*Article* **A Detailed Machinability Assessment of DC53 Steel for Die and Mold Industry through Wire Electric Discharge Machining**

**Sarmad Ali Khan 1, Mudassar Rehman 2, Muhammad Umar Farooq 1,3,\*, Muhammad Asad Ali 1,\*, Rakhshanda Naveed 1, Catalin I. Pruncu 4,5,\* and Waheed Ahmad <sup>1</sup>**


**Abstract:** Recently, DC53 die steel was introduced to the die and mold industry because of its excellent characteristics i.e., very good machinability and better engineering properties. DC53 demonstrates a strong capability to retain a near-net shape profile of the die, which is a very challenging process with materials. To produce complex and accurate die features, the use of the wire electric discharge machining (WEDM) process takes the lead in the manufacturing industry. However, the challenge is to understand the physical science of the process to improve surface features and service properties. In this study, a detailed yet systematic evaluation of process parameters investigation is made on the influence of a wire feed, pulse on duration, open voltage, and servo voltage on the productivity (material removal rate) and material quality (surface roughness, recast layer thickness, kerf width) against the requirements of mechanical-tooling industry. Based on parametric exploration, wire feed was found the most influential parameter on kerf width: KW (45.64%), pulse on time on surface roughness: SR (84.83%), open voltage on material removal rate: MRR (49.07%) and recast layer thickness: RLT (52.06%). Also, the optimized process parameters resulted in 1.710 μm SR, 10.367 mm3/min MRR, 0.327 mm KW, and 10.443 μm RLT. Moreover, the evolution of surface features and process complexities are thoroughly discussed based on the involved physical science. The recast layer, often considered as a process limitation, was explored with the aim of minimizing the layers' depth, as well as the recast layer and heat-affected zone. The research provides regression models based on thorough investigation to support machinists for achieving required features.

**Keywords:** WEDM; DC53 steel; recast layer thickness; material removal rate; Kerf

#### **1. Introduction**

Die-making industries employ a wide variety of engineering materials, such as variants of steel, for the fabrication of tools, dies, and molds based on their considerable application performance and increasing demand. Conventional steels involving D2 and D3 steel have been engaged for over a decade in the manufacturing of dies and molds. Among these steel families, DC53 steel is considered as an advancement over D2 and D3 steel in terms of its high hardness (64 HRC), better toughness, improved fatigue strength and wear resistance. Various engineering applications of DC53 steel involve the manufacturing of different rolling, forging, injection molding, extrusion, and stamping dies along with molds, cutting tools, along with a wide variety of high speed and wear resistant parts [1].

**Citation:** Khan, S.A.; Rehman, M.; Farooq, M.U.; Ali, M.A.; Naveed, R.; Pruncu, C.I.; Ahmad, W. A Detailed Machinability Assessment of DC53 Steel for Die and Mold Industry through Wire Electric Discharge Machining. *Metals* **2021**, *11*, 816. https://doi.org/10.3390/met11050816

Academic Editor: George A. Pantazopoulos

Received: 7 April 2021 Accepted: 14 May 2021 Published: 17 May 2021

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**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

The processing of such materials also becomes challenging as a result of their improved properties. Therefore, advanced machining setups are employed to fulfil the requirements. These involve electrochemical machining, electric discharge machining, plasma arc cutting, ultrasonic machining and abrasive water jet machining. These setups are considered an improvement in machining hard materials and generating a variety of machining profiles. Processing of hard materials such as titanium alloys and various other hardened steel grades—for instance, DC53 steel—may be difficult in a conventional machining scenario because of their excessive tool wear during machining. Therefore, non-conventional machining processes may be employed to serve the same purpose with little/no tool wear. Wire electric discharge machining (WEDM) is one of the non-traditional machining processes in which spark-based discharge energy is produced among two electrodes (wire electrode and workpiece) and responsible for material erosion during machining with no mechanical stresses generated unlike traditional machining processes [2].

WEDM is employed to process D2, D3 and different tool and die steel materials. Several investigations are made on the performance attributes like kerf width, material removal rate, and surface morphology, including roughness and microstructural examination involving recast layer [3–5]. The aspects of DC53 steel machining have not been thoroughly explored, therefore, are mainly investigated herein. Thiagarajan et al. [6] reported the combined influence of machining variables like pulse on duration (Pon), pulse off time (Poff), wire feed (WF) and wire tension (WT) at the MRR and SR in electric discharge machining of AISI D3 steel. A detailed study as multi-objective optimization was made by Manajaiah et al. [7] for AISI D2 steel in WEDM and inferred that the MRR, SR and recast layer thickness (RLT) are found in direct proportion with Pon. Ikram et al. [8] carried an insight investigation in WEDM of AISI D2 steel. The study reports that Pon is influenced more on SR (52.14%), MRR (49.62%), and KW (47.06%). In the study, results proved that Pon is two times more significant for SR compared to open voltage (OV), the combined influence of (WT, Pon and OV) found significant for KW, and the combination of servo voltage (SV), OV and Pon found significant for MRR respectively.

The experimental investigation performed by Vaghela et al. [9] for AISI D3 steel in WEDM inferred that the set of process variables peak current, Pon and Poff to maximize MRR, minimize KW and SR, respectively. Zhang et al. [10] performed mathematical modelling using back-propagation neural-network integrated with genetic algorithm and response surface methodology (RSM) to obtain optimal values of MRR and SR in WEDM of SKD11(D2 steel). Rupajati et al. [11] determined the machining performance regarding SR and recast layer thickness (RLT) for AISI H13 tool steel in electric discharge machining using Taguchi methodology along with the fuzzy-logic technique.

Significant improvements were obtained in RLT (22.04% reduction) and SR (13.15% reduction) from design of experiments results. It was also inferred that the significant variables for SR and RLT included Pon (40.08%) and OV (30.38%), respectively. Hasriadi et al. [12] machined two different tool steel grades in WEDM for the assessment of surface morphology in terms of SR, RLT, and density of microcracks and resulted in the previously stated response variables forming a direct linear relation with both Pon and the arc on duration. Castillo et al. [13] explored the parametric effects on AISI 304 stainless steel.

Saini et al. [14] achieved multi-objective optimization in WEDM of 16MnCr5 alloy steel. Obwald et al. [15] conducted an analysis of different pulses types generated in high-speed WEDM. A detailed study was made by Solomon et al. [16] to comprehend the effect of variation in process variables for obtaining optimized parameters in WEDM of the steel family. Multi-objective optimization performed by Shivade and Shinde [17] in WEDM of AISI D3 steel resulted that gap current, and MRR varied directly with Pon and peak current, and inversely with the machining time (tm). Azam et al. [18] optimized cutting speed (C.S) by the variation in Pon, Poff, and pulse frequency in WEDM of HSLA steel. The machined surface characterization was conducted by Dhobe et al. [19] in the electric discharge of AISI D2 steel. It was reported that RLT is found directly proportional with both SR and fatigue life. Based upon scanning electron microscopy (SEM) and X-ray diffraction results, it was reported that triple tempering (a heat treatment process) is better than single tempering as it improves the machined surface quality by reducing RLT and SR. Khanna and Singh [20] performed a comparative study in WEDM of cryogenic-treated and normal D3 tool steel for the cutting rate, MRR and SR. It was reported that the cryogenic treatment significantly influenced both the MRR (decreased 5.6%) and SR (surface finish increased 10.6%) compared to untreated D3 steel. Sharma et al. [21] endorsed similar findings on AISI D2 steel.

Ramaswamy et al. [22] predicted an optimal setting of machining parameters while performing optimization using a desirability function approach. Payla et al. [23] inferred that Pon directly influenced the MRR and power consumption during electric discharge machining of EN-31 die steel. It was also concluded that the MRR is reduced with an increase in SV because the energy density decreased as the spark gap expanded. Chen et al. [24] found that discharge capacitance has a direct and significant influence on MRR and the machining gap in microreciprocated WEDM of SKD11 (D2 steel). Singh et al. [25] supported the phenomenon for EN-31 tool steel. Abdulkareem et al. [26] worked to enhance the SR because of more adhesion of the debris particles and surface irregularities on the processed surface. Mouralova et al. [27] concluded that the frequency of discharge occurrence of the recast layer is highly influenced by cutting speed. Negrete [28] made a similar finding on AISI 01 tool steel. Kanlayasiri and Boonmung [1] investigated the influence of Pon, Poff, peak current and WT on SR in WEDM of DC53 steel. Nawaz et al. [29] used molybdenum to machine steel with the aim of achieving higher material removal rate and lesser surface roughness. The study quantified the influence of process in enhancing the pulse discharge energy because of the deeper craters produced on the machined surface. Similarly, Rehman et al. [30] evaluated gamma wire and resulted the significant influence of Pon for C.S (80.21%), KW (48.25%), and MRR (45.21%) during WEDM of DC53 steel.

