5. Fracture toughness of structural materials

cantilever deflection λ, except for λе, contain a part of the equation λ<sup>p</sup> = λ λ<sup>е</sup> that is not related to the change in specimen ductility. The crack opening values of υ measured in the same way contain the plastic deformation contribution υ<sup>p</sup> = υ υe. The values of λ<sup>p</sup> and υ<sup>p</sup> are

Using Eq. (13), according to the experimentally measured value of cantilever deflection λ (Figure 7), one can determine the relative value of (λλе)/λ<sup>е</sup> = λp/λ<sup>е</sup> as an additional fracture toughness characteristic. It is obvious that the more ductile a material is, the higher is its fracture toughness. The value of λ<sup>p</sup> is not associated with change in specimen ductility since it is determined only by the elastic deflection of the specimen. The stress distribution in the plastic deformation zone is significantly different from the stress field in an elastic medium with a crack. On the way of crack propagation, the material is always subjected to a certain degree of plastic deformation. This means that crack is always surrounded by a layer of the plastically deformed material. The calculations made in Ref. [21] by the method of relaxation elements showed that stress field in the plastic deformation zone differs significantly from the crack stress field in the elastically deformable medium. Plastic deformation leads to stress relaxation. For this reason, there is no singularity in the crack mouth. The maximum stress

very important when simulating the fracture process in the chevron-notched zone.

concentration is observed in the plastic deformation zone.

Figure 7. Scheme of the cantilever deflection.

Figure 6. Dependence υ<sup>e</sup> on Δl and Δλe.

224 Contact and Fracture Mechanics

This section presents the calculation results of the fracture toughness characteristics of VT6 (Ti + 6%Al + 4%V) alloy, Fe-35.4% Ni and 12GBA tube steel.

The specimens 21 � <sup>10</sup> � 6 mm<sup>3</sup> in size were cut from the work piece by the electroerosion method. Then a notch 0.3 mm thick was made with a chevron angle α = 60� (see Figure 4). The crack length at the pre-fracture stage was determined by the specimen images. Alloys with different ability to plastic deformation and with different values of the Young's modulus E were tested. The loading of specimens made of VT6 and Fe + 34.6%Ni alloys was performed by the intrusion of a narrow wedge into the notch at a motion rate of 5 μm/s (Figure 8). The 12GBA tube steel loadings were performed by application of opposite forces to the tips of the notch (Figure 7).

Figure 8 shows the scheme of the specimen wedging. The constant motion rate of the wedge provides the prolonged stage of stable crack propagation initiated at the chevron. The equation for the calculation of P bending the cantilever is obtained from the condition of equilibrium of forces:

$$P = \frac{F \cdot \cos \chi}{2\left[\sin\left(\beta/2\right) + \kappa \cdot \cos\left(\beta/2\right)\right]},\tag{24}$$

where F is the load on the wedge, κ and γ are the friction factor and interplanar angle between the wedge and cantilever, respectively, β is the angle of wedge opening.

As seen from Eq. (19), in order to determine the bending force P, it is important to calculate the friction factor κ. Substituting Eq. (22) into Eq. (8) instead of P, we obtain the following equation for κ:

$$\kappa = \frac{\Delta F}{\Delta L} \frac{2 \cos \chi \left[2l\_0 + a \operatorname{ctg} \left(\alpha/2\right)\right]^2}{\sin \left(\beta/2\right) \left(4l\_0 + a \operatorname{ctg} \left(\alpha/2\right)\right) aEl\_0} \left(\frac{b}{l\_0}\right)^3 - \operatorname{tg} \frac{\beta}{2},\tag{25}$$

5.1. VT6 alloy (Ti–6Al–4V)

coarse-crystalline state (CC).

Figure 9. Loading diagram of UFG VT6 alloy.

(Figure 8).

