Modelling and simulation of the influence of forming processes on the structural behavior of high strength steels

J.C. Gelin, S. Thibaud, N. Boudeau

FEMTO-ST Institute – Applied Mechanics Laboratory ENSMM and CNRS, 24 Rue de l'Epitaphe, 25000 Besançon, France

jean-claude.gelin@ens2m.fr; sebastien.thibaud@ens2m.fr; nathalie.boudeau@ens2m.f

Abstract. The paper first describes experiments and modeling concerning the identification of material behavior for high strength steels with phase transformations associated to plastic deformation. The experiments consist of tensile and bulging tests carried out on 316L stainless steels and TRIP 700 steels used in automotive industry. These experiments have permitted to determine the hardening curves of such materials vs. the martensite volume fraction associated to plastic deformation. It has been demonstrated that the stress triaxiality has a major role in the martenstic transformation and a model is proposed to define the flow stress vs. effective strain accounting planar anisotropy and variation of martenstic volume fraction. Then a plasticity model has been proposed in an anisotropic form and the related flow rules have been defined. The resulting model has been implemented in different finite elements software, and applied in numerical simulations of stamping and hydroforming of typical components to prove the effects of forming processes on the resulting properties of the components. Finally, the structural behavior of the resulting components is investigated and the effects of forming processes on the resulting structural behaviour are analyzed. Two cases are presented, one concerns the deep drawing of a cylindrical cup and the other concerns the stamping of a closed U channel used as a structural part for crash frames. Is has been clearly proved that the variation of martensite volume fraction arising during processing has a strong influence on the resulting behaviour of the parts considering springback and crash resistance.

INTRODUCTION

Nowadays, automotive industry is confronted with two antagonist problems. In one hand, the competition between the different constructors is reliable. The automotive must assure the security of their occupants. This fact leads to design vehicle with passive and active security parts. The active parts permit to control and eventually to correct the conductor’s actions. The passive parts generally play a role in case of crash. All these security systems increase considerably the weight of the vehicles. In the other hand, the automotive industry must satisfy the Kyoto Protocol which is an international and legally binding agreement to reduce greenhouse gases emissions world wide. It is known that a reduction of 100 kg leads to a fuel saving of about 0.4 liter per 100 km. A way to reduce the cars weight is to use thinner sheet metal but then the functionality is not always insured. In order to solve these difficulties, the steel makers have developed new steels [1] that combine both high ductility and high strength among which the TRIP steels.

In the following, the TRIP steels and the physics of plasticity will be presented. In section 3, a model for

TRIP steels will be introduced as well as the identification methods. Section 4 will be devoted to the presentation of numerical results and will show the necessary of a model for TRIP steels. Section 5 will summarize and conclude the paper.

TRIP STEELS AND PHYSICAL ASPECTS

TRIP steels belong to the family of High Strength Steels. For plastic formability an important ductility is required. For crash a high structural strength is needed. Generally the ductility decreases when the strength increases. These two factors are then in contradiction. High Strength Steels, and particularly TRIP steels, combine these two requirements [2].

The increasing of the strength and the ductility is obtained by the activation of a martensite-type transformation phase under mechanical loading. TRIP steels present a microstructure composed of ferrite, bainite and retained austenite phases as shown in figure 1. Austenite (FCC structure) can transform itself, with a controlled annealing, in ferrite, bainite, martensite and retained austenite, all characterized by

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a BCC structure. In TRIP steels, only ferrite, bainite and retained austenite phases can be found.

FIGURE 1. Typical microstructure of TRIP steels

The state diagram of TRIP effect is described in

figure 2. Between MS and Mσ, the transformation is induced by an elastic mechanical loading and is called assisted transformation. Between Mσ and M f, the transformation is induced by a plastic deformation and is called transformation plasticity. Martensite germination and growing in the austenite phase is stimulated by the plastic deformation. Thus the TRIP effect is characterized by an additional plastic flow during hardening.

The material model for TRIP steels to be developed needs to describe the influence of the TRIP effect on the elastic properties and the hardening curve. It must also take into account the sheet metal anisotropy, the Bauschinger effect for precise springback predictions [3], the strain rate sensitivity for a large domain of variations (0.001 to 500 s-1) and the temperature (for crash simulation).

FIGURE 2. State diagram of TRIP effects

MODELLING AND IDENTIFICATION OF TRIP EFFECTS IN STEELS

In this section the basic equations for the modeling of TRIP effect are presented. The main differences between standard steels and ASS or TRIP ones are associated to the martensitic transformation phase resulting from mechanical and thermal loadings. So the main driving variables associated to the deformation resulting from processing such materials are the strain tensorε , the martensite volume fraction z

and the temperature T. To describe the initial anisotropic behaviour, the yield surface f is expressed as:

0:: =−−= RHf yσξξ (1)

with X−= σξ , yσ is the yield limit in tension and R is

associated to isotropic hardening and is done by a logarithmic strain sensitive form:

( ) ( ) ( )( ) ����

����

+�������

�+

������ += 1lnln0ε

εεεε νναγαγ �

�pnpnp bazKKR

(2)

where iK , in , νa , νb and 0ε� are material parameters. H

is the Hill operator which depends on the Lankford

coefficient r , pε� is the effective strain rate defined as

the Euclidian norm of the plastic strain tensor pε .

