Regarding quality inspection of technologically important nanocomposite hard coatings based on Ti, B, Si, C, and N and bioceramics such as hydroxyapatite that are used in small-scale high-precision devices and bio-implants, it is essential to study the failure mechanisms associated with nanoindentation, such as fracture, delamination, and chipping. The stress imposed by the indenter can affect the fracture morphology and the interfacial fracture energy, depending on indenter shape, substrate type, crystallographic properties, pre-existing flaws, internal micro-cracks, and pre-strain. Reported here are finite-element-based fracture studies that provide insights into the different cracking mechanisms related to the aforementioned failure process, showing that the fracture morphology is affected by the interaction of different cracking events. The interfacial fracture energy, toughness, and residual stress are calculated using existing models with minor adjustments, and it is found that increasing the indenter sharpness improves the shear stress distribution, making the coating more prone to separation. Depending on the prevailing type of stress, the stress distribution beneath the depression results in either crack formation or a dislocation pile-up leading to strain hardening. Different forms of resistances resulting from the indentation process are found to affect the tip–sample conduction, and because of its stronger induced plasticity than that of a Berkovich indenter tip, a sharper cube-corner tip produces more resistance.

HIGHLIGHTS

  • Fracture morphologies caused by nanoindentation on hard Si coatings are studied.

  • Interfacial energies, fracture toughness, and stress distributions are analyzed.

  • Indenter tip sharpness is found to influence electrical conduction.

Nanoindentation is used extensively for the nanomechanical characterization of materials used in microelectronics. Nanocomposite hard coatings comprising phases such as SiC, Si3N4, CNx, TiC, TiN, TiB2, and cBN have applications in the fabrication of nano/microelectromechanical systems (N/MEMS) devices, interconnects, and metallurgical protective coatings, and biomaterials such as manufactured (prosthetics and bio-implants) and natural (bone, tissue, etc.) ones are also being used in nanoindentation. Obtaining attributes such as hardness, decreased modulus, fracture toughness, adhesion, and wear from nanoindentation depends on making contact between the indenter tip and the material being studied,1,2 and assessing fracture behavior is important when considering the durability of these coatings in adverse conditions or being subjected to external stimuli for film failure.3,4

Begun by Hertz in 1881, the study of indentation-based fracture has developed over the years, such as with the energy-based criterion due to Griffith and the energy balance analysis due to Frank and Lawn.5–12 The mechanisms behind the different cracking phenomena that occur in micro/nanoindentation using indenters of different shapes have been analyzed and reported extensively over the years.13–16 

For coated samples, the fracture mode depends on the coating thickness and the indenter geometry. A sharper indenter causes more plastic deformation, with mode-I fracture more prevalent for a higher ratio of tip radius to sample thickness. The nature of the substrate and interface and the load applied also affect the fracture morphology for coated systems. The cracked segments also experience multiple minor cracks and branches because of stress relaxation after indentation (load withdrawal), and coatings subjected to indentations by smaller indenters are found to be more prone to interfacial failure.17–21 The stress imposed by the indenter affects the fracture nature depending on the coating’s mechanical and crystallographic properties and the existence of any pre-existing flaws, internal micro-cracks, and pre-strain. Plate or membrane bending models have been used for Hertzian (spherical) contacts,22–25 and the stress distribution and determination of interfacial fracture associated with hard pyramidal indenters have been reported based on models proposed by den Toonder et al.,4 Bull,14 and Thouless.26 

In fracture investigations of film/substrate systems, crack-based stress intensities are transferred to the substrate, resulting in various cracking events, including radial (palmist), median, half-penny, lateral, secondary palmist, and shallow lateral cracks.3 Radial cracks are related to fracture toughness and so have been used to estimate it using crack-opening-displacement models. Lateral cracks, film delamination, and chipping show how the substrate is also implicated, as are the adhesive capabilities of the films. Additionally, methods based on geometric mapping of the chipped region as well as an energy-based technique have been published for determining the interfacial toughness.3,4,14,27 The stress distribution during fracture caused by indentation is so complicated that it demands further in-depth analysis. Finite-element analysis (FEA) has been used previously to determine the fracture toughness and trajectories of cracks using extended finite-element modeling (FEM), the cohesive zone model (CZM), and the virtual crack closure technique. However, the different approaches must be combined to assess mixed-mode fractures.28,29 Herein, we seek to enrich this area of study by correlating the film failure phenomena with FEA and trying to understand the interactions among different cracking phenomena.

Hard films of the nanocomposites SiCN and TiB2 were deposited on silicon substrates by RF magnetron sputtering (HINDHIVAC, Bangalore) using 2-in. sintered ceramic targets of SiC and TiB2 with a supply of argon and nitrogen gas, the details of which have been reported previously.30,31 The nanoindentation tests were performed using nanoindenters (MTS, USA) in the form of a three-sided pyramidal Berkovich indenter and a cube-corner indenter. Images of the nanoindented regions were captured using an optical microscope (LEICA Microsystems, Germany).

