True Stress
Calculate the true stress, σ_t = s × (1 + e), from the engineering stress s (MPa) and the engineering strain e. Engineering stress uses the specimen's initial area, but during a tensile test the real cross-section shrinks; true stress corrects this using the instantaneous area (assuming constant volume in the uniform region), always giving a higher value than engineering stress. It is essential to build the true stress-strain curve and model strain hardening (σ = K·εⁿ). The result is in the same unit as the input stress. Enter the engineering stress and strain.
Result
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Tensão verdadeira
A tensão de engenharia que se lê num ensaio de tração é a força dividida pela área inicial do corpo de prova (s = F/A₀). O problema é que, conforme o material estica, a seção transversal diminui — então a área inicial subestima a tensão que o material realmente sente. A tensão verdadeira corrige isso usando a área instantânea: σ_v = F/A. Assumindo que o volume se conserva na região de deformação uniforme (A·L = A₀·L₀), chega-se à relação prática σ_v = s × (1 + e), onde e é a deformação de engenharia. Como (1 + e) é sempre maior que 1, a tensão verdadeira é sempre maior que a de engenharia, e a diferença cresce com a deformação. A curva tensão-deformação verdadeira é a que revela o comportamento físico do material: ao contrário da curva de engenharia (que 'cai' após a tensão máxima por causa da estricção), a curva verdadeira continua subindo, mostrando que o material continua encruando. Na região plástica uniforme ela costuma seguir a lei de potência σ = K·εⁿ, onde n é o expoente de encruamento. Informe a tensão e a deformação de engenharia.
Related Tools
True Strain
Calculate the true (logarithmic) strain, ε = ln(1 + e), from the engineering strain e (dimensionless or fractional). While engineering strain uses the fixed initial length as reference, true strain integrates the instantaneous length changes, being additive and better suited to large plastic deformations such as in metal forming (rolling, extrusion, drawing). The result is the actual strain accumulated by the material. For small strains, ε ≈ e; the difference grows as strain increases. Enter the engineering strain.
Bolt Tensile Stress
Calculate the tensile stress in a bolt, σ = F_b ÷ A_t, from the total bolt tensile force F_b (N) and the tensile stress area A_t (mm²). It is the basic strength check of a tensioned bolt: the acting stress (force over resisting area) must be below the material strength with a safety margin. The force F_b is the total load the bolt carries — in a preloaded joint, the preload plus the fraction of external load reaching the bolt (F_i + C·P). The resulting stress is compared with the proof strength S_p (the limit up to which the bolt can be loaded without permanent deformation — typically 85-90% of yield) or the ultimate strength, per the criterion. The bolt strength class (marked on the head: 8.8, 10.9, 12.9 metric; or SAE grades 2, 5, 8) sets these allowable stresses — a class 8.8 bolt has a proof strength of 580-600 MPa, a 12.9 reaches ~970 MPa. Verifying σ does not exceed the allowable, considering preload and service load, is essential: overloaded bolts yield (losing preload) or break. With the fatigue and separation checks, it defines the tensioned joint's safety. Enter the total bolt force and the tensile area.
Percent Elongation
Calculate the percent elongation, A% = (L_f − L₀) ÷ L₀ × 100%, from the initial gauge length L₀ and the final length L_f measured after rupture in a tensile test (fitting the two halves of the specimen back together). The result, in %, is a direct measure of the material's ductility — how much it stretches before breaking. Ductile steels reach 20–40%; brittle materials, a few percent. Elongation depends on the gauge length used, so it is always quoted with it (e.g. A% over 50 mm). Enter the initial and final lengths.
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