Multiple cohesive cracking during nanoindentation in a hard W-C coating/steel substrate system by FEM

Stress evolution and subsequent cohesive cracking in the hard and stiff W-C coating on steel substrate during nanoindentation have been investigated using finite element modelling (FEM) and eXtended FEM (XFEM). The FEM simulations showed that the maximum principal stresses in the studied system were tensile and always located in the coating. They evolved in several stages. At indentation depths below 15% of the relative indentation depth, the maximum principal tensile stresses of ∼3 GPa developed at the top surface of the coating along the indenter/coating interface. At relative depths range 15–60%, the maximum tensile stresses of ∼6–8 GPa concentrated under the indenter tip in the coating along the interface with the substrate. At relative depths exceeding 60%, the maximum stresses gradually increased up to 10 GPa and they were located in the sink-in zone outside the indent as well as below the indenter tip. The first and subsequent cohesive cracks developed when the maximum tensile stresses in the sink-in zone at the top surface of the coating (and at the coating/substrate interface under the indenter) repeatedly reached the ultimate tensile strength of the coating. The hardness profile as well as cohesive cracking is controlled by the deformation of the substrate defined by the ration of the yield stresses of the coating and substrate. Very good correlation between the experimentally obtained cracks and multiple cracks predicted by XFEM confirmed the ability of the applied modelling in the prediction of fracture behavior of the studied coating/substrate system.     

Nanoindentation Method for Measuring Residual Stress in Brittle Materials

The lowered threshold load for cracking with the cube-corner indenter has been used in developing a method that can be used to measure residual stresses in small volume brittle materials. By studying a series of orthogonal cracks generated at loads not exceeding 10 mN with the cube-corner indenter, a variation of crack length with position around a large Vickers impression in soda–lime glass was observed. Using an indentation fracture mechanics approach residual stresses were evaluated at the positions where the cube-corner indents had been made. The stress values thus evaluated were generally higher than those reported in the literature where micro-Vickers indents had been used to measure the stresses. Possible reasons for the disparity are discussed.     

Effect of Flaw State on the Strength of Brittle Coatings on Soft Substrates

A study is made of the role of flaw state on the strength properties of brittle ceramic coating layers bonded to soft polycarbonate substrates. We introduce Vickers radial cracks at prescribed loads into the coating undersurfaces prior to bonding to control the sizes and locations of the starting flaws. A spherical indenter is then loaded on the top bilayer surfaces, directly above the Vickers indentation sites, subjecting the radial cracks to flexural tensile stress. Radial crack responses are monitored in situ , using a camera located below the transparent substrate. Critical loads to cause radial crack instability, and ensuing growth of the arrested cracks, are recorded. Conventional biaxial flexure tests on corresponding monolith coating materials provide a baseline for data comparison. Relative to the monolith flexure specimens, the bilayers show higher strengths, the more so the larger the flaw, indicating enhanced flaw tolerance. A simple fracture mechanics analysis of the radial crack evolution in the concentrated-load field, with due account for distribution of flexural tensile stresses at the coating undersurface, is unable to account completely for the enhanced bilayer strengths for the larger Vickers flaws. It is hypothesized that the epoxy used to bond the bilayer components enters the cracks, causing crack-wall adherence and providing an increased resistance to radial crack instability. The fracture mechanics are nevertheless able to account for the arrest and subsequent stable extension of the radial cracks beyond the critical loads once this extraneous adherence has been overcome.     

Stress Analysis of Contact Deformation in Quasi-Plastic Ceramics

A stress analysis is made of Hertzian contact deformation in relatively tough ceramics with heterogeneous microstructures, where the response is essentially quasi-plastic rather than ideally elastic-brittle. Contact data for two such heterogeneous ceramics, a micaceous glass-ceramic with modest hardness and a silicon nitride with high hardness, are presented as illustrative cases. Data from a soft steel serve as a comparative baseline. Two distinctive aspects of the deformation response are explored: indentation stress-strain nonlinearity; and size and shape of the damage zone. For the harder ceramics, the stress-strain nonlinearity is less pronounced, and the quasi-plastic zone is more tightly confined beneath the contact, than in traditional ductile metals. As in metals, the deformation process in the ceramic structures is essentially shear driven, but has its origin in microstructurally localized interfacial sliding faults rather than in dislocation slip. Finite element modeling (FEM) is used to compute the shear stress distributions beneath the spherical indenters for selected experimental loading conditions. The underlying basis of the FEM calculations is an elastic-plastic constitutive relation based on a critical shear condition for yield, but incorporating a strain-hardening characteristic to allow for local elastic constraints on the sliding shear faults. The FEM calculations are able to simulate the main features of the stress-strain curves and the evolving deformation zone geometries. In addition, the calculated tensile stress distributions are able to account, at least in part, for the suppression of conventional brittle fracture tendencies in tougher ceramics.     

钢化真空玻璃球形支撑的玻璃压痕应力场理论及分析

针对钢化真空玻璃球形支撑物对玻璃压痕的应力场分布问题,采用接触力学,对Hertzian压痕方程进行了修正,推导了三维应力场方程,同时,对完全发展的锥形裂纹的应力强度因子进行了数值求解。结果表明,在球体与玻璃接触区域内,所有的主应力都是压应力,主应力σ₁导致了裂纹的萌生,而主应力σ₂形成了环形裂纹。与玻璃表面正交的最小主应力从接触边缘向外偏离,形成的近似平行的曲线即为锥形裂纹的形状,而最大拉应力总是垂直于这些曲线。因此,在最大主拉应力的作用下,球体加载后裂纹遵循最小主应力的轨迹。裂纹尖端的应力强度因子决定了断裂韧性,随着裂纹的扩展,应力强度因子减小,在离表面一定距离后,应力强度因子达到临界值,裂纹停止。不同压痕载荷下的归一化应力强度因子是一组具有相似形状的曲线。     

Analytical estimation of fracture toughness for circumferential cracks in thin hard films on ductile substrates

In this study, the fracture toughness of circumferential crack caused by indentation effect of a rigid indenter on a thin and elastic coating deposited on the elastic substrate was calculated. In the coating and substrate, the analytical solution of displacement and stress field was used. The complete adhesion was considered for the coating on the substrate. The location of maximum circumferential stress was investigated using the analytical calculation of the stress and it was found that this place was located at a distance away from the center of the indenter. Then, the stress intensity factor and energy release rate for plane strain state was determined, and consequently, the energy release rate for a channel crack was calculated. Finally, the fracture toughness was calculated with energy release rate curves for plane strain crack and crack channeling. This method was used to calculate the fracture toughness of TiN/TiCrN ceramic multilayer coating which was deposited on the GTD450 substrate using the Cathodic