Stir Casting Method Research Articles

Parametric optimization of abrasive waterjet machining for aluminum 7075/boron carbide/zirconium silicate hybrid composites

In the present work, an attempt was made to study the machining characteristics of Hybrid Metal Matrix Composites (HMMCs) using Abrasive Waterjet Machining (AWJM). For preparing the composites, Aluminum alloy 7075 is cast with boron carbide (B4C) and zirconium silicate (ZrSiO4) reinforcement by the method of stir casting. Experimental investigation of the machining parameters on Depth of Cut (DoC), Material Removal Rate (MRR), and Surface Roughness (SR) was done. The independent parameters include Abrasive Mesh Size (AMS), Abrasive Flow Rate (AFR), Water Jet Pressure (WJP), and Traverse Rate (TR). The results of experiments reveal that low TRs increase SR, while short AMSs, high flow rates, and large WJPs increase DoC and MRR. Surface maps made by SEM exposed information about the surface texturing and the material removal processes. It was found that the optimal DoC was achieved at an AMS 80#, AMS of 340 g/min, WJP of 200 MPa, and TR of 60 mm/min for both unreinforced Al and the composite of Al + 5% B4C + 5% ZrSiO4. The results enable the development of proper AWJM procedures for HMMCs to ensure better surface finish and workability. From the experiments, it was observed that while smaller mesh sizes and greater AFR will improve MRR and DoC, it can at the same time have a negative effect on the overall performance of Kerf Taper angle (KT) and Surface Roughness (SR).

MECHANICAL AND MICROSTRUCTURAL BEHAVIOR OF ZE41 MAGNESIUM ALLOY REINFORCED WITH INCONEL FOR HIGH-PERFORMANCE APPLICATIONS

Abstract Magnesium alloys are known for their lightweight and desirable properties, as they hold significant potential for innovative engineering applications. The present study investigated the mechanical and microstructural characteristics of a magnesium alloy (ZE41) reinforced with Inconel ceramic particulates. The Magnesium Metal Matrix Composites (MMMC) were fabricated using the stir casting method, with varying weight percentages (wt. %) of Inconel (0, 2, 4, 6, 8, 10, 12 wt. %). The microstructural examinations of the MMMC specimens were performed using SEM, SEM+EDS analyses, and Optical Microscopy (OM), which revealed a strong interfacial bond well-defined between the Magnesium matrix and the Inconel particulates. This uniform distribution of reinforcement particulates significantly enhanced the mechanical properties of the composite materials. The tensile tests showed that the Ultimate Tensile Strength (UTS) improved progressively with up to 8% Inconel reinforcement, achieving a maximum UTS of 202.56 MPa, a 24.47% improvement compared to the base Magnesium alloy. However, the UTS decreased beyond 8% Inconel due to increased brittleness. Hardness tests indicated that the highest hardness value of 76.1 HV was achieved for the composite containing 12 wt.% Inconel, marking an 18.85% increase over the base alloy. Additionally, the wear rate decreased with increasing Inconel reinforcement, demonstrating improved wear resistance. Specifically, the wear rate dropped from 2.58 × 10-7 g/mm at 0% Inconel to 0.84 × 10-7 g/mm at 12% Inconel, showing a 67.44% reduction in wear rate compared to the pure AA6082 matrix. The findings from the present work, indicate the potential of Inconel-reinforced ZE41 composites towards achieving optimized strength and hardness levels for applications requiring high-performance materials. The present research is a contribution to the body of knowledge on the development of magnesium composites and highlights the importance of reinforcement compositions for enhancing their mechanical and microstructural characteristics.

Optimization of Aluminium Casting with Alumina Reinforcement via Stir Casting: Impact on Physical and Mechanical Properties

Aluminum casting using the stir casting method is a common practice in the industrial sector. This study aims to optimize the effect of stirring speed on the physical and mechanical properties of aluminum casting reinforced with alumina powder (Al2O3). The material used in this study is derived from discarded vehicle rim waste. The stir casting method was performed at varying speeds of 500, 600, and 700 rpm, with a mold temperature of 250°C and a pouring temperature of 700°C. Physical testing to examine the microstructure was conducted using optical metallography, hardness testing was performed using the Rockwell hardness scale B, and tensile strength was measured using a Universal Testing Machine. The microstructure observations showed that a stirring speed of 500 rpm yielded the best results, with minimal porosity. The highest hardness value recorded was 65 HRB at 500 rpm, consistent with the microstructure observations. The highest tensile strength was also recorded at 500 rpm, reaching 262 MPa.

