2.2. Ductile-brittle transition region

the vast majority of fracture toughness tests are performed on either CT or SE(B) specimens. Figure 2 shows basic dimensions of both types of specimens of these two specimen types, assuming the same characteristic dimensions (B, W, a). It can be seen that the specimen design is such that all of the key dimensions (i.e., a, B and W � a) are approximately equal and, thus,

Figure 2. Comparison of the profiles of CT and SE(B) specimens with the same in-plane characteristic dimensions (B, W, a).

In order to fulfill the size requirements for size-independent fracture toughness value determination according to the ASTM E399, the minimal specimen thickness is 1.6 mm, while the

yield strength. Considering recommended proportion of the thickness B which is nominally one-half the specimen width W and crack length, a, is nominally between 0.45 and 0.55 times

expressed using Eq. (2), which is not literally listed in the standard ASTM E399 but is noted

σYS <sup>2</sup>

Because the size requirements of ASTM E 399 are very stringent, it is very difficult and sometimes impossible to measure a valid KIc for most of the structural materials. As an example, we can consider structural steel with σYS = 330 MPa and typical KIc values of 210 MPa.m0.5. According to Eq. (2), the required thickness must be higher than 1 m, and the width (since a/W = 0.5) must be more than 2 m (see Table 1). Materials are seldom available in such dimensions, and if yes, machining and testing would have to be done using special machine, and all investigation would be extremely expensive. On the other hand, material such as tool steels exhibits high yield strength and low fracture toughness, and Table 1 shows combination of these two values for obtaining valid fracture toughness value under plain

Example σYS KIc B, a B, a

Steel\_1 330 210 1012 1012.4 Steel\_2 1600 40 0.002 1.6

MPa MPa.m0.5 m mm

2

2

0:45 ≤ a=W ≤ 0:55 (2)

, where σYS is the 0.2% offset

. These limits could be

geometry selection is only question of less material consumption from semi-product.

specimen ligament size (W-a) must be not less than 2.5(KIc/σYS)

Table 1. Examples of the calculated thickness B for given σYS and KIc values.

in Anderson [4]:

146 Contact and Fracture Mechanics

the width W, the thickness must be also not less than 2.5(KIc/σYS)

B, a, Wð Þ � <sup>a</sup> <sup>≥</sup> <sup>2</sup>, <sup>5</sup> � <sup>K</sup>IC

In this region, micro-mechanisms of cleavage fracture cause that the cleavage toughness data tend to be highly scattered when compared to the lower shelf region, and thus a statistical analysis must be performed as shown in Table 3. Rather than single value of toughness at a particular temperature, the material has a toughness distribution. Research over the past three decades on the fracture of ferritic steels in the ductile-brittle transition region has led to two important conclusions:


Table 2. Calculated requested parameter KIc for valid plain strain condition considering investigated material in this chapter.


Table 3. Test matrix for the fracture toughness tests.


ASTM E1921 [5] implements this knowledge, and the standard outlines a fracture toughness test method that is based on the Master Curve concept for ferritic steels with yield strengths ranging from 275 to 825 MPa. Thanks to previous research, methodology for determination of toughness distribution is greatly simplified including size effect prediction. In order to directly compare toughness data obtained from different thickness specimens, a statistical size correction is employed to equilibrate the highly stressed material volume sampled at the crack tip by cleavage. The following Eq. (3), derived from ASTM E1921, shall be used for conversion to an equivalent value of KJc(1T) for a reference 1 T specimen with thickness of B1T = 25 mm:

$$K\_{\mathbb{K}(1T)} = 20 + \left(K\_{\mathbb{K}(X)} - 20\right) . \left(\frac{B\_X}{B\_{1T}}\right)^{1/4} \tag{3}$$

where E is the Young's modulus, σys is the material yield strength at the test temperature and

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It should be also mentioned that specimens can have side grooves, but they are optional (see Figure 4). In fact, side grooving may be indispensable as a means for controlling crack front straightness in bend bars of square cross section. The total side-grooved depth shall not exceed 0.25B. Side grooves with an included angle of 45 and a root radius of 0.5 0.2 mm usually

