Utility of micro-indentation technique for characterization of the constitutive behavior of skin and interior microstructures of die-cast magnesium alloys

This paper introduction was written based on the 'Utility of micro-indentation technique for characterization of the constitutive behavior of skin and interior microstructures of die-cast magnesium alloys' published by 'Elsevier'.

1. Overview:

  • Title: Utility of micro-indentation technique for characterization of the constitutive behavior of skin and interior microstructures of die-cast magnesium alloys
  • Author: Zhaohui Shan, Arun M. Gokhale
  • Publication Year: 2003
  • Publishing Journal/Academic Society: Materials Science and Engineering A
  • Keywords: Micro-indentation; Magnesium alloys; Die-castings; Finite element analysis

2. Abstracts

There has been increasing thrust lately on the development of lightweight cast magnesium alloy components for structural automotive and other applications. The microstructure of the high-pressure die-cast Mg alloys usually contains a fine-grained "skin" having a microstructure significantly different from that of the bulk material. Characterization of the local constitutive behavior of the skin microstructure is of interest as it can affect the overall mechanical response of the component. However, the standard mechanical tests on the macro-specimens are not useful for characterization of the local stress-strain response of the skin microstructure. In this contribution, we present a novel methodology based on a combination of micro-indentation experiments and three-dimensional (3D) finite elements based simulations that permits computation of the local stress-strain (constitutive) behavior of the skin and the interior microstructures at the length scales of 100 µm in a cast high-pressure die-cast AM60 Mg-alloy. The methodology involves development of a numerical solution to the inverse problem. The computed constitutive equations are then utilized to simulate the effect of skin thickness on the overall global mechanical response of the alloy under uniaxial compression.

3. Research Background:

Background of the Research Topic:

The increasing demand for lightweight structural materials in the automotive industry has driven the development of cast magnesium alloys. High-pressure die-casting, a common process for manufacturing automotive Mg-alloy components, results in a "skin effect". This phenomenon is characterized by a fine-grained "skin" microstructure near the surface of the casting, which is significantly different from the coarser microstructure in the interior. This microstructural variation can lead to differences in mechanical behavior between the skin and interior regions.

Status of Existing Research:

Traditional macro-scale mechanical tests are inadequate for characterizing the local stress-strain response of the skin microstructure due to its small size. Nano-indentation techniques are useful for characterizing individual precipitates or particles at length scales of approximately 10 µm. However, they are not efficient for assessing the average constitutive behavior of multi-phase cast microstructures at length scales larger than 25 µm, where the dendrite cell size is in the order of 5–10 µm. Micro-indentation, with larger indent sizes around 100 µm, appears more suitable for characterizing the average constitutive behavior of such multi-phase microstructures.

Necessity of the Research:

For accurate Finite Element (FE) based modeling of the mechanical response of high-pressure die-cast Mg-alloy components, it is crucial to account for potential differences in the constitutive behavior between the skin and interior regions. Understanding the local stress-strain relationships in these distinct regions is essential for reliable computation of local stress distributions and for predicting the overall mechanical performance of die-cast components.

4. Research Purpose and Research Questions:

Research Purpose:

The primary objective of this research is to develop and validate a methodology using micro-indentation techniques combined with 3D FE simulations to characterize the average stress-strain behavior of both the skin and interior microstructures of high-pressure die-cast Mg alloys. This methodology aims to compute the constitutive equations for these regions and utilize them to simulate the effect of skin thickness on the overall mechanical response of the die-cast alloy.

Key Research:

  • To experimentally obtain load-depth curves from micro-indentation tests performed on the skin and interior regions of a high-pressure die-cast AM60 Mg-alloy.
  • To develop a numerical solution to the inverse problem using 3D FE simulations to compute the constitutive behavior of the skin and interior microstructures from the micro-indentation data.
  • To utilize the computed constitutive equations in FE simulations to analyze the effect of skin thickness on the global mechanical response of the alloy under uniaxial compression.

