1 Introduction

Owing to their low density, desirable mechanical properties, and corrosion resistance, as well as their good cast ability, aluminum (Al) alloys have been widely applied for automobile engine cylinder heads^[1]. Under operational conditions, a cylinder head is subject to dynamic stresses at elevated temperatures, which can evoke failures due to several independent failure mechanisms and their interactions. In applications of Al cast alloy involving the elevated temperature, it is important to understand the temperature-dependent mechanical properties. For instance, the fatigue behavior should be evaluated as a function of the strain range and operating temperatures, and then modeled to predict the response under the range of expected service conditions^[2-3]. The repeated thermal-mechanical stresses in automotive engines can cause gradual degradation, which decreases the low cycle fatigue (LCF) resistance of these cast alloys. However, most researches have concentrated on the high cycle fatigue (HCF) behavior of Al cast alloys^[4-5]. Fewer studies on the LCF behavior have been reported, especially at the elevated temperature^[6-7].

The LCF testing is generally conducted under the strain control actuation^[8]. In strain controlled fatigue tests, contact extensometers are generally used to measure the deformation of the specimen gauge length, and the strain is used as a feedback control signal for the loading system. The use of surface-mounted contact extensometers requires special attention as sharp contacts could cause localized damage to the specimen and potentially facilitate fatigue crack initiation. To avoid this concern, as well as to gain more insight into the fatigue behavior of Al cast alloys, a non-contact strain measurement system is needed. While non-contact optical extensometers are widely available for use with universal testing systems at ambient temperatures, the elevated temperature testing generally precludes their use. Therefore, a dedicated optical extensometer is needed for evaluating the high temperature fatigue response and other aspects of the mechanical behavior.

The objective of this work is to evaluate the mechanical behavior, including the LCF response, of an Al cast alloy over a range of elevated temperature. A specialized optical extensometer is developed based on the digital image correlation (DIC) to support the objective. Strain measurements obtained using the optical extensometer are validated using a conventional mechanical extensometer. Then, the uniaxial tension, the LCF testing, and the creep tests are conducted at temperatures up to 300 ℃.

2 Material and method 2.1 Material

The material evaluated is a cast Al-Si alloy currently being used for automobile engine blocks. Specifics regarding the composition, pouring conditions and heat treatment are not available for disclosure. Cylindrical specimens were extracted from the four combustion chambers on the fire face side of the engine cylinder heads. Sixty specimens were machined following ASTM E606^[8] with a gauge length of 16 mm and an outer diameter of 6 mm. To minimize the potential effects of surface roughness, the specimens were all polished axially and circumferentially to a surface roughness less than 0.4 μm^[9].

2.2 Experimental setup

Room and elevated temperatures tests were performed on a mechanical testing and simulation (MTS) Bionix servo-hydraulic test machine (MTS, U. S. A.) combined with MTS 653.04 high temperature furnace for thermal control (see Fig. 1). The center-split feature of the furnace enabled smooth opening and closing, and easy mounting of the specimens. The furnace was 220 mm long, which posed a challenge to accommodate the short specimen length extracted from the engine block castings. Therefore, a pair of specially prepared grips were designed to withstand the tensile/compressive stress and the isothermal strain-controlled fatigue conditions. Both ends of the grips were cooled by internal water circulation.