In the ASTM E1921 is noted that at high values of fracture toughness relative to specimen size and material flow properties, the values of KJc that meet the requirements of Eq. (3) may not always provide a unique description of the crack front stress strain fields due to some loss of constraint caused by excessive plastic flow. The application which played a key role for development of small specimen test technology (SSTT) was the evaluation of properties of irradiated materials. For example, many investigations for integrity assessments of nuclear components were done in VTT in Finland where also Master Curve method was developed [7] and validated [8]. Wallin et al. were further developing SSTT for Master Curve determination using mini-Charpy specimen (KLST) since 1997 [9]. Scibetta et al. [10] investigated different reactor pressure vessel steels using standard and miniature specimens. The reference temperatures obtained from subsize SE(B) and C(T) geometry tend to give a lower reference temperature by about 8.5C than larger specimens which was considered as a consequence of the constraint loss. Kima et al. [11] investigated effects of specimen size on fracture toughness using 1 CT, 1/2 CT and 1/4 CT. It was found that small specimen test technique for F82H steel can be applicable to evaluate the fracture toughness properties due

b0 is ligament W-a.

produce the desired results.

to no substantial effects of specimen size.

Figure 3. Validity window of the Master Curves for the ferritic materials [6].

where KJc(X) is measured fracture toughness of the tested specimen and Bx refers to the nominal thickness of the tested specimen in millimeters, regardless of side grooves. Once toughness values at a fixed temperature have been converted to 1 T equivalent values, the further evaluation which leads to a reference transition temperature T0 is performed according to standard as for 1 T specimen.

The reference temperature T0 should be relatively independent of the test temperature that has been selected. Hence, data that are distributed over a restricted temperature range, namely, T0 � 50�C, can be used to determine T0. This temperature range together with the specimen size requirement (see Eq. (4)) provides a validity window for application of the Master Curve methodology. As an example, such a validity window for Charpy-size fracture specimens (W = B = 10 mm, a/W = 0.5) is shown in Figure 3.

$$K\_{\rm fC(limit)} = \sqrt{\frac{Eb\_0 \sigma\_{ys}}{30.(1 - \nu^2)}}\tag{4}$$

where E is the Young's modulus, σys is the material yield strength at the test temperature and b0 is ligament W-a.

It should be also mentioned that specimens can have side grooves, but they are optional (see Figure 4). In fact, side grooving may be indispensable as a means for controlling crack front straightness in bend bars of square cross section. The total side-grooved depth shall not exceed 0.25B. Side grooves with an included angle of 45 and a root radius of 0.5 0.2 mm usually produce the desired results.

In the ASTM E1921 is noted that at high values of fracture toughness relative to specimen size and material flow properties, the values of KJc that meet the requirements of Eq. (3) may not always provide a unique description of the crack front stress strain fields due to some loss of constraint caused by excessive plastic flow. The application which played a key role for development of small specimen test technology (SSTT) was the evaluation of properties of irradiated materials. For example, many investigations for integrity assessments of nuclear components were done in VTT in Finland where also Master Curve method was developed [7] and validated [8]. Wallin et al. were further developing SSTT for Master Curve determination using mini-Charpy specimen (KLST) since 1997 [9]. Scibetta et al. [10] investigated different reactor pressure vessel steels using standard and miniature specimens. The reference temperatures obtained from subsize SE(B) and C(T) geometry tend to give a lower reference temperature by about 8.5C than larger specimens which was considered as a consequence of the constraint loss. Kima et al. [11] investigated effects of specimen size on fracture toughness using 1 CT, 1/2 CT and 1/4 CT. It was found that small specimen test technique for F82H steel can be applicable to evaluate the fracture toughness properties due to no substantial effects of specimen size.

Figure 3. Validity window of the Master Curves for the ferritic materials [6].

1. Scatter in fracture toughness data in the transition region follows a characteristic statistical

).