FEA was performed using ABAQUS 6.13, with 3D FEM of quarter specimens because of symmetry and to reduce the computational time. The boundary conditions used in the model are shown in Fig. 1(a). Eight-node isoparametric hexahedral elements with eight Gauss points were used for the calculations, and reduced integration was done with full Newtonian nonlinear analysis computation for all the specimens. The mesh was refined with an element volume of 0.0002 × 0.0002 × 0.0002 mm3 in the region ahead of the indenter, and the element size was kept constant near the crack tip to facilitate calculation of the stress distribution.

FIG. 1.

(a) Quarter model showing boundary conditions, and (b) mesh distribution of quarter specimen.

FIG. 1.

(a) Quarter model showing boundary conditions, and (b) mesh distribution of quarter specimen.

Close modal

In total, 38 360 linear hexahedral elements of type C3D8R were used for the analysis. Elastic-plastic FEA was performed using ABAQUS 6.13, and the Young’s modulus E, Poisson’s ratio, and yield stress vs plastic strain required for the FEA were obtained from the nanoindentation tests. The material behavior for the analysis was isotropic elastic and isotropic hardening plastic. To induce the large strain expected in the indenter tip, large-deformation theory was used. The mesh distribution is shown in Fig. 1(b). The indenter was taken as a discrete rigid object, and surface-to-surface contact was established between the indenter and the film. The indenter surface was considered as the master surface, and the film was considered as the slave surface. The discretization method was node to surface. A reference point was created on the indenter through which displacement was provided.

Figure 2 shows the distribution of shear stress (σxy) obtained from FEA [Fig. 2(a)] and the fracture region showing different cracking and film failure phenomena [Fig. 2(b)]. A schematic of the indentation-chipped segment showing the geometrical parameters required for estimating the interfacial fracture energy as per the proposed models is shown in Fig. 3(a). The fracture features that occurred during the indentation process as observed in Fig. 1(b) are shown schematically in Fig. 3(b). Different types of cracks such as radial (r1), lateral (L1, L2), secondary radial (r2), and edge (e1, e2) were observed and marked. The mechanisms of cracking phenomena for radial (Palmqvist), secondary radial, and lateral cracks as shown in Figs. 3(c) and 3(d) have been reported previously,3 but some novel features were observed in addition to the aforementioned cracking. The indentation mechanism is a hybrid of radial and lateral cracks, and edge cracks may be observed to be developing on both surfaces. These result from a pre-existing fault that causes cracks to expand when loads are applied. Delamination occurs before the phenomena of chipping. The chipped segment C1 in Fig. 2(b) is surrounded by delamination. The delaminated (going to be chipped) regions C2 and C3 are due to edge cracks and not lateral cracks. The interaction between the radial and lateral cracks causing the bending of the radial crack toward the delaminated region is shown schematically in Fig. 3(d).

FIG. 2.

(a) Distribution of shear stress σxy. (b) Different cracking phenomena during nanoindentation performed at higher load on an SiCN film deposited on an Si substrate (reproduced with permission from Ref. 1. Copyright 2023 John Wiley & Sons Ltd.

FIG. 2.

(a) Distribution of shear stress σxy. (b) Different cracking phenomena during nanoindentation performed at higher load on an SiCN film deposited on an Si substrate (reproduced with permission from Ref. 1. Copyright 2023 John Wiley & Sons Ltd.

Close modal
FIG. 3.

Schematics of (a) indentation-chipped segment showing geometrical parameters required for estimating interfacial fracture energy as per proposed models,14 (b) fracture features occurring during indentation process as observed in Fig. 1(b), and mechanisms for (c) radial (Palmqvist) and lateral cracks and (d) edge cracks and interaction between radial and lateral cracks causing bending of radial crack.

FIG. 3.

Schematics of (a) indentation-chipped segment showing geometrical parameters required for estimating interfacial fracture energy as per proposed models,14 (b) fracture features occurring during indentation process as observed in Fig. 1(b), and mechanisms for (c) radial (Palmqvist) and lateral cracks and (d) edge cracks and interaction between radial and lateral cracks causing bending of radial crack.

