen.
(a)
Global mesh (b)
Detail of crack-tip meshThe mechanical properties of the test specimens are a Young’s modulusE of 206 GPa and a Poisson’s ratio ν of 0.3. The FEA material behavior was assumed to be governed by the J2 incremental theory of plasticity, the isotropic hardening rule, and the Prandtl-Reuss flow rule. Two total true stress-strain curves, shown in Figure 3(b), were averaged and used in the EP-FEA. WARP3D [32] was used as the FEA solver.First, to validate the EP-FEA results, the EP-FEAP-Vg diagram for the 25t specimen was compared with the experimental results in Figure 6. The open rectangles represent the EP-FEA results.Figure 6
Comparison of theP-Vg diagrams of the 25t SE(B) specimen: EP-FEA results shown with open rectangles show good agreement with the experimental results (S55C, 20°C).As shown in Figure6, the path of the EP-FEA P-Vg diagram showed good agreement with the experimental results. Therefore, the EP-FEA result was considered to be valid and proceeded to obtain the critical stress σ22c.The relationship betweenσ22d (i.e., crack-opening stress measured at a distance from the crack-tip equal to 4δt on x1-axis at the specimen midplane) and JFEA for each load step was summarized in Figure 7. The stars in the figure indicate the fracture toughness values (Jc’s) obtained from the experiments.Figure 7
The relationship betweenσ22d and JFEA of the 25t SE(B) specimen (S55C, 20°C): fracture always occurred after σ22d reached σ22c=3.82σYS0.From this figure, it is revealed that fracture always occurred afterσ22d reached 3.82σYS0; thus, this value was determined as the critical value σ22c of the (4δt,σ22c) criterion. If the criterion is applicable to miniaturized specimens, fracture is predicted when σ22d for these miniaturized specimens reaches the identical critical value of 3.82σYS0.


## 4. Applicability of the(4δt,σ22c) Failure Criterion to Examine the Feasibility of Miniaturized Charpy Type SE(B) Specimens

### 4.1. Selection of Miniaturized Specimen Size for Examination

Wallin et al. [33] noted that the minimum size of a Charpy type SE(B) specimen that satisfies the requirement of M≥30 for a RPV steel and tested at the temperature T0 (master curve reference temperature) ±50°C is a thickness of 5 and a width of 5 mm (hereinafter denoted as the 5t specimen). Considering that T0 was approximately equal to 20°C for S55C steel, the minimum size for the S55C steel to observe KJc fracture was expected to be 5t. However, some smaller specimens, such as 3.3t, have been examined in the past [34, 35]. Because we are examining the feasibility of miniature specimens with M<30 to exhibit KJc fracture, smaller specimens were also considered.By usingJc = 33.5~61.1 N/mm of 25t specimen and σYS0=394 MPa and assuming crack length a=W/2 and Jc∝B-1/2, the range of M for 10t was estimated to be in the range of 20.4~37.2, that is, close to 30. This is different from the abovementioned Wallin et al.’s prediction. Thus, to be conservative, the 10t specimen was selected as the specimen for which KJc fracture is expected. For the specimens below M<30, the 3t specimen was selected as a candidate of KJc fracture from the past experience of the 3.3t specimen (though there might be an opinion that the material and test temperature were different). The 2t specimen was selected as a possible candidate for which KJc fracture should not be observed.The configurations of the 10t, 3t, and 2t SE(B) specimens are shown in Figure8. The support span size was set as equal to 4W.Figure 8
Dimensions of miniaturized SE(B) specimens.
(a)
10t (b)
3t (c)
2t


