Residual stress evolution with compressive plastic deformation in
6061Al-15 vol.% SiCw composites as studied by neutron diffraction
R.Fernández a,1, G.Bruno b,c, G.González-Doncel a,*
a Dept. of Physical Metallurgy, Centro Nacional de Investigaciones Metalúrgicas (CENIM), C.S.I.C., Av. de Gregorio del Amo 8, E-28040 Madrid, Spain
b Institut Laue-Langevin, ILL, Rue Jules Horowitz, BP 156F-38042 Grenoble Cedex 9, France
c Manchester Materials Science Centre, Grosvenor str., Manchester M1 7HS, UK.
Keywords: Metal Matrix Composites, Residual Stress, Neutron Diffraction, Plastic Deformation.
Abstract
The evolution of the residual stress (RS) with compressive plastic deformation of several discontinuously reinforced 6061Al-15 vol.% SiCw metal-matrix composites (MMCs) has been investigated. The composites were obtained by a powder metallurgical route and heat treated to a fully hardened, T6, condition. The RS was determined from neutron diffraction. The results show that deformation relaxes the hydrostatic component of the macroscopic RS (M-RS) progressively until a minimum is reached, around 2-5% plastic strain. Similarly, the hydrostatic component of the microscopic RS (m-RS) relaxes rapidly with deformation. Relaxation continues with further strain and at ≈15% this m-RS component disappears. The deviatoric components of both the M-RS and the m-RS, however, remain unaltered with increasing plastic strain. The increase of the full width at the half maximum (FWHM) of the Al diffraction peaks with strain reveals the increased lattice distortion and microscopic RS gradient around the reinforcing particles. The linear correlation found between the FWHM of the two phases suggests also the activation of a lattice distortion transfer mechanism from the Al phase to the SiC phase.
1, Present address: Thin Film R&D Dept. INDO, SA, 08902 L'Hospitalet de Llobregat, Barcelona, SPAIN
* Corresponding author. E-mail address,
Tel.: +34 915538900; fax: +34 915347425.
1. Introduction
Discontinuously reinforced metal-matrix composites (MMCs), in particular aluminum alloys reinforced by silicon carbide, have better mechanical properties than the corresponding metallic matrices [1, 2]. Among the factors responsible for this improvement, the residual stress (RS) arising from several sources plays a crucial role. Of particular importance is the microscopic RS originated on the different thermal expansion of the matrix and the reinforcement. This stress account, for example, for the strength differential effect observed between uniaxial tensile and compressive test [3,4]. Despite the well-known correlation between RS and the mechanical behavior, it is not yet well understood how this stress evolves with plastic deformation and how it can affect service life performance of structural components [5]. Some few studies analyzing the influence of plastic deformation on the RS state in MMCs have been conducted [5-8]. Following the separation of the RS into macroscopic and microscopic RS (M-RS and m-RS) and the separation of the m-RS into an elastic mismatch term and a thermo-plastic contribution (misfit stress) [6], it has been shown that a small amount of plastic deformation (≈1%) is sufficient to reduce the misfit stress and that thermal and plastic stresses are of the same nature [7]. The deformation processes employed in these studies center mostly on bending tests. The effect of plasticity has been also studied at the front of crack front of notched samples and in the vicinity of a cold expanded hole [9] with the aim of understanding the effect of changes in the misfit stress on the fatigue crack propagation in MMCs [8]. Whereas the conclusions resulting from these studies are relevant, they do not analyze the effect of accumulative (increasing) plasticity on the RS of these materials.
The purpose of this research is, therefore, to study the evolution of the RS state in 6061Al-15 vol.% SiCw composites with accumulative compressive plastic deformation and to understand the mechanisms that govern RS relaxation.
2. Materials and experiment
The materials studied were three 6061Al-15 vol.% SiCw composites, labeled C38, C45 and E219, and the unreinforced 6061Al alloy, labeled E220, prepared by powder metallurgy (PM) involving hot extrusion [10-12]. Letters C and E of material’s code denote conical and flat extrusion dies, respectively. This characteristic of materials preparation did not affect the RS state of the composites [13]. The evolution of RS with deformation was studied in a T6 condition obtained after solution treatment at ≈520ºC followed by water quenching and annealing at 146ºC (see [10-12] for details).
The microstructure was studied by scanning electron and optical microscopy (SEM and OM) and the texture of the Al and SiC phases by X-ray diffraction. The detailed analysis of this study is reported elsewhere [11]; only a brief description will be given here.