Research Hypotheses:

  • Micro-indentation technique, in conjunction with 3D FE simulations, can effectively characterize the distinct constitutive behaviors of the skin and interior microstructures in die-cast magnesium alloys.
  • The skin region and the interior region of die-cast magnesium alloys exhibit different constitutive behaviors due to their microstructural variations.
  • The thickness of the skin layer significantly influences the overall mechanical response of the die-cast magnesium alloy component.

5. Research Methodology

Research Design:

This research employs a combined experimental and numerical approach. Micro-indentation experiments were conducted to generate load-depth curves for the skin and interior regions of AM60 Mg-alloy. These experimental data were then used in conjunction with 3D FE simulations to solve an inverse problem, aiming to determine the constitutive stress-strain relationships for each region. Finally, these constitutive models were applied in further FE simulations to assess the impact of skin thickness on the alloy's overall mechanical behavior under compression.

Data Collection Method:

Micro-indentation tests were performed using a Vicker's hardness indenter on a commercial AM60 magnesium alloy plate, cast under high-pressure die-cast conditions. Load-depth curves were recorded during both loading and unloading cycles at multiple locations within the skin and interior regions. Six random indentations were made in each region to obtain average load-depth characteristics.

Analysis Method:

The analysis involved an inverse problem-solving approach using 3D FE simulations with ANSYS® 5.7 and ABAQUS® 6.3 software. An iterative process was used:

  1. An initial stress-strain curve was assumed for both skin and interior.
  2. 3D FE simulations of the micro-indentation process were performed.
  3. The simulated load-depth curves were compared with the experimental curves.
  4. The stress-strain curves were iteratively adjusted until a good agreement was achieved between simulated and experimental load-depth curves.
    The unloading part of the load-depth curve was used to calculate the reduced modulus ($E_r$) and subsequently Young's modulus ($E$) using equation (1):
$ \frac{1}{E_r} = \frac{1-\nu_m^2}{E_m} + \frac{1-\nu_i^2}{E_i} $
$ E_m = \frac{(1-\nu_m^2)E_i E_r}{E_i - (1-\nu_i^2)E_r} $

where $E_m, \nu_m$ and $E_i, \nu_i$ are Young's modulus and Poisson's ratio of the material and indenter, respectively, and $E_r$ is the reduced modulus.
The plastic properties were extracted by fitting a power-law hardening model (Eq. (4)):

$ \sigma = \sigma_y + K\epsilon_p^n $

Research Subjects and Scope:

The research focused on a commercial AM60 Mg-alloy plate produced by high-pressure die-casting. The study investigated the skin and interior regions of this alloy, characterizing their constitutive behavior at a microstructural length scale of approximately 100 µm using micro-indentation. The scope included determining the local mechanical properties and assessing the influence of skin thickness on the overall compressive mechanical response of the AM60 alloy.

6. Main Research Results:

Key Research Results:

  • Micro-indentation tests revealed that the load at the same indentation depth was higher in the skin region compared to the interior region, indicating a difference in mechanical properties.
  • 3D FE simulations, iteratively refined to match experimental load-depth curves, successfully determined distinct stress-strain curves for the skin and interior microstructures.
  • The skin region exhibited a higher yield stress and strain-hardening coefficient than the interior region.
  • FE simulations of uniaxial compression tests, incorporating the derived constitutive models for skin and interior, demonstrated that increasing skin thickness enhances the overall mechanical response of the AM60 alloy.

Analysis of presented data:

  • Figure 1: Micrographs showing the microstructure of the AM60 die-casting Mg-alloy, illustrating the skin and interior regions at different magnifications. The skin region exhibits a finer microstructure compared to the interior.
  • Figure 2: Micro-indentation markers on the AM60 Mg-alloy at different locations, showing the scale of indentations.
  • Figure 3: A typical load-displacement (depth) curve of the AM60 alloy in the micro-indentation test, demonstrating the loading and unloading behavior.
  • Figures 5 and 6: Loading parts of individual and average load-depth curves for the skin and interior regions, respectively, showing variations and average trends.
  • Figure 7: Comparison of average loading curves at the skin and interior regions, highlighting the higher load in the skin region at the same depth.
  • Figure 8: Contour plots of Von Mises stress from 3D FE simulations at 5 µm indentation depth for skin and interior regions, visualizing stress distribution.
  • Figure 9: Comparison of experimental and simulated load-depth curves for skin and interior regions, demonstrating good agreement and validation of the FE models.
  • Figure 10: Comparison of stress-strain curves for skin and interior regions derived from FE simulations, showing differences in constitutive behavior.
  • Figure 12: Comparison of computed overall mechanical response of Mg alloys for different skin thickness values, illustrating the effect of skin thickness on stress-strain behavior under compression.

