Experimental and numerical characterisation of in-plane deformation in two-phase materials

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Abstract

The aim of the present work consists in the comparison of in-plane strain fields with out-of-plane displacements in micro-areas of an Ag/Ni-composite after a macroscopic compressive deformation of 8.6%. The in-plane deformations in an Ag/Ni-composite have been analysed experimentally with a high resolution object grating technique and numerically using the finite element method. The out-of-plane displacements were measured with an atomic force microscope (AFM). The development of local strain fields in micro-areas at the surface of an Ag/Ni-composite was simulated numerically using the FE-method in plane strain condition. A real cut-out of the microstructure served as input for the calculation. The out-of-plane displacements determined by AFM measurements were used further to correct the in-plane values of strains evaluated by the object grating technique. The roughness on the surface of the sample was characterised by fractal dimensions and compared with the in-plane strains in the same micro-region.

Introduction

Stress and strain distribution in two-phase materials under loading is inhomogeneous. The magnitude of the inhomogeneity as well as local strain patterns depend on the microstructure (i.e. the elastic–plastic behaviour, volume fraction and phase arrangement of the components). The knowledge of the microstructure/deformation-relationship enables “tailoring” of materials with desired profiles of properties. The critical concentration of strain, stress or hydrostatic stress can lead to damage initiation and failure of the component. By an optimised microstructure design such stress and strain concentrators can be avoided or reduced.

Section snippets

Material and microstructure

The subject of the following experimental and numerical investigations is a model material Ag/Ni(57%)-particulate composite with a coarse microstructure with an average Ni-phase size of 77μm and an Ag-phase size of 60μm (Table 1). This material was produced by a powder metallurgical route using hot isostatic pressing (HIP 900°/200 MPa/1 h) [1]. Ag and Ni as mutually insoluble elements exist in a composite as “pure” phases without any transient zone. This is the reason that this material's

Compression test and an object grating technique

The Ag/Ni-material has been tested under uniaxial compression in the chamber of a scanning electron microscope using a specific in situ compression device that is able to generate loads of up to 10 000 N. A cylindrical sample (6 mm diameter and 8 mm length) with a Rastegaev-type geometry [3] and grease at both sides of the sample in order to reduce friction was used. Two symmetric flat planes were manufactured along the sample in order to facilitate the observation with the SEM. One of these was

Discussion

Experimental and numerical investigations on the same cut-out of the Ag/Ni-particulate composite have been performed in order to correlate in-plane strain components and out-of-plane displacements. The comparison of the results influenced the development and improvement of all these methods.

For the numerical simulation it can be concluded that 2D-calculations provide results with a good qualitative agreement but they are not able to reproduce the experimental details quantitatively. For this

Conclusions

  • Corrections of the equivalent strain performed using out-of-plane displacements in an Ag/Ni-composite as measured by AFM at a macroscopic deformation of 8.6% are negligibly small.

  • The comparison between experimental and calculated distributions of equivalent strains shows a good qualitative agreement – quantitative agreement is expected for the case of well-defined experimental boundary conditions as well as 3D-calculations instead of a 2D-simulation. In the case of coarse grain size comparable

Acknowledgements

This work was performed in the frame of the PROCOPE-Project “Experimental and numerical investigations of the deformation in Ag/Ni-particulate composites: correlation between in-plane-, out-of-plane-deformation and microstructure” and Research Group “Investigation of the deformation behaviour of heterogeneous materials by direct combination of experiment and computation”, subproject DFG Schm 746/16-1, 2. The authors gratefully acknowledge the financial support by the APAPE, DAAD and Deutsche

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Paper contributed to Ninth International Workshop on Computational Mechanics of Materials, J. Olschewski, S. Schmauder (Eds.), BAM, Berlin, Germany, October 4–5, 1999, Comp. Mater. Sci. 19 (2000).

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