Close modal
The shear stress distribution found via FEA can be related to the fracture shape. The sample encounters a sharp tip, inducing plastic deformation, and this causes the maximum stress area directly below the indentation. However, there are surrounding regions of hydrostatic stress (σhydro), which is expressed as
σhydro=13(σx+σy+σz),
(1)
where σx, σy, and σz are the normal stresses in the X, Y, and Z directions. This hydrostatic stress can also cause phase transformation in the silicon substrate. At the interface, the shear components of the hydrostatic stress are important because they add to the pre-existing residual stress (σres) due to the difference in the material configuration of the film and substrate, causing film failure after a certain threshold value.
The radial (Palmqvist) crack occurs in the coating region, and the stress distribution is confined to a small region and eventually moves to the surface. The radial crack—which is a measure of toughness—is seen to deviate from its linear path, indicating good toughness due to the formation of nanocrystallites during the film deposition process.31 The interfacial region is very important in the case of the lateral crack, which is related to film adhesion and wear. A clear demarcation in the flow of σhydro can be seen at the film–substrate interface. The stress is seen to take a path along the interface and is transferred to the substrate, from the load applied to the specimen creating lateral cracks. This inhomogeneity in stress distribution becomes more severe and leads to delamination and eventually chipping. The geometrical parameters of the chipped segment as shown in Fig. 2(b) can be used to determine the interfacial fracture energy as3,4,14,26,27
Γi=1.42Et5L4αL+βπ2αL+βπ2+t(1ν)σ2E+3.361νt3σL2αL+βπ2αL+βπ.
(2)
Approximate estimates of the interfacial energies of the different zones were calculated as per Eq. (2) using the parameters obtained from the figures and given in Table I. The coating thickness was t = 1.5 μm, Poisson’s ratio was ν = 0.25, and the elastic modulus was E = 200 GPa. The first term in Eq. (2) is very large and is the dominant term for the result, so the other terms were neglected for the calculations. Note that 1 GPa μm is equivalent to 1 kJ/m2, the unit of interfacial fracture energy. The calculated values show that the interfacial fracture energy was 59 J/m2 for the chipped segment C1 and 68 J/m2 for C4. The residual stress causing film failure can be evaluated approximately from Γi by dividing it by L, giving values of 5.9 and 5.7 GPa for C1 and C4, respectively. The interfacial modulus (Ei) and toughness (Kic) can also be determined as3,
1Ei=121Ec+1Es1;Kic=ΓEi,
(3)
where Ec and Es are the modulus of the coating and substrate, respectively, which were 200 GPa for SiCN and 140 GPa for silicon, giving an interfacial modulus of 167 GPa. The interfacial fracture toughness was more than 3 MPam for C1 and C4. Another way of determining the fracture toughness is by applying3 
Kc4=Pc3421200cotθ2/3H4E,
(4)
where Pc (100 mN) is the critical load for generating a lateral crack, H and E are the hardness and modulus, respectively, and θ is the indenter half-angle, which is 35° for the Berkovich indenter, giving a similar value of fracture toughness of ∼3 MPam.
TABLE I.

Parameters for calculation of interfacial energy from chipped segments.

Segmentα (μm)L (μm)β (deg)β (rad)αL+βπ2αL+βπ1.42Et5L4 (GPa μm)Interfacial energy Γi (J m−2)Residual stress σres (GPa)Interfacial toughness Kic (MPam)
C1 10 45 0.78 0.53 0.21 59 5.9 3.14 
C4 12 45 0.78 0.57 0.21 68 5.7 3.37 
Segmentα (μm)L (μm)β (deg)β (rad)αL+βπ2αL+βπ1.42Et5L4 (GPa μm)Interfacial energy Γi (J m−2)Residual stress σres (GPa)Interfacial toughness Kic (MPam)
C1 10 45 0.78 0.53 0.21 59 5.9 3.14 
C4 12 45 0.78 0.57 0.21 68 5.7 3.37 
Pre-existing tensile stress promotes adhesive failure via chipping, while compressive stress helps more in radial cracking. For a coating–substrate system, a modified form of Stoney’s equation can be used,32 i.e.,
σt=plnkEh26p1ν+1;p=h3D2E13.51ν210.3,
(5)
where h is the thickness of the total film–substrate system, and t is the coating thickness. The parameter D is the diameter of the coating considering the shape to be circular and is taken as 1 cm. The deposited film was 1-μm thick on a 1-mm-thick Si substrate, so h is considered as 1 mm. The value of the spring constant k is taken as the stiffness 0.1 mN/nm (MN/m), giving a surface stress of 300 MPa, which increases on application of indentation.
In a coating–substrate system, through-thickness fracture and interfacial delamination give information about the coating toughness and adhesion, respectively. The residual stress σres in the coating is related to the interfacial toughness as given by33,
Kc=β(E/H)1/2P/c3/2+2 σres(c/π)1/2
(6)
where β is a constant equal to 0.016, E and H are the modulus and hardness, respectively, P is the applied load (∼100 mN), and c is the crack length (15 μm). Considering Kc = 3 MPam gives σres = 667 MPa. A shape factor is also included as given by3 
Kc=β(E/H)1/2P/c3/2+Zσres(c/π)1/2;Z =1.12πd/c3π8+π8dc2,
(7)
where the additional parameter d is the depth of the radial crack, which we take instead as the crack width [3 μm as shown in Fig. 2(b)], giving Z = 0.33.
For the interfacial fracture toughness for a plane-strain mode-I fracture, the energy-based model gives
KIC=[EUf/(1ν2)Af]0.5
(8)
where Uf is the fracture dissipated energy and Af is the fracture area, giving σres = 4 GPa, which is close to the value in Table I. According to Griffith’s criterion, the total energy release rate (G) for a crack in a coating subjected to mode-I and mode-II loading is given by G = GI + GII, where
GI=αKI2/E& GII=αKII2/E.
(9)
Crack extension occurs in the direction in which the total energy release rate is maximum and takes place when the maximum energy release rate reaches a critical value Gc given by
Gc=αKIC2/E
(10)
which from pure mode-I loading is Gc = 45 J/m2 for plane stress (α = 1).

