True Strain
True strain, also called logarithmic or natural strain, is the natural logarithm of the ratio of current length to original length: ε_true = ln(L/L0). Unlike engineering strain, it updates the reference length continuously, so it remains accurate in large plastic deformation and pairs with true stress for work-hardening analysis. It is essential for forming, rolling, and drawing calculations.
On the shop floor, true strain becomes relevant whenever a part is pushed beyond elastic limits—deep drawing, stretching, rolling, or multi-pass reduction. In these operations, the original gauge length no longer reflects the actual material state because the cross-section shrinks while the part elongates. True stress and true strain data are needed to model work hardening, predict thinning, and decide whether an intermediate anneal is required. For example, a drawing die that looks acceptable on paper may produce excessive localized strain because the engineering numbers hide how fast the section weakens. Feeding true stress-strain data into FEA material cards and forming simulations avoids those surprises. Many material models expect true values, so tensile test results must be converted using ε_true = ln(1 + ε_eng). This conversion also matters when selecting reduction schedules, bend radii, and pass sequences, since allowable deformation is often specified as a percentage of true strain.
- Engineering strain creeping in on big reductions: treating a large draw or reduction as linear underestimates true deformation once dimensions change significantly, so the part runs deeper into strain hardening than the calculations suggest, risking unexpected thinning or fracture.
- Ignoring area reduction in forming loads: judging a sheet or bar only by elongation while instantaneous cross-section shrinks hides the true stress rise, underestimating die wear, necking risk, and crack onset.
- Feeding engineering data into FEA material cards: simulation gets nominal test data without conversion, producing incorrect hardening curves and forming-force estimates that distort yield progression, post-yield hardening, and necking prediction.
What is the exact formula for true strain in uniaxial deformation?
True strain is defined as ε_true = ln(L/L0), where L0 is original length and L is current length. In terms of engineering strain, it is equivalently ε_true = ln(1 + ε_eng).
Why is true strain preferred in plasticity and work-hardening analysis?
Because true strain accumulates deformation incrementally and remains physically meaningful as the specimen changes length. It tracks the instantaneous gauge length, making it accurate for large plastic strains and for comparing different loading paths.
How does true strain connect to true stress in forming practice?
True stress uses instantaneous cross-sectional area rather than original area. The true stress–true strain curve is used to characterize strain hardening beyond yield and to model behavior before and around necking, giving a realistic load state in drawn, rolled, or stretched parts.