2.3 Optical extensometer

An optical extensometer was developed to support the elevated temperature testing. Kanchanomai and Mutoh^[10] pioneered the use of digital image systems in the strain-controlled fatigue testing of solder materials, where the displacements were measured by converting the grayscale images into a binary signal. The spatial resolution of the images (512×480 pixels) was limited, which restricted the precision of strain measurement, and the minimum detectable strain was only 0.08%. Tao and Xia^[11] developed a non-contact real-time strain measurement and control system based on the DIC for the fatigue testing of polymer materials. The minimum detectable strain was 0.01%, but the strain data acquisition frequency was limited to 10 Hz due to the search algorithm used. As a consequence, the actual strain peak values that the specimen experienced would be larger than the predefined limits due to the delay time of 0.1 s. Zhang et al.^[12] developed a microscopic imaging system to characterize the strain-life behavior of thin sheet metal that is also based on the DIC. Using a dedicated fast image sampling strategy, the minimum detectable strain was 0.002% with a frequency of 10 Hz. Despite the high precision of strain measurements, the relative low frequency of data acquisition remained an issue for the measurement of strain amplitude, which was a concern for the fatigue testing. Very recently, Wu et al.^[13] proposed a two-step integer-pixel search strategy combined with a sub-pixel search strategy. This approach enabled a strain sampling rate of 60 Hz with use of parallel computing. Thus, a non-contact real-time strain measurement system with high precision for high temperature strain-controlled fatigue tests is possible. An optical extensometer based on the DIC could serve as a viable option, since it enabled both the high strain precision and the high measurement frequency.

The optical extensometer used for strain control consisted of the hardware for image acquisition and the software for real-time image processing. The optical imaging system included a digital monochrome (b/w) progressive scan camera (Baumer TXG12, Germany) with resolution of 1 296 × 966 pixels and a desktop computer with a quad-core processer (Inter(R) Core (TM) i5-3470 CPU with the main frequency of 3.20 GHz, 4 GB RAM). During dynamic tests, the camera was set as a binning mode with spatial resolution of 1 296×483 pixels to enable imaging acquisition at 65 frames per second. The camera was aligned such that the image horizontal direction coincided with the axial direction of the specimen. The digital images were transmitted with a gigabit ethernet cable. A 75 mm C-mount lens was attached to the camera to enable imaging an area of 32 mm × 24 mm at a distance of 400 mm.

To achieve the high precision with the minimal time, the real-time DIC process is performed in the integer pixel and sub-pixel domains. A particle swarm optimization (PSO) algorithm^[14] was applied for the integer-pixel search. A swarm of randomly generated integer-pixel positions, taken as particles in the target images, fly through a two-dimensional search space. The zero-mean normalized cross-correlation criteria (ZNCC) is utilized as the optimization function for each particle. Each particle searches for the best position in the target image near its original location by finding the maximum correlation coefficient (C_pbest), and every particle will adjust the flying direction towards the global best position P_gbest with the maximum C_pbest in the swarm. During this process, the best position could be possibly updated if a greater C_pbest is found. In the next generation, the movement of the particle i in the image updates its position (P_i=(p_i1, p_i2)) and velocity (V_i=(v_i1, v_i2)) based on Eqs. (1) and (2)^[14]. This process continues until the location with the global optimum is determined.

(1)

(2)

where the subscript d stands for the flying direction in the two-dimensional digital image, c₁ and c₂ are the positive acceleration coefficients, and r₁ and r₂ are two independent uniform random variables between 0 and 1. t means the current generation, and t+1 is the next generation. w is the inertial weight factor in the generation which can be calculated through the following equation:

(3)

In this equation, G_max is the maximum generation number. In order to avoid excessive roaming outside the search space [P_{d, min}, P_{d, max}], the value of each component in v_i should be restricted to the range of [V_{d, min}, V_{d, max}]. The generation process is terminated until the preseted maximum G_max is reached. With this search strategy, the neighborhood location with the global optimum can be rapidly determined.

The maximum gradient search (MGS) algorithm^[15-16] is used to determine the location with the maximum correlation coefficient quickly by finding the location with the maximum gradient. This location is then used as the initial guess in the inverse compositional Gauss-Newton (IC-GN) algorithm for the following sub-pixel registration. Parallel computing based on the OpenMP programming is adopted for real-time multi-point tracking by means of the multi-core CPU. Once the displacements of the pixel points are obtained, the strain in the effective gauge area (between the pixel points) can be calculated according to the following equation:

(4)

where l is the distance between the two reference points (l₁, l₂), and Δl is the change in the distance between these two points (l₁, l₂) resulting from the deformation. The strain output rate could reach 60 Hz using the aforementioned hardware and software^[13].