Figure 4(a) shows the FEA-determined stress distribution for a 1-μm-thick TiB2 coating on a silicon substrate using a cube-corner indenter. The strain regions arising during nanoindentation are due to the tensile and compressive fields. The tensile field exists in the first region, which makes it expand in-plane without getting deeper horizontally. The region below it has compressive stress, which causes more in-depth expansion than lateral and touches the coating–substrate interface. In Fig. 4(b), the compressive and shear stress distributions are plotted with respect to the displacement of the tip from the contact point into the film. The results show a higher variation of the compressive stress along the axis of indentation, with a slope of 80 MPa/nm compared 40 MPa/nm for the shear stress. The shear stress was prevalent parallel to the film–surface interface, increasing the chances of coating detachment.

FIG. 4.

(a). Results of finite-element modeling (FEM) of nanoindentation of TiB2 coating on Si substrate. (b) Distributions of compressive and shear stress. (c) Geometries of Berkovich and cube-corner indenters.

FIG. 4.

(a). Results of finite-element modeling (FEM) of nanoindentation of TiB2 coating on Si substrate. (b) Distributions of compressive and shear stress. (c) Geometries of Berkovich and cube-corner indenters.

Close modal

Different types of cracking phenomena can occur during the indentation process, especially when using a sharp indenter such as the pyramidal Berkovich indenter or the cube-corner indenter. The equivalent cone angle associated with the Berkovich indenter is 70.3° (half-angle 35.15°), which becomes 42.23° for the sharper cube-corner indenter [Fig. 4(c)]. The stress distribution is different for the two cases. The influence of pre-existing microcracks in the sample is somewhat mitigated by increased sharpness, which also lessens the through-thickness lateral cracking in the coating. The radial cracking is linked to film toughness, whereas the lateral cracking is linked to the coating’s adhesion and wear resistance. Greater shear stress generation parallel to the film substrate interface results from greater sharpness, increasing the likelihood of the film separating from the substrate. The radial cracking occurs on the film and is influenced negligibly by the substrate, whereas the substrate is an important factor for lateral cracking, which causes the coating to detach from the substrate. For sharper indenters, however, the radial cracking becomes more dominant in causing film failure, the experimental evidence for which has been reported earlier.30,34

FEM using the CZM has been used to study thin-film failure processes such delamination and interfacial fracture related to coating adhesion, which is an important parameter for the performance of microelectronic devices. As discussed above when considering interfacial adhesion, the interfacial fracture energy release rate is affected by the stress distribution that develops beneath the indentation.35 Nanoindentation and stress analysis have also been done for SAC (Sn–Ag–Cu) lead-free solder joints used in electronic packaging.36 The fractured or heavily plastically deformed regions also influence the electrical properties because they indicate high strain fields surrounding the indentations, which interfere with the flow of free electrons. An influence of the electric field on nanoindentation due to competition between mechanical load and electric field in the domain switching process has been reported,37,38 and an effect of charge states on the yield and elastic modulus was obtained via stress–strain plots based on nanoindentation using the power-law hardening model for LixSn alloys.39 

Because current can pass through the contact region of the indenter and sample surface, the resistivity encountered by the current varies with the applied force causing plastic deformation. Plastic deformation is a major contributor to resistivity, which is very well established as dislocations acting as scattering centers for electrons. The resistance R of the contact region has two contributions, i.e., R = Rc + Rf, where Rc is the constriction resistance and depends on the bulk properties, and Rf is the contact resistance due to the surface layer.39 

