Two relevant thermomechanical processes in high — temperature structural applications are creep and stress relaxation. Steady-state creep deformation, or time-dependent strain under an elevated — temperature stress, has been observed for ZrC. In general, creep rate is dependent on applied stress (s) and temperature (T) according to

є = Aan exp —§ [12]

where є is strain rate, A is a constant dependent on the material and creep mechanism, n is an exponent dependent on the creep mechanism, R is the gas constant, and Qis the activation energy of the creep mechanism. Activation energies for creep under various conditions are summarized in Table 4. Zubarev and Kuraev13 proposed a creep mechanism map of stress normalized to shear modulus versus homologous temperature, based on compressive creep in He atmosphere of ZrC10 with 14 pm grain size. The authors distinguished between different temperature-stress regimes governed by creep pro­cesses having low or high activation energies. Indeed,

aKumashiro et a/.,124 Vickers indentation in {100} surface, for

(100)(001), (110)(001), and (111)(110) slip systems, respectively.

bDarolia and Archbold,117 compression in vacuum.

cLee and Haggerty,116 compression in vacuum along (111) crystal

axis.

dLeipold and Nielsen,72 1-5% porosity, 1.6-2.5 wt% free carbon. eMiloserdin et a/.,125 tension, 3.4-9.8MPa, 7% porosity. fSpivak et a/.,126 creep in He atmosphere, 4-6% porosity. 9Zubarev and Dement’ev,127 in tension, bending, and compression, respectively, 0.96-19.6 MPa, inert atmosphere, 15-17% porosity.

hZubarev and Shmelev,128,129 in tension, 0.96-73.5 MPa, Ar atmosphere, 3-5% porosity, 0.38-1.1 wt% free carbon.

‘Single crystal.

the two activation energies provided by Leipold and Nielsen72 are attributed to a change in creep mecha­nism above 2423 K.

At low or intermediate temperatures (below about 1623-2473 K for ZrC, or <0.5Tm) and high stress relative to shear modulus, creep has a low activation energy and is controlled by the movement of disloca­tions. Zubarev and Kuraev130 proposed more specific mechanisms for various regions ofthis overall regime, such as dislocation multiplication, cross-slip, disloca­tion climb, work-hardening, and gross plastic yield. The TEM analysis of Britun et a/.119 supports these hypotheses, revealing intragranular dislocations and slip bands after compression of ZrC098 between 1420 and 2100 K.

At high temperatures (generally >2073 K for ZrC) and intermediate or low stress, creep has a higher activation energy and is controlled by diffusion. The activation energy for creep in this regime is close to that of bulk self-diffusion in ZrC, which is ^500 kJ moP1 for C and ^700 kJ moP1 for Zr, as detailed in Table 4. The diffusion rate of the lower-mobility species should be rate-limiting, so creep in this regime is usually attributed to self-diffusion of Zr. However, diffusion along grain boundaries may reduce the activation energy for creep relative to that of bulk diffusion. Diffusional mass transfer (Nabarro-Herring creep) and grain boundary sliding are suggested mechanisms,130 with the latter con­firmed by scanning electron microscopy (SEM) cer — amography and not applicable to single crystals.13 Britun eta/.119 also confirmed grain boundary shear and rotation by TEM ceramography of ZrC098 com­pressed at 2100-2500 K.

The dependence of creep mechanism on grain size has been studied by Zubarev eta/.131 Analysis of creep mechanisms among polycrystalline (14-1000 pm grain size) and single-crystal ZrC10 revealed that with increasing grain size and with the single crystal, dislo­cation creep mechanisms occurred at lower threshold stresses, and the Nabarro-Herring and grain boundary sliding processes diminished in importance or disap­peared. Free carbon has been reported to facilitate grain boundary creep.131

Creep has been studied as a function of C/Zr ratio. Creep in compression of ZrC0.89-096 at 2773­2973 K132 showed a monotonically decreasing creep rate with decreasing C/Zr ratio. In the same work, a v-shaped trend of creep rate with C/Zr ratio was found for creep in bending of NbC0 82-0.98 at 2273­2473 K, decreasing to a minimum creep rate at a composition of approximately NbC0 85. They specu­lated that such a trend may exist for ZrC*, but that the associated minimum existed below the composi­tional range they investigated. Based on creep of ZrC075-098 between 2400 and 3030 K, Spivak et a/.126 found activation energy increased with increasing C/Zr ratio. This would be consistent with expectations of enhanced diffusion with an increase in C vacancies. However, their earlier work83 reported activation energy for self-diffusion of Zr in ZrC as being composition-independent between ZrC0 84_0 97, and that of C decreasing with increasing C/Zr ratio. Some hypotheses have been put forth (see Section 2.13.4.4), but further study of Zr diffusion in ZrC* is required to explain this conclusively.

Stress relaxation, or an evolution in stress with time for a component at fixed strain, has been inves­tigated to a lesser degree than creep. Repeated four — point bend loading of ZrC095-1 (6-35 pm grains) at 1873-2273 K, with unloading at intervals, resulted in increased resistance to relaxation, via work hard­ening, upon subsequent loading cycles.9 , The authors concluded that under these conditions slip occurs by diffusion along grain boundaries. At higher temperatures, up to 2473 K, no beneficial effects were imparted by repeated loading, and the authors con­cluded that no work hardening occurred. They judged stress relaxation and creep in ZrC to be con­trolled by different mechanisms.