VT6 UFG

VT6 CC

The structural VT6 alloy is mainly used for the manufacturing of large welded and built-up air-craft structures, balloons working under internal pressure over a wide temperature range

Alloy <sup>P</sup>, N <sup>λ</sup>e, mm <sup>λ</sup>, mm <sup>λ</sup>p/λ<sup>e</sup> <sup>υ</sup>e, <sup>μ</sup><sup>m</sup> <sup>υ</sup>, <sup>μ</sup><sup>m</sup> <sup>υ</sup>p/υ<sup>e</sup> <sup>G</sup>, kJ/m<sup>2</sup> KI, MPa<sup>m</sup>1/2

277.7 (max) 0.453 0.453 0 0 0 – 11.9 35.5 193.1 (stable) 0.407 0.374 0.09 15.1 23.8 0.53 4.58 22.5

Determination of Fracture Toughness Characteristics of Small-Size Chevron-Notched Specimens

http://dx.doi.org/10.5772/intechopen.72643

227

522.6 (Δl = 0) 0.827 1.275 0.54 0 0 – 43.04 68.81 584.1 (max) 1.162 2.100 0.81 39.6 162.5 3.10 43.40 69.09

1175.2 (max) 0.695 1.038 0.49 30.8 89.9 1.92 30.27 75.51

Ni-Fe 936.0 (Δl = 0) 0.426 0.474 0.11 0 0 – 23.63 70.44

12GBA 2776 (max) 0.095 0.379 2.6 0 0 – 51.7 104.2

The studies were conducted using the material in the initial coarse-crystalline (CC) state (grain size of 7–5 μm) and with ultra-fine grained (UFG) structure (grain size of 500 nm) obtained by the severe plastic deformation [22]. The loading was carried out by a wedge with β equal 20

Figure 9 shows a typical loading diagram of the UFG VT6 alloy. The load-peak corresponds to the moment of crack initiation at the tip of the chevron. A sudden stress drop is caused by the spontaneous crack propagation to a certain length along the chevron notch. After that there is slow and stable crack propagation to the critical length, which determines the final fracture of

The measured values of l<sup>0</sup> and Δl are equal to 18.12 and 3.767 mm, respectively, а = b = 4.35 mm. The same values were used for calculating the fracture toughness of the VT6 alloy in the

the material. In the calculations for the VT6 alloy, E was equal to 110 GPa [23–25].

from 196 to 450C, and a number of other structural elements.

Table 1. Fracture toughness characteristics of structural materials.

where ΔF/ΔL is the decline of the initial elastic segment of the experimental loading diagram "load P–wedge displacement L".

The calculations showed that κ is equal to 0.08 to an accuracy of 10%.

Table 1 shows the fracture toughness characteristics of the studied materials.

Figure 8. The scheme of the chevron-notched specimen wedging.

Determination of Fracture Toughness Characteristics of Small-Size Chevron-Notched Specimens http://dx.doi.org/10.5772/intechopen.72643 227


Table 1. Fracture toughness characteristics of structural materials.

#### 5.1. VT6 alloy (Ti–6Al–4V)

<sup>P</sup> <sup>¼</sup> <sup>F</sup> � cos<sup>γ</sup>

the wedge and cantilever, respectively, β is the angle of wedge opening.

The calculations showed that κ is equal to 0.08 to an accuracy of 10%.

Table 1 shows the fracture toughness characteristics of the studied materials.

<sup>κ</sup> <sup>¼</sup> <sup>Δ</sup><sup>F</sup> ΔL

Figure 8. The scheme of the chevron-notched specimen wedging.

"load P–wedge displacement L".

for κ:

226 Contact and Fracture Mechanics

where F is the load on the wedge, κ and γ are the friction factor and interplanar angle between

As seen from Eq. (19), in order to determine the bending force P, it is important to calculate the friction factor κ. Substituting Eq. (22) into Eq. (8) instead of P, we obtain the following equation

where ΔF/ΔL is the decline of the initial elastic segment of the experimental loading diagram

2cosγ½ � <sup>2</sup>l<sup>0</sup> <sup>þ</sup> <sup>a</sup> ctg ð Þ <sup>α</sup>=<sup>2</sup> <sup>2</sup> sin <sup>β</sup>=<sup>2</sup> ð Þ <sup>4</sup>l<sup>0</sup> <sup>þ</sup> <sup>a</sup> ctg ð Þ <sup>α</sup>=<sup>2</sup> aEl<sup>0</sup>

2 sin <sup>β</sup>=<sup>2</sup> <sup>þ</sup> <sup>κ</sup> � cos <sup>β</sup>=<sup>2</sup> , (24)

b l0 <sup>3</sup>

� tg <sup>β</sup>

<sup>2</sup> , (25)

The structural VT6 alloy is mainly used for the manufacturing of large welded and built-up air-craft structures, balloons working under internal pressure over a wide temperature range from 196 to 450C, and a number of other structural elements.