### 4.2. Prediction ofKJc Cleavage Fracture and Jc for Miniaturized Specimens by Applying the (4δt,σ22c) Criterion

EP-FEA was run for the 10t, 3t, and 2t specimens shown in Figure8 to predict whether KJc cleavage fracture occurs. Details of EP-FEA are fundamentally identical to those for the 25t specimen, except the near crack-tip generated meshes; ρ was in a range of 1.84 to 3.98 μm and Rs was in a range of 0.46 to 2.3 mm. The relationships between σ22d and JFEA are shown in Figure 9. The value 3.82 in the figure indicates the critical value obtained from the 25t specimens.Figure 9
The relationships betweenσ22d and JFEA for the 10t, 3t, and 2t SE(B) specimens (S55C, 20°C): σ22d for 10t specimen reached the critical stress σ22c; the stress level was maintained for increasing JFEA, indicating occurrence of cleavage fracture within negligible stable crack extension (KJc fracture). In contrast, σ22d for 3t and 2t specimens showed a maximum for increasing load, indicating low possibility of KJc fracture.
(a)
10t (b)
3t (c)
2tFrom Figure9(a), KJc fracture was predicted for the 10t specimen because σ22d reached the critical value σ22c=3.82σYS0 and the stress level was maintained for increasing load. The constancy of σ22d for increasing load assures that even if a significant microcrack is not located at the original crack-tip, cleavage fracture might occur after small stable crack extension and a significant microcrack is encountered (SWL model). Thus, the minimum Jc for the 10t specimen was predicted as 58 N/mm because σ22d exceeded the critical value σ22c when JFEA reached 58 N/mm.In contrast,σ22d for the 3t and 2t specimens showed a maximum for increasing load; the stress level could not be maintained. Because σ22d is measured at a variable location of x1=4δt and because 4δt increases with load, Figures 9(b) and 9(c) indicate that the region of high stress level does not continue to grow after the load σ22d shows a maximum for JFEA. Thus, qualitatively, large stable crack extension was expected. This was the first experience for the (4δt,σ22c) criterion and out of scope of what was considered within the criterion. However, because large stable crack extension was expected, KJc fracture was not predicted for the 3t and 2t specimens.


### 4.3. Fracture Toughness Tests for the Miniaturized Specimen

Fracture toughness testing for the miniaturized specimen was conducted in accordance with ASTM E1921 [21]. The exception was the ligament size requirement of M≥30 and the quantity of the tests. The dimensions of the miniaturized SE(B) specimens are shown in Figure 8. The 3t and 2t specimens were cut from the 10t specimen after the fatigue crack was inserted.Fatigue precrack was inserted using loads corresponding toKmax=20 MPam1/2 for both the 1st and final stage, which satisfied the requirement from the standard of Kmax≤25 and 20 MPam1/2. For each discrete step, the reduction in Pmax for any of these steps was 13–15%, which satisfied the suggestion from the standard that the reduction in Pmax for any of these steps be no greater than 20%. The ratio of the maximum force Pmax and the minimum force Pmin, or R=Pmin/Pmax=0.1, was used, and the loading frequency was 30 Hz.In the fracture toughness test, the loading rate was controlled to be within a specified range from 0.1 to 2.0 MPam1/2/s, which resulted in an actual range between 0.12 and 1.4 MPam1/2. In the following, the test results for the 10t, 3t, and 2t SE(B) specimens are described.


