The invention provides a method for making Zr alloy nuclear reactor fuel cladding having excellent corrosion resistance and creep properties. The method includes performing hot forging, solution heat treatment, hot extruding, and repeated cycles of annealing and cold rolling of a Zr alloy including, by weight, 0.2 to 1.7% Sn, 0.18 to 0.6% Fe, 0.07 to 0.4% Cr and 0.05 to 1.0% Nb, with the remainder being Zr and incidental impurities, and the incidental nitrogen impurity content being 60 ppm or less, and then performing final stress relief annealing thereon. The annealing is performed at a temperature of 550 C. to 850 C. for 1 to 4 hours such that the accumulated annealing parameter Ai=tiexp(-40,000/Ti) satisfies relationships -20 log Ai-15, and -18-10X. sub.Nb log Ai-15-3.75 (X.sub.Nb -0.2), wherein Ai represents the annealing parameter for the i- th annealing, ti represents the annealing time (hours) for the i-th annealing, Ti represents the annealing temperature (K) for the i-th annealing, and X. sub.Nb represents the Nb concentration (wt %).
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