Material Tests Region of fracture toughness results

2. The shape of the fracture toughness vs. temperature curve in the transition range is virtually identical for all ferritic steels. The only difference between steels is the absolute

ASTM E1921 [5] implements this knowledge, and the standard outlines a fracture toughness test method that is based on the Master Curve concept for ferritic steels with yield strengths ranging from 275 to 825 MPa. Thanks to previous research, methodology for determination of toughness distribution is greatly simplified including size effect prediction. In order to directly compare toughness data obtained from different thickness specimens, a statistical size correction is employed to equilibrate the highly stressed material volume sampled at the crack tip by cleavage. The following Eq. (3), derived from ASTM E1921, shall be used for conversion to an

equivalent value of KJc(1T) for a reference 1 T specimen with thickness of B1T = 25 mm:

KJcð Þ <sup>1</sup><sup>T</sup> <sup>¼</sup> <sup>20</sup> <sup>þ</sup> KJc Xð Þ � <sup>20</sup> � �: BX

where KJc(X) is measured fracture toughness of the tested specimen and Bx refers to the nominal thickness of the tested specimen in millimeters, regardless of side grooves. Once toughness values at a fixed temperature have been converted to 1 T equivalent values, the further evaluation which leads to a reference transition temperature T0 is performed according to standard as

The reference temperature T0 should be relatively independent of the test temperature that has been selected. Hence, data that are distributed over a restricted temperature range, namely, T0 � 50�C, can be used to determine T0. This temperature range together with the specimen size requirement (see Eq. (4)) provides a validity window for application of the Master Curve methodology. As an example, such a validity window for Charpy-size fracture specimens

s

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Eb0σys 30: 1 � ν<sup>2</sup> ð Þ

KJCð Þ limit ¼

B1<sup>T</sup> � �<sup>1</sup>=<sup>4</sup>

(3)

(4)

distribution that is very similar for all ferritic steels.

Tensile tests Facture toughness tests

Standard Mini 1 T-CT 0.16 T-CT CVN KLST 2 T-CT 15CH2NMFA X X X X X X X Transition region AISI 304 X X X X X X Upper shelf Ti6AL4V X X X Upper shelf

position of this curve on the temperature axis.

Note: CVN, standard Charpy V-notched specimen (10 � <sup>10</sup> � 55 mm3

Table 3. Test matrix for the fracture toughness tests.

148 Contact and Fracture Mechanics

(W = B = 10 mm, a/W = 0.5) is shown in Figure 3.

for 1 T specimen.

Figure 4. Side grooves in a fracture mechanics test specimen.

Recently, great attention is focused on mini-CT (0.16 T-CT) specimen geometry that can be made out of the broken halves of standard Charpy specimens. In 2014, round robin program focused on verification of the reliability and robustness of experimental data of the mini-CT was carried out among different laboratories. The results of the round robin confirmed that the mini-CT specimens offer a very attractive opportunity to derive the same fracture toughness reference temperature values, T0, as those derived by larger fracture toughness specimens [12].

correction [15, 17]. However closer description of these approaches is out of the scope of the

Figure 5. Layout of mini-0.16 T-CT specimens that can be extracted out of the broken halves of Charpy specimens and its

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In the case of ductile materials, first the blunting of preexisting cracks occurs during loading followed by formation of voids ahead of the crack tip at the critical strain. These voids finally coalesce with the crack tip leading to the crack propagation. Hence, the ductile crack initiation cannot be defined as a point in the J-Δa curve but rather as a process which occurs over a range. For a J-R curve determination, it is necessary to know the crack length at corresponding loading level. There are basically two approaches: single-specimen and multiple specimen methods. For the multiple specimen test method, several "identical" specimens are loaded to different levels, and the achieved crack lengths are usually measured visually at the fracture surface. In the case of the single-specimen method, in order to obtain a full range pf crack lengths for J-R curve determination from only one specimen, three widely used single-specimen test methods were developed with the crack lengths being monitored during the test. One is the elastic unloading compliance method that is the most often used out of the single-specimen methods. Another technique is the electrical potential drop method and also the normalization method, both described in the

From a J-R curve, the characteristic values of elastic-plastic fracture mechanics are determined. One of the significant parameters is the plane strain initiation toughness JIc that provides a measure of the crack growth resistance near the onset of stable crack growth for mode-I cracks. Since it is difficult to define the instance of crack initiation in ductile metals, different definitions of the initiation toughness were used in different test standards. ASTM E1820 adopts an engineering definition of JIc at the intersection of a 0.2-mm offset construction line and the J-R

current chapter.

overall dimensions.

