Experimental investigation on solid particle erosion behaviour of glass/epoxy Quasi-isotropic laminates

Quasi-isotropic laminates were prepared by reinforcing unidirectional E-Glass fiber with Lapox L-12 epoxy resin. E-glass fibers with density of 2.54 g cm⁻³, an average thickness of 0.2 mm and aerial weight of 300 GSM procured from CFW enterprises, New Delhi, India. Lapox L-12 and K6 hardener supplied by Atul Ltd India. The quasi-isotropic laminates with a stacking sequence of [0/90/±45]_S fabricated by hand lay-up followed by vacuum bagging technique. The average experimental density of 30 samples were estimated using Archimedes principle and found to be 1.54 g cm⁻³ as reported [18]. The samples for erosion test with a dimension of 25 × 25 × 3 mm were prepared from the fabricated laminate.

Erosion behaviour of glass/epoxy quasi-isotropic laminates was studied according to ASTM G76 [19]. Figure 1 shows the schematic representation of the Ducom Air Jet Erosion test set up.

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The test utilizes dry compressed air to accelerate the erodent particles to the required velocity and feed rate. Table 1 shows the erosion test parameters used to conduct the test. Initial and final weight after erosion measured with an accuracy of 0.0001 mg using a precision electronic balance [ALC-210.4, Acculab, England]. The irregular shaped Aluminium Oxide (Al₂O₃) with a mean size of 50 μm is used as erodent particle. Figure 2 shows the SEM image of the Al₂O₃ particles. The specimens firmly fixed in a holder and tests were carried out at predetermined parameter levels for a duration of 600 s [19].

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Erosion rate of the samples estimated as ratio of sample weight loss to weight of the erodent particles as per equation (1) [20–22].

$$\begin{eqnarray}&&{\rm{Eorosion}}\,{\rm{rate}}\left({\rm{ER}}\right)=\displaystyle \frac{{W}_{L}}{{W}_{R}}({\rm{gram}}/{\rm{gram}})\end{eqnarray} \tag{ 1 }$$

Where ${W}_{L}$ was the weight loss of the target specimen and ${W}_{R}$ is the total weight of the Al₂O₃ particles impacted on the target surface during 600 s of testing.

Design of experiments (DOE) is an effective statistical tool used for conducting experiments in a systematic approach. The DOE tools helps to identify the combinational effect of each factor at every stage of the experiment. Response surface method (RSM) is a mathematical and statistical tool used to analyse the interaction effect of different parameters with the help of minimum number of experiments [23–26]. In the present study, RSM used to identify the interaction effect between Impact velocity, A (m/s), Impact angle, B (ϴ) and feed rate, C (g/m) on erosion rate (g/g) of quasi-isotropic glass/epoxy laminates. The selection of parameters and experimental designs were carried out in statistics software. Central composite design selected for determining the influence of dependent parameters on erosion behaviour of specimens. For the selected input independent parameters second order polynomial regression equation is used to represent the response erosion rate and is given by the equation (2) [27, 28]

$$\begin{eqnarray}&&y={\beta }_{0}+\displaystyle \sum {\beta }_{i}{x}_{i}+\displaystyle \sum {\beta }_{i}{x}_{i}^{2}+\displaystyle \sum {\beta }_{ij}{x}_{i}{x}_{j}+\varepsilon \end{eqnarray} \tag{ 2 }$$

For the three selected input parameters polynomial regression equation can be written as per equation (3) [27, 28]

$$\begin{eqnarray}&&ER={b}_{0}+{b}_{1}(A)+{b}_{2}(B)+{b}_{3}(C)+{b}_{11}{A}^{2}+{b}_{22}{B}^{2}+{b}_{33}{C}^{2}+{b}_{12}(AB)+{b}_{13}(AC)+{b}_{23}(BC)\end{eqnarray} \tag{ 3 }$$

Where b_o is the average of response and b₁, b₂ ..... b₂₃ are the coefficients of mean and interaction parameters.

Erosion rate estimation and optimization experiments were conducted by varying three operating parameters. The experiments designed based on the three factors each with three levels. Three input levels of each factors is shown in table 2.

Using central composite design model and three-level full factorial L₂₀ randomized experimental design table developed using statistics software and same shown in table 3. Erosion rate of quasi-isotropic glass/epoxy laminate as a function of three independent parameters at different levels is also shown in table 3.

Figures 3(a) and (b) shows the residual plot of normal probability and residuals versus fit for erosion rate of glass/epoxy laminates. Probability plot 3(a) reveals that residuals fall in a straight line indicating normal distribution of the errors. All the residuals spread around the fitted model in the figure representing the normality assumption is true. The plot of residuals v/s fitted value to check the trend or the pattern of residuals. Residuals are expected to scattered randomly without following any pattern. From the figure 3(b) it is observed that, residuals are not following any continuous decreasing or increasing pattern.