#### 4.3.1. Test Results for the 10t SE(B) Specimens

TheP-Vg diagrams of the 10t SE(B) specimens are compared with VgASTM, which is the Vg calculated from the elastic compliance given in ASTM E1820 [36].As shown in Figure10, the two experimental P-Vg diagrams showed good reproducibility. Moreover, the linear slope of the experimental P-Vg diagrams exhibited good agreement with the P-VgASTM. Therefore, the experimental results of the 10t SE(B) specimens were considered to be valid and capable of being compared with the numerical predictions, despite the fact that only two tests were conducted.Figure 10
P - V g diagram of the 10t SE(B) specimens (S55C steel, 20°C): KJc fracture followed after relatively large plastic deformation.TheP-Vg diagrams for both tests showed a sudden increase in Vg after the maximum load was reached, indicating that the clip gauge dropped off. This suggested that an unstable fracture occurred.The fracture surface of the 10t specimens clearly showed cleavage fracture after very small stable crack extensionΔap, satisfying the ASTM E1921 requirement to be less than min⁡((W-a)/20,1mm)=0.23mm. The values of the measured Δap are listed in Table 2. Thus, the so-called KJc fracture was observed, as predicted with the (4δt,σ22c) criterion.Table 2
Fracture toughness test results of 10t SE(B) specimens (S55C steel, 20°C). Here,μ and Σ denote the mean and standard deviation of each parameter, respectively. Though M was smaller than 30, cleavage fracture with negligible stable crack extension was observed.
Specimen id 1 2 μ Σ 2Σ/μ% a / W 0.54 0.54 0.54 0 P c (kN) 4.46 4.25 4.36 0.105 K c (MPam1/2) 54.2 51.6 52.9 1.30 J c (N/mm) 79.8 68.1 74.0 5.85 K J c (MPam1/2) 134 124 129 5.00 7.75 Δ a p (mm) 0.13 0.02 0.075 0.055 M 22.7 26.6 24.7 1.95Fracture toughness test results are summarized in Table2. The average of Jc=74.0 N/mm was 1.7 times larger than that of the 25t SE(B) specimen. This magnification agreed with the empirical thickness relationship describing Jc, that is, (10/25)−1/2 = 1.6. M was close to but smaller than 30, as predicted. Although only two data points were available, the standard deviation to the average ratio of KJc was 7.75% for the current data, which was sufficiently small compared with the ASTM E1921 prediction of 2Σ/μ=56(1-20/μ)% = 47%. Thus, from a fracture toughness standpoint, the experimental results for the 10t SE(B) specimens were considered to be valid and capable of being compared with the numerical predictions, despite the fact that only two data points were obtained.Considering the fact that thea/W used in the EP-FEA was 0.50, which was different from the experimental result of 0.54, EP-FEA with a/W=0.54 was rerun, resulting in negligible small difference in the predicted minimum Jc of 58 N/mm. Comparing the test results of Jc=79.8 and 68.1 N/mm with the updated prediction, it was concluded that the (4δt,σ22c) criterion could properly and consequently predict the minimum Jc of the 10t SE(B) specimen.In summary, it was concluded that the(4δt,σ22c) criterion could properly predict the occurrence of KJc fracture and the minimum Jc of the 10t SE(B) mm specimen, despite the fact that the M for the specimen did not satisfy ASTM E1921’s requirement of M≥30.


#### 4.3.2. Test Results for the 3t and 2t SE(B) Specimens

Fracture surfaces andP-Vg diagrams of the 2t and 3t specimens are summarized in Figures 11 and 12, respectively. Note that Vg=1 mm does not represent the value at final fracture, because the maximum measurement capacity of the clip gauge was this value. As expected, the 2t specimens in Figure 11 showed that large stable crack extension Δap preceded before cleavage fracture, obviously not satisfying the ASTM E1921 requirement of Δap<(W-a)/20. Thus, the (4δt,σ22c) criterion properly predicted the nonoccurrence of KJc fracture for the 2t SE(B) specimen.Figure 11
Fracture surfaces and loadP versus crack-mouth opening displacement Vg diagrams of the 2t SE(B) specimens (S55C, 20°C). Large stable crack extension before cleavage fracture was observed, as predicted from the (4δt,σ22c) failure criterion. Note that Vg=1 mm does not correspond to the final fracture.Figure 12
Fracture surfaces and loadP versus crack-mouth opening displacement Vg diagrams of the 3t SE(B) specimens (S55C, 20°C). Pop-in correlated with cleavage mechanism was observed for specimen id 1. However, large stable crack extension before cleavage fracture was observed for specimen id 2, as predicted from the (4δt,σ22c) failure criterion. Note that Vg=1 mm does not correspond to the final fracture.
(a) (b)P - V g diagrams for the 3t specimens (Figure 12(b)) were different from those of the 2t specimens; that is, specimen id 1 showed “pop-in” phenomena. From the fracture surface of specimen id 1 in Figure 12(a), this pop-in was correlated with one of the two significant cleavage fracture areas on the fracture surface. Because ASTM E1921 states that “all pop-in crack initiation K values for cracks that advance by a cleavage-driven mechanism are to be regarded as eligible KJc data,” specimen id 1 showed KJc fracture. This might have some relationship with the fact that σ22d exceeded σ22c for the 3t SE(B) specimen, but further study in the future is necessary. The fracture surface of specimen id 2 showed an obviously large stable crack extension. In summary, one of the two 3t specimens did not show KJc fracture. Thus, it was concluded that the (4δt,σ22c) criterion properly predicted the nonoccurrence of KJc fracture for the 3t SE(B) specimen.In summary, it was concluded that the(4δt,σ22c) criterion could appropriately predict invalid KJc fracture for the 2t and 3t SE(B) specimens.