2.3. Ductile region

ASTM 1820 [18].

curve, as shown by JQ in Figure 6.

Sokolov [13, 14] tested in 2016 and 2017 the mini-CTspecimens with dimension of 10 <sup>10</sup> 4 mm3 (see Figure 5) on materials HSST Plate 13B and un-irradiated Linde 80 WF-70 weld, respectively. The T0 value derived from a relatively small number of mini-CT specimens in these studies is in remarkable agreement with the T0 value previously reported from a much larger number of conventional fracture toughness specimens. At the same time, these studies indicate that in the real practice, it is highly advisable to use much larger number of specimens than the minimum amount prescribed in ASTM E1921, when mini specimens are employed.

Also Wallin in work [15] focused his attention on mini-CT specimen. His work indicates that miniature C(T) specimens fulfilling the ASTM E1921 size requirement behave like larger specimens loaded to the same proportional loading. Side grooving was found to have a minor effect on the initiator locations and was not significantly affected by the side groove geometry.

For completeness, it should be noted that three different methods to quantify constraint have also been proposed, J small scale yielding correction, Q-parameter and the T-stress. [16]. Also Wallin considers Q-parameter and the T-stress for Master Curve reference temperature T0

Figure 5. Layout of mini-0.16 T-CT specimens that can be extracted out of the broken halves of Charpy specimens and its overall dimensions.

correction [15, 17]. However closer description of these approaches is out of the scope of the current chapter.

#### 2.3. Ductile region

Recently, great attention is focused on mini-CT (0.16 T-CT) specimen geometry that can be made out of the broken halves of standard Charpy specimens. In 2014, round robin program focused on verification of the reliability and robustness of experimental data of the mini-CT was carried out among different laboratories. The results of the round robin confirmed that the mini-CT specimens offer a very attractive opportunity to derive the same fracture toughness reference temperature values, T0, as those derived by larger fracture tough-

Sokolov [13, 14] tested in 2016 and 2017 the mini-CTspecimens with dimension of 10 <sup>10</sup> 4 mm3 (see Figure 5) on materials HSST Plate 13B and un-irradiated Linde 80 WF-70 weld, respectively. The T0 value derived from a relatively small number of mini-CT specimens in these studies is in remarkable agreement with the T0 value previously reported from a much larger number of conventional fracture toughness specimens. At the same time, these studies indicate that in the real practice, it is highly advisable to use much larger number of specimens than the minimum

Also Wallin in work [15] focused his attention on mini-CT specimen. His work indicates that miniature C(T) specimens fulfilling the ASTM E1921 size requirement behave like larger specimens loaded to the same proportional loading. Side grooving was found to have a minor effect on the initiator locations and was not significantly affected by the side groove geometry. For completeness, it should be noted that three different methods to quantify constraint have also been proposed, J small scale yielding correction, Q-parameter and the T-stress. [16]. Also Wallin considers Q-parameter and the T-stress for Master Curve reference temperature T0

amount prescribed in ASTM E1921, when mini specimens are employed.

ness specimens [12].

150 Contact and Fracture Mechanics

Figure 4. Side grooves in a fracture mechanics test specimen.

In the case of ductile materials, first the blunting of preexisting cracks occurs during loading followed by formation of voids ahead of the crack tip at the critical strain. These voids finally coalesce with the crack tip leading to the crack propagation. Hence, the ductile crack initiation cannot be defined as a point in the J-Δa curve but rather as a process which occurs over a range. For a J-R curve determination, it is necessary to know the crack length at corresponding loading level. There are basically two approaches: single-specimen and multiple specimen methods. For the multiple specimen test method, several "identical" specimens are loaded to different levels, and the achieved crack lengths are usually measured visually at the fracture surface. In the case of the single-specimen method, in order to obtain a full range pf crack lengths for J-R curve determination from only one specimen, three widely used single-specimen test methods were developed with the crack lengths being monitored during the test. One is the elastic unloading compliance method that is the most often used out of the single-specimen methods. Another technique is the electrical potential drop method and also the normalization method, both described in the ASTM 1820 [18].