The literature review reveals that a significant amount of work has already been done on various tools and die steels, especially D2, and D3 steel, to improve machining accuracy and productivity in wire electric discharge machining. However, we have noted a lack of systematic evaluation for the main parameters affecting the output responses in the WEDM of DC53 steel (having superior mechanical properties and machining performance over D2 and D3 steel), which was the key objective of this research. Moreover, the supremacy of zinc-coated brass wire (as recommended by literature) is not thoroughly studied, which may provide superior results as compared to previous established methodologies. To resolve this problem and further improve the state of the art, the following issue are discussed in this research:


The results gathered in this work are of paramount importance for the forging industry (i.e., metal forming, flow forming, spinning) in order to create tools with higher integrity and superior surface characteristics.

#### **2. Materials and Methods**

DC53 steel has numerous applications in die- and mold-making industries and is the workpiece material for investigation. DC53 is a high chromium steel with high strength, good toughness, wear-resistance and excellent machinability over that of D2 and D3 steel. The composition details and other characteristics of DC53 are shown in Table 1. A DC53 steel flat bar was used with density of 7.85 × <sup>10</sup><sup>3</sup> kg⁄m3. Experimental trials were performed in deionized water dielectric medium using zinc-coated brass wire of 0.25-mm diameter as an electrode on a CNC wire EDM setup (G43S CHMER, KNB Technologies Sdn Bhd, Malaysia). The wire electrode is recommended for fast-roughing and fine-trimming with low SR features providing less frequent breakage. Wire breakage is limiting phenomena that minimizes the productivity and upsurges the tooling cost. A detailed demonstration to illustrate the machining setup and 3D CAD view of the machined specimen accompanied by its dimensions are presented in Figure 1.

The effects of four machining variables, namely wire feed (WF), pulse on duration (Pon), open voltage (OV), and servo voltage (SV) have been carefully analyzed on the kerf width (KW), material removal rate (MRR), surface roughness (SR), and recast layer thickness (RLT). The choice of the said input parameters was made based on a comprehensive literature survey [1,15–17,19–25]. Additionally, preliminary experimentation (six trial experiments) was also performed before the mature experimentation to express the process parameter levels. In addition, the dielectric resistivity was carefully monitored and maintained at same level throughout the entire experimentation phase. Variables, in addition to the machining variables, were considered as the fixed factors. The particulars relating to the input variables and their ranges along with constant factors are reported in Table 2.

The use of full factorial design as an experimental process involves the consumption of time and cost [32] compared to the Taguchi experimental design. The Taguchi methodology is considered useful because of its precise and robust analysis by a reduction in experimental runs [30]. Consequently, Taguchi's fractional factorial design orthogonal array (OA) has been used for performing the experimentation. In total, 18 experiments under mature experimentation were successfully completed using L18 OA and were followed by the measurement of the established output responses.


**Table 1.** Key features of DC53 steel.

**Figure 1.** Illustration of experimental setup along with the workpiece.


Kerf-width is the measurement of extra material removed from the processed surface of the workpiece during machining. KW was examined by measuring the cutting slot distance using a calibrated video probe of a coordinate-measuring-machine (CMM) (CE-450DV, Chien Wei Precise Technology Co., Ltd., Fengshan District, Taiwan), as illustrated in Figure 2. MRR calculation methodology is reported in Equation (1):

$$\text{MRR} = \left[\frac{\text{W}\_{\text{b}} - \text{W}\_{\text{a}}}{\text{t}\_{\text{m}} \* \rho\_{\text{w}}}\right] \tag{1}$$

where Wb and Wa denoted the weights of the workpiece before and after processing; tm symbolized the machining time for each machining experiment, and *ρ*<sup>w</sup> showed the workpiece density, respectively. The surface texture meter (Surtronic S128, Taylor Hobson Leicester, United Kingdom) measured the surface roughness SR of the machined surface. The SR measurements were performed at three different points on the machined work surface by calibrating at an evaluation length of 4 mm and a cut-off length of 0.8 mm. The averages of measurements were used for analytical purposes. A scanning electron microscope (Vega 3-TESCAN, TESCAN, Brno, Czechia) was employed for microstructural examination of machined surface of the workpiece and recast layer thickness was measured by using optical microscope (Olympus MM6C-PS2, Olympus Corporation, Tokyo, Japan).

**Figure 2.** Schematic and physical representation of (**a**) kerf width along with physical evidence of its measurement using CMM, (**b**) For Exp. 1 (WF 5 mm/s, Pon 4 μs, OV 80 volt, SV 40 volt), (**c**) For Exp. 10 (WF 8 mm/s, Pon 4 μs, OV 80 volt, SV 60 volt), and (**d**) Exp. 18 (WF 8 mm/s, Pon 6 μs, OV 100 volt, SV 50 volt).

> To carry out the microscopic examination, samples were prepared by mounting, etching, grinding and polishing. SEM-based morphological analysis was used to explain the process science and physical phenomenon. The statistical analysis was completed by using Minitab 19 software (Minitab, LLC, State College, Pennsylvania, USA). Confirmatory experimentation was performed based on parametric settings for the validation of research results.

#### **3. Results and Discussion**

The experimentation on the DC53 steel work part was successfully performed according to Taguchi L18 to examine and investigate the behaviour of input process variables for output responses. The results of the examination are more profoundly observed and analysed using statistical analysis techniques, optical microscopy and the scanning electron microscopy. These analyses are conducted to enlighten the machining effects along with process physics involved on the microstructure of machined surface. The design of experiments (DOE) results revealed that minimum kerf width (KW) of 0.318 mm, least (average) surface roughness (SR) of 1.69 μm, higher material removal rate (MRR) of 17.82 mm3/min, and a least average recast layer thickness (RLT) of 9.63 μm were obtained. The obtained MRR results have shown maximum values as pulse on duration (Pon) was increased. In addition to this, KW, SR, and RLT values were also decreased by reducing Pon because it influenced directly on the number of sparks produced resulting in adequate melting of the workpiece during machining. The facts explanation pertaining to the analysis are stated in the upcoming segments of discussion in variance and trend analyses.

#### *3.1. Parametric Significance Analysis*

Variance analysis is considered a decisive tool to determine each process parameter's influence for a certain output response [8,30,33,34]. The insights of this analysis have been reported in Table 3, containing the *p*-value and percent contribution (PCR). The *p*-value describes the significance in such a way that the process parameter with lower (<0.05) value is considered highly influential for a specific output response compared to other control variables [35]. The is because variables with a *p*-value ≤ 5% in statistical output data, indicating a 95% confidence interval, were regarded as significant with respect to other input parameters [33]. Percentage contribution is another tool to determine the more detailed control of the machining parameters on responses. In this study, PCR was estimated to evaluate and prioritize their significance in accordance with output responses as described by formula reported in Equation (2).

$$\text{Percentage contribution (PCR)} = \left[\frac{\text{Adj SS}}{\text{Total SS}} \times 100\right] \% \tag{2}$$

where Adj SS = Adjusted sum of squares, and Total SS = Total sum of squares are used from analysis of variance to calculate the contribution. The detailed results of variance analysis from Table 3 inferred that WF (45.648%), Pon (41.56%), and SV (3.77%) are the significant factors for KW. However, the detailed influential variables for SR include Pon (84.83%), WF (8.32%), OV (2.10%), and SV (1.15%). Open voltage, pulse on duration, and wire feed with percentage-contribution of 49.07%, 32.81%, and 10.51%, respectively, influenced on material removal. Continually, the significant variables for recast layer thickness involved OV (52.06%) and Pon (40%). Thorough analysis of the statistical data reported in Table 3 resulted in the finding that the pulse on duration: Pon was the common and most influential input parameter for all defined output responses in this study.


thickness (RLT) 0.593 **<0.001 <0.001** 0.56 0.17 40.00 52.06 0.20 92.45% 90.13%

**Table 3.** Summary of analysis of variance.

#### *3.2. Process-Parametric Effect Analysis*

The parametric-effect analysis was done to study the behaviour of process variables through graphical trends of output responses and the results based on statistical analysis. The analysis is shown in Figures 3–7.