Tribological behaviour of AZ31 Mg hybrid bio-composite reinforced with zirconium dioxide and seashell bio-ceramics

Abstract In the fast moving world, the material requirements are higher and also needed for tailor-end applications. Most of the applications require lightweight materials especially in the biomedical application and it should be biocompatible. Magnesium (Mg) alloys are the best candidate for biomedical application but it has low tribological property. So that, the present work focus on the improvement of tribological behaviour of AZ31 Mg hybrid bio- composite with addition of seashell powder (SSP) and zirconium di oxide (ZrO2) as reinforcements. The bio-composite was synthesized by reinforcing 2 wt.% SSP and 10 wt.% ZrO2 through stir casting method. For the tribological studies, a pin-on-disc machine was used to carried out the dry sliding wear test under varying conditions of input factors namely, applied load (L), sliding velocity (V) and sliding distance (D). A Taguchi integrated with TOPSIS approach were applied to find the best factors for less wear rate (WR) and the co-efficient of friction (COF) of the proposed bio-composite. The results ensured that ‘L’ has the most determinant factor for controlling the responses followed by ‘D’. Moreover, the worn surface morphology depicts that the bio-composite shows higher resistance to wear due to the addition of reinforcements developing the oxide layer thus protecting the specimen surface.

Mechanical and Wear Behavior of Aluminium Metal Matrix Composites Reinforced Ceramics Materials for Light Structures

Aluminium Alloy based Metal Matrix Composites (AAMMCs) has widely used in defense, aircraft and automobile applications because of their enhanced engineering properties with light weight metals. Nano sized silicon nitride (80 μm) is used as a reinforcement in this study, whereas aluminium alloy 8011 is selected as the matrix material. Using the stir casting method, metal matrix composites made of aluminium alloy 8011 with varying weight percentages of Si3N4 (0, 4, 8, 12, and 16) are created. The stir casted AL 8011/Si3N4 composites further heated under T6 condition. The AL 8011/Si3N4 – T6 composites are further subjected to Energy Dispersive X ray Analysis (EDAX) and Scanning Electron Microscope (SEM) to identify by the presence of elements and study the microstructure characterization, respectively. The density, microhardness and wear test are conducted by employing Archimedes principle, Vickers hardness tested and pin on disc equipment, respectively. The wear test is done at different sliding distances like (500, 1000, 1500 and 2000 m), applied load like (10, 20, 30 and 40 N) and kept sliding at a speed of 1 m/s. The increasing weight percentage of silicon nitride expands the increasing of density and Vickers hardness up to 12 wt % of silicon nitride and decreasing by 16 wt % addition. The wear resistances of AL 8011/12 wt % Si3N4 –T6 composite exhibits higher wear resistance than other Al8011 based composites.

Wear Behavior of 2024 Aluminum Alloy Reinforced with SiC Particles

The wear behavior of Aluminum Alloy (AA) 2024 reinforced with SiC particles were investigated at room conditions. Stir casting method was used to prepare the matrix composite of AA 2024 alloy reinforced with different weight percentages of SiC (3, 6, 9, 12 wt%). The wear behavior of both AA 2024 and AA 2024/SiC composite was studied using the reciprocating wear test. Loads of 2.5, 5, 7.5, 10, and 12.5 N were applied with sliding speeds of .0.55, 0.72, 0.88, 1.04 and 1.2 m/sec in dry sliding contact conditions. The microstructure and phase distribution were investigated using Optical Microscope (OM) and Scanning Electron Microscopy (SEM). The results demonstrate the presence of fine dendritic structure with semi-homogeneously distributed SiC particles in the alloy matrix. The micro-hardness increased with increasing SiC percentage. The highest value of hardness of 79.3 HV was found at 12 wt% SiC, from the initial 44 HV of the base alloy. The wear tests showed that the wear rate increased with increasing applied normal contact load at a contact sliding speed of 0.88 m/sec. The wear rate of the as cast material was 18.59 ×10-8 g/cm. Adding the SiC particles decreased the wear rate to 13.78, 9.76, 7.98, and 5.81 ×10-8 g/cm for 3, 6, 9, 12 wt% SiC addition at 12.5 N applied load, respectively. SEM examination of worn surfaces showed that severe and abrasive wear was exhibited at higher loads in the dry case while mild and adhesive wear were observed at lower loads in the lubricated condition.

