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Investigation of scratching sequence influence on material removal mechanism of glass-ceramics by the multiple scratch tests
Author’s Accepted Manuscript Investigation of scratching sequence influence on material removal mechanism of glass-ceramics by the multiple scratch tests Xue Yang, Zhongjun Qiu, Xue Li www.elsevier.com/locate/ceri
PII: DOI: Reference:
S0272-8842(18)32730-5 https://doi.org/10.1016/j.ceramint.2018.09.256 CERI19655
To appear in: Ceramics International Received date: 3 September 2018 Revised date: 25 September 2018 Accepted date: 25 September 2018 Cite this article as: Xue Yang, Zhongjun Qiu and Xue Li, Investigation of scratching sequence influence on material removal mechanism of glass-ceramics by the multiple scratch tests, Ceramics International, https://doi.org/10.1016/j.ceramint.2018.09.256 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Investigation of scratching sequence influence on material removal mechanism of glass-ceramics by the multiple scratch tests
Xue Yang, Zhongjun Qiu*, Xue Li
State Key Laboratory of Precision Measuring Technology & Instruments, Tianjin University, Tianjin 300072, China
*
Corresponding author. Tel./fax: +86 022 27403753. [email protected]
Abstract The existing research on grinding mechanism by single scratch method cannot reflect the interaction among multiple scratches caused by the stochastic distribution of numerous grits on the grinding wheel surface. To clarify the effect of multi-scratch interaction on material removal mechanism during grinding of glass-ceramics, a multi-scratch experiment with different scratching sequences was conducted on glass-ceramics using a nanoindenter in this paper. A model of multi-scratch stress field is established to analyze the material removal mechanism such as surface morphology, material deformation, crack propagation and chip removal strength. The results show that successive scratching sequence promotes to the severe crack propagation of glass-ceramics due to its higher maximum principal stress whereas non-successive scratching sequence is prone to result in chip removal owing to its deeper stagnation 1
region. These findings provide critical insight of grinding mechanics for glass-ceramics components by considering the interactions among multiple scratches.
Keywords: Glass-ceramics; Material removal mechanism; Stress analysis; Multiple scratch tests
1
Introduction Glass-ceramic is a typical high-performance material for manufacturing many
optical components such as large reflective telescopes, integrated lens arrays and laser gyroscope due to its superior properties of low thermal expansion coefficient, high strength, high abrasion resistance, good chemical durability and high transmissibility etc. [1]. Excellent surface quality is required for these glass-ceramics components applied in precision optics field to improve their functional performance and lifetime [2]. However, the hard-brittle nature of glass-ceramic limits its machinability. Grinding, lapping and polishing are the main methods for machining of glass ceramics [3]. For hard-brittle materials, the traditional fabrication of a high-precision surface begins with grinding which leads to extensive machining-induced damages [4]. To diminish these damages resulting from grinding, subsequent lapping and polishing processes are used to obtain an acceptable roughness and integrity of surface, but these processes are time consuming and expensive due to their low material removal rates [5]. In order to reduce time and cost, surface quality achievable by grinding processes becomes more important [6]. Nevertheless, it is still being challenging to improve the surface quality in grinding 2
process due to the random distribution of numerous grits on grinding wheel surface [7]. Therefore, the fundamental understanding of the material removal mechanism during grinding of glass-ceramics is a prerequisite for ensuring an acceptable surface quality. Many efforts have been made to study the material removal mechanism by a single scratch method which is a simplified analogy of grit-workpiece interactions in the grinding process. Crack propagation, material deformation, or the combination of both are the manifestations of material removal during grinding. Therefore, scholars have carried out extensive experimental and theoretical investigations using the single scratch method from perspectives of crack propagation and material deformation. Study of crack propagation contributes to optimize the grinding process and furthermore improve the surface quality of glass-ceramics components by suppressing the crack extension [8-10]. Apart from crack propagation, material deformation also plays a crucial role in the material removal mechanism [11, 12]. Li et al. [13, 14] carried out nanoscratch tests on optical glass BK7 and single crystal GGG (Gd3Ga5O12). The results show that the residual depth of scratch, elastic recovery rate and residual stress caused by material deformation have an important effect on the surface quality. Moreover, analysis of single grit-workpiece interaction is easy to study the effect of speed, and depth of cut on the material removal mechanism. High grinding speed and low depth are prone to suppress the crack propagation and achieve ductile-regime grinding [15, 16]. The effect of grit characteristics (like wear, rake angle, sharpness, shape and size etc.) on material removal also has been investigated [17-20]. Although single scratch method makes it easy to demonstrate the contribution of individual grit to material removal, the 3
mechanism of material removal in single scratch process may be substantially differs from that in actual grinding. In real grinding process, the material removal is mainly as a result of multi-grit combined interaction which is not a simple superposition of single-grit scratch. Simplified single-grit scratch cannot represent this intrinsic complex interaction characteristic of the grinding process. The interaction among scratches produced in grinding process partly results from the stochastic distribution of the numerous abrasive grits on the surface of the grinding wheel, which causes not only the different scratch distances but also the difference of the produced order of the scratches i.e. scratch sequence. For scratch distance, Qiu [21] and Li [22] have studied the effect of the scratch distance on the crack propagation and material deformation, respectively. However, studies on the scratch sequence caused by the grit random distribution are rare for now. To study the effect of the scratch sequence on the mechanisms of material removal and deformation, research on the multiple scratch (at least three scratches) is an important step to reveal the comprehensive interferential effect of numerous abrasive grits on the surface of the grinding wheel. In the current study, the material removal mechanism of interactional multiple scratches is investigated by analysing the multi-scratch stress field in glass-ceramics. The analytical model of multi-scratch stress field is utilized to analyze the multi-scratch experimental results. The multi-scratch experiment with successive scratching sequence and non-successive scratching sequence is conducted on glass-ceramics by using Berkovich indenter to simulate the actual grinding process. The surface morphology, material deformation, crack propagation and chip removal strength of glass-ceramics, 4
which are measured by using the Nano Indenter system, SEM and AFM, are used to demonstrate the interactional material removal behaviour of multi-scratch under different scratching sequences. 2
Material and methods
2.1 Definition of scratching sequence Numerous abrasive grits on the grinding tool are characterized by the irregular geometry, undefined grit protrusion height, and stochastic distribution associating with scratch distance and scratching sequence as shown in Fig. 1. Scratching sequence caused by the grit stochastic distribution is the focus of present work in which the protrusion height and geometry of grits are assumed to be uniform to avoid introducing more variables. Scratching sequence is classified into two types: successive scratching sequence and non-successive scratching sequence. Three scratches at least are required to describe the feature of scratching sequence. Successive scratching sequence results 1 , grit ○ 2 and grit ○ 3 while non-successive from the distribution pattern such as grit ○ 4 , grit ○ 5 and scratching sequence is caused by the distribution pattern similar to grit ○ 6 (see Fig. 1). Detailed schematic diagrams of successive scratching and grit ○
non-successive scratching sequences are illustrated in Fig. 2 where the scratches on the surface of glass-ceramics after the experiments are g1, g2 and g3 along y-axis. Major difference between the two scratching types lies in the scratching order. In successive scratching sequence as shown in Fig. 2a, g1 is firstly conducted on glass-ceramics, which is followed by g2 and g3 successively. Unlike successive scratching sequence, the scratches in non-successive scratching sequence as shown in Fig. 2b are conducted in 5
order of g1, g3 and g2. 2.2 Specimen preparation and experimental procedure Present study adopted the lithium aluminosilicate (LAS) glass-ceramic with dimensions of ϕ25 (diameter) × 5 mm (thickness). The material properties of LAS glass-ceramic were listed in Table 1. The specimen was embedded in resin with dimensions of ϕ40 (diameter) × 23 mm (thickness) and then was polished successively by using 10 μm, 5 μm, and 3 μm diamond powder and 0.04 μm silica gel suspension liquid to get a smooth surface. The polished specimen was mounted on the workbench of Nano Indenter (Keysight G200) as shown in Fig. 3a. Experiments were carried out by Berkovich indenter with a tip radius about 100 nm and experimental details were illustrated in Fig. 3b. The Berkovich indenter was face-forward and was conducted repeatedly multiple times on the surface of the workpiece to produce the three taper scratches of each sequence group. For convenience of analysis, the distance between adjacent scratches after the experiment is equal to d in the present study. Detailed experimental parameters are given in Table 2. Each group of multi-scratch tests has been repeatedly performed on glass-ceramic specimen three times to validate the repeatability of experimental results and the most typical experimental results are shown in this paper. 2.3 Measurement After producing the scratches on glass-ceramics, the scratch depth h and residual depth hr were measured by the in situ detection of the nano-indenter to analyze the material deformation characteristics (elastic and plastic deformations). Scanning 6
electron microscopy (Nanolab Nova 200) was used to observe the surface morphology in different scratching sequences. In order to explore the effect of scratching sequence on material removal of ductile mode, chip removal strength defined by subtracting the total pile-up area from the total scratch groove was introduced. The atomic force microscopy (AFM) was utilized to measure the surface morphology to extract the cross sections profile and furthermore to obtain the areas of groove and pile-up, which were calculated by the integration method. 3
