For designing SOFC with high mechanical reliability, it is necessary to analyze stress state of cells and stacks under various operating conditions. Based on this concept, our group has attempted to construct multiscale model which can simulate elastic and inelastic deformation and fracture probability with consideration of electro-chemical, thermal and mechanical properties of constituent materials. In this study, we focus on strength of SOFC materials including 8YSZ electrolyte, 10GDC barrier layer and LSCF6428 cathode which are well-known as brittle materials. Their elastic properties and fracture strengths are evaluated as a function of temperature. 2. Experiments

Evaluation of elastic and fracture properties

Mechanical strength evaluation is performed by Small Punch (SP) tests. The tests were performed on a universal testing machine (INSTRON 5565). The circular specimens were simply supported at the circumferential edge of an alumina tube and subjected to a concentrated load at their center position. The load was applied through a puncher at a crosshead speed of 0.05 mm/min until a final failure occurred. The load-line deflection of the specimens was measured by monitoring the movement of an Al₂O₃ rod of which one end is made in contact with the bottom surface of the sample, and the position of the other end is monitored using a laser displacement transducer. The elastic modulus E_SP and fracture stress σ_{f_SP} were calculated using the following equations : E_SP= f(t/a)[3a²(1-ν)(3+ν)P/4πδt³], σ_{f_SP}=P_max(1+ν)[0.485ln(a/t)+0.52+3/2π(1+ν)]/t², where P_max is the load applied by the puncher, δ is the load-line deflection, t is the thickness of the specimen,n is Poisson’s ratio, a is the radius of the load support, and f(t/a) is a correction factor of the specimen thickness for the thin plate theory given by the following equation: f(t/a)=1.5136(t/a)²+0.0162(t/a)+0.9962. The elastic modulus E_SP was computed from the linear slope of the load versus load-line deflection records (P/δ), and the fracture stress σ_{f_SP} was calculated from the peak load P_max.

Sample preparation

Commercial powders of 10 mol% gadolinia doped ceria (10GDC) was obtained from Shin-Etsu Chemical Co., Ltd.(Tokyo, Japan) and La_0.6Sr_0.4Co_0.2Fe_0.8O_3-δ (LSCF6428) from Noritake Co.,Ltd.(Nagoya, Japan). The 10GDC and LSCF6428 powders were uniaxially pressed to f10mm disc-shape with pressure 100 MPa and then with a cold isostatic press (CIP) at 170 MPa. After that, 10GDC green samples were sintered at 1550˚C for 6 hours with 5˚C/min heating rate and 2˚C/min cooling rate. LSCF6428 green samples were sintered at 1300˚C for 6 hours with the same heating and cooling rates. As a SP test specimen, sintered discs were polished to a uniform thickness about 0.5mm by mechanical polishing. One side of the pellet was mirror-polished with a diamond paste of 3mm. 8 mol % Y₂O₃stabilized zirconia (8YSZ) plates of 7×7×0.5 mm with one side polished were supplied by Japan Fine Ceramic Co., Ltd (Sendai, Japan).

 We performed ten experiments for respective materials at selected temperature between R.T. and 800˚C in air. Average and standard deviation of elastic moduli and scale and shape parameters of fracture stress based on Weibull distribution were calculated from experimental results at each temperature. Scale parameter means fracture stress at fracture probability 63.2% and, shape parameter indicates the degree of dispersion of fracture stress on Weibull distribution. Lager shape parameter means the dispersion of fracture stress is smaller, and the strength stability is higher.

3. Result and discussion

The temperature dependences of elastic moduli and scale and shape parameters of 8YSZ, 10GDC and LSCF6428 are shown in Fig.1 (a), (b). For 8YSZ, elasticity, scale and shape parameters showed minimum at 400˚C. It means decrease of elasticity and fracture stress of 8YSZ is accompanied by increase in the dispersion of fracture stress. For 10GDC, both elasticity and scale parameter decreased up to 200˚C, and gradually increased with further increase in temperature. It should be noted that shape parameter increased with temperature increasing. It shows that the strength stability increased with temperature. For LSCF6428, elasticity once dropped between 200˚C and 400˚C, increased with further heating up to 800˚C. Scale parameter tendency is similar to 10 GDC, but the strength stability of both is switched at 600˚C. In this way, the quantitative characterization of the strength stability in 8YSZ, 10GDC and LSCF6428 are evaluated with their fracture stress and elasticity.