Optimization of reinforcement ratio and stirring speed on mechanical properties of Al-TiB2-B4C hybrid composite using Taguchi – grey relational analysis

Abstract The aim of the research is to optimise percentage raio of hybrid reinfoecements and stirring speed to maximize the mechanical properties of the hybrid composite by and Taguchi analysis and grey relational analysis. The matrix material employed in this study is Al 7075, while boron carbide (B4C) and titanium diboride (TiB2) serve as the reinforcement materials.. The hybrid metal matrix composite is produced via the stir casting method. For experimental design Taguchi L9 orthogonal array was adopted, with the weight percentage of the reinforcement materials and stirring speed identified as experimental factors. the specified levels of weight percentage for the reinforcements B4C and TiB2 were established at 3%, 6%, and 9%. The mechanical properties analysed as response parameters consist of tensile strength, hardness, impact strength, and flexural strength. The Taguchi analysis, particularly the signal-to-noise (S/N) ratio evaluation, reveals that the percentage weight of TiB2 is the predominant factor affecting tensile strength. In contrast, the percentage weight of B4C significantly influences both hardness and flexural strength, while stirring speed is the most critical parameter for impact strength. The optimal parameters identified for maximizing tensile strength, hardness, and flexural strength are 9% B4C, 9% TiB2, and a stirring speed of 600 rpm. The highest grey relational grade was attained in experiment number 9, which utilized these optimal parametric values.

Review of Aluminium (AA6061) Metal Matrix Composite (MMC) by Stir Casting Method

Industrial development has boosted the use of aluminium to accommodate high demand. Among the most popular aluminium alloys is the AA6061 of the 6xxx series due to it characteristics. AA6061 is a preferred matrix material for Metal Matrix Composite (MMC) fabrication. This study comprehensively reviews an AA6061 aluminium matrix composite produced through the liquid processing technique-stir casting. This review focuses on process parameters, manufacture of conventional mixtures, range of reinforcement, mechanical and tribology properties of AA6061 composites. Significant findings show that increased reinforcement in AA6061 matrix composites greatly improves the properties, such as strength, hardness, ductility, and wear resistance. Producing AA6061 composites with various reinforcements such as organic, inorganic (carbide, oxides, borides and nitrides), hybrid, and other nanomaterials makes the composites more appropriate for high-stress applications. The AA6061 matrix has effectively included a broad spectrum of reinforcing materials, from micro to nanoscale, showcasing the adaptability and versatility of the stir casting method. Future studies should focus on improving AA6061 composite manufacture using advanced casting processes and comprehensive material characterization. These composites have great potential as advanced materials for several industrial applications due to its remarkable mechanical and tribological properties.

Study on the influence of aluminium nitride particulates on the dry sliding wear behavior and mechanical properties of aluminium 6061 alloy developed using stir casting method

Study on the influence of aluminium nitride particulates on the dry sliding wear behavior and mechanical properties of aluminium 6061 alloy developed using stir casting method

Microstructure and mechanical properties of strength-ductility synergetic SiC/ZK60 composites by a pre-dispersion strategy

The strength-ductility trade-off presents a significant challenge in the development of magnesium matrix composites (MMCs). A novel strategy that combines powder pre-dispersion, nano-SiC/Al master alloy sintering, stir casting, and hot extrusion combined method was introduced to prepare the strength-ductility synergetic SiC/ZK60 composites. The microstructural evolution and mechanical properties of these composites have been thoroughly investigated and compared. The results demonstrate that SiC particles are uniformly distributed within the as-solution-treated composites, and extrusion processes promote cluster refinement. Microstructural characterization shows that adding nano-SiC/Al enhances grain refinement and facilitates the precipitation of secondary phases. The grain refinement is attributed to the accelerated dynamic recrystallization (DRX) and nano-particle pinning, where particle stimulated nucleation (PSN), continue DRX (CDRX), and discontinue DRX (DDRX) are the dominant DRX mechanisms of composites. This process is further enhanced by increased nucleation sites induced by SiC, which facilitate the precipitation of MgZn2 and Zr phases. Additionally, a microscale Al3Zr phase precipitates within the composites due to aluminum addition. Notably, both strength and ductility, as well as elastic modulus (E) of 10SiC/ZK60 and 20SiC/ZK60 composites were improved simultaneously, with optimal ultimate tensile strength and elongation (EL) increasing by nearly 10 %. Grain refinement emerges as a primary factor contributing to enhanced mechanical properties. Also, load transfer and stress release caused by multiple crack sources contribute significantly to strength and ductility strengthening, respectively.