Results Surface morphology, material deformation and chip removal strength are important
for identifying material removal mode, improving machining precision and surface quality of glass-ceramic component, and therefore are investigated in this section. 3.1 Surface morphology SEM image enables the observation of surface morphology so that the dependence of surface quality on scratching sequence is explained. Fig. 4 shows the overall surface morphology of successive scratching sequence and non-successive scratching sequence. Fig. 5 shows the surface morphology and cross section profile at L = 35 m in both scratching sequences. It can be seen that the residual depth of scratches in both scratching sequences is all about 30 nm and equivalent to a single scratch without interaction. In contrast, at L = 180 m, the surface morphology in Fig. 6 indicates that three scratches in each scratching sequence interact with each other. The interaction effect causes that the residual depth of scratches in both scratching sequences is different from each other. In successive scratching sequence (see Fig. 6a), due to lack of 7
material support on the left side, the material of g3 moves toward the groove of g2, which results in the prior groove being partially covered and leaning to the left. Similarly, the groove of g1 is incomplete owing to the material extruded by g2 covering the partial groove of g1. Unlike surface morphology in successive scratching sequence, the entire surface morphology in non-successive scratching sequence presents symmetry (see Fig. 6b). This comes along with the existence of g1 and g3 produced previously, which lead to a lack of material support on both sides of g2. When g2 is performed, the material is pushed into the groove of g1 and g3, and hence this makes the bottom of g1 groove incline towards the left side while the bottom of g3 groove tilts toward the right side. Surface morphology in both scratching sequence differs and this will result in different thickness of hardening layer of the workpiece, which affects the surface integrity. The symmetry surface morphology acquired by non-successive scratching sequence contributes to a relatively uniform hardening layer and surface integrity. Fig. 7 depicts that cracks emerge at the end of multi-scratch in both scratching sequences because the maximum principal stress exceeds the fracture stress required for crack propagation. Scratches produced in successive scratching sequence and non-successive scratching sequence show different characteristics in terms of material removal mechanism. It is found that successive scratching sequence more easily causes noticeable material peeling due to a greater extent of micro crack propagating and merging (see Fig. 7a), while there are micro cracks in non-successive scratching sequence but no material peeling due to the absence of the mergence among cracks (see Fig. 7b). 8
Comparing results in double scratching sequences, it can be concluded that the scratching sequence has a significant impact on surface morphology and material removal behaviour. Compared to non-successive scratching sequence, successive scratching sequence promotes a material removal mode transition from ductile to brittle. Therefore, optimization of the distribution of grits on the grinding wheel surface for maximizing the non-successive multiple scratches is an option to achieve ductile regime grinding. This contributes to the crack-free surface and further to the improvement of performance as well as reliability of glass-ceramics parts. 3.2 Material deformation characteristics In ductile regime grinding of glass-ceramics, the interactional material deformation induced by multi-scratch plays an important role in the machining accuracy. Therefore, the scratch depth and residual depth were analyzed to investigate the effect of scratching sequence on material deformation of glass-ceramics. Fig. 8 shows the relationships between scratch depth h, residual depth hr and the scratch length L as well as the normal force P. Clearly, the scratch depth and residual depth increase with P rising, but curves of three scratches in each group are not identical. According to the deviation among curves, it can be observed that there are three deformation phases in both scratching sequence types: complete elastic deformation, plastic deformation without interaction and plastic deformation with interaction. Complete elastic deformation occurs with a small region at the start of scratches, in which hr equals to 0 due to the elastic recovery on unloading. With P increasing, hr starts to be larger than 0 and this indicates the material deformation enters into the 9
plastic deformation stage. The curves of h and hr in this stage are identical, which demonstrates no interaction occurring among scratches. This case corresponds to the surface morphology in Fig. 5. As P further increases and exceeds a critical value where the curves of the three scratches are separated, this means that the scratches in each scratching sequence start to interact with each other. This is the phase of plastic deformation with interaction, which corresponds to the surface morphology in Fig. 6. Within the interaction phase, the deviation of curves is attributed to the difference in elastic recovery rate , defined as (h – hr) / h. Fig. 9 presents the variation of elastic recovery rate of g1, g2 and g3. In both scratching sequences, the elastic recovery rate of multi-scratch decreases with the increase of P and gradually tends to be stable. There is a noticeable deviation in of g1, g2 as well as g3 (see Fig. 9a) in successive scratching sequence compared to that in non-successive scratching pattern (see Fig. 9b). This fact is attributed to that successive scratching sequence intensifies the interaction of deformed material of neighbouring scratches and furthermore enhances the hardness of material. Comparing the deformation characteristics of glass-ceramics in two scratching sequences, non-successive scratching sequence results in a relatively uniform material deformation due to the slight variation in elastic recovery rate. Uniform deformation is benefit for obtaining better surface roughness during grinding of glass-ceramics. Therefore, non-successive scratching sequence is a choice employed to improve the surface quality of glass-ceramic parts in actual grinding process. 3.3 Chip removal strength 10
In ductile regime grinding, the chip removal strength is a measure method of material removal rate across the sectional area of the scratch as shown in Fig. 10a [19]. As shown in Fig. 4, there are three phases of the material removal mechanism in grinding, namely, rubbing, ploughing, and cutting. Only in the cutting phase, the material is removed in form of a chip. To investigate the influence of scratching sequence on the mechanism of material removal in ductile mode, current section emphasizes on the chip removal strength according to the extracted the transection profiles perpendicular to the scratch. Fig. 10b shows the chip removal strength for P=20mN. It is obvious that the chip removal strength in non-successive scratching sequence is higher than that in successive scratching sequence. This indicates that non-successive scratching sequence allows materials to flow upward more easily and thus results in prominent chip removal. 4
Discussions In the current study, it is noticeable that scratching sequence has an evident effect
on both crack propagation and chip removal strength of glass-ceramics. Damage and material deformation induced during grinding result from stress distribution. Therefore, establishment of the stress field for multi-scratch facilitates to gain a deep understanding of the mechanisms of crack propagation and material deformation. However, most of the previous studies always focused on the stress field of a single-scratch. The stress field of multi-scratch was rarely investigated due to its complex interactions among the multiple scratches. To thoroughly clarify the complex material removal mechanism of multi-scratch, a need has arisen to establish a model of 11
multi-scratch stress field to analyze the crack propagation and plastic deformation of glass-ceramics in different scratching sequences. 4.1 Establishment of stress field model for multi-scratch During a single scratch process, the stress field around the indenter is constructed as the superposition of Boussinesq field ij, Cerruti field ij, and the sliding blister field ij, respectively, due to the normal force P, the tangential force Q and the residual stress [24, 25]. The stress field of a single scratch is expressed as [26]
ij k0 ij ij +k2 ij ,
(1)
where subscripts i and j represent the stress component directions like i, j = x, y, and z, while k0 is a constant that takes 1 on loading, and 0 on unloading. Expressions for ij, ij, and ij are given in Appendix A. The factor k2 represents the relative strength of sliding blister field and can be expressed as k2
1.09 H 3 2 E cot 2 , E 4 (1 2 )(1 ) H
(2)
where E, H, and are elastic modulus, hardness, half-apex angle of a grit and Poissons ratio, respectively. The dimensionless geometric parameter
3 is
obtained according to the relationship between the Berkovich indenter and its equivalent axial-symmetric cone indenter [27]. In microscale grinding process, the friction coefficient is related to , scratch depth h, grit tip radius R, and half scratch width a together [28]. It can be expressed as
12
2 2 a 2 sin -1 a a 1 h / R 1 sin R R R 2 cot 4 cot 2 - 2a 2 1 h / R 1 sin cot R .
(3)
Half width of scratch depends on the normal force and material hardness, and it is determined as
a P H
(4)
.
Based on the interactive feature of multiple scratching and the stress field of a single scratch, the multi-scratch stress field ij is established by coordinate transformation (see Fig. 2), and it is given by
n 1
m 1
ij x, y, z k2 ij x, y d m , z
k
0
ij x, y d n , z ij x, y d n , z k 2 ij x, y d n , z
n k2 ij x, y d m , z m 1 k0 ij x, y d n , z ij x, y d n , z
(5)
,
where dm represents the distance from any previously conducted scratch to the firstly conducted scratch and dn stands for the distance from the last conducted scratch to the firstly conducted one which is taken as x-axis as shown in Fig. 2. Constant n stands for the total number of scratches and constant m ranges from 1 to n (i.e. the first scratch to the last one). According to Eq. (5), in successive scratching sequence, the interactional stress field is constructed as the superposition of ij, ij (due to the last conducted scratch g3) and ij (due to g1, g2 and g3) and it is given by 13
ij x, y, z k2 ij x, y, z k2 ij x, y d , z k0 ij x, y 2d , z ij x, y 2d , z k2 ij x, y 2d , z .
(6)
Similarly, the interactive stress field in non-successive scratching sequence is the sum of ij, ij (due to the last conducted scratch g2) and ij (due to g1, g2 and g3) and it is given by
ij x, y, z k2 ij x, y, z k2 ij x, y 2d , z k0 ij x, y d , z ij x, y d , z k2 ij x, y d , z .