The constriction resistance is Rc = ρ/a, where ρ is the resistivity and a is the radius of the contact area. The other contributions to the resistance are Rtip from the indenter tip (a material property) and Rintf from the interface. Rf is also a material property and depends on the compositional texture of the film (the phases formed in the TiB2 or SiCN). If the contact region is considered as a circle of radius a, then we have Rc = ρ1+ρ22a, where ρ1 is the resistivity due to the tip and ρ2 is that for the sample, giving Rc=ρ1+ρ22πHF, where H is the hardness and F is the applied force. For the Berkovich indenter, the contact region is no longer circular, and instead we take the contact area as 24.5h2, which modifies the resistance equation as Rc(B)=ρ1+ρ22hπ24.5. For the cube-corner indenter, the contact area is 2.6h2, which gives
Rc(C)=Rc(B)24.52.63Rc(B).
(11)

This shows that the constriction resistance Rc(C) with the cube-corner indenter is three times the constriction resistance Rc(B) with the Berkovich indenter. A sharper indenter also causes a higher degree of plastic deformation, leading to the material being strain hardened in a localized zone surrounding the indentation region. The plastic zone near the crack tip is the dislocation distribution area with dimension rc=1πΓiH,40 where Γi is the interfacial fracture energy and is taken as being 65 J/m2 as an average of the values obtained previously (Table I). The parameter H (∼20 GPa) is the hardness, giving rc = 1 nm for the Berkovich indenter. Because of the higher indentation sharpness due to the projected areas being different, the plastic-zone radius for the cube-corner indenter is 9 nm, which again shows that dislocations piling up around a crack tip and causing strain hardening is much more prevalent with the sharper cube-corner indenter than with the Berkovich indenter. The constriction resistance Rc(B) being smaller than Rc(C), the tip voltage will be much higher with the Berkovich indenter than with the cube-corner indenter when used as a conducting tip and also as a MEMS nanoindenter with an integrated AFM cantilever gripper for nanomechanical characterizations, as in transducers for biosensing.41 

For conduction to take place between the indenter tip and sample surface, an external bias is applied with the current direction as shown in Fig. 5(a) (inset, top). The constriction resistance Rc and the contact resistance Rf are those that are affected by the indentation and any related phenomena.42 The red dotted lines indicate the current flow, which constricts at the contact causing Rc and is affected by indentation as per Matthiessen’s rule, which states the contribution of deformation (plastic) in conduction. In addition to Rc, the other resistance component that is affected by mechanical stimulus from the indenter in the case of a film–substrate system is the resistance Rintf at the coating–substrate interface, which may not be active at shallow indentation depths (less than 10% of the thickness).

FIG. 5.

(a) Electrical conduction between indenter tip and sample with different resistances with load depth and time on sample plot showing pop-in due to fracture. (b) Determination of energy dissipated due to fracture. (c) AFM image of the indentation region with line profile of one of the radial cracks showing its (d) area and (e) depth.

FIG. 5.

(a) Electrical conduction between indenter tip and sample with different resistances with load depth and time on sample plot showing pop-in due to fracture. (b) Determination of energy dissipated due to fracture. (c) AFM image of the indentation region with line profile of one of the radial cracks showing its (d) area and (e) depth.

Close modal
Nanoindentation performed on TiB2 films on silicon substrates showed fracture events as represented by pop-in in the load–depth plot [Fig. (5a)]. The maximum shear stress τmax and the maximum tensile stress induced during the indentation process at the point of pop-in are given as
τmax=0.316Er2π3R2Po1/3,
(12a)
σmaxtensile=(12ν)Po2πa2,
(12b)
where R is the tip radius, Po is the pop-in load, Er is the reduced modulus, and a is the contact radius at the pop-in. The time for which the fracture (pop-in) took place was estimated to be ∼10 s, and the impulse (ΔPt) that caused the fracture was 0.02 mN/s. This impulse usually sends a shock wave into the film and can hamper any conduction process taking place between the tip and the sample. The pop-in event corresponds to the onset of inelastic deformation and a competition between dislocation-induced plasticity (by τmax) and crack formation (σmaxtensile), which depends on the stress beneath the indenter tip. The ratio between the two stress factors (σmaxtensile/τmax) is 0.54, taking Poisson’s ratio as 0.25. For a sharper indenter, dislocation plasticity occurs prior to crack formation, and the maximum tensile strength is related to the crack length c and the fracture toughness (KIC) as σmaxtensile = KIC/πc.43 The energy released during the fracture process was 1.5 pJ obtained from the area calculated as shown in Fig. 5(b).

