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Metallic Materials

A Hosford-Based Orthotropic Plasticity Model in LS-DYNA

n this contribution, we present a new orthotropic plasticity model available in LS-DYNA. Over the last decades, several orthotropic material models have been proposed in the literature where many of them have been implemented in LS-DYNA. Among these models, the model proposed by Barlat and Lian in 1989 [1], available in LS-DYNA in *MAT_036 [2], is a popular choice, especially in forming simulations. This model allows the user to define up to three R values (Lankford parameters) related to three material directions, namely 0°, 45° and 90° with respect to the rolling direction. Some years ago, the original orthotropic formulation by Barlat and Lian, available under *MAT_036 in LS-DYNA, was extended in such manner that the yield stress can depend on the different material directions. From a user point of view, this meant that up to five flow curves could be defined. Furthermore, up to five R values could also be used where these could be either constant or a function of the plastic strain. In *MAT_036, the extended model is activated by setting the flag HR to 7. However, the extended formulation incorporates the orthotropy in the yield stress as well. The consequence is that these two effects (orthotropy in the effective stress and also in the yield stress) concur against each other. For many materials, especially mild sheet steels, this aspect has often no major influence on the results. However, certain materials do exhibit quite dissimilar R values in the different material directions meanwhile the yield strength is very similar. This is, for instance, the case of many aluminum alloys. In such cases, the extended formulation available through HR=7 in *MAT_036 (or HOSF=0 in *MAT_036E) might lead to concave yield surfaces which, in turn, might lead to numerical instabilities. Therefore, a new option, issued through the flag HOSF, has been implemented in LS-DYNA in *MAT_036E. If HOSF is set to 1, a “Hosford-based” effective stress is used in yield function. This modification tends to alleviate the numerical instabilities observed in the model where the “Barlat-based” effective stress was used whenever the R values were very dissimilar. In a certain sense, the modification can be seen as a new plasticity model because in the new formulation the yield condition is not formulated using any information related to the R values but merely from the flow curves in the different directions. The R values are instead only used in the plastic flow rule. In this paper, we will show the advantages of such formulation as well as the results of the calibration of the material parameters for an aluminum sheet material. The results show that the simulation with the new material model can reproduce the strain fields captured in experiments through DIC very accurately.

Modelling of Thermo-Viscoplastic Material Behavior Coupled with Nonlocal Ductile Damage

The postcritical behaviour due to mechanical loading of the high strength steel HX340LAD (ZStE340), typically used for cold forming of complex structures is modelled by means of a yield curve in the softening part of the material. Due to local heating, caused by viscoplastic deformations particularly for high strain rates, a thermo-mechanical coupled simulation is carried out by taking into account the conversion of plastic work into heat. Moreover, a temperature and rate dependent material model, coupled with ductile damage, is applied to allow the prediction of damage and failure of metal components caused by large plastic deformations during forging or sheet metal forming. The constitutive equations are implemented as a user defined material model into LS-DYNA and include the temperature dependency of the material parameters such as for the YOUNG's modulus, the initial yield stress, the nonlinear isotropic hardening parameter, the strain rate sensitivity as well as for the moduli of a continuum damage mechanics based approach. The nonlocal damage option *MAT_NONLOCAL in LS-DYNA is used to prevent localisation of the damaged zone for small elements. Test data of tensile specimens are considered under different strain rates from 0.006 1/s (quasistatic) up to 100 1/s for identifying the model parameters with the optimisation software LS-OPT. Finally, the numerically predicted stress-strain curves are compared to the according test data for the model verification. In addition, the computed heat evolution due to plastic flow is compared to the experimental measured data in terms of time-temperature courses. Finally, the plastic necking of the tensile specimen is investigated by means of the spatial strain distribution.

