Straight ahead approximation

The straight ahead approximation, which disregards the influence of small deflections upon the deep penetration and thus sets coz — 1 in (4), has been the object of many early investigations. It yields the same expression (11) as the Wick procedure but with erroneous values of k and t] see [1, 11]. 

The soak zone should be divided into three zones across the furnace width to permit profiling of the temperature of the product. With small to medium sized bars in a straight ahead mill, the head ends should be approximately 50 F above the body temperature and the tail should be about 60 F above the body temperature. The reason for the higher temperatures for the head and tail is overfill and underfill of the roll passes when the head and tail of the billets are not being stretched between mill stands, which is a problem even with loopers between roll stands. 

These measurements show that the shape of the craze is well described by the Dugdale plastic zone model originally proposed for metals. The tip of the craze is approximated by a straight line perpendicular to the direction of advance of the crack and the thickness profile can be deduced from the assumption that there is a constant craze stress normal to the plane of the craze. Provided that cr cTcr, where a is the applied tensile stress causing the crack, the length R of the craze ahead of the crack tip is given by... 

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