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Three-dimensional finite element method is utilized to analyze the plasticityinducedcrack closure (PICC) phenomenon in a through thickness centre-cracked plate underconstant amplitude cyclic loading. To accurately capture the PICC process, the choice ofmaterial model employed is of significant importance. This paper considers a relatively newmodel, the Ellyin-Xia elastic-plastic constitutive relations, and the more widely used kinematichardening model. The study shows considerable difference in the results obtained whileemploying the two models. Experimental results support the predictions by the Ellyin-Xiamaterial model.