Extracting true stresses and strains from nominal stresses and strains in tensile testing

Abstract

Seemingly a simple task, the extraction of the flow curve (true stress vs. true plastic strain) from nominal stresses and strains in standard tensile testing still has its unsolved points. This study addresses two of them: (i) in materials without yield point phenomenon (or generally in the region of homogeneous plastic deformation), the true stress is typically calculated assuming constant volume, ignoring the elastic volume changes. Here, we derive a set of exact analytical solutions for true stresses and strains with remarkable simplicity and beauty that fully account for the elastic volume changes. This set of exact solutions is cross‐checked by finite element simulations as well as zeroth‐ and first‐order approximations; perfect agreement has been found. (ii) In materials with a pronounced yield point phenomenon, a complicated three‐dimensional stress state inevitably arises at the edge of the Lüders bands, which masks the real (or inherent) material behaviour. To determine the real material behaviour in the Lüders region, here we use a new macroscopic analytical approach characterised by a high true upper yield point, a typical strain hardening behaviour common for many materials, and the triaxiality of the stress state that inevitably develops at the edges of the Lüders bands and that determines the stress level at the observed lower yield point. This approach is verified by experiments (including video observations as well as digital image correlation (DIC) strain distribution measurements) and finite element simulations with very good agreement.

Mechanical Properties and Energy Absorption of Integrated AlSi10Mg Shell Structures with BCC Lattice Infill

“…For the finite element analysis, the obtained experimental nominal stress and strain were converted to true stress and strain [37]. The true strain is expressed as follows: where ε nom is the nominal strain, which can be obtained as where l 0 is the original length, l is the current measured length, all can be obtained from the test.…”

High‐performance ZSR/P(MMA/BA) composites with enhanced thermal and excellent water resistance properties

“…As shown in Figure 7a,b, all samples showed a local maximum near or at the initial yield point rather than a continuously increasing nominal stress-strain curve during tensile deformation, which commonly referred to as the yield point phenomenon and indicated the composite films changed from elastic deformation to plastic deformation. 47,48 The elongation at break and the fracture energy of the ZSR/P(MMA/BA) composite films showed a tendency to first increase and then decrease with increasing ZSR content, and their maximum values were reached at 7 wt% ZSR content. Compared to S1, the elongation and fracture energy of the S4 were significantly increased by 28.8% and 89.0% respectively.…”

A novel application of cryogenics in dieless sheet metal piercing

“…Three specimens were used, and the average nominal stress-strain curve was computed for the identification process. The approach suggested in Schwab and Harter [4] was adopted to estimate the true stress strain curve 𝜎𝜎 = 𝑓𝑓(𝜀𝜀) from the corresponding nominal quantities (s and e). The identification of the parameters was twofold.…”