The RS was studied by neutron diffraction (ND) using the REST diffractometer at Studsvik Neutron Research Laboratory, Sweden. The neutron wavelength was 1.7 Å. Appropriate slits were selected to produce a gauge volume of 3x3x3 mm3. Because of the cylindrical symmetry of the extrusion process, the principal directions were assumed to be the axial (extrusion axis), the radial, and the hoop, mutually perpendicular. Samples of 13 mm length and 6.5 mm diameter (with the sample axis parallel to the extrusion direction), also suitable for compression tests, were used. Reference samples for the aluminum phase included the 6061Al alloy and 6061Al powder. The same heat treatment given to the alloy was given to the powder to achieve also the T6 condition. Loose SiC powder was measured as reference of this phase.
Samples for ND measurements underwent ex-situ compression tests. These tests were conducted up to different strain levels in a conventional screw driven testing machine at a strain rate of 10-4 s-1. Particular interest was focused on the initial regions of plastic deformation, where a rapid hardening rate is observed [4]. Determination of RS at high plastic strain values, however, was also conducted in two of the composites under study. Specifically, strain values were selected around 1, 2, 5, and 15% compressive deformation.
3. Residual stress determination
The diffraction peaks were fitted with simple Gaussian functions. The sin2y method (with y the angle between the sample axis direction and the scattering vector, Q), using the w geometry (the sample is tilted within the scattering plane), was utilized. The lattice parameter of the 311 planes of both the Al and SiC phases was determined [14] by applying Bragg equation. Then, the lattice strains at different tilt angles, from y=0º (axial direction, parallel to the extrusion axis) to y=±90º (radial direction) could be calculated (see [4, 12] for more details). The axial and radial RS components could been finally obtained from the residual strain data using the generalized Hooke´s law, which for the case of cylindrical symmetry it reads:
(1a)
(1b)
where E and n are the Young modulus and Poisson ratio, respectively. The radial and hoop terms of the strain and stress tensors coincide because the measurements have been performed at the center of the samples. An analysis of the full width at the half maximum (FWHM) of both the Al and SiC peaks (FWHMAl and FWHMSiC, respectively) was also conducted. The calculation of the RS from equations (1a) and (1b) was done using plane-specific diffraction elastic constants as evaluated by means of a Kröner model [15]:
E311-Al = 69 GPa ; n311-Al = 0.35 E311-SiC = 387 GPa ; n311-SiC = 0.19
These elastic constants are very similar to macroscopic values for both Al and SiC.
Errors have been calculated according to error propagation formulae [16].
4. Results
The microstructure, the texture, and the initial residual stress of the materials are described in previous works [4, 11, 12]. In summary, the extrusion process of the Al/SiC powder blends leads to a <111>+<100> fiber texture (with the fiber axis parallel to the extrusion axis) of the 6061Al matrix, typical in extruded aluminum alloys [11, 17], and to a slight trend of the short SiC fibers to be aligned with the extrusion axis. Figure 1 describes, through inverse pole figures of the extrusion axis direction, the texture of: a) the unreinforced alloy, b) the aluminum matrix of the composite E219, and c) the SiC whiskers of this composite. As can be seen, the composite matrix and the alloy develop similar texture components. The texture is more accentuated in the alloy than in the composites. All composites have, roughly, a similar microstructure and texture.
The initial total RS state of the materials in the T6 condition is fully described in Table 1 of [12]. It is very similar in all composites. In summary, the RS is tensile in the matrix and compressive in the reinforcement, and accounts for the presence of m-RS with length-scale of the order of the SiC inter-particle distance [18]. This m-RS term is caused by the different coefficient of thermal expansion, CTE, of aluminum and of silicon carbide [19]. Also, the absolute total axial RS (at y=0º) is higher than the radial one (at y=±90º): i.e., a deviatoric RS state is developed.
Although smaller than in the composites, also a tensile RS with a deviatoric character builds up in the 6061Al alloy [12]. This RS is macroscopic and is raised during the high temperature gradient brought about by the quenching prior to the annealing for the T6 condition. A tensile M-RS resulting from material’s quenching has been obtained in several investigations [20-22].