## 4.1. Selection of Miniaturized Specimen Size for Examination

Wallin et al. [33] noted that the minimum size of a Charpy type SE(B) specimen that satisfies the requirement of M≥30 for a RPV steel and tested at the temperature T0 (master curve reference temperature) ±50°C is a thickness of 5 and a width of 5 mm (hereinafter denoted as the 5t specimen). Considering that T0 was approximately equal to 20°C for S55C steel, the minimum size for the S55C steel to observe KJc fracture was expected to be 5t. However, some smaller specimens, such as 3.3t, have been examined in the past [34, 35]. Because we are examining the feasibility of miniature specimens with M<30 to exhibit KJc fracture, smaller specimens were also considered.By usingJc = 33.5~61.1 N/mm of 25t specimen and σYS0=394 MPa and assuming crack length a=W/2 and Jc∝B-1/2, the range of M for 10t was estimated to be in the range of 20.4~37.2, that is, close to 30. This is different from the abovementioned Wallin et al.’s prediction. Thus, to be conservative, the 10t specimen was selected as the specimen for which KJc fracture is expected. For the specimens below M<30, the 3t specimen was selected as a candidate of KJc fracture from the past experience of the 3.3t specimen (though there might be an opinion that the material and test temperature were different). The 2t specimen was selected as a possible candidate for which KJc fracture should not be observed.The configurations of the 10t, 3t, and 2t SE(B) specimens are shown in Figure8. The support span size was set as equal to 4W.Figure 8
Dimensions of miniaturized SE(B) specimens.
(a)
10t (b)
3t (c)
2t


## 4.2. Prediction ofKJc Cleavage Fracture and Jc for Miniaturized Specimens by Applying the (4δt,σ22c) Criterion

EP-FEA was run for the 10t, 3t, and 2t specimens shown in Figure8 to predict whether KJc cleavage fracture occurs. Details of EP-FEA are fundamentally identical to those for the 25t specimen, except the near crack-tip generated meshes; ρ was in a range of 1.84 to 3.98 μm and Rs was in a range of 0.46 to 2.3 mm. The relationships between σ22d and JFEA are shown in Figure 9. The value 3.82 in the figure indicates the critical value obtained from the 25t specimens.Figure 9
The relationships betweenσ22d and JFEA for the 10t, 3t, and 2t SE(B) specimens (S55C, 20°C): σ22d for 10t specimen reached the critical stress σ22c; the stress level was maintained for increasing JFEA, indicating occurrence of cleavage fracture within negligible stable crack extension (KJc fracture). In contrast, σ22d for 3t and 2t specimens showed a maximum for increasing load, indicating low possibility of KJc fracture.
(a)
10t (b)
3t (c)
2tFrom Figure9(a), KJc fracture was predicted for the 10t specimen because σ22d reached the critical value σ22c=3.82σYS0 and the stress level was maintained for increasing load. The constancy of σ22d for increasing load assures that even if a significant microcrack is not located at the original crack-tip, cleavage fracture might occur after small stable crack extension and a significant microcrack is encountered (SWL model). Thus, the minimum Jc for the 10t specimen was predicted as 58 N/mm because σ22d exceeded the critical value σ22c when JFEA reached 58 N/mm.In contrast,σ22d for the 3t and 2t specimens showed a maximum for increasing load; the stress level could not be maintained. Because σ22d is measured at a variable location of x1=4δt and because 4δt increases with load, Figures 9(b) and 9(c) indicate that the region of high stress level does not continue to grow after the load σ22d shows a maximum for JFEA. Thus, qualitatively, large stable crack extension was expected. This was the first experience for the (4δt,σ22c) criterion and out of scope of what was considered within the criterion. However, because large stable crack extension was expected, KJc fracture was not predicted for the 3t and 2t specimens.


## 4.3. Fracture Toughness Tests for the Miniaturized Specimen

Fracture toughness testing for the miniaturized specimen was conducted in accordance with ASTM E1921 [21]. The exception was the ligament size requirement of M≥30 and the quantity of the tests. The dimensions of the miniaturized SE(B) specimens are shown in Figure 8. The 3t and 2t specimens were cut from the 10t specimen after the fatigue crack was inserted.Fatigue precrack was inserted using loads corresponding toKmax=20 MPam1/2 for both the 1st and final stage, which satisfied the requirement from the standard of Kmax≤25 and 20 MPam1/2. For each discrete step, the reduction in Pmax for any of these steps was 13–15%, which satisfied the suggestion from the standard that the reduction in Pmax for any of these steps be no greater than 20%. The ratio of the maximum force Pmax and the minimum force Pmin, or R=Pmin/Pmax=0.1, was used, and the loading frequency was 30 Hz.In the fracture toughness test, the loading rate was controlled to be within a specified range from 0.1 to 2.0 MPam1/2/s, which resulted in an actual range between 0.12 and 1.4 MPam1/2. In the following, the test results for the 10t, 3t, and 2t SE(B) specimens are described.


