Minimum Bend Radius
Estimate a sheet's minimum bend radius, R_min = t·(50/r − 1), from the thickness t (mm) and the material's percent reduction of area r in the tensile test (%, a ductility measure). The minimum radius is the smallest inner radius you can bend a sheet to WITHOUT cracking the outer face (which is in tension). Bending below the minimum causes cracks or rupture in the outer fiber, where tensile strain exceeds the material's capacity. The minimum radius depends strongly on the material's DUCTILITY (here via reduction of area r): very ductile materials (annealed aluminum, low-carbon steels) can be bent to nearly zero radius (sharp bend), while brittle or work-hardened materials need large radii. It also depends on the bend ORIENTATION relative to the sheet's rolling direction (bending across the rolling direction allows smaller radii than along it, due to anisotropy). Knowing the minimum radius is essential in bent-part design: specifying a smaller radius than possible leads to crack scrap. It is common to express the minimum radius as multiples of thickness (e.g. '2t'). Enter the thickness and the material's reduction of area.
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Minimum bend radius
The minimum bend radius of a sheet is estimated by R_min = t·(50/r − 1), from the thickness t and the percent reduction of area r of the material in the tensile test (a measure of ductility). The minimum radius is the smallest inner radius to which a sheet can be bent without cracking the outer face, the one under tension. Bending to a radius tighter than the minimum produces cracks or fracture in the outer fiber, where tensile strain exceeds what the material can take. The minimum radius depends heavily on the ductility of the material (expressed here by the reduction of area r): very ductile materials such as annealed aluminum and low-carbon steels can be bent to an almost zero radius (a sharp bend), while brittle or work-hardened materials call for generous radii. The minimum radius depends as well on the orientation of the bend relative to the rolling direction of the sheet — bending across the rolling direction allows tighter radii than bending along it, owing to the anisotropy the rolling process introduces. Knowing the minimum radius is essential when designing bent parts: specifying a radius tighter than what the material allows leads to scrap from cracking and rework. Shops commonly express the minimum radius as a multiple of the thickness (for example '1t' or '2t'). Enter the thickness and the reduction of area of the material.
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Blank Diameter for Cup
Calculate the blank (initial flat disc) diameter needed to draw a cylindrical cup, D = √(d² + 4·d·h), from the cup diameter d (mm) and the cup height h (mm), by area conservation. The calculation rests on a fundamental drawing principle: the operation does NOT significantly change the sheet thickness (ideally drawing conserves volume and, with constant thickness, conserves surface AREA). So the flat disc area must equal the cup surface area (bottom + side wall). Equating π·D²/4 = π·d²/4 + π·d·h and solving for D gives the formula. This is the starting point of any drawn-part design: it sets the disc size to cut from the coil or sheet, which determines material consumption (and thus cost and yield, optimized by blank arrangement — nesting). For cups with flange, rounded bottom or non-straight walls, add the corresponding areas. Correct blank calculation avoids waste (disc too big) and incomplete parts (disc too small). Enter the cup diameter and height.
The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.