To separate m- and M-RS terms appropriate stress equilibrium condition has been applied [7],
(2)
where, , sub-indexes Tot, Mac, and mic refer to total, macroscopic, and microscopic RS, respectively, sub-index i refers to, axial and radial (hoop) component, and fr is the volume fraction of the reinforcement. The bars stand for the fact that average stress values over the gauge volume are determined. This is a large region if compared to the microstructural scale of these composites. The magnitude of the hydrostatic and deviatoric stress terms could be readily calculated using shd = (sax+2srad)/3 (with srad=shoop≠sax) and sd =sax-srad.
As it has been already summarized in previous works [4,12], the M-RS in the undeformed condition is mostly hydrostatic, and higher in the alloy than in the composites in agreement with the higher CTE of the former [23]. A certain deviatoric character is present because of sample shape: the temperature gradient along the axial and the radial directions are different. The m-RS is tensile in the matrix and compressive in the reinforcement, and is also strongly hydrostatic because the SiC is mostly randomly oriented. The deviatoric term is due to the population of short SiC fibers aligned with the extrusion axis (≈ 30%, [12]). The m-RS.
The compressive tests revealed the improved mechanical response of the composites in the T6 condition in comparison to that of the alloy, Fig. 2. The pronounced strain hardening rate of the composites in the early stages of deformation, up to 0.05 strain, accounts for a rapid multiplication rate of geometrically necessary dislocations (GNDs). This is not observed in the E220 alloy in which the dislocation-precipitate interaction (cutting mechanism) should predominate, leading to a limited strain hardening rate. At high values of strain, the composites and the alloy behave similarly. This is because the multiplication of statistical dislocations dominates the hardening process similarly in the alloy and the composites [24]. The slight differences in the stress-strain curves of the composites is attributed to the differences in the orientation/distribution and to the inter-particle spacing of the SiC.
The evolution of the M-RS and m-RS components with compressive plastic deformation is shown in Figs. 3 and 4, respectively. A rapid drop of the hydrostatic M-RS occurs with small plastic strain in all materials investigated, Fig. 3. Relaxation of RS with plastic deformation is consistent with previous investigation on the effect of plasticity on the RS state of MMCs [7]. The M-RS reaches a minimum around 2-5% of deformation. However, it increases again with further plasticity. A RS value close to that in the undeformed condition is reached at 15% of deformation in composites C38 and C45. On the other hand, the deviatoric term remains essentially constant in the complete range of deformation.
Similarly to the M-RS, the axial and radial components of the m-RS evolve in parallel, such that the deviatoric term remains constant with plastic deformation, Fig. 4. This result is consistent with the observation that the stress-strain curves in tension and compression run nearly parallel, separated by a certain stress value: i.e., the strength differential effect SDE [4]. The hydrostatic m-RS relaxes progressively with plastic pre-deformation. Relaxation occurs rapidly during the initial stages of plastic deformation, <2%, and slowly at high levels of strain.
The radial component of the m-RS reverts its sign (becomes compressive in the matrix and tensile in the reinforcement) at about 2% of plastic deformation, Fig. 4. Sign reversal of the m-RS with strain has been reported in a cold expanded hole (expanded 4% by a split sleeve technique) at a distance up to some 5 mm from the edge of the hole in a 2124Al-17 vol.% SiCp plate [9]. Since deformation was imposed by the split-sleeve technique (it depends on the distance from the edge of the hole and on the strain hardening behavior of the material), it is not evident from [9] the amount of plastic deformation needed to achieve sign reversal of the RS. The present work indicates that sign reversal occurs with only ≈ 2% strain. This effect has been attributed to a mechanism of load transfer from the matrix to the reinforcement [9, 25].
Although the instrumental contribution could not be separated in the analysis of the FWHM, it can be assumed to be the same at the diffraction angles for the Al and SiC phases (they are relatively near). Therefore, a deconvolution of the different sources of peak broadening was not needed. In this way, the variation of the FWHM can be attributed only to microstructural changes with plastic pre-strain (lattice micro-strains or type-III RS, m-RS-III [17]). The evolution of FWHMAl and FWHMSiC with plastic strain is summarized in the plots of Fig. 5. As can be seen, the FWHM increases with increasing plastic deformation in all materials. The increase of FWHMAl is more evident than that of FWHMSiC.
5. Discussion
Once the different components of the RS are known, it is worth comparing the evolution of the hydrostatic and devatoic M-RS and m-RS of the composites with accumulative plastic strain. This is shown in the plots of Figs. 6a) and 6b) for the C38, and C45 composites, respectively.