#### 3.2.1. Effects of the Wire Feed

The main effects result for WF, presented in Figure 3, has inferred that kerf width and surface roughness were decreased by increasing WF. The key reason behind this reduction is the rapid transport of wire, which resulted in less workpiece–wire electrode interaction, and produced a small heat-affected zone (HAZ). Moreover, it resulted in minor thermal damages, therefore, less molten material/debris was redeposited on the workpiece surface (will be revealed in Section 3.4). The machining efficiency of the wire electrode in WEDM was increased by increasing the WF. The effect was experienced irrespective of considering wire consumption because of a larger amount of the material removed in a shorter machining cycle was due to a rapid traverse of wire. Therefore, the material removal rate (MRR) increased with an increasing level of WF. Similar results on the wire feed were reported by Mussada et al. [36] and Negrete and Carmita [28]. It was confirmed that the increase in the WF assisted in the stable spark discharges produced and thus resulted in more melting and a redeposit of work material.

**Figure 3.** Parametric effects of wire feed (WF) for (**a**) kerf width (KW), (**b**) surface roughness (SR), and (**c**) material removal rate (MRR).

**Figure 4.** Parametric effects of pulse on duration (Pon) for (**a**) kerf width (KW), (**b**) surface roughness (SR), (**c**) material removal rate (MRR), and (**d**) recast layer thickness (RLT).

**Figure 5.** Representation of the recast layer formed on the machined work surface at random experimental settings (**a**) Pon 4 μsec (**b**) Pon 5 μsec.

**Figure 6.** Parametric effects of open voltage (OV) for (**a**) recast layer thickness (RLT), (**b**) surface roughness (SR), (**c**) material removal rate (MRR).

**Figure 7.** Parametric effects of servo voltage (SV) for kerf width (KW).

Kerf-width is defined as the measurement of excessive material removed during machining and its measurement demonstration is indicated in Figure 2. The analysis of means is shown as main effect plots in Figure 3a. It indicated an inverse relationship of WF with KW. The decreasing trend is observed for KW from 0.350 to 0.335 mm by increasing WF level from 5 to 8 mm/s. The rationale behind this effect lies in the minimal spark gap produced because of enhanced WF. The continual incoming fresh wire assisted in the minimizing the workpiece–wire electrode interaction time, and thus reduced the removal of excessive material from the work surface during machining.

However, the excessive increase in the WF produces irregularities on the machined surface, as reported by Somashekhar et al. [37]. The intensity of the current is enhanced because of consistent incoming fresh wire. This is because of the availability of increasingly present fresh ions and interacting surface. Furthermore, the wire breakage frequency may also be reduced because of adequate increase in WF. The decrease in KW happened at low Pon values. Hence, the kerf width is decreased by increasing the wire feed. Based on variance analysis from Table 3, the wire feed was also found to be top significant factor for kerf width (45.64%) compared to other process variables.

Surface roughness is the measurement of surface asperities on the machined surface [38]. The graphical trends of WF for SR from Figure 3b have resulted that the surface roughness was declined from 1.92 to 1.86 μm because of increased levels of wire feed. This is because of less contact duration between the wire electrode and the workpiece. Therefore, a greater amount of debris is flushed away by the dielectric and less discrepancies occurred on the machined surface thus resulted in small SR. Similar findings were identified by Tilekar et al. [39] and it was also inferred that the incoming fresh wire in the machining zone assisted in reducing the heat energy (function of heat transfer and plasma generation) because of instability of discharges resulting from higher wire feed which produced less irregularities on the machined surface. In addition, increased wire feed decreases the spark stability time due to the speedy motion of the wire and increases the tooling cost (similar science is discussed by Farooq et al. [40]). ANOVA observations also indicated that WF was identified as the influential factor for SR (8.20%).

The material removal rate is the measurement of amount of material-removed in a particular machining time [38]. Higher MRR is usually desired to enhance the overall machining productivity of the machine and the process. The results data have indicated that the MRR increased from 8.5 to ~10.3 mm3/min by increasing the WF values (Figure 3c). The reason is the improved stability of thermal energy produced in the cutting zone with the help of constantly moving electrode wire. This has caused an increase in the sparks density in a shorter duration of machining cycle, which leads to enhance material melting and vaporization and thus resulted in more MRR. The comparison of the MRR trends was

made with the existing literature and similar findings were obtained [37]. Wire feed was found to be significant variable for MRR (10.51%) as viewed from the variance analysis in Table 3.

#### 3.2.2. Effects of Pulse-On Duration

The analysis of the parametric effects of pulse-on duration on the selected output responses is indicated in Figure 4. It is generally said that Pon plays its key role in improving the machining performance/machinability of WEDM. The statistical data results have elaborated that all the response measures namely KW, SR, MRR and RLT were linearly boosted up by increasing Pon. The reason is that by increasing this variable leads to increase in the discharge energy among two electrodes and creates a plasma energy channel among the workpiece and wire electrode gap. This plasma channel consists of pool of electrons and ions melted material because of the generation of an adequate heat-affected zone on the machined surface. Therefore, it usually plays an important role in influencing on the machining quality. Similar insights were reported by Rehman et al. [30] and coherent results were obtained in their experimental investigation.

The graphical trend of Pon for KW is similar as of WF for MRR. The parametric plots from Figure 4a have shown the direct effect of pulse-on duration (Pon) on KW, which means that kerf width is alleviated by varying the duration of pulses. This was because the number of sparks was amplified by increasing the time interval, resulting in the enhancement of the sparks energy and thus, a larger heat-affected zone was produced. The kerf width was increased by increasing the pulse duration. However, the analysis of trends also inferred that a small increase in KW was obtained when the pulse on duration was increased to one upper level from 4 to 5 μs, whereas a sudden increase in the KW was observed as Pon was promoted from 5 to 6 μs. However, 5 μs is a threshold level of the pulse on duration, after which relatively more thermal energy is produced to melt the extra material from the sides of the workpiece because of consistently increasing sparks erosion. The variance analysis findings have also proved the most influential of Pon (41.56%) for KW.

The trend analysis of Pon is shown in Figure 4b,c for surface roughness (SR) and material removal rate (MRR), respectively. The melt material is highly depended on increased number of discharges and the discharge energy generates a large pool of electrons and ions. Thus, with the increase in the amount of material removed and surface asperities on the machined surface of the workpiece also increase. Pulse duration was found as the most remarkable parameter for SR (84.83%) and also influential variable for MRR (32.81%).

The white layer is produced during machining when the leftover melt material resolidifies on the machined surface of the workpiece [41]. Therefore, the recast layer thickness plays a vital role in evaluating the surface integrity of the machined specimen. The number of leftover debris and unflushed material on the surface has increased linearly with the increase of spark on duration. The reason is thermally affected region due to enhanced thermal energy and stability of sparks because of more spark's duration. Therefore, the number of unflushed particles were increased as the Pon is increased from 4 to 6 μs, resulting in a greater recast layer thickness, as shown in Figure 4d. A microscopic overview of the recast layer formation is shown in Figure 5. The craters produced are shallow and wider whereas the density of microcracks formation is also increased by increasing the Pon.

#### 3.2.3. Effects of Open Voltage

The role of the open voltage is to perform a thermal breakdown to generate plasma channel [33]. SR was enhanced greatly by increasing OV as can be seen in Figure 6. SR possessed a direct relationship with OV similar to RLT. The thorough analysis of observations indicated that the increase in OV resulted in increasing SR, and RLT. The key reason involves discharge energy phenomenon because of thermal breakdown during machining.

The plasma channel width is increased because of the enhanced open voltage levels resulting in a larger thermal affected zone. The surface irregularities were increased at higher values of OV as shown in Figure 6a. The surface asperities are enhanced because of increased discharge energy. This enlarged the width of the plasma channel, creating deeper craters. The volume of the material removed was decreased by increasing the OV from 80 to 100 V because of the instability of discharge energy (Figure 6b). The phenomenon involves inadequate melt generation due to a small amount of thermal energy and poor flushing conditions, resulting in the insufficient removal of melt. OV was found to have significant influence (49.07%) in controlling MRR.

The thickness of the recast layer increased linearly by enhancing the OV, as presented in Figure 6c. In this case, from OV from 80 to 100 V, a linearly increasing trend of RLT is observed similar to SR was obtained due to plasma energy channel. It was produced because the material was melted and redeposited in the surface. Therefore, discharge energy was enhanced by increasing OV leaving more material behind on the work surface. The open voltage was found as foremost significant variable (52.06%) compared to other variables affecting the recast layer thickness.

#### 3.2.4. Effects of Servo Voltage

Servo voltage is usually responsible for the transfer of heat flux on the dedicated workpiece surface through controlling the workpiece and wire electrode gap. All the output responses possessed quadratic behaviour by increasing the SV. A detailed discussion of SV provided herein, and trends are shown in Figure 7.

