Elsevier

Acta Materialia

Volume 55, Issue 5, March 2007, Pages 1681-1693
Acta Materialia

Application of the Raman technique to measure stress states in individual Si particles in a cast Al–Si alloy

https://doi.org/10.1016/j.actamat.2006.10.028Get rights and content

Abstract

While Raman spectroscopy is often used to measure stresses, the analyses are almost always limited to cases with simple stress states (uniaxial, equibiaxial). Recently we provided an experimental methodology to determine the full state of stress in Si wafers. Here we extend that methodology to interrogate stress states in Si particles embedded in an Al–Si alloy. Such determinations will ultimately be valuable for predicting ductility of cast Al, since a primary source of damage is cracking of eutectic Si particles. We combine electron back-scattered diffraction with the frequency shift, polarization and intensity of the Raman light to determine stress states. Stress states are measured both in the as-received residually stressed state and under in situ uniaxial loading. Comparison with finite element calculations shows good agreement. As an application of the technique, we show the determination of strength of an individual Si particle and compare the stress evolution with various models.

Introduction

The increased use of lightweight materials such as cast Al in the automobile industry has highlighted a need to better understand their mechanisms of fracture. It has been observed [1], [2] that the initial step in the ductile fracture of cast Al is the cracking of eutectic Si particles. The density of particle cracks increases with the far-field applied strain, as more and more load is transferred from the compliant and plastic Al matrix to the stiffer Si particles. The cracking of particles leads to enhanced plastic strain in the matrix that is in the immediate vicinity of the cracks and this is followed by void nucleation in the local matrix. Eventually the matrix cracks join through a mechanism of ductile rupture and ultimate failure of the alloy.

Thus, in order to predict ductile failure it is necessary to know the rate of load transfer to the particles from the matrix as functions of the local strain and of particle properties and environment. By this we mean particle size, orientation and morphology as well as how the particles may be clustered. Furthermore, we will need to know the states of stress that cause Si particles to crack and how the cracking of particles redistributes the load. There have been a number of theoretical approaches employed to estimate stresses and damage evolution in particle-reinforced composite systems, both with and without heterogeneous microstructures [3], [4], [5], [6], [7], [8], [9]. However, these approaches are not necessarily valid for the complex-shaped and highly clustered particles that are present in cast Al. And while neutron scattering can provide experimental measurements for strains in eutectic Si particles, the values obtained are typically averaged over many thousands of particles that may be subjected to a wide range of local environments.

Raman spectroscopy has often been used to measure stresses in microstructural elements, but the assumption has nearly always made, explicitly or implicitly, that the stress can be described as a scalar, e.g., uniaxial, equal biaxial, etc. [10], [11], [12], [13], [14]. Such an assumption would be suspect when applied to eutectic Si particles. Proposals to evaluate the stress states using Raman measurements have been made recently by Loechelt et al. [15], Bonera et al. [16] and Narayanan et al. [17], but none of these groups provided experimental verification of their strategy. To our knowledge, there have been no measurements of the stress states of individual eutectic Si particles in cast Al. Indeed, the only other technique of which we are aware that may provide stress states in individual 1–10 μm size particle reinforcements of any crystalline material is microtomography, utilizing synchrotron X-ray radiation [18], [19]. However, even here, we are not aware if such attempts have yet been made. Such measurements will be necessary to test calculations and estimates that have been published [1], [2], and to validate computational models that account for local cluster environment and complex particle morphology. In addition, in situ loading measurements can provide the states of stress that cause particles to fracture under far-field applied load.

We have recently implemented a strategy [20], originally proposed by Narayanan et al. [17], that uses micro-Raman spectroscopy to determine the state of stress of a Si wafer at its surface. The wafers that we used were [1 1 1]- and [1 1 0]-oriented (i.e., the normals to the surface were [1 1 1] and [1 1 0]), but the technique is applicable in principle to any single crystal of Si, unless the crystal is [0 0 1] oriented. We aim to use this technique to provide experimental in situ information on the stress states of individual Si particles before and during ductile fracture experiments on cast Al. These would include measurements in cracked particles, whose presence can have an important effect on matrix flow [21], as well as in particles near cracked particles.

However, we must first ask whether a technique that has been validated for Si wafers can be applied to a eutectic Si particle in cast Al. The purpose of the present work is to answer this question. There are at least two concerns. (i) A Si wafer is a perfect crystal. Eutectic Si particles are nominally single crystals, but there is no reason to expect that they are of very high quality; they have been observed to be twinned [22] and can suffer from any number of other defects [23]. In such cases, an assumption behind the Raman analysis is called into question. (ii) The stress state of a particle at the surface will vary with depth. Thus, the goal must be to measure stress components averaged through the depth of the particle. This is made possible by the fact that Si is moderately transparent at the laser wavelength, allowing the beam to penetrate through the particles. We used finite element (FE) modeling to help guide this approach.

In the present analysis we examine these issues by interrogating eight eutectic Si particles that have an orientation close to [1 1 1]. These particles have residual stresses generated when the alloy cooled from the processing temperature, because of mismatch of coefficient of thermal expansion (CTE) between the Si and Al phases. Our analyses suggest: (i) for most of the particles the Raman technique does allow us to determine the state of stress of the particle; and (ii) those particles for which the technique is not applicable can be identified.

Section snippets

Experimental

Raman measurements were made on eutectic Si particles in an A356-T6 cast Al bar of approximate composition Al–7Si–0.3Mg, all measured in weight percent. The material had a secondary dendrite arm spacing (SDAS) of 90 μm and was heat treated to the peak aged T6 condition. The material was strontium modified such that the eutectic Si particles appeared small and rounded, rather than possessing the long plate-like morphology of unmodified Al–Si alloys. The yield strength, tensile strength and

Results and analysis

Fig. 3 shows an optical profile that identifies the eight particles that we selected for interrogation. They are 3–5 μm in diameter, compared with a laser spot diameter of around 2 μm and their Euler angles E = (ϕ1,Φ,ϕ2) are given in Table 1. To a first approximation all eight particles have a [1 1 1] normal. For all of the particles except particle 7, the 1¯1¯2 direction is approximately parallel to the y-axis, while the 1¯10 direction is approximately parallel to the x-axis. ϕ1 is within a few

Discussion

The purpose of this work is to determine whether or not a strategy that is successful for measuring the stress state of a Si wafer can be applied to eutectic Si particles. In the absence of an independent measurement of the particle stress states, we cannot answer this question with certainty. But we have provided data and an analysis that suggests a positive answer.

The signal-to-noise ratios of our data are not adequate to provide quantitative information about the out-of-plane stresses.

Conclusions

The following conclusions may be drawn from this work:

  • (i)

    The Raman technique can be used to measure stress state in Si particles embedded in a matrix such as Al. This in-plane stress state is an important advancement over other such measurements, where stress was treated essentially as a scalar.

  • (ii)

    The Raman technique can be used to measure particle stresses in the elastic–plastic regime of deformation, including measuring the stress in the particle at fracture. In this way, the strength of particles

Acknowledgments

Part of this work was supported by NSF Grant CMS0309519 to New Mexico Tech. We thank Mahesh Erukullu of NMT for the 3-D microstructural characterization of the Si particles, Dr. Bill Weber and Prof. Somnath Ghosh for valuable discussions and Dr. John Allison for inspiring this project.

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