(7)
4.2 Analysis of the maximum principal stress To explain the phenomenon in Fig. 7 and reveal the material removal mechanism of multi-scratch, the stress field of multi-scratch is discussed. According to the maximum principal stress criterion, crack is activated and extends when the maximum principal stress exceeds the fracture stress. The maximum principal stress 1 can be obtained from the multi-scratch stress field. Because material peeling in brittle-regime scratching is as a result of lateral crack merging with radial crack or itself, it is obvious that the lateral crack is mainly responsible for the material removal [29]. Therefore, the maximum principal stress at the bottom of the plastic zone where lateral crack occurs is analysed as shown in Fig. 11a. Plastic zone radius b can be obtained based on the literature [26], which equals to 2.3662 m for P of 30 mN corresponding to Fig. 7. For convenience of comparison, the maximum principal stress is normalized as 1b2/P. Fig. 11b shows the normalized maximum principal stress of single-scratch which is used as a reference to be compared with that of multi-scratch to explore the effect of multi-scratch on crack propagation. The maximum principal stress of multi-scratch on a y- z plane is extracted as shown 14
in Fig.12a. From Fig. 12b and c, it can be seen that the average stress magnitude of multi-scratch in both scratching sequences is higher than that of single-scratch (see Fig. 11b). This indicates that compared with a single scratch, the interactional effect of multi-scratch is prone to cause brittle mode of material removal due to the enhanced maximum principal stress. Therefore, the ductile to brittle transition (DBT) depth obtained by single-scratch test cannot be used as an effective basis for selecting grinding depth during actual grinding of glass-ceramic, because single-scratch test neglect the interaction effect amongst multiple scratches. During grinding of glass-ceramics, it is suggested to select a much smaller grinding depth than DBT depth of single-scratch to achieve ductile removal mode. Normalized principal stress in different scratching sequences is compared to explain the effect of scratching sequence on the crack propagation. Fig. 12b gives that the distribution of complete stress along y-axis in successive scratching sequence, which is composed of residual stress due to g1 and g2 on unloading as well as the stress caused by g3 on loading. In particular, the normalized principal stress reaches its maximum at the location between g1 and g2, and has a second peak near g2. The fact is that the last conducted scratch elevates the residual stress of prior existing scratches, and this explains why the material peeling occurs near g2 in Fig. 7a. Different from the concentrated distribution of stress in successive scratching sequence, the maximum principal stress in non-successive scratching sequence is much smaller and relatively uniform as shown in Fig. 12c, but still greater than that of a single scratch. Uniform stress distribution caused by non-successive scratching sequence is able to result in 15
crack activation but the extended size of crack is not sufficient to cause crack interference and material peeling. This is consistent with the observation in Fig. 7b. In summary, the scratching sequence has a strong influence on the stress distribution responsible for crack propagation and material removal mode. Successive scratching process induces a higher maximum principal stress and leads to a greater extent of crack propagation as well as material peeling. This provides the ability to rationalize the phenomenon in Fig. 7. 4.3 Analysis of the deviatoric stress In ductile mode of material removal, generation of scratch groove, pile-up and chip is caused by the material flow behaviour ahead of a grit. As shown in Fig. 13a, the stagnation region S divides the material flowing in two directions: some material flowing upward and the remaining material flowing downward. The material below S generates the scratch groove, while the remaining material above S leads to the pile-up and chip formation (see Fig. 13b) [30, 31]. Clearly, material flow behaviour is important for understanding the material removal mechanism in ductile regime grinding. However, in previous studies, the focus was just on the analysis of crack initiation and propagation using the stress field. The evolution of material flow caused by the stress field ahead of an indenter was seldom investigated. Therefore, present work will focus on analyzing the stress components responsible for material flow ahead of an indenter. In the current investigation, the elastic stress field solutions are utilized to rationalize the observed chip removal in our study by analyzing the material flow in glass-ceramics [32, 33]. The material flow results from the deviatoric stress ahead of an 16
indenter [34]. According to Eq. (5), the deviatoric stress component Sij can be given by S xx Sij S xy S xz
S xy S yy S yz
xx m S xz xy xz S yz ij m xy yy m yz xz S zz yz zz m ,
(8)
where σm is the hydrostatic stress. Apparently, analysis of the deviatoric stress facilitates to gain a deep insight into the surface generation due to scratch groove and pile-up, as well as chip formation. For clarity, as the indenter moves forward on the workpiece surface, the two-dimensional (2-D) distribution and orientation of the material flow on an x-z plane are shown in Fig. 14a. The stagnation region is a prerequisite for chip formation, and is characterized by the deviatoric stress component along z-axis equivalent to 0. To identify the depth of the stagnation region, the deviatoric stress component along z-axis Sz is needed to be deeply analyzed and it is expressed as
S z S zz S xz .
(9)
Fig. 14b presents the distribution of the normalized deviatoric stress component Szh2/P at (a, 0, z). At the location close to workpiece surface, the deviatoric stress component is larger than 0 and this means that the material flows upward to form pile-up and a chip. However, as z/h increased, the deviatoric stress component gradually decreases from positive to negative. The negative value of the deviatoric stress indicates that the material flows down to generate the scratch groove. Note that the stagnation region depth hs is 0.11h at P=20mN. Different from the stress field of a single scratch, the stress field of multi-scratch is more complex due to the combined interactions. In multi-scratch process, the stress field of each scratch on loading is needed to be analyzed due to the chip removal mainly 17
occurring ahead of an indenter. The deviatoric stress component Sz of g2 and g3 on loading can be obtained by combining the Eq. (5), Eq. (8) and Eq. (9). Fig. 15 shows the distribution of normalized Sz of g2 and g3 in both scratching sequences except that of g1 which is the same as the single scratch. The 2-D plot clearly shows that the stagnation region depth hs of g2 and g3 in both multi-scratch types is larger than that of single-scratch. The fact indicates that the interaction of multiple scratches facilitates the chip formation by deepening the stagnation region. Comparing the normalized deviatoric stress component Szh2/P of scratches in different scratching types, the stagnation region depth of g2 in non-successive sequence is the largest. Although the stagnation region depth of g3 in non-successive sequence is smaller, its contact area of grit-workpiece is larger due to the pile-up produced by previous scratches as shown in Fig. 16a, especially for g2, and this induces more material chip removal. In contrast, the contact area of grit-workpiece in successive scratching sequence is relatively smaller due to the distinctly enhanced hardness as shown in Fig. 16b. Due to the deeper stagnation region and larger contact area of grit-workpiece, it is inferred that the non-successive scratching sequence promotes higher chip removal strength. This can rationalize the high chip removal strength in non-successive scratching sequence (see Fig. 10b). The above comments show the interaction of multiple grit can increase the material removal by increasing the deviatoric stress. Thus, this analysis gives a clear indication that the non-successive arrangement of grits is beneficial to chip removal when grinding of glass-ceramics. 18
Conclusions The interaction of numerous grits on grinding wheel surface is a typical feature of the grinding process, and influences the surface quality as well as reliability of components made out of glass-ceramics. To be in agreement with the feature of grit stochastic distribution, combination of theoretical analysis and experimental observations of multiple scratches is utilized to clarify the material removal mechanism of interactional multiple scratches. Based on the experimental and analytical results, major conclusions can be drawn as following: 1) An analytical model of multi-scratch stress field which takes the scratching sequence into account is established to reveal the material removal mechanism of interactional multiple scratches in term of analyzing the experimental results. 2) Compared with the non-successive scratching sequence, the successive scratching sequence causes a higher maximum principal stress and a lower stagnation region depth, which promotes the material removal transition from ductile to brittle mode and lower chip removal strength, respectively. Therefore, in the actual grinding process, non-successive arrangement of grits is preferred to achieve ductile removal mode of glass-ceramics and to ensure the prominent cutting ability. 3) Multi-scratch induces a higher maximum principal stress than that in a single scratch, which leads to a lower ductile to brittle transition depth and easily causes brittle removal mode of glass-ceramics. Thus, the grinding depth during actual grinding of glass-ceramics should be chosen to be smaller than the ductile to brittle 19
transition depth of a single scratch. Multi-scratch leads to a deeper stagnation region than that of a single scratch, and this is prone to chip formation. 4) When the interaction occurs amongst the multiple scratches, there exists a remarkable deviation in residual depth of scratches in successive scratching sequence due to the high elastic recovery rate. In contrary, the uniform material deformation of scratches caused in the non-successive scratching sequence contributes to the improvement of surface quality during grinding of glass-ceramics. We hope that the results of the present study will benefit to give a deep insight into the material removal mechanism induced by multiple abrasive grits, which are close to real grinding process of glass-ceramics. Moreover, the model of multi-scratch stress field can be used to explain and predict the material flow and crack propagation of multiple scratches by extracting the maximum principal stress and deviatoric stress.
Acknowledgments This work was supported by the National Natural Science Foundation of China (Nos. 51875405 & 51375336) and the National Key Research and Development Program of China (No. 2018YFB1107605).
Appendix A The Boussinesq field is expressed:
20
xx ( x, y, z )
P 2
1 2 2 r
z x 2 y 2 zy 2 3zx 2 1 3 5 2 r
(A.1)
yy ( x, y, z )
P 2
1 2 z y 2 x 2 zx 2 3zy 2 3 5 2 1 2 r r
(A.2)
zz ( x, y, z ) xy ( x, y, z )
3P z 3 2 5
P 2
1 2 2 r
(A.3) z xy xyz 3xyz 1 2 3 5 r
(A.4)
yz ( x, y, z )
3P yz 2 2 5
(A.5)
zx ( x, y, z )
3P xz 2 2 5
(A.6)
The Cerruti field is expressed using the scratch speed vs and scratch length ls: xx ( x, y, z )
3x 3 x P 3x x3 2 x3 3 2 1 2 3 2 2 3 2 ( z) ( z) ( z) 5
(A.7)
yy ( x, y, z )
x P x xy 2 2 xy 2 3xy 2 1 2 3 2 ( z )2 3 ( z )2 2 ( z )3 5
(A.8)
zz ( x, y, z ) xy ( x, y, z )
P 3xz 2 2 5
(A.9)
P y x2 y 2 x 2 y 3x 2 y 3 2 1 2 2 2 2 ( z ) ( z )3 5 ( z)
(A.10)
yz ( x, y, z )
P 3xyz 2 5
(A.11)
zx ( x, y, z )
P 3x 2 z 2 5
(A.12)
The blister field is expressed using the scratch speed vs and scratch length ls: 2 ( y 2 z 2 ) x 2 2 x 4 y 2 2 x 2 y 4 2 2 2 ( y z 2 )2 5 (y z )
xx ( x, y, z ) 2 P
6 x 2 y 4 2 y 6 4 y 6 2 x 4 z 2 4 x 2 y 2 z 2 2 x 2 y 2 z 2 3 y 4 z 2
6vy 4 z 2 2 x 2 z 4 4 x 2 z 4 z 6 2 z 6
21
(A.13)
2 y 2 ( y 2 3z 2 ) x 2 2x4 y 4 6x2 y6 2 2 3 2 3 5 ( y z ) ( y z )
yy ( x, y, z ) 2 P
2 x 2 y 6 4 y 8 2 y 8 6 x 4 y 2 z 2 7 x 2 y 4 z 2 6 x 2 y 4 z 2 2 y 6 z 2 8 y 6 z 2
(A.14)
12 x 2 y 2 z 4 6 x 2 y 2 z 4 15 y 4 z 4 12 y 4 z 4 x 2 z 6
2 x 2 z 6 8 y 2 z 6 8 y 2 z 6 z 8 2 z 8
2z2 (z2 3y2 ) xz 2 6 x 4 y 2 15 x 2 y 4 9 y 6 2 2 3 ( y 2 z 2 )3 5 (y z )
zz ( x, y, z ) 2 P
2 x 4 z 2 10 x 2 y 2 z 2 12 y 4 z 2 5 x 2 z 4 3 y 2 z 4 6 z 6 2 2 2 2 2 1 x 2(1 ) y z 2 z sxy ( x, y, z ) 2 P y 5
y z 4x y z 2
yz ( x, y, z ) 2 P 4 yz
2
(A.15)
(A.16)
2
4
2 3
y 2 10 x 2 y 4 6 y 6
4 x 4 z 2 3 y 4 z 2 10 x 2 z 4 12 y 2 z 4 9 z 6 2 2 3 5 y z
(A.17)
xyz
zx ( x, y, z ) 2 P z
2x
2
2 y 2 z 2 5
(A.18)
where r2=x2+y2 and ρ2=x2+y2+z2.
