Introduction

LaPO4 and Y2O3 ceramic materials possess excellent thermal stability, high melting temperature, low diffusivity and least thermal expansion coefficient. Earlier studies on LaPO4 reveal that this material tends to form a suitable inter-phase material and also act as a reinforcement element in the composite mixture [1]. LaPO4 form a structure layer material and helps in formation of weak bond with Al2O3 and ZrO2 composite. While performing the machining operation, this rare earth phosphate material forms an interfacial bond that prevents crack growth and further avoid in the deflection of crack [2]. LaPO4 composite has proved to be machinable ceramic [3] and the addition of LaPO4 in Al2O3 composites enhance in control of grain growth [4].

Among the rare earth oxides, yttrium oxide (Y2O3) possesses excellent properties like thermodynamic stability, ability to withstand high temperature, no phase transformation. Hence Y2O3 has been preferred to be an additive material to get a stabilized phase in ceramic and metal matrix composites [5]. Besides Y2O3 is recorded as a functional material for Eu3+, Tb3+, Er3+, Yb3+, Tm3+ ions in phosphorus materials and also enhance in densification of the composite with sintering temperatures [6]. Further Y2O3 grains will impart synergistic effects of higher hardness and strength at elevated temperature. Y2O3 has higher hardness compared to lanthanum phosphate material. The addition of Y2O3 in LaPO4 will enhance the hardness of the composite which predominantly determines the machining effects of LaPO4/ Y2O3 composite.

Water jet cutting is an industrial technology capable for cutting a wide variety of materials using high-pressure jet of water, or a mixture of water and an abrasive substance. AWJM has proven to have no heat affected zone and have the thermal free cut surface [7]. Experimental observations using AWJM on different materials over surface finish reveals that smooth cut surface is acquired for the brittle materials with wear track and erosion type of failure on ductile materials [8]. The significant effect of JP is noticed while machining cast iron and to get smooth surface finish low levels of SOD and TS are preferred in AWJM [9]. The thickness of the materials significantly affects the performance of AWJM. The influence of TS on Ra is found to be superior over other operating parameters in AWJM [10]. The influence of abrasive flow rate and the abrasive particle size on Ra is studied with varied input parameters on aluminum materials that show diverged results with change in each parameters of AWJM [11]. The desire property of the cut material will determine the kerf angle of the cut region [12, 13]. While machining glass using different abrasives by AWJM, SOD signifies KA and MRR to greater extent [14]. The mechanism of the wear behavior of the material mainly depends on the material property and the abrasive particle [15, 16]. The impingement effect of different abrasives on eight different ceramic materials exhibits its own wear mechanism, hence it is concluded that the hard abrasives can be used to machine high toughness materials [17].

AWJM studies on Si3N4 show that the second-order polynomial equation of RSM fits the desire experimental values with less than 2% accuracy [18]. Earlier studies on RSM model show that JP and abrasive flow rate plays a significant role while machining AA6531 material and is stated that RSM model is a desirable method for the interpretation of the optimistic function [19]. An improved quality characteristic is obtained by using RSM with integrated Grey-RSM approach [20]. It is reported that an enviable optimistic condition on multi objective optimization was obtained in electrical discharge machining by RSM. In this study, RSM model is used to optimize the three output responses of AWJM.

The present study machines LaPO4/Y2O3 composite prepared by aqueous sol-gel process using AWJM. The pressure comes through the nozzle (JP). The stand-off distance (SOD) is the distance between the nozzle and the work piece which is also known as the work distance. Traverse speed (TS) that denotes the cutting speed or the nozzle movement is taken as the independent parameter. MRR is measure of quantity of materials removed during the cut and the taper that formed due to the abrasives flow is measured and reported as KA and surface roughness are taken as the dependent responses. The machining and influencing effect of each independent parameter on LaPO4/Y2O3 composite in AWJM is analyzed with the help of RSM.

