WELDING RESEARCH Fig. 8 — A quarter model for solid parts and fluid inside the roll. NOVEMBER 2016 / WELDING JOURNAL 435-s 16 h, the roll was heated to about 200C. After heating for 24 h, the roll was heated to about 1066C. Then, the roll temperature was kept constant for 100 h and then cooled to about 200C within 24 h. During creep-fatigue analysis, the heating cycle was repeated 10 times. CreepFatigue Analysis A creep-fatigue analysis procedure was developed using the ABAQUS commercial finite element code in which isotropic creep- and plasticity-coupled behavior was modeled by solving a coupled system of constitutive equations. This analysis procedure has been successfully used in modeling the creep behavior of a nuclear pipe system (Ref. 28). For simplicity, the power-law creep model was used in this study. The mechanical load and gravity were applied as a constant load and the thermal load was applied as low cyclic loads. Figure 5 shows a one-cycle thermal load in which the holding time is about 100 h. The long hold time made the power-law creep model suitable for the analysis of the furnace roll. During heating and cooling, a dynamic analysis was conducted and creep process was not modeled because the temperature quickly dropped to a low value. At a given temperature, the rate of steady-state creep can be calculated by the power law (Refs. 29, 30): • where is creep strain rate, is the applied stress, A is a constant dependent on the material, and n is an exponent dependent on the creep mechanism. The creep constants A and n at different temperatures, listed in Table 1, were obtained by fitting the data from Refs. 23 to 26 and the data from an industrial customer. Steel sheet tension of 31136 N was transferred to the roll through contact on one-fourth of the roll circumference over a width of 1270 mm in the center of the roll length, as shown in Fig. 6A. The combined force in the 45- = An (3) Fig. 9 — Predicted effective creep strain after 10 loading cycles for both cool to 204C and cool to 427C. Table 2 — Air Properties as a Function of Temperature (Ref. 32) Temperature Specific Heat Viscosity Thermal Conductivity Density (C) (J/kg C) (10–5 kg/m s) (10–2 W/m C) (kg/m3) 26.85 1004.9 1.846 2.624 1.177 101.85 1010.6 2.181 3.186 0.941 226.85 1029.5 2.670 4.041 0.706 326.85 1051.1 3.017 4.661 0.588 426.85 1075.0 3.332 5.236 0.504 526.85 1098.7 3.624 5.774 0.441 626.85 1120.9 3.897 6.276 0.392 726.85 1141.1 4.153 6.754 0.353 826.85 1158.9 4.396 7.209 0.321 926.85 1174.6 4.626 7.640 0.294 1026.85 1188.4 4.846 8.054 0.272
Welding Journal | November 2016
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