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Chinese Journal of Materials Research  2017, Vol. 31 Issue (9): 703-713    DOI: 10.11901/1005.3093.2016.577
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Numerical Analysis in Mesoscopic Scale and Experimental Verification for Sodium Expansion Induced Stress of Cathode Carbon Blocks
Qingsheng LIU(), Shaojun ZENG, Dancheng ZHANG
Falculty of Metallurgical and Chemical Engineering, Jiangxi University of Science and Technology, Ganzhou 341000, China
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Qingsheng LIU, Shaojun ZENG, Dancheng ZHANG. Numerical Analysis in Mesoscopic Scale and Experimental Verification for Sodium Expansion Induced Stress of Cathode Carbon Blocks. Chinese Journal of Materials Research, 2017, 31(9): 703-713.

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Abstract  

The cathode carbon block was regarded as a two-phase composite material composed of aggregates and binder in mesoscopic scale, for description of which, a two-dimensional random aggregate model was established by Monte Carlo method. Then the numerical simulation of sodium expansion induced stress of aggregate model was established by the thermal analysis module of ANSYS finite element software in consideration of different shapes, gradations and contents of the aggregate. The results show that the nonuniformity of the meso-structure in the cathode carbon block causes the nonuniform distribution of the stress induced by the sodium expansion. Particularly, the presence of the tensile stress can lead to the damage of the cathode carbon block. The sodium expansion of the carbon blocks with the carbon aggregate within the gradation of 0.003-0.015 m is the lowest, while those within the gradation of 0.003-0.006 m is the highest. The sodium expansion of the carbon block with 80% carbon aggregate is the lowest, while that with 60% carbon aggregate is the highest. The numerical simulation results are in accordance with the experimental results,which means that this model can reasonably and effectively describe the sodium expansion and stress distribution of the carbon block. Thus it can be used as an effective auxiliary way to study phenomena related with the sodium expansion induced stress.
Key words:  foundation discipline in materials science      model of sodium expansion stress      numerical stress      numerical simulation      cathode carbon block      meso-structure     
Received:  30 September 2016     
ZTFLH:  TF821  
Fund: Supported by National Natural Science Foundation of China (Nos.51264011 & 51564019)
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Qingsheng LIU
Shaojun ZENG
Dancheng ZHANG

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https://www.cjmr.org/EN/10.11901/1005.3093.2016.577     OR     https://www.cjmr.org/EN/Y2017/V31/I9/703

Number Shape Filling ratio Diameter of grading
1 circle 60% 0.003~0.009 m
2 circle 70% 0.003~0.006 m
3 circle 70% 0.003~0.009 m
4 circle 70% 0.003~0.015 m
5 circle 80% 0.003~0.009 m
6 ellipse 70% 0.003~0.009 m
7 polygon 70% 0.003~0.009 m
Table1  Control parameters of different aggregate model
Fig.1  Finite element meshes of model 2 (a) solid pattern, (b) Aggregate unit, (c) Binder unit
Fig.2  Constraint of model
Aggregate Binder
Density (kg/m3) 1940 1200
Modulus of elasticity (GPa) 9 6
Poisson's ratio 0.32 0.28
Diffusion coefficient of
sodium (mm2/s)		 8.9×10-3 9.7×10-2
Table 2  Material parameters of cathode carbon block
Sodium concentration /%, mass fraction 1 2 3
Aggregate (10-5) 0.65 1.3 1.95
Binder (10-5) 1.09 2.18 3.28
Table 3  Expansion coefficient of Sodium
Fig.3  Single aggregate expansion stress distribution (unit:Pa) (a) X direction, (b) Y direction
Fig.4  Distribution of sodium concentration in aggregate with different shapes 3600 s (unit: mm) (a) circle, (b) ellipse, (c) polygon
Fig.5  Aggregate model Y direction expansion displacement in different shapes 10800 s (unit: mm) (a) circle, (b) ellipse, (c) polygon
Fig.6  Aggregate model X direction stress distribution in different shapes10800 s (unit: Pa) (a) circle, (b) ellipse, (c) polygon
Fig.7  Aggregate model Y direction stress distribution in different shapes10800 s (unit: Pa) (a) circle, (b) ellipse, (c) polygon
Fig.8  Expansion displacement and stress curve of aggregate model in different shapes (a) expansion displacement time curve, (b) radial element X direction stress, (c) radial element Y direction stress
Fig.9  Distribution of sodium concentration in different graded aggregate mode 3600 s (unit: mm) (a) 0.003~0.006 m, (b) 0.003~0.009 m, (c) 0.003~0.015 m
Fig.10  Aggregate model Y direction expansion displacement in different grading 10800 s (unit: mm) (a) 0.003~0.006 m, (b) 0.003~0.009 m, (c) 0.003~0.015 m
Fig.11  Aggregate model X direction stress distribution in different grading 10800 s (unit: Pa) (a) 0.003~0.006 m, (b) 0.003~0.009 m, (c) 0.003~0.015 m
Fig.12  Aggregate model Y direction stress distribution in different grading 10800 s (unit: Pa) (a) 0.003~0.006 m, (b)0.003~0.009 m, (c) 0.003~0.015 m
Fig.13  Expansion displacement and stress curve of aggregate model in different gradin (a) expansion displacement time curve, (b) radial element X direction stress, (c) radial element Y direction stress
Fig.14  Distribution of sodium concentration in different aggregate model 3600 s (unit: mm) (a) 60%, (b) 70%, (c) 80%
Fig.15  Aggregate model Y direction expansion displacement in different content 10800 s (unit: mm) (a) 60%, (b) 70%, (c) 80%
Fig.16  Aggregate model X direction stress distribution in different content 10800 s (unit: Pa) (a) 60%, (b) 70%, (c) 80%
Fig.17  Aggregate model Y direction stress distribution in different content 10800 s (unit: Pa) (a) 60%, (b) 70%, (c) 80%
Fig.18  Expansion displacement and stress curve of aggregate model of different content 10800 s (a) expansion displacement time cur, (b) radial element X direction stress, (c) radial element Y direction stress
Fig.19  Schematic diagram of sodium expansion test device
Fig.20  Comparison of numerical simulation and actual test
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