Rate-independent Elastic-Plastic Hardening Models for Monotonic Loading

Rate-independent elastic-plastic material behaviors are among the most commonly used constitutive models for metals in nonlinear simulations.

The most common physical test used to characterize the elastic-plastic response is a monotonic uniaxial tension test in which the tester loaded the test sample past necking to failure. This section describes the case where you want to calibrate an elastic-plastic material model using a single uniaxial test data set.

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The app offers a wide range of elastic-plastic material models intended for various loading scenarios. The Johnson-Cook and isotropic-tabular models are well suited for monotonic loading of metals past yield. The two most important numbers that define the initial yield behavior are the elastic modulus and the initial plastic yield stress.

Johnson-Cook Plasticity

Johnson-Cook plasticity uses an analytical hardening model with a small number of material parameters. For typical temperature ranges (those below two-thirds of the melting temperature on an absolute scale) the app requires only three parameters. This approach makes Johnson-Cook particularly well suited for calibration, and it is the default hardening model in the app.

Isotropic-tabular Model

The isotropic-tabular option is more general than Johnson-Cook and can capture a wider variety of yield behaviors. Instead of material parameters, a table of yield stress and plastic strain pairs characterizes the hardening response. The tabular values are the design variables available for calibration.

The isotropic-tabular model has one drawback for calibration. The number of design variables it uses can be large, and the sensitivity of each tabular value during calibration can be small. This combination can lead to convergence challenges. A best practice while calibrating a tabular hardening law is to limit the number of stress-strain pairs to ten or fewer and to designate only the strains or the stresses as design variables—not both.

Conversion Mode

When you select a tabular hardening law, the app enables a conversion mode by default to simplify the process of defining the material model. In conversion mode, the app applies an algorithm to get a “best fit” to the yield data without performing an actual calibration. While conversion mode is active, modifying the Young’s modulus, the initial yield, or the number of tabular points prompts the app to recalculate the other stress-strain pairs automatically to get a new best fit. With a few manual iterations on the modulus and the initial yield, you can often achieve a very good fit to the uniaxial test data without ever launching a calibration. If you do run a calibration, the quality of the initial fit provided by the conversion mode typically improves the overall convergence characteristics of the optimization algorithm.

If you disable the conversion mode, the app does not automatically recalculate the stress-strain pairs to get a new best fit when you modify the modulus or initial yield.

Imported Uniaxial Test Data

Imported uniaxial test data might require some additional edits. The app assumes that a homogenous deformation field exists within the test coupon. Once necking occurs, the homogenous assumption is no longer valid. If you import a uniaxial test data set that includes data past the Ultimate Tensile Strength (UTS), you should remove all the test data points past the UTS before running a calibration or using the conversion mode.