2. Specimen size and geometry influence on fracture toughness parameters

The effect of the specimen size and the geometry is variable with the material fracture behavior. Most of the technical materials exhibit transition behavior, and thus three basic regions can be distinguished: the lower shelf, transition and upper shelf.

All values of KJ could be obtained by conversion from J-values using Eq. (1):

but prior to attaining the maximum load (the onset of the transition region).

scatter of material properties, tB could be within the (tDBL-tDBU) region. tC—the lower shelf fracture toughness regime is below this temperature.

2.1. Brittle region (lower shelf region)

tDBL—ductile-brittle lower; the end of the region with the above fracture mode.

The following transition temperatures are denoted in the diagrams:

Figure 1. Schematic representation of fracture toughness-temperature dependence.

KJ ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi J:E <sup>1</sup> � <sup>ν</sup><sup>2</sup> ð Þ <sup>s</sup>

Fracture Toughness Determination with the Use of Miniaturized Specimens

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tDBU—ductile-brittle upper; the cleavage fracture occurs after certain amount of ductile tearing

tB—brittle-fracture transition temperature; the onset of the region, where cleavage fracture is initiated ahead of the blunted crack tip but without prior ductile tearing. Due to inherent

When a material behaves in a linear elastic manner prior to failure, such that the plastic zone is small compared to the specimen dimensions, a critical value of the Mode I stress intensity factor KIc may be an appropriate fracture parameter. In the ASTM E 399 [3] and similar test methods, KIc is referred to as "plane strain fracture toughness." Four specimen configurations are permitted for the fracture toughness determination by the current version of E 399: the compact tension (CT), single edge-notched bend bar (SE(B)), arc-shaped and disc-shaped specimens. However,

(1)

145

Holzmann and Vlach [1, 2] suggested schematic diagram of fracture toughness behavior with temperature (see Figure 1), where following fracture toughness parameters are used for an analysis of the fracture behavior:

KJ0.2—fracture toughness after 0.2 mm of blunting and crack extension.

KJm—value of KJ at the maximum load Fmax for stable fracture behavior and nonlinear test record.

KJu—post-ductile tearing cleavage fracture toughness; only Jc-tests terminated by cleavage prior to attaining the maximum load Fmax were taken into account.

KJC—fracture toughness for the onset of cleavage fracture after elastic-plastic deformation, but with no prior ductile tearing.

KC—the fracture toughness at the onset of brittle fracture; test record linear or with no significant deviation from linearity, but size validity requirements of ASTM E399 are not met.

KIC—plane strain fracture toughness.

Fracture Toughness Determination with the Use of Miniaturized Specimens http://dx.doi.org/10.5772/intechopen.73093 145

Figure 1. Schematic representation of fracture toughness-temperature dependence.

All values of KJ could be obtained by conversion from J-values using Eq. (1):

$$K\_{\rm J} = \sqrt{\frac{\rm J.E.}{(1 - \nu^2)}}\tag{1}$$

The following transition temperatures are denoted in the diagrams:

tDBU—ductile-brittle upper; the cleavage fracture occurs after certain amount of ductile tearing but prior to attaining the maximum load (the onset of the transition region).

tDBL—ductile-brittle lower; the end of the region with the above fracture mode.

tB—brittle-fracture transition temperature; the onset of the region, where cleavage fracture is initiated ahead of the blunted crack tip but without prior ductile tearing. Due to inherent scatter of material properties, tB could be within the (tDBL-tDBU) region.

tC—the lower shelf fracture toughness regime is below this temperature.

#### 2.1. Brittle region (lower shelf region)

experimental material is only available can be residual service life assessment of in-service components, when the experimental material only by semi-destructive approach can be obtained. Cases during development of new materials, generally preparation of the materials with limited volume such as severe plastic deformation processes for bulk nanomaterials preparation. Recently, also for the assessment of the parts produced by additive manufacturing

This chapter is going to provide overview of reporting values of the results obtained with the use of miniaturized specimens with hints how can be small-size-based results related to the standard-sized specimen results. These techniques enable assessment of the fracture behavior from small material volumes allowing, for example, also local anisotropy assessment. In the first part of the chapter, some theoretical background for small-size specimen testing is provided for different fracture regime behaviors ranging from brittle up to full ductile behavior. Several mini specimens' geometries are demonstrated here that are subsequently applied on the experimental materials. Three materials are presented here, ferritic steel used for Master Curve-based assessment and then stainless steel and Ti-alloy produced by additive manufacturing technology. The results are summarized in order to provide inside into the facture behavior assessment with the use of miniaturized specimens providing background for practical application of these

2. Specimen size and geometry influence on fracture toughness

be distinguished: the lower shelf, transition and upper shelf.

KJ0.2—fracture toughness after 0.2 mm of blunting and crack extension.

prior to attaining the maximum load Fmax were taken into account.