The studies were conducted using the material in the initial coarse-crystalline (CC) state (grain size of 7–5 μm) and with ultra-fine grained (UFG) structure (grain size of 500 nm) obtained by the severe plastic deformation [22]. The loading was carried out by a wedge with β equal 20 (Figure 8).

Figure 9 shows a typical loading diagram of the UFG VT6 alloy. The load-peak corresponds to the moment of crack initiation at the tip of the chevron. A sudden stress drop is caused by the spontaneous crack propagation to a certain length along the chevron notch. After that there is slow and stable crack propagation to the critical length, which determines the final fracture of the material. In the calculations for the VT6 alloy, E was equal to 110 GPa [23–25].

The measured values of l<sup>0</sup> and Δl are equal to 18.12 and 3.767 mm, respectively, а = b = 4.35 mm. The same values were used for calculating the fracture toughness of the VT6 alloy in the coarse-crystalline state (CC).

Figure 9. Loading diagram of UFG VT6 alloy.

Table 1 shows that plastic deformation does not affect the displacement of the notch sides prior to the crack initiation in the UFG VT6 alloy (λp/λ<sup>e</sup> = 0). This means that the specimen is deformed only elastically prior to crack initiation. At the stage of pre-fracture, the influence of plastic deformation was observed: λp/λ<sup>e</sup> = 0.09. The contribution of plastic deformation to the crack opening at the tip of the chevron is comparable with that of elastic deformation: υp/υ<sup>e</sup> = 0.53.

A comparison shows that the method used to obtain the UFG structure in the VT6 alloy leads to a strong decrease in ductility, crack initiation stress (two-fold) and stress of stable crack propagation (three-fold). For this reason, the SMC VT6 alloy is characterized by the low fracture toughness. The behavior of the SMC VT6 alloy can be explained as follows. The low ductility of the alloy practically eliminates the stress relaxation factor in the chevron-notch zone and, as a consequence, reduces the crack initiation stress in the chevron. Stable propagation is determined by the stress con-centration at the tip of the crack, which is higher than that at the tip of the chevron prior to crack initiation. In this connection, a stress decrease takes place. The calculations have shown that the fracture toughness criteria for the SMC VT6 alloy are the values of SFE <sup>G</sup><sup>c</sup> = 4.58 0.2 kJ/m2 and SIF KI<sup>с</sup> = 22.5 0.2 MPa∙m1/2 at the stage of stable crack propagation.

Determination of Fracture Toughness Characteristics of Small-Size Chevron-Notched Specimens

http://dx.doi.org/10.5772/intechopen.72643

229

Table 1 also includes the data for the iron-nickel invar Fe + 34.6% Ni, which is widely used in modern industry and technology as an alloy with thermal linear expansion coefficient (TLEC)

The structural state of the alloy corresponds to that after the multi-axial forging. The alloy has a polycrystalline structure with an average crystallite size d equal 8 μm. The value of Young's modulus E in the calculation is 210 GPa. Figure 11 shows a loading diagram of this alloy. The moment of crack initiation at the tip of the chevron is marked with an arrow 1. The beginning of crack initiation and propagation occurs long before the external load reaches a maximum. According to Eq. (13), the SFE from the moment of crack propagation (at Δl = 0) is equal to

. The corresponding value of KI is 70.5 0.1 MPa<sup>m</sup>1/2.

The intermittent nature of the loading curve demonstrates that crack propagation occurs abruptly. Experimentally measured displacement of the load application point up to the moment of crack initiation is λ = 0.47 0.02 mm. According to Eq. (12), the portion of displacement that takes place due to the specimen elastic deformation is λ<sup>e</sup> = 0.43 0.02 mm. Therefore, within the limits of the experimental error, the relative value of λp/λ<sup>e</sup> does not exceed 10%. Thus, the plastic deformation prior to the moment of crack initiation in the

chevron makes a minor contribution to the displacement of the load application point.

close to zero. When loading the specimen, a wedge with β = 40 was used.

5.2. The Fe + 34.6%Ni-alloy

<sup>G</sup> = 23.6 0.20 kJ/m<sup>2</sup>

Figure 11. Loading diagram of the Fe-Ni alloy.

