Fatigue Life Prediction of Aluminum Alloy 6063 for Vertical Axis Wind Turbine Blade Application
Vertical axis wind turbine (VAWT) blades are fatigue-critical parts that must endure at least one billion stress cycles within their design life. Integrated Computational Materials Engineering (ICME) methodology is used in combination with the Mississippi State University Internal State Variable (MSU-ISV) plasticity-damage model and MultiStage Fatigue (MSF) model to predict the fatigue life of VAWT blades manufactured from extruded aluminum alloy 6063. Multiscale modeling is implemented at various length scales and the MSU-ISV model is used to establish the stress state of the blade, which is passed on to the MSF model to calculate fatigue life. Results from this analysis can be used to optimize the design life of aluminum alloys made for VAWT blade applications.
Keywords: 6063 aluminum alloy, Fatigue, Vertical axis wind turbine (VAWT), Integrated Computational Materials Engineering (ICME), MultiStage Fatigue (MSF) Model, Internal State Variable (ISV) plasticity-damage model
Author(s): S. Kazandjian
Energy demand is on the rise throughout the world despite efforts to curb energy consumption. Finite fossil fuel based energy sources release large amounts of greenhouse gasses (GHG) into the atmosphere harming the environment. As a result, society has sought various ways of harnessing renewable energy. One promising source of renewable energy is wind power. The majority of wind turbines currently in use are horizontal axis wind turbines (HAWTs). However, HAWTs continue to expand in size and HAWT wind farms require more land area to accommodate for this increase (Bou-Zeid et al., 2017). Conventional HAWTs have up to 8,000 components and reach heights greater than 100 meters. In comparison, VAWTs on average are less than half the height of HAWTs and contain only 12-20 components. This reduction in size and components leads to longer system life, less maintenance, reduced operational costs, and less impact on the environment and wildlife (McMahon, 2017).
Although VAWTs have many advantageous qualities compared to HAWTs, wind turbines in general are fatigue-critical machines that experience more fatigue cycles than airplanes and helicopters as shown in Figure 1. However, this fact was not well recognized between the 1970’s and 1990’s; neither were the fatigue properties of extrudable aluminum 6063 VAWT blades. This led to many cases of VAWT aluminum blade fatigue failure, mainly due to stress concentrations located at the blade joints. Consequently, it was believed VAWTs were innately more susceptible to fatigue compared to HAWTs, which is false because both VAWTs and HAWTs are vulnerable to fatigue failure (Ashwill et al., 2012). In fact, 50 to 90 percent of all mechanical failures are the result of fatigue, making it the most common mechanical failure mode among metals (Stephens et al., 2000).
Material Structure and Properties
Fatigue strength (SNf) is the hypothetical stress value obtained at Nf (fatigue life) cycles, which is defined as “the number of cycles of stress or strain of a specified character that a given specimen sustains before failure of a specified nature occurs” (Stephens et al., 2000). Table 1 lists the mechanical properties of aluminum alloy 6063 including fatigue strength, which is 69 MPa for alloy 6063-T5 and 6063-T6. The fatigue strength values from Table 1 are captured at 5x10^8 cycles using fully reversed R.R. Moore rotating bending tests. Aluminum alloy 6063 has a face-centered cubic (FCC) crystal structure. Aluminum (Al) makes up to 97.5% weight of this material and other elements comprise less than 3% weight of the total composition as shown in Table 2.
Figure 2 (a) below compares the fully reversed S-N fatigue curves for aluminum alloy and mild steel in bending (“Atlas of Fatigue Curves”). Constant-amplitude fatigue tests for aluminum alloys display the “knee” characteristic corresponding to the fatigue limit (i.e., limiting value of stress as Nf increases without bound) (Sundstrom, 2018; Stephens et al., 2000). According to the Aluminum Association, most aluminum alloys reach their fatigue limit at 500 M cycles (Sundstrom, 2018). Sutherland (Sutherland, 2000) reports at 107 cycles to failure the slope of 6063-T5 aluminum abruptly changes signifying an infinite fatigue life for stress values under 80 MPa. However, specimens with variable-amplitude loading do not display a fatigue limit. As a result, the linear extension of the initial slope shown in Figure 2 (b) should be utilized for the design of spectrally loaded wind turbines (Sutherland, 2000).