From a J-R curve, the characteristic values of elastic-plastic fracture mechanics are determined. One of the significant parameters is the plane strain initiation toughness JIc that provides a measure of the crack growth resistance near the onset of stable crack growth for mode-I cracks. Since it is difficult to define the instance of crack initiation in ductile metals, different definitions of the initiation toughness were used in different test standards. ASTM E1820 adopts an engineering definition of JIc at the intersection of a 0.2-mm offset construction line and the J-R curve, as shown by JQ in Figure 6.

Figure 6. A typical J-R curve with test data points, construction lines and limitation bounds required by ASTM E1820.

A valid J-R curve consists of the measured data points in a region defined by the coordinate axis and the Jmax and Δamax limits. These two limits describe the measurement capacity of test specimen. The maximum J-integral capacity for a specimen is given by the smaller of:

$$\mathbf{J}\_{\text{max}} = b \sigma\_Y / 10 \text{ or } \mathbf{J}\_{\text{max}} = B \sigma\_Y / 10 \tag{5}$$

where σ<sup>Y</sup> is an effective yield strength assumed as the average of the 0.2% offset yield strength σYS and the ultimate tensile strength σtS. The maximum crack extension capacity for a specimen was defined as

$$
\Delta a\_{\text{max}} = 0.25 \,\text{b}\_0 \tag{6}
$$

Figure 8. Specimen size effects were interpreted here in terms of an increase in the plain stress state region and plastic zone size at the crack tip in the specimen. From the point of specimen thickness effect, this work summarized that the fracture toughness increased as the specimen thickness decreased. From the point of ligament size effect, the fracture toughness decreases

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Figure 7. The J-R curve dependency on the a/W ratio for HY80 steel obtained by Zhu and Joyce [19] using SE(B) specimens

Figure 8. J-R curves of JLF-1 steel (left) and corresponded specimen size (right) [20].

and normalization method.

when the specimens were miniaturized while keeping the same proportions.

where b0 is the initial crack ligament.

Application of fracture mechanics methods to engineering design and structural integrity assessment requires fracture toughness values to be transferred from the laboratory test to a structural application. Experiments have shown that the crack depth, section thickness, specimen size, crack geometry and loading configuration all can have a strong effect on the fracture toughness measurements (K, G, J and d). These effects are referred to as "constraint effect." Joyce and Link [19] tested SE(B) specimens with various a/W ratios to investigate the constraint effect on J-R curves. Figure 7 shows that significant differences exist between the J-R curves for deep and shallow cracks. Similar trend can be observed when only one type of geometry with the same ratio of a/W but with different sizes is used.

Ono et al. [20] tested JLF-1 steel using 1 CT, 1/2 CT and 1/4 CT in the upper shelf region. Obtained J-R curve are very illustrative and showed shallow shape with decreasing size; see Figure 8. Specimen size effects were interpreted here in terms of an increase in the plain stress state region and plastic zone size at the crack tip in the specimen. From the point of specimen thickness effect, this work summarized that the fracture toughness increased as the specimen thickness decreased. From the point of ligament size effect, the fracture toughness decreases when the specimens were miniaturized while keeping the same proportions.

Figure 7. The J-R curve dependency on the a/W ratio for HY80 steel obtained by Zhu and Joyce [19] using SE(B) specimens and normalization method.

Figure 8. J-R curves of JLF-1 steel (left) and corresponded specimen size (right) [20].

A valid J-R curve consists of the measured data points in a region defined by the coordinate axis and the Jmax and Δamax limits. These two limits describe the measurement capacity of test

Figure 6. A typical J-R curve with test data points, construction lines and limitation bounds required by ASTM E1820.

where σ<sup>Y</sup> is an effective yield strength assumed as the average of the 0.2% offset yield strength σYS and the ultimate tensile strength σtS. The maximum crack extension capacity for a speci-

Application of fracture mechanics methods to engineering design and structural integrity assessment requires fracture toughness values to be transferred from the laboratory test to a structural application. Experiments have shown that the crack depth, section thickness, specimen size, crack geometry and loading configuration all can have a strong effect on the fracture toughness measurements (K, G, J and d). These effects are referred to as "constraint effect." Joyce and Link [19] tested SE(B) specimens with various a/W ratios to investigate the constraint effect on J-R curves. Figure 7 shows that significant differences exist between the J-R curves for deep and shallow cracks. Similar trend can be observed when only one type of geometry with