To facilitate the use of the optical extensometer, the surface of the specimens was painted with white correction fluids and then sprayed with black speckles as shown in Fig. 2. The strain within the gauge section resulting from the axial loads was calculated using four points, which are divided into two groups. The distance between the points 1 and 2 and the points 3 and 4 serves as the gauge length of the specimen. The axial strain of the specimen is defined as the average strain of these two groups, which can be calculated according to Eq. (4).

To validate the real-time optical extensometer, strain estimates obtained using the system were compared with measurements obtained using a commercial mechanical extensometer at the room temperature. The MTS axial extensometer (Model 632.13F-20) with the gage length of 10 mm was attached onto the cylindrical specimen. The specimen was loaded in uniaxial tension at 5 mm/min under displacement control. The longitudinal strain was then measured with both the contact and non-contact (optical) extensometers, respectively.

2.4 Tensile test

To understand the importance of temperature to the mechanical properties of the alloy, uniaxial tensile tests were performed at the ambient temperature 25 ℃, and three different elevated temperatures including 100 ℃, 200 ℃, and 300 ℃. For the elevated temperature tests, the furnace was not fully closed to have a slender opening at the center. The specimen was visible external to the furnace and illuminated with halogen lamp fiber optics. Images of this surface were captured while loading. The axial stress was calculated from the axial load and the initial cross sectional area of the specimen, and the axial strain was calculated according to Eq. (4). These measures were used to generate stress-strain curves at each of the evaluation temperatures.

2.5 LCF

LCF experiments were conducted with a strain ratio (ε_min/ε_max) of R=-1.0 and a frequency of 0.5 Hz in accordance with ASTM E606^[8]. The tests were conducted at temperatures of T=25 ℃, 100 ℃, 200 ℃, and 300 ℃. A symmetric triangular displacement waveform was adopted to achieve fully reversed strain-control loading in the fatigue tests, with elongation and compression components of the equal magnitude. The strain within the gauge section was measured with the aforementioned optical imaging system in the real time. The stress was calculated from the load and cross-section geometry of the test section. Knowledge of both the stress and strain responses enabled construction of the stress-strain hysteresis loops to define all the necessary parameters for characterizing the cyclic response (see Fig. 3). The maximum (σ_max) and minimum (σ_min) stresses of the fatigue cycle corresponded to the extreme points on the hysteresis loop. The stress amplitude (σ_a) for each cycle was calculated according to the following equation:

(5)

The elastic strain amplitude (ε_a^e) was determined from the stress amplitude (σ_a) divided by Young's modulus of the alloy, which was assessed through the uniaxial tensile response at each temperature. The plastic strain amplitude (ε_a^p) was then calculated by subtracting the elastic strain amplitude (ε_a^e) from the total strain amplitude (ε_a). According to Manson-Coffin's equation, the relationship between the total strain amplitude (ε_a) and the number of reversals to failure (2N_f) is expressed as

(6)

where σ_f' and b are the fatigue strength coefficient and the exponent, respectively, and ε_f' and c are the fatigue ductility coefficient and exponent, respectively. The parameter E is Young's modulus of the Al cast alloy at the specific temperature. The optical extensometer was used to measure the real-time strain during the cyclic loading experiments. The total strain amplitude (ε_a) was simply the difference between the maximum and minimum strains. Similarly, the stress amplitude (σ_a) was obtained from the difference between the maximum and minimum stresses. Using these quantities, a complete stress-strain hysteresis curve was obtained at the half-life time. Following the standard evaluation process ASTM E606, the fatigue strength coefficient and exponent, and the fatigue ductility coefficient and exponent were determined by Manson-Coffin's equation from results at the four different temperatures.

