Temperature Dependences of the Strength and Creep

The working temperature of materials in different parts of HGAs in NREs in transient and stationary regimes changes in a broad range from 300 to 3,000 K. since it is necessary to know the variations in mechanical and physical properties. For structural and fuel materials of the interstitial phase type, the problem of preventing a brittle collapse is of primary importance. Such collapse is caused by the high brittleness of materials of this class in a broad range of temperatures, loading methods and

rates, along with a relatively low tensile strength (compared, for example, with metal materials). Refractory carbide compounds with a high level of resistance to the motion of dislocations are characterized by no monotonic dependence of the strength [14]. First, the strength is virtually unchanged with increasing the temperature and begins to increase only when microplasticity develops, achieving a maximum (Fig. 4.18) at the brittle-ductile transition temperature Tb-d, due to the thermally activated relaxation of local peak stresses near concentrators-structural defects contained in the material. As the temperature was further increased (T > Tb-d), microplasticity developed in ceramics and their strength monotonically decreased, as in metals. The presence of nonmetal (O2, N2, C, Si) or metal impurities (Fe, C, Ni) due to the formation of phases and low-melting eutectics can change the transcrystalline type of collapse to the intercrystalline one and also change the temperature dependence of the strength.

The brittle-ductile transition temperature in ceramics, unlike Tb-d in metals, strongly changes (by a few hundred degrees) upon changing the type of the stressed state and the deformation rate. As the deformation rate of ZrC rise under tension from 10-3 to 10-1 s-1, the temperature Tb-d increases from 0.6 to 0.8Tm. In the case of shock loadings with rates exceeding the relaxation rates of micro — and macrostresses, the strength remains almost at the level of its value at room temperature. A similar behavior is also observed for oxide materials and weakly plastic Si and Ge metals with strongly manifested covalent bonds (Fig.4.19).

Transition temperature Tb-d for complex solid ZrC + UC, ZrC + NbC + UC solutions is higher than for the single-phase ZrC.

Long-term strength with increase of loading time drops. Time of fracture т and stationary creep rate є’ are connected with applied stress о. Laws of creep kinetics inherent to metals are observed and for ceramic materials [22, 26]. In a general view dependence of creep rate є’ on applied stress о can be written down:

t = B ■ am ■ exp(U/RT) є’ = A ■ an ■ exp(-Q/RT)

where A, B, n, m—constants, Q and U—activation energy of creeps and long frac­ture processes. For carbide materials tested in a temperature band 2,500-3,000 K, activation energy Q and U and exponent’s n and m of stresses practically coincide.

Creep rate depends from a mostly under the linear law in an interval of small stresses 10-20MPa at high temperatures 0.6Tm. According to this, we usually dis­tinguish threshold (i. e. developed at stresses surpassing some stress a > at) and not threshold creep; the last can be observed at any as much as small a. No threshold creep is carried out by the directed diffusion of atoms and proceeds on vacancy-diffusion mechanism of Nabarro-Herring. Creep rate inversely proportional to a square size of grain and in a strong degree depends on stochiometric of the compound (Fig. 4.20a).

At stresses a > at alongside with diffusive processes, conservative movement of dislocations is initiated and dependence є’ from becomes power mode є’ ~ a(3-4) (Fig.4.20a) and the intergranular sliding at the final stage of creep generate microp­orosity on the grain boundaries that causes appreciable decrease of density. Generally, creep deformation is caused by passing not one but several processes (diffusive flu­idity. sliding on grain borders, dislocation moving), the contribution of each process depends on conditions of carrying out of experiences (temperature, stress, duration) and structural characteristics of the object.

The instantaneous and unsteady stages of creep are absent in most cases at stresses greater at, but smaller yield point a0,2. Accumulation of a plastic strain basically occurs at stages of the stationary at and accelerated creep, and duration of a final site leaves approximately 1/3 from time before fracture. The general accumulated plastic strain during creep

Fig. 4.20 Dependence of creep rate of ZrC with various grain value versus stress at T = 2,900 K (a) and (b) for fuel materials 1-ZrC-UC, 2- ZrC-UC-C, 3- ZrC-UC-7mass.%NbC, 4-ZrC-UC — 48mass %NbC T = 2,800K

where є’—creep rate on the stationary stage; єш—deformation on the accelerated stage; t—time.

The structure of ceramics changes with increase of a creep strain, agglomeration of microspores in the form of chains on borders occur in grains, perpendicular to action of loading. Structural changes result in to change of density and physical properties. Increase of porosity, for example, in beryllium from 1.4 up to 12% raises є’ in 2-4 times. Generally, porosity dependence of creep can be expressed by empirical expression.

є’~ (1 — p2/3)-1 or є’~ (1 — p)-3’ where p is porosity of a sample.

The fatigue behaviors of zirconium carbide [14] under cyclic loading have demon­strated that fatigue cracks in ceramics can grow at lower stress than static strength. The cyclic tests were carried out under compressive loading at room temperature in ambient air. Subcritical crack velocity is described by:

dl/dN = a(Ki /Kic)n

where Ki is a current stress intensity. Kic is the fracture toughness, a and n constants depending on type of loading and the environment, Kic is determined by the developed method under uniaxial compression for plane specimens with a central cut at a certain angle to an axis. The crack starts at Kic and after sporadically increasing length stress intensity drops to a lower Kia value. The subsequent crack growth is possible only at increasing external load, these permits to multiply determination of the fracture toughness on one specimen. The results of cyclic tests show that crack propagates even at Ki < Kia with velocities 1-3-10-3 mm/s. The value dl/N increases to 1 mm/s at Ki > Kic, and n value in the range 75-89. The observed subcritical crack growth under compression at room temperature is connected with accumulated localized microcracking and crushing of fracture-surface roughness at the unloading stage. Internal local stresses play an important role in the fatigue behavior of ceramics. The origin of these local stresses depends on heterogeneity of chemical composition, structure, and anisotropy of sintered ceramic blanks [14]. Cyclic loading of cylindrical ZrC samples at room temperature does not decrease the strength ab under constant bending stresses equal to 0.8-0.9 of the mean, ab for a number of cycles up to 106. The cyclic bending of ZrC samples at temperature above 2,300 K increases the strength because of viscous intergranular flow and stress relaxation of local stresses.

The resistance of ceramics to the propagation of cracks can be strongly influ­enced by the microstructure but optimization of fracture toughness and strength usually involves different choices of microstructure: individual toughening mecha­nisms including phase transformations. Microcracking, twining, ductile reinforce­ment, flber/whisker reinforcement and grain bridging as regarded thoroughly in [3]. The optimum structure of ZrC with small grain, pore size below 1 ^ and medium porosity of 8-10 % has the maximum Kic = 3.3MPa — m1/2 and bending strength near 650MPa [14]. The Kic of most refractory carbides, nitrides, and borides does not exceed 5 MPa-m1/2 [2]. The polycrystals based on two modifications of boron nitride with large internal local stresses have extremely high Kic up to 18MPa — m1/2 [2].

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