References [1] W. Holland, G. Beall, Glass-ceramic technology, American Ceramic Society, Columbus, OH, 2002. [2] A. Esmaeilzare, A. Rahimi, S.M. Rezaei, Investigation of subsurface damages and surface roughness in grinding process of Zerodur® glass-ceramic, Appl. Surf. Sci. 313 (2014) 67-75. [3] S. Yin, H. Ohmori, Y. Dai, Y. Uehara, F. Chen, H. Tang, ELID grinding characteristics of glass-ceramic materials, Int. J. Mach. Tools Manuf. 49 (2009) 333-338. [4] W. M. Lin, H. Ohmori, Y. Yamagata, S. Moriyasu, Improvement in the ground surface roughness of fused silica X-ray mirror with ELID-grinding, Trans Tech Publications. 238 (2003) 143-146. [5] B. Zhao, S. Gao, R. Kang, X. Zhu, D. Guo, Surface and subsurface integrity of glass-ceramics induced by ultra-precision grinding, Advanced Materials Research. 1136 (2016) 497-502. 22
[6] E. Brinksmeier, Y. Mutlugunes, F. Klocke, J.C. Aurich, P. Shore, H. Ohmori, Ultra-precision grinding, CIRP Ann. 59 (2010) 652-671. [7] W. Liu, Z. Deng, Y. Shang, L. Wan, Effects of grinding parameters on surface quality in silicon nitride grinding, Ceram. Int. 43 (2017) 1571-1577. [8] T.G. Bifano, T.A. Dow, R.O. Scattergood, Ductile-Regime Grinding: A New Technology for Machining Brittle Materials, Journal of Engineering for Industry. 113 (1991) 184-189. [9] P. Wang, P. Ge, W. Bi, T. Liu, Y. Gao, Stress analysis in scratching of anisotropic single-crystal silicon carbide, Int. J. Mech. Sci. 141 (2018) 1-8. [10] Y. Sun, D. Zuo, H. Wang, Y. Zhu, J. Li, Mechanism of brittle-ductile transition of a glass-ceramic rigid substrate, Int. J. Miner. Metall. Mater. 18 (2011) 229-233. [11] D. Ghosh, G. Subhash, G.R. Bourne, Inelastic deformation under indentation and scratch loads in a ZrB2-SiC composite, J. Eur. Ceram. Soc. 29 (2009) 3053-3061. [12] J. Wang, B. Guo, Q. Zhao, C. Zhang, Q. Zhang, W. Zhai, Evolution of material removal modes of sapphire under varied scratching depths, Ceram. Int. 43 (2017) 10353-10360. [13] C. Li, F. Zhang, Y. Ding, L. Liu, Surface deformation and friction characteristic of nano scratch at ductile-removal regime for optical glass BK7, Appl. Opt. 55 (2016) 6547-6553. [14] C. Li, F. Zhang, B. Meng, X. Rao, Y. Zhou, Research of material removal and deformation mechanism for single crystal GGG (Gd3Ga5O12) based on varied-depth nanoscratch testing, Mater. Des. 125 (2017) 180-188. [15] Y. Liu, B. Li, C. Wu, L. Kong, Y. Zheng, Smoothed particle hydrodynamics simulation and experimental analysis of SiC ceramic grinding mechanism, Ceram. Int. 44 (2018) 12194-12203. [16] P. Bandyopadhyay, A. Dey, A.K. Mandal, N. Dey, S. Roy, A.K. Mukhopadhyay, Effect of scratching speed on deformation of soda-lime-silica glass, Appl. Phys. A. 107 (2012) 685-690. [17] B. Denkena, J. Koehler, A. Moral, Ductile and brittle material removal mechanisms in natural nacre-A model for novel implant materials, J. Mater. Process. Technol. 210 (2010) 1827-1837. [18] R. Transchel, C. Leinenbach, K. Wegener, Cutting and ploughing forces for small clearance angles of hexa-octahedron shaped diamond grains, CIRP Ann. 63 (2014) 325-328. [19] T.T. Öpöz, X. Chen, Experimental investigation of material removal mechanism in single grit grinding, Int. J. Mach. Tools Manuf. 63 (2012) 32-40. 23
[20] D. Anderson, A. Warkentin, R. Bauer, Comparison of spherical and truncated cone geometries for single abrasive-grain cutting, J. Mater. Process. Technol. 212 (2012) 1946-1953. [21] Z. Qiu, C. Liu, H. Wang, X. Yang, F. Fang, J. Tang, Crack propagation and the material removal mechanism of glass-ceramics by the scratch test, J. Mech. Behav. Biomed. Mater. 64 (2016) 75-85. [22] C. Li, F. Zhang, X. Wang, X. Rao, Repeated nanoscratch and double nanoscratch tests of Lu2O3 transparent ceramics: Material removal and deformation mechanism, and theoretical model of penetration depth, J. Eur. Ceram. Soc. 38 (2018) 705-718. [23] X. Yang, Z. Qiu, C. Lu, X. Li, J. Tang, Modelling the strain rate sensitivity on the subsurface damages of scratched glass ceramics, Ceram. Int. 43 (2017) 12930-12938. [24] K. L. Johnson, Contact Mechanics. Cambridge University Press, Cambridge, 1985 [25] Y. Ahn, T.N. Farris, S. Chandrasekar, Sliding microindentation fracture of brittle materials: Role of elastic stress fields, Mech. Mater. 29 (1998) 143-152. [26] X. Jing, S. Maiti, G. Subhash, A new analytical model for estimation of scratch-induced damage in brittle solids, J. Am. Ceram. Soc. 90 (2007) 885-892. [27] J.A. Williams, Analytical models of scratch hardness, Tribol Int. 29 (1996) 675-694. [28] H. Sin, N. Saka, N.P. Suh, Abrasive wear mechanisms and the grit size effect, Wear. 55 (1979) 163-190. [29] R.F. Cook, G.M. Pharr, Direct observation and analysis of indentation cracking on glasses and ceramics, J. Am. Ceram. Soc. 73 (1990) 787-817. [30] R.S. Hahn, On the mechanics of the grinding process under plunge cut conditions, J. Eng. Ind. 88 (1966) 72-80. [31] R. Komanduri, Some aspects of machining with negative rake tools simulating grinding, International Journal of Machine Tool Design and Research, 11 (1971) 223-233. [32] D. Ghosh, G. Subhash, R. Radhakrishnan, T.S. Sudarshan, Scratch-induced microplasticity and microcracking in zirconium diboride-silicon carbide composite, Acta Mater. 56 (2008) 3011-3022. [33] C. Zhang, P. Feng, J. Zhang, Ultrasonic vibration-assisted scratch-induced characteristics of C-plane sapphire with a spherical indenter, Int. J. Mach. Tools Manuf. 64 (2013) 38-48. 24
[34] A.S. Khan, S. Huang, Continuum theory of plasticity, John Wiley & Sons, Inc., New York, 1995.
Fig. 1. Characteristic of grit stochastic distribution on grinding wheel surface. Fig. 2. Schematic diagram of multi-scratch: (a) successive scratching sequence and (b) non-successive scratching sequence. Fig. 3. Experimental procedure: (a) experimental setup and (b) experimental details in multi-scratch tests. Fig. 4. Overall surface morphology of (a) successive scratching sequence and (b) non-successive scratching sequence. Fig. 5. Surface morphology at L = 35 m in (a) successive scratching sequence and (b) non-successive scratching sequence. Fig. 6. Surface morphology at L = 180 m in (a) successive scratching sequence and (b) non-successive scratching sequence. Fig. 7. Scratch morphologies at L = 200 m in (a) successive scratching sequence and (b) non-successive scratching sequence. Fig. 8. Scratch depth and residual depth in (a) successive scratching sequence and (b) non-successive scratching sequence. Fig. 9. Elastic recovery rate in (a) successive scratching sequence and (b) non-successive scratching sequence. Fig. 10. Chip removal strength: (a) schematic illustration and (b) comparison between two scratching sequences. Fig. 11. Analysis of a single scratch as reference: (a) schematic diagram in brittle mode of material removal, and (b) normalized principal stress distribution at (x, y, z) = (0, y, b). Fig. 12. Analysis of normalized principal stress distribution at (x, y, z) = (0, y, b): (a) Schematic diagram of extracting the maximum principal stress of multi-scratch, (b) successive scratching sequence, and (c) non-successive scratching sequence. Fig. 13. Schematic diagram of (a) material flow ahead of a grit, and (b) surface generation in ductile mode of material removal. 25
Fig. 14. Stress analysis of a single scratch: (a) material flow ahead of the indenter and (b) distribution of normalized deviatoric stress component on a x-z plane at x =a. Fig. 15. Distribution of normalized deviatoric stress component along z-axis. Fig. 16. Schematic diagram of grit-workpiece contact area in (a) non-successive scratching sequences and (b) successive scratching sequence.
6 5 3 2
4
1
Fig. 1.
3 ○ 2 ○
5 ○
1 ○ g3 d
g2
4 ○ g3
g1
d
d
y
x
6 ○
g2
d
y
x
z
z
(a)
(b)
Fig. 2. .
26
g1
65 77
(a)
d
d
d
L
d
1 Grit ○ 2 Grit ○ 3 Grit ○
g3
g2
g1
g3
g2
g1
L
4 Grit ○ 6 Grit ○ 5 Grit ○
(b)
Fig. 3. .
0
50
100
150
200 L (m)
(a)
(b)
Fig. 4..
27
20
Cross section depth (nm)
10 0 -10 -20
g1
-30
g3
g2 -40 0
5
10
15
20
Cross section distance ( m)
(a)
Cross section depth (nm)
20 10 0 -10 -20
g1 g3
-30
g2 -40 0
2
4
6
8
10
12
14
Cross section distance ( m)
(b)
Fig. 5.
28
16
18
20
100
Cross section depth (nm)
50 0 -50
g1
-100
g2
-150
g3
-200 0
10
20
30
40
Cross section distance ( m)
(a)
Cross section depth (nm)
100 50 0 -50
g1
-100
g3
g2 -150 0
5
10
15
20
Cross section distance ( m)
(b)
Fig. 6.
g1
g2
g1
g3
(a)
g2
(b)
Fig. 7..