To described the influence of Bauschinger effect, the kinematic hardening evolution is described by the way of a non-linear model [3] as

XX pp εγεδ −= (3)

where δ and γ are material parameters.

Phase Transition Kinetic

The determination of phase transition is quite complex, but it has been expressed below, one search to express the phenomenological behaviour. The evolution of transition phase is dependent of stress state (the evolutions in biaxial state is faster than uniaxial and shear states), temperature T and the martensite volume fraction z. One scalar parameter can described the stress state, this factor is the so-called triaxiality parameter χ used in continuum damage mechanics as expressed by

σσχ h= (4)

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where σ is the equivalent stress and hσ is the

hydrostatic stress defined by :

σσ trh 3

1= (5)

The characteristics of transition exhibit a saturation phenomenon. One propose the following relation to described the kinetic of phase transition

( ) ( )( ) pnzbazzz εχ +−= ∞ (6)

where ∞≤≤ zz0 . The material parameter ∞z is the

saturation volume fraction, a , b and n are parameter which influence the evolution of phase transition and are temperature dependant. In the case of proportional loading, this equation is easily integrated

( ) ( ) ( ) �� ��−−+= −+−

∞a

pnbaezzzz εεχ100 (7)

0z is the initial volume fraction and aε is the

deformation of the transition activation.

Elastic Modulus Variation

The elastic properties of austenite and martensite are quite different. By using a vibrometric method, the variation of Young modulus with hardening has been obtained and an expression expressing the module vs. martensite volume fraction has been proposed [4]:

( ) ( ) ������−−+= −

∞qzeEEEzE β100 (8)

where 0E , ∞E , β and q are material parameters.

Identification Procedure and Results

In the proposed model, one can obtain up to 30 material parameters but there are no necessary measured from directly testing procedures. An inverse identification based on the combination of FEM simulations of experiments and optimization [5] has been used to perform identification.

In Table 1 are presented the best parameters which

permit to retrieve experimental results. The parameters are used to perform the subsequent FEM analyses. In this study, coefficients associated to kinematic hardening are not yet available. Figures 3 and 4 are respectively represented the evolution of equivalent stress and martensite volume fraction in comparison with Lani et al. results [6].

FIGURE 3 Experimental and modeling uniaxial tensile test on a TRIP 350/700 steel

FIGURE 4. Comparison between modeling and experimental results (Lani et al. [6])

NUMERICAL RESULTS

The model has been implemented in LS-DYNA®. In the following section, two numerical examples carried out with LS-DYNA® will be presented.

The first one is the deep-drawing of a cylindrical cup [7]. This example demonstrates first the non validity of the common approach generally adopted for TRIP steels. Secondly, springback predictions conducted

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with or without the TRIP steel model will be compared.

The second example corresponds to the nowadays preoccupation in automotive industry. The crash of a passive security part obtained from forming and then assembling will be presented. Again, the results obtained with and without the TRIP steel model will be compared.

Deep Drawing of a Cylindrical Cup

This forming process consists in drawing a 1mm thick sheet metal with a cylindrical punch associated to a cylindrical die with 90 mm high. The drawing ratio is 1.84 and the friction coefficient is supposed to be equal to 0.145.

The simulations have been carried out with LS-DYNA v970 parallel release (MPP).

Numerical Model

For the numerical simulations presented thereafter, the finite element model contains 25540 elements and 26042 nodes. Adaptive mesh is not used and the material behaviour is supposed to be initially isotropic. The chosen finite elements are shell elements with complete integration and 5 integration points in the thickness. Symmetry and mass scaling are not used due to the respect of the real processing conditions.

Material Modeling

Two simulations have been conducted. The first one (model n°1) corresponds to the way numerical simulations are carried out nowadays in the automotive industry. The hardening curve is simply fitted by a piecewise linear segments to fit the experimental curve. The second one (model n°2) has been carried out by using the TRIP steel model presented in section 3 with the material data listed in table 1.

(a)

(b)

FIGURE 5. Results on formability for the cylindrical cup: equivalent plastic strain with: (a) Piecewise linear curve fitting (b), Proposed model.

Results on Formability

The simulations carried out with model n°1 show a localization of deformation as the formability is insured with model n°2 in the case of a blank holder force equal to 240 kN [7] (figure 5).

