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Role of Si modification on the compressive flow behavior of Al–Si based alloy
Materials Characterization 110 (2015) 272–281
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Role of Si modification on the compressive flow behavior of Al–Si based alloy Sudha Joseph ⁎, S. Kumar Department of Materials Engineering, Indian Institute of Science, Bangalore 560 012, India
a r t i c l e
i n f o
Article history: Received 13 July 2015 Received in revised form 27 October 2015 Accepted 28 October 2015 Available online 30 October 2015 Keywords: Al–Si alloy Si modification Strain rate sensitivity Finite element modeling Deformation mechanisms
a b s t r a c t The flow characteristics of a near-eutectic heat-treated Al–Si based cast alloy have been examined in compression at strain rates varying from 3 × 10−4 to 102 s−1 and at three different temperatures, i.e., room temperature (RT), 100°C and 200°C. The dependence of flow behavior on modification is examined by testing the alloy in both the unmodified and modified conditions. Modification has strong influence on strain rate sensitivity (SRS), strength and work hardening behavior of the alloy. The strength of the alloy is found to increase with increase in strain rate for both the conditions. The increase is more rapid above the strain rate of 10−1 s−1 for the unmodified alloy at all the temperatures. This rapid increase is observed at 1 s−1 at RT and 100°C, and at 10−2 s−1 at 200°C for the modified alloy. The thermally dependent process of the Al matrix is rate controlling in the unmodified alloy. On the other hand, the thermally dependent process of both Al matrix and Si particles are rate controlling, which is responsible for the higher strain rate sensitivity (SRS) in the modified alloy. The unmodified alloy exhibits a larger work hardening rate than the modified alloy during the initial stages of straining due to fiber loading of unmodified Si particles. However, the hardening rate decreases sharply at higher strains for the unmodified alloy due to a higher rate of Si particle fracture. Thermal softening is observed for both alloys at 200 °C due to precipitate coarsening, which leads to a decrease in SRS at higher temperatures. Stress simulations by microstructure based finite element method support the experimentally observed particle and matrix fracture behavior. Negative SRS and serrated flow are observed at lower strain rate regime (3 × 10−4 to 10−2 s−1) at RT and 100°C, in both alloys. The critical onset strain is found to be lower and the magnitude of serration is found to be higher for the modified alloy, which suggests that, in addition to dynamic strain aging, Si particle size and morphology also play a role in serrated flow. © 2015 Elsevier Inc. All rights reserved.
1. Introduction Hypoeutectic and near eutectic Al–Si alloys are widely used in the automotive industry owing to their excellent foundry characteristics and good mechanical properties. These alloys typically contain 6– 12 wt.% Si and, given that the maximum solubility of Si in Al is 0.05 wt.% at room temperature (RT), excess Si will exist in the form of large particles in the eutectic providing strength to the alloy. Alloying elements, such as, Cu and Mg are also added to the alloy to increase strength by the formation of precipitates on heat treatment. The microstructure of the alloy is primarily characterized by two phases: low strength ductile α-Al and a eutectic consisting of α-Al and high strength brittle Si particles, the α-Al phase acts as a matrix for Si particles. The flow behavior of the alloy is dictated by the behavior of these constituent phases, i.e., the work hardening of the ductile matrix, which in turn depends on the type of heat treatment and work softening due to fracture of Si particles, which depends on the intrinsic strength of Si ⁎ Corresponding author at: Department of Materials, Imperial College London, South Kensington Campus, London SW7 2AZ, UK. E-mail address: [email protected] (S. Joseph).
http://dx.doi.org/10.1016/j.matchar.2015.10.036 1044-5803/© 2015 Elsevier Inc. All rights reserved.
particles and the load transferred to the particles from the matrix. The fracture of Si particles limits the ductility of the alloy [1–6], even though these particles impart high strength. Si modification is found to have an impact in determining the fracture behavior and ductility of the alloy [1,3–6]. It is reported that the size of the largest Si particles controls the ductility of the alloy [3]. Yet another viewpoint is that the ductility of unmodified alloys is controlled by the mean size of the Si particles, whereas that of modified alloy is determined by their distribution [4]. Fracture of Si particles also depends on orientation and volume fraction of Si particles [3–6]. The authors of this manuscript have carried out a detailed investigation on a near-eutectic Al–Si based alloy and have reported the effects of heat treatment [7] and Si modification [8] on particle fracture under compression. The important conclusions were: 1) particle fracture increases with heat treatment and 2) fracture is more in unmodified particles and particles oriented nearly perpendicular to the loading axis. Particle size refinement and homogenization of distribution are known to improve fracture resistance [9,10]. The reduced load carrying capacity on fracture of Si particles affects the overall load carrying capacity and work hardening of the alloy [11,12]. These effects can play an important role in the determination of the mechanical instability. Fracture occurs when a critical level of damage takes place [13]. The
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increase in flow stress near the fractured particle in the matrix leads to a greater load transfer to the neighboring particles, thereby increasing the rate of damage development [14]. Heat treatment given to the alloy modifies the matrix microstructure and hence controls the rate of particle damage. The modification of Si particles is found to reduce particle fracture, since there is no fiber loading when the particles are small and globular [8]. Extensive experimental results are available on the flow behavior of Al–Si based alloys, but are mainly restricted to tensile loading. Results are also available for the independent effects of strain rate [15] and temperature [14,16]. However, the exact deformation mechanisms responsible for the observed flow behavior are not explained in detail. To our knowledge, there is no literature available on the combined effect of strain rate and temperature under compression. The effect of heat treatment on the compressive flow behavior of Al–Si alloy at different strain rates and temperatures is reported in a recent publication of the present authors [17]. The present manuscript discusses the role of Si modification on the compressive flow behavior of Al–Si based alloy. This work further explores the effect of strain rates and temperatures on the compressive response of the alloy. The deformation mechanisms responsible for the observed flow and hardening behavior of the alloy are elucidated in detail. Serrated flow is also investigated, which is related to the strain rate sensitivity of the alloy.
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2. Experimental work
technique and examined under a FEI scanning electron microscope (SEM). The samples were subjected to orientation imaging microscopy using a FEI-SIRION® field emission gun SEM having Electron Back Scattered Diffraction (EBSD) facility. For EBSD analysis, a final polishing in the colloidal silica suspension was carried out after the standard metallographic procedure. The samples were also examined under 300 kV field emission TEM-STEM (FEI Tecnai F30) equipped with EDX. Samples of 3 mm discs for TEM analysis were thinned down to 100 μm by mechanical polishing and then final polishing was done in a Gatan precision ion polishing system (PIPS) using argon ions. Quantitative metallography using Sigma ScanPro image analyzer was carried out to calculate the fraction of fractured particles. Measurements were carried out over a large area of approximately 2 × 10 6 μm 2 at different strains (10%, 20% and 30%), strain rates (3 × 10− 4 , 10 − 1 , 1 s − 1 , 10 1 and 102 s − 1 ) and temperatures (RT, 100°C and 200°C). Measurements were made on the surface parallel to the compression axis at the center of the sample. Each quantitative measurement was performed on at least 50 fields of view per sample at a magnification of 500 ×. The effect of strain was studied at the lowest strain rate of 3 × 10 − 4 s− 1 and RT, the effect of strain rate was studied at RT and 10% strain and the effect of temperature was studied at the lowest strain rate of 3 × 10− 4 s− 1 and 10% strain. In each field of view, the number of damaged Si particles was counted manually, and the total number of Si particles was counted by using automatic digital image analysis.
2.1. Material and heat treatment
2.4. Microstructure based modeling
As-cast and heat treated Al–Si–Cu–Mg based alloy samples were supplied by GM (General Motors), USA, in unmodified and modified conditions. The chemical composition and heat treatment given to the material can be found elsewhere [8].
The stress evolution in the different phases (Al matrix and Si particles) of the alloy was studied by finite element methods. The process for conducting the analysis is shown in Fig. 1, of Ref. [19]. The Al matrix was modeled as an isotropic elasto-plastic solid with Young's modulus EAl = 70 GPa and Poisson's ratio of 0.3. The experimentally obtained properties of the Al matrix from micro-hardness tests (Section 2.2) were assigned to describe the plastic behavior of the matrix. The isotropic linear elastic properties were assigned to Si particles with Young's modulus ESi = 130 GPa and Poisson's ratio 0.28 [20]. The meshed microstructure was subjected to uniaxial compression to 3% strain. The maximum principal stress in Si particles and the equivalent plastic strain (PEEQ) in the matrix were considered as the output parameters of the numerical analysis.
