Neutron Diffraction Study of Phase Stresses in Al/SiC_p Composite During Tensile Test

Materials tested in this work are the Al2124 alloys (Table 1) either unreinforced or reinforced with SiC particles. The Al/SiC_p composite produced by powder metallurgy route was provided by Materion Aerospace Metal Composites, Farnborough, Hampshire, UK. This technique is based on blending and compaction of mixed aluminium and SiC powders. The amount of the reinforcement particles in the composite is 17.8% by volume and the particle average size is 0.7 μm.

Two types of the material with different heat treatments were studied. The first one was subjected to the T6 heat treatment (i.e. solution treatment at 491 °C for 6 h and then cold water quenching to produce a supersaturated solid solution, and finally artificial aging for 4 h at 191 °C). This treatment resulted in the hardening of the Al2124 alloy by semi-coherent Cu-Al–Mg precipitates [33]. The second part of the composite was subjected to the T1 heat treatment, consisting in the natural aging with a calm air cooling directly after 6 h annealing at 491 °C. In this work, the composite specimens subjected to the heat treatments T6 and T1 are marked respectively Al/SiC_p-T6 and Al/SiC_p-T1, while the unreinforced aluminium alloy sample subjected to T6 treatment is labelled as Al2124-T6.

In Fig. 1, the SEM image of the examined Al/SiC_p specimen is presented. A significant dispersion of the particles size around the nominal value 0.7 µm and their not perfectly uniform spatial distribution can be observed. However, in the case of the relatively large gauge volume in the diffraction experiment, a macroscopically homogeneous material was assumed in this study.

The crystal structure and crystallographic texture of the composite phases were determined on the Panalytical Empyrean diffractometer using Cu Kalpha X-ray radiation. The Rietveld analysis of the experimental results showed that the 6H polytype with hexagonal structure is dominant (content of ca. 80%) in the investigated SiC powder (used as a reinforcement in the composite), while the aluminium alloy Al2124 exhibits a face centred cubic structure. No significant crystallographic texture was found in both phases of the composite.

The lattice strains in the studied materials were measured using a time of flight (TOF) neutron diffraction method on the EPSILON-MDS and FSD diffractometers [34, 35] installed at the IBR-2 pulsed reactor in the JINR in Dubna (Russia). The example diffractograms obtained using both instruments are shown in Fig. 2. On the FSD diffractometer the evolutions of crystal structure and coefficients of thermal expansion at temperature range 22 °C-500 °C were investigated for the SiC powder and the Al2124 alloy [36]. It was found that in the investigated range of the temperature crystallographic structure of SiC powder does not change and the increase of lattice parameter is caused by thermal expansion of the material (Fig. 2b, [36]).

The main experiments were performed on the EPSILON-MDS diffractometer (at ambient temperature) using two configurations presented in Fig. 3. The first configuration with two detectors L2 and L8 (other detectors were shaded by the tensile rig) was applied during the in situ tensile test for the dog-bone shaped samples having a square cross section 4 mm × 4 mm and a gauge length of 15 mm. The specimens were cut using the electrical discharge machining (EDM) method in such a way that the sample axes were parallel to the sheet edges. The applied loads were measured in situ by load cell and the macroscopic strain was determined ex situ by an extensometer connected to an identical sample subjected to the same loads. To obtain satisfactory counting statistics, the diffraction measurements through the whole cross section of the sample were done using the wide incident beam with an aperture of 10 mm. The diffraction measurements were performed for constant grip positions (corresponding to given sample strains), after stabilisation of the applied load, which decreased over a period of about ½ h. Both composite samples (Al/SiC_p-T1 and Al/SiC_p-T6) fractured very close to the macroscopic strain of E₁₁ = 3% and in such a case the last diffraction measurement was done on the broken sample. Consequently, the last measurement of unreinforced alloy Al2124-T6 was also performed after the sample unloading at E₁₁ = 3%.

The interplanar spacings in both phases were determined from the diffractograms (e.g. Figure 2b) by fitting of pseudo-Voigt function to the measured diffraction peaks. The relative lattice strains in direction of the load \(\left\langle {\varepsilon_{11} } \right\rangle_{{\{ hkl\} }}\) and in the transverse direction \(\left\langle {\varepsilon_{22} } \right\rangle_{{\left\{ hkl\right\} }}\) were calculated using Eq. 1:where \(\left\langle d \right\rangle_{{\left\{ {hkl} \right\}}}^{\varSigma }\) and \(\left\langle d \right\rangle_{{\left\{ {hkl} \right\}}}^{0}\) are the interplanar spacings determined for the loaded (for given applied stress \(\varSigma_{11}\)) and non-loaded sample (initial, i.e. for \(\varSigma_{11} = 0\)) and the <…>_{hkl} brackets denotes an average over the diffracting grains volume for a given reflection hkl. Indices LD and TD mean that the interplanar spacing were measured in the direction of the applied load and in the transverse direction, respectively.