Kerf width was increased gradually by increasing the SV from 40 to 50 V. The rationale of the gradual increase in KW at the first two levels of SV is the relatively small amount of erosion of the material from both edges of the workpiece. However, a relatively greater increase in KW with increased servo voltage levels from 50 to 60 V is due to increased spark gap between the wire and workpiece electrodes, which resulted in a wider kerf. The phenomenon behind the increasing trend of KW was endorsed by Rehman et al. [30].

#### *3.3. Mathematical Modelling and Parametric Optimization*

To determine the predictability of responses (productivity and quality), the general regression model is developed through converting variable parameters to continuous predictive variables [42]. The general algebraic expression of model is given as following.

$$\mathbf{y} = \mathbf{b}\_0 + \mathbf{b}\_1 \mathbf{x}\_1 + \mathbf{b}\_2 \mathbf{x}\_2 \dots \dots \dots \dots + \mathbf{b}\_k \mathbf{x}\_k \tag{3}$$

In the general model, y represents the value of the response while b0 is the constant value and b1, b2, b3, ... , bk represents the estimated variation in mean response for each unit change in the variable parameters. Experimental data was used to generate regression models using variable parameters as continuous predictors. The relationship of WEDM variable parameters on productivity quality measures using multiple regression analysis.

$$\text{RLT} = -14.03 - 0.070 \text{ WF} + 1.947 \text{ Pon} + 0.2222 \text{ OV} - 0.0139 \text{ SV} \tag{4}$$

$$\text{W} = 0.3007 - 0.005037 \,\text{W} \,\text{F} \,\text{+} + 0.00883 \,\text{Pon} \,\text{+} + 0.000192 \,\text{W} + 0.000267 \,\text{S} \,\text{V} \,\text{} \tag{5}$$

$$\text{SR} = 1.3159 - 0.02074 \text{ WF} + 0.12167 \text{ Pon} + 0.001917 \text{ WV} - 0.001417 \text{ SV} \tag{6}$$

$$\text{MRR} = 18.53 + 0.624 \text{ WF} + 2.027 \text{ Pon} - 0.2478 \text{ OV} - 0.0223 \text{ SV} \tag{7}$$

Where "WF", "Pon", "OV" and "SV" are representing wire feed (mm/s), pulse on time (μs), open voltage (V), and servo voltage (V), respectively.

Utilizing the experimental data, Minitab 19 was used to develop multiple regression models associated with recast layer thickness, kerf width, surface roughness and material removal rate presented in Equations (4)–(7), respectively. The output values of the response measures were predicted after obtaining the optimal parameters for each response, and the optimization results were validated by performing confirmatory experiments. The results of the experimentation (three experiments) as a result of this optimization produced a very minute standard deviation from the design of experiments results.

Moreover, the desirability function was employed to optimize process settings, such as the minimum, which was better for recast layer thickness, kerf width, surface roughness, and the maximum, which was better for the material removal rate. The results of the experimentation provided a major process improvement. The optimized parameters obtained are "WF 8 mm/s", "Pon 4 μs", "OV 80 V" and "SV 56V". In Table 4, the close agreement is shown between the predicted values and experimental trials on the optimized process settings ensures the adequacy of empirical models.


**Table 4.** Measured responses on optimized process parameters.

#### *3.4. Recast Layer Measurement and Microstructural Evaluation*

The microscopic analysis is usually performed to analyse the physical phenomena on the surface morphology of the workpiece. The optical and scanning electron microscopybased analyses are explored herein.

#### 3.4.1. Optical-Based Microscopic Analysis

The detailed recast layer thickness analysis was carried out through optical microscope, (Figure 8A,B) to investigate the physics involved on the morphological alterations on the workpiece surface. The recast layer was measured at three distinct positions on the processed surface and average of the measurements was chosen for the analysis purpose.

**Figure 8.** Optical microscopic examination (at three different points for one experiment) for recast layer measurement at different parametric settings for (**A**) WF 5 mm/s, Pon 4 μs, OV 80 V, and SV 40 V (**B**) WF 5 mm/s, Pon 6 μs, OV 100 V, and SV 40 V.

It can be extracted from Figure 8A,B that the significant thickness is deposited on the base metal layer. Its microstructure is different from the unaffected surface consisting of primary carbides. It was inferred that the maximum recast layer thickness of 19.52 μm was obtained at the minimum WF (5 mm/s), high level of Pon (6 μs), higher value of OV (100 V), and the minimum SV (40 V). Similarly, the higher control is responsible for the thermal breakdown to improve the sparks' stability and smaller control level means that the sparks energy is focused on the specific region where material melting and redeposition occurred. Therefore, the recast layer thickness was increased at these parametric settings. Similarly, a minimum RLT was observed at WF 5 mm/s, Pon (4 μs), OV (80 V), and SV (40 V). The reason is that the debris redeposition is decreased as the sparks on duration is decreased because Pon is highly influential parameter for the recast layer thickness compared to other variables.

#### 3.4.2. Scanning Electron Microscopic Analysis

The detailed investigation for the microstructure of the processed surface is demonstrated in Figure 9a,b. The evidence shows that microcracks appeared on the machined surface. Moreover, the properties of melt material redeposit on machined surface varied because of bonding and cracks generated in heat effected region. The recast layer properties are primarily different from the base metal because of heat treatment and quenching, as shown in Figure 9. The thermal energy generated between wire electrodes results in enlarged heat effected zone produced on the machined surface, providing opportunity to redeposit onto the machined layer.

**Figure 9.** Scanning electron microscopy results of machined specimens (**a**) WF1, Pon1, OV2, SV2, (**b**) WF1, Pon3, OV1, and SV2.

It can be seen from Figure 9 that the craters of different sizes and shapes, microcracks and thermally redeposit melt material/debris were evident on machined surface. The density of crack formation and the size of the craters increased by increasing the sparkson duration (the discharge energy is linearly dependent on it). Likewise, the process is influenced by process variables on the microstructural evaluation, as evident from Table 3. Similarly, pulse on duration influenced its maximum on controlling the craters size, density of cracks formation, and size of debris globules formed on the processed surface. The measured RLT on the machined surface was found 9.62 μm. The analysis of SEM images from Figure 9 inferred that an oxide layer formed just below the heat-affected layer. This process-affected region was generated because of large plasma channel width, resulting

in more irregularities on the machined surface. The layer below the process affected zone was considered as the safe region, consisting of primary carbides of carbon.

#### *3.5. Comparison with Previous Studies*

The tabular comparison of current output results was also compared with the published literature for DC53 steel in WEDM and summary is reported in Table 5. The research findings were found almost in good agreement with the existing results which also validated the experimental work. In addition, machinability of DC53 steel with zinc-coated wire produced superior results in comparison to established practices [29,30].


**Table 5.** Comparison of the obtained results with the existing literature.

#### **4. Conclusions**

This work was dedicated to providing experimental insight into the machining of DC53 die steel, and considering the most important process variables, namely wire feed-WF, pulse on duration-Pon, open voltage-OV, and servo voltage-SV. The influence of these variables on kerf width-KW, surface roughness-SR, material removal rate-MRR, and recast layer thickness-RLT during wire electric discharge machining was studied. Through rigorous analysis based on physical phenomenon on surface morphology and material characteristics, the following conclusions are extracted:


Future work that could further improve the quality of dies tools should be focused on experimental investigation using other control variables like flushing pressure, wire tension, and corner accuracy (both top and bottom) in WEDM of DC53 steel using different wire electrodes.

**Author Contributions:** Conceptualization, S.A.K. and W.A.; Data curation, W.A.; Formal analysis, R.N. and M.R.; Funding acquisition, M.U.F., M.A.A. and C.I.P.; Investigation, W.A., M.R. and R.N.; Methodology, S.A.K. and M.R.; Resources, R.N.; Software, W.A. and M.R.; Supervision, S.A.K.; Validation, S.A.K., R.N. and C.I.P.; Visualization, M.U.F., M.A.A. and C.I.P.; Writing—original draft, M.U.F., M.R. and M.A.A.; Writing—review & editing, M.U.F., M.A.A., C.I.P. All authors have read and agreed to the published version of the manuscript.