Material and methods

Material preparation

LaPO4 sol is used as the primary material for the preparation of LaPO4/Y2O3 ceramic composite. To fabricate 20 g of LaPO4 ceramic powder, 11.6938 g of lanthanum chloride hexa hydrate solution is mixed with 5.4 ml of 88% orthophosphoric acid with continuous stirring. The pH is brought down to ~ 2. After stirring for 2 h, 25% ammonia solution is added drop wise to flocculate the lanthanum phosphate. The precipitate formed is washed and centrifuged to remove Cl− ions and the excess phosphate from the medium and it is then heated at a temperature of 1400 °C.

To synthesis 5 g of LaPO4 + 20% Y2O3 nano composite, yttrium nitrate of 17 g is dissolved in minimum amount of distilled water, further 11.6938 g LaPO4 sol is added under constant stirring condition. With a continuous stirring of about 3 h, the precipitation of Y(OH)3 as well as flocculation of LaPO4 will be slowly achieved. The pH is adjusted to 8 by addition of 25% NH3 solution in the mixture. The precipitate obtained is then dried over water bath and further heat treated to 1400 °C to remove the moisture content. The gained powder is die compacted to a pressure of 480 MPa at ambient condition to acquire a disc shape of 36 mm × 7 mm. Finally the compressed sample is sintered to 1400 °C for 2 h. The theoretical density of the composite is calculated by rule of mixtures and is recorded as 4.95 g/cm3. By employing Archimedes principle the experimental density is found to be 4.87 g/cm3. The relative density of 98.4% is achieved for the developed composite.

Methods

LaPO4/Y2O3 composite has low electrical conductivity and brittle in nature. The prepared composite is machined using AWJM of Model DIP 6D-2230. AWJM has an orifice diameter 0.25 mm with WC nozzle diameter of 0.67 mm. Garnet of 80 mesh size is used as abrasive particle. Figure 1 shows the experimental set up of AWJM.

Fig. 1
figure 1

AWJM experimental setup

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The surface roughness tester of model SJ-411 is used to measure the surface roughness. The measurement is performed over a span of 5 mm with the measurement range and probe speed of 350 μm and 0.25 mm/s, respectively.

The high precision weighing balance of Shimadzu made of model AUX 220 is used to measure the weight of the composite material. The quantity of material removed per second is calculated using the following eq. 1.

$$ MRR=\frac{\left( Wf- Wi\right)\ast 1000}{Dw\ast t} $$
(1)

Where, W i—initial weight of work piece in grams before cutting, W f—final weight of work piece in grams after cutting, D w—density of the work piece (gm/cm3) and t—period of trial (seconds).

Micro structural characterization studies

SEM analysis is employed to examine the mode of failure occurred while machining the LaPO4/Y2O3 composite at different working conditions in AWJM. The operation performed on the cut surface of the sample expels the failure mechanism and also delivers the condition of surface finish at different operated levels. ZEISS EVO series of high definition Scanning Electron Microscopy is used at a voltage level of 17.5 KV with the varied magnification.

Response surface design

Design of experiment (DOE) is a systematic method to investigate the comprehensive assessment obtained through data collection and analysis. To accrue the appropriate mathematical equations with less complexity, the second-order central composite design (CCD) is experimented. The limited number of variables in the obtained mathematical equation reduces complexity and increases the possibility of higher degree of accuracy. This action enhances the researchers to do the experimental optimization with the second-order CCD [21, 22]. The significant effect of each individual independent parameter on each dependent parameter is interrogated. The design model of L20 orthogonal array for AWJM that constitutes of 6 repetitive center level observations are done at varied time intervals. Table 1 shows the list of factors and levels. Statistical software tool of MINITAB 17 is used for the random generation of the order of the experiments. The RSM approach is used to construct the empirical equations for the three output response. The influence of each independent response and its squares are studied through the analysis of variance (ANOVA) with 95% confidential level. The quadratic equation of RSM is shown in Eq. 2.

$$ Y={b}_o+{\sum}_{i=1}^{\infty }{\mathrm{b}}_i{\mathrm{X}}_{\mathrm{i}}+{\sum}_{\mathrm{i}=1}^{\infty }{\mathrm{b}}_{ii}{\mathrm{X}}_{\mathrm{i}}^2+{\sum}_{\mathrm{i}=1}^{\infty }{\sum}_{\mathrm{j}>1}^{\infty }{\mathrm{b}}_{\mathrm{i}\mathrm{j}}{\mathrm{X}}_{\mathrm{i}}{\mathrm{X}}_{\mathrm{j}}+\upvarepsilon $$
(2)

where, Y = response factor (MRR, KA and Ra), β0 = co-efficient (Free Term), βi = linear co-efficient, βii = quadratic co-efficient, βij = interaction co-efficient and Xi, Xj = dimensionless coded independent variables.