Ono et al. [20] tested JLF-1 steel using 1 CT, 1/2 CT and 1/4 CT in the upper shelf region. Obtained J-R curve are very illustrative and showed shallow shape with decreasing size; see

Jmax ¼ bσY=10 or Jmax ¼ BσY=10 (5)

Δamax ¼ 0:25 b0 (6)

specimen. The maximum J-integral capacity for a specimen is given by the smaller of:

men was defined as

152 Contact and Fracture Mechanics

where b0 is the initial crack ligament.

the same ratio of a/W but with different sizes is used.

Namely, RPV steel GOST 15Ch2NMFA with ferritic-martensitic microstructure, austenitic stainless steel EN X5CrNi18-10 (AISI 304) and Ti-Alloy Ti6Al4V produced by Additive Manufacturing (AM) technology are employed in this study. Ductile and brittle materials facture behavior is investigated here with the use of miniaturized specimens applying J-R

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As the assessment of the fracture toughness parameters requires also tensile test data as input parameters for the evaluation, determination of tensile properties with the use of miniature

Material GOST 15Ch2NMFA were delivered in a form of rod with diameter of 130 mm and length 150 mm. At first, three 2 T-CT specimens were produced in R-C orientation (according to the standard ASTM E399-09 [3]). Technical drawing of 2 T-CT specimens is depicted in Figure 10. Broken halves of the 2 T-CT specimens were subsequently used for production of

Material EN X5CrNi18-10 (AISI 304) was delivered in the form of hot rolled rod with quadratic

Material Ti6Al4V was investigated in the form of bar with dimension of 10 <sup>20</sup> 100 mm<sup>3</sup>

Designation of specimen orientation was done according to the standard [25]. Where the first letter represents the direction normal to the crack plane and second latter represents the expected direction of crack extension. Orientation and its designation of the specimens in the

Tensile test were carried out on standard- and miniature-sized specimens at room temperature under quasi-static loading conditions for demonstration of comparable results obtained with the use of miniaturized specimens. Tests were following procedure according to standard (ISO CSN EN 6892-1) in the case of the full-size specimen testing. Testing procedure based on

. All specimens were produced in T-L orienta-

.

155

curve and Master Curve assessment approaches.

cross section of dimensions 60 <sup>30</sup> 400 mm<sup>3</sup>

3.1. Experimental materials

tion according to standard [3].

prism are depicted in Figure 11.

Figure 10. 2 T-CT specimen geometry.

3.2. Tensile tests

tensile test (M-TT) specimens is also demonstrated here.

the other specimens (tensile test specimens, Charpy specimens, etc.).

Figure 9. Results obtained at room temperature from mini-CT and 1 T-CT specimens of 18MND5 steel [24].

Seok et al. [21] investigated effect of specimen configurations using 0.5–2 T CT and further specimens with constant width (101.6 mm) but different thickness plus specimens with same thickness but different width. Therefore, the effect of plane size, specimen size and thickness could be investigated. Moreover, the effect of the crack length and side grooves was discussed as well. The resulting J-R curve increased with increasing plane size, though there is a difference of increasing amount according to the material states, base or weld metal and stainless or carbon steel. The resulting J-R curves decreased with increasing crack length and showed that the effect of the crack length was significant. However, relatively weak influence was observed from the change of the specimen thickness and size. It was also observed that the J-R curve decreased by applying the side grooves and the effect of side groove was related to material properties.

Lucon et al. [22–24] investigated mini-CT specimen (10 <sup>10</sup> 4.15 mm<sup>3</sup> ) applicability for fracture toughness determination in the upper shelf region. As a general conclusion, in these investigations it was observed that mini-CT specimens consistently and systematically underestimate elastic-plastic fracture toughness as measured from 1 T-CT specimens, in terms of both ductile initiation and tearing resistance. Figure 9 shows an example of such a behavior and also shows that, below approximately J = 200 kJ/m<sup>2</sup> , no significant deviation was observed between data measured from mini-CT and 1 T-CT specimen; below this threshold, mini-CT could therefore provide a reliable measurement of the material's toughness.