**Funding:** This study did not receive any funding.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The data is available as request from corresponding authors.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **Abbreviations**


#### **References**


**Konstantinos Tserpes 1,\*, Panagiotis Bazios 1, Spiros G. Pantelakis 1, Maria Pappa <sup>2</sup> and Nikolaos Michailidis <sup>2</sup>**


**Abstract:** The difficulty of producing sufficient quantities of nanocrystalline materials for test specimens has led to an effort to explore alternative means for the mechanical characterization of small material volumes. In the present work, a numerical model simulating a nanoindentation test was developed using Abaqus software. In order to implement the model, the principal material properties were used. The numerical nanoindentation results were converted to stress–strain curves through an inverse algorithm in order to obtain the macroscopic mechanical properties. For the validation of the developed model, nanoindentation tests were carried out in accordance with the ISO 14577. The composition of 75% wt. tungsten and 25% wt. copper was investigated by producing two batches of specimens with a coarse-grain microstructure with an average grain size of 150 nm and a nanocrystalline microstructure with a grain diameter of 100 nm, respectively. The porosity of both batches was derived to range between 9% and 10% based on X-ray diffraction analyses. The experimental nanoidentation results in terms of load–displacement curves show a good agreement with the numerical nanoindentation results. The proposed numerical technique combined with the inverse algorithm predicts the material properties of a fully dense, nanocrystalline material with very good accuracy, but it shows an appreciable deviation with the corresponding compression results, leading to the finding that the porosity effect is a crucial parameter which needs to be taken into account in the multiscale numerical methodology.

**Keywords:** nanocrystalline materials; finite element analysis; inverse algorithm

#### **1. Introduction**

Notable attempts have been made, in recent years, at the production of materials with a nanocrystalline microstructure, due to their improved mechanical properties [1,2]. The enhancement in terms of strength by decreasing the grain size has been described by the Hall-Petch equation effect [3].

Various manufacturing methods are applied to obtain nanocrystalline alloys (i.e., a grain size less than 100 nm), including electrodeposition [1,4], powder metallurgy [5,6], magnetron sputtering [7–10], and inert gas condensation followed by the consolidation of powders [1] and severe plastic deformation (SPD) [11,12]. The vast majority of nanocrystalline materials are produced by the mechanical alloying method or electrodeposition technique. The electrodeposition technique has some inherent limitations in terms of the quality of the produced specimens because they show extensive porosity or impurities. On the other hand, the fabrication technique of mechanical alloying is able to produce materials with a nanocrystalline microstructure at a high manufacturing speed and with complete control of the fabrication parameters, so as to obtain defect-free bulk materials [13]. However, the main obstacle of the mechanical alloying method is the production of specimens without a uniform grain size, which in turn influences the macroscopic mechanical response of the materials, especially in a harsh environment. The material

**Citation:** Tserpes, K.; Bazios, P.; Pantelakis, S.G.; Pappa, M.; Michailidis, N. Mechanical Characterization of Nanocrystalline Materials via a Finite Element Nanoindentation Model. *Metals* **2021**, *11*, 1827. https://doi.org/10.3390/ met11111827

Academic Editor: George A. Pantazopoulos

Received: 11 October 2021 Accepted: 10 November 2021 Published: 13 November 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

microstructure changes rapidly at elevated temperatures. This is the commonly-known coarsening effect. The mechanical response of said materials is completely influenced by their different interphases into the microstructure. This kind of material is the so-called graded material [14,15].

Taking for granted said facts, all of the proposed production techniques are costeffective, but the produced materials are influenced by several imperfections (like flaws and pores) which drive to the degradation of the material properties. With respect to limitations in the manufacturing methods of nano-crystalline materials, the mass production of fully dense, bulk forms with a nanocrystalline microstructure at sufficient quantities has hardly been achievable up to now, and it has not been industrialized.

With the aforementioned increasing interest in the production of innovative metallic materials, mechanical testing procedures using small material volumes are more than necessary nowadays. Moreover, the conventional testing techniques like tensile or compression testing become noticeably challenging with specimens of small volume. Furthermore, limited results are shown in journals concerning the correlation between the microstructure and the resulting material properties. Some of the desirable material properties in the frame of nanocrystalline materials are the yield stress, the ultimate strength at fracture, the enhanced wear resistance and the improved plasticity compared to that of their microcrystalline counterparts [16–20]. A more detailed and extensive mechanical characterization is needed so as to obtain more reliable results.

Based on the obstacles of the mechanical characterization utilizing conventional experimental tests, scientific progress has resulted in the extensive use of nanoindentation experiments [21–34]. Berkovich indenters allow precise measurements by varying the force of the nanoindentation (*P*) in relation to the depth of penetration (*h*). Observations through experimental nanoindentation tests were performed on many materials so as to determine material features such as residual stresses and hardness [23–25,29,33–37].

At the same time, a noticeable effort has been made to use analytical and numerical investigations in order to determine the deformation mechanisms and the contact mechanics of the nanoindentation effect. The main purpose is to define the mechanical response to the applied load of nanoindentation (*P*) versus penetration depth (*h)* diagrams acquired from instrumented nanoindentation [23,25,31,32,36–41]. More specifically, researchers [23,25] suggested analytical approaches in which the modulus of elasticity and hardness could be extracted from the *Pmax* and the unloading incline at the starting stages. Additionally, Giannakopoulos and Suresh [40] proposed a procedure in which all of elastoplastic properties may be extracted through a *P-h* diagram. Based on [40], Suresh and Giannakopoulos [42] developed an up-to-date methodology which was able to export the residual stresses. In terms of numerical methods, several numerical attempts were conducted on the case studies of thin-film systems [43–45].

To conclude, a methodology was developed by Hill et al. [46] for the case study of materials with power law plastic behavior under the indentation load of a spherical indenter. The calculations of a sharp indenter, such as a Berkovich indenter, for the case of elastoplastic materials were numerically extracted by Larsson et al. [47] and Giannakopoulos et al. [38]. Moreover, scale factors were carried out so as to investigate bulk materials [31,32,39] and coated material [45]. To this end, researchers [32] have developed a comprehensive analytical approach, and several investigations were conducted on the basis of the dimensional analysis of sharp indentation. The results from the aforementioned approach showed that Kick's Law is a constitutive factor of the dimensional analysis of sharp indentation.

The scope of the present paper is to develop an innovative multiscale finite element methodology simulating the nanoindentation test which accounts for the different material phases, as they are described in [48], in order to define the macroscopic mechanical response of nanocrystalline materials. Through the aforementioned model, the nanoindentation behavior of nanocrystalline materials was extracted, and the corresponding macroscopic mechanical behavior was evaluated via the implementation of an inverse analytical algorithm. By utilizing a homogenized RVE for the last simulation in conjunction with the inverse algorithm, we are able to predict the macroscopic mechanical response.

#### **2. Modelling**

#### *2.1. Analytical Approach*

As referred to above, the nanoindentation method is a very attractive testing procedure to obtain the mechanical properties of such kinds of materials as nanocrystalline metals, which are difficult to produce in large quantities, leading to the need for the mechanical characterization of small-volume specimens. The uniqueness of the nanoindentation technique relies on the extracted results which come from the *P-h* diagram. More specifically, the estimation of the contact pressure between the nano-indenter and the target material and the resulting hardness—comes from the measurement of the contact area between said parts in terms of the indentation load and penetration depth. A continuous data acquisition in the loading phase of a typical indentation test is involved. In the following unloading part of the *P-h* diagram, the Young's modulus and Poisson ratio of the indented material can be exported at the early stages of the unloading phase because of the strain relaxation within the material [49,50]. Furthermore, material features like residual stress [46,51], initial plasticity [51–53], creep [54], and hardening [55] are very important parameters for property extraction in the nanoindentation testing method. Additionally, the surface deformation around the plastic deformation induced by the nano-indenter creates sink-in and pile-up residual strains, which are very important for the mechanical characterization of the target material [56]. The aforementioned alteration of the surface plays an important role in determining the contact area, and is also an effective factor for the definition of material properties like the strain-hardening behavior [57,58].

According to the literature for the indentation testing method, a nanoindentation test is commonly known for the creation of a non-uniform stress field at the surface of the target material, which leads to the average calculation of induced stresses [59]. The mean value of stresses in terms of von Mises stress, according to Meyer s hardness [49,59], is defined utilizing the Tabor Relation [59–61]:

$$
\sigma \approx \frac{H}{3},
\tag{1}
$$

$$H = \frac{P}{A'} \tag{2}$$

where *H* is the resulting hardness, *P* is the applied force of the nano-indenter on the target material, and *A* is the contact area of the Berkovich nanoindenter. The indentation area is calculated taking into consideration the geometry of the nanoindenter's tip and the pileup or sink-in that take place around the tip, as shown in Figure 1.

