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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Raio mínimo de dobra
O raio mínimo de dobra de uma chapa é estimado por R_min = t·(50/r − 1), a partir da espessura t e da redução de área percentual r do material no ensaio de tração (uma medida de ductilidade). O raio mínimo é o menor raio interno com que se pode dobrar uma chapa sem trincar a face externa (que está sob tração). Dobrar com raio menor que o mínimo provoca fissuras ou ruptura na fibra externa, onde a deformação de tração excede a capacidade do material. O raio mínimo depende fortemente da ductilidade do material (expressa aqui pela redução de área r): materiais muito dúcteis (alumínio recozido, aços baixo carbono) podem ser dobrados com raio quase nulo (dobra viva), enquanto materiais frágeis ou encruados exigem raios grandes. O raio mínimo também depende da orientação da dobra em relação à direção de laminação da chapa — dobrar perpendicular à laminação permite raios menores que paralelo, por causa da anisotropia introduzida pelo processo de laminação. Conhecer o raio mínimo é essencial no projeto de peças dobradas: especificar um raio menor que o possível leva a refugo por trincas e retrabalho. É comum expressar o raio mínimo como múltiplos da espessura (ex.: '1t', '2t'). Informe a espessura e a redução de área do material.
Related Tools
V-Bending Force
Calculate the force to bend a sheet in a V-die, F = (C·σ_r·L·t²) ÷ V, from the process constant C (~1.33 for free V-bending), the material tensile strength σ_r (N/mm²), the bend length L (mm), the sheet thickness t (mm) and the V-die opening V (mm). V-bending is the most common forming operation on press brakes: the sheet rests on a V-shaped die and a punch forces it in, bending it to the desired angle. Force grows with the SQUARE of thickness (thicker sheets need much higher forces) and with material strength, and decreases with die opening (larger V → lower force, but larger bend radius). The rule of thumb uses V ≈ 6-8 times the thickness. Computing the force is essential to select the press brake (tonnage) and not overload the tooling. The bend-tonnage tables ubiquitous in sheet shops are exactly this formula applied to combinations of thickness, material and die opening. Enter the constant, tensile strength, length, thickness and die opening.
Percent Cold Work
Calculate the percent cold work (area reduction), %CW = (A₀ − A_f) ÷ A₀ × 100%, from the initial cross-section area A₀ and the final area A_f after cold plastic deformation (rolling, drawing, stamping). The result, in %, shows how much the material was deformed below the recrystallization temperature. Cold work strain-hardens the metal: it raises the yield strength and hardness and lowers ductility as dislocations multiply and tangle. It is the parameter used to control properties before an anneal. Enter the initial and final areas.
Railway Minimum Curve Radius
Calculate the minimum railway curve radius for a design speed, R = (B·V²) ÷ (127·(h_max + I_max)), from the gauge B (mm), speed V (km/h), maximum allowable cant h_max (mm) and maximum allowable cant deficiency I_max (mm). The minimum radius is set by combining the two comfort/safety limits available to 'absorb' lateral acceleration at the desired speed: the maximum buildable cant (limited by overturning risk of slow/stopped trains) and the maximum deficiency allowed to passengers. The larger these limits, the smaller the radius for a given speed — but both have normative caps. This is central to railway alignment: it defines how sharp a curve can be without speed reduction. Sharper curves require slowing down, penalizing travel time and line capacity — so high-speed railways need huge radii (kilometers). Enter the gauge, speed, maximum cant and maximum deficiency.
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.