Indentations performed at higher loads showed the formation of radial cracks and accompanying delamination as shown in Fig. 5(c). The deflection of the radial cracks implies resistance to crack growth due to the nanocrystalline nature of the material, as reported earlier.31 Sink-in is indicated by the curved nature of the indentation sides, as shown schematically in the inset of Fig. 5(c). If the ratio of the corner area and the actual contact area of the indenter impression (Aactual/Acc) is less than one, this implies sink-in, which is associated with plastic deformation and has a degree that depends on the ratio E/Y (elastic modulus divided by yield strength) and the strain-hardening properties of the material. For materials with low E/Y (such as glasses and ceramics), the plastic zone is often contained within the circle of contact, but the elastic deformations that expand to fill indentation’s volume are spread out farther from the indenter, so sink-in is more likely to happen. Additionally, for materials that exhibit strain hardening, the innermost material in the plastic zone is softer and more prone to plastic deformation as the indentation progresses and the material is driven deeper into the specimen material, resulting in sink-in.44 Sink-in is less likely to occur with a cube-corner indenter because the extent of shear stress (responsible for plastic deformation) is confined less, as found and discussed above. Line profiles through one of the radial cracks show a gradual change in area and a crack depth of 180 nm [Figs. 5(d) and 5(e)]. The thickness of the coating being less than 2 μm, the crack growth affects the plastic zone below it and the stress distribution reaches the interface, making Rintf sufficiently active to contribute to the total resistance to the tip–sample conduction of the system.

In the study reported herein, the various failure modes that occur during indentation were related to the shear stress distribution calculated using FEA. Existing models with minor modifications were used to calculate the interfacial energy and residual stress, and the distribution of directional and shear stress changed significantly when a Berkovich indenter and a sharper cube-corner indenter were compared. The likelihood of coating delamination was found to increase with a sharper indenter, which was found to be related more to higher shear stress generated parallel to the coating–substrate contact. With indentation, there is competition between the mechanisms driving dislocation-induced plasticity and fracture development. Furthermore, applying an external voltage to an indenter tip allows its use as a nanomechanical sensor. The tip–sample conduction is influenced by the tip resistance, constriction resistance, and the resistance due to the interface region, which is activated by crack formation at higher loads. Therefore, a sharper indenter such as a cube-corner one is less useful for conduction because it imposes a significantly higher resistance to current flow due to the higher constriction resistance compared to that with a Berkovich indenter. These results improve the understanding of the mechanics of tip–sample contact failure, thereby helping with the fabrication of MEMS devices and materials used in biomedical applications such as bone implants.

The authors thank Dr. S. K. Mishra at CSIR-National Metallurgical Laboratory for the experimental facilities.

The authors have no conflicts to disclose.

The data that support the findings of this study are available from the corresponding author on reasonable request.