**Figure 1.** Indentation geometry showing the pile-up and sink-in.

The mathematical expressions followed for the calculation of the projected contact area of the nanoindenter are presented in Equation (3) for the case study of a Berkovich indenter's tip [62], and in Equation (4) for the case study of the spherical indenter's tip:

$$A = 24.5 \text{h}\_{\text{c}}^{2} + \text{Cl}\_{\text{c}} \tag{3}$$

$$A = \pi \left( 2Rh\_c - h\_c^{-2} \right),\tag{4}$$

where *hc* is the penetration depth of the indenter tip into the target specimen, *C* is a constant for the case of Berkovich indenters (150 nm) referring to the geometrical features of the specific indenter [62], and *R* refers to the curvature of the nanoindenter. The penetration depth of the indenter's tip was calculated according to the contact mechanics' analytical expressions (Figure 1) [49,59,63]:

$$h\_c = h - h\_s = h - \delta \left(\frac{P\_{\text{max}}}{S}\right),\tag{5}$$

$$S = \frac{dP}{dh'} \tag{6}$$

where *h* is the overall displacement of the nanoindenter; *δ* is a geometric constant parameter referring to the geometrical characteristics of the indenter's tip, which is equal to 0.75 for Berkovich indenters; the variable *hs* describes the displacement of the target material's surface during the nanoindentation load, taking into account the pile-up and sink-in deformation mechanisms; and *S* is the stiffness at the unloading phase. At this point, it is of paramount importance to mention that the stiffness at the unloading step is defined by the incline of the *P-h* diagram (an indicative plot is shown in Figure 2).

**Figure 2.** Indentation load–penetration depth curve from an indentation test.

It is noteworthy to mention that Equations (2)–(6) were from research papers in the frame of homogeneous materials. Based on this aspect, extensive work needs to be carried out so as to verify the effectiveness of the proposed mathematical procedure on heterogeneous materials like the nanocrystalline tungsten–copper materials produced and tested in the present paper. The selection of the tungsten–copper alloy was made in the frame of the European FET-Open project ICARUS [64] due to its inherent thermodynamic stability for aerospace applications. Moreover, the strain rate of the indentation at the surface of the target material is also non-uniform, and it leads to the creation of the corresponding non-uniform stress field, as referred to above. It is of paramount importance to define the mean deformation rate as the rate of the complete penetration depth into the target material over the current total displacement of the indenter [60]:

.

$$
\dot{\varepsilon} = \frac{\dot{h}}{h} \tag{7}
$$

#### *2.2. Numerical Model*

For the purpose of the nanoindentation simulation of a nanostructured material, a FE-based model was utilized. The recommended numerical methodology is utilized on RVEs with a nanocrystalline morphology. The numerical methodology is presented in the flowchart of Figure 3. The methodology begins with the computer tomograph YXLON FF35 CT (YXLON International GmbH, Hamburg, Germany) and X-ray diffraction images (Bruker D8 Discover, Bruker Corp., Billerica, MA, USA), and evolves with the image analysis and the multi-level simulation [48].

**Figure 3.** Flowchart of the methodology.

As it is commonly known, RVE is the smallest numerical volume for any material in which a macro-mechanical property can be defined through a multi-scale modelling approach. Due to the microscopic size of representative-volume elements, the detailed morphology of the materials' microstructural characteristics can be modelled. The analysis' objective is focused on the development of a numerical procedure via the parametric interaction representing the geometrical characteristics of nanostructured metals. The presumptions and the extensive numerical methodology used in the present work are described extensively in [48,65], on account of the completeness of the paper. The nanocrystalline materials are heterogeneous materials due to their discrete areas showing different physico-chemical and mechanical properties at the microscale level. Based on this paradox, the mechanical response, taken by the proposed numerical methodology shown in [48,65], is the homogenized average medium of the equivalent heterogenous nanocrystalline material. More specifically, in [48,65], the presumptions were applied for the investigation of mechanical behavior of a fully dense, nanocrystalline material under uniaxial compressive

loading, so as to extract the stress–strain response of an equivalent homogenized material from the heterogenous RVE (see Figure 4) at the nanoscale level under compression loading. In the present publication, we follow strictly the above-said numerical methodology by extending it to the application of a nanoindentation testing method, so as to define the mechanical response of nanocrystalline metals at the microscale level.

**Figure 4.** The representative volume element of a tungsten–copper nanocrystalline alloy.

The finite element modeling of the nanoindentation test was developed utilizing Abaqus CAE (Computer Aided Engineering) (Dassault Systemes Simulia Corp., Providence, RI, USA). The model was developed in three dimensions consisting of 2 objects, a representative pyramidal-like indenter with the real dimensions of Berkovich indenter and a cube representing the specimen with dimensions of 5 μm × 5 μm × 3 μm (Figure 5). The indenter was modeled to be rigid. The definition of elastoplastic response of cubic specimen was achieved by using the innovative nanoscale numerical model which was described above [48]. The material properties applied to the cubic specimen were extracted from the RVE as the homogenized average medium. The aforementioned mechanical properties were achieved by applying a compressive loading on the RVE. Additionally, a surface-to-surface frictional contact with a coefficient of 0.1 was implemented for the indentation model. Several numerical investigations have shown that the frictional coefficient between the indenter and target material is an insignificant parameter regarding the experimental nanoindentation outcomes. In the present work, the influence of the frictional contact was taken into account in the numerical model in order to develop numerically the same experimental conditions, with the ultimate goal of the maximum similarity between the numerical model and the experiments. Regarding the numerical parameters, the target material was meshed with 62,000 hexahedral elements of type C3D8R (eight node), with a dense mesh at the area of the target material directly beneath Berkovich's tip. Moreover, the indenter had a constant penetration speed of 5.5 nm/s until it reached the load of 15 mN, in the loading phase, which is a pre-defined setup parameter. After this step, the indenter was removed from the target material with a constant speed of 16 nm/s in the unloading phase. At this point, it is important to mention that the ratio of the cube's height to the maximum penetration depth is approximately equal to 8 in the current model, so as to reduce computational time. From the scope of parametric study, higher ratios of 10 and 20 were also investigated, and the results presented an insignificant divergence in the resulting *P-h* diagram compared to that of the ratio of 8.

**Figure 5.** Three-dimensional finite element model of the nanoindentation: (**a**) the dimensions of the target material, (**b**) the dimensions of the Berkovich indenter, (**c**) the meshed model and (**d**) the meshed Berkovich indenter.

The main advantage of the numerical nanoindentation models is that they are able to acquire the load-versus-depth curve of a specified reference point by continuous data acquisition throughout the duration of the simulation, just as during an experiment in situ. Furthermore, another important aspect that should be mentioned is that the proposed numerical methodology has taken into account the importance of the dimensional definition of the indented cube. In this way, the boundary effects are eliminated on the nanoindentation model, and the assumption of a continuous medium was validated. During the setup of the FE parameters, one of the most important boundary conditions applied in this model is the fixation of the target material's base so as to ensure an ideal indentation test. A second important boundary condition applied is the constraint of the nanoindenter in such a way that the nanoindenter is fixed to allow motion in the vertical direction.

#### *2.3. Inverse Analysis Algorithm*

A comprehensive analytical methodology for instrumented indentation was identified in this paper, which allows us to define the mechanical properties of materials by using a Berkovich nanoindenter. The current paper is focused on the development of an inverse analysis algorithm so as to obtain the material properties via nanoindentation tests and numerical nanoindentation models. Figure 2 shows the *P-h* curve for a Berkovich indenter. In the loading phase, it seems that the curve is in consistency with the relation *P* = *Ch*2, where parameter *C* is responsible for the indentation curvature. This curvature represents the resistance of the target material to the indentation effect. Additionally, the calculated pressure of contact, *pav* = *Pmax*/*Amax*, could be determined with the hardness of the target material, where *Pmax* is the maximum applied force for the indentation. The *Pmax* provides the necessary energy to the nanoindenter to penetrate the target material by a depth of *hmax*, by that means creating the *Amax* (the maximum projected contact area on the surface of the target material). Elastoplastic FE models with a Berkovich indenter, conducted on the present paper utilizing computational analyses comparable with those presented in reference [38], also show that

$$\frac{h\_r}{h\_{\text{max}}} = 1 - d^\* S\_\prime \tag{8}$$

where *d*\* = 4.678 for the case of a Berkovich indenter. Equation (8) is in rational accordance with the experimental observations of Breval and MacMillan [66]. Taking into consideration the true contact area on three-dimensional numerical models and the strain hardening effects imposed on pile-up and sink-in strains, the subsequent mathematical expression, which correlates *Amax* with *hmax*, was obtained for the case study of elastic–plastic materials [30,38]:

$$\frac{A\_{\text{max}}}{h^2\_{\text{max}}} = 9.96 - 12.64 \ast (1 - \text{S}) + 105.42 (1 - \text{S})^2 - 229.57 (1 - \text{S})^3 + 157.67 (1 - \text{S})^4, \text{ with } \text{S} = \frac{p\_{av}}{E^\circ} \tag{9}$$

The aforementioned mathematical expression is a polynomial regression to the calculated values of *Amax*/*h*<sup>2</sup> *max*. In Equation (9), the resulting Young's modulus of the Berkovich nanoindenter–target material system, *E*\*, is derived as:

$$E^\* = \frac{1}{c^\* \sqrt{A\_{max}}} \left(\frac{dP}{dh}\right),\tag{10}$$

where *dP*/*dh* is the incline of the *P-h* diagram at the unloading phase from *Pmax*, while the *c*\* parameter is equal to 1.167 for the case study of the Berkovich nanoindenter. Furthermore, the ratio of the residual penetration depth *hr* to the maximum depth of indentation, *hmax*, is typical of the magnitude of strain hardening and plastic deformation [41,67,68]:

$$\frac{\sigma\_{0.29} - \sigma\_y}{0.29E^\*} = 1 - 0.142\frac{h\_r}{h\_{\text{max}}} - 0.957 \left(\frac{h\_r}{h\_{\text{max}}}\right)^2\tag{11}$$

In the aforementioned Equation, *σ<sup>y</sup>* refers to the yield strength, while *σ*0.29 refers on the indicative plastic strain of 0.29 for the target material in uniaxial loading.