Figure Name List:

Fig. 2. Micro-indentation markers on the AM60 Mg-alloy at different locations.
Fig. 2. Micro-indentation markers on the AM60 Mg-alloy at different locations.
Fig. 4. Boundary condition for the micro-indentation modeling.
Fig. 4. Boundary condition for the micro-indentation modeling.
Fig. 5. Loading parts of five individual: (a) load–depth curves and (b) the average load–depth curve at the skin region.
Fig. 5. Loading parts of five individual: (a) load–depth curves and (b) the average load–depth curve at the skin region.
Fig. 6. Loading parts of five individual: (a) load–depth curves and (b) the average load–depth curve at the interior region.
Fig. 6. Loading parts of five individual: (a) load–depth curves and (b) the average load–depth curve at the interior region.
Fig. 7. Comparison of the average loading curves at the skin and the interior region.
Fig. 7. Comparison of the average loading curves at the skin and the interior region.
Fig. 8. Contour plot of the Von Mises stress in the 3D FE-simulations: (a) at the skin and (b) the interior region at the indentation depth of 5 m.
Fig. 8. Contour plot of the Von Mises stress in the 3D FE-simulations: (a) at the skin and (b) the interior region at the indentation depth of 5 m.
Fig. 9. Comparison of experimental and simulated load–depth curves: (a) at the skin and (b) the interior region.
Fig. 9. Comparison of experimental and simulated load–depth curves: (a) at the skin and (b) the interior region.
Fig. 10. Comparison of stress–strain curves of the skin and the interior regions obtained from finite element simulation on the indentation curves: (a) whole curve, and (b) plastic deformation part.
Fig. 10. Comparison of stress–strain curves of the skin and the interior regions obtained from finite element simulation on the indentation curves: (a) whole curve, and (b) plastic deformation part.
Fig. 11. Geometrical model, loading and boundary condition, and the finite element mesh in the simulation of compression test of the Mg alloys
Fig. 11. Geometrical model, loading and boundary condition, and the finite element mesh in the simulation of compression test of the Mg alloys
Fig. 12. Comparison of the computed overall mechanical response of the Mg alloys for four different skin thickness values.
Fig. 12. Comparison of the computed overall mechanical response of the Mg alloys for four different skin thickness values.
  • Fig. 1. Microstructure of the AM60 die-casting Mg-alloy: (a) with low magnification picture shows the skin and the interior regions; a high magnification picture of (b) the interior region, and (c) the skin region.
  • Fig. 2. Micro-indentation markers on the AM60 Mg-alloy at different locations.
  • Fig. 3. Typical load-displacement (depth) curve of the AM60 alloy in the micro-indentation test.
  • Fig. 5. Loading parts of five individual: (a) load-depth curves and (b) the average load-depth curve at the skin region.
  • Fig. 6. Loading parts of five individual: (a) load-depth curves and (b) the average load-depth curve at the interior region.
  • Fig. 7. Comparison of the average loading curves at the skin and the interior region.
  • Fig. 8. Contour plot of the Von Mises stress in the 3D FE-simulations: (a) at the skin and (b) the interior region at the indentation depth of 5 µm.
  • Fig. 9. Comparison of experimental and simulated load-depth curves: (a) at the skin and (b) the interior region.
  • Fig. 10. Comparison of stress-strain curves of the skin and the interior regions obtained from finite element simulation on the indentation curves: (a) whole curve, and (b) plastic deformation part.
  • Fig. 11. Geometrical model, loading and boundary condition, and the finite element mesh in the simulation of compression test of the Mg alloys.
  • Fig. 12. Comparison of the computed overall mechanical response of the Mg alloys for four different skin thickness values.

