Development of a “Universal Material Law” for the Hardening Parameters in Cyclic Plasticity

Project Description

The investigation of the low cycle fatigue behavior of engineering structures requires the determination of material parameters in the elastic-plastic range, particularly also concerning hardening. Strain-controlled tests are performed to obtain hysteresis curves for any ductile materials and to determine their high amplitude cyclic loading behaviors. These measurements are used to calibrate combined hardening parameters for further simulations in FE models and practical engineering applications of the material subjected to high amplitude cyclic loading.

However, the appropriate strain-controlled cyclic tests and measurements are expensive, complex, difficult, and time-consuming processes when especially very accurate measurements are required. Moreover, the critical data for the material properties may not be available in the early stage of any design. Furthermore, the definition of the suitable material model and calibration of the material parameters to evaluate their effect on the material behaviors is a big challenge. Hence, engineers require practical approaches to decrease expenses and shorten product development time.

The researcher may only have some material constants (e.g., Ramberg-Osgood constants for monotonic and stabilized cyclic stress-strain curves) but not any detailed hysteresis curves. Additionally, evaluation and determination of the material properties are very difficult in particular cases, especially non-ideal and imperfect test results are achieved. Hence, engineers require very practical and efficient tools to generate material properties (particularly combined hardening parameters), especially in case of the absence of the hysteresis curve test results.

Main Goals

In the project, a practical and compact model and methodology are developed to estimate nonlinear isotropic and kinematic hardening parameters to use in the case of the absence of the hysteresis curve test data. The model is suitable to use by industrial partners to obtain very fast and practical but also reasonable results. The model provides a relation between Ramberg-Osgood constants for monotonic & stabilized cyclic stress-strain curves and isotropic & kinematic hardening parameters. It is able to generate the hardening parameters without any test data of the hysteresis curve. Moreover, the overall methodology is faster than the optimization models, which would require very long preparation and computation time.

The Model

A practical and compact model is presented to estimate nonlinear hardening parameters for the case of the absence of experimental hysteresis curve data. The model requires only Ramberg-Osgood constants (as inputs) to obtain kinematic and isotropic hardening parameters. Hence, with this model, the cyclic plasticity behavior of the ductile material can be represented with a good agreement by using only six hardening parameters, including two isotropic and four kinematic hardening parameters, which is the case in which the fewest number of parameters has been employed according to the literature review. This “non-experiment-based characterization” process is extremely faster than other material characterization (optimization) methods. The algorithm of the model is given in figure 1.

Flowchart from INPUT to OUTPUT

Figure 1: The algorithm of the model


The model is applied to six different materials. The simulation results are very accurate as observed in the comparison of the results with the experimental cyclic test results. A sample comparison between test and FE simulation results for the hysteresis curve is presented in figure 2.

Two graphics of a test simulation with red and black envelopes

Figure 2: The use of static and cyclic curves (on left) as inputs to obtain reasonable hysteresis curve in FE simulation when compared to the experiment results (right)

Cooperation Partner


  • December 2020 - April 2022


Privatdoz. Dr. Eray Arslan

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