At this point, it is noteworthy to mention that the combination of Equations (8) and (9) gives an important relationship which correlates *Amax* with *hmax*. Using the aforementioned combined mathematical expression, we are able to extract the true contact area from the *P-h* diagram without the need of any visual examination. Knowing that

$$P\_{\max} \approx C h\_{\max} \, ^2 \prime \tag{12}$$

we can calculate the parameter *C* so as to use it into the following equation, which comes from 3D numerical simulations of elastic–plastic nanoindentation, in addition to the corresponding experiments [36,38,42,67,68]:

$$C = \frac{P}{h^2} = M\_1 \sigma\_{0.29} \left\{ 1 + \frac{\sigma\_y}{\sigma\_{0.29}} \right\} \left\{ M\_2 + \ln \frac{E^\*}{\sigma\_y} \right\} \tag{13}$$

The constants in this mathematical expression are *M*<sup>1</sup> and *M*2, where *M*<sup>1</sup> is equal to 6.618 and *M*<sup>2</sup> is equal to −0.875 for the case study of a Berkovich indenter [40].

With all of the values calculated using the above-said analytical expressions, the strain hardening exponent can be easily calculated by applying the subsequent equation:

$$n \approx \ln\left\{\sigma\_{0.29} - \ln(\sigma\_{\mathcal{Y}})\right\}/5\tag{14}$$

#### **3. Experimental**

*3.1. Materials*

To begin with, the tungsten–copper alloy system was selected for the present investigation. As mentioned above, the selection of the present alloying element combination was made in the frame of the European project ICARUS [64], which was focused on the investigation of coarsening-resistant alloys for aerospace applications. The alloy consisted of 75% tungsten and 25% copper in weight. For this material composition, two different types of tungsten–copper alloy were produced in terms of the resulting microstructure. Both types were manufactured using the same powders originating from the same powder batch.

The coarse-grained tungsten–copper specimens (cW-Cu) were fabricated through the simple mixture of the as-received commercial powders of tungsten and copper elements without any grain refinement process being involved. Additionally, the well-known manufacturing approach consisting of cold pressing, hot isostatic pressing (HIP) (University of Miskolc, Miskolc, Hungary) and heat treatment was implemented so as to obtain the consolidated specimens. The coarse-grained tungsten–copper specimen has an average grain size of 150 nm.

On the other hand, the high energy ball milling (HEBM) (MBN Nanomaterialia S.p.A., Treviso, Italy) method was utilized in order to mill tungsten and copper powders, achieving a nanocrystalline morphology with a grain diameter of 100 nm. The nanocrystalline tungsten– copper powders used for the production of the alloy will be referred in the following as W-Cu. Following the same consolidation technique of the cW-Cu specimens for the production of the corresponding W-Cu specimens, the fabrication method of cold pressing, hot isostatic pressing (HIP) and heat treatment was implemented here again. An extensive description of the produced materials' microstructures and their resulting imperfections (pores and impurities) can be found in [48]. The above-mentioned production of the two types of tungsten–copper alloys was performed by the company MBN Nanomaterialia.

#### *3.2. Nanoindentation Test*

Nanoindentation refers to a variety of hardness tests which are applied on a small scale. Penetration is perhaps the most common way of checking the mechanical properties of materials facilitated by high-precision instrumentation in the nanometer scale. In 2008, the ISO/TR 29381 was published, allowing for the evaluation of the tensile properties of metallic materials by instrumented indentation [69].

A nanoindentation device was developed at the Physical Metallurgy Laboratory, and is presented in Figures 6 and 7. The device performs testing using a Berkovich, Vickers, or Knoop diamond, or 0.5–2 mm indenters. The travel distance of the workbench can reach 50 by 140 mm, guided by specially developed computer software. The height of the optics is measured by means of a laser distance meter coupled with a rotary encoder attached to the fine adjustment dial of the microscope. The accuracy of the device in the XY direction is in the order of 1 μm. The applied load can vary from 1 to 1000 mN with a resolution of 0.1 mN, strictly following the ISO 14577 [70]. The measurement consists of two stages: the loading phase and the unloading phase. During the loading, force is applied gradually to the diamond indenter, and as it penetrates the test piece, the depth measurement is recorded. During the unloading, a residual depth remains due to the plastic deformation of the sample, which depends on the properties of the material, the size of the applied force, and the geometry of the indenter. The maximum indentation depth fluctuations measured on the same sample are mainly induced by different contact conditions between the indenter tip and the tested surface due to roughness [71]. The roughness effect can be confronted with the execution of an appreciable number of measurements to attain the stabilization of

the maximum indentation depth's mean value [71]. The proper preparation of the examined specimens is a meticulous and time-consuming process that ensures the repeatability and robustness of the results, while eliminating those parameters that could tamper with the outcome due to mishandling or human error. The mounted samples were gently, mechanically ground and polished in several sequential steps employing a BUEHLER VanguardTM 2000 (Lake Bluff, IL, USA) automatic sample preparation system [72]. The mechanical grinding took place in several sequential steps, starting with coarse grinding discs (60 grit) and ending with finer ones (1600 grit). The polishing was obtained by employing an aqueous suspension of fine alumina powder with a particle size of 0.3 μm applied on the respective polishing cloths. In this work, 50 nanoindentation tests were performed on each specimen to eliminate roughness effects.

**Figure 6.** Nanoindentation test of nanocrystalline specimens according to ISO 14577.

**Figure 7.** Specimen's fixation for the nanoindentation test.

The evolution of FEM-based algorithms in the evaluation of nanoindentation results offers advanced capabilities in the determination of the exact contact between the indenter and the test piece, thus allowing the accurate calculation of the material's hardness and the stress–strain curve. The FEM model simulating the nanoindentation procedure and the actual indenter tip geometry, introduced in [72], can be applied to calculate the contact geometry during the loading and the shape of the surface impression after unloading. The "SSCUBONI" algorithm employed for the continuous simulation of the nanoindentation enables the extraction of materials' stress–strain laws. FEM-supported methods offer advanced capabilities in the determination of mechanical properties, such as the Young's modulus, yield and rupture strength. Stress–strain curves of various materials—such as cemented carbide, ceramics and hardened steels—determined by a FEM-based algorithm of nanoindentation can be applied in FEM-supported simulations of micro- and macro-scale indentation procedures to allow the capture of the material response at various scales [73].

#### **4. Results**

The indentation force (*P*)–penetration depth (*h*) curves obtained using a Berkovich indenter tip, after a set of 50 measurements that were statistically evaluated to present the averages for the cW-Cu and the W-Cu type of alloy are presented in Figure 8, as well as the scatter of the measurement at the maximum indentation depth. As shown in Figure 8, the coarse-grained tungsten–copper alloy (cW-Cu) exhibits a higher penetration of about 400nm depth at an indentation load of 15 mN [73,74] compared to that of nanocrystalline the tungsten–copper alloy (W-Cu), which presents a penetration depth of about 250 nm at the applied penetration load of 15 mN, correspondingly. The aforementioned outcomes are reasonable due to the fact that the Hall–Petch effect governs this type of material, and the yield stress is increased by decreasing the grain size. Thus, the nanocrystalline specimen shows a higher "resistance" to the indentation effect and to plastic deformation.

**Figure 8.** (**a**) The experimental results of cW-Cu and WCu specimens in accordance with ISO 14577, and (**b**) the scatter of the nanoindentation results.