Investigations on Microstructure, Mechanical, and Wear Properties, with Strengthening Mechanisms of Al6061-CuO Composites

Metal matrix composites (MMCs) reinforced with Copper Oxide (CuO) and Aluminum (Al) 6061 (Al6061) alloys are being studied to determine their mechanical, physical, and dry sliding wear properties. The liquid metallurgical stir casting method with ultrasonication was employed for fabricating Al6061-CuO microparticle-reinforced composite specimens by incorporating 2–6 weight percent (wt.%) CuO particles into the matrix. Physical, mechanical, and dry sliding wear properties were investigated in Al6061-CuO MMCs, adopting ASTM standards. The experimental results show that adding CuO to an Al6061 alloy increases its density by 7.54%, hardness by 45.78%, and tensile strength by 35.02%, reducing percentage elongation by 40.03%. Dry wear measurements on a pin-on-disc apparatus show that Al6061-CuO MMCs outperform the Al6061 alloy in wear resistance. Al6061-CuO MMCs’ strength has been predicted using many strengthening mechanism models and its elastic modulus through several models. The strengthening of Al6061-CuO MMCs is predominantly influenced by thermal mismatch, more so than by Hall–Petch, Orowan strengthening, and load transfer mechanisms. As the CuO content in the composite increases, the strengthening effects due to dislocation interactions between the matrix and reinforcement particles, the coefficient of thermal expansion (CTE) difference, grain refinement, and load transfer consistently improve. The Al6061-CuO MMCs were also examined using an optical microscope (OM), energy-dispersive spectroscopy (EDS), X-ray diffraction (XRD), and scanning electron microscopy (SEM) before and after fracture and wear tests. The investigation shows that an Al6061-CuO composite material with increased CuO reinforcement showed higher mechanical and tribological characteristics.

Fabrication and mechanical characterization of AlSi10Mg-reinforced hybrid composites using bottom pouring top-loaded stir-casting method

Fabrication and mechanical characterization of AlSi10Mg-reinforced hybrid composites using bottom pouring top-loaded stir-casting method

Microstructural modification and simultaneous enhancement of strength, ductility in a novel nano-composite

Present study aims at microstructural modification in hypereutectic Al-20Si by addition of nano-AlN and nano-TiN through stir casting method followed by isothermal heat treatment. Different samples were then characterized metallographically and mechanical properties were evaluated. Results indicate drastic modification in microstructure in the nano-composite. This is attributed to the presence of AlN and TiN nano-particles which acted as nucleating agents. Moreover, divorced eutectic formation in the nano-composite resulted in reduction in aspect ratio of eutectic Si in the nano-composite. UTS increased by overall 81 %, 0.2 % YS by 85 % and % strain by 74 % in the heat treated nano-composite. Refinement of primary Si spheroidisation of eutectic Si resulted in improvement in strength and ductility both.

Microstructural, mechanical, and wear properties of ultrasonic assisted stir casted A356 Alloy/AlN composite

The ultrasonic-assisted stir-casting method has effectively prepared A356 alloy/AlN composites. The ultrasonic treatment and integration of AlN particles are shown to greatly enhance the mechanical and wear characteristics of the matrix via grain refinement. By incorporating 9 vol.% of AlN reinforced particles, the average grain size of A356 alloy was decreased from 36 μm to 10 μm. Additionally, the hardness and tensile strength experienced a respective rise of 60.6% and 32%. With an increase in the volume percentage of AlN particles, it is found that both the wear rate and the friction coefficient decreased. It is also observed that the A356 alloy displayed severe wear, whereas the composites exhibited moderate wear.