2.6 Creep testing

Creep testing is also conducted on the Al alloy under the uniaxial tension at 200 ℃ and 300 ℃. At each temperature, four specimens were prepared and evaluated under various load amplitudes. A pair of specially prepared grips was used to allow the specimen to be mounted in the furnace and maintained in the constant temperature condition. The test machine was operated in the load control mode, and a constant predefined axial load was applied to the specimen after achieving the uniform temperature. The longitudinal strain was monitored with the optical extensometer over the time until either the specimen fractured or 100 test hours were reached. In each creep test, the minimum creep rate was obtained by fitting the strain-time curve in the steady-state creep regime. The relationship between the stress and creep rate at each temperature was plotted in semi-logarithmic coordinates, and the creep limit was defined as the intercept of the stress at a rate of 10^-6 %/h.

3 Results 3.1 Uniaxial monotonic tensile test

A comparison of the stress-strain responses for the Al cast alloy obtained with the two methods of strain measurement is shown in Fig. 4. The maximum strain difference between these two methods is 0.000 6 and occurs when the strain measured by the mechanical extensometer reaches 0.02. The consistency in the measured strain demonstrates the effectiveness of the real-time optical extensometer.

The mechanical properties of the Al alloy are evaluated from results of the tensile tests at the four temperatures and are listed in Table 1. In general, there is a decrease in Young's modulus, yield strength, and ultimate strength with the increasing temperature, as expected. However, the apparent ductility, as indicated by the percent elongation, was the smallest at 100 ℃.

3.2 LCF responses

Stress-strain hysteresis loops are obtained for all specimens, and representative responses for a strain amplitude of 0.4% are presented in Fig. 5 for both 200 ℃ and 300 ℃ conditions. As evident from a comparison of the responses, the hysteresis loop at the half-life and 300 ℃ exhibits the lower stress amplitude compared with that at 200 ℃, which suggests that the stress amplitudes in the fatigue decrease with the increasing temperature. The same behavior is observed for the other strain amplitudes, which indicates that the component of plastic deformation resulting from cyclic loading increases with the temperature, as expected.

Figure 6 shows the evolution of stress amplitude in terms of the temperature and the total strain amplitude, which depicts the stress hardening/softening responses of the cast Al alloy. Strain hardening occurs at 25 ℃, 100 ℃, and 200 ℃. However, only very marginal strain hardening occurs at 200 ℃, and cyclically softening is evident at 300 ℃.

In analyzing the cyclic responses, the number of cycles to failure (N_f) is defined at the point in which the stress amplitude drops to a value of 30% below the stabilized cyclic stress amplitudes, according to Ref. [17]. The number of reversals to failure is then defined accordingly. The total strain amplitude responses are shown in terms of the number of reversals to failure (2N_f) in Fig. 7 at 200° and 300 ℃. An exponential decay is evident in the fatigue life diagrams at both temperatures. Furthermore, the LCF resistance at 300 ℃ is lower than that at 200 ℃. The lower fatigue resistance at 300 ℃ demonstrates the detrimental effects of the increasing inelastic deformation with the temperature on the LCF life.

Manson-Coffin's relationship is developed from the components of elastic and plastic deformations. The fatigue parameters for the cast Al alloy are obtained from regression of the experimental data and are listed in Table 2. To further explore the influence of the temperature on the fatigue properties, the elastic and plastic components of the fatigue responses are plotted in Figs. 8(a) and 8(b), respectively. In Fig. 8(a), the slope indicates the fatigue strength exponent (b), which decreases with the increasing temperature. In addition, the fatigue strength coefficient (σ_f') is defined by the intercept of these lines and decreases with the increasing temperature. Interestingly, the fatigue ductility curve at 100 ℃ is different from those at the other temperatures as evident in Fig. 8(b). The material exhibits substantially lower values of the fatigue ductility exponent and coefficient at this temperature with respect to the others considered.