### 4.3.1. Test Results for the 10t SE(B) Specimens

TheP-Vg diagrams of the 10t SE(B) specimens are compared with VgASTM, which is the Vg calculated from the elastic compliance given in ASTM E1820 [36].As shown in Figure10, the two experimental P-Vg diagrams showed good reproducibility. Moreover, the linear slope of the experimental P-Vg diagrams exhibited good agreement with the P-VgASTM. Therefore, the experimental results of the 10t SE(B) specimens were considered to be valid and capable of being compared with the numerical predictions, despite the fact that only two tests were conducted.Figure 10
P - V g diagram of the 10t SE(B) specimens (S55C steel, 20°C): KJc fracture followed after relatively large plastic deformation.TheP-Vg diagrams for both tests showed a sudden increase in Vg after the maximum load was reached, indicating that the clip gauge dropped off. This suggested that an unstable fracture occurred.The fracture surface of the 10t specimens clearly showed cleavage fracture after very small stable crack extensionΔap, satisfying the ASTM E1921 requirement to be less than min⁡((W-a)/20,1mm)=0.23mm. The values of the measured Δap are listed in Table 2. Thus, the so-called KJc fracture was observed, as predicted with the (4δt,σ22c) criterion.Table 2
Fracture toughness test results of 10t SE(B) specimens (S55C steel, 20°C). Here,μ and Σ denote the mean and standard deviation of each parameter, respectively. Though M was smaller than 30, cleavage fracture with negligible stable crack extension was observed.
Specimen id 1 2 μ Σ 2Σ/μ% a / W 0.54 0.54 0.54 0 P c (kN) 4.46 4.25 4.36 0.105 K c (MPam1/2) 54.2 51.6 52.9 1.30 J c (N/mm) 79.8 68.1 74.0 5.85 K J c (MPam1/2) 134 124 129 5.00 7.75 Δ a p (mm) 0.13 0.02 0.075 0.055 M 22.7 26.6 24.7 1.95Fracture toughness test results are summarized in Table2. The average of Jc=74.0 N/mm was 1.7 times larger than that of the 25t SE(B) specimen. This magnification agreed with the empirical thickness relationship describing Jc, that is, (10/25)−1/2 = 1.6. M was close to but smaller than 30, as predicted. Although only two data points were available, the standard deviation to the average ratio of KJc was 7.75% for the current data, which was sufficiently small compared with the ASTM E1921 prediction of 2Σ/μ=56(1-20/μ)% = 47%. Thus, from a fracture toughness standpoint, the experimental results for the 10t SE(B) specimens were considered to be valid and capable of being compared with the numerical predictions, despite the fact that only two data points were obtained.Considering the fact that thea/W used in the EP-FEA was 0.50, which was different from the experimental result of 0.54, EP-FEA with a/W=0.54 was rerun, resulting in negligible small difference in the predicted minimum Jc of 58 N/mm. Comparing the test results of Jc=79.8 and 68.1 N/mm with the updated prediction, it was concluded that the (4δt,σ22c) criterion could properly and consequently predict the minimum Jc of the 10t SE(B) specimen.In summary, it was concluded that the(4δt,σ22c) criterion could properly predict the occurrence of KJc fracture and the minimum Jc of the 10t SE(B) mm specimen, despite the fact that the M for the specimen did not satisfy ASTM E1921’s requirement of M≥30.