2.2. Mechanical tests Cylindrical compression samples with 15 mm height and 10 mm diameter were machined from the cast plates. The two flat faces of the compression samples were lubricated with MoS2 to reduce friction during compression. The compression tests were carried out under a displacement controlled Dartec servo hydraulic machine at seven different strain rates, viz., 3 × 10−4, 10−3, 10−2, 10−1, 1, 101 and 102 s−1 and three different temperatures, viz., RT, 100 °C and 200°C. Prior to compression, the specimens were heated to the desired temperature and soaked for approximately 10 min. Three samples were tested at each test conditions to obtain reliable data. At each strain rate and temperature, the samples were compressed up to failure. The samples were compressed to 10%, 20% and 30% strain for microstructural quantification, if they did not fail before the respective strain. To understand the hardening behavior of Al matrix at different strain rates and temperatures, hardness tests were carried out on the samples. The indentation was carried out using CSM microhardness tester with 10 μm size spherical indenter. The sample was carefully indented on Al matrix at different strain rates, viz., 3 × 10− 4, 10− 2, 10− 1 and 1 s−1. At each strain rate, the indentations were made at three different temperatures RT, 100°C and 200°C. Under each test condition, a series of indentations were made at a progressively increasing load and five indents were made to get a reliable value. Yield strength was obtained by taking one-third of the hardness value and the hardening exponent was obtained by calculating Meyer's index [18]. 2.3. Metallography Microstructural analyses were carried out in as-received condition and after compression. After the compression tests, the samples were sectioned along the central vertical plane containing the applied load direction. They were then polished using standard metallographic
3. Results 3.1. As-cast microstructure The typical as-cast microstructure of the alloys is shown in Fig. 1. The typical morphology of Si particles in the eutectic region of the alloy in the unmodified and modified conditions can be seen in Fig. 1(a) and (b) respectively. The eutectic Si particles in the unmodified alloy are present in the form of a plate-like structure in 3D, which manifests itself as long elongated particles on 2D metallographic sections. In the modified alloy, the eutectic Si particles are more globular with more than half of the particles having aspect ratio between 1 and 2. The TEM analysis of the precipitates present in the Al matrix of the alloy is depicted in Fig. 2. Fig. 2(a) shows the TEM image of precipitates along [001]Al zone axis. The HRTEM image of these precipitates in Fig. 2(b) shows the (200) crystallographic planes of Al with interplanar spacing of d200 = 2.02 Å and sets of Moiré fringes due to double diffraction between Al matrix and precipitates. From the spacing between the Moiré fringes (DM) and the angle it makes with the matrix (ω), the d spacing of the precipitate can be calculated using the following formula [21]. 1 1 ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi dp 2 2 jdAl j þ jDM j −2jdAl jjDM j cosω
ð1Þ
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Fig. 1. SEM micrograph showing the eutectic region of Al–Si based alloy in (a) unmodified and (b) modified conditions.
where dp is the interplanar spacing of the precipitate and dAl is the interplanar spacing of Al matrix. Two different types of Morié fringes can be seen in Fig. 2(b) with spacing marked as DMI and DMII. The Morié fringes of type I show a d spacing of 13.3 Å, which matches only with the (003) spacing of Al7Cu4Ni [22]. They are spherical in shape with 4– 6 nm in size. The type II Morié fringes correspond to S′ precipitates and have two variants, i.e., (021)Al//(001)S′ and (021)Al//(001)S′ [23]. The precipitates along [011]Al zone axis shown in Fig. 2(c) are plate shaped parallel to {111} planes of Al, 3–7 atomic layers thick and 5–
6 nm long. They are also found to be coherent with the matrix. These precipitates consist of two variants formed along the [111] and [111] directions of Al, as is evident from the image and the diffraction pattern. The FFT (which is shown as an inset) shows streaks in the directions normal to the habit planes of the zones, reflecting the shape of the precipitates. Dark contrast of the zones might be due to the segregation of atoms, which have higher atomic scattering amplitude for electrons [24]. Both Cu and Mg are expected to aggregate along these planes, which acts as a precursor to S′ phase. Fig. 2(d) shows the large
Fig. 2. (a) Bright field image of the precipitates along [001]Al zone axis, (b) HRTEM image showing Moiré fringes due to precipitates along [001]Al zone axis, (c) HRTEM image along [011]Al zone axis showing plate shaped zones on {111} planes of Al and (d) HRTEM image showing coherency strains around the zone.
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coherency strains around the zone, which is due to the bending of planes around the precipitate. 3.2. Compression test results 3.2.1. Strength of the alloy The typical stress–strain curves of the alloy with unmodified and modified particles are shown in Fig. 3(a). The effect of strain rate and temperature can also be seen in this figure. It is clear that modification improves both strength and ductility of the alloy. The effect of strain rate and temperature on 0.2% proof stress (PS) can be more clearly seen in Fig. 3(b). The 0.2% PS increases on modification and it increases with increase in strain rate, in general. Above a certain strain rate, the increase is found to be steeper, which is being termed here as transition strain rate. The unmodified alloy exhibits this transition at 10−1 s−1 at all the three temperatures studied. The modified alloy exhibits the transition at 1 s−1 at RT and 100 °C, and at 10−2 s−1 at 200 °C. It is also observed that the modified alloy exhibits higher SRS than the unmodified alloy. The 0.2% PS decreases with increase in temperature for both the alloys, as expected. The decrease is steeper from 100 °C to 200 °C than from RT to 100 °C for both the alloys. Further, the SRS decreases with increase in temperature for both the alloys. 3.2.2. Work hardening behavior of the alloy Work hardening rate of the alloy is determined by numerically differentiating the experimentally obtained stress–strain data. Fig. 4 shows the work hardening rate θ (dσ/dε) as a function of normalized stress (σ/σy) for the unmodified and modified alloys at a quasi-static strain rate of 3 × 10−4 s−1 and RT. The curves begin immediately after yielding and get truncated at the peak stress. Initial hardening rate is higher for both the alloys and it decreases with stress. Between the two alloys, it is higher for the unmodified alloy and the decrease with stress is also more rapid for this alloy. Both alloys show a plateau region where the hardening rate is nearly zero. Further, this plateau region is prolonged for the modified alloy (for σ/σy ≥ 2.75) as compared to the unmodified alloy (for σ/σy ≥ 2). The σ/σy value beyond which the region is considered to be the plateau region is shown by the vertical dotted lines in the figure. The effect of strain rate on the hardening behavior of the alloys in the unmodified and modified conditions at RT is shown in Fig. 5(a) & (b) respectively. In general, the initial hardening rate increases with increase in strain rate and the hardening rate decreases with increase in stress for both alloys. The decrease in hardening rate with stress is steeper for strain rates above 10− 1 s− 1 (i.e., for strain rates, 1, 10 and 102 s− 1) than that at strain rates 3 × 10−4 s−1 and 10−1 s−1 for the unmodified alloy, as shown in Fig. 5(a). For the modified alloy, the hardening rate curves are steeper for strain rates 10 and 102 s−1 than those observed at 3 × 10−4, 10−1 and 1 s−1. Thus, the hardening rate curves of both alloys are found to be strain rate sensitive at RT and it becomes steeper
Fig. 4. Work hardening rate as a function of normalized stress showing the effect of Si modification.
above 10−1 s−1 for the unmodified alloy and above 1 s−1 for the modified alloy. The hardening behavior of the alloys at different temperatures for the lowest strain rate 3 × 10−4 s−1 is shown in Fig. 6(a & b). The initial hardening rate decreases with increase in temperature and the hardening rate decreases with increase in stress for both the alloys. The decreasing trend is almost the same at RT and 100 °C but it falls rapidly at 200 °C. 3.2.3. Negative strain rate sensitivity and serrated flow Serrations were observed in the flow (σ–ε) curves of the alloys in unmodified and modified conditions in the lower strain rate regimes, from 3 × 10−4 s−1 to 10−2 s−1, at RT and 100°C. Serrations observed in σ–ε curves for both the alloys at 3 × 10−4 s−1 and RT is shown in Fig. 7(a). The SRS, m, of flow stress at 10% strain was evaluated from the σ–ε data of the compression tests using the following relation. m¼
logðσ 2 =σ 1 Þ logðε_ 2 =ε_ 1 Þ
ð2Þ
where, σ1 and σ2 are the flow stresses at strain rates ε_ 1 and ε_ 2respectively. The SRS variation is shown in Fig. 7(b). It can be seen that the SRS values are close to zero or negative in the lower strain rate regime (3 × 10−4, 10−3 and 10−2 s−1) at RT and 100°C. Serrated flow is characterized by critical onset plastic strain εc, i.e., the value of plastic strain at which serrated flow starts, and the average magnitude of stress drop Δσavg. The variation of εc and Δσavg (in the strain range of 10% to 15%) with ε_ at RT and 100°C is shown in Fig. 8(a) for the two alloys within the serrated flow regime. It can be seen that εc increases with increase
Fig. 3. (a) Representative stress–strain curves of the alloy showing the effect of Si modification, strain rate and temperature and (b) effect of strain rate on 0.2% proof stress at different temperatures.
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Fig. 5. Effect of strain rate on work hardening rate as a function of normalized stress at RT in (a) unmodified and (b) modified conditions.
Fig. 6. Effect of temperature on work hardening rate as a function of normalized stress at a strain rate of 3 × 10−4 s−1 in (a) unmodified and (b) modified conditions.
in ε_ and decreases with increase in T for both alloys. The εc value is found to be lower for the modified alloy as compared to the unmodified alloy at all the strain rates and temperatures. The variation of Δσavg with ε_ at RT and 100°C within the serrated flow regime is shown in Fig. 8(b). It is observed that Δσavg decreases with increase in ε_ and increases with increase in T. Further, Δσavg value is observed to increase on modification.
3.3. Hardness test results 3.3.1. Strength of the matrix To understand the flow behavior of the Al matrix under different loading conditions, microhardness tests were carried out on the matrix region of the alloy. Since both the unmodified and modified alloys are given the same heat treatment, the properties expected in the matrix of both alloys are same. Hence, the properties of the matrix of only the unmodified alloy are examined and the results are given in this section.