Spontaneous crack propagation from the moment of its initiation is accompanied by the reduction in the elastic deflection λ<sup>e</sup> of a single cantilever of the specimen and reduction in the fracture tough-ness characteristics of G and KI. This alloy shows quite different fracture regularities in the coarse-crystalline state. A qualitative view of the loading diagrams and consistent patterns of crack propagation in the chevron-notch zone (Figure 10) show the following. The beginning of crack initiation and propagation occurs long before the external load reaches a maximum. This is marked with an arrow 1 shown in Figure 10. Crack initiation is preceded by the plastic deformation of the material in the chevron-notch zone. The contribution of plastic deformation λ<sup>p</sup> to the displacement of load application point P up to the moment of crack initiation is comparable with that of elastic deformation: λp/λ<sup>e</sup> = 0.54 (see Table 1).

Peaks and plateaus on the loading diagram are caused by abrupt nature of crack propagation. The specific fracture energy of G and KI is almost unchanged until it reaches the maximum load Pmax marked with an arrow 2 in Figure 10. Thus, a fracture toughness criterion for the CC VT6 alloy are the values of SFE <sup>G</sup><sup>c</sup> = 43.2 0.2 kJ/m<sup>2</sup> and SIF KI<sup>с</sup> = 68.9 0.2 MPa∙m1/2. The SIF value coincides with the value of 66.4 MPa∙m1/2 to an accuracy of 3.6% in Ref. [24] for standard test conditions.

During crack propagation, a contribution of plastic deformation to the displacement of the notch tips increases. The equation λp/λ<sup>e</sup> = 0.81 corresponds to the maximum load. The contribution of plastic deformation to the crack opening at the tip of the chevron is 3 times higher than that of elastic deformation: υp/υ<sup>e</sup> = 3.1. The subsequent loading leads to a drop in the external load and to the reduction of G and KI characteristics. In this case, the λр/λ<sup>е</sup> ratio goes up due to the λ<sup>р</sup> increase and λ<sup>e</sup> decrease.

Figure 10. Loading diagram of the CC VT6 alloy.

A comparison shows that the method used to obtain the UFG structure in the VT6 alloy leads to a strong decrease in ductility, crack initiation stress (two-fold) and stress of stable crack propagation (three-fold). For this reason, the SMC VT6 alloy is characterized by the low fracture toughness. The behavior of the SMC VT6 alloy can be explained as follows. The low ductility of the alloy practically eliminates the stress relaxation factor in the chevron-notch zone and, as a consequence, reduces the crack initiation stress in the chevron. Stable propagation is determined by the stress con-centration at the tip of the crack, which is higher than that at the tip of the chevron prior to crack initiation. In this connection, a stress decrease takes place. The calculations have shown that the fracture toughness criteria for the SMC VT6 alloy are the values of SFE <sup>G</sup><sup>c</sup> = 4.58 0.2 kJ/m2 and SIF KI<sup>с</sup> = 22.5 0.2 MPa∙m1/2 at the stage of stable crack propagation.

#### 5.2. The Fe + 34.6%Ni-alloy

Table 1 shows that plastic deformation does not affect the displacement of the notch sides prior to the crack initiation in the UFG VT6 alloy (λp/λ<sup>e</sup> = 0). This means that the specimen is deformed only elastically prior to crack initiation. At the stage of pre-fracture, the influence of plastic deformation was observed: λp/λ<sup>e</sup> = 0.09. The contribution of plastic deformation to the crack opening at the tip of the chevron is comparable with that of elastic deformation: υp/υ<sup>e</sup> = 0.53.

Spontaneous crack propagation from the moment of its initiation is accompanied by the reduction in the elastic deflection λ<sup>e</sup> of a single cantilever of the specimen and reduction in the fracture tough-ness characteristics of G and KI. This alloy shows quite different fracture regularities in the coarse-crystalline state. A qualitative view of the loading diagrams and consistent patterns of crack propagation in the chevron-notch zone (Figure 10) show the following. The beginning of crack initiation and propagation occurs long before the external load reaches a maximum. This is marked with an arrow 1 shown in Figure 10. Crack initiation is preceded by the plastic deformation of the material in the chevron-notch zone. The contribution of plastic deformation λ<sup>p</sup> to the displacement of load application point P up to the moment of crack initiation is comparable