OPTIMIZATION OF WEAR RESISTANCE OF ALUMINUM MATRIX COMPOSITE (AL-7050/10WT% EGGSHELL) BY STUDY OF EFFECT STIRRING SPEED AND STIRRING TIME

This study investigates the impact of stirring speed (X1) and stirring time (X2) composite materials (Al-7050/10 wt. %eggshell) renforcemented by eggshell particles of the on wear resistance by using the MINITAB 16 program. A composite material was produced by the stir casting method; the ingot was melted, and a molten metal vortex was produced by varying the stirring speed (200, 300, 400, 500, 600 rpm) and stirring duration (10, 20, 30, 40, and 50 minutes). Eggshell particles with a fixed weight fraction of (10% wt.) and sizes (21–30 μm) were used. It was concluded if the variables (X1 = 543.4343 rpm) and (X2 = 48.1818 min.) wear loss of (0.0061 g) could be achieved. In practice, wear loss (0.0063 g) was obtained using the values of X1 and X2, which were obtained using the programs. Was wear loss is almost identical to the value obtained by the program. Additionally, the results manifested that the stirring time (X2) and stirring speed (X1) have a significant impact on the wear loss, where increase in stirring speed and time leading to an increase in wear strength. Furthermore, the effect of stirring speed (X1) on the wear loss is larger than that of stirring time (X2).

Increasing the high-temperature mechanical properties of Mg-Gd-Y-Zn alloys by adding AlN/Al particles

The AlN particles reinforced Mg-10Gd-3Y-1Zn (GWZ) composites were prepared by mixing AlN/Al particles using ball milling followed by stirring casting method. The influence of AlN/Al particles on the microstructural evolution and high-temperature mechanical properties of GWZ alloys were revealed and discussed. With AlN/Al particles added into the as-cast alloys, the Mg3RE phase was transformed into lamellar LPSO phase, while the content of Al2RE and LPSO phase increased. Since the Al2RE and AlN were effective nucleation sites for α-Mg, the grain size of AlN/Al-GWZ composites was reduced obviously from 126.1 to 39.8 μm. After homogenization, due to the coherent lattice matching relationships between 18R-LPSO phase and Al2RE or AlN particles, the 18R-LPSO phase nucleated on the Al2RE and AlN particles. After ageing treatment, the 2AlN/Al-GWZ composite showed the optimum mechanical properties at 250 °C, with the yield strength, ultimate tensile strength and elongation of 247.1 MPa, 265.5 MPa and 4.0%, respectively. The strengthening effect was primarily originated from the AlN particles, Al2RE and LPSO phases in the 2AlN/Al-GWZ composite. Besides, the composites can achieve the enhancement of high-temperature strength without the sacrifice of plasticity due to the coordinated deformation of AlN particles as well as the refinement of grains.

Wear behaviour of T4 and T6 heat treated LM28 composite reinforced with ZrO2 particles by stir casting method

Abstract The current study was performed to investigate the metal alloy LM28’s wear characteristics, strengthened by fine and coarse ZrO2 were investigated after undergoing thermal treatment with T4 and T6 process. Aluminium degasification tablets were used during the stir casting liquid metallurgy process to produce the composites with less porosity. ZrO2 was employed as fine (10–30 μm) and coarse (80–120 μm) particles in a step size of 3% from 0 to 12 wt%. The traditional T4 and T6 HT process was applied to the composite materials (LM28 nZrO2). T4 heat treatment involved in elevating the composites to 450 °C for 120–180 min before quenching them into the oil and age them naturally for 8–42 days at ambient room temperature. T6 HT was performed in a routine fashion, but also underwent artificial aging at 190–240 °C for 3–7 h before normal cooling. When compared to T4 HT process and non-HT composites, the hardness of T6 HT composites gives better results against wear property. The ideal level of hardness and resistance to wear of the composite was found in T6 HT composites when tested with a pin on a disk throughout a range of sliding distances and loads. Scanning electron microscopy demonstrated that T4 HT and non-HT composites suffered more surface damage than T6 HT composites when subjected to the same load and sliding distance. Initially, material was removed by an abrasive wear process, but this shifted to an adhesive one as sliding distance increased. T6 thermal treated composites are ideal for usage in tough conditions as a result of their excellent hardness and resilience to wear.