Yield strength values of the matrix (σym) calculated from microhardness tests are shown in Fig. 9. From the figure it is clear that the matrix is strain rate sensitive at all temperatures, i.e., the yield strength value increases with increase in strain rate at all temperatures. Further, the rate of increase of σym with strain rate decreases with temperature. 3.3.2. Work hardening behavior of the matrix A series of indentations were made in Al matrix at progressively increasing loads and the size of the indentation was measured at each load. Meyer [18] proposed an empirical relation between the load and the size of the indentation: n0
P ¼ kd
ð3Þ
where P is the applied load, d is the diameter of indentation, k is a material constant and n′ is Meyer's index. The parameter n′ is the slope of the straight line obtained from log P vs. log d plot. This Meyer's index n′
Fig. 7. (a) Typical true stress–true strain plots showing the serrations in unmodified and modified conditions at 3 × 10−4 s−1 & RT and (b) variation of strain rate sensitivity, m, with temperature at 10% strain.
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Fig. 8. Variation of (a) critical onset plastic strain and (b) average stress drop with strain rate at different temperatures in unmodified and modified conditions.
is related to the hardening exponent of the material n by n′ = n + 2. Using this relation, the value of n is obtained at different strain rates and temperatures, which is shown in Table 1. It can be seen that the n value of matrix decreases with increase in both strain rate and temperature. 3.4. Particle fracture The effect of strain, strain rate and temperature on the fraction of fractured Si particles is shown in Fig. 10. The other test conditions are shown in the inset of the figure. For all the test conditions, the unmodified alloy shows a greater number of Si particles fracturing than in the modified alloy. Particle fracture increases with increase in strain and it increases more rapidly in the unmodified alloy than in the modified alloy, as shown in Fig. 10(a). The particle fracture is very less at 10 & 20% strains in the modified alloy and increases rapidly at 30% strain. From Fig. 10(b), it is clear that the particle fracture increases after 10−1 s−1 in the unmodified condition and after 1 s−1 in the modified condition. Particle fracture decreases with temperature, as shown in Fig. 10(c). The decrease is lesser from RT to 100 °C than from 100 °C to 200 °C for both alloys. 3.5. Predictions from microstructure based modeling Following the procedures mentioned in Section 2.4, finite element simulations are performed and the results are presented here. The maximum principal stress distribution in Si particles under a uniaxial compressive strain of 3% is shown in Fig. 11(a–d). The other test conditions are also given in the inset of the figure. The stress distribution in Si particles for the unmodified and modified alloys can be compared by comparing Fig. 11(a) and (b) and (c) and (d). It can be seen that the
stress in the particles is higher in the unmodified alloy than in the modified alloy. The simulations have been carried out at different strain rates, viz., 3 × 10−4, 10−2, 10−1 and 1 s−1 and at different temperatures, viz., RT, 100°C and 200°C. For brevity, the results are shown only for 3 × 10−4 & 1 s−1 strain rates and RT & 200°C temperatures. The effect of strain rate on stress values can be seen by comparing Fig. 11(a) and (c) for the unmodified alloy and by comparing Fig. 11(b) and (d) for the modified alloy. The stress in particles increases with increase in strain rate for both the alloys. Plastic strain in the matrix of the unmodified alloy at RT and 200 °C is shown in Fig. 11(e) and (f), respectively. Plastic strain is found to be quite inhomogeneous and shear can be seen in the matrix at higher temperatures. 4. Discussion 4.1. Stress–strain response The alloy shows a rapid increase of flow stress with applied strain in lower strain regimes for ε ≤ 5%, as shown in Fig. 3(a). This is due to the resistance offered by the second phase Si particles to the flow of Al matrix, which results in high work hardening rate [13,25–27]. The pile-up of dislocations against Si particles happens when the particles are either unmodified or modified, but the dislocation interaction with the unmodified particles is less significant. The pile-up of dislocations against Si particles in the modified alloy can be seen in Fig. 12(a). The unmodified Si particles merely act as load bearing constituent of the alloy. The load transfer to the modified particles will not be as efficient as in the case of unmodified particles due to the lower aspect ratio and larger number density of the globular particles. This is the reason for the observed higher initial hardening rate in the case of unmodified alloy (Fig. 4). Furthermore, the additional resistance is offered by the nanosized Al2CuMg and Al7Cu4Ni precipitates, which form during heat treatment in both the alloys. The precipitate-dislocation interaction in the alloy is shown in Fig. 12(b). This figure contains some striking features of dislocation-precipitate interaction mechanisms. Most of the dislocations are pinned by the nano-size precipitates. The dislocations are bowed between precipitates, under the effect of the applied stress. Precipitates are located using both loss of contrast on dislocation lines and curvature of dislocation segments. The dislocations, which are pinned by the precipitates, overcome obstacles and propagate in its slip plane
Table 1 Hardening exponent of A1 matrix obtained from micro-hardness test. n value at different strain rates at RT 3 × 10−4 s−1 0.177
Fig. 9. Effect of strain rate and temperature on yield strength of Al matrix obtained from microhardness test.
10−2 s−1 0.137
1 s−1 0.117
n value at different temperatures at a strain rate of 3 × 10−4 s−1 RT 100°C 200°C 0.177 0.105 0.01
102 s−1 0.063
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Fig. 10. Fraction of fractured Si particles as a function of (a) strain, (b) strain rate and (c) temperature.
Fig. 11. Results of microstructure based modeling (a, b, c & d) Maximum principal stress distributions in Si particles and (e & f) Equivalent plastic strain in the matrix. The test conditions are given in the inset of the figures.
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Fig. 12. TEM micrograph of the alloy showing the (a) pile-up of dislocations against modified Si particles, (b) pinning of dislocations by the hardening precipitates in a sample deformed at 10−1 s−1–RT–5% strain and (c) dislocations in sample deformed at 1 s−1–RT–5% strain.
before being stopped again by other precipitates. If displacements occur with no loop formation, it is assumed that dislocations shear the precipitates. The shearing of precipitates could not be directly observed in this alloy. Further straining results in a decrease in hardening rate with strain. This lower strain hardening can be seen above 10% strain for a sample deformed at 3 × 10−4 s−1 and RT in Fig. 3(a). The decrease in work hardening rate with stress can be clearly seen in Fig. 4. This decrease is found to be more rapid for the unmodified alloy than the modified alloy. The unmodified Si particles in these alloys act as a main load bearing constituent and fracture when fracture strength of particles is
reached. The Si particle fracture in the alloy is found to start at lower strains in the unmodified alloy than in the modified alloy due to significant load transfer to the unmodified particles, and decreases the load carrying capacity of the alloy. Once a Si particle fractures, the matrix surrounding it experiences higher load. The EBSD analysis of a sample after 10% strain is shown in Fig. 13. We can observe localized strains in the region where Si particles have fractured. This strain is due to the extra load transferred to the surrounding matrix after fracture of a particle. In addition, precipitate shearing also takes place at higher strains, even though it offers resistance to dislocation motion during initial stages of straining in both the unmodified and modified alloys. So, the matrix
Fig. 13. (a) Orientation imaging map and (b) Kernel Average Misorientation (KAM) showing strained regions in the Al matrix in unmodified condition at 10% strain.
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gets softened at higher strains and it cannot support the load. The extra load will be transferred to the neighboring particles, which leads to higher rate of particle fracture. The higher rate of damage accumulation for the unmodified alloy can be seen in Fig. 10(a) in terms of a larger fraction of broken particles with strain. The decrease in hardening rate with stress for the modified alloy is not as sharp as for the unmodified alloy. In both the cases, matrix softening will be there due to precipitate shearing, but the rate of particle fracture will be lower in the modified alloy than in the unmodified alloy (shown in Fig. 10(a)), since modified particles are not subjected to fiber loading. The stress simulations by FEM described in Section 3.5 also confirm that the load transferred will be lesser in the modified particles. Hence, both matrix softening due to precipitate shearing and Si particle fracture results in decrease in hardening rate at higher strains. The decrease in work hardening rate is steeper in the unmodified alloy due to higher rate of Si particle fracture.