### 4.3.2. Test Results for the 3t and 2t SE(B) Specimens

Fracture surfaces andP-Vg diagrams of the 2t and 3t specimens are summarized in Figures 11 and 12, respectively. Note that Vg=1 mm does not represent the value at final fracture, because the maximum measurement capacity of the clip gauge was this value. As expected, the 2t specimens in Figure 11 showed that large stable crack extension Δap preceded before cleavage fracture, obviously not satisfying the ASTM E1921 requirement of Δap<(W-a)/20. Thus, the (4δt,σ22c) criterion properly predicted the nonoccurrence of KJc fracture for the 2t SE(B) specimen.Figure 11
Fracture surfaces and loadP versus crack-mouth opening displacement Vg diagrams of the 2t SE(B) specimens (S55C, 20°C). Large stable crack extension before cleavage fracture was observed, as predicted from the (4δt,σ22c) failure criterion. Note that Vg=1 mm does not correspond to the final fracture.Figure 12
Fracture surfaces and loadP versus crack-mouth opening displacement Vg diagrams of the 3t SE(B) specimens (S55C, 20°C). Pop-in correlated with cleavage mechanism was observed for specimen id 1. However, large stable crack extension before cleavage fracture was observed for specimen id 2, as predicted from the (4δt,σ22c) failure criterion. Note that Vg=1 mm does not correspond to the final fracture.
(a) (b)P - V g diagrams for the 3t specimens (Figure 12(b)) were different from those of the 2t specimens; that is, specimen id 1 showed “pop-in” phenomena. From the fracture surface of specimen id 1 in Figure 12(a), this pop-in was correlated with one of the two significant cleavage fracture areas on the fracture surface. Because ASTM E1921 states that “all pop-in crack initiation K values for cracks that advance by a cleavage-driven mechanism are to be regarded as eligible KJc data,” specimen id 1 showed KJc fracture. This might have some relationship with the fact that σ22d exceeded σ22c for the 3t SE(B) specimen, but further study in the future is necessary. The fracture surface of specimen id 2 showed an obviously large stable crack extension. In summary, one of the two 3t specimens did not show KJc fracture. Thus, it was concluded that the (4δt,σ22c) criterion properly predicted the nonoccurrence of KJc fracture for the 3t SE(B) specimen.In summary, it was concluded that the(4δt,σ22c) criterion could appropriately predict invalid KJc fracture for the 2t and 3t SE(B) specimens.


## 4.3.1. Test Results for the 10t SE(B) Specimens

TheP-Vg diagrams of the 10t SE(B) specimens are compared with VgASTM, which is the Vg calculated from the elastic compliance given in ASTM E1820 [36].As shown in Figure10, the two experimental P-Vg diagrams showed good reproducibility. Moreover, the linear slope of the experimental P-Vg diagrams exhibited good agreement with the P-VgASTM. Therefore, the experimental results of the 10t SE(B) specimens were considered to be valid and capable of being compared with the numerical predictions, despite the fact that only two tests were conducted.Figure 10
P - V g diagram of the 10t SE(B) specimens (S55C steel, 20°C): KJc fracture followed after relatively large plastic deformation.TheP-Vg diagrams for both tests showed a sudden increase in Vg after the maximum load was reached, indicating that the clip gauge dropped off. This suggested that an unstable fracture occurred.The fracture surface of the 10t specimens clearly showed cleavage fracture after very small stable crack extensionΔap, satisfying the ASTM E1921 requirement to be less than min⁡((W-a)/20,1mm)=0.23mm. The values of the measured Δap are listed in Table 2. Thus, the so-called KJc fracture was observed, as predicted with the (4δt,σ22c) criterion.Table 2
Fracture toughness test results of 10t SE(B) specimens (S55C steel, 20°C). Here,μ and Σ denote the mean and standard deviation of each parameter, respectively. Though M was smaller than 30, cleavage fracture with negligible stable crack extension was observed.
Specimen id 1 2 μ Σ 2Σ/μ% a / W 0.54 0.54 0.54 0 P c (kN) 4.46 4.25 4.36 0.105 K c (MPam1/2) 54.2 51.6 52.9 1.30 J c (N/mm) 79.8 68.1 74.0 5.85 K J c (MPam1/2) 134 124 129 5.00 7.75 Δ a p (mm) 0.13 0.02 0.075 0.055 M 22.7 26.6 24.7 1.95Fracture toughness test results are summarized in Table2. The average of Jc=74.0 N/mm was 1.7 times larger than that of the 25t SE(B) specimen. This magnification agreed with the empirical thickness relationship describing Jc, that is, (10/25)−1/2 = 1.6. M was close to but smaller than 30, as predicted. Although only two data points were available, the standard deviation to the average ratio of KJc was 7.75% for the current data, which was sufficiently small compared with the ASTM E1921 prediction of 2Σ/μ=56(1-20/μ)% = 47%. Thus, from a fracture toughness standpoint, the experimental results for the 10t SE(B) specimens were considered to be valid and capable of being compared with the numerical predictions, despite the fact that only two data points were obtained.Considering the fact that thea/W used in the EP-FEA was 0.50, which was different from the experimental result of 0.54, EP-FEA with a/W=0.54 was rerun, resulting in negligible small difference in the predicted minimum Jc of 58 N/mm. Comparing the test results of Jc=79.8 and 68.1 N/mm with the updated prediction, it was concluded that the (4δt,σ22c) criterion could properly and consequently predict the minimum Jc of the 10t SE(B) specimen.In summary, it was concluded that the(4δt,σ22c) criterion could properly predict the occurrence of KJc fracture and the minimum Jc of the 10t SE(B) mm specimen, despite the fact that the M for the specimen did not satisfy ASTM E1921’s requirement of M≥30.