The effect of the specimen size and the geometry is variable with the material fracture behavior. Most of the technical materials exhibit transition behavior, and thus three basic regions can

Holzmann and Vlach [1, 2] suggested schematic diagram of fracture toughness behavior with temperature (see Figure 1), where following fracture toughness parameters are used for an

KJm—value of KJ at the maximum load Fmax for stable fracture behavior and nonlinear test

KJu—post-ductile tearing cleavage fracture toughness; only Jc-tests terminated by cleavage

KJC—fracture toughness for the onset of cleavage fracture after elastic-plastic deformation, but

KC—the fracture toughness at the onset of brittle fracture; test record linear or with no significant deviation from linearity, but size validity requirements of ASTM E399 are not met.

techniques are application for small-size specimen testing.

approaches.

144 Contact and Fracture Mechanics

parameters

record.

analysis of the fracture behavior:

with no prior ductile tearing.

KIC—plane strain fracture toughness.

When a material behaves in a linear elastic manner prior to failure, such that the plastic zone is small compared to the specimen dimensions, a critical value of the Mode I stress intensity factor KIc may be an appropriate fracture parameter. In the ASTM E 399 [3] and similar test methods, KIc is referred to as "plane strain fracture toughness." Four specimen configurations are permitted for the fracture toughness determination by the current version of E 399: the compact tension (CT), single edge-notched bend bar (SE(B)), arc-shaped and disc-shaped specimens. However,

strain condition for thickness 1.6 mm. Considering investigated material in this chapter, Table 2 shows hypothetic KIc value under plain strain condition for different specimen geometries and sizes. Note that the toughness level calculated here corresponds to the lower shelf for these materials. Thus valid KIc tests on these materials would be possible only at low

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147

In ASTM E 399 it is listed that "Variation in the value of KIc can be expected within the allowable range of specimen proportions, a/W and W/B. KIc may also be expected to rise with increasing ligament size. Notwithstanding these variations, however, KIc is believed to represent a lower limiting value of fracture toughness (for 2 % apparent crack extension) in the

Therefore, valid KIc is generally accepted as size-independent value though some minor deviation could not be avoided. As it can be seen from Tables 1 and 2, it is very difficult to obtain valid fracture toughness values with the use of subsized specimens in this region, except for very brittle materials. Therefore, subsided specimens will most yield size-dependent values of

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

Material Specimen geometry and size σYS B, a Requested KIc

M-CT 4.0 20.1 CVN 10 10 55 10.0 31.7 KLST 4 2 27 2.0 14.2

M-CT 4.0 26.3 CVN 10 10 55 10.0 41.6 KLST 4 2 27 2.0 18.6

M-CT 4.0 37.1 CVN 10 10 55 10.0 58.6 KLST 4 2 27 2.0 26.2

15CH2NMFA 1 T-CT 502 25.0 50.2

AISI 304 1 T-CT 657 25.0 65.7

AM Ti6Al4V 1 T-CT 927 25.0 92.7

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

MPa mm MPa.m0.5

temperatures, where the materials are too brittle for most structural applications.

environment and at the speed and temperature of the test."

the fracture toughness.

important conclusions:

2.2. Ductile-brittle transition region

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

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

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 specimen ligament size (W-a) must be not less than 2.5(KIc/σYS) 2 , where σYS is the 0.2% offset 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 the width W, the thickness must be also not less than 2.5(KIc/σYS) 2 . These limits could be expressed using Eq. (2), which is not literally listed in the standard ASTM E399 but is noted in Anderson [4]:

$$B, a, (\mathcal{W} - a) \ge 2, \dots \ge \left(\frac{\mathcal{K}\_{\text{IC}}}{\sigma\_{\text{YS}}}\right)^2\\0.45 \le a/\mathcal{W} \le 0.55\tag{2}$$

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


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

strain condition for thickness 1.6 mm. Considering investigated material in this chapter, Table 2 shows hypothetic KIc value under plain strain condition for different specimen geometries and sizes. Note that the toughness level calculated here corresponds to the lower shelf for these materials. Thus valid KIc tests on these materials would be possible only at low temperatures, where the materials are too brittle for most structural applications.

In ASTM E 399 it is listed that "Variation in the value of KIc can be expected within the allowable range of specimen proportions, a/W and W/B. KIc may also be expected to rise with increasing ligament size. Notwithstanding these variations, however, KIc is believed to represent a lower limiting value of fracture toughness (for 2 % apparent crack extension) in the environment and at the speed and temperature of the test."

Therefore, valid KIc is generally accepted as size-independent value though some minor deviation could not be avoided. As it can be seen from Tables 1 and 2, it is very difficult to obtain valid fracture toughness values with the use of subsized specimens in this region, except for very brittle materials. Therefore, subsided specimens will most yield size-dependent values of the fracture toughness.