4.2. Effect of strain rate and temperature From Fig. 3(b), it is clear that the 0.2% PS of both the alloys increases with increase in strain rate and the increase is sharper after certain strain rates. This transition is observed at 10−1 s−1 for the unmodified alloy at all temperatures. The modified alloy shows this transition at 1 s−1 at RT and 100°C and at 10− 2 s− 1 at 200°C. These observations show that the alloy is strain rate sensitive at all the temperatures whether the Si particles are unmodified or modified. This might be due to the precipitates formed during heat treatment and these precipitates act as obstacles to dislocations. The transition observed in the alloys at RT can be explained as follows. The dislocation arrival at an obstacle depends on the applied strain rate. The dislocation may bypass the obstacle and relieve the stresses accumulated at the obstacle. At lower strain rates (3 × 10−4 to 10−1 s−1 for the unmodified alloy and 3 × 10− 4 to 1 s−1 for the modified alloy), the rate at which dislocations bypass the precipitates is able to match the dislocation arrival rate and relieve the stress accumulation at the precipitate. On the other hand, at higher strain rates (1 to 102 s−1 for the unmodified alloy and 101 and 102 s−1 for the modified alloy) the dislocation arrival rate becomes greater than the rate at which dislocations bypass the precipitates. Hence, at higher strain rates, there is an accumulation of dislocations, which results in increase in flow stress values. The schematic in Fig. 14 depicts the situation at low and high strain rate deformations. The dislocations observed in the samples deformed at 10−1 s−1 and 1 s−1 are shown in Fig. 12(b and c). It can be seen that the dislocation accumulation is higher in samples deformed at 1 s−1 than that at 10−1 s−1. The different transition strain rates observed in the unmodified and modified alloys are due
to the interaction of dislocations with Si particles in addition to dislocation-precipitate interaction in the modified condition. The critical strain rate above which the transition can occur, has the following relationship with temperature [28]. ε_ c ¼
αDv Gab 3
d kT
ð4Þ
where, α is a constant, Dv is bulk diffusivity, a is atomic volume, b is Burgers' vector, d is precipitate size, k is Boltzmann constant and T is temperature. This equation shows that the transition will occur at lower strain rates for higher temperatures. The modified alloy shows a decrease in the transition strain rate with increase in temperature according to Eq. (4). The transition is observed at 1 s− 1 at RT and 100°C, whereas the transition occurs at 10−2 s−1 at 200°C. However, the unmodified alloy does not show a decrease in transition strain rate with increase in temperature in the temperature regimes studied. In this alloy, this may occur at temperatures, which are not covered in the present analysis. Further, the SRS of 0.2% PS decreases with increase in temperature for both alloys. Coarsening of precipitates at higher temperatures is responsible for this behavior. There is a strong effect of strain rate on the hardening behavior of both the alloys, as shown in Fig. 5. The hardening curves in Fig. 5(a) and (b) shows a sharp decrease in hardening rate above 10− 1 s−1 for the unmodified alloy and above 1 s− 1 for the modified alloy at RT. As explained earlier, the dislocation accumulation rate, annihilation rate and precipitate size are responsible for this transition. The strain rate sensitivity of both the matrix and modified Si particles are responsible for the observed behavior in the modified alloy, whereas the matrix alone plays a role in the unmodified alloy. The SRS of the matrix can be seen in Fig. 9, in which σym increases with strain rate at all temperatures. Hence, at higher strain rates, a greater load will be transferred to the Si particles, which results in a greater number of particle fracture at higher strain rates, as observed in Fig. 10(b). The stress simulation in Si particles by FEM (Fig. 11(c and d)) also confirms this fact. The work hardening rate decreases with increase in temperature for both alloys (Fig. 6(a) and (b)) and the decrease is greater at higher temperatures. This might be due to matrix softening by precipitate coarsening. It can be seen in Fig. 11(f) that the alloy exhibits matrix shear at 200°C. The load transferred to the particles by the softened matrix is lower and the particle fracture also decreases with increase in temperature in the unmodified alloy (Fig. 10(c)). In the modified alloy, the dislocations accumulated at particles are relaxed thermally, instead of cutting the particles. Hence, the strain rate and temperature sensitivity of the unmodified alloy is controlled by the matrix microstructure. The unmodified Si particles merely act as obstacles to the flow of the matrix. On the other hand, in the modified alloy, both the matrix and Si particles play a role. 4.3. Serrated flow
Fig. 14. Schematic showing dislocation–precipitate interactions at low and high strain rates.
Negative SRS (nSRS) is observed in the lower strain rate regimes (3 × 10−4 to 10−2 s−1) at RT and 100°C for both the alloys, and serrated flow is also observed in the same strain rate and temperature regimes. Serrated flow has been found to be invariably accompanied by nSRS in the literature [29], which is commonly attributed to dynamic strain aging (DSA) mechanism, i.e., the interaction between mobile dislocations and dissolved solute atoms, originally proposed by Cottrell [30]. McCormick and van den Beukel further developed a model to demonstrate how DSA can give rise to nSRS [31,32]. Critical onset strain of serrated flow (εc) increases with increase in strain rate and decreases with increase in temperature (Fig. 8a). The magnitude of serrations (Δσavg) decreases with increase in strain rate and increases with increase in temperature (Fig. 8b). This is the normal serrated flow behavior, which can be explained by the DSA mechanism [30–32]. An increase in strain rate increases dislocation velocity,
S. Joseph, S. Kumar / Materials Characterization 110 (2015) 272–281
resulting in an increase in strain at which solute atoms are able to diffuse to dislocations and pin them, giving rise to serrated flow. On the other hand, an increase in temperature increases the diffusivity of solute atoms, thereby lowering the strain at which they can diffuse to dislocations and pin them, giving rise, again, to serrated flow. This kind of strain rate and temperature dependence of εc has been reported for several alloys exhibiting serrated flow in the literature. The value of εc is found to be lower and Δσavg is found to be higher for the modified alloy as compared to the unmodified alloy at all strain rates and temperatures. Thus, it appears that the size and morphology of Si particles also affects serrated flow. 5. Conclusions The compressive flow behavior of Al–Si based cast alloy is characterized in the unmodified and modified conditions. The effect of strain rate and temperature is also investigated. The deformation mechanisms responsible for the flow behavior are explained. The following conclusions can be drawn from the present investigation: • Modification is found to increase the strength and SRS of the alloy at all temperatures studied. The thermally dependent processes of both the Al matrix and Si particles are rate controlling, which are responsible for the higher SRS in the modified alloy. On the other hand, the thermally dependent process of the matrix alone is rate controlling in the unmodified alloy. • The SRS of both the unmodified and modified alloys decreases with increase in temperature due to precipitate coarsening. • The initial work hardening rate is higher in the unmodified alloy than in the modified alloy due to fiber loading of unmodified particles. The hardening rate decreases sharply at higher strains in the unmodified alloy due to the higher rate of Si particle fracture. • Work hardening rate of both the alloys decreases sharply at 200°C due to precipitate coarsening. • Microstructure based finite element simulations support the experimentally observed particle and matrix fracture behavior at all the strain rates and temperatures studied. • Serrated flow seems to be also affected by the size and morphology of Si particle. • All observations made suggest that the properties are matrix microstructure dominated and Si particles merely act as obstacles to the flow of the matrix in the unmodified alloy. Both matrix and Si particles dictate the properties in the modified alloy.
References [1] C.H. Caceres, C.J. Davidson, J.R. Griffiths, The deformation and fracture behavior of an Al–Si–Mg casting alloy, Mater. Sci. Eng. A 197 (1995) 171–179. [2] D.S. Wilkinson, E. Maire, J.D. Embury, The role of heterogeneity on the flow and fracture of two-phase materials, Mater. Sci. Eng. A 233 (1997) 145–154. [3] J.C. Jaquet, 2nd Int. Conf. on Molten Aluminium Proc., Orlando, FL, 1989, American Foundrymen's Society, Des Plaines, IL, 1989 (paper 2–1).