Corrosion behaviour of the magnesium-cerium binary alloy designed for degradable medical implants

ABSTRACT Magnesium (Mg) alloys containing rare earths (RE) gained special attention as promising candidates for degradable implant applications. Cerium (Ce) is one of the RE elements which can be tolerated by the human physiological system when used as an alloying element in Mg alloys. In this current research work, Mg-Ce binary alloys (0%, 0.5%, 1%, 1.5%, and 2% Ce by weight) were prepared by the stir-casting method. The developed alloys were characterised, and corrosion performance was assessed by immersion experiments in normal saline solution and by electrochemical experiments. The degradation rate of the developed alloys was measured as decreased with the increased Ce content up to 1.5%. From the polarisation studies, lower corrosion current density values 3.5 × 10−5 A/cm2 and 4.1 × 10−5 A/cm2 were observed for Mg-1.5%Ce and Mg-2%Ce alloys, respectively compared with the other samples. The surface morphologies after removing the corrosion products revealed more degraded regions for Mg and alloys with lower Ce content (0.5% and 1%) compared with 1.5% and 2% Ce. From the results, it is concluded that developing an Mg-Ce alloy with an optimum fraction of Ce (1.5%) is promising to produce degradable Mg-based medical implants with controlled degradation.

Gray relational analysis for parametric optimization of micro-EDM of thermo-mechanically processed AA7075 and AA7075/SiC/Gr composite

The AA7075 alloy and AA7075/SiC/Gr hybrid composite prepared by the stir-casting method have been further thermo-mechanically processed through unidirectional hot rolling and hot cross-rolling routes to eliminate casting defects like voids, blow holes etc. Three initial sample temperatures, that is, 350℃, 400℃, and 450℃, have been considered for the hot cross-rolling. The Al alloy and its hybrid composite prepared at different rolling temperatures are studied to investigate their micro-machining behavior through micro-electric discharge machining (µ-EDM). The micro-holes are made on the rolled samples along the rolling direction of the final rolling pass using a tool with twist drill bit geometry. Further, multi-objective optimization of the µ-EDM process parameters considering the response parameters viz. material removal rate (MRR) and tool wear rate (TWR) has been carried out using the gray relational analysis (GRA) technique. The µ-EDM parameters chosen to optimize in this study are voltage, pulse on time, and tool rotation. The obtained GRA results are further analyzed through normality and equal variance tests. The R-squared values of 95.02% and 95.53% for AA7075 alloy and hybrid composite, respectively, indicate that the data fit well with the statistical model. In material removal, the different electrical and thermal characteristics of the Al matrix and the reinforcements possibly generate sparks with a different characteristic that ultimately affects the MRR of the composite. Through scanning electron microscopy (SEM), the morphological study confirmed the presence of globules and voids on the machined surface. The formation of globules and voids is more significant in the AA7075 alloy than in the composite.

Evaluation of tribological parameters for boron carbide and graphite infused aluminium hybrid composite fabricated by stir casting technique

The present work focuses on suggesting Gr as a valuable self-lubricating reinforcement for hybrid composite samples and offering a minimum wear rate for sliding pairs with fewer mechanical surface defects at the same time. A series of samples were fabricated using the route by stir casting method considering B4C and Gr as the two reinforcements. The morphology of the sample has been studied using the X-ray diffraction graphs, Energy dispersive X-ray analysis and Scanning electron imaging stating the homogeneity of reinforcement in various composite cast. The theoretical and experimental density of the series of samples has been studied and compared stating the low porosity of the samples fabricated. A maximum wear rate (Wr) of 0.351 × 10−4 mm3/m. was found for pure aluminium sample against EN31 steel disc with 0.053 as friction coefficient (µ). Wr was somehow seen to reduce up to 0.286 × 10−4 mm3/m for Al-B4C composite with µ of 0.48. For hybrid samples, the wear rate was further seen to improve to 0.187 × 10−4 mm3/m for Al-B4C and Gr 2.0% weight with µ of 0.38. Least Wr was found for composite having Gr 3.5% weight, of 0.149 × 10−4 mm3/m. with µ of 0.36. SEM images of the worn surface give evident results for delamination and crack formation on the pin face for the pure-Al sample. Taguchi-ANOVA analysis has been carried out showing the valid contribution of pin type, load and sliding speed on Wr and friction coefficient as the P-value lies below 0.05 for input parameters considering the 95% confidence level of the model developed. An F-value of 44.57 with R2 of 0.895 is developed for Wr model and an F-value of 54.2 with R2 of 0.934 for the µ model.