1.
Dash
R
,
Bhattacharyya
K
,
Bhattacharyya
AS
.
Fracture associated with static and sliding indentation of multicomponent hard coatings on silicon substrates
.
Fatigue Frac Eng Mater Struct
2023
;
46
(
4
):
1641
1645
.
2.
Dash
R
,
Bhattacharyya
K
,
Kumar
RP
,
Bhattacharyya
AS
.
Intensified chipping during nanoindentation and the effect of friction on the interfacial fracture for thin films used in N/MEMS
.
Eng Res Exp
2022
;
4
(
4
):
045012
.
3.
Chen
J
.
Indentation-based methods to assess fracture toughness for thin coatings
.
J Phys D: Appl Phys
2012
;
45
(
20
):
203001
.
4.
Den Toonder
J
,
Malzbender
J
,
With
GD
,
Balkenende
R
.
Fracture toughness and adhesion energy of sol-gel coatings on glass
.
J Mater Res
2002
;
17
(
1
):
224
233
.
5.
Fischer-Cripps
AC
.
The Hertzian contact surface
.
J Mater Sci
1999
;
34
:
129
137
.
6.
Auerbach
F
.
Measurement of hardness
.
Ann Phys Chem
1891
;
279
(
5
):
61
100
.
7.
Griffith
AA
.
The phenomena of rupture and flow in solids
.
Philos Trans R Soc London, Ser A
1921
;
221
:
163
198
.
8.
Irwin
GR
,
Fracture
,
Handbuch der Physik
.
Berlin
:
Springer-Verlag
.
1958
. Vol.
6
. p.
551
.
9.
Frank
FC
,
Lawn
BR
.
On the theory of Hertzian fracture
,
Proc R Soc
1967
;
A229
:
291
306
, https://www.jstor.org/stable/2415836.
10.
Oliver
WC
,
Pharr
GM
.
An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments
.
J Mater Res
1992
;
7
(
6
):
1564
1583
.
11.
Fischer-Cripps
AC
.
Elastic–plastic response of materials loaded with a spherical indenter
J Mater Sci
1997
;
32
(
3
):
727
736
.
12.
Tanaka
K
.
Elastic/plastic indentation hardness and indentation fracture toughness: The inclusion core model
J Mater Sci
1987
;
22
:
1501
1508
.
13.
Kruzic
JJ
,
Kim
DK
,
Koester
KJ
,
Ritchie
RO
.
Indentation techniques for evaluating the fracture toughness of biomaterials and hard tissues
.
J Mech Behav Biomed Mater
2009
;
2
(
4
):
384
395
.
14.
Bull
SJ
.
Nanoindentation of coatings
.
J Phys D: Appl Phys
2005
;
38
(
24
):
R393
.
15.
Holmberg
K
,
Ronkainen
H
,
Laukkanen
A
,
Wallin
K
,
Hogmark
S
,
Jacobson
S
,
Wiklund
U
,
Souza
RM
,
Ståhle
P
.
Residual stresses in TiN, DLC and MoS2 coated surfaces with regard to their tribological fracture behaviour
.
Wear
2009
;
267
(
12
):
2142
2156
.
16.
Thornton
JA
,
Hoffman
DW
.
Stress-related effects in thin films
.
Thin Solid Films
1989
;
171
(
1
):
5
31
.
17.
Dash
R
,
Bhattacharyya
K
,
Bhattacharyya
AS
.
Film failure at earlier and later stages of nanoindentation in static and sliding mode
.
Eng Fail Anal
2023
;
150
:
107353
.
18.
Mercier
D
,
Nicolay
A
,
Boudiba
A
,
Vanden Eynde
X
,
Libralesso
L
,
Daniel
A
,
Olivier
M
.
Mechanical properties and decohesion of sol–gel coatings on metallic and glass substrates
.
J Sol-Gel Sci Technol
2020
;
93
:
229
243
.
19.
Pajares
A
,
Wei
L
,
Lawn
BR
,
Berndt
CC
.
Contact damage in plasma‐sprayed alumina‐based coatings
.
J Am Ceram Soc
1996
;
79
(
7
):
1907
1914
.
20.
Li
X
,
Diao
D
,
Bhushan
B
.
Fracture mechanisms of thin amorphous carbon films in nanoindentation
.
Acta Mater
1997
;
45
(
11
):
4453
4461
.
21.
Malzbender
J
,
De With
G
,
Den Toonder
JM
.
Elastic modulus, indentation pressure and fracture toughness of hybrid coatings on glass
.
Thin Solid Films
2000
;
366
(
1–2
):
139
149
.
22.
Bahr
D
,
Woodcock
C
,
Pang
M
,
Weaver
KD
,
Moody
NR
.
Indentation induced film fracture in hard film – soft substrate systems
.
Int J Fract
2003
;
119–120
:
339
349
.
23.
Kramer
D
,
Huang
H
,
Kriese
M
,
Robach
J
,
Nelson
J
,
Wright
A
,
Bahr
D
,
Gerberich
WW
.
Yield strength predictions from the plastic zone around nanocontacts
.
Acta Mater
1998
;
47
(
1
):
333
-
343
.
24.
Timoshenko
S
,
Woinowsky-Krieger
S
.
Theory of plates and shells
.
New York
:
McGraw-Hill
.
1959
.
25.
Hainsworth
SV
,
Chandler
HW
,
Page
TF
.
Analysis of nanoindentation load-displacement loading curves
.
J Mater Res
1996
;
11
:
1987
1995
.
26.
Thouless
MD
.
An analysis of spalling in the microscratch test
.
Eng Fract Mech
1998
;
61
(
1
):
75
81
.
27.
Bhattacharyya
AS
,
Priyadarshi
S
,
Sonu
,
Shivam
S
,
Anshu
S
.
Nanoindentation stress–strain for fracture analysis and computational modeling for hardness and modulus
.
J Mater Eng Perform
2018
;
27
:
2719
2726
.
28.
Sun
L
,
Ma
D
,
Wang
L
,
Shi
X
,
Wang
J
,
Chen
W
.
Determining indentation fracture toughness of ceramics by finite element method using virtual crack closure technique
.
Eng Fract Mech
2018
;
197
:
151
159
.
29.
Haddad
M
,
Sepehrnoori
K
.
Integration of XFEM and CZM to model 3D multiple-stage hydraulic fracturing in quasi-brittle shale formations: Solution-dependent propagation direction
.