Table 1 Selected factor and levels
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Results and discussion

Developed empirical model of AWJM for LaPO4/Y2O3 composite

The experimental observations of LaPO4/Y2O3 composite for L20 orthogonal array is shown in Table 2.

Table 2 The experimental observations of LaPO4/Y2O3 composite
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ANOVA for MRR, KA and Ra for LaPO4/Y2O3 composite are shown in Table 3. From the predicted model, the probability value (P value) for the linear equations of MRR, KA and Ra are found to be zero. Lower the P value reply and the linear dependency of all independent variables over the output responses. The lack of fit of P value for the MRR, KA and Ra are identified to be significant because the achieved P values through the regression are found to be lesser than 0.05%.

Table 3 ANOVA of MRR, KA, and Ra
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Table 4 shows the estimated regression co-efficient for MRR, KA and Ra. The significant relation exists between the co-efficient can be identified through smaller P value and either by larger T value [23]. For MRR model, all the three linear models of the independent parameter have P value as zero. This shows the influence of each independent parameter over the output responses. To identify the maximum level of influence among the independent parameters, the T value is taken into consideration. The higher T value gives a significant effect on the dependent variables. Through T value observation from the regression table, the influencing effect for MRR can be stated in the decreasing order by the linear JP, followed by linear SOD and linear TS. However for MRR, the three independent parameters show almost equal contributions and a least effect is caused by quadratic TS. The interaction between JP*TS have found to have a significant effect on MRR.

Table 4 Estimated regression co-efficient of MRR, KA, and Ra
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From the predicted model for KA, it is identified that almost all the three independent parameters have an equal contribution on output response. P value for the three linear independent parameters is zero, by considering T value from the regression table, the level of influencing effects can be ordered from high to low as linear JP, followed by SOD and TS. Quadratic JP and the interaction between JP*TS and SOD*TS had found to produce a least significant effect over KA.

Similar observations like other two dependent variables (MRR and KA) models are found for Ra. Based on T value, the significant effects for Ra are rated from high to low as; linear SOD, followed by JP and TS. The rate of influence of JP and SOD are found to be the same and produce the similar effect with change in levels irrespective of TS, while machining this new composite. Quadratic TS and the interaction between JP*TS and SOD*TS had found to have a least significant effect on Ra. It is also observed that other interaction parameters had contributed a very least effect on Ra.

The percentage of residual square (R 2) for MRR, KA and Ra are found to be greater than 95%. Hence, the generated model of MRR, KA and Ra are said to be significant. The empirical equations for MRR, KA and Ra are shown in Eqs. (3), (4) and (5), respectively.

$$ \mathrm{MRR}=0.198-0.00148\ \mathrm{JP}-0.0087\ \mathrm{SOD}-0.0004\ \mathrm{TS}+0.000003\ {\mathrm{JP}}^{\ast}\mathrm{JP}+0.001428\kern0.5em {\mathrm{SOD}}^{\ast}\mathrm{SOD}+0.000019\ {\mathrm{JP}}^{\ast}\mathrm{SOD}+0.000037\ {\mathrm{SOD}}^{\ast}\mathrm{TS} $$
(3)
$$ \mathrm{KA}=\kern0.5em -0.769+0.0057\ \mathrm{JP}+0.072\ \mathrm{SOD}-0.0039\ \mathrm{TS}+0.00805\ {\mathrm{SOD}}^{\ast}\mathrm{SOD}+0.000060\kern0.5em {\mathrm{TS}}^{\ast}\mathrm{TS}-0.000306\ {\mathrm{JP}}^{\ast}\mathrm{SOD}-0.000163\ {\mathrm{SOD}}^{\ast}\mathrm{TS} $$
(4)
$$ \mathrm{Ra}=13.3-0.161\ \mathrm{JP}+3.257\ \mathrm{SOD}+0.130\ \mathrm{TS}+0.000432\ {\mathrm{JP}}^{\ast}\mathrm{JP}-0.187\ {\mathrm{SOD}}^{\ast}\mathrm{SOD}-0.00698\ {\mathrm{JP}}^{\ast}\mathrm{SOD}-0.000201\ {\mathrm{JP}}^{\ast}\mathrm{TS}-0.00104\ {\mathrm{SOD}}^{\ast}\mathrm{TS} $$
(5)