Additionally, the ex situ diffraction measurements were performed for the initial as well deformed/fractured samples using the second configuration with nine detector banks arranged around the sample at the EPSILON-MDS diffractometer (L1–L9) as shown in Fig. 3b [34]. In this case the tensile machine was removed and the measurements were performed for two sample positions, the first at the orientation shown in Fig. 3 and the next after rotation by 90° around the sample long axis. In principle, the measurements of interplanar spacings for 18 orientations enable determining of the stress tensor for each phase if the strain free lattice parameters are known.

In this work, the prediction of stresses evolution during elastic–plastic processes was done using the EPSC model proposed by Lipinski and Berveiller [37, 38] and applied to two phase materials by Baczmanski et al. [7, 24]. This model is based on the interaction of the grains with the surrounding matrix described by Eshelby tensor [19]. The model predictions were performed for a set of 2000 spherical grains representing 17.8% volume fraction of SiC reinforcement (356 grains) and 82.2% of the Al matrix (1644 grains). Because of weak crystallographic textures, the orientations of grain lattice were randomly generated and corresponding single crystal elastic constants were assigned to the grains of both phases (cf. Table 2). The spherical inclusions and zero initial stresses were assumed for the particles of SiC reinforcement and for the Al2124 matrix.

The elastic–plastic deformation with slip systems <110> {111} were assumed for aluminium, while only elastic deformation was assumed for SiC grains. Predictions of a tensile test were performed for various values of the critical resolved shear stress (CRSS, \(\tau_{c}\)) and the hardening parameter (H) of the Al2124 matrix [7, 24, 37, 38] (assuming linear and isotropic work hardening process for small deformations). The optimal values of \(\tau_{c}\) and H were determined by comparing the experimental and theoretical lattice strain evolutions for all the measured reflections, as well as macroscopic dependence of overall stress versus sample strain. The same procedure of experimental data analysis was carried out for the Al2124-T6 alloy, but in this case the single phase polycrystalline aggregate consisting of 2000 aluminum grains was considered.

Firstly, the dependence of the applied stress versus sample strain was analysed in order to choose the best model parameters. In Fig. 4a the macroscopic plots obtained in the tensile test for the Al2124-T6 alloy and Al/SiC_p-T6 composite are compared with the prediction of the EPSC model. The values of \(\tau_{c}\) and H for slip system <110> {111} were adjusted in order to fit the theoretical macroscopic stress–strain plot to the experimental one obtained for the Al2124-T6 alloy. A very good convergence of the model and experimental plots both in the elastic and plastic ranges of deformation was obtained for the elastic constants given in Table 2 and plastic slip system parameters shown in Table 3. Next, the properties of the unreinforced Al2124-T6 alloy were assumed for the matrix of the Al/SiC_p-T6 composite (cf. the T6 treatment in Table 3), and the tensile test was predicted for this composite, using elastic constant of the 6H-SiC polytype given in Table 2. It was found that the EPSC model correctly predicts elastic and plastic deformation of the studied composite at a macroscopic scale (Fig. 4a), when the CRSS and hardening parameter determined for Al2124-T6 alloy (Table 3) are used for the matrix.

Using the model prediction, the role of SiC_p in the hardening of Al/SiC_p was also studied. To do this, the evolution of von Mises stress calculated for each phase within the Al/SiC_p-T6 composite as well as for the Al2124-T6 alloy are shown in Fig. 4b. It was found that this stress changes almost identically in the Al2124-T6 alloy (without reinforcement) and in the same alloy creating matrix of the Al/SiC_p-T6 composite, i.e. the theoretical curves representing aluminium overlap and agree with the experimental ones obtained for the unreinforced Al2124-T6 alloy. This means that the SiC_p particles do not cause significant hardening of the aluminium matrix. The overall macrostress for the composite is much higher comparing with Al2124-T6 alloy exclusively due to large stress accumulated in elastically deformed SiC_p reinforcement, as shown in Fig. 4b. It should be emphasized, however, that until now no experimental information on the state of stresses in SiC_p is provided, therefore the stress partitioning between the composite phases is shown in Sect. 3.3.

The analysis of the macroscopic stress versus strain dependence was performed also for the Al/SiC_p-T1 composite. It was found that the value of the CRSS determined from the EPSC model adjustment to the macroscopic curves (Fig. 5) is much lower for the T1 treatment in comparison with that for the T6 treatment, while the hardening parameter H is similar for both treatments (cf. Table 3). The macroscopic stress versus strain plots (Fig. 5) showed an important influence of the matrix state on the overall mechanical behaviour of the composite, which is much softer after the T1 treatment than after the T6 treatment.