7. Conclusion:

Summary of Key Findings:

This study successfully demonstrated the utility of combining micro-indentation and 3D FE simulations to characterize the constitutive behavior of the skin and interior microstructures in high-pressure die-cast AM60 Mg-alloy. The skin region was found to have a higher local yield stress and strain hardening coefficient compared to the interior. Furthermore, FE simulations revealed that increasing skin thickness improves the overall mechanical response of the die-cast alloy under compression.

Academic Significance of the Study:

The research provides a novel methodology for characterizing local mechanical properties in materials with microstructural gradients, particularly relevant to die-cast alloys exhibiting the "skin effect". This approach offers a valuable tool for virtual prototyping and for understanding the influence of processing-induced microstructural variations on component performance. The study highlights the importance of considering the distinct constitutive behaviors of different microstructural regions in FE modeling for accurate predictions.

Practical Implications:

The developed methodology can be applied to optimize die-casting processes and alloy compositions to achieve desired skin layer characteristics for enhanced mechanical performance. By understanding the relationship between skin thickness and overall mechanical response, engineers can design die-cast magnesium alloy components with improved structural integrity and performance, particularly for automotive and other weight-sensitive applications.

Limitations of the Study and Areas for Future Research:

The study focused on AM60 Mg-alloy and uniaxial compression. Further research could explore the applicability of this methodology to other die-cast magnesium alloys and under different loading conditions, such as fatigue and impact. Investigating the influence of various die-casting process parameters on the skin layer characteristics and their subsequent impact on mechanical behavior would also be a valuable extension of this work.

8. References:

  • [1] B.L. Mordike, T. Ebert, Mater. Sci. Eng. A 302 (2001) 37-45.
  • [2] F.H. Froes, D. Eliezer, E. Aghion, J. Metals 50 (9) (1998) 30-34.
  • [3] A. Luo, M.O. Pekguleryuz, J. Mater. Sci. 29 (20) (1994) 5259-5271.
  • [4] MTS Nanoindentor Manual.
  • [5] W.C. Oliver, G.M. Pharr, J. Mater. Res. 7 (1992) 1564-1583.
  • [6] A.E. Giannakopoulos, S. Suresh, Scripta Mater. 40 (1999) 1191-1198.
  • [7] W.D. Nix, Mater. Sci. Eng. A 237 (1997) 37-44.
  • [8] X. Li, B. Bhushan, Mater. Charact. 48 (2002) 11-36.
  • [9] D. Tabor, Philos. Mag. A 74 (1996) 1207-1221.
  • [10] G.M. Pharr, Mater. Sci. Eng. A 253 (1998) 151–159.
  • [11] P. Maier, A. Richter, R.G. Faulkner, R. Ries, Mater. Charact. 48 (2002) 329-339.
  • [12] B. Bhushan, Handbook of Micro/Nano-Tribology, second ed., CRC Press, Boca Raton, FL, 1999.
  • [13] M. Goeken, M. Kempf, W.D. Nix, Acta Mater. 49 (2001) 903-911.
  • [14] J. Mencik, D. Munz, E. Quandt, E.R. Weppelmann, J. Mater. Res. 12 (1997) 2475.
  • [15] J.Y. Rho, T.Y. Tsui, G.M. Pharr, Biomaterials 18 (1997) 1325-1330.
  • [16] E. Martínez, J. Esteve, Appl. Phys. A 72 (2001) 319-324.
  • [17] T. Chudoba, F. Richter, Surf. Coat. Technol. 148 (2001) 191–198.
  • [18] N. Huber, W.D. Nix, H. Gao, Proc. R. Soc. London (Ser. A) 458 (2002) 1593-1620.
  • [19] A.E. Giannakopoulos, S. Suresh, Scripta Mater. 40 (1999) 1191–1198.
  • [20] Y. Gu, T. Nakamura, L. Prchlik, S. Sampath, J. Wallace 345 (2003) 223-233.

9. Copyright:

  • This material is "Zhaohui Shan, Arun M. Gokhale"'s paper: Based on "Utility of micro-indentation technique for characterization of the constitutive behavior of skin and interior microstructures of die-cast magnesium alloys".
  • Paper Source: https://doi.org/10.1016/S0921-5093(03)00529-X

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