Effect of control parameters of MRR

Three-dimensional (3-D) surface plot of control response (dependent parameter) for MRR is shown in the Fig. 2. Through Figure (a), it is observed that MRR increases with the increase in levels of JP and SOD. High pressure water beam accelerates the abrasive particles and these abrasives hit within themselves, also the pressure variation creates a wider jet beam before it hits the top surface of the sample. SOD has greater influence on increase in the width of the jet beam. At low JP, the rate of increase of MRR is low with respect to SOD. However, from the plot it is observed that the optimum operating conditions for MRR is expected to lie within the range of acceptance. From Figure (b), it is observed that MRR of LaPO4/Y2O3 reduces on increase in TS, where the change in levels of JP creates an adverse effect on machining. High TS limits the machining time and creates surface waviness on the rough cut region. The surface plotted between MRR and SOD vs TS is shown in Figure (c) which exhibits a similar effect as in Figure (b). The influence of SOD and TS on MRR is linear and the maximum point for the experimental region will be located outside the plotted region. The predicted working condition of independent variable is suggested to be JP = 220 bar, SOD = 1.10 mm and TS = 40 mm/s. The RSM model gives a new level for SOD to acquire a minimum MRR.

Fig. 2
figure 2

Surface plots of the combined effects of the independent parameters on MRR

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Effect of control parameters on KA

The 3-D surface plot of independent parameters for KA is shown in Fig. 3. From Figure (a), a slight increase with decreasing trend for KA is observed with the progressive increase of JP and SOD. Figure (b) shows a linear change in KA with increase in JP and TS, respectively. However the effect of TS is recorded to be superior to JP, while machining LaPO4/Y2O3 composite. Rapid movement of the nozzle irrespective of JP creates a narrow cut in the bottom region. Figure (c) of KA shows a slight decrease and progressive rise with change in SOD. The progressive increase on TS is recorded. From the result, it is observed that the influence of JP and TS are high irrespective of SOD. To perform a cutting operation in AWJM for this composite, a minimum level of JP and TS is recommended because the optimal point is expected to be on the outside of the plotted region. Increase in TS irrespective of JP reduces the high accelerated abrasives flow in the bottom region of the composite. This action reduces the MRR and produces a tapered surface that deliberately creates an increase in kerf angle. The optimum working condition to acquire minimum KA is predicted to be JP = 220 bar, SOD = 1 mm and TS = 20 mm/s.

Fig. 3
figure 3

Surface plots of the combined effects of the independent parameters on KA

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Effect of control parameters on Ra

The 3-D response surface plot of Ra from the predicted model is shown in Fig. 4. The combined effect of JP and SOD with Ra is shown in Figure (a). The contribution of these two parameters on Ra is found to exhibit a saddle point at some point in the plotted region. This point is an inflection point between a relative maximum and a relative minimum. To obtain a maximum or minimum response to a studied system, the saddle point coordinates do not serve as optimal values. Again, it is possible to find the optimum region through visual inspection of the surfaces. The optimal working condition might be occurred at some different operating levels.

