Manufacturing Process Simulation Team
Simulation of Vickers Micro- Indentation Tests on DualPhase Steel utilizing VCAD-based Software N. Esmaeili* , J.L. Alves**, C. Teodosiu* *
Manufacturing Process Simulation Team, VCAD System Research Program **
Department of Mechanical Engineering, University of Minho, Portugal
[email protected],
[email protected],
[email protected]
Abstract VCAD-based software is used to simulate the Vickers micro-hardness test on dual-phase steels as a method to indirectly determine the mechanical properties of their constituents. In this context, VCAD offers an excellent environment for model creation, mesh generation and contact analysis. The VCAD software allows studying the mesh-size dependency, different element types and their effects, the influence of martensite volume fraction, orientation and distribution, as well as mutual effect of soft and hard phases. 1. Introduction In recent years, advanced high strength and more complex multiphase (MP) steels are increasingly been used in the automobile industry. Most recently, dual-phase (DP) steels have been recognized as a favorable material for outer body panel application, due to their inherent formability [1]. DP steel features a soft ferrite matrix containing islands of harder martensite as the secondary phase (Fig.1a). Different mechanical properties for ferrite and martensite phases in DP steels have been reported by various researchers [2]. Clearly, the macroscopic behavior of DP steels depends on the properties of both phases. Therefore, to test the mechanical property of each single phase is of significant importance for understanding and controlling the mechanical behavior of the bulk multiphase material.
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Fig. 1, a: DP steel, b: Experimental values of Vickers hardness tests [From NSC]
Micro-indentation hardness tests are valuable tools to provide the straightforward solution for quantitatively characterizing each of these phases [3]. On the other hand, numerical simulation of these tests can produce the hardness information of the material, too. Meanwhile, the simulation can also facilitate studying the influence of the size, shape and spatial distribution of the martensite particles, which is supposed to be the cause of scattering data in the martensite hardness case of Fig.1b.
2.
The Vickers hardness test
As a method to measure the hardness of the materials, the basic principle of Vickers hardness test is to observe the material's ability to resist plastic deformation from a standard source. The method consists of indenting the test material with a diamond indenter, in the form of a right pyramid with a square base and an
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angle of 136 degrees between opposite faces, subjected to a load of 10 to 1000 N, as shown in Fig. 2. The unit of hardness given by the test is known as the Vickers Pyramid Number (HV): HV = Constant x test force / indent diagonal squared
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Fig. 2, a: Schematic of Vickers hardness test, b: Pyramid indenter (partially meshed) and an indentation left in ferrite
It is worth noting that this hardness number is not really a true property of the material, but merely an empirical value that should be seen in conjunction with the experimental methods and hardness scale used.
2.
Finite element simulation model
Taking into consideration the real microstructure of DP steels, a simplified model has been created, which consists of an individual ellipsoid-like martensite island surrounded by ferrite matrix. As illustrated by Fig. 3a, due to the symmetry of the model, it is sufficient to simulate a quarter of it. Next, a multi-material linear/quadratic tetrahedral mesh is generated using the mesh generation software developed within the VCAD System Research Program. Finally, the mesh is simplified until a target number of tetrahedral is reached, under constraints related to mesh quality criteria [4] and while preserving specified materials or regions [5]. This later feature is quite essential for this study, since very fine mesh is required in the contact or indentation area, while the rest of domain can be discretized by a coarser mesh. In the parallelepipedic FE model shown in Fig.3a, the normal displacement is constrained on all sides except the top one. Then, employing V-Stamp, which is a VCAD-based software dedicated for press forming analysis, the contact between this model and pyramidshaped indenter/ tool can be simulated.
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b Fig.3, a: FE model, b: Tetrahedral mesh after simplification
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4. Results and discussion The simulations have been performed for homogeneous domains consisting of only martensite or ferrite, as well as for DP heterogeneous domains. For the DP case, different martensite depths inside the ferrite matrix have been investigated. These results were obtained with the constitutive parameters defined from the experiments of Fig. 1. For both single phases and heterogeneous DP domain, the indentation force versus indentation depth is depicted in Fig. 4a. The figure also contains the Hv values for all domains, where, reasonable agreement with the experimental results can be seen. In particular, the results for ferrite were very close to the experiment. However, the constitutive behaviour of martensite remained hypothetical. Also, it was found that the friction coefficient between the indenter and the tested material plays a negligible role in the hardening identification. An adequate simulation of the Vickers test requires a more detailed investigation of mesh-size dependency, different element types and their effects, the influence of matrensite volume fraction, orientation and distribution, as well consideration of neighbouring inclusion and its effect. Furthermore, the complete exploitation of the loading-unloading curves could provide additional elements for a semi-inverse determination of the mechanical properties of the constituents of dual- and multi-phase steels.
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Fig.4, a: Indentation force Vs indentation depth, b: Indented model and diagonal (d) place
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References
[1] Sun X, KS Choi, WN Liu, and MA Khaleel; 2009; “Predicting Failure Modes and Ductility of Dual Phase Steels Using Plastic Strain Localization” ; Int. J. Plasticity; 25(10):1888-1909. [2] Sakaki, T., Ohnuma, K., Sugimoto, K., Ohtakara, Y.; 1990; “Plastic Anisotropy of Dual-Phase Steels”; Int. J. Plasticity, 6 (5), 591–613. [3] Vander V. George F., Lucas Gabriel M; 1998; “Microindentation hardness testing”; Adv. Mat. & Proc.; 21-25. [4] Ohtake Y., Kawaharada H.; 2007; “Tetrahedral Mesh Generation of Multi-material Solids from 3D Segmented Images”; Proc. of 2007 JSPE Autumn Meeting, 323. [5] Moriguchi M.; 2010; “Tetrahedral Meshing with Size Control for Physical Simulation”; VCAD- 2010Symposium, these proceedings.
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