Can the mismatch in the coefficients of thermal expansion at "a" and "c" directions of a hexagonal structure lead to the formation of stresses at the grain boundaries of poly-crystal ceramics during the sintering process?
Many thanks.
Would you please send me the link or upload the reference?
Yes, a typical example is TiB2. Due to the mismatch in a and c directions, thermal stresses are produced resulting in cracking during cooling.
Many thanks.
Would you please send me the link or upload the reference?
Dear Mehdi,
Please go for below links,
1. R. Nagarajan, Z. Xu, J.H. Edgar, F. Baig, J. Chaudhuri, Z. Rek, E.A. Payzant, H.M. Meyer, J. Pomeroy, and M. Kuball, J. Cryst. Growth 273 431‐438 (2005).
2. C. E. Whiteley, M. J. Kirkham, J. H. Edgar, The coefficients of
thermal expansion of boron arsenide (B12As2) between 25°C and 850°C. Journal of
Physics and Chemistry of Solids, 74(5), 673-676 (2013).
Dear Mehdi,
The mismaching berween the two linear expansion coefficients of the constituents will exert additianal forc in the lattice which may cause micro cracks and may developed to macrocracks during heating or cooling processes.
This stress may be very low, and in fact this stress does exist in any polycrystalline ceramic with an anisotropic crystal structure with any small directional difference in thermal expansion coefficient. This stress may also be high enough to cause microcracking and grain boundary separation if there is a large difference in CTE along different axes. The stresses will be greater in pollycrystalline ceramics with larger grain sizes and with higher elastic moduli. In theory, if the grain size is made small enough, even ceramics with different thermal expansion coefficients can be sintered with no microcracking. This "microcracking threshold" of grain size can be estimated by this equation from Cleveland and Brandt:
Critical grain size = ((14.4*gf)/(E*(a1-a2)2*(T1-T2)2))
Where gf is the surface energy of fracture, E is the Young's modulus of elasticity, (a1-a2) is the largest difference in CTE values in the material (can be between different lattice directions of the same material or between different phases), (T1-T2) is the maximum temperature difference over which stresses will accumulate. The surface energy can by calculated with:
gf = (KIc2*(1-n2))/(2E)
Where KIc is the fracture toughness of the material and n is the Poisson's ratio. If this estimate works with your material, then grain sizes below this critical grain size should not microcrack. Here is the reference:
Cleveland JJ, Brandt RC (1978). Grain size/microcracking relations
for pseudobrookite oxides.JAm Ceram Soc 61:478-481.
Discussing on the thermo-mechanical properties anisotropy of ceramic-forming phases everybody hasn't to forget about the substances, which have extremely great difference in thermal expansion along the main hexagonal axis. These are graphene-like carbon and boron nitride. At temperatures from 500 to 3000 0C for graphite flakes the ratio between the linear thermal expansion along c and a directions (so-called the anisotropy coefficient "zeta") is about 25-30 (for BN-flakes it is about 40), but at lower temperatures "zeta" for graphene-like phases can achieved 103-106 (!) or even more... Thus, the ceramics containing graphene-like phases formed at higher temperatures perform very "unusual" behaviour in comparison with conventional single- or multi-phase technical ceramics. An unusually high damage tolerance of this type of ceramics is caused by the so-called pre-stressed state that results in the inherent ability to absorb and dissipate the elastic energy released during crack propagation and their capability to blunt and divert a propagating crack. This ceramics demonstrate clearly its higher fracture toughness and thermal shock resistance; because of its very specific structure and properties it had been termed specially as "high-E - low-E" composites (by Prof Dick Hasselman with his colleagues) or hetero-modulus ceramics (by me and my colleagues). My practical experience as a aerospace/rocketry engineer has showed many times that ceramics not containing graphene-like phase inclusions have no chance to be applied in rocket and spacecraft technologies. The best examples encouraged this my view point are connected with the application of hetero-modulus ceramics for anti-ballistic missile leading edges and ion rocket engines.
Some other details connected with design, production, properties and applications of hetero-modulus ceramics could be found in my recently published book Ultra-High Temperature Materials, Vol. 1, chapter Carbon (Graphene/Graphite) and other publications and presentations on my ResearchGate account/page.
Dear Mehdi:
This paper is useful for understanding the problem.
V. Tvergaard, J. W. Hutchinson, "Microcracking in Ceramics Induced by Thermal Expansion or Elastic Anisotropy", J. Am. Ceram. Soc., 71(3)157-166(1988)
- Badges
- Science topic
- Similar topics
- Physical Sciences
- Materials Science
- Materials
- Inorganic Materials
- Ceramics