Here, the analysis of phase stresses in the initial and fractured composite specimens is presented (based on results of the ex situ measurement with nine detectors, Fig. 3b). Data analysis was performed with the Kröner-Eshelby model used for calculation of the X-ray elastic constants (XECs) for each phase separately [42]. In the case of 6H-SiC, the diffraction peaks for 006/102, 108/110 and 116/202 reflections were measured, while for the Al2124 matrix—111, 200, 220, 311 and 220 reflections were taken into account. The stress values were calculated on the basis of experimental data using the least square method in which the three principal stress components were adjusted, while the shear stresses were neglected due to symmetry of the sheet from which the samples were cut. The measurements at elevated temperatures up to 500 °C (cf. Fig. 2a and [36]) performed for 6H-SiC powder showed that the structure of SiC_p did not change during T1 and T6 heat treatments. Therefore the stress free interplanar spacings of the SiC_p reinforcement were assumed to be equal to these measured at room temperature for the same silicon carbide powder that was used in the production of the composite. In the case of the composite matrix, the accurate value of the stress free lattice parameter (\(a_{0}\)) is influenced by the precipitation process occurring in the Al2124 alloy. Consequently, the value of \(a_{0}\) measured for the unreinforced Al2124 alloy (or powder) cannot be used in stress analysis for the matrix, because during thermal treatments the precipitation process can proceed differently in the unreinforced and reinforced alloy [36].

The stress analysis was based on the decomposition of the stress tensor into two parts, containing the hydrostatic component (p) and deviatoric components (\(q\), \(r\), \(s\)):The deviatoric stresses were correctly determined for both phases because they do not depend on the values of the stress free lattice parameters. Also, the value of hydrostatic stress p for SiC_p reinforcement, based on the lattice parameters determined for SiC powder, can be determined. Because the stress free lattice parameter for the composite matrix subjected to the given heat treatment is not available, the hydrostatic stress in the matrix should be deduced from the equilibrium law for the non-loaded sample:where f = 0.178 is a volume fraction of SiC_p and the above law is fulfilled for all stress components as well as for deviatoric and hydrostatic stresses.

In stress analysis performed for aluminium matrix, an approximated value of \(a_{0}\) was temporarily assumed. Then, the determined hydrostatic stresses were adjusted by shifting p by the same value simultaneously for the results obtained for the initial and fractured samples in order to fulfil Eq. 3. This correction corresponds to the adjustment of \(a_{0}\) value for both states (initial and fractured), subjected previously to the same heat treatment. The so-obtained stresses for all specimens examined during the tensile test and for both phases are presented in Tables 4 and 5, for the Al/SiC_p-T1 and Al/SiC_p-T6 specimens, respectively. It was found that the mean p values calculated over both phases (according to Eq. 3) are approximately equal to zero within the uncertainty range, simultaneously for the initial and deformed samples. This condition is fulfilled for both materials subjected to the treatments T6 and T1 (cf. the first columns in Tables 4, 5). An evolution of the hydrostatic stresses during deformation was also calculated from relative changes of interplanar spacings for the deformed sample with respect to the initial one. Although the latter method does not allow for calculating the absolute values of the hydrostatic stresses, however in the calculations of the relative changes of these stresses \((\Delta p)\) the values of \(a_{0}\) are not required. As shown in the second columns of Tables 4 and 5, the \(\Delta p\) values are very close to the differences between the hydrostatic stresses p for the deformed and initial samples (cf. the first columns). Moreover, the equilibrium law (Eq. 3) applied to the \(\Delta p\) values gives the mean value close to zero (within uncertainty range), i.e. the equilibrium condition is fulfilled. Therefore, it can be concluded that the values of the hydrostatic stresses p and their changes \(\Delta p\), are correctly determined.

As shown in Tables 4 and 5 the deviatoric phase stresses and their evolution are less significant, when compared with the hydrostatic ones. It was found that the large hydrostatic compressive stress in SiC_p reinforcement and tensile stress in aluminium matrix were generated during T1 or T6 treatment. This effect is caused by a difference in coefficient of thermal expansion (CTE) for the composite components (Table 2), leading to larger volume contraction for aluminium matrix comparing with particles of SiC_p, during the cooling process. On the other hand, small deviatoric stresses in the initial sample are caused by possible temperature gradients in the heat treated sheets as well as plastic deformation during sample machining. Also, it should be stated that the equilibrium condition (Eq. 3) is not strictly fulfilled for the components of deviatoric stresses in the initial samples, probably due the relatively large experimental uncertainties, comparing to small values of these stresses. More pronounced deviatoric stresses, resulting from phase interaction during plastic deformation, were measured after tensile test. The components of the latter stresses in some approximation fulfil equilibrium condition.

