Vol. 21
May Issue
Year 2020

Science Update

in Vol. 21 - May Issue - Year 2020
Grey-Taguchi Analysis For Optimisation Of 7150-T651 Shot-Peened Aluminium Alloy

Table 1. Shot peen factors and their levels

Figure 1. Specimen profiles: Dimensions for the coupon (a) and the hourglass (b). Dimensions are in mm. The drawings are not to scale.

Table 2. Orthogonal array and its factors, control levels, with responses. Shaded cells (run 8) provide optimum control parameters.









Table 3. Normalised data and GR grade performance characteristics. Shaded value in column Grey Relational Grade (GRG) is and indicative of the optimum conditions.

Figure 2. Axial loading, constant amplitude S-N curves for peened at resulted conditions and un-peened specimens of AA 7150-T651

Table 4. Response table for GRG at each level of the process parameters


In the aerospace industry, this process must be accomplished to very stringent specifications to meet safety requirements. This latter demands selection and control of peening parameters. In this sense, the main parameters that control the performance of this process can be identified as media (shot), intensity, incidence angle and coverage. Meanwhile, residual stresses, surface roughness and work hardening are recognized as the main effects induced in the surface layers of the material [1]. To obtain optimised and improved conditions for effective strengthening, there should be an adequacy for making a decision on the parameters and their levels; therefore, optimisation of complicated multiple process parameters and the corresponding responses calls for the creation of a customised selection strategy. 
Over the last three decades, a large amount of research has been accomplished regarding the SP process optimisation [2-5]. Research has utilised statistical design of experiments (DOE) techniques to evaluate the interaction effect of the process parameters [7, 8] from where the Taguchi approach has become a widespread tool because it utilises a particular design of an orthogonal array to assess the quality characteristics through a reduced number of experiments [9]. Nevertheless, the Taguchi method is limited when dealing with multi-response problems. To address this issue, numerical approaches like finite elements (FE) [10], response surface methodology (RSM) [11], artificial intelligence (AI) methods and Grey Relational Analysis (GRA) effectively performs the conversion of multi-response optimisation to the single objective, etc. In this way, the non-linear and complex relationship of the SP process parameters can conveniently be investigated on the mechanical responses through the use of the hybrid GRA-Taguchi approach.

Materials And Methods

This research focuses in obtaining the optimal SP conditions applied on the Aluminium Alloy (AA) 7150-T651. This material is commonly utilised by aircraft struc-tures [6]. Two different specimen profiles were employed for applying the SP and from where data are extracted. A coupon specimen, for assessing the peening mechanical and microstructural characteristics and an hourglass shape specimen for the constant amplitude fatigue testing is shown in Fig. 1.

Chemical composition of the AA is (% wt): 0.5 S, 0.5 Fe, 3.8-4.9 Cu, 0.3-0.9 Mn, 1.2-1.8 Mg, 0.1 Cr, 0.25 Zn, 0.15 Ti, Al Base. Mechanical properties are: Yield strength = 325 MPa, Ultimate strength = 470 MPa, Young Modulus = 72.5 GPa, Fatigue Limit = 220 MPa and microhardness Vickers = 120-130. In this study, three factors of control and four levels are utilised and listed in Table 1. The assumption is based on the supposition that there is no interaction between each factor.

Shot S230, CCW20, S110 and S330 are little balls made of steel with 0.34, 0.72. 0.55 and 0.84 mm in diameter respectively. The CCW20 shot is a particular rounded steel shot but manufactured from wire; however, coverage is given in percentages, where 100% represents a surface completely indented and the incidence angle is given in sexagesimal degrees, where 90° is considered an output position of the shot through the nozzle, perpendicular to the surface to be impacted.

Grey-Taguchi Approach

A L16(43) orthogonal array experiment was selected to produce a uniform distribution of multi-responses under experimental control factors (Table 2). Orthogonal arrays exhibit self-balancing properties and make up only a fraction of full factorial experiments. The signal-noise ratio (S/N) was employed for adjusting the quality of output in the Taguchi method. In this piece of research, the-smaller-the-better S/N metric was assigned to the surface roughness factor. It was estimated by the following mathematical expression:


where Yi is the experimental value of the ith trial, and n is the number of trials. For the residual stresses and work hardening properties, the-larger-the-better estimation was used and can be defined as:


Based on the orthogonal results, the conversion of multi-response optimisation to the single objective method is carried out by GRA effectively. This is performed according to the following parts;
(a) The response should be normalised and S/N ratio is then used. Using (3) provides calculation for normalised values of kth performance of the sequence x*i(k); for this particular case, the-larger-the-better metric is used for the residual stresses and work-hardening responses;