29
g3
25
30
g1 Plastic deformation without interaction
Complete elastic deformation
g2
Plastic deformation with interaction
g3 Plastic deformation without interaction
Plastic deformation with interaction
Scratch depth h
Scratch depth h
Residual depth h r
Residual depth h r
Complete elastic deformation
(a)
(b)
Fig. 8.
g1
g2
(a)
g3
(b)
Fig. 9.
30
Chip
Grit Area of pile-up
Area of groove (a)
(b)
Fig. 10.
Radial crack Grit (0, 1.19) x
Material peeling
Plastic core
y Plastic zone
Elastic-plastic boundary
Median crack
b
Lateral crack z (a)
(b)
Fig. 11. .
31
Plastic zone Grit
Grit
Grit
y/b
0 1b 2b Cracks 3b 4b z/b (a)
g1 (0, 1.41) g1 (0, 1.26)
g3 (1.69, 1.25)
g2 (0.85, 1.23) g2 (0.85, 1.12) g3 (1.69, 0.84)
(b)
(c)
Fig. 12.
Chip Grit Scratch direction
Plastic deformation
Groove x
Pile-up hs h
S Plastic core
y
Plastic zone
Elastic recovery
b
Elastic-plastic boundary
Elastic zone z
(a)
(b)
Fig. 13.
32
Scratch direction 0
S
S
z /h
S zh 2 /P
0.5
1
0.11 1.5 0
1
2
3
4
5 z/h
x/h (a)
(b)
Fig. 14.
S
0.29 0.21
Fig. 15.
33
0.39 0.45
g2
g3 g1 g3
g1
y y
x
z
x
z
(a) g3 g2 g2 g1 g1
y y
x
z x
z
(b)
Fig. 16.
Table 1 Material properties of LAS glass-ceramic [23] Parameters
Value
Hardness H (GPa)
9.25
Elastic modulus E (GPa)
88.7
Poisson’s ratio
0.25
34
Table 2 Experimental parameters Value Parameters
Successive scratching
Non-successive scratching
sequence
sequence
Half-apex angle of Berkovich indenter
65
65
The maximum normal load P (mN)
30
30
Scratch length L (m)
200
200
Scratching speed (m/s)
50
50
2
2
Order of g1 conducted
Firstly
Firstly
Order of g2 conducted
Secondly
Thirdly
Order of g3 conducted
Thirdly
Secondly
Distance d between adjacent scratches (m)
35
PII: DOI: Reference:
S0272-8842(18)32730-5 https://doi.org/10.1016/j.ceramint.2018.09.256 CERI19655
To appear in: Ceramics International Received date: 3 September 2018 Revised date: 25 September 2018 Accepted date: 25 September 2018 Cite this article as: Xue Yang, Zhongjun Qiu and Xue Li, Investigation of scratching sequence influence on material removal mechanism of glass-ceramics by the multiple scratch tests, Ceramics International, https://doi.org/10.1016/j.ceramint.2018.09.256 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Investigation of scratching sequence influence on material removal mechanism of glass-ceramics by the multiple scratch tests
Xue Yang, Zhongjun Qiu*, Xue Li
State Key Laboratory of Precision Measuring Technology & Instruments, Tianjin University, Tianjin 300072, China
*
Corresponding author. Tel./fax: +86 022 27403753. [email protected]
Abstract The existing research on grinding mechanism by single scratch method cannot reflect the interaction among multiple scratches caused by the stochastic distribution of numerous grits on the grinding wheel surface. To clarify the effect of multi-scratch interaction on material removal mechanism during grinding of glass-ceramics, a multi-scratch experiment with different scratching sequences was conducted on glass-ceramics using a nanoindenter in this paper. A model of multi-scratch stress field is established to analyze the material removal mechanism such as surface morphology, material deformation, crack propagation and chip removal strength. The results show that successive scratching sequence promotes to the severe crack propagation of glass-ceramics due to its higher maximum principal stress whereas non-successive scratching sequence is prone to result in chip removal owing to its deeper stagnation 1
region. These findings provide critical insight of grinding mechanics for glass-ceramics components by considering the interactions among multiple scratches.
Keywords: Glass-ceramics; Material removal mechanism; Stress analysis; Multiple scratch tests
1
Introduction Glass-ceramic is a typical high-performance material for manufacturing many
optical components such as large reflective telescopes, integrated lens arrays and laser gyroscope due to its superior properties of low thermal expansion coefficient, high strength, high abrasion resistance, good chemical durability and high transmissibility etc. [1]. Excellent surface quality is required for these glass-ceramics components applied in precision optics field to improve their functional performance and lifetime [2]. However, the hard-brittle nature of glass-ceramic limits its machinability. Grinding, lapping and polishing are the main methods for machining of glass ceramics [3]. For hard-brittle materials, the traditional fabrication of a high-precision surface begins with grinding which leads to extensive machining-induced damages [4]. To diminish these damages resulting from grinding, subsequent lapping and polishing processes are used to obtain an acceptable roughness and integrity of surface, but these processes are time consuming and expensive due to their low material removal rates [5]. In order to reduce time and cost, surface quality achievable by grinding processes becomes more important [6]. Nevertheless, it is still being challenging to improve the surface quality in grinding 2
process due to the random distribution of numerous grits on grinding wheel surface [7]. Therefore, the fundamental understanding of the material removal mechanism during grinding of glass-ceramics is a prerequisite for ensuring an acceptable surface quality. Many efforts have been made to study the material removal mechanism by a single scratch method which is a simplified analogy of grit-workpiece interactions in the grinding process. Crack propagation, material deformation, or the combination of both are the manifestations of material removal during grinding. Therefore, scholars have carried out extensive experimental and theoretical investigations using the single scratch method from perspectives of crack propagation and material deformation. Study of crack propagation contributes to optimize the grinding process and furthermore improve the surface quality of glass-ceramics components by suppressing the crack extension [8-10]. Apart from crack propagation, material deformation also plays a crucial role in the material removal mechanism [11, 12]. Li et al. [13, 14] carried out nanoscratch tests on optical glass BK7 and single crystal GGG (Gd3Ga5O12). The results show that the residual depth of scratch, elastic recovery rate and residual stress caused by material deformation have an important effect on the surface quality. Moreover, analysis of single grit-workpiece interaction is easy to study the effect of speed, and depth of cut on the material removal mechanism. High grinding speed and low depth are prone to suppress the crack propagation and achieve ductile-regime grinding [15, 16]. The effect of grit characteristics (like wear, rake angle, sharpness, shape and size etc.) on material removal also has been investigated [17-20]. Although single scratch method makes it easy to demonstrate the contribution of individual grit to material removal, the 3
mechanism of material removal in single scratch process may be substantially differs from that in actual grinding. In real grinding process, the material removal is mainly as a result of multi-grit combined interaction which is not a simple superposition of single-grit scratch. Simplified single-grit scratch cannot represent this intrinsic complex interaction characteristic of the grinding process. The interaction among scratches produced in grinding process partly results from the stochastic distribution of the numerous abrasive grits on the surface of the grinding wheel, which causes not only the different scratch distances but also the difference of the produced order of the scratches i.e. scratch sequence. For scratch distance, Qiu [21] and Li [22] have studied the effect of the scratch distance on the crack propagation and material deformation, respectively. However, studies on the scratch sequence caused by the grit random distribution are rare for now. To study the effect of the scratch sequence on the mechanisms of material removal and deformation, research on the multiple scratch (at least three scratches) is an important step to reveal the comprehensive interferential effect of numerous abrasive grits on the surface of the grinding wheel. In the current study, the material removal mechanism of interactional multiple scratches is investigated by analysing the multi-scratch stress field in glass-ceramics. The analytical model of multi-scratch stress field is utilized to analyze the multi-scratch experimental results. The multi-scratch experiment with successive scratching sequence and non-successive scratching sequence is conducted on glass-ceramics by using Berkovich indenter to simulate the actual grinding process. The surface morphology, material deformation, crack propagation and chip removal strength of glass-ceramics, 4
which are measured by using the Nano Indenter system, SEM and AFM, are used to demonstrate the interactional material removal behaviour of multi-scratch under different scratching sequences. 2
Material and methods
2.1 Definition of scratching sequence Numerous abrasive grits on the grinding tool are characterized by the irregular geometry, undefined grit protrusion height, and stochastic distribution associating with scratch distance and scratching sequence as shown in Fig. 1. Scratching sequence caused by the grit stochastic distribution is the focus of present work in which the protrusion height and geometry of grits are assumed to be uniform to avoid introducing more variables. Scratching sequence is classified into two types: successive scratching sequence and non-successive scratching sequence. Three scratches at least are required to describe the feature of scratching sequence. Successive scratching sequence results 1 , grit ○ 2 and grit ○ 3 while non-successive from the distribution pattern such as grit ○ 4 , grit ○ 5 and scratching sequence is caused by the distribution pattern similar to grit ○ 6 (see Fig. 1). Detailed schematic diagrams of successive scratching and grit ○
non-successive scratching sequences are illustrated in Fig. 2 where the scratches on the surface of glass-ceramics after the experiments are g1, g2 and g3 along y-axis. Major difference between the two scratching types lies in the scratching order. In successive scratching sequence as shown in Fig. 2a, g1 is firstly conducted on glass-ceramics, which is followed by g2 and g3 successively. Unlike successive scratching sequence, the scratches in non-successive scratching sequence as shown in Fig. 2b are conducted in 5
order of g1, g3 and g2. 2.2 Specimen preparation and experimental procedure Present study adopted the lithium aluminosilicate (LAS) glass-ceramic with dimensions of ϕ25 (diameter) × 5 mm (thickness). The material properties of LAS glass-ceramic were listed in Table 1. The specimen was embedded in resin with dimensions of ϕ40 (diameter) × 23 mm (thickness) and then was polished successively by using 10 μm, 5 μm, and 3 μm diamond powder and 0.04 μm silica gel suspension liquid to get a smooth surface. The polished specimen was mounted on the workbench of Nano Indenter (Keysight G200) as shown in Fig. 3a. Experiments were carried out by Berkovich indenter with a tip radius about 100 nm and experimental details were illustrated in Fig. 3b. The Berkovich indenter was face-forward and was conducted repeatedly multiple times on the surface of the workpiece to produce the three taper scratches of each sequence group. For convenience of analysis, the distance between adjacent scratches after the experiment is equal to d in the present study. Detailed experimental parameters are given in Table 2. Each group of multi-scratch tests has been repeatedly performed on glass-ceramic specimen three times to validate the repeatability of experimental results and the most typical experimental results are shown in this paper. 2.3 Measurement After producing the scratches on glass-ceramics, the scratch depth h and residual depth hr were measured by the in situ detection of the nano-indenter to analyze the material deformation characteristics (elastic and plastic deformations). Scanning 6