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[4] C.W. Meyers, A. Saigal, J.T. Berry, Fracture related properties of A357–T6 cast alloy and their interrelation with microstructure, AFS Trans. 91 (1983) 281–288. [5] M.F. Hafiz, T. Kobayashi, A study on the microstructure–fracture behavior relations in Al–Si casting alloys, Scr. Metall. Mater. 30 (1994) 475–480. [6] G. Guiglionda, W.J. Poole, The role of damage on the deformation and fracture of Al– Si eutectic alloys, Mater. Sci. Eng. A 336 (2002) 159–169. [7] S. Joseph, A. Tewari, S. Kumar, The fracture characteristics of a near eutectic Al–Si based alloy under compression, Metall. Mater. Trans. A 44 (2013) 2358–2368. [8] S. Joseph, S. Kumar, A systematic investigation of fracture mechanisms in Al–Si based eutectic alloy—effect of Si modification, Mater. Sci. Eng. A 588 (2013) 111–124. [9] A.K. Vasudevan, O. Richmond, F. Zok, J.D. Embury, The influence of hydrostatic pressure on the ductility of Al–SiC composites, Mater. Sci. Eng. A 107 (1989) 63–69. [10] Y. Brechet, J. Newell, S. Tao, J.D. Embury, A note on particle comminution at large plastic strains in Al–SiC composites, Scr. Metall. Mater. 28 (1993) 47–51. [11] W.J. Poole, E.J. Dowdle, Experimental measurements of damage evolution in Al–Si eutectic alloys, Scr. Mater. 39 (1998) 1281–1287. [12] M.T. Kiser, F.W. Zok, D.S. Wilkinson, Plastic flow and fracture of a particulate metal matrix composite, Acta Mater. 44 (1996) 3465–3476. [13] C.H. Caceres, J.R. Griffiths, Damage by the cracking of silicon particles in an Al–7Si– 0.4Mg casting alloy, Acta Mater. 44 (1996) 25–33. [14] E. Rincon, H.F. Lopez, M.M. Cisneros, H. Mancha, Temperature effects on the tensile properties of cast and heat treated aluminum alloy A319, Mater. Sci. Eng. A 519 (2009) 128–140. [15] M.D. Dighe, A.M. Gokhale, M.F. Horstemeyer, D.A. Mosher, Effect of strain rate on damage evolution in a cast Al–Si–Mg base alloy, Metall. Mater. Trans. A 31 (2000) 1725–1731. [16] A.M. Gokhale, M.D. Dighe, M. Horstemeyer, Effect of temperature on silicon particle damage in cast microstructure of A356 alloy, Metall. Mater. Trans. A 29 (1998) 905–908. [17] S. Joseph, S. Kumar, P. Babu, Compressive flow behavior of Al–Si based alloy: role of heat treatment, Mater. Sci. Eng. A 629 (2015) 41–53. [18] E. Meyer, Untersuchungen über härteprüfung und härte Brinell methoden, Z. Ver. Deut. Ing. 52 (1908) 645–835. [19] S. Joseph, S. Kumar, V.S. Bhadram, C. Narayana, Stress states in individual Si particles of a cast Al–Si alloy: micro-Raman analysis and microstructure based modeling, J. Alloys Compd. 625 (2015) 296–308. [20] K. Gall, M. Horstemeyer, D.L. McDowell, J. Fan, Finite element analysis of the stress distributions near damaged Si particle clusters in cast Al–Si alloys, Mech. Mater. 32 (2000) 277–301. [21] M. Klimenkov, S. Nepijko, H. Kuhlenbeck, H.-J. Freund, Transmission electron microscopic investigation of an ordered Al2O3 film on NiAl(110), Surf. Sci. 385 (1997) 66–76. [22] M.G. Bown, The structure of rhombohedral T(NiCuAl), Acta Crystallogr. 9 (1956) 70–74. [23] Z.Q. Feng, Y.Q. Yang, B. Huang, X. Luo, M.H. Li, M. Han, M.S. Fu, Variant selection and the strengthening effect of S precipitates at dislocations in Al–Cu–Mg alloy, Acta Mater. 59 (2011) 2412–2422. [24] P.B. Hirsch, A. Howie, R.B. Nicholson, D.W. Pashley, M.J. Whelan, Electron Microscopy of Thin Crystals, R.E. Krieger, Florida, 1977 505. [25] L.M. Brown, W.M. Stobbs, The work hardening of copper-silica I. A model based on internal stresses with no plastic relaxation, Philos. Mag. 23 (1971) 1185–1189. [26] L.M. Brown, W.M. Stobbs, The work hardening of copper-silica II. The role of plastic relaxation, Philos. Mag. 23 (1971) 1201–1233. [27] M.F. Ashby, The deformation of plastically non-homogeneous materials, Philos. Mag. 21 (1970) 399–424. [28] F.J. Humphreys, P.N. Kalu, Dislocation–particle interactions during high temperature deformation of two-phase aluminium alloys, Acta Metall. 35 (1987) 2815–2829. [29] R.A. Mulford, U.F. Kocks, New observations on the mechanisms of dynamic strain aging and of jerky flow, Acta Metall. 27 (1979) 1125–1134. [30] A.H. Cottrell, A note on the Portevin–Le Chatelier effect, Philos. Mag. 44 (1953) 829–832. [31] P.G. McCormick, A model for the Portevin-Le Chatelier effect in substitutional alloys, Acta Metall. 20 (1972) 351–354. [32] A. van den Beukel, Theory of the effect of dynamic strain aging on mechanical properties, Phys. Status Solidi 30 (1975) 197–206.
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Materials Characterization journal homepage: www.elsevier.com/locate/matchar
Role of Si modification on the compressive flow behavior of Al–Si based alloy Sudha Joseph ⁎, S. Kumar Department of Materials Engineering, Indian Institute of Science, Bangalore 560 012, India
a r t i c l e
i n f o
Article history: Received 13 July 2015 Received in revised form 27 October 2015 Accepted 28 October 2015 Available online 30 October 2015 Keywords: Al–Si alloy Si modification Strain rate sensitivity Finite element modeling Deformation mechanisms
a b s t r a c t The flow characteristics of a near-eutectic heat-treated Al–Si based cast alloy have been examined in compression at strain rates varying from 3 × 10−4 to 102 s−1 and at three different temperatures, i.e., room temperature (RT), 100°C and 200°C. The dependence of flow behavior on modification is examined by testing the alloy in both the unmodified and modified conditions. Modification has strong influence on strain rate sensitivity (SRS), strength and work hardening behavior of the alloy. The strength of the alloy is found to increase with increase in strain rate for both the conditions. The increase is more rapid above the strain rate of 10−1 s−1 for the unmodified alloy at all the temperatures. This rapid increase is observed at 1 s−1 at RT and 100°C, and at 10−2 s−1 at 200°C for the modified alloy. The thermally dependent process of the Al matrix is rate controlling in the unmodified alloy. On the other hand, the thermally dependent process of both Al matrix and Si particles are rate controlling, which is responsible for the higher strain rate sensitivity (SRS) in the modified alloy. The unmodified alloy exhibits a larger work hardening rate than the modified alloy during the initial stages of straining due to fiber loading of unmodified Si particles. However, the hardening rate decreases sharply at higher strains for the unmodified alloy due to a higher rate of Si particle fracture. Thermal softening is observed for both alloys at 200 °C due to precipitate coarsening, which leads to a decrease in SRS at higher temperatures. Stress simulations by microstructure based finite element method support the experimentally observed particle and matrix fracture behavior. Negative SRS and serrated flow are observed at lower strain rate regime (3 × 10−4 to 10−2 s−1) at RT and 100°C, in both alloys. The critical onset strain is found to be lower and the magnitude of serration is found to be higher for the modified alloy, which suggests that, in addition to dynamic strain aging, Si particle size and morphology also play a role in serrated flow. © 2015 Elsevier Inc. All rights reserved.
1. Introduction Hypoeutectic and near eutectic Al–Si alloys are widely used in the automotive industry owing to their excellent foundry characteristics and good mechanical properties. These alloys typically contain 6– 12 wt.% Si and, given that the maximum solubility of Si in Al is 0.05 wt.% at room temperature (RT), excess Si will exist in the form of large particles in the eutectic providing strength to the alloy. Alloying elements, such as, Cu and Mg are also added to the alloy to increase strength by the formation of precipitates on heat treatment. The microstructure of the alloy is primarily characterized by two phases: low strength ductile α-Al and a eutectic consisting of α-Al and high strength brittle Si particles, the α-Al phase acts as a matrix for Si particles. The flow behavior of the alloy is dictated by the behavior of these constituent phases, i.e., the work hardening of the ductile matrix, which in turn depends on the type of heat treatment and work softening due to fracture of Si particles, which depends on the intrinsic strength of Si ⁎ Corresponding author at: Department of Materials, Imperial College London, South Kensington Campus, London SW7 2AZ, UK. E-mail address: [email protected] (S. Joseph).
http://dx.doi.org/10.1016/j.matchar.2015.10.036 1044-5803/© 2015 Elsevier Inc. All rights reserved.
particles and the load transferred to the particles from the matrix. The fracture of Si particles limits the ductility of the alloy [1–6], even though these particles impart high strength. Si modification is found to have an impact in determining the fracture behavior and ductility of the alloy [1,3–6]. It is reported that the size of the largest Si particles controls the ductility of the alloy [3]. Yet another viewpoint is that the ductility of unmodified alloys is controlled by the mean size of the Si particles, whereas that of modified alloy is determined by their distribution [4]. Fracture of Si particles also depends on orientation and volume fraction of Si particles [3–6]. The authors of this manuscript have carried out a detailed investigation on a near-eutectic Al–Si based alloy and have reported the effects of heat treatment [7] and Si modification [8] on particle fracture under compression. The important conclusions were: 1) particle fracture increases with heat treatment and 2) fracture is more in unmodified particles and particles oriented nearly perpendicular to the loading axis. Particle size refinement and homogenization of distribution are known to improve fracture resistance [9,10]. The reduced load carrying capacity on fracture of Si particles affects the overall load carrying capacity and work hardening of the alloy [11,12]. These effects can play an important role in the determination of the mechanical instability. Fracture occurs when a critical level of damage takes place [13]. The
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increase in flow stress near the fractured particle in the matrix leads to a greater load transfer to the neighboring particles, thereby increasing the rate of damage development [14]. Heat treatment given to the alloy modifies the matrix microstructure and hence controls the rate of particle damage. The modification of Si particles is found to reduce particle fracture, since there is no fiber loading when the particles are small and globular [8]. Extensive experimental results are available on the flow behavior of Al–Si based alloys, but are mainly restricted to tensile loading. Results are also available for the independent effects of strain rate [15] and temperature [14,16]. However, the exact deformation mechanisms responsible for the observed flow behavior are not explained in detail. To our knowledge, there is no literature available on the combined effect of strain rate and temperature under compression. The effect of heat treatment on the compressive flow behavior of Al–Si alloy at different strain rates and temperatures is reported in a recent publication of the present authors [17]. The present manuscript discusses the role of Si modification on the compressive flow behavior of Al–Si based alloy. This work further explores the effect of strain rates and temperatures on the compressive response of the alloy. The deformation mechanisms responsible for the observed flow and hardening behavior of the alloy are elucidated in detail. Serrated flow is also investigated, which is related to the strain rate sensitivity of the alloy.