Fatigue can be divided into high cycle fatigue (HCF) and low cycle fatigue (LCF) regimes. HCF is dependent on surface conditions and is characterized by elastic stresses with numerous cycles (100 k to 500 M) until fracture. On the other hand, LCF fracture occurs below 100 k cycles as a result of plastic strain. Stress-life (S-N) and strain-life (S-ε) curves are obtained through strain controlled LCF and stress controlled HCF experimental fatigue testing.
Integrated Computational Materials Engineering (ICME)
Integrated computational materials engineering (ICME) is used to accurately estimate the fatigue life of aluminum VAWT blades by bridging information “from two or more experimentally validated models or simulation codes in which structure property information passes from one code to another” (Horstemeyer, 2018). Figure 3 illustrates the ICME process where multiscale material modeling information is input into the ISV damage model, which is implemented into a finite element analysis (FEA) simulation that outputs parameters such as stresses and strains required for the MSF model.
Hybrid ICME consists of two integrated parts, horizontal and vertical ICME. Horizontal ICME involves the integration of process-property-structure-performance relationships, with an initial focus on end performance goals. Vertical ICME is the process of linking cause-effect relationships at various lengths. Both vertical and horizontal ICME require the establishment of downscaling requirements, upscaling results, and quantification of uncertainty due to error as seen in Figure 4. Validation occurs “when the uncertainty of the simulations results are less than those of experimental results around a mean value” (Horstemeyer, 2018).
MultiStage Fatigue (MSF) Model
The ICME methodology is used in conjunction with the multistage fatigue (MSF) model created by McDowell et al. (McDowell et al., 2003), which predicts the number of cycles until the presence of a measurable crack. This is done by integrating microstructure information into the three stages of fatigue life, which include incubation, microstructurally small crack (MSC)/physically small crack (PSC), and long crack (LC) growth. The total fatigue life equation (Equation 1) represents the sum of the fatigue cycles for incubation, MSC/PSC, and LC growth. Listed below are the governing equations of the MSF model (Horstemeyer, 2018; Huddleston et al., 2018).
The incubation life (Ninc) or number of cycles to start a fatigue crack is estimated using a modified Coffin-Manson law (Equation 2). This equation relates microplasticity with incubation life. The local average maximum shear strain amplitude, β, is equated with the product of the linear coefficient for fatigue crack incubation (Cinc), and the incubation life to the power of α. Yield stress and ultimate stress are the two mechanical stress quantities used to calibrate the MSF incubation model. They represent the percolation and early strain thresholds (Horstemeyer, 2012; Huddleston et al., 2018).
The equation for β varies depending on the value of l/D measuring the micronotch root plasticity due to inclusion. The maximum particle diameter is given by D and l represents the size of the plastic zone at the notch root. The length scale, l, is restricted to the range 0≤l≤D. When l/D equals unity, microplasticity changes into macroscopic cyclic plasticity. The remote applied strain amplitude (εa) value at the macroscopic yield point is related to the percolation limit (k) value, marking the transition point between LCF and HCF regimes. Incubation life transitions to MSC at a percolation limit of approximately 0.3. Micromechanical simulations can be used to determine β as a function of εa for various pore and particle sizes and distributions or to estimate the influence of NND or proximity to the free surface (McDowell et al., 2003). Microscale simulations are also frequently used to calculate the exponent, q, and geometric linear factor, ξ, in Equations 3 and 4 below (Horstemeyer, 2012; Huddleston et al., 2018).
The MSC/PSC crack growth rate is equivalent to the difference between the crack tip displacement range (ΔCTD) and threshold (ΔCTDth). The constant, χ, is usually approximated as 0.32 for aluminum alloys, and the Burger’s vector is taken as the value of ΔCTDth. ΔCTD is a function of remote loading, initial crack length (ai), uniaxial effective stress amplitude (∆σ ̂), and the maximum principal stress range (Δσ1) among other terms such as grain size (GS) and orientation (GO), which are normalized to the reference grain size (GSo) and orientation (GOo). The microstructure is linked to microstructurally small crack growth through the material parameters CI, CII, and the exponent n in Equation 6, where CI and CII represent HCF and LCF constants for small crack growth, respectively (Horstemeyer, 2012; Huddleston et al., 2018).
After the MSC stage, the long crack growth regime is coupled to the MSF model using linear elastic fracture mechanics (LEFM). Once the material reaches the LC region, the driving force for crack growth is much greater than any resistance the crack may encounter. Equation 9 represents the transition from MSC to LC growth and Equation 8 is based upon the range of the stress intensity factor and crack growth parameter (A) (Horstemeyer, 2012).
