Mechanical properties and micro-deformation of sintered metallic hollow sphere structure

https://doi.org/10.1016/j.commatsci.2013.03.010Get rights and content

Highlights

Abstract

This paper presents experimental and numerical analysis of sintered metallic hollow sphere structure (SMHSS). For the first time, finite element analysis is based directly on the complex material meso-structure captured by micro-computed tomography scanning. In parallel, experimental tests are performed on cylindrical specimens of two different sample sizes in order to test for size effects. A total of 14 samples are subjected to uni-axial compressive loading in order to measure Young’s modulus, the R70 hysteresis stiffness and the 0.2% offset yield strength. Micro-computed tomography data of two of the tested samples is used for advanced numerical analysis. Numerical findings are compared to experimental data for verification and are used to test for material anisotropy. In addition, finite element analysis is applied to study the micro-deformation inside the sintered metallic hollow sphere structure SMHSS.

Introduction

This paper addresses the mechanical properties of sintered metallic hollow sphere structure (SMHSS). This material belongs to the group of cellular metals, a relatively new material class that stands out because of its multifunctional properties. Cellular metals combine high specific strength [1], controlled energy absorption [1], [2], adjustable thermal properties [3], [4], mechanical and acoustic damping [5], [6] with large surface area [7]. Based on these properties, cellular metals have great potential for a wide range of application for example in lightweight engineering, crash absorbers, heat exchangers or catalysts [8]. However, application of these promising materials is limited by the scatter of material parameters caused predominantly by small changes within the complex material meso-structure [9], [10], [11]. The inconsistent material properties must be considered in engineering design and this vastly decreases the efficiency of cellular metals. The problem can be overcome by increasing the control of material meso-structure thus decreasing the scatter of material properties.

A successful approach has proven to be in the use of hollow spheres as building elements that are joined to form interconnected cellular structures (see Fig. 1a). Interconnected hollow sphere structures are created using different joining techniques such as adhesive bonding, soldering and sintering [12]. An advantage of adhesive bonding is the use of a second phase that allows the scaling of mechanical [13] or thermal [14] properties. However, the interface between adhesive and metallic sphere surface has been shown to delaminate at relatively low stress levels decreasing the strength of the material [15]. In sintered structures, the focus of the current research, spherical green bodies are pre-compacted and sintered as bulk material. As a result, weak interfaces can be avoided, potentially increasing the strength of the material.

The mechanical properties of 405 stainless steel HSS with a sphere diameter of 2 mm were addressed in [16]. Quasi-static compressive testing of single hollow spheres and sintered structures was performed. A minimum size of 10 spheres per edge was identified as a representative volume, i.e. no change in mechanical properties was found for larger samples. Sintered sphere structures exhibit both interconnected and closed porosity. Comparison with other metallic foams showed that the mechanical properties of SMHSS follow more closely open-cell relations for Young’s modulus and strength. In [17] uni-axial compressive testing on 316L stainless steel HSS was conducted. Two sphere diameters 1.7 mm and 2.6 mm were considered and cylindrical samples of different size were tested. In good agreement with the previous study, 7 spheres across the cylinder diameter were found sufficient to form a representative volume. Experimental stress strain data were used to develop power-law relations for plateau stress, unloading modulus and energy absorption. In addition, micro-computed tomography scans of the samples at different stages of compression allowed the visualisation of sphere deformation inside the sample. This work was continued in [18] for uni-axial tensile loading of the 2.6 mm sintered sphere structures. Depending on the shell thickness, failure occurred due to shell-tearing (thin shells) or neck failure (thick shells) at elevated stresses. Veyhl et al. [19] conducted uni-axial compressive tests on SMHSS with diameters 1.6 mm and 2.6 mm. A notable effect of the sample geometry (i.e. cube and cylinder) was found within the linear-elastic range. Tasdemirci et al. [20] performed compressive split Hopkinson tests of 316L stainless steel HSS with a mean sphere diameter of 2 mm. Experimental testing was performed up to strain rates 600 s−1. Stress levels were found to increase with higher strain rates, predominantly due to the strain rate sensitivity of the cell wall material. Additional numerical analysis was performed on a simplified model structure presuming a primitive cubic arrangement of spheres. The deformation behaviour found in the experimental analysis, i.e. the formation of plastic hinges, indentation of spheres and sphere wall buckling was replicated in the numerical analysis. An independent numerical study [21] found similar deformation behaviour for adhesively bonded MHSS. A major advantage of numerical analysis of SMHSS is in providing a tool to investigate stress concentrations and deformation within the complex meso-structure formed by hollow sphere shells and sintering bonds. Simplified models of MHSS often use cubic arrangement in combination with symmetry boundary conditions [13], [22], [23], [24]. As a result, only a relatively small section of the geometry needs to be modelled in order to simulate an infinite structure and calculate effective material properties. However, the simplification of geometry eliminates effects found in real materials such as local variation of mechanical properties, anisotropy or the initial collapse of damaged spheres, etc. A relatively new approach is the use of micro-computed tomography scans of cellular metal to generate finite element calculation models [25], [26]. In contrast to simplified models, the complex and random meso-structure is accurately represented in the resulting calculation model. In [27] computed tomography data was used to identify centre coordinates of hollow sphere and use this information to generate a simplified calculation model for vibration analysis. This approach was further refined in [28] where the complex SMHSS geometry obtained by computed tomography scanning was approximated using shell elements.