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2. Experimental work
technique and examined under a FEI scanning electron microscope (SEM). The samples were subjected to orientation imaging microscopy using a FEI-SIRION® field emission gun SEM having Electron Back Scattered Diffraction (EBSD) facility. For EBSD analysis, a final polishing in the colloidal silica suspension was carried out after the standard metallographic procedure. The samples were also examined under 300 kV field emission TEM-STEM (FEI Tecnai F30) equipped with EDX. Samples of 3 mm discs for TEM analysis were thinned down to 100 μm by mechanical polishing and then final polishing was done in a Gatan precision ion polishing system (PIPS) using argon ions. Quantitative metallography using Sigma ScanPro image analyzer was carried out to calculate the fraction of fractured particles. Measurements were carried out over a large area of approximately 2 × 10 6 μm 2 at different strains (10%, 20% and 30%), strain rates (3 × 10− 4 , 10 − 1 , 1 s − 1 , 10 1 and 102 s − 1 ) and temperatures (RT, 100°C and 200°C). Measurements were made on the surface parallel to the compression axis at the center of the sample. Each quantitative measurement was performed on at least 50 fields of view per sample at a magnification of 500 ×. The effect of strain was studied at the lowest strain rate of 3 × 10 − 4 s− 1 and RT, the effect of strain rate was studied at RT and 10% strain and the effect of temperature was studied at the lowest strain rate of 3 × 10− 4 s− 1 and 10% strain. In each field of view, the number of damaged Si particles was counted manually, and the total number of Si particles was counted by using automatic digital image analysis.
2.1. Material and heat treatment
2.4. Microstructure based modeling
As-cast and heat treated Al–Si–Cu–Mg based alloy samples were supplied by GM (General Motors), USA, in unmodified and modified conditions. The chemical composition and heat treatment given to the material can be found elsewhere [8].
The stress evolution in the different phases (Al matrix and Si particles) of the alloy was studied by finite element methods. The process for conducting the analysis is shown in Fig. 1, of Ref. [19]. The Al matrix was modeled as an isotropic elasto-plastic solid with Young's modulus EAl = 70 GPa and Poisson's ratio of 0.3. The experimentally obtained properties of the Al matrix from micro-hardness tests (Section 2.2) were assigned to describe the plastic behavior of the matrix. The isotropic linear elastic properties were assigned to Si particles with Young's modulus ESi = 130 GPa and Poisson's ratio 0.28 [20]. The meshed microstructure was subjected to uniaxial compression to 3% strain. The maximum principal stress in Si particles and the equivalent plastic strain (PEEQ) in the matrix were considered as the output parameters of the numerical analysis.
2.2. Mechanical tests Cylindrical compression samples with 15 mm height and 10 mm diameter were machined from the cast plates. The two flat faces of the compression samples were lubricated with MoS2 to reduce friction during compression. The compression tests were carried out under a displacement controlled Dartec servo hydraulic machine at seven different strain rates, viz., 3 × 10−4, 10−3, 10−2, 10−1, 1, 101 and 102 s−1 and three different temperatures, viz., RT, 100 °C and 200°C. Prior to compression, the specimens were heated to the desired temperature and soaked for approximately 10 min. Three samples were tested at each test conditions to obtain reliable data. At each strain rate and temperature, the samples were compressed up to failure. The samples were compressed to 10%, 20% and 30% strain for microstructural quantification, if they did not fail before the respective strain. To understand the hardening behavior of Al matrix at different strain rates and temperatures, hardness tests were carried out on the samples. The indentation was carried out using CSM microhardness tester with 10 μm size spherical indenter. The sample was carefully indented on Al matrix at different strain rates, viz., 3 × 10− 4, 10− 2, 10− 1 and 1 s−1. At each strain rate, the indentations were made at three different temperatures RT, 100°C and 200°C. Under each test condition, a series of indentations were made at a progressively increasing load and five indents were made to get a reliable value. Yield strength was obtained by taking one-third of the hardness value and the hardening exponent was obtained by calculating Meyer's index [18]. 2.3. Metallography Microstructural analyses were carried out in as-received condition and after compression. After the compression tests, the samples were sectioned along the central vertical plane containing the applied load direction. They were then polished using standard metallographic
3. Results 3.1. As-cast microstructure The typical as-cast microstructure of the alloys is shown in Fig. 1. The typical morphology of Si particles in the eutectic region of the alloy in the unmodified and modified conditions can be seen in Fig. 1(a) and (b) respectively. The eutectic Si particles in the unmodified alloy are present in the form of a plate-like structure in 3D, which manifests itself as long elongated particles on 2D metallographic sections. In the modified alloy, the eutectic Si particles are more globular with more than half of the particles having aspect ratio between 1 and 2. The TEM analysis of the precipitates present in the Al matrix of the alloy is depicted in Fig. 2. Fig. 2(a) shows the TEM image of precipitates along [001]Al zone axis. The HRTEM image of these precipitates in Fig. 2(b) shows the (200) crystallographic planes of Al with interplanar spacing of d200 = 2.02 Å and sets of Moiré fringes due to double diffraction between Al matrix and precipitates. From the spacing between the Moiré fringes (DM) and the angle it makes with the matrix (ω), the d spacing of the precipitate can be calculated using the following formula [21]. 1 1 ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi dp 2 2 jdAl j þ jDM j −2jdAl jjDM j cosω
ð1Þ
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Fig. 1. SEM micrograph showing the eutectic region of Al–Si based alloy in (a) unmodified and (b) modified conditions.
where dp is the interplanar spacing of the precipitate and dAl is the interplanar spacing of Al matrix. Two different types of Morié fringes can be seen in Fig. 2(b) with spacing marked as DMI and DMII. The Morié fringes of type I show a d spacing of 13.3 Å, which matches only with the (003) spacing of Al7Cu4Ni [22]. They are spherical in shape with 4– 6 nm in size. The type II Morié fringes correspond to S′ precipitates and have two variants, i.e., (021)Al//(001)S′ and (021)Al//(001)S′ [23]. The precipitates along [011]Al zone axis shown in Fig. 2(c) are plate shaped parallel to {111} planes of Al, 3–7 atomic layers thick and 5–
6 nm long. They are also found to be coherent with the matrix. These precipitates consist of two variants formed along the [111] and [111] directions of Al, as is evident from the image and the diffraction pattern. The FFT (which is shown as an inset) shows streaks in the directions normal to the habit planes of the zones, reflecting the shape of the precipitates. Dark contrast of the zones might be due to the segregation of atoms, which have higher atomic scattering amplitude for electrons [24]. Both Cu and Mg are expected to aggregate along these planes, which acts as a precursor to S′ phase. Fig. 2(d) shows the large
Fig. 2. (a) Bright field image of the precipitates along [001]Al zone axis, (b) HRTEM image showing Moiré fringes due to precipitates along [001]Al zone axis, (c) HRTEM image along [011]Al zone axis showing plate shaped zones on {111} planes of Al and (d) HRTEM image showing coherency strains around the zone.
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coherency strains around the zone, which is due to the bending of planes around the precipitate. 3.2. Compression test results 3.2.1. Strength of the alloy The typical stress–strain curves of the alloy with unmodified and modified particles are shown in Fig. 3(a). The effect of strain rate and temperature can also be seen in this figure. It is clear that modification improves both strength and ductility of the alloy. The effect of strain rate and temperature on 0.2% proof stress (PS) can be more clearly seen in Fig. 3(b). The 0.2% PS increases on modification and it increases with increase in strain rate, in general. Above a certain strain rate, the increase is found to be steeper, which is being termed here as transition strain rate. The unmodified alloy exhibits this transition at 10−1 s−1 at all the three temperatures studied. The modified alloy exhibits the transition at 1 s−1 at RT and 100 °C, and at 10−2 s−1 at 200 °C. It is also observed that the modified alloy exhibits higher SRS than the unmodified alloy. The 0.2% PS decreases with increase in temperature for both the alloys, as expected. The decrease is steeper from 100 °C to 200 °C than from RT to 100 °C for both the alloys. Further, the SRS decreases with increase in temperature for both the alloys. 3.2.2. Work hardening behavior of the alloy Work hardening rate of the alloy is determined by numerically differentiating the experimentally obtained stress–strain data. Fig. 4 shows the work hardening rate θ (dσ/dε) as a function of normalized stress (σ/σy) for the unmodified and modified alloys at a quasi-static strain rate of 3 × 10−4 s−1 and RT. The curves begin immediately after yielding and get truncated at the peak stress. Initial hardening rate is higher for both the alloys and it decreases with stress. Between the two alloys, it is higher for the unmodified alloy and the decrease with stress is also more rapid for this alloy. Both alloys show a plateau region where the hardening rate is nearly zero. Further, this plateau region is prolonged for the modified alloy (for σ/σy ≥ 2.75) as compared to the unmodified alloy (for σ/σy ≥ 2). The σ/σy value beyond which the region is considered to be the plateau region is shown by the vertical dotted lines in the figure. The effect of strain rate on the hardening behavior of the alloys in the unmodified and modified conditions at RT is shown in Fig. 5(a) & (b) respectively. In general, the initial hardening rate increases with increase in strain rate and the hardening rate decreases with increase in stress for both alloys. The decrease in hardening rate with stress is steeper for strain rates above 10− 1 s− 1 (i.e., for strain rates, 1, 10 and 102 s− 1) than that at strain rates 3 × 10−4 s−1 and 10−1 s−1 for the unmodified alloy, as shown in Fig. 5(a). For the modified alloy, the hardening rate curves are steeper for strain rates 10 and 102 s−1 than those observed at 3 × 10−4, 10−1 and 1 s−1. Thus, the hardening rate curves of both alloys are found to be strain rate sensitive at RT and it becomes steeper
Fig. 4. Work hardening rate as a function of normalized stress showing the effect of Si modification.
