# Brittleness

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## brittleness

[′brid·əl·nəs]
(mechanics)
That property of a material manifested by fracture without appreciable prior plastic deformation.

## Brittleness

the property whereby a material fractures at a small, generally elastic deformation under the action of stresses, the average level of which is below the yield point.

The formation of a brittle crack and the development of brittle fracture are related to the formation of small zones of plastic deformation (seeSTRENGTH OF SOLIDS). The relative fractions of elastic and plastic deformations in brittle fracture depend on the properties of the material (the nature of the interatomic or inter-molecular bonds and the microscopic and crystal structures) and on the conditions of use. A material’s transition to a brittle state is facilitated by the application of tensile stresses along the three major axes (triaxial stress state), the concentration of stresses at sites of an abrupt change in the cross section of a part, a decrease in temperature, an increase in the cyclic rate of stressing, and an increase in the amount of elastic energy stored in a stressed structure. For example, marble, a relatively elastic material, undergoes brittle fracture upon tensile stressing, but under conditions of asymmetric compression relative to the three major axes, it behaves as a plastic material. The brittleness of a material becomes more evident as the stress concentration becomes greater. Thus, brittleness must be considered with respect to the conditions under which the material is used.

A condition for the growth of a brittle crack is a breakdown in the equilibrium between the energy of elastic deformation released in the process and the increase in the total surface energy, including the work of plastic deformation of the thin layer adjacent to the edges of the crack. The tensile strength of a component with a crack is inversely proportional to , where l is half the length of the crack. A constant of the material (fracture toughness factor) is introduced in the linear theory of elastic failure mechanics to characterize the resistance to the development of a crack under conditions of planar deformation. A brittle crack propagates at a high velocity—approximately 1,000 m/sec in steel, which is approximately one-fifth of the propagation velocity of an elastic shear wave.

The tendency of a material toward brittle fracture is usually measured according to the temperature dependence of the work of fracture or of the ductility characteristics, which permit determination of the brittle temperature Tb, that is, the temperature of the transition from the ductile state to the brittle state. The higher the value for Tb, the greater the tendency toward brittle failure.

Two independent characteristics, namely, the resistance to plastic deformation (the yield point σs) and the resistance to brittle fracture (the tensile strength, or resistance to direct tensile force, St), must be taken into account in examining the macroscopic features of brittle fracture. The yield point σs increases more rapidly than St, upon a decrease in testing temperature, the introduction of notches (stress concentrators), and an increase in the rate of deformation; as a result, a transition occurs from ductile fracture to brittle fracture (Figure 1).

Figure 1. Transition of rock salt from the ductile state to the brittle state with decreasing temperature of tensile testing (after A. F. Ioffe)

The concept of the occurrence of brittle failure as a result of a small, preliminary plastic deformation constitutes the basis of the dislocation theory of fracture. The generation of brittle cracks is related to the planar accumulation of linear defects of the crystal lattice, or dislocations, in front of some barrier, which may be the boundary of a grain, subgrain, or various inclusions. A high stress concentration is produced in this process, which is proportional to the tangential stress of the external load and the length of dislocation accumulation.

A characteristic feature of cold-brittle transition elements is a sharp increase in the yield point upon a decrease in temperature below 20 percent of the melting point and upon an increase in the rate of cyclic deformation. An increase in the resistance to plastic deformation hinders the relaxation of stresses in a metal under load both in the stage of crack generation (in front of a dislocation accumulation) and in the stage of crack elaboration (in the plastic zone in front of the tip of the growing crack), thereby facilitating the metal’s transition to the brittle state.

Brittleness also depends on a material’s structure. An increased brittle temperature results from nonuniformities in metal structure and composition, an increase in grain size, the presence of contaminants, and the segregation of brittle phases, especially at grain boundaries. The atoms of elements that form interstitial solid solutions interact with dislocations, decreasing the mobility of the dislocations and facilitating a transition to the brittle state. The removal of interstitial atoms of carbon, oxygen, and nitrogen in metals lowers the brittle temperature. Alloying may either increase or decrease the brittle temperature by changing the phase composition and structure of metals, as well as by altering the mobility of dislocations in the metal. Irradiation of metals with high-energy particles causes an increase in resistance to the movement of dislocations, increases the degree of fixation of dislocations, and leads to an increase in the brittle temperature. An ordered arrangement of atoms also increases the brittle temperature.

Studies of fracture surfaces show that in brittle fracture, cracks in metals and alloys propagate along crystallographic planes of low index (cleavage) or along grain boundaries. The latter phenomenon is caused by the absorption enrichment of grain boundaries by contaminants (P, S, Sb, and other elements in steels), which sharply reduces the binding strength between grains.

Special types of brittleness, such as acid brittleness (hydrogen embrittlement) and the delayed fracture of steel and alloys, are seen only at very high loading rates or upon prolonged action of a static load below the yield point. In such cases, the metal may not display an increased tendency toward brittle fracture in ordinary impact testing. The fracture develops in three stages: an incubation period, a stage of slow growth of the brittle fracture, and rapid fracture after the crack reaches some critical length. The slow, discontinuous growth of a brittle fracture in tempered steel is related to the generation of elastic microstresses during tempering, which facilitate the growth of cracks at low, externally applied stresses. On the other hand, the facilitation of the growth of cracks in the case of acid brittleness is caused by the diffusion of hydrogen into the region of the stressed state in front of the growing crack.

### REFERENCE

Drozdovskii, B. A., and Ia. B. Fridman. Vliianie treshchin na mekhanicheskie svoistva konstruktsionnykh stalei. Moscow, 1960.
Atomnyi mekhanizm razrusheniia. Moscow, 1963. (Translated from English.)
Cherepanov, G. P. Mekhanika khrupkogo razrusheniia. Moscow, 1974.

S. I. KISHKINA and V. I. SARRAK

## Brittleness

That characteristic of a material that is manifested by sudden or abrupt failure without appreciable prior ductile or plastic deformation. A brittle fracture occurs on a cleavage plane which has a crystalline appearance at failure because each crystal tends to fracture on a single plane. On the other hand, a shear fracture has a fibrous appearance because of the sliding of the fracture surfaces over each other. Brittle failures are caused by high tensile stresses, high carbon content, rapid rate of loading, and the presence of notches. Materials such as glass, cast iron, and concrete are examples of brittle materials.

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