Peaks and plateaus on the loading diagram are caused by abrupt nature of crack propagation. The specific fracture energy of G and KI is almost unchanged until it reaches the maximum load Pmax marked with an arrow 2 in Figure 10. Thus, a fracture toughness criterion for the CC VT6 alloy are the values of SFE <sup>G</sup><sup>c</sup> = 43.2 0.2 kJ/m<sup>2</sup> and SIF KI<sup>с</sup> = 68.9 0.2 MPa∙m1/2. The SIF value coincides with the value of 66.4 MPa∙m1/2 to an accuracy of 3.6% in Ref. [24] for standard

During crack propagation, a contribution of plastic deformation to the displacement of the notch tips increases. The equation λp/λ<sup>e</sup> = 0.81 corresponds to the maximum load. The contribution of plastic deformation to the crack opening at the tip of the chevron is 3 times higher than that of elastic deformation: υp/υ<sup>e</sup> = 3.1. The subsequent loading leads to a drop in the external load and to the reduction of G and KI characteristics. In this case, the λр/λ<sup>е</sup> ratio goes

with that of elastic deformation: λp/λ<sup>e</sup> = 0.54 (see Table 1).

up due to the λ<sup>р</sup> increase and λ<sup>e</sup> decrease.

Figure 10. Loading diagram of the CC VT6 alloy.

test conditions.

228 Contact and Fracture Mechanics

Table 1 also includes the data for the iron-nickel invar Fe + 34.6% Ni, which is widely used in modern industry and technology as an alloy with thermal linear expansion coefficient (TLEC) close to zero. When loading the specimen, a wedge with β = 40 was used.

The structural state of the alloy corresponds to that after the multi-axial forging. The alloy has a polycrystalline structure with an average crystallite size d equal 8 μm. The value of Young's modulus E in the calculation is 210 GPa. Figure 11 shows a loading diagram of this alloy. The moment of crack initiation at the tip of the chevron is marked with an arrow 1. The beginning of crack initiation and propagation occurs long before the external load reaches a maximum. According to Eq. (13), the SFE from the moment of crack propagation (at Δl = 0) is equal to <sup>G</sup> = 23.6 0.20 kJ/m<sup>2</sup> . The corresponding value of KI is 70.5 0.1 MPa<sup>m</sup>1/2.

The intermittent nature of the loading curve demonstrates that crack propagation occurs abruptly. Experimentally measured displacement of the load application point up to the moment of crack initiation is λ = 0.47 0.02 mm. According to Eq. (12), the portion of displacement that takes place due to the specimen elastic deformation is λ<sup>e</sup> = 0.43 0.02 mm. Therefore, within the limits of the experimental error, the relative value of λp/λ<sup>e</sup> does not exceed 10%. Thus, the plastic deformation prior to the moment of crack initiation in the chevron makes a minor contribution to the displacement of the load application point.

Figure 11. Loading diagram of the Fe-Ni alloy.

The observations show that the crack propagates along a complex trajectory, sharply changing the motion direction (Figure 12). The maximum value of SFE <sup>G</sup><sup>с</sup> = 30.8 0.3 kJ/m2 corresponds to the maximum load. The corresponding value of KI<sup>с</sup> is equal to 80.4 0.2 MPam1/2. Note that the value obtained practically coincides with those of Kc = 81.2 MPam1/2, obtained for the Fe-17%Ni alloy [26]. The critical value of crack opening δ<sup>e</sup> = 2υ<sup>e</sup> = 61.56 μm can also be used as a fracture toughness characteristic. The experimental value of δ is 179.8 μm. Hence, υp/υ<sup>e</sup> is equal to 1.92. Thus, at the stage of prefracture, the crack opening in the chevron-notch zone contains a significant contribution related to the plastic deformation, which is almost twice greater than that of the elastic deformation of the specimen. A subsequent increase in crack length leads to a drop in the values of G<sup>с</sup> and KIс. In this case, the υp/υ<sup>e</sup> ratio increases due to the increase of υ<sup>p</sup> contribution and decrease in υ<sup>e</sup> contribution.

velocity increases sharply. The calculations by Eq. (5) determine the value of KI<sup>с</sup> = 104 kJm1/2

Determination of Fracture Toughness Characteristics of Small-Size Chevron-Notched Specimens

http://dx.doi.org/10.5772/intechopen.72643

231

In contrast to the titanium-based alloys, significant processes of plastic deformation are developed in the SMC 12GBA steel in the chevron-notch zone resulting to the extremely viscous fracture behavior. Figure 14 illustrates the consistent patterns of crack propagation in the chevron-notch zone. From the moment of crack initiation, this process is accompanied by a