above 10−1 s−1 for the unmodified alloy and above 1 s−1 for the modified alloy. The hardening behavior of the alloys at different temperatures for the lowest strain rate 3 × 10−4 s−1 is shown in Fig. 6(a & b). The initial hardening rate decreases with increase in temperature and the hardening rate decreases with increase in stress for both the alloys. The decreasing trend is almost the same at RT and 100 °C but it falls rapidly at 200 °C. 3.2.3. Negative strain rate sensitivity and serrated flow Serrations were observed in the flow (σ–ε) curves of the alloys in unmodified and modified conditions in the lower strain rate regimes, from 3 × 10−4 s−1 to 10−2 s−1, at RT and 100°C. Serrations observed in σ–ε curves for both the alloys at 3 × 10−4 s−1 and RT is shown in Fig. 7(a). The SRS, m, of flow stress at 10% strain was evaluated from the σ–ε data of the compression tests using the following relation. m¼
logðσ 2 =σ 1 Þ logðε_ 2 =ε_ 1 Þ
ð2Þ
where, σ1 and σ2 are the flow stresses at strain rates ε_ 1 and ε_ 2respectively. The SRS variation is shown in Fig. 7(b). It can be seen that the SRS values are close to zero or negative in the lower strain rate regime (3 × 10−4, 10−3 and 10−2 s−1) at RT and 100°C. Serrated flow is characterized by critical onset plastic strain εc, i.e., the value of plastic strain at which serrated flow starts, and the average magnitude of stress drop Δσavg. The variation of εc and Δσavg (in the strain range of 10% to 15%) with ε_ at RT and 100°C is shown in Fig. 8(a) for the two alloys within the serrated flow regime. It can be seen that εc increases with increase
Fig. 3. (a) Representative stress–strain curves of the alloy showing the effect of Si modification, strain rate and temperature and (b) effect of strain rate on 0.2% proof stress at different temperatures.
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Fig. 5. Effect of strain rate on work hardening rate as a function of normalized stress at RT in (a) unmodified and (b) modified conditions.
Fig. 6. Effect of temperature on work hardening rate as a function of normalized stress at a strain rate of 3 × 10−4 s−1 in (a) unmodified and (b) modified conditions.
in ε_ and decreases with increase in T for both alloys. The εc value is found to be lower for the modified alloy as compared to the unmodified alloy at all the strain rates and temperatures. The variation of Δσavg with ε_ at RT and 100°C within the serrated flow regime is shown in Fig. 8(b). It is observed that Δσavg decreases with increase in ε_ and increases with increase in T. Further, Δσavg value is observed to increase on modification.
3.3. Hardness test results 3.3.1. Strength of the matrix To understand the flow behavior of the Al matrix under different loading conditions, microhardness tests were carried out on the matrix region of the alloy. Since both the unmodified and modified alloys are given the same heat treatment, the properties expected in the matrix of both alloys are same. Hence, the properties of the matrix of only the unmodified alloy are examined and the results are given in this section.
Yield strength values of the matrix (σym) calculated from microhardness tests are shown in Fig. 9. From the figure it is clear that the matrix is strain rate sensitive at all temperatures, i.e., the yield strength value increases with increase in strain rate at all temperatures. Further, the rate of increase of σym with strain rate decreases with temperature. 3.3.2. Work hardening behavior of the matrix A series of indentations were made in Al matrix at progressively increasing loads and the size of the indentation was measured at each load. Meyer [18] proposed an empirical relation between the load and the size of the indentation: n0
P ¼ kd
ð3Þ
where P is the applied load, d is the diameter of indentation, k is a material constant and n′ is Meyer's index. The parameter n′ is the slope of the straight line obtained from log P vs. log d plot. This Meyer's index n′
Fig. 7. (a) Typical true stress–true strain plots showing the serrations in unmodified and modified conditions at 3 × 10−4 s−1 & RT and (b) variation of strain rate sensitivity, m, with temperature at 10% strain.
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Fig. 8. Variation of (a) critical onset plastic strain and (b) average stress drop with strain rate at different temperatures in unmodified and modified conditions.
is related to the hardening exponent of the material n by n′ = n + 2. Using this relation, the value of n is obtained at different strain rates and temperatures, which is shown in Table 1. It can be seen that the n value of matrix decreases with increase in both strain rate and temperature. 3.4. Particle fracture The effect of strain, strain rate and temperature on the fraction of fractured Si particles is shown in Fig. 10. The other test conditions are shown in the inset of the figure. For all the test conditions, the unmodified alloy shows a greater number of Si particles fracturing than in the modified alloy. Particle fracture increases with increase in strain and it increases more rapidly in the unmodified alloy than in the modified alloy, as shown in Fig. 10(a). The particle fracture is very less at 10 & 20% strains in the modified alloy and increases rapidly at 30% strain. From Fig. 10(b), it is clear that the particle fracture increases after 10−1 s−1 in the unmodified condition and after 1 s−1 in the modified condition. Particle fracture decreases with temperature, as shown in Fig. 10(c). The decrease is lesser from RT to 100 °C than from 100 °C to 200 °C for both alloys. 3.5. Predictions from microstructure based modeling Following the procedures mentioned in Section 2.4, finite element simulations are performed and the results are presented here. The maximum principal stress distribution in Si particles under a uniaxial compressive strain of 3% is shown in Fig. 11(a–d). The other test conditions are also given in the inset of the figure. The stress distribution in Si particles for the unmodified and modified alloys can be compared by comparing Fig. 11(a) and (b) and (c) and (d). It can be seen that the
stress in the particles is higher in the unmodified alloy than in the modified alloy. The simulations have been carried out at different strain rates, viz., 3 × 10−4, 10−2, 10−1 and 1 s−1 and at different temperatures, viz., RT, 100°C and 200°C. For brevity, the results are shown only for 3 × 10−4 & 1 s−1 strain rates and RT & 200°C temperatures. The effect of strain rate on stress values can be seen by comparing Fig. 11(a) and (c) for the unmodified alloy and by comparing Fig. 11(b) and (d) for the modified alloy. The stress in particles increases with increase in strain rate for both the alloys. Plastic strain in the matrix of the unmodified alloy at RT and 200 °C is shown in Fig. 11(e) and (f), respectively. Plastic strain is found to be quite inhomogeneous and shear can be seen in the matrix at higher temperatures. 4. Discussion 4.1. Stress–strain response The alloy shows a rapid increase of flow stress with applied strain in lower strain regimes for ε ≤ 5%, as shown in Fig. 3(a). This is due to the resistance offered by the second phase Si particles to the flow of Al matrix, which results in high work hardening rate [13,25–27]. The pile-up of dislocations against Si particles happens when the particles are either unmodified or modified, but the dislocation interaction with the unmodified particles is less significant. The pile-up of dislocations against Si particles in the modified alloy can be seen in Fig. 12(a). The unmodified Si particles merely act as load bearing constituent of the alloy. The load transfer to the modified particles will not be as efficient as in the case of unmodified particles due to the lower aspect ratio and larger number density of the globular particles. This is the reason for the observed higher initial hardening rate in the case of unmodified alloy (Fig. 4). Furthermore, the additional resistance is offered by the nanosized Al2CuMg and Al7Cu4Ni precipitates, which form during heat treatment in both the alloys. The precipitate-dislocation interaction in the alloy is shown in Fig. 12(b). This figure contains some striking features of dislocation-precipitate interaction mechanisms. Most of the dislocations are pinned by the nano-size precipitates. The dislocations are bowed between precipitates, under the effect of the applied stress. Precipitates are located using both loss of contrast on dislocation lines and curvature of dislocation segments. The dislocations, which are pinned by the precipitates, overcome obstacles and propagate in its slip plane
Table 1 Hardening exponent of A1 matrix obtained from micro-hardness test. n value at different strain rates at RT 3 × 10−4 s−1 0.177
Fig. 9. Effect of strain rate and temperature on yield strength of Al matrix obtained from microhardness test.
10−2 s−1 0.137
1 s−1 0.117
n value at different temperatures at a strain rate of 3 × 10−4 s−1 RT 100°C 200°C 0.177 0.105 0.01
102 s−1 0.063
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Fig. 10. Fraction of fractured Si particles as a function of (a) strain, (b) strain rate and (c) temperature.
Fig. 11. Results of microstructure based modeling (a, b, c & d) Maximum principal stress distributions in Si particles and (e & f) Equivalent plastic strain in the matrix. The test conditions are given in the inset of the figures.
