Elsevier

Computational Materials Science

Volume 126, January 2017, Pages 393-399
Computational Materials Science

Numerical study of stress distribution and size effect during AZ31 nanoindentation

https://doi.org/10.1016/j.commatsci.2016.10.012Get rights and content

Highlights

  • Twins initiate at higher stress during nanoindentation compare to uniaxial loading.

  • The CRSS values determine the position of the twin shear stress peak.

  • The indenter radius dominantly influences the stress field in the material.

Abstract

A numerical study of the nano-indentation of the AZ31 alloy was performed in order to analyze the stress fields at the onset of twinning. The model considers indentation of the (101¯0) and (12¯10) planes by a spherical indenter with radii of 5, 10 and 50 μm. Material behavior is described by a crystal plasticity constitutive model with three critical resolved shear stresses for different slip modes. The CRSS values were obtained by fitting to experimental load-displacement curves. The stress and strain distributions are analyzed with a view to understanding twin initiation. The twins initiate during indentation at the stress level order of magnitude higher compare to uniaxial tests.

Introduction

Nanoindentation is relatively easy to perform but its evaluation can be complicated due to the complex stress state under the indenter. Material yield parameters cannot be easily extracted directly from the loading curves, particularly for hcp metals such as magnesium with different critical resolved shear stresses (CRSS) for different slip systems. Twinning can also occur under certain conditions. In order to study hcp deformation using nanoindentation, it is necessary to complement the experiments with numerical simulations. Several numerical studies of magnesium indentation have appeared in the recent literature. Kitahara et al. [1] performed crystal plasticity simulations for a 1 mm spherical indenter. Comparison with experiments on pure Mg showed that the model was able to match the general regions with increased slip and twinned activity. The shape of the pile-up and sink-in areas close to indent were also well replicated by the model. A similar study with similar results was carried out using a cono-spherical indenter by Selvarajou et al. [2]. An extended numerical study on pure Mg with a conical indenter was performed by Sánchez-Martín et al. [3]. They found that the ratio of the prismatic to basal CRSS is particularly important for the cases of (101¯0) and (12¯10) plane indentation. The evolution of twinning around the indenter was studied experimentally in [4]. This study showed strong size effect for the twin initiation and the necessity of reaching the critical stress value in the sufficiently large volume of material. The twins initiate preferably in the area under the indenter for the indentation of the (101¯0) and (12¯10) planes. Increasing the test temperature caused suppression of twinning as the slip became easier to activate [5]. While numerical studies have provided insight into slip activity, twinning has been studied via experimental nanoindentation without the support of simulations. The following numerical study is focused on the nature of the stress distribution under the indenter during glide mediated deformation. The aim is to help understand the stress state immediately prior to twinning and provide a general estimate of the CRSS value for the twin nucleation. Indents were made using 5 μm radius indenter. Grains with two different orientations were tested. These orientations correspond to the indentation of the (101¯0) and (12¯10) planes respectively. Typical experimental indentation curves are shown in Fig. 1(a). The most distinctive feature of the curves is the pop-in which is the present case related to the sudden onset of twinning [6]. Twinning initiate when slip is not able to accommodate deformation induced by indentation. Loads at which the first pop-in occur can be illustrated as cumulative frequencies as shown in Fig. 1(b). The cumulative frequency analysis reveals the typical load range in which the pop-ins occur. The curves show that the pop-ins for the (101¯0) orientation appear at lower loading level compared to the (12¯10) orientation. A typical AFM image of the indented area is illustrated in Fig. 1(c). The most visible features on the imprints are the basal slip lines that extend far from the indented area and twins that appear from inside the indented area. The basal slip lines form first at the point of yielding and the twins form at the pop-in. More detailed description of the experiments can be found in reference [6]. The paper is organized as follows: first the constitutive behavior and the finite element model is described. Following sections describe the results and finally we present an interpretation.

Section snippets

Constitutive model

The elasto-plastic simulations are based on continuum crystal plasticity. The theory is based on a decomposition of the deformation gradient into elastic and plastic parts [7], [8].F=FeFpwhere plastic part is related to the slip occurring in the slip systems characterized by the slip direction (ms) and normal to the slip plane (ns). It can be written as:ḞpFp-1=s=1nγ̇smsns.

The slip rate at the given slip system γ̇s is defined by the following expression:γ̇s=|τs|-τhsKnsign(τs)where τs is the

Results

The stress conditions under the indenter are described below using 2D maps of the X-Y plane (perpendicular to c-axis) and the Z-Y (parallel to c-axis) plane. The stress analysis is performed at an indentation force equal to 1 mN. This value represents the lower bound of the interval in which the pop-ins occur using a 5 μm indenter. This force is reached at different levels of indentation depth for the different sets of CRSS values. Therefore, the dimensions are normalized by the length of the

Discussion

The simulated loading curves pass through the location of the pop-in events in the experiments which validates that the stress level in the simulations is similar to the real stress state in the material. The corresponding stress level in the simulations was achieved only by using relatively high values of CRSS. However, these values can be justified in terms of an indentation size effect which is caused by geometric strain gradient induced during the indentation [11]. Taylor equation for

Conclusions

The finite element simulations of nanoindentation have been performed. The results are compared with the experimental measurements on AZ31 alloy. The numerical results are used for an explanation of the observed phenomena. The following conclusions can be drawn from the results:

  • The grain orientation (101¯0) undergoes higher stress, therefore the twins initiate earlier during the indentation.

  • Twins initiate during nanoindentaion at the stress level that is about order of magnitude higher compare

Acknowledgment

Work on this study has been supported by the Czech Science Foundation via the project 15-21292Y.

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