High-Strength Alloyed Steel: Modelling Dynamic and Multiaxial Loading Conditions

This work reports on the modelling of failure behaviour in case of a high strength alloyed steel, experimentally subjected to a range of strain rates and states of stress triaxiality. This material combines high strength with exceptionally high ductility, which makes it difficult to describe material behaviour based on well-known constitutive models such as Johnson-Cook [1] [2]. To solve this challenge, extensive experimental investigations were performed to record stress-strain relations and, in particular, failure behaviour. Different states of triaxiality were attained based on the specimen geometry. Experiments with flat, unnotched and notched specimens yielded triaxial stress-states under uniaxial loading conditions. Stress-states due to shear stress and combinations of shear and tensile stresses were studied with biaxial tensile specimens. The triaxiality of the uniaxial tensile specimens was calculated based on the approximation suggested by Bridgman [3]. Based on the detected data, the material models suggested by Johnson-Cook [1] [2] was parameterized. Parameterization was carried out with the software LS-OPT [5]. The parameters of the constitutive models were found in an optimization procedure which minimized the difference between simulation prediction and experimental results. The discretization and element size was varied in order to study discretization effects. Smaller element sizes enabled a more constant triaxiality over the duration of the simulation. The parameter space of the Johnson-Cook model allowed for a satisfactory agreement in case of uniaxial experiments with a value of the stress triaxiality ≥ 1/3. However, the more complex problem of accurately modelling failure at other values of stress triaxiality between 0 (pure shear) and 1/3 (uniaxial tension) could not be solved. We discuss possible reasons for the apparent inability of the Johnson-Cook failure model to describe the effects induced by triaxiality at large failure strains and under shear stresses.

Influence of Strain Rate on Deformation and Failure Behavior of Sheet Metals under Shear Loading

In order to improve the reliability of deformation and failure prediction of automotive lightweight con-structions in real crash situations, appropriate input data for crash simulations are necessary which re-present the material behavior under high strain rates and complex multiaxial loading situations. Espe-cially under shear dominated loading failure is difficult to reach and there is still a lack of information concerning the strain rate dependency under these loading conditions. Therefore an experimental pro-cedure for strain rate dependent shear tension tests on sheet metals was developed which bases on asymmetrical notched shear tensile specimen geometries without surface processing. The specimen design of the shear zone was optimized by varying the shear length dependent on the sheet thickness and the notch position dependent on material data of uniaxial tension tests. For different advanced high strength steels (AHSS) numerical and experimental investigations were performed regarding the evolution of load paths in the shear zone and near the notch region as well as the failure location. Based on these experimental results and related numerical simulations recommendations are derived for an optimized design of asymmetrical notched shear tensile specimens. These recommendations are dependent on the sheet thickness and on material properties. The experiments should be carried out comparable to strain rate dependent flat tension tests with an appropriate mounting. The sugges-ted specimen design procedure is validated by experiments on steels in a wide range of strength as well as on exemplary batches of aluminum and copper. The shear characterization for AHSS results in large strain values in the shear zone up to failure under quasi-static loading with a significant negative strain rate effect. These experimental results of improved strain rate dependent shear characterization can be used for enhanced failure prediction in the future.

MAT_291: A New Micromechanics-Inspired Model for Shape Memory Alloys

This paper presents a new micromechanics-inspired constitutive model for shape memory alloys (SMAs) based on [1]. Shape memory alloys, e.g. Nitinol (Nickel-Titanium alloy), are widely utilized in the medical device industry because of their superelasticity. Superelastic properties of Nitinol enable its use in self-expanding stents and heart valve frames that can be inserted through a vein or artery using a thin delivery device and expanded at the target location. Motivated by the increased use of SMAs in the medical device industry, *MAT_291 (*MAT_SHAPE_MEMORY_ALLOY) is a first step towards more accurate and reliable material modeling. This material is currently available for solid elements and for explicit and implicit analysis. SMAs consist of two solid crystallographic phases, austenite (a high symmetry crystal structure, stable at high temperatures) and martensite (a low symmetry crystal structure that can be twinned or de-twinned, stable at low temperatures). Reversible transformation between the different phases gives rise to the shape-memory effect and superelasticity. The former implies that seemingly permanent deformation in the martensite phase can be recovered upon transformation to austenite by heating. The latter implies the material can undergo large strains in tension which can be recovered upon unloading. However, the superelastic stress-strain cycle will show elastic hysteresis similar to rubber-like materials, resulting from the transformation between twinned martensite, detwinned martensite, and austenite, see Figure 1.