If the blank holder load is reduced to 180kN, both

approaches indicate that the formability is assured. In [8], it has been shown that the part can be formed under these conditions. These results indicate that it is necessary to take into account the influence of the TRIP effect on hardening. The CPU time is reasonable: 9h17 for model n°2 against 8h05 for model n°1.

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Results on Springback

The springback test consists in cutting different rings along a generative line of the cylindrical cup resulting from the deep drawing stage. Then the rings are cut and the resulting openings between both sides are measured.

The springback test has been done with the two models and differences have been observed as it is shown in figure 6 and resumed in Table 2. Springback is more important in the case of model n°2 because the austenite to martensite transformation phase leads to a variation of the Young’s modulus. The Young’s modulus of the martensite is smaller than one of the austenite. These results are in agreement reported results comparing a High Strength Steel and a common one (DC04) as published in [7].

FIGURE 6. Influence of TRIP effect on springback, (Projection of the ring profiles onto the YZ plane).

Ring

(Height position)

10 mm

30 mm

50 mm

70 mm

Model 1 (mm)

105.96 91.67 76.38 70.39

Model 2 (mm)

115.75 96.06 76.56 69.62

TABLE 2. Springback prediction, comparison between Model 1 and Model 2

Crash test

This example consists in a crash test of a passive security part and is inspired from [8]. One study the

impact of a 850 kg mass with an initial velocity equal 54km/h. Two types of simulations have been done. First, the crash test has been carried out on the security part CAD model. No initial stress exists in the part. It s called model n°3.

Secondly, the crash test has been conducted on a security part obtained by the complete chain of simulations: forming, springback, assembly. The TRIP model has been used for the simulations, this is model n°4.

The comparison between models n°3 and 4 shows a difference in the deformed shape after crash (figure 7). Taking into account the forming effects (model n°4), a crushing can be observed first and then localization appears. A plastic kneecap appears after the embossed part that breaks the wave propagation. In model n°3, without forming effects, a crushing followed by a buckling is observed.

For energy absorption, the same observations can be done. Between 0 and 8 ms, the deformation is localized in the embosses. After, the behaviour is different. The results obtained with model n°4 are in agreement with experimental works [8] showing that the dynamic buckling doesn’ t appear.

(a)

(b) FIGURE 7. Deformed shape obtained after crash test: (a) model 3 and (b) model 4

CONCLUSIONS

In this paper, a phenomenological approach of induced plasticity is proposed. The effects of the phase transition on elastic-plastic properties is described and adapted to simulate the behaviour of stamped part and in-use properties. The model consists to account the

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TRIP effects both on the hardening curve of the material, as well as on the plasticity yield. The associated variation of the elastic moduli has also taken into account. Then the resulting model has been implemented in various FE codes. The results obtained from simulations clearly show the effects of hardening associated to phase transformations, both on springback after unloading, and on crash resistance associated to high speed impact.

REFERENCES

1. Jacques, P.J., Transformation – Induced Plasticity, Ph. D Thesis, Université Catholique de Louvain, 2002.

2. Tsuchida, N., Tomota, Y., A Micromechanic Modelling for Transformation Induced Plasticity in Steels, Mat. Sc. And Engineering, A285, 345-352, (2000).

3 Geng, L., Wagoner, R.H., Role of Plastic Anisotropy and its Evolution on Springback, Int. J. of Mechanical Sciences, 44,123-148 (2002).

4 Thibaud, S., Boudeau, N., Gelin, J.C., Influence of Initial and Induced Hardening in Sheet Metal Forming, Int. J. of Damage Mechanics 13, 107-122 ( 2002).

5 Gelin, J.C., Ghouati, O., The inverse approach for the determination of constitutive equations in metal forming, Annals of CIRP 44/1, 189-192 (1995).

6 Lani, F., Furnemont, Q., Jacques, P.J., Delannay, F., Pardoen, T., Modèle Micromécanique du Comportement Plastique des Matériaux Biphasés avec Transformation de Phase, Matériaux 2002,1-5

7 Rohleder, M., Brosius, A., Roll, K., Kleiner, M., Investigation of Springback in Sheet Metal Forming Using Two Different Testing Methods, Esaform 2001.

8 Krusper, A., 2003, Influences of the Forming Process on the Crash Performance. Master’s thesis, Chalmers University and Volvo Car Corporation.

9 Gelin, J.C., , Thibaud, S., Influence of initial and induced hardening on the formability in sheet metal forming, Int. J. Forming Processes, 2-3-4, 500-520 (2002).

a b n εa z∞ σy (MPa) Kγ � (MPa) nγ Kα �(MPa) nα

1,445 1,25 3,5 0,01 0,12 332 736,7 0,179 1092 0,24 E0 (GPa) E∞ (GPa) β q z0 ν aν bν 0ε� (s-1) r

202 165 129,3 1,68 0 0,3 1e-3 1,05e-2 6,6 1,05

Table 1. Material parameters for a TRIP350/700 steel (thickness : 1 mm)

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