electron microscopy (Nanolab Nova 200) was used to observe the surface morphology in different scratching sequences. In order to explore the effect of scratching sequence on material removal of ductile mode, chip removal strength defined by subtracting the total pile-up area from the total scratch groove was introduced. The atomic force microscopy (AFM) was utilized to measure the surface morphology to extract the cross sections profile and furthermore to obtain the areas of groove and pile-up, which were calculated by the integration method. 3
Results Surface morphology, material deformation and chip removal strength are important
for identifying material removal mode, improving machining precision and surface quality of glass-ceramic component, and therefore are investigated in this section. 3.1 Surface morphology SEM image enables the observation of surface morphology so that the dependence of surface quality on scratching sequence is explained. Fig. 4 shows the overall surface morphology of successive scratching sequence and non-successive scratching sequence. Fig. 5 shows the surface morphology and cross section profile at L = 35 m in both scratching sequences. It can be seen that the residual depth of scratches in both scratching sequences is all about 30 nm and equivalent to a single scratch without interaction. In contrast, at L = 180 m, the surface morphology in Fig. 6 indicates that three scratches in each scratching sequence interact with each other. The interaction effect causes that the residual depth of scratches in both scratching sequences is different from each other. In successive scratching sequence (see Fig. 6a), due to lack of 7
material support on the left side, the material of g3 moves toward the groove of g2, which results in the prior groove being partially covered and leaning to the left. Similarly, the groove of g1 is incomplete owing to the material extruded by g2 covering the partial groove of g1. Unlike surface morphology in successive scratching sequence, the entire surface morphology in non-successive scratching sequence presents symmetry (see Fig. 6b). This comes along with the existence of g1 and g3 produced previously, which lead to a lack of material support on both sides of g2. When g2 is performed, the material is pushed into the groove of g1 and g3, and hence this makes the bottom of g1 groove incline towards the left side while the bottom of g3 groove tilts toward the right side. Surface morphology in both scratching sequence differs and this will result in different thickness of hardening layer of the workpiece, which affects the surface integrity. The symmetry surface morphology acquired by non-successive scratching sequence contributes to a relatively uniform hardening layer and surface integrity. Fig. 7 depicts that cracks emerge at the end of multi-scratch in both scratching sequences because the maximum principal stress exceeds the fracture stress required for crack propagation. Scratches produced in successive scratching sequence and non-successive scratching sequence show different characteristics in terms of material removal mechanism. It is found that successive scratching sequence more easily causes noticeable material peeling due to a greater extent of micro crack propagating and merging (see Fig. 7a), while there are micro cracks in non-successive scratching sequence but no material peeling due to the absence of the mergence among cracks (see Fig. 7b). 8
Comparing results in double scratching sequences, it can be concluded that the scratching sequence has a significant impact on surface morphology and material removal behaviour. Compared to non-successive scratching sequence, successive scratching sequence promotes a material removal mode transition from ductile to brittle. Therefore, optimization of the distribution of grits on the grinding wheel surface for maximizing the non-successive multiple scratches is an option to achieve ductile regime grinding. This contributes to the crack-free surface and further to the improvement of performance as well as reliability of glass-ceramics parts. 3.2 Material deformation characteristics In ductile regime grinding of glass-ceramics, the interactional material deformation induced by multi-scratch plays an important role in the machining accuracy. Therefore, the scratch depth and residual depth were analyzed to investigate the effect of scratching sequence on material deformation of glass-ceramics. Fig. 8 shows the relationships between scratch depth h, residual depth hr and the scratch length L as well as the normal force P. Clearly, the scratch depth and residual depth increase with P rising, but curves of three scratches in each group are not identical. According to the deviation among curves, it can be observed that there are three deformation phases in both scratching sequence types: complete elastic deformation, plastic deformation without interaction and plastic deformation with interaction. Complete elastic deformation occurs with a small region at the start of scratches, in which hr equals to 0 due to the elastic recovery on unloading. With P increasing, hr starts to be larger than 0 and this indicates the material deformation enters into the 9
plastic deformation stage. The curves of h and hr in this stage are identical, which demonstrates no interaction occurring among scratches. This case corresponds to the surface morphology in Fig. 5. As P further increases and exceeds a critical value where the curves of the three scratches are separated, this means that the scratches in each scratching sequence start to interact with each other. This is the phase of plastic deformation with interaction, which corresponds to the surface morphology in Fig. 6. Within the interaction phase, the deviation of curves is attributed to the difference in elastic recovery rate , defined as (h – hr) / h. Fig. 9 presents the variation of elastic recovery rate of g1, g2 and g3. In both scratching sequences, the elastic recovery rate of multi-scratch decreases with the increase of P and gradually tends to be stable. There is a noticeable deviation in of g1, g2 as well as g3 (see Fig. 9a) in successive scratching sequence compared to that in non-successive scratching pattern (see Fig. 9b). This fact is attributed to that successive scratching sequence intensifies the interaction of deformed material of neighbouring scratches and furthermore enhances the hardness of material. Comparing the deformation characteristics of glass-ceramics in two scratching sequences, non-successive scratching sequence results in a relatively uniform material deformation due to the slight variation in elastic recovery rate. Uniform deformation is benefit for obtaining better surface roughness during grinding of glass-ceramics. Therefore, non-successive scratching sequence is a choice employed to improve the surface quality of glass-ceramic parts in actual grinding process. 3.3 Chip removal strength 10
In ductile regime grinding, the chip removal strength is a measure method of material removal rate across the sectional area of the scratch as shown in Fig. 10a [19]. As shown in Fig. 4, there are three phases of the material removal mechanism in grinding, namely, rubbing, ploughing, and cutting. Only in the cutting phase, the material is removed in form of a chip. To investigate the influence of scratching sequence on the mechanism of material removal in ductile mode, current section emphasizes on the chip removal strength according to the extracted the transection profiles perpendicular to the scratch. Fig. 10b shows the chip removal strength for P=20mN. It is obvious that the chip removal strength in non-successive scratching sequence is higher than that in successive scratching sequence. This indicates that non-successive scratching sequence allows materials to flow upward more easily and thus results in prominent chip removal. 4
Discussions In the current study, it is noticeable that scratching sequence has an evident effect
on both crack propagation and chip removal strength of glass-ceramics. Damage and material deformation induced during grinding result from stress distribution. Therefore, establishment of the stress field for multi-scratch facilitates to gain a deep understanding of the mechanisms of crack propagation and material deformation. However, most of the previous studies always focused on the stress field of a single-scratch. The stress field of multi-scratch was rarely investigated due to its complex interactions among the multiple scratches. To thoroughly clarify the complex material removal mechanism of multi-scratch, a need has arisen to establish a model of 11
multi-scratch stress field to analyze the crack propagation and plastic deformation of glass-ceramics in different scratching sequences. 4.1 Establishment of stress field model for multi-scratch During a single scratch process, the stress field around the indenter is constructed as the superposition of Boussinesq field ij, Cerruti field ij, and the sliding blister field ij, respectively, due to the normal force P, the tangential force Q and the residual stress [24, 25]. The stress field of a single scratch is expressed as [26]
ij k0 ij ij +k2 ij ,
(1)
where subscripts i and j represent the stress component directions like i, j = x, y, and z, while k0 is a constant that takes 1 on loading, and 0 on unloading. Expressions for ij, ij, and ij are given in Appendix A. The factor k2 represents the relative strength of sliding blister field and can be expressed as k2
1.09 H 3 2 E cot 2 , E 4 (1 2 )(1 ) H
(2)
where E, H, and are elastic modulus, hardness, half-apex angle of a grit and Poissons ratio, respectively. The dimensionless geometric parameter
3 is
obtained according to the relationship between the Berkovich indenter and its equivalent axial-symmetric cone indenter [27]. In microscale grinding process, the friction coefficient is related to , scratch depth h, grit tip radius R, and half scratch width a together [28]. It can be expressed as
12
2 2 a 2 sin -1 a a 1 h / R 1 sin R R R 2 cot 4 cot 2 - 2a 2 1 h / R 1 sin cot R .
(3)
Half width of scratch depends on the normal force and material hardness, and it is determined as
a P H
(4)
.
Based on the interactive feature of multiple scratching and the stress field of a single scratch, the multi-scratch stress field ij is established by coordinate transformation (see Fig. 2), and it is given by
n 1
m 1
ij x, y, z k2 ij x, y d m , z
k
0
ij x, y d n , z ij x, y d n , z k 2 ij x, y d n , z
n k2 ij x, y d m , z m 1 k0 ij x, y d n , z ij x, y d n , z
(5)
,
where dm represents the distance from any previously conducted scratch to the firstly conducted scratch and dn stands for the distance from the last conducted scratch to the firstly conducted one which is taken as x-axis as shown in Fig. 2. Constant n stands for the total number of scratches and constant m ranges from 1 to n (i.e. the first scratch to the last one). According to Eq. (5), in successive scratching sequence, the interactional stress field is constructed as the superposition of ij, ij (due to the last conducted scratch g3) and ij (due to g1, g2 and g3) and it is given by 13
ij x, y, z k2 ij x, y, z k2 ij x, y d , z k0 ij x, y 2d , z ij x, y 2d , z k2 ij x, y 2d , z .
(6)
Similarly, the interactive stress field in non-successive scratching sequence is the sum of ij, ij (due to the last conducted scratch g2) and ij (due to g1, g2 and g3) and it is given by
ij x, y, z k2 ij x, y, z k2 ij x, y 2d , z k0 ij x, y d , z ij x, y d , z k2 ij x, y d , z .