#### *4.1. Validation of the Numerical Nanoindentation Model*

Using the numerical multiscale model, the homogenized nanoindentation response of the fully dense, indented material was calculated for the case of a coarse-grained W-Cu (cW-Cu) material, and is shown in Figure 9. In this Figure, the computed *P-h* curves of a fully dense, nanocrystalline material using two Berkovich indenters—one with a sharp tip and one with a rounded tip with a roundness of 100 nm—are displayed and compared to the respective experimental curve. The geometrical features and the material properties applied on the cubic specimen are described extensively in [48]. The divergence of the numerical outcomes from the experimental result is negligible because the nanoindentation model does not take into account any defect (like pores) which might be located in the microstructure of the specimens. The aforementioned assumption of the absence of defects on the numerical model leads to the simulation of a fully dense, homogeneous-like material which may be different from that reality. On the other hand, the existing impurities or pores are mostly located at the lower layers of specimens, and as a result the nanoindenter cannot reach it through the nanoindentation test due to the very small indentation depth.

This phenomenon leads to the prediction of a nanoindentation response of a fully dense material without microstructure irregularities.

**Figure 9.** Comparison of the experimental result of the cW-Cu specimen with the numerical results utilizing sharp and rounded Berkovich indenters.

Taking for granted the above assumption, the only parameter which plays an important role on the definition of the nanoindentation response is the sharpness of the nanoindenter. In terms of the tip sharpness, both the tungsten–copper alloys and their corresponding numerical results (Figures 9 and 10) present the same tendency. More specifically, the numerical results of the sharp Berkovich indenter present the higher penetration depth of both materials. This phenomenon is reasonable due to the extensive stress concentration beneath the Berkovich tip. The sharper the tip, the higher the stress concentration factor is. On the other hand, the implementation of a rounded tip of the Berkovich indenter is a more realistic approach due to the unavoidable degeneration of the nanoindentation apparatus through its extensive usage. The above fact is logical, and the effect of the indenter's sharpness on the mechanical response in nanoindentation experiment was reported in [75]. Taking this aspect for granted, the numerical results of the rounded Berkovich indenter tend to show the most reliable nanoindentation behavior.

**Figure 10.** Comparison of the experimental result of a W-Cu specimen with the numerical results of a fully dense model utilizing sharp and rounded Berkovich indenters.

To sum up, the experimental *P-h* curve better reflects the nanoindentation behavior of a fully dense material than of a material with an extensive porosity like the examined specimens in this paper. The proposed numerical methodology shows a very good convergence with the nanoindentation test. On the other hand, utilizing the inverse algorithm as it is shown in Section 4.2, the macroscopic compression behavior obtained by the inverse algorithm of the numerical nanonindentation results will differ from the experimental compression tests examined in [48] because it does not take into account the inherent defects (impurities and pores) of the microstructure.

#### *4.2. Comparison of Nanoindentation Experimental Results Utilizing the SSCUBONI Algorithm*

Implementing the SSCUBONI algorithm, the resulting representative von Mises stress– strain curves of the cW-Cu and W-Cu specimens from the nanoindentation tests are shown in Figures 11 and 12, respectively. The aforementioned curves are compared to those of the compression tests for the same batches.

**Figure 11.** Comparison of the S-S curves of the experimental compression test with the corresponding inverse SSCUBONI-based experimental test for the cW-Cu specimens.

**Figure 12.** Comparison of the S-S curves of the experimental compression test with the corresponding inverse SSCUBONI-based experimental test for the W-Cu specimens.

As can be seen from both Figures, the inverse experimental nanoindentation results present a remarkable deviation from the compression test of the cW-Cu and W-Cu counterparts. More specifically, in Figure 11, the inverse SSCUBONI nanoindentation curve exhibits a Young's modulus of 200 GPa and a yield stress of 1340 MPa, while the corresponding compression curve shows a Young's modulus of 180 GPa and a yield stress of 450 MPa. Moreover, in the case of W-Cu specimens (Figure 12), the inverse SSCUBONI curve from the experimental nanoindentation curve shows a Young's modulus of 250 GPa and a yield stress of 2.8 GPa, while the respective compression curve for the case of the W-Cu specimen exhibits a Young's modulus of 220 GPa and a yield stress of 1150 MPa.

It is evident that the deviation of the inverse experimental nanoindentation outcomes from the experimental compression results is appreciable but reasonable. The porosity effect is the main characteristic which relies on the aforementioned deviation. As was already explained above, the nanoindenter penetrates the target material at a contact area of a few nanometers for an indentation depth of some nanometers. The contact area of the nanoindentation is extremely small compared to the volume of the specimen, and as a result the obtained experimental results reflect a nanoindentation behavior of a homogeneous-like material excluding all of the present heterogeneities into its microstructure by extracting a nanoindentation behavior of an ideal material. This procedure leads to unreliable results in the case of a material with several defects or impurities in its microstructure. The experimental test is not able to perceive the extensive presence of pores which are located in the lower layers. In our case, the experimental *P-h* curve better reflects the nanoindentation behaviour of a fully dense material than that of a material with an extensive porosity like the examined specimens of the current project.

#### *4.3. Comparison of Numerical Nanoindentation Results Utilizing the Inverse Algorithm*

In an effort to predict the macroscopic material properties via the nanoindentation testing method, an inverse algorithm was proposed and utilized in this paper. The macroscopic mechanical responses of the experimental results and the numerical outcomes of nanoindentation models were calculated for the case of a cW-Cu material and a W-Cu material, and they are shown in Figures 13 and 14, respectively. As can be seen, the experimental nanoindentation results obtained from the SSCUBONI algorithm show an appreciable convergence with the corresponding numerical nanoindentation results obtained by the proposed inverse algorithm.

**Figure 13.** Comparison of the S-S curves of the experimental compression test with the corresponding inverse numerical nanoindentation results and the inverse SSCUBONI-based experimental test for the cW-Cu specimens.

**Figure 14.** Comparison of the S-S curves of the experimental compression test with the corresponding inverse numerical nanoindentation results and the inverse SSCUBONI-based experimental test for the W-Cu specimens.

Both of the inverse analysis algorithms seem to be efficient in converting the penetration load–indentation depth curve to stress–strain curves, but the proposed multiscale nanoindentation model in conjunction with the inverse algorithm provides an advantage to the scientific community because it is able to predict the macroscopic mechanical response of any nanocrystalline material without executing any experimental test. However, it is noteworthy to mentioned at this point that the porosity effect is a crucial parameter for the mechanical behavior. For the aforementioned reason, the numerical multiscale nanoindentation methodology implementing the porosity effect for the case study of porous nanocrystalline alloys in combination with the proposed inverse analysis algorithm needs to be developed so as to predict the macroscopic mechanical response more efficiently.

#### **5. Conclusions**

Herein, a methodology was developed for the simulation of the nanoindentation testing of fully dense nanocrystalline materials utilizing a combination of numerical and analytical approaches. The numerical nanoindentation outcomes correlate very well with the experimental nanoindentation results, which validates the proposed methodology in terms of simulating the nanoindentation test. However, in the scope of the prediction of mechanical properties at the macroscale level, the proposed methodology shows an appreciable divergence with the experimental compression tests due to the porosity effect. For the aforementioned reason, it is of paramount importance that the proposed multiscale numerical methodology be modified so as to take into account the porosity effect. Additionally, a thorough investigation of the proposed methodology has to be carried out by applying different indentation loads, through numerical simulations and experimental tests, and by testing various specimens with different alloying elements, compositions and grain sizes so as to be validated for any alloy. Considering the above, it can be stated that the proposed numerical approach in conjunction with the inverse algorithm represents a preliminary contribution towards the development of a numerical nanoindentation model, and may serve as the basis for the development of large-scale models to be applied in the quality control of the mass production systems of the aforementioned promising materials in the near future.

**Author Contributions:** Conceptualization, S.G.P., K.T. and N.M.; methodology, S.G.P. and K.T.; software, P.B.; validation, P.B. and M.P.; formal analysis, P.B.; investigation, P.B.; data curation, P.B. and M.P.; writing—original draft preparation, P.B.; writing—review and editing, P.B. and M.P.; visualization, P.B.; supervision, S.G.P., K.T. and N.M.; project administration, S.G.P. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by ICARUS, grant agreement No. 713514, of the European Union's Horizon 2020 research and innovation programme.

**Data Availability Statement:** Data sharing not applicable.

**Acknowledgments:** The work described in this paper received funding from the European Union s Horizon 2020-FETOPEN research and innovation programme under Grant Agreement no. 713514: ICARUS project (Innovative Coarsening-resistant Alloys with enhanced Radiation tolerance and Ultrafine-grained Structure for aerospace application). This paper originated from a presentation made in the frame of the sixth International Conference of Engineering Against Failure-ICEAF VI.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**