3.3 Fracture behavior

Representative micrographs obtained from the fracture surfaces of the fatigue samples evaluated at 200 ℃ and 300 ℃ are shown in Figs. 9 and 10, respectively. At 200 ℃, typical scanning electron microscope (SEM) images of the fracture surfaces from samples subject to strain amplitudes of 0.5% and 0.3% are shown in Figs. 9(a) and 9(c), respectively. Extensive tear ridges can be observed on the fracture surface in Fig. 10(a), in addition to some unequiaxed dimples in the areas of plastic rupture. These features are adjacent to the fatigue fracture regions. Under higher magnification (see Fig. 9(b)), secondary cracks can be found at the grain boundaries, which is evidence of transgranular crack propagation. Fatigue striations can also be observed in Fig. 9(d) from a sample which fractures with the total cyclic strain amplitude of 0.3%. The appearance of striations suggests that a crack develops and undergoes cyclic growth, preferential to the plastic deformation. There are also oxide particles evident on the fracture surfaces (see Fig. 9(c)) at the lower strain amplitude, and their participation in the fatigue response is unclear. The fracture surface at the total strain amplitude of 0.5% shows more dominant tear ridges, suggesting transgranular fracture akin to the features noted in tensile fracture of this alloy. Fatigue striations are also observed under smaller cyclic strain and correspond to a transition to ductile cyclic slip.

Micrographs of the fracture surface for samples evaluated at 300 ℃ are shown in Fig. 10. For the total strain amplitude of 0.5% (see Fig. 10(a)), shallow unequiaxed dimples are evident, but there are no clear tear ridges. At higher magnification in Fig. 10(b), some cleavage facets can be observed. This combination of features suggests that the material exhibits a mixed fatigue mechanism, consisting of quasi-cleavage brittle fracture and the plastic deformation as characterized by the predominant dimples and tear ridges around the periphery of the cleavage facets. Cleavage facets with the step pattern are also apparent in Fig. 10(c) resulting from cyclic loading with the total strain amplitude of 0.3%, signifying that the contribution of cleavage fracture to failure increases with the decreasing total strain amplitude. In contrast to the results from fatigue at 200 ℃, fatigue striations are not evident in the fracture surface of the specimens evaluated at 300 ℃ (see Fig. 10(d)).

3.4 Creep

Figure 11 shows the relationships of the applied stress and creep rate at temperatures of 200 ℃ and 300 ℃. The creep parameters are listed in Table 3. At the temperature of 300 ℃, the Al alloy undergoes a greater degree of creep deformation, as expected, compared with that at the lower temperature.

4 Discussion

Using the optical extensometer, the mechanical behavior, including the LCF response, of an Al cast alloy over a range of elevated temperatures can be performed successfully. Compared with typical experimental methods for strain-life fatigue testing using mechanical extensometers, the optical extensometer based on the real-time DIC is a non-contact technique to measure the strain, which can protect the specimen from damage during the strain measurement. Since the two-step search scheme is adopted in the integer domain, an initial guess with C_pbest equal to or larger than 0.75 can be positioned for the next subpixel registration. Combined with the IC-GN method, it is possible to output strains at a rate of 60 Hz with the current hardware. This feature allows the optical extensometer applicable in monitoring the strain amplitudes which usually vary within 2 Hz. This enables 120 strain points in one cycle at 0.5 Hz to retrieve a smooth strain curve. Theoretically, an increase in the sampling frequency will enhance the precision of capturing the peak and valley strains. Compared with the non-contact method proposed by Tao and Xia^[11], the peak and valley strain precision contributed by the high sampling frequency is higher in our optical imaging system.

Another concern in adopting the optical extensometer based on the real-time DIC for strain measurement is the measurement precision. Wu et al.^[13] compared the mean bias and the standard deviation obtained with the aforementioned method with those obtained with the classic DIC method. The results show that they are at the same level, indicating that the accuracy of the proposed method is acceptable. Before the isothermal LCF tests, a uniaxial monotonic tensile test is also performed with both the mechanical extensometer and the optical extensometer simultaneously to verify the strain accuracy. In the stress-strain curve, good agreement can be achieved with the two methods, which means that the real-time DIC can work equally well compared with the mechanical extensometer in the LCF tests.