Downscaling Requirements and Upscaling Results
Microstructure information from lower scales is necessary to calibrate the MSF model and capture fatigue behavior at the macroscale level. Downscaling requirements are dependent upon the ultimate performance goal. The performance objective for VAWT blades made from aluminum alloy 6063 is to achieve 30 years of life by withstanding (at minimum) 10^9 stress cycles (Ashwill et al., 2012). Once the end goal and downscaling requirements are established, simulations and experiments are performed beginning from the electronic scale all the way up to the macroscale as shown in Figure 5.
Mesoscale studies focus on single crystals or grains while macroscale analyses are associated with polycrystalline material. In order to capture lower scale heterogeneities and plasticity, the macroscale analysis should begin with a crack tip opening displacement frame of reference. To bridge the mesoscale to the macroscale, the relationship between the local plastic shear strain range and crack tip opening displacement relative to the crystal orientation is required to determine the incubation of fatigue cracks and MSCs. Mesoscale FEA simulations are used to obtain incubation and MSC equation parameters for the MSF model at the macroscale including the nonlocal plasticity limit ηlim, the ratio GS/GS0 representing the length scale barrier for dislocations, and the Schmid factor GO/GO0 related to grain texture (Horstemeyer, 2012).
Analysis of variance (ANOVA) statistical methods such as design of experiments (DOE) can be used to distinguish which structures have the greatest effect on certain material properties. These structures can then be bridged up to the microscale. Based on various DOE fatigue studies, it was found that early particle fracture and debonding were most influenced by particle shape and alignment for Al-Mg cast alloy. Moreover, crack growth in the MSC regime is most influenced by the load ratio followed by the maximum load and number of initially active slip systems according to micromechanical simulations. Particles are more resistant to MSC fatigue crack growth compared to grain boundaries. However, the elastic modulus of a particle has the least impact on fatigue crack incubation while applied displacement is the greatest factor (Horstemeyer, 2012). The MSC equations in the MSF model can be calibrated to the crack growth rates obtained from scanning electron microscope (SEM) experiments, repliset methods, strain-life data, or FEA simulations. SEM fractography is used to magnify the striations on the fracture surface to obtain growth rates of small fatigue cracks. The repliset method counts each fatigue cycle making it the most accurate way to calibrate the MSF model (Horstemeyer, 2012; Huddelston et al., 2018).
The MSC region includes inclusions (e.g, pores, particles, oxides, and distributed porosity) up to roughly one millimeter in length until the onset of the LC stage (Horstemeyer, 2012). The values in Table 3 are representative of wrought and cast aluminum alloys. MD simulations are best restricted to less than 1 µm in length due to computational resource limitations. Discrete nanoscale atomistic simulations such as molecular statics (MS), molecular dynamics (MD), EAM, and MEAM provide information on the crack tip driving force. The Burgers vector is known from the lattice structure and is used to estimate CDTth in Equation 5 and bridge the microscale to macroscale.
Fatigue is a relatively time consuming process, which makes it difficult to perform electronic or nanoscale simulations requiring vast computational resources. However, lower scale research exists with focus on topics such as stacking fault energy (SFE) and surface formation energy, which have an important effect on fatigue. Deformation of metals mainly occurs through slip (i.e., shear deformation) and twinning. Dislocations within grains occur in the direction of crystallographic planes; dislocation density is low for ductile materials, but increases with inelastic deformation leading to dislocation immobility (Stephens et al., 2000). Full dislocation deformation occurs when the ratio of stable SFE to unstable SFE or unstable twinning energy to unstable SFE approaches unity; deformation by partial dislocations and twins is dominant for low ratio values (Wu et al., 2010). Furthermore, the SFE of an aluminum alloy is correlated with its alloying element composition. The probability of partial dislocations or twinning also greatly increases with the use of Mg and Ga as alloying elements and the highest SFE values are observed for aluminum alloys composed of Mn and Si (Muzyk et al., 2011). The surface formation energy plays an important role on the surface condition of FCC metals and is related to fatigue, adsorption, oxidation, corrosion, and crystal growth; the (1 1 1) closed-packed surface exhibits the lowest surface energy. Surface formation energy can be calculated using embedded atom method (EAM) and modified EAM (MEAM) methods (Wu et al., 2010).
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