Proceedings of the AADE National Technical Conference and Exhibition, AADE2015
.
San Antonio, TX
:
2015
. pp.
8
9
, http://www.aade.org/app/download/7240655923/AADE-15-NTCE-28.pdf.
30.
Rupa
PK
,
Chakraborti
PC
,
Mishra
SK
.
Mechanical and deformation behaviour of titanium diboride thin films deposited by magnetron sputtering
.
Thin Solid Films
2009
;
517
(
9
):
2912
2919
.
31.
Bhattacharyya
AS
,
Mishra
SK
.
Micro/nanomechanical behavior of magnetron sputtered Si–C–N coatings through nanoindentation and scratch tests
.
J Micromech Microeng
2010
;
21
(
1
):
015011
.
32.
Liu
H
,
Dai
M
,
Tian
X
,
Chen
S
,
Dong
F
,
Lu
L
.
Modified Stoney formula for determining stress within thin films on large-deformation isotropic circular plates
.
AIP Adv
2021
;
11
(
12
):
125009
.
33.
Bull
SJ
.
Analysis methods and size effects in the indentation fracture toughness assessment of very thin oxide coatings on glass
.
C R Mec
2011
;
339
(
7–8
):
518
-
531
.
34.
Dash
R
,
Bhattacharyya
AS
.
Crack growth based on indentation along substrate and nanocrystallites in titanium diboride thin films
.
Fatigue Fract Eng Mater Struct
2023
;
46
(
7
):
2714
2719
.
35.
Reuther
GM
,
Albrecht
J
,
Dudek
R
,
Rzepka
S
.
Determining adhesion of critical interfaces in microelectronics–A reverse finite element modelling approach based on nanoindentation
.
Microelectron Reliab
2022
;
133
:
114530
.
36.
Char
M
,
Chakraborty
AK
,
Bhattacharyya
AS
,
Kar
A
.
A comparative study on the influence of SAC305 lead‐free solder sandwiched by Sn on the micromechanical and electrical properties of the joints
.
Adv Eng Mater
2021
;
24
:
2100679
.
37.
Zhou
H
,
Pei
Y
,
Li
F
,
Luo
H
,
Fang
D
.
Electric-field-tunable mechanical properties of relaxor ferroelectric single crystal measured by nanoindentation
.
Appl Phys Lett
2014
;
104
:
061904
.
38.
Gao
X
,
Ma
Z
,
Jiang
W
,
Zhang
P
,
Wang
Y
,
Pan
Y
,
Lu
C
.
Stress–strain relationships of LixSn alloys for lithium ion batteries
.
J Power Sources
2016
;
311
:
21
28
.
39.
Soshnikov
AI
,
Kravchuk
KS
,
Maslenikov
II
,
Ovchinnikov
DV
,
Reshetov
VN
.
Measuring the local resistivity by the nanoindentation and force-spectroscopy methods
.
Instrum Exp Tech
2013
;
56
:
233
239
.
40.
Ly
TH
,
Zhao
J
,
Cichocka
MO
,
Li
LJ
,
Lee
YH
.
Dynamical observations on the crack tip zone and stress corrosion of two-dimensional MoS2
.
Nat Commun
2017
;
8
(
1
):
14116
.
41.
Li
Z
,
Gao
S
,
Brand
U
,
Hiller
K
,
Wolff
H
.
A MEMS nanoindenter with an integrated AFM cantilever gripper for nanomechanical characterization of compliant materials
.
Nanotechnology
2020
;
31
(
30
):
305502
.
42.
Dassonneville
SC
,
Volpi
F
,
Parry
G
,
Pellerin
D
,
Verdier
M
,
Resistive nanoindentation: Contact area monitoring by real-time electrical contact resistance measurement
MRS Commun
2019
;
9
:
1008
1014
.
43.
Fang
X
,
Bishara
H
,
Ding
K
,
Tsybenko
H
,
Porz
L
,
Höfling
M
,
Bruder
E
,
Li
Y
,
Dehm
G
,
Durst
K
.
Nanoindentation pop‐in in oxides at room temperature: Dislocation activation or crack formation?
.
J Am Ceram Soc
2021
;
104
(
9
):
4728
-
4741
.
44.
Bhattacharyya
AS
,
Kumar
RP
,
Mandal
R
,
Kumar
N
,
Rajak
N
,
Sharma
A
,
Kant
S
.
Substrate effect and nanoindentation fracture toughness based on pile up and failure
2016
, arXiv:1602.07657.

Ritambhara Dash is a research scholar in the Department of Metallurgical and Materials Engineering at the Central University of Jharkhand. She has an M.Sc. degree in physics from SMU, Sikkim. Her research is in silicon-based cantilever sensors, nanomechanical fracture studies of hard coatings, energy storage, silicon photonics, microelectronic device fabrication, modeling and simulation using MATLAB, and finite-element analysis.

Kushal Bhattacharyya is an assistant professor in the Department of Mechanical Engineering at Netaji Subhash Engineering College Kolkata. He has B.E., M.E., and Ph.D. degrees in mechanical engineering from Jadavpur University Kolkata. His research is in fracture mechanics, damage control, material testing of reactor pressure vessels, and finite-element modeling. He has more than 10 years of teaching and research experience.

Arnab S. Bhattacharyya is an assistant professor in the Department of Metallurgical and Materials Engineering at Central University of Jharkhand, Ranchi. He has a Ph.D. degree from CSIR-National Metallurgical Laboratory, Jamshedpur. His research is in nanomechanical fracture, transition metal oxides, silicon photonics, high-temperature polymers, conducting polymers, and bioceramics for medical applications. He has more than 12 years of research and teaching experience.