(b) The Eq. (4) is the-smaller-the-better metric used for the stress concentration response;

A normalised matrix is generated with (3) and (4). From this matrix, a reference value is determined as the largest value of normalised value for each criterion:


The difference matrix by taking the difference between the normalised entity and reference value is determined as:


The relationship between the ideal and actual normalised results are expressed by evaluating the grey relational coefficient.


where ζ (0 ≤ ζ ≤ 1) is known as the distinguish coefficient or the index for distinguishability. If the value of ζ is small, there will be higher distinguishability. In most situations, ζ is taken as the value of 0.5 because this value provides moderate distinguishing effects and good stability [16]. The grey relational grade is a single numerical value that depicts the optimisation of the multiple performance characteristics, mathematically expressed as:


The grey relational grade is calculated by using (8) while considering the same weightage for performance characteristics, i.e. 1. In (8) m represents the number of performance characteristics assuming that they are equally important. Hence, the greatest value of grey relational grade represents the level of process parameters for optimal performance characteristics.

Results And Discussion

A normalised matrix was constructed for the three experimental responses by Eqs. (1-4). The grey relational coefficients were determined and the grey relational grade of comparability sequence for k = 1-16 was obtained as shown in Table 3.

The average of the GRG for each level of the test parameters is compiled in Table 4. This response table contains values obtained when the highest number is withdrawn from each row. The rank is an indicative of the significance in the contribution of the particular parameter under analysis. It can be readily deduced from the response table that incidence angle has the highest contribution, followed by coverage, and then shot parameter. The optimal condition for the tested parameters for maximum residual stresses and work hardening and minimum stress concentrations (surface roughness) is found to be A2 (shot type/size = CCW20), B4 (coverage = 400%) and D2 (incidence angle = 90°). These optimum parameters are in line with the resulted parameters from experiment 8, as can be seen in Table 3 along with Table 2. As previously stated, the largest value for the GRG, i.e. run 8, corresponds to the optimum condition that satisfies the selected criteria of the multi-responses.

Conventional uniaxial tension-tension fatigue tests were carried out using hourglass specimens as described in section 2.1. SP of the specimens was undertaken according to optimum conditions, i.e. A2(shot type/size = CCW20), B4(coverage = 400%) and D2 (incidence angle = 90°). The results of fatigue tests are graphically presented in the form of Wöhler stress versus cycles to failure (S-N) curves over a wide range of applied stresses as depicted in Fig. 2. The fatigue endurance is defined as the endurance stress at or below which a specimen can sustain cycling for up to 7x106 cycles without failing.
Trends observed in the fatigue life curves revealed that shot-peened specimens have a marginally superior life compared to those unpeened, specifically at an intermediate zone of the low cycle fatigue regions. Optimum peening conditions, on the whole, were found to be better as expected from the grey estimations. Furthermore, there was a discernible improvement in endurance by peened specimens when tested at stresses around 300 MPa. The fatigue endurance for the unpeened material was approximately 230 MPa, whilst for the peened at optimum condition was 225 MPa.

Final Remarks

The plethora of variables capable of altering the peening process, and hence fatigue life, is a strict process control and therefore a systematic study using ANFIS is pertinent. Coverage and incidence angle were identified as largely the peening responses.
The AA 7150-T651 peened to optimum conditions (CCW20, 400%, 90º) exhibited superior fatigue performance than initial peened conditions, and also to un-penned surfaces. Surface integrity degradation precedes fatigue damage. The geometry of the indentation is a prime damage feature. The advantages of the grey relational analysis approach compared to classical methods lay in speed, simplicity, and low cost; therefore, this approach can be considered for applications in engineering situations, as shot peening, laser peening, burnishing, water peening, etc. However, given the degree of uncertainty observed in the response table, integrated grey relational analysis with adaptive neural fuzzy integrated system has to be used to optimise the shot peening process parameters.


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Author: PhD José Solis Romero
For Information:  
PhD José Solis Romero
E-mail: jose.sr1@tlalnepantla.tecnm.mx
MSc. Sandra Silvia Roblero Aguilar
PhD Nelva Nely Almanza Ortega
PhD Víctor Augusto Castellanos Escamilla
PhD Alejandro Rodríguez Molina

Public Education Secretary of Mexico
Tecnológico Nacional de México/IT de Tlalnepantla
Postgraduate Office/Department of Mechanical Engineering