## 4.3.2. Test Results for the 3t and 2t SE(B) Specimens

Fracture surfaces andP-Vg diagrams of the 2t and 3t specimens are summarized in Figures 11 and 12, respectively. Note that Vg=1 mm does not represent the value at final fracture, because the maximum measurement capacity of the clip gauge was this value. As expected, the 2t specimens in Figure 11 showed that large stable crack extension Δap preceded before cleavage fracture, obviously not satisfying the ASTM E1921 requirement of Δap<(W-a)/20. Thus, the (4δt,σ22c) criterion properly predicted the nonoccurrence of KJc fracture for the 2t SE(B) specimen.Figure 11
Fracture surfaces and loadP versus crack-mouth opening displacement Vg diagrams of the 2t SE(B) specimens (S55C, 20°C). Large stable crack extension before cleavage fracture was observed, as predicted from the (4δt,σ22c) failure criterion. Note that Vg=1 mm does not correspond to the final fracture.Figure 12
Fracture surfaces and loadP versus crack-mouth opening displacement Vg diagrams of the 3t SE(B) specimens (S55C, 20°C). Pop-in correlated with cleavage mechanism was observed for specimen id 1. However, large stable crack extension before cleavage fracture was observed for specimen id 2, as predicted from the (4δt,σ22c) failure criterion. Note that Vg=1 mm does not correspond to the final fracture.
(a) (b)P - V g diagrams for the 3t specimens (Figure 12(b)) were different from those of the 2t specimens; that is, specimen id 1 showed “pop-in” phenomena. From the fracture surface of specimen id 1 in Figure 12(a), this pop-in was correlated with one of the two significant cleavage fracture areas on the fracture surface. Because ASTM E1921 states that “all pop-in crack initiation K values for cracks that advance by a cleavage-driven mechanism are to be regarded as eligible KJc data,” specimen id 1 showed KJc fracture. This might have some relationship with the fact that σ22d exceeded σ22c for the 3t SE(B) specimen, but further study in the future is necessary. The fracture surface of specimen id 2 showed an obviously large stable crack extension. In summary, one of the two 3t specimens did not show KJc fracture. Thus, it was concluded that the (4δt,σ22c) criterion properly predicted the nonoccurrence of KJc fracture for the 3t SE(B) specimen.In summary, it was concluded that the(4δt,σ22c) criterion could appropriately predict invalid KJc fracture for the 2t and 3t SE(B) specimens.


