連續退火線(Continuous Annealing Line, CAL)具有生產效率高，產品種類多樣化，產品質量高，生產成本低等許多優勢。然而為了成本與空間考量，連續退火爐內的爐輥尺寸都設計很小，鋼帶在通過爐輥時因而產生較大的彎曲應力；鋼帶在退火爐高溫環境內材料降伏強度會降低，在加上鋼帶張力以及彎曲應力，經由每個爐輥反覆彎折，會導致鋼帶發生塑性變形，因此產生橫向與縱向的翹曲量。縱向翹曲量原因是因為鋼帶沿厚度方向塑性應分佈不均所造成；另外錐度會造成鋼帶沿寬度方向之溫度與應力分佈不均，導致鋼帶縱向翹曲量沿寬度方向分佈不平均。本文發展了一套數值模型預測鋼帶在各爐輥的降伏狀態，並計算出鋼帶的塑性應變量、殘留應力以及縱向翹曲量。

The continuous annealing line (CAL) realizes high productivity and quality stability at a lower cost and has the capability to produce a wide range of product types. However the size of the hearth rolls in CAL is usually designed as small as possible due to limitation of space and cost. Therefore, the bending stress of steel strip becomes larger while passing through each roll. Because of the combination of high temperature in annealing furnace, which decreases the yield strength of strip, the strip tension and bending stress, it is inevitable that plastic bending occurs after passing the rolls in CAL. The strip thus creates longitudinal and transverse warps. The major cause of longitudinal warp is the non-uniformly distribution of plastic strain along the strip thickness. The crown of the hearth roll will cause the inconsistency of stress, temperature and also longitudinal warps along width direction as well. A numerical model developed to predict the phenomenon of yielding and magnitude of plastic strain, residual stress and longitudinal warp of steel strip in CAL is described and discussed.

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