The present paper bases finite element calculation models directly on micro-computed tomography data. Three-dimensional volume meshes corresponding to the CT data are generated in order to create highly accurate representation of the complex geometry of real samples. The investigated low carbon steel MHSS contain spheres with a mean outer diameter of 3.6 mm and wall thickness 110 μm. Experimental analysis is performed in accordance with DIN 50134. Furthermore, micro-computed tomography scans of SMHSS are used to generate geometrically accurate calculation models. The numerical simulation in conjunction with micro-computed tomography analysis allows the calculation of stress and strain distribution inside of the actual sample with high geometric precision. Numerical results and experimental findings obtained using exactly the same sample are compared. A second calculation model is used to test for material anisotropy and to analyse the deformation mechanisms in MHSS.

Section snippets

Metallic hollow sphere structure

In the compass of this study, sintered steel (99.6% iron and 0.4% carbon) HSS were investigated. A picture of an actual cylindrical 30 mm sample is shown in Fig. 1 prior (a) and after (b) compressive testing. The mean outer sphere diameter of spheres is 3.6 mm (±0.1 mm) and the mean sphere wall thickness is 110 μm. The mean porosity of the HSS samples is 86.7% and their average density is 1.04 g/cm3. The manufacturing process of MHSS is described in detail in [12]. In short, a polystyrene core is

Experimental analysis

Uni-axial compressive tests were executed according to the DIN 50134 standard for compression test of metallic cellular materials. All experimental tests were conducted on a Zwick Z100 testing machine. To this end, MHSS samples were located between two hardened steel pressure stamps lubricated with graphite powder in order to minimise friction effects. The force F was measured using a 100 kN XForce load cell attached to the upper pressure stamp and displacement u was obtained using a strain

Numerical analysis

Finite element analysis of two samples was conducted in order to investigate material anisotropy and study stress and strain distribution inside the material meso-structure. To this end, micro-computed tomography data was obtained prior to experimental testing. One cylindrical 1 mm and 30 mm sample each were scanned with computed tomography reconstructions of these samples shown in Fig. 2. The 3D image acquisition of the hollow structures were carried out using the CT system v|tome|x s of the

Results

Fig. 3 shows the stress–strain diagrams obtained by experimental testing. The macroscopic deformation behaviour is shown in Fig. 3a. The typical stress plateau for cellular metals is visible followed by onset of densification at high strains ε > 0.5. At large strains, the comparison between small (15 mm) and large (30 mm) cylinders reveals no systematic deviation. In order to obtain the plateau stress R, a sample of each size (15 mm and 30 mm cylinders) were compressed prior to the main tests. The

Conclusions

This paper presented experimental and numerical analysis of metallic hollow sphere structure (MHSS). The sintered steel spheres have a chemical composition of 99.6% iron and 0.4% carbon, a mean outer diameter of 3.6 mm and a mean wall thickness of 110 μm. The porosity of the MHSS is 86.7% and its average density is 1.04 g/cm3. Results of uni-axial compressive testing indicate a Young’s modulus E = 920–1180 MPa, Poisson’s ratio ν = 0.2, hysteresis modulus m = 1160–1400 MPa, specific energy absorption EV = 

References (34)

  • A.G. Evans et al.

    Curr. Opin. Solid State M

    (1998)
  • S. Tanaka et al.

    Measurement

    (2011)
  • T.J. Lu et al.

    Acta Mater.

    (1998)
  • T. Fiedler et al.

    Comp. Mater. Sci.

    (2010)
  • Z. Xie et al.

    Mater. Sci. Eng. A

    (2006)
  • J. Banhart

    Prog. Mater. Sci.

    (2001)
  • S. Hyun et al.

    Comp. Mater. Sci.

    (2009)
  • U. Ramamurty et al.

    Acta Mater.

    (2004)
  • C. Augustin et al.

    Mater. Lett.

    (2009)
  • T. Fiedler et al.

    Scripta Mater.

    (2008)
  • T. Fiedler et al.

    Mater. Lett.

    (2008)
  • T.J. Lim et al.

    Acta Mater.

    (2002)
  • P. Lhuissier et al.

    Mater. Lett.

    (2009)
  • P. Lhuissier et al.

    Scripta Mater.

    (2010)
  • A. Tasdemirci et al.

    Int. J. Impact Eng.

    (2010)
  • W.S. Sanders et al.

    Mater. Sci. Eng. A

    (2003)
  • W.S. Sanders et al.

    Mater. Sci. Eng. A

    (2003)
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