6. Conclusion

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>

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).

contribution and decrease in υ<sup>e</sup> contribution.

Figure 13. Loading diagram for the 12GBA steel.

5.3. The 12GBA tube steel

230 Contact and Fracture Mechanics

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 the fracture toughness characteristics of the material.

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 method allows us to use the low-power test machines and does not require large amounts of material for the production of specimens, as well as fatigue precracking. The method allows us to certify fracture toughness of the material without restrictions regarding the amount of plastic deformation and in front of the crack tip and in the specimen as a whole. The theoretical analysis has shown that G<sup>c</sup> compared to KIc depends on the Young's modulus E of the material. The higher E is, the lower is G<sup>с</sup> under all other conditions being equal. For this reason, the relative values of G<sup>c</sup> and KIc characteristics can differ essentially. Thus, the value of G<sup>c</sup> for the Fe-Ni alloy is lower that for the CC VT6 alloy, and the value of KIc is, on the contrary, higher (Table 1).

[5] Miyazaki H, Hyuga H, Yoshizawa YI, Hirao K, Ohji T. Relationship between fracture toughness determined by surface crack in flexure and fracture resistance measured by indentation fracture for silicon nitride ceramics with various microstructures. Ceramics

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

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

233

[6] Bončina T, Zupanič F, Čekada M, Markoli B. Microindentation of dispersed phases in an Al94Mn 2Be2Cu2 alloy. Journal of Alloys and Compounds. 2010;505:486-491. DOI:

[7] Barker LM. Theory for determining KIc from small, non-LEFM specimens, supported by experiments on aluminum. International Journal of Fracture. 1979;16:515-536. DOI: 10/

[8] Wang CT, Pillar RM. Short-rod elastic-plastic fracture toughness test using miniature specimens. Journal of Materials Science. 1989;24:2391-2400. DOI: 10.1007/BF01174501

[9] Grant TJ, Weber L, Mortensen A. Plasticity in Chevron-notch fracture toughness testing. Engineering Fracture Mechanics. 2000;67:263-276. DOI: 10.1016/S0013-7944(00)00061-8

[10] Soderholm K-J. Review of the fracture toughness approach. Dental Materials. 2010;26:

[11] Rakhimkulov RR. Matching of fracture toughness values of К1с, obtained in chevron-notched specimens and based on standard technique for a steel St3sp. Neftegazovoe delo. 2010;2:1-10.

[12] Hertzberg RW. Deformation and Fracture Mechanics of Engineering Materials. 3rd ed.

[13] Matvienko YG. Models and Criteria of Fracture Mechanics. Moskow: FIZMATLIT; 2006

[14] Timoschenko S, Goodier JN. Theory of Elasticity. New York, Toronto: McGraw-Hill Book

[15] Broek D. Elementary Engineering Fracture Mechanics. Leyden, Netherlands: Noordhoff

[16] Salem JA, Shannon JI Jr, Jenkins MG. Some observations in fracture toughness and fatigue testing with chevron-notched specimens. In: Brown K, Baratta F, editors. Chevron-Notch Fracture Test Experience: Metals and Non-Metals. ASTM STP 1172. Philadelphia: American

[17] Barker LM. A simplified method for measuring plane strain fracture toughness. Engineering Fracture Mechanics. 1977;9:361-369. DOI: 10.1016/0013-7944(77)90028-5

[18] Ruggieri C, Mathias L. Fracture-resistance testing of pipeline girth welds using bend and

[19] Roy H, Ray A, Barat K, et al. Structural variations ahead of crack tip during monotonic and cyclic fracture tests of AISI 304LN stainless steel. Materials Science & Engineering, A.

tensile fracture specimens. Journal of Pipeline Engineering. 2013;12:217-227

Available from: http://www.ogbus.ru/authors/Rakhimkulov/Rakhimkulov\_1.pdf

International. 2009;35:493-501. DOI: 10.1016/j.ceramint.2008.01.006

10.1016/j.jallcom.2010.06.111

e63-e77. DOI: 10.1016/j.dental.2009.11.151

1007/BF00019921

New York: Wiley; 1989

International Publishing; 1974

Society for Testing and Materials; 1992. pp. 9-25

2013;561:88-99. DOI: 10.1016/msea.2012.10.074

Company; 1951

It is proposed to consider the λр/λ<sup>е</sup> ratio as an additional fracture toughness characteristic that determines the plastic deformation contribution to the displacement of load application point in relation to the elastic deformation.

Therefore, in order to make fracture toughness certification of the material more complete, it is recommended to determine three fracture toughness characteristics of the material: SIF, SFE and the λр/λ<sup>е</sup> ratio. According to this method, the fracture toughness characteristics of the VT6, Fe-35.4%Ni alloy and the 12GBA tube steel are determined, which differ in the ability to fracture toughness and the Young's modulus.
