CENTRE FOR ENERGY RESEARCH
PROGRESS REPORT 2022
EXTENDING THE RELIABILITY OF TENSILE TESTS WITH A NOVEL
EVALUATION FRAMEWORK
Tamás Fekete, Levente Tatár, Dániel Antók, Péter Bereczki
Objective
The tensile test is one of the most widely used engineering tests, codified in numerous national and international standards.
The basic theoretical model generally used for evaluation of the test is extremely simple. The basic results of a tensile test
(yield strength, ultimate tensile strength) are widely used for design and verification. This over-simplifying approximation
may be enough for some simple cases assuming that the safety factor is large enough. For more complicated cases, where
small scale yielding is permitted, assessment needs an accurate description of the plasticity. With a clip gauge type
extensometer and simple analytical formulae the elasto-plastic flowcurve can be reliably described until necking. These
formulae cannot describe the post-necking behaviour of the specimen.
For heavy loaded large, complex engineering structures simple approaches are insufficient. In this case Structural Integrity
(SI) approach has to be applied, often involving plasticity. This requires more precise and more complete description of the
material properties than those obtainable from simple analytical formulae.
A framework created for determination of a stress-strain curve based on traditional measurements (force, extensometer)
complemented by optical measurements has been presented in [1] and [2]. Main elements of the framework are measurements
and simulations.
Methods
The measurements are performed on a Gleeble 3800 thermomechanical simulator. Cylindrical specimens and specimens with
square cross section were used. The specimens were equipped with a clip gauge extensometer. Most important data provided
by the testing machine were force, strain (measured by extensometer) and a triggering signal.
For specimens with square cross section regular patterns were created at two sides of the specimens. A dual camera system
was used for taking pictures of the specimen during the test. Both cameras were triggered by the same triggering signal.
Digital twins (DT) of the measurements were developed for simulation of the tests. Figure 1. presents an overview of the
process. Specimen contours and mapping of the grid were obtained from pictures. With this data the stress-strain curve can
be extended over the validity of measurements by extensometer. Due to the fact that the stress field becomes triaxial, a
correction has to be applied to the curve. Validity of such curves can be verified and further developed by FEM computations.
Figure 1: Overview of the process
Results
From pictures taken during the test contours to be used for extending the true strain true stress curves were determined by a
multistep procedure. Extraction of the contours consisted in oversampling the original picture, then a slight blurring followed
by thresholding and vectorizing. The real dimensions of the curves were obtained by using the laws of geometric optics.
Adiacent averaging has been applied to raw curves for smoothing and for specimens where necking was present an analytical
“bell-shaped” curve was fitted to the smoothed curves. Based on this formula the radius of the curvature at the minimal cross
section has been determined. For cylindrical specimens, the Bridgman correction formula has been used (1).
 eq 
In this formula


a 
 2R  
1 
  ln 1 

a   2R 

is the axial stress in the minimal cross-section ( 
is the von Mises equivalent stress,
Figure 2.
a
is the mimumal radius,
R
(1)
 F S ) axial stress in the minimal cross-section,  eq
is the curvature radius at the lowest point of necking conform
CENTRE FOR ENERGY RESEARCH
PROGRESS REPORT 2022
Figure 2: Notatioins used for Bridgman correction
For specimens with square cross section we used the Choung-Cho formula. The formula computes a corrective factor, based
 
on the exponent of the Ludwick formula    y  K   pl
n
. It can be written as:
 eq     pl , n    ,


where   pl , n is the correction factor computed using the equivalent plastic strain
(2)
 pl and the Ludwick exponent n . More
details are presented in [3].
For the square specimens it could be clearly observed, that the deformation of the specimen is different in different directions,
meaning that the material is anisotropic. Another important observation is that the curvature radiuses are different for
different contours.
DTs of the tensile tests represent Finite Element (FE) models using the MSC Marc-Mentat FE system. Axial symmetric models
were used for the cylindrical specimens, while for specimens with square cross-section we used 3D models. Von Mises
plasticity theory was used with multilinear strain-hardening plasticity. We considered homogeneous and isotropic material.
Large strain–large displacement kinematics was used in updated Lagrangian setting.
The Bridgman formula is quite adequate for cylindrical, the Choung-Cho formula for specimens with square cross-section.
However, mainly at the end of the process there are significant differences between measurements and simulations. Figure 3
presents measured Force-thickness reduction curves along with simulation using not corrected flowcurve as well as
simulation using corrected flowcurve.
Figure 3: Measured and simulated curves: (left) original flow curve, (right) Choung-Cho correction with n=0.145.
Remaining work
In the process of evaluation of measurements results indicating anisotropy of materials are averaged. and the FE models use
isotropic material properties. A possible direction of development would be taking into account of the anisotropy and material
damage.
Related publication
[1]
T. Fekete, D. Antók, L. Tatár, P. Bereczki, E. Kocsó: Evaluation Framework for Tensile Measurements, EK-CER progress
report 2021.
[2]
D. Antók, T. Fekete, L. Tatár, P. Bereczki: (2022) Evaluation Framework for Tensile Measurements, based on Full-Field
Deformation Measurements and Digital Twins, In: ICSI 2021 The 4th International Conference on Structural Integrity,
Structural Integrity Procedia 37 pp. 796–803. (2022)
[3]
D. Antók, T. Fekete., L. Tatár, P. Bereczki: Extending reliability of FEM simulations, based on optically assisted tensile tests
and digital twins, In: 23 European Conference on Fracture - ECF23, Structural Integrity Procedia XX pp. YYY–ZZZ.
(Submitted) (202X)