Analysing the results presented in Tables 4 and 5, it can concluded that an important decrease in hydrostatic compressive stress occurred in the SiC_p reinforcement corresponding to the relaxation of initially large thermal stress. Also, the decrease in the hydrostatic part of the mean tensile stress in the Al2124 matrix has been observed as a consequence of stress relaxation around the SiC_p inclusions. The process of stress relaxation has been studied post factum for the already fractured sample, but it is interesting to determine when this phenomenon start to occur. To solve this problem, it is necessary to follow the evolution of the stresses and lattice strains measured in situ during the deformation tests.

The lattice strain evolutions in the Al and SiC_p phases along the direction of applied load \(\left\langle {\varepsilon_{11} } \right\rangle_{{\left\{ {hkl} \right\}}}\) and in the perpendicular direction \(\left\langle {\varepsilon_{22} } \right\rangle_{{\left\{ {hkl} \right\}}}\) (Eq. 1) were determined in situ using configuration with two detectors shown in Fig. 3a and compared with EPSC model (Figs. 6, 7, 8). Model calculations were performed up to the maximum sample strain (i.e. E₁₁ = 3%), followed by sample fracture/unloading with values of the CRSS \((\tau_{c} )\) and hardening parameter (H), determined previously for the studied materials on the basis of the mechanical curves (Table 3). It should be mentioned that the macrostrains of the fractured composite samples were unknown, therefore the experimental points (lattice strains) for the broken samples were placed in Figs. 7 and 8 close to the plastic macrostrain predicted by model after unloading of the sample.

A very good result of the experiment—model comparison was found for the relative lattice strains (cf. Eq. 1) measured for the Al2124-T6 specimen under the tensile load both in the elastic and elastic–plastic range of deformation up to E₁₁ = 3%. The model predicted values of lattice strains are slightly overestimated during the tensile test, but for the unloaded sample the modelling calculations hit the experimental points correctly (Fig. 6). The lattice strain evolution for different hkl reflections confirms that the EPSC model correctly predicts the partitioning of stresses between the grains in the Al2124-T6 alloy and well reproduces the anisotropy of plastic deformation for the different groups of grains, cf. [9, 42‐44].

To solve the problem of stress partitioning between phases, the lattice strains measured in situ in the SiC_p and in Al2124 constituents of the composite during the tensile test were analysed. The important influence of the evolution of mean values of lattice strain along loading direction measured for reflections 200, 111, 220, 311 in aluminium matrix and for reflections 006/102, 108/110, 202/116 in SiC reinforcement is visible in Fig. 7. In this figure, the results for the sample subjected to the treatments T6 and T1 are shown. The experimentally measured relative lattice strains were determined using Eq. 1 and then the strains caused by initial stresses (cf. Tables 4, 5) were superimposed. Subsequently, the lattice strains were calculated using the EPSC model with two assumptions, i.e. accounting for the initial stresses given in Tables 4 and 5 or setting zero stresses for both phases.

Analysing Fig. 7, it was found that for the elastic deformation, a good agreement between the experiment and model was obtained taking into account the initial stresses, while for the further elastic–plastic deformation much better accordance was observed with zero initial stress assumption (cf. Fig. 7). Therefore, it can be concluded that the initial phase stresses relax at very small tensile deformation (ca. 0.2%–0.8%), and consequently do not influence further stress partitioning and mechanical behaviour of the composite phases. The residual lattice strains in both phases (last points in Figs. 7, 8 obtained for the fractured samples) are also well predicted by the model, assuming zero initial stresses. This results agree well with previous works showing relaxation and complete exchange of stress state in the Al/SiC_p composite and also in other materials subjected to plastic deformation [11, 13, 30, 31]. The new finding of the present work is that the stress relaxation occurs very early i.e. for a small elastic–plastic deformation, close to the yield point of the matrix. It should be also emphasised that the EPSC model does not predict the relaxation of initial phase stresses having mostly a hydrostatic character. This is why in the present research two assumptions were used (i.e. the material with and without initial stresses) to model the complete history of the tensile test.

Finally, in Fig. 8 the lattice strains for individual reflections hkl in both phases of Al/SiC-T6 sample, measured along applied load and in the transverse direction, are shown. The experimental results agree with the model prediction if in the calculation the initial stresses are taken into account for the beginning of deformation (up to about E₁₁ = 0.5% of sample strain), and zero initial stress is assumed for further deformation (above about E₁₁ = 0.5% of sample strain). This can be explained due to the discussed above relaxation of initial stresses in the beginning of plastic deformation.