PSI - Issue 72

Levente Tatár et al. / Procedia Structural Integrity 72 (2025) 345–353

346

1. Introduction Many metals exhibit large scale plasticity, which is a very useful behaviour in different areas of the industry. A plastic reserve is beneficial for structures as usually the most dangerous accidental situations arise from sudden, unexpected brittle fracture. Ductile behaviour before break could act as an indicator of overloading and required measures can be taken to prevent catastrophic failure. Plasticity is at the base of hot and cold forming. With the extent of computers, the need of simulation of plastic deformation processes arose, however modelling plastic behaviour of metallic materials has still uncertainties. Tensile testing is an old and reliable method for determining elastic and plastic properties of materials. At the beginning of the testing process very simple analytical formulae can be used for evaluating raw data. Main results of tensile tests are strains and stresses. Depending on how initial raw data is processed, we can distinguish engineering stress – engineering strain and true stress – true strain data. A common practice is, that after processing the raw measured data only the mechanical characteristics of the metallic material, such as ultimate tensile strength, maximum elongation, yield strength, and area reduction are considered as important and are archived. For simple engineering design, values of these characteristic values are sufficient. For more sophisticated analyses however, like simulation of cold and hot working processes, elasto-plastic Fracture Mechanics, Damage Mechanics, etc. a full and reliable flowcurve is required. 1.1. Difficulties of flowcurve determination To determine a plastic flowcurve which can be used in FEM simulations the starting point is the raw measured data, which is usually a force – strain curve. Force is provided by the testing equipment, while longitudinal type strain gauges give average engineering strain for a given gauge length. For determining engineering stress the only other available data besides force is the area of initial cross section. Until observable macroscopic necking, the deformation can be considered uniform for the length of the specimen. By using the approximation of volume constancy for the gauge length true strain and true stress can be simply determined from engineering strain – engineering stress curve by the well-known formulae (1),     t t 1 ; ln 1           (1) where ε and σ are engineering strain and stress, ε t and σ t are true strain and true stress respectively. When macroscopic necking develops, the simple analytical formulae progressively lose their validity. There are two different reasons for this: 1. The strain gauge measures average strain, whilst the strain has some kind of distribution over the length of the specimen 2. The stress-strain field becomes triaxial. The problem of localized strain – vs. average strain can be handled in a relatively easy way, as by optical observation one can measure the minimum cross-section instead of the gauge length. In such way, based on the area reduction true stress and true strain values can be defined (Equations (2)) A 0 is area of the initial cross-section of the specimen, A min is the minimal cross-section at the necking for each moment of time of the test. Nomenclature DT Digital twin FEM Finite Element Method FE Finite Element(s)