1. Introduction

Various methods for determining fracture toughness of materials are well-known and widely used when testing standard specimens with induced fatigue crack [1–3], when testing the Charpy notched specimens for fracture toughness [4], by the micro indentation method [5–7], et al.

An essential feature of these methods is that the characteristics of loading diagrams and the existing fracture length are measured, and then fracture toughness characteristics of the material are calculated by the semi-empirical formulas. As a rule, the critical stress intensity factor

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(SIF) of the 1st kind КI<sup>с</sup> (for cleavage crack) is taken for the main fracture toughness characteristics of the material. The plane strain state condition of the loaded specimen is required in the experiments. In this regard, standard tests are conducted on specimens at least 10 mm thick.

occur if the system can release energy required to initiate crack propagation to the elementary distance dl. The energy needed for crack growth, appears only due to the elastic deformation

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

The reliable fracture toughness characteristic is the critical value of the elastic energy release rate (ERR) during the crack propagation Gc. In the two-dimensional version, this characteristic is equivalent to the value of the J-integral [13, 14]. For brevity, the value of G will be called specific fracture energy. The specific fracture energy (SFE) is defined as energy that is spent on

In practice, there is a decrease in specimen stiffness or structure at initiation and propagation of the crack. The specimen stiffness M is defined as the ratio of load P, applied to the specimen, to the displacement of load application point λ<sup>е</sup> at elastic deformation of the specimen: М = P/λе.

The necessary condition for through-crack propagation in the flat specimen of unit thickness

where dη/dl is the change in specimen ductility during crack propagation, dl is the short distance, to which a straight-line crack front propagates. At the stage of stable crack propagation, this value characterizes the fracture toughness G<sup>c</sup> of the material. As follows from Eq. (1), elastic energy per unit of new crack surface at its propagation to dl in the specimen in thickness а is equal to

> dη <sup>2</sup>adl <sup>¼</sup> <sup>P</sup><sup>2</sup>

There is a classic example for calculating the stress intensity factor KI to test a double cantilever beam specimen with a straight-through notch [15]. The relation between G and KI for the plane

Let us consider the case of double-cantilever beam specimens with a straight-through notch in detail, since the result will be used in the calculation of G for the chevron-notched specimens. Figure 1 presents the double-cantilever beam specimens with a straight-through notch. Distance from the load application point P to the crack front is the initial crack length l. As follows from the cantilever bending theory, displacement of the load application point λ<sup>e</sup> (Figure 1) is

double cantilever beam specimen, displacement of load application points ζ is 2λe. Therefore,

dη

, where E is the Young's modulus, b is the cantilever thickness. For the

dη

<sup>G</sup> <sup>¼</sup> <sup>P</sup><sup>2</sup>

<sup>G</sup> <sup>¼</sup> <sup>P</sup><sup>2</sup>

<sup>G</sup> <sup>¼</sup> <sup>K</sup><sup>2</sup>

where dS = 2adl is the elementary increment of the crack surface area.

<sup>P</sup> <sup>¼</sup> <sup>8</sup> Ea l b <sup>3</sup> : . The unit of measurement for SFE is J/m<sup>2</sup>

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

<sup>2</sup>dl , (1)

dS , (2)

<sup>I</sup> <sup>1</sup> � <sup>ν</sup><sup>2</sup> <sup>=</sup>E: (3)

.

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energy that occurs in-side the material under the applied external force.

The reciprocal of the stiffness is defined as a specimen compliance η: η = λе/P.

the formation of the crack surface with area 1 m2

obeys the equation [12–14]

stress state obeys the equation

Ea l b <sup>3</sup>

the specimen ductility <sup>η</sup> is <sup>η</sup> <sup>¼</sup> <sup>ζ</sup>

equal to <sup>λ</sup><sup>e</sup> <sup>¼</sup> <sup>4</sup><sup>P</sup>

Disadvantages of used methods are as follows:


As a rule, during a fracture toughness test of small-size specimens, the chevron-notched specimens are used [7–11]. The specimens with this configuration do not require the preliminary fatigue crack. When testing the small-size chevron-notched specimens, many of the above-mentioned problems are absent.

This chapter proposes a new method for fracture toughness determination of structural materials using the small-size chevron-notched specimens. The method allows us to determine fracture toughness characteristics without severe restrictions on the specimen ability to plastic deformation. There are no phenomenological dependencies and empirical constants in the calculations.

The fracture toughness characteristics comply with the conditions of continuous loading of specimens, without using the "loading-unloading" operation.

The important calculation works were carried out associated with the use of chevron-notched specimens during testing.