(7)
4.2 Analysis of the maximum principal stress To explain the phenomenon in Fig. 7 and reveal the material removal mechanism of multi-scratch, the stress field of multi-scratch is discussed. According to the maximum principal stress criterion, crack is activated and extends when the maximum principal stress exceeds the fracture stress. The maximum principal stress 1 can be obtained from the multi-scratch stress field. Because material peeling in brittle-regime scratching is as a result of lateral crack merging with radial crack or itself, it is obvious that the lateral crack is mainly responsible for the material removal [29]. Therefore, the maximum principal stress at the bottom of the plastic zone where lateral crack occurs is analysed as shown in Fig. 11a. Plastic zone radius b can be obtained based on the literature [26], which equals to 2.3662 m for P of 30 mN corresponding to Fig. 7. For convenience of comparison, the maximum principal stress is normalized as 1b2/P. Fig. 11b shows the normalized maximum principal stress of single-scratch which is used as a reference to be compared with that of multi-scratch to explore the effect of multi-scratch on crack propagation. The maximum principal stress of multi-scratch on a y- z plane is extracted as shown 14
in Fig.12a. From Fig. 12b and c, it can be seen that the average stress magnitude of multi-scratch in both scratching sequences is higher than that of single-scratch (see Fig. 11b). This indicates that compared with a single scratch, the interactional effect of multi-scratch is prone to cause brittle mode of material removal due to the enhanced maximum principal stress. Therefore, the ductile to brittle transition (DBT) depth obtained by single-scratch test cannot be used as an effective basis for selecting grinding depth during actual grinding of glass-ceramic, because single-scratch test neglect the interaction effect amongst multiple scratches. During grinding of glass-ceramics, it is suggested to select a much smaller grinding depth than DBT depth of single-scratch to achieve ductile removal mode. Normalized principal stress in different scratching sequences is compared to explain the effect of scratching sequence on the crack propagation. Fig. 12b gives that the distribution of complete stress along y-axis in successive scratching sequence, which is composed of residual stress due to g1 and g2 on unloading as well as the stress caused by g3 on loading. In particular, the normalized principal stress reaches its maximum at the location between g1 and g2, and has a second peak near g2. The fact is that the last conducted scratch elevates the residual stress of prior existing scratches, and this explains why the material peeling occurs near g2 in Fig. 7a. Different from the concentrated distribution of stress in successive scratching sequence, the maximum principal stress in non-successive scratching sequence is much smaller and relatively uniform as shown in Fig. 12c, but still greater than that of a single scratch. Uniform stress distribution caused by non-successive scratching sequence is able to result in 15
crack activation but the extended size of crack is not sufficient to cause crack interference and material peeling. This is consistent with the observation in Fig. 7b. In summary, the scratching sequence has a strong influence on the stress distribution responsible for crack propagation and material removal mode. Successive scratching process induces a higher maximum principal stress and leads to a greater extent of crack propagation as well as material peeling. This provides the ability to rationalize the phenomenon in Fig. 7. 4.3 Analysis of the deviatoric stress In ductile mode of material removal, generation of scratch groove, pile-up and chip is caused by the material flow behaviour ahead of a grit. As shown in Fig. 13a, the stagnation region S divides the material flowing in two directions: some material flowing upward and the remaining material flowing downward. The material below S generates the scratch groove, while the remaining material above S leads to the pile-up and chip formation (see Fig. 13b) [30, 31]. Clearly, material flow behaviour is important for understanding the material removal mechanism in ductile regime grinding. However, in previous studies, the focus was just on the analysis of crack initiation and propagation using the stress field. The evolution of material flow caused by the stress field ahead of an indenter was seldom investigated. Therefore, present work will focus on analyzing the stress components responsible for material flow ahead of an indenter. In the current investigation, the elastic stress field solutions are utilized to rationalize the observed chip removal in our study by analyzing the material flow in glass-ceramics [32, 33]. The material flow results from the deviatoric stress ahead of an 16
indenter [34]. According to Eq. (5), the deviatoric stress component Sij can be given by S xx Sij S xy S xz
S xy S yy S yz
xx m S xz xy xz S yz ij m xy yy m yz xz S zz yz zz m ,
(8)
where σm is the hydrostatic stress. Apparently, analysis of the deviatoric stress facilitates to gain a deep insight into the surface generation due to scratch groove and pile-up, as well as chip formation. For clarity, as the indenter moves forward on the workpiece surface, the two-dimensional (2-D) distribution and orientation of the material flow on an x-z plane are shown in Fig. 14a. The stagnation region is a prerequisite for chip formation, and is characterized by the deviatoric stress component along z-axis equivalent to 0. To identify the depth of the stagnation region, the deviatoric stress component along z-axis Sz is needed to be deeply analyzed and it is expressed as
S z S zz S xz .
(9)
Fig. 14b presents the distribution of the normalized deviatoric stress component Szh2/P at (a, 0, z). At the location close to workpiece surface, the deviatoric stress component is larger than 0 and this means that the material flows upward to form pile-up and a chip. However, as z/h increased, the deviatoric stress component gradually decreases from positive to negative. The negative value of the deviatoric stress indicates that the material flows down to generate the scratch groove. Note that the stagnation region depth hs is 0.11h at P=20mN. Different from the stress field of a single scratch, the stress field of multi-scratch is more complex due to the combined interactions. In multi-scratch process, the stress field of each scratch on loading is needed to be analyzed due to the chip removal mainly 17
occurring ahead of an indenter. The deviatoric stress component Sz of g2 and g3 on loading can be obtained by combining the Eq. (5), Eq. (8) and Eq. (9). Fig. 15 shows the distribution of normalized Sz of g2 and g3 in both scratching sequences except that of g1 which is the same as the single scratch. The 2-D plot clearly shows that the stagnation region depth hs of g2 and g3 in both multi-scratch types is larger than that of single-scratch. The fact indicates that the interaction of multiple scratches facilitates the chip formation by deepening the stagnation region. Comparing the normalized deviatoric stress component Szh2/P of scratches in different scratching types, the stagnation region depth of g2 in non-successive sequence is the largest. Although the stagnation region depth of g3 in non-successive sequence is smaller, its contact area of grit-workpiece is larger due to the pile-up produced by previous scratches as shown in Fig. 16a, especially for g2, and this induces more material chip removal. In contrast, the contact area of grit-workpiece in successive scratching sequence is relatively smaller due to the distinctly enhanced hardness as shown in Fig. 16b. Due to the deeper stagnation region and larger contact area of grit-workpiece, it is inferred that the non-successive scratching sequence promotes higher chip removal strength. This can rationalize the high chip removal strength in non-successive scratching sequence (see Fig. 10b). The above comments show the interaction of multiple grit can increase the material removal by increasing the deviatoric stress. Thus, this analysis gives a clear indication that the non-successive arrangement of grits is beneficial to chip removal when grinding of glass-ceramics. 18
Conclusions The interaction of numerous grits on grinding wheel surface is a typical feature of the grinding process, and influences the surface quality as well as reliability of components made out of glass-ceramics. To be in agreement with the feature of grit stochastic distribution, combination of theoretical analysis and experimental observations of multiple scratches is utilized to clarify the material removal mechanism of interactional multiple scratches. Based on the experimental and analytical results, major conclusions can be drawn as following: 1) An analytical model of multi-scratch stress field which takes the scratching sequence into account is established to reveal the material removal mechanism of interactional multiple scratches in term of analyzing the experimental results. 2) Compared with the non-successive scratching sequence, the successive scratching sequence causes a higher maximum principal stress and a lower stagnation region depth, which promotes the material removal transition from ductile to brittle mode and lower chip removal strength, respectively. Therefore, in the actual grinding process, non-successive arrangement of grits is preferred to achieve ductile removal mode of glass-ceramics and to ensure the prominent cutting ability. 3) Multi-scratch induces a higher maximum principal stress than that in a single scratch, which leads to a lower ductile to brittle transition depth and easily causes brittle removal mode of glass-ceramics. Thus, the grinding depth during actual grinding of glass-ceramics should be chosen to be smaller than the ductile to brittle 19
transition depth of a single scratch. Multi-scratch leads to a deeper stagnation region than that of a single scratch, and this is prone to chip formation. 4) When the interaction occurs amongst the multiple scratches, there exists a remarkable deviation in residual depth of scratches in successive scratching sequence due to the high elastic recovery rate. In contrary, the uniform material deformation of scratches caused in the non-successive scratching sequence contributes to the improvement of surface quality during grinding of glass-ceramics. We hope that the results of the present study will benefit to give a deep insight into the material removal mechanism induced by multiple abrasive grits, which are close to real grinding process of glass-ceramics. Moreover, the model of multi-scratch stress field can be used to explain and predict the material flow and crack propagation of multiple scratches by extracting the maximum principal stress and deviatoric stress.
Acknowledgments This work was supported by the National Natural Science Foundation of China (Nos. 51875405 & 51375336) and the National Key Research and Development Program of China (No. 2018YFB1107605).