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Fig. 12. TEM micrograph of the alloy showing the (a) pile-up of dislocations against modified Si particles, (b) pinning of dislocations by the hardening precipitates in a sample deformed at 10−1 s−1–RT–5% strain and (c) dislocations in sample deformed at 1 s−1–RT–5% strain.
before being stopped again by other precipitates. If displacements occur with no loop formation, it is assumed that dislocations shear the precipitates. The shearing of precipitates could not be directly observed in this alloy. Further straining results in a decrease in hardening rate with strain. This lower strain hardening can be seen above 10% strain for a sample deformed at 3 × 10−4 s−1 and RT in Fig. 3(a). The decrease in work hardening rate with stress can be clearly seen in Fig. 4. This decrease is found to be more rapid for the unmodified alloy than the modified alloy. The unmodified Si particles in these alloys act as a main load bearing constituent and fracture when fracture strength of particles is
reached. The Si particle fracture in the alloy is found to start at lower strains in the unmodified alloy than in the modified alloy due to significant load transfer to the unmodified particles, and decreases the load carrying capacity of the alloy. Once a Si particle fractures, the matrix surrounding it experiences higher load. The EBSD analysis of a sample after 10% strain is shown in Fig. 13. We can observe localized strains in the region where Si particles have fractured. This strain is due to the extra load transferred to the surrounding matrix after fracture of a particle. In addition, precipitate shearing also takes place at higher strains, even though it offers resistance to dislocation motion during initial stages of straining in both the unmodified and modified alloys. So, the matrix
Fig. 13. (a) Orientation imaging map and (b) Kernel Average Misorientation (KAM) showing strained regions in the Al matrix in unmodified condition at 10% strain.
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gets softened at higher strains and it cannot support the load. The extra load will be transferred to the neighboring particles, which leads to higher rate of particle fracture. The higher rate of damage accumulation for the unmodified alloy can be seen in Fig. 10(a) in terms of a larger fraction of broken particles with strain. The decrease in hardening rate with stress for the modified alloy is not as sharp as for the unmodified alloy. In both the cases, matrix softening will be there due to precipitate shearing, but the rate of particle fracture will be lower in the modified alloy than in the unmodified alloy (shown in Fig. 10(a)), since modified particles are not subjected to fiber loading. The stress simulations by FEM described in Section 3.5 also confirm that the load transferred will be lesser in the modified particles. Hence, both matrix softening due to precipitate shearing and Si particle fracture results in decrease in hardening rate at higher strains. The decrease in work hardening rate is steeper in the unmodified alloy due to higher rate of Si particle fracture.
4.2. Effect of strain rate and temperature From Fig. 3(b), it is clear that the 0.2% PS of both the alloys increases with increase in strain rate and the increase is sharper after certain strain rates. This transition is observed at 10−1 s−1 for the unmodified alloy at all temperatures. The modified alloy shows this transition at 1 s−1 at RT and 100°C and at 10− 2 s− 1 at 200°C. These observations show that the alloy is strain rate sensitive at all the temperatures whether the Si particles are unmodified or modified. This might be due to the precipitates formed during heat treatment and these precipitates act as obstacles to dislocations. The transition observed in the alloys at RT can be explained as follows. The dislocation arrival at an obstacle depends on the applied strain rate. The dislocation may bypass the obstacle and relieve the stresses accumulated at the obstacle. At lower strain rates (3 × 10−4 to 10−1 s−1 for the unmodified alloy and 3 × 10− 4 to 1 s−1 for the modified alloy), the rate at which dislocations bypass the precipitates is able to match the dislocation arrival rate and relieve the stress accumulation at the precipitate. On the other hand, at higher strain rates (1 to 102 s−1 for the unmodified alloy and 101 and 102 s−1 for the modified alloy) the dislocation arrival rate becomes greater than the rate at which dislocations bypass the precipitates. Hence, at higher strain rates, there is an accumulation of dislocations, which results in increase in flow stress values. The schematic in Fig. 14 depicts the situation at low and high strain rate deformations. The dislocations observed in the samples deformed at 10−1 s−1 and 1 s−1 are shown in Fig. 12(b and c). It can be seen that the dislocation accumulation is higher in samples deformed at 1 s−1 than that at 10−1 s−1. The different transition strain rates observed in the unmodified and modified alloys are due
to the interaction of dislocations with Si particles in addition to dislocation-precipitate interaction in the modified condition. The critical strain rate above which the transition can occur, has the following relationship with temperature [28]. ε_ c ¼
αDv Gab 3
d kT
ð4Þ
where, α is a constant, Dv is bulk diffusivity, a is atomic volume, b is Burgers' vector, d is precipitate size, k is Boltzmann constant and T is temperature. This equation shows that the transition will occur at lower strain rates for higher temperatures. The modified alloy shows a decrease in the transition strain rate with increase in temperature according to Eq. (4). The transition is observed at 1 s− 1 at RT and 100°C, whereas the transition occurs at 10−2 s−1 at 200°C. However, the unmodified alloy does not show a decrease in transition strain rate with increase in temperature in the temperature regimes studied. In this alloy, this may occur at temperatures, which are not covered in the present analysis. Further, the SRS of 0.2% PS decreases with increase in temperature for both alloys. Coarsening of precipitates at higher temperatures is responsible for this behavior. There is a strong effect of strain rate on the hardening behavior of both the alloys, as shown in Fig. 5. The hardening curves in Fig. 5(a) and (b) shows a sharp decrease in hardening rate above 10− 1 s−1 for the unmodified alloy and above 1 s− 1 for the modified alloy at RT. As explained earlier, the dislocation accumulation rate, annihilation rate and precipitate size are responsible for this transition. The strain rate sensitivity of both the matrix and modified Si particles are responsible for the observed behavior in the modified alloy, whereas the matrix alone plays a role in the unmodified alloy. The SRS of the matrix can be seen in Fig. 9, in which σym increases with strain rate at all temperatures. Hence, at higher strain rates, a greater load will be transferred to the Si particles, which results in a greater number of particle fracture at higher strain rates, as observed in Fig. 10(b). The stress simulation in Si particles by FEM (Fig. 11(c and d)) also confirms this fact. The work hardening rate decreases with increase in temperature for both alloys (Fig. 6(a) and (b)) and the decrease is greater at higher temperatures. This might be due to matrix softening by precipitate coarsening. It can be seen in Fig. 11(f) that the alloy exhibits matrix shear at 200°C. The load transferred to the particles by the softened matrix is lower and the particle fracture also decreases with increase in temperature in the unmodified alloy (Fig. 10(c)). In the modified alloy, the dislocations accumulated at particles are relaxed thermally, instead of cutting the particles. Hence, the strain rate and temperature sensitivity of the unmodified alloy is controlled by the matrix microstructure. The unmodified Si particles merely act as obstacles to the flow of the matrix. On the other hand, in the modified alloy, both the matrix and Si particles play a role. 4.3. Serrated flow
Fig. 14. Schematic showing dislocation–precipitate interactions at low and high strain rates.
Negative SRS (nSRS) is observed in the lower strain rate regimes (3 × 10−4 to 10−2 s−1) at RT and 100°C for both the alloys, and serrated flow is also observed in the same strain rate and temperature regimes. Serrated flow has been found to be invariably accompanied by nSRS in the literature [29], which is commonly attributed to dynamic strain aging (DSA) mechanism, i.e., the interaction between mobile dislocations and dissolved solute atoms, originally proposed by Cottrell [30]. McCormick and van den Beukel further developed a model to demonstrate how DSA can give rise to nSRS [31,32]. Critical onset strain of serrated flow (εc) increases with increase in strain rate and decreases with increase in temperature (Fig. 8a). The magnitude of serrations (Δσavg) decreases with increase in strain rate and increases with increase in temperature (Fig. 8b). This is the normal serrated flow behavior, which can be explained by the DSA mechanism [30–32]. An increase in strain rate increases dislocation velocity,
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resulting in an increase in strain at which solute atoms are able to diffuse to dislocations and pin them, giving rise to serrated flow. On the other hand, an increase in temperature increases the diffusivity of solute atoms, thereby lowering the strain at which they can diffuse to dislocations and pin them, giving rise, again, to serrated flow. This kind of strain rate and temperature dependence of εc has been reported for several alloys exhibiting serrated flow in the literature. The value of εc is found to be lower and Δσavg is found to be higher for the modified alloy as compared to the unmodified alloy at all strain rates and temperatures. Thus, it appears that the size and morphology of Si particles also affects serrated flow. 5. Conclusions The compressive flow behavior of Al–Si based cast alloy is characterized in the unmodified and modified conditions. The effect of strain rate and temperature is also investigated. The deformation mechanisms responsible for the flow behavior are explained. The following conclusions can be drawn from the present investigation: • Modification is found to increase the strength and SRS of the alloy at all temperatures studied. The thermally dependent processes of both the Al matrix and Si particles are rate controlling, which are responsible for the higher SRS in the modified alloy. On the other hand, the thermally dependent process of the matrix alone is rate controlling in the unmodified alloy. • The SRS of both the unmodified and modified alloys decreases with increase in temperature due to precipitate coarsening. • The initial work hardening rate is higher in the unmodified alloy than in the modified alloy due to fiber loading of unmodified particles. The hardening rate decreases sharply at higher strains in the unmodified alloy due to the higher rate of Si particle fracture. • Work hardening rate of both the alloys decreases sharply at 200°C due to precipitate coarsening. • Microstructure based finite element simulations support the experimentally observed particle and matrix fracture behavior at all the strain rates and temperatures studied. • Serrated flow seems to be also affected by the size and morphology of Si particle. • All observations made suggest that the properties are matrix microstructure dominated and Si particles merely act as obstacles to the flow of the matrix in the unmodified alloy. Both matrix and Si particles dictate the properties in the modified alloy.
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