The λр/λ<sup>е</sup> ratio can serve as a quantitative characteristic of viscosity. For these materials, it differs quite considerably, in particular, at the load peak λр/λ<sup>е</sup> is 2.6 for 12GBA and λр/λ<sup>е</sup> is

These examples show that at fracture toughness certification of the material, except for SFE, it is important to know the characteristics of λр/λ<sup>е</sup> and υp/υe, which determine the effect of plastic deformation on the displacement of load application points and crack opening, respectively. The proposed method allows us to study the fracture toughness of materials without

This chapter presents a new method for determining fracture toughness of materials according to the test data of non-standard small-size chevron-notched specimens. The analytical expressions are obtained being based and derived from the constitutive equations of engineering fracture mechanics to determine the crack-driving force G (specific fracture energy) and the stress intensity factor (SIF) KIc. Experimental determination of crack length Δl is of principle importance in calculations. During testing, loading diagrams and photographic images of the specimens taken in time intervals are obtained. The displacement of the notch sides, crack opening at the tip of the chevron notch and crack length during its initiation and propagation are measured. This allows us to distinguish the plastic deformation contribution to the displacements that is not related to the change in specimen ductility and therefore does not affect

Due to the fact that change in specimen ductility with increase in the crack length is analytically considered in constitutive relations, the periodic unloading of the specimen applied under standard test conditions of the chevron-notched specimens is excluded in the experiments.

There are no empirical constants and phenomenological dependencies in the calculations. All necessary calculation parameters are determined according to the experimental data. The

for 12GBA, which is much higher than for the Fe-Ni alloy (75.51 MPam1/2).

Figure 14. Crack propagation in the chevron-notched zone. The 12GBA tube steel in the UFG state.

monotonous drop in the external load (Figure 13).

restrictions on the plastic zone size at the crack tip.

the fracture toughness characteristics of the material.

0.81 for the CC VT6 alloy.

6. Conclusion

#### 5.3. The 12GBA tube steel

The low-carbon low-alloy 12GBA steel is widely used in the construction of main oil and gas pipelines. The material was subjected to plastic deformation by rolling to the finite cross-section of bars of 8 8 mm2 for several passes with step-like temperature decrease from 750 to 550<sup>С</sup> [27]. After severe plastic deformation, the steel has a fibrous UFG structure with a lateral fragment size of 0.5 μm. In the longitudinal direction, the length of fragments is 15–20 μm.

The 12GBA tube steel loading was performed by opening of the chevron-notch sides (Figure 6).

Figure 13 shows a loading diagram "force P – displacement of notch tips λ" for the 12GBA tube steel. Crack initiation at the tip of the chevron notch is preceded by considerable plastic deformation. A crack initiates at the moment when the load reaches practically reaches a maximum (marked with an arrow). First, the crack slowly grows, and then its propagation

Figure 12. Crack in the chevron-notch zone prior to the fracture (a) and the specimen fracture after 4 s (b).

Figure 13. Loading diagram for the 12GBA steel.

Figure 14. Crack propagation in the chevron-notched zone. The 12GBA tube steel in the UFG state.

velocity increases sharply. The calculations by Eq. (5) determine the value of KI<sup>с</sup> = 104 kJm1/2 for 12GBA, which is much higher than for the Fe-Ni alloy (75.51 MPam1/2).

In contrast to the titanium-based alloys, significant processes of plastic deformation are developed in the SMC 12GBA steel in the chevron-notch zone resulting to the extremely viscous fracture behavior. Figure 14 illustrates the consistent patterns of crack propagation in the chevron-notch zone. From the moment of crack initiation, this process is accompanied by a monotonous drop in the external load (Figure 13).

The λр/λ<sup>е</sup> ratio can serve as a quantitative characteristic of viscosity. For these materials, it differs quite considerably, in particular, at the load peak λр/λ<sup>е</sup> is 2.6 for 12GBA and λр/λ<sup>е</sup> is 0.81 for the CC VT6 alloy.

These examples show that at fracture toughness certification of the material, except for SFE, it is important to know the characteristics of λр/λ<sup>е</sup> and υp/υe, which determine the effect of plastic deformation on the displacement of load application points and crack opening, respectively. The proposed method allows us to study the fracture toughness of materials without restrictions on the plastic zone size at the crack tip.