Results from the tensile tests show that Young's modulus, the yield strength, and the ultimate strength decrease with the increasing temperature. The reduction in the strength is expected due to the contribution of thermal energy to dislocation movement^[18-19]. In general, the resistance to dislocation motion decreases with the increasing temperature. The contribution of this mechanism is most evident in the stress hardening/softening responses in Fig. 6. Although strain hardening occurs at the lower temperatures, marginal strain hardening occurs at T≥ 200 ℃ (see Fig. 6(c)). Indeed, the potential for dislocation climb increases with the increase in the thermal energy, which is expected to be the primary contribution to the cyclic stress softening at 300 ℃ (see Fig. 6(d)).

The elongation to failure increases at T≥ 200 ℃. Indeed, there is evidence of an increasing ductility in the tensile responses at 200 ℃ and 300 ℃ (see Table 1). In addition, the hysteresis loops show evidence of a greater contribution from the plastic deformation, especially at 300 ℃. However, the fatigue life decreases overall with the increase in the temperature. The observed fracture features (see Figs. 9 and 10) provide greater understanding of the fatigue life responses. Unequiaxed dimples and tear ridges are identified on the fracture surfaces at temperatures of 200 ℃, whereas at 300 ℃ there is evidence of the quasi-brittle phenomenon, including cleavage and quasi-cleavage fracture. These mechanisms contribute to an inelastic component of deformation, which is not based on the enhanced slip. In the creep tests, the creep behavior is extensive at 300 ℃, and there is evidence of a creep assisting the fatigue phenomenon. In contrast, at the lower temperature of 200 ℃, there is no obvious fatigue creep phenomenon. Hence, the creep-fatigue damage mechanism becomes more dominant at the temperature larger than 200 ℃. Maintaining operating temperatures of the engine block below 200 ℃ will be important to the performance of this cast Al alloy.

Results of the creep testing show that the creep limit at 200 ℃ is 173 MPa, which is very close to the yield strength at that temperature (199 MPa). However, at 300 ℃, the creep limit reduces sharply to 87 MPa, which is essentially half of the value at 200 ℃, and only 50% of the yield strength at 300 ℃. Thus, the potential contribution of creep to the fatigue response is far more dominant at 300 ℃. Creep can contribute to the LCF response by facilitating crack initiation and propagation^[21], causing a decrease in the fatigue resistance. That is expected to be the primary mechanism contribution to the decrease in the fatigue resistance at 300 ℃. Based on these results, application of this cast alloy should be avoided at the operating temperatures exceeding 200 ℃. Alternatively, further efforts should be invested in processing to increase the creep resistance and the corresponding high temperature fatigue resistance of this alloy.

5 Conclusions

A non-contact real-time strain measurement system based on the real-time DIC is established for conducting mechanical experiments for the Al alloy. The method includes an accelerated initial guess determination by means of the PSO and MGS in the integer-pixel domain algorithm followed by the sub-pixel registration using the IC-GN algorithm, which has an acceptable strain measurement accuracy. By adopting the parallel computing technology, the system can measure strain with a frequency of 60 Hz at least. The capability of the system is verified through recording the real strain during displacement control in high temperature LCF tests. Results from the tensile tests show that Young's modulus, as well as yield and ultimate strengths, decreases with the increasing temperature. Interestingly, the ductility is the lowest at 100 ℃. In the LCF test, the fatigue strength coefficient decreases with the increasing temperature, while the fatigue strength exponent increases. In comparison to results at the other temperatures, the fatigue ductility coefficient and exponent exhibit the minimum values at 100 ℃. The creep resistance is found to decrease with the increasing temperature from 200 ℃ to 300 ℃.