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In order to predict the influence of various parameters on erosion rate, analysis of variance (ANNOVA) performed on the experimental data [14]. Table 4 shows the result of analysis of variance for the erosion rate of glass/epoxy laminates. Analysis carried out at 95% confidence level. The goodness of the fit of the model is predicted using R² value and found to be 87.8%. ANNOVA analysis shows that model has significant with p = 0.002 and Lack of fit is Not significant with p = 0.017. From table 4 it is clear that impact velocity (p = 0.002), impact angle (p = 0.006) and feed rate (p = 0.028) have great influence on the erosion rate glass/epoxy quasi-isotropic laminates. The interaction effect of velocity × Angle (p = 0.001) has significant influence on the erosion rate of laminates. Interaction effect of velocity × feed (p = 0.234) and angle × feed (p = 0.200) showed low influence on the erosion rate of the laminates. The fitted regression equation in terms of actual parameters is given by equation (4) as;

$$\begin{eqnarray}&&\begin{array}{l}Erosion\,rate,ER=0.0384-0.000439\times A-0.001218\times B-0.00234\times C\\ \,\,\,\,\,\,\,+\,0.000001\times {A}^{2}+0.000009\times {B}^{2}+0.000597\times {C}^{2}\\ \,\,\,\,\,\,\,+\,0.000014\times A\times B-0.00003\times A\times C-0.000044\times B\times C\end{array}\end{eqnarray} \tag{ 4 }$$

The effect of individual parameters on air jet erosion of quasi-isotropic glass/epoxy laminates is shown in figure 4.

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The plot indicates that in order to reduce the erosion rate impact velocity and impact angle of particles should be reduced while the feed rate of particles should be increased. It is evident from table 4 and figure 4 that impact velocity (p-value = 0.002) and impact angle (p-value = 0.006) is the most dominating factor controlling the erosion rate of composite laminate along with feed (p-value = 0.028). With increase in impact angle, the total impact load exerted by each particle on the target surface will increase. The total impact energy will dissipate with the formation of micro cracks on the surface. High the impact velocity results in increment of the erodent flow rate per unit time during the impact on the target surface. This leads to repetitive plastic deformation on the target surface and erosion proceeds with micro cracking and surface cracking.

Figure 5 shows the contour plots of erosion rate of glass/epoxy laminates corresponding to independent input variables. Various regions of the counter plot is used to understand the interaction effect.

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The erosion rate of target material increases with the increase of impact angle and velocity. From the contour plot, it is clear that the influence of change in feed rate of the impact particles is comparatively low as compared to other two parameters. As the impact angle is increased (above 30°), the contact area of the particles with target surface also increases. Sliding of impact particles easily removes debris from the surface and leads to higher erosion rate. Lower impact velocity and angle is the optimum operating conditions to enhance the erosion resistance of the glass/epoxy laminates.

The validity of the erosion rate model was evaluated by conducting air jet erosion test on quasi-isotropic laminates at different values of the experimental parameters such as Impact velocity, A (m/s), Impact angle, B (θ) and feed rate, C (g/m). The independent variable selected for the confirmation experiments were chosen within the low and high values of the initial input values. Three confirmation experiments were performed for the estimation of erosion rate of the laminates. The results obtained from the validation experiments and their comparison with the predicted erosion rate were listed in table 5. The error between the experimental and theoretical values were estimated and the value of observed error varies between 4.58 to 7.39%. These small error values validates the theoretical erosion rate prediction model of the quasi-isotropic glass/epoxy laminates [25, 29].

The specimens with high and low erosion rate (Specimen 4 and 7) used to study the surface morphology of the erosion process. The test conducted at a velocity of 72 m s⁻¹, impact angle of 60° and a feed rate of 2 g min⁻¹ showed high erosion rate and test conducted at a velocity of 32 m s⁻¹, impact angle of 60° and a feed rate of 6 g min⁻¹ showed low erosion rate. Surface morphology of both specimens is shown in figures 6(a) and (b) respectively. SEM images shows the material removal pattern from the target surface at steady state erosion process. Maximum erosion occurs at an impact angle of 60° because of larger exposure area of the target material to the impacting particles; which results in initiation of clearly visible micro cracks and removal bulk matrix material from the target surface as shown in figure 6(a). Image also reveals formation of large cavities between fibre/matrix interphase along the fibre direction. High kinetic energy of the impacting particles resulted in plastic deformation of the matrix material and resulted in erosion in the form of flakes of matrix material as shown in figure 6(a). Low erosion rate observed at a higher feed rate and at low impact velocity. Kinetic energy of the impact particles is depended on interference between arriving and rebounding particles. High feed rate resulted in reduction of kinetic energy of the impacting particles and reduced erosion rate of the target surface. SEM images of low erosion specimens shows initiation of micro cracks on the target surface as shown in figure 6(b).

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