Appendix A The Boussinesq field is expressed:
20
xx ( x, y, z )
P 2
1 2 2 r
z x 2 y 2 zy 2 3zx 2 1 3 5 2 r
(A.1)
yy ( x, y, z )
P 2
1 2 z y 2 x 2 zx 2 3zy 2 3 5 2 1 2 r r
(A.2)
zz ( x, y, z ) xy ( x, y, z )
3P z 3 2 5
P 2
1 2 2 r
(A.3) z xy xyz 3xyz 1 2 3 5 r
(A.4)
yz ( x, y, z )
3P yz 2 2 5
(A.5)
zx ( x, y, z )
3P xz 2 2 5
(A.6)
The Cerruti field is expressed using the scratch speed vs and scratch length ls: xx ( x, y, z )
3x 3 x P 3x x3 2 x3 3 2 1 2 3 2 2 3 2 ( z) ( z) ( z) 5
(A.7)
yy ( x, y, z )
x P x xy 2 2 xy 2 3xy 2 1 2 3 2 ( z )2 3 ( z )2 2 ( z )3 5
(A.8)
zz ( x, y, z ) xy ( x, y, z )
P 3xz 2 2 5
(A.9)
P y x2 y 2 x 2 y 3x 2 y 3 2 1 2 2 2 2 ( z ) ( z )3 5 ( z)
(A.10)
yz ( x, y, z )
P 3xyz 2 5
(A.11)
zx ( x, y, z )
P 3x 2 z 2 5
(A.12)
The blister field is expressed using the scratch speed vs and scratch length ls: 2 ( y 2 z 2 ) x 2 2 x 4 y 2 2 x 2 y 4 2 2 2 ( y z 2 )2 5 (y z )
xx ( x, y, z ) 2 P
6 x 2 y 4 2 y 6 4 y 6 2 x 4 z 2 4 x 2 y 2 z 2 2 x 2 y 2 z 2 3 y 4 z 2
6vy 4 z 2 2 x 2 z 4 4 x 2 z 4 z 6 2 z 6
21
(A.13)
2 y 2 ( y 2 3z 2 ) x 2 2x4 y 4 6x2 y6 2 2 3 2 3 5 ( y z ) ( y z )
yy ( x, y, z ) 2 P
2 x 2 y 6 4 y 8 2 y 8 6 x 4 y 2 z 2 7 x 2 y 4 z 2 6 x 2 y 4 z 2 2 y 6 z 2 8 y 6 z 2
(A.14)
12 x 2 y 2 z 4 6 x 2 y 2 z 4 15 y 4 z 4 12 y 4 z 4 x 2 z 6
2 x 2 z 6 8 y 2 z 6 8 y 2 z 6 z 8 2 z 8
2z2 (z2 3y2 ) xz 2 6 x 4 y 2 15 x 2 y 4 9 y 6 2 2 3 ( y 2 z 2 )3 5 (y z )
zz ( x, y, z ) 2 P
2 x 4 z 2 10 x 2 y 2 z 2 12 y 4 z 2 5 x 2 z 4 3 y 2 z 4 6 z 6 2 2 2 2 2 1 x 2(1 ) y z 2 z sxy ( x, y, z ) 2 P y 5
y z 4x y z 2
yz ( x, y, z ) 2 P 4 yz
2
(A.15)
(A.16)
2
4
2 3
y 2 10 x 2 y 4 6 y 6
4 x 4 z 2 3 y 4 z 2 10 x 2 z 4 12 y 2 z 4 9 z 6 2 2 3 5 y z
(A.17)
xyz
zx ( x, y, z ) 2 P z
2x
2
2 y 2 z 2 5
(A.18)
where r2=x2+y2 and ρ2=x2+y2+z2.
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[20] D. Anderson, A. Warkentin, R. Bauer, Comparison of spherical and truncated cone geometries for single abrasive-grain cutting, J. Mater. Process. Technol. 212 (2012) 1946-1953. [21] Z. Qiu, C. Liu, H. Wang, X. Yang, F. Fang, J. Tang, Crack propagation and the material removal mechanism of glass-ceramics by the scratch test, J. Mech. Behav. Biomed. Mater. 64 (2016) 75-85. [22] C. Li, F. Zhang, X. Wang, X. Rao, Repeated nanoscratch and double nanoscratch tests of Lu2O3 transparent ceramics: Material removal and deformation mechanism, and theoretical model of penetration depth, J. Eur. Ceram. Soc. 38 (2018) 705-718. [23] X. Yang, Z. Qiu, C. Lu, X. Li, J. Tang, Modelling the strain rate sensitivity on the subsurface damages of scratched glass ceramics, Ceram. Int. 43 (2017) 12930-12938. [24] K. L. Johnson, Contact Mechanics. Cambridge University Press, Cambridge, 1985 [25] Y. Ahn, T.N. Farris, S. Chandrasekar, Sliding microindentation fracture of brittle materials: Role of elastic stress fields, Mech. Mater. 29 (1998) 143-152. [26] X. Jing, S. Maiti, G. Subhash, A new analytical model for estimation of scratch-induced damage in brittle solids, J. Am. Ceram. Soc. 90 (2007) 885-892. [27] J.A. Williams, Analytical models of scratch hardness, Tribol Int. 29 (1996) 675-694. [28] H. Sin, N. Saka, N.P. Suh, Abrasive wear mechanisms and the grit size effect, Wear. 55 (1979) 163-190. [29] R.F. Cook, G.M. Pharr, Direct observation and analysis of indentation cracking on glasses and ceramics, J. Am. Ceram. Soc. 73 (1990) 787-817. [30] R.S. Hahn, On the mechanics of the grinding process under plunge cut conditions, J. Eng. Ind. 88 (1966) 72-80. [31] R. Komanduri, Some aspects of machining with negative rake tools simulating grinding, International Journal of Machine Tool Design and Research, 11 (1971) 223-233. [32] D. Ghosh, G. Subhash, R. Radhakrishnan, T.S. Sudarshan, Scratch-induced microplasticity and microcracking in zirconium diboride-silicon carbide composite, Acta Mater. 56 (2008) 3011-3022. [33] C. Zhang, P. Feng, J. Zhang, Ultrasonic vibration-assisted scratch-induced characteristics of C-plane sapphire with a spherical indenter, Int. J. Mach. Tools Manuf. 64 (2013) 38-48. 24
[34] A.S. Khan, S. Huang, Continuum theory of plasticity, John Wiley & Sons, Inc., New York, 1995.
Fig. 1. Characteristic of grit stochastic distribution on grinding wheel surface. Fig. 2. Schematic diagram of multi-scratch: (a) successive scratching sequence and (b) non-successive scratching sequence. Fig. 3. Experimental procedure: (a) experimental setup and (b) experimental details in multi-scratch tests. Fig. 4. Overall surface morphology of (a) successive scratching sequence and (b) non-successive scratching sequence. Fig. 5. Surface morphology at L = 35 m in (a) successive scratching sequence and (b) non-successive scratching sequence. Fig. 6. Surface morphology at L = 180 m in (a) successive scratching sequence and (b) non-successive scratching sequence. Fig. 7. Scratch morphologies at L = 200 m in (a) successive scratching sequence and (b) non-successive scratching sequence. Fig. 8. Scratch depth and residual depth in (a) successive scratching sequence and (b) non-successive scratching sequence. Fig. 9. Elastic recovery rate in (a) successive scratching sequence and (b) non-successive scratching sequence. Fig. 10. Chip removal strength: (a) schematic illustration and (b) comparison between two scratching sequences. Fig. 11. Analysis of a single scratch as reference: (a) schematic diagram in brittle mode of material removal, and (b) normalized principal stress distribution at (x, y, z) = (0, y, b). Fig. 12. Analysis of normalized principal stress distribution at (x, y, z) = (0, y, b): (a) Schematic diagram of extracting the maximum principal stress of multi-scratch, (b) successive scratching sequence, and (c) non-successive scratching sequence. Fig. 13. Schematic diagram of (a) material flow ahead of a grit, and (b) surface generation in ductile mode of material removal. 25
Fig. 14. Stress analysis of a single scratch: (a) material flow ahead of the indenter and (b) distribution of normalized deviatoric stress component on a x-z plane at x =a. Fig. 15. Distribution of normalized deviatoric stress component along z-axis. Fig. 16. Schematic diagram of grit-workpiece contact area in (a) non-successive scratching sequences and (b) successive scratching sequence.
6 5 3 2
4
1
Fig. 1.
3 ○ 2 ○
5 ○
1 ○ g3 d
g2
4 ○ g3
g1
d
d
y
x
6 ○
g2
d
y
x
z
z
(a)
(b)
Fig. 2. .
26
g1
65 77
(a)
d
d
d
L
d
1 Grit ○ 2 Grit ○ 3 Grit ○
g3
g2
g1
g3
g2
g1
L
4 Grit ○ 6 Grit ○ 5 Grit ○
(b)
Fig. 3. .
0
50
100
150
200 L (m)
(a)
(b)
Fig. 4..
27
20
Cross section depth (nm)
10 0 -10 -20
g1
-30
g3
g2 -40 0
5
10
15
20
Cross section distance ( m)
(a)
Cross section depth (nm)
20 10 0 -10 -20
g1 g3
-30
g2 -40 0
2
4
6
8
10
12
14
Cross section distance ( m)
(b)
Fig. 5.
28
16
18
20
100
Cross section depth (nm)
50 0 -50
g1
-100
g2
-150
g3
-200 0
10
20
30
40
Cross section distance ( m)
(a)
Cross section depth (nm)
100 50 0 -50
g1
-100
g3
g2 -150 0
5
10
15
20
Cross section distance ( m)
(b)
Fig. 6.
g1
g2
g1
g3
(a)
g2
(b)
Fig. 7..
29
g3
25
30
g1 Plastic deformation without interaction
Complete elastic deformation
g2
Plastic deformation with interaction
g3 Plastic deformation without interaction
Plastic deformation with interaction
Scratch depth h
Scratch depth h
Residual depth h r
Residual depth h r
Complete elastic deformation
(a)
(b)
Fig. 8.
g1
g2
(a)
g3
(b)
Fig. 9.
30
Chip
Grit Area of pile-up
Area of groove (a)
(b)
Fig. 10.
Radial crack Grit (0, 1.19) x
Material peeling
Plastic core
y Plastic zone
Elastic-plastic boundary
Median crack
b
Lateral crack z (a)
(b)
Fig. 11. .
31
Plastic zone Grit
Grit
Grit
y/b
0 1b 2b Cracks 3b 4b z/b (a)
g1 (0, 1.41) g1 (0, 1.26)
g3 (1.69, 1.25)
g2 (0.85, 1.23) g2 (0.85, 1.12) g3 (1.69, 0.84)
(b)
(c)
Fig. 12.
Chip Grit Scratch direction
Plastic deformation
Groove x
Pile-up hs h
S Plastic core
y
Plastic zone
Elastic recovery
b
Elastic-plastic boundary
Elastic zone z
(a)
(b)
Fig. 13.
32
Scratch direction 0
S
S
z /h
S zh 2 /P
0.5
1
0.11 1.5 0
1
2
3
4
5 z/h
x/h (a)
(b)
Fig. 14.
S
0.29 0.21
Fig. 15.
33
0.39 0.45
g2
g3 g1 g3
g1
y y
x
z
x
z
(a) g3 g2 g2 g1 g1
y y
x
z x
z
(b)
Fig. 16.
Table 1 Material properties of LAS glass-ceramic [23] Parameters
Value
Hardness H (GPa)
9.25
Elastic modulus E (GPa)
88.7
Poisson’s ratio
0.25
34
Table 2 Experimental parameters Value Parameters
Successive scratching
Non-successive scratching
sequence
sequence
Half-apex angle of Berkovich indenter
65
65
The maximum normal load P (mN)
30
30
Scratch length L (m)
200
200
Scratching speed (m/s)
50
50
2
2
Order of g1 conducted
Firstly
Firstly
Order of g2 conducted
Secondly
Thirdly
Order of g3 conducted
Thirdly
Secondly
Distance d between adjacent scratches (m)
35