Fig. 4
figure 4

Surface plots of the combined effects of the independent parameters on Ra

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Figure (b) shows the combined regression surface plot of JP and TS for Ra and the effects of these parameters produce a similar effect as JP and SOD on Ra. However, the influencing effect of TS is high with change in JP. Figure (c) shows the parametric effect of SOD and TS on Ra. The higher the operating levels of TS larger the value of Ra. Through the obtained surface plot, it became possible to predict the optimal condition. From Figure (a–c), it could be confirmed that all the three independent parameters have a significant effect on Ra. However the rate of change of the three influencing factors on Ra increases with increase in operating levels. The acceptable level of Ra is achieved at low level operating conditions of JP = 220 bar, SOD = 1 mm and TS = 20 mm/s in AWJM.

Sub-microscopic analysis

SEM image on the cut surface shows the presence of both transgranular and intergranular fractures and is shown in Fig. 5. Figure (a) shows the presence of rupture region all over the cut surface with dimples and micro crack confirms that the machined surface is plastic deformation surface. The micro level wear track and scar that are created by the impinged of the abrasives are clearly visible. As the high accelerated abrasive hits the composite surface and when it expels out after machining, it collides with new abrasives and creates wear track in a random order. The wear track demonstrates the abrasive flow direction. On closer observation, it is noticed that the micro level crack propagated along the grains and the grain boundary and is shown in Figure (b). Micro cracks are formed due to the simultaneous heating and cooling effects on the cut surface. As the hard abrasives impinge the composite, there is a raise in temperature. Since the working medium is water, cooling takes place at the instant create micro cracks.

Fig. 5
figure 5

SEM micrograph of AWJM cut region of LaPO4/Y2O3 composite

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The hard abrasives tear the composite and create the peaks and valley regions on the cut surface. The high accelerated abrasive tends to break the bond energy between the elements in the composite and hence the machining is done by erosion. The mechanism behind the removal of materials confirms the ease of machinability of the composite material by AWJM.

The microscopic observation clearly delivers that the effect of high traverse speed will significantly enhance the surface property of the composite. Further it is noticed that in AWJM irrespective of TS, even at all level operating conditions an acceptable level of Ra is obtained with the measure of 1.664, 2.635 and 2.482 μm. The consequences of increase in the width of the water beam tend to increase the machined area of the top surface of the composite. Owing to the increase in TS, a smaller opening is observed at the bottom of the composite. This leads to form the striation on the bottom region of the cut surface, which substantially affects Ra of the composite material.

Conclusions

This study evaluates the influences and the significant effects of the three independent variables (JP, SOD and TS) of AWJM on LaPO4/Y2O3 composite on use of garnet as abrasive and the conclusions drawn as follows:

  • By RSM model, the correlation exists between the JP, SOD and TS of AWJM on LaPO4 + 20%Y2O3 that are examined. From the obtained results it can be stated that all the three considered independent parameters had played a significant role to the output responses.

  • From ANOVA table, it is estimated that the three independent parameters affect the MRR in the equal proportion, however based on their influencing effect it is in the following decreasing order; linear JP, SOD and TS. A least significant effect is observed by Quadratic TS. To the interaction part a least effect of JP*TS is recorded.

  • By ANOVA table, the significant effect of three independent parameters on KA shows equal contribution. Based on the influencing factors, the order is that JP is followed by SOD and TS. Among the other determinant factors, quadratic JP and the interaction between JP*TS and SOD*TS have a least significant effect.

  • By ANOVA of Ra, it is stated that SOD has the most significant role, followed by JP and TS. Further, quadratic TS and interaction between JP*TS and SOD*TS has a least influencing effect.

  • SEM analysis on the machined surface reveals the presence of micro wear cracks and wear track over the regions. Further the presence of rupture region with dimples confirm the plastic deformation cut surface. Peeling off and deep wear track explain the ease of machinability of the functional composite by other conventional machining practices.

  • The predicted optimization conditions for each output responses of LaPO4/Y2O3 composite in AWJM are estimated to be; for MRR is JP = 220 bar, SOD = 1.10 mm and TS = 40 mm/s, for KA is JP = 220 bar, SOD = 1 mm and TS = 20 mm/s and for Ra JP = 220 bar, SOD = 1 mm and TS = 20 mm/s