## 5. Discussion

This paper examined whether the(4δt,σ22c) failure criterion was applicable to the miniaturized SE(B) specimens. Past experience of application of the criterion to small SE(B) was for (W,B)=(6.4,15.9) and (12.7,8) mm for A533B steel [18]. The guideline of the minimum miniaturized Chary type SE(B) specimen satisfying the ASTM E1921 requirements (e.g., M≥30 and stable crack extension Δap<(W-a)/20; described as KJc fracture in this paper) was known to be 5t in size [33]. Considering the restriction M≥30 for the material S55C and these backgrounds, 2t-, 3t-, 10t-, and 25t-sized Charpy type SE(B) were examined. Focus was placed on (1) whether the criterion could predict the occurrence of KJc fracture and (2) whether σ22c is identical to that observed in full-sized specimens in the case where KJc fracture occurred.Regarding point (1), the results showed that the(4δt,σ22c) criterion could appropriately predict a KJc fracture naturally for specimens for the 25t and 10t specimens. The (4δt,σ22c) criterion could also predict that KJc fracture does not occur for the 3t and 2t specimens if the necessary condition, that is, “the stress level of σ22d is maintained as σ22c for increasing load,” is explicitly considered. This necessary condition was not stated in the original proposal of the criterion [3] but seems to be automatically satisfied for ordinary-sized specimens whose M≫30. Because σ22d is measured at a variable location of x1=4δt and because 4δt increases with load to reflect the stable crack extension, cases such as Figures 9(b) and 9(c) indicate that the region of high stress level ahead of the crack cannot be maintained after the load σ22d shows a maximum for JFEA. Thus, qualitatively, large stable crack extension was expected.Regarding point (2),σ22c obtained from the 10t specimen exhibited only a small difference with that of 25t. The minimum JFEA that could satisfy σ22d=σ22c for the 10t specimen conservatively predicted experimental Jc. The process can definitely be applied to the reverse case; σ22c obtained from the 10t mm specimen can be used to predict the Jc obtained from the 25t specimens.In summary, the results from this work appear to demonstrate the applicability of the modified Ritchie-Knott-Rice (i.e.,(4δt,σ22c)) failure criterion for examining the feasibility of miniaturized Charpy type SE(B) specimens. It is expected that if a KJc fracture is predicted by the (4δt,σ22c) criterion and the implicit necessary condition (i.e., “the stress level of σ22d is maintained as σ22c for increasing load”) is satisfied for a miniaturized SE(B) specimen for a specific material and temperature, it is possible to transfer Jc obtained using this miniaturized specimen to the Jc expected for a 25t SE(B) specimen.There might be an opinion that in the experiments cleavage fracture occurs after microductile (or stable) crack extension, whereas in the FE-modeling a stationary crack without crack extension is treated. Strictly speaking, the current FE-modeling reflects some crack extension due to crack-tip blunting, which has been understood to correspond to the stretch-zone. Though the stable crack extension is very large compared with this stretch-zone, the conclusions of the current study are considered as valid, because the effect of the crack-length on the critical stressσ22c is small. The (4δt,σ22c) criterion was originally proposed to transfer Jc’s obtained with specimens of different crack length [3] and σ22c was the critical value that is independent of the crack length.There might be another opinion that the condition “stress level ofσ22d is maintained for increasing load” is questionable. However, it has long been known that crack-tip stress distribution reaches a steady state above some load level if distance from the crack-tip is normalized as (rσYS0/J) [31]. Usually, δt has a linear relationship with J in this load range; thus, σ22d is expected to be constant and independent of J. Considering the fact that KJc fracture was always observed to occur after σ22d reached σ22c for A533B steel [20] and for S55C steel in this work and in [14], the minimum J that can satisfy σ22d=σ22c seems to correspond to the minimum Jc observed with the specimen configuration and the material at a specific temperature. This finding is consistent with the opinion of Chen et al. that “the minimum fracture toughness is a definite parameter determined by the specimen geometry and yielding properties” [26] and will be examined in more detail in the future.


## 6. Conclusions

This paper examined whether the(4δt,σ22c) failure criterion, which is one of the modified RKR criteria, was applicable to the miniaturized Charpy type SE(B) specimens, that is, (1) whether the criterion could predict the occurrence of cleavage fracture accompanied by negligibly small stable crack extension (denoted as KJc fracture in this paper) and (2) whether σ22c is identical to that observed in full-sized specimens in the case where KJc fracture occurred. 25t, 10t, 3t, and 2t Charpy type SE(B) specimens manufactured with S55C steel were tested at 20°C. The results showed that the (4δt,σ22c) criterion could appropriately distinguish the occurrence of KJc fracture, by explicitly considering the necessary condition (i.e., “the stress level of σ22d is maintained as σ22c for increasing load”) with the original criterion (i.e., “KJc fracture occurs when σ22d exceeds a critical value σ22c”). The σ22c obtained for the 25t and 10t specimens exhibited only a small difference, indicating that Jc obtained from the 10t mm specimens can be used to predict the Jc that will be obtained with the 25t specimens.



---

*Source: 3728035-2016-10-27.xml*