# Material model for TRIP-steels

## Overview

In materials with TRIP-effect (TRIP - TRansformation Induced Plasticity), a phase transformation from austenite to martensite occurs during forming that significantly affects the hardening behavior. The effect is sensitive to the amount of straining as well as the temperature. The hardening is more severe at low temperatures, e.g. 0C, than at high temperatures, e.g. 100C.

The material model has been implemented in LS-DYNA 971 as *MAT_TRIP.

## Forming

Applications of the material model include forming operations such as deep drawing, stretching, and hydroforming.

The modeling approach can be outlined as follows for a stamping operation. A standard element for stamping such as the Belytschko-Tsay shell element is used both for tools and blank. The tools are rigid. In short the modeling can be done following standard practice for stamping simulation with the following exceptions:

- Thermo-mechanical solution.
- Thermal contacts allowing heat transfer between tools and blank.
- TRIP material model.

Preferable thick thermal elements THSELL=1 on CONTROL_SHELL are used for the tools.

The thermal solver in LS-DYNA is implicit and a much larger, e.g. 100 times, time-step can often be used in the thermal solver than in the mechanical part of the simulation. In combination with the efficient iterative thermal solver this means that the run time is often only slightly increased compared to a standard forming simulation.

## Forming effects in crash

The material model can also be used for crash simulations where forming effects are taken into account. In a crash simulation the TRIP material model does not need to be run with the thermal solver activated, instead the temperatures are calculated using an adiabatic temperature calculation approach.

## Theory

The *MAT_TRIP material model uses the von Mises yield surface in combination with isotropic hardening and is taken from Hänsel et al. [1]. The hardening is temperature dependent and therefore this material model must be run either in a coupled thermo-mechanical solution, using prescribed temperatures or using the adiabatic temperature calculation option. Setting the parameter CP to the specific heat Cp of the material activates the adiabatic temperature calculation that calculates the temperature rate from the equation

where the nominator is the plastically dissipated heat. Using the Kelvin scale is recommended, even though other scales may be used without problems.

The hardening behavior is described by the following equations. The Martensite rate equation is

where

- = effective plastic strain and
- T = temperature.

The martensite fraction is integrated from the above rate equation:

It always holds that 0.0< <1.0. The initial martensite content is and must be greater than zero and less than 1.0. Note that is not used during a restart or when initializing the history variable using *INITIAL_STRESS_SHELL.

The yield stress is

The parameters p and B should fulfill the following condition

(1+B)/B

if not fulfilled then the martensite rate will approach infinity as approaches zero. Setting the parameter larger than zero, typical range 0.001-0.02 is recommended.

## Identifying material parameters

Material parameters can for austenitic stainless steels be determined using the following procedure. The methodology worked out by Hänsel et al. can be used [1]. It is comprised by tensile testing of standard tensile test specimens at a constant strain rate to a preset strain level and then unloading. The temperature and martensite content are recorded during the whole tensile test, including unloading. The martensite content is recorded with a ferritoscope mounted on the specimen and the temperature is measured using e.g. a thermocouple fixed to the tensile sample.

A number of tension tests must be performed with varying strain rate and starting temperature. Different histories of temperature, martensite volume fraction, and true stress as a function of plastic strain are obtained from these tests. The material parameters in the material model are identified through a least squares fit of the true stresses predicted by the material model to the true stresses measured in the tension tests.

## Example material parameters

Material parameters from Schedin et al. [2] are given in the two tables below for austenitic stainless steel HyTensX, Outokumpu Stainless, with a very pronounced TRIP-effect. The parameters were obtained using the approach described above.

**References**

[1] C. Hänsel, P. Hora, and J. Reissner, "Model for the kinetics of strain-induced martensitic phase transformation at isothermal conditions for the simulation of sheet metal forming processes with metastable austenitic steels," Simulation of Materials Processing: Theory, Methods, and Applications, Huétink and Baaijens (eds), Balkema, Rotterdam, (1998).

[2] E. Schedin, L. Prentzas, and D. Hilding, "Finite Element Simulation of the TRIP-effect in Austenitic Stainless Steel," presented at SAE 2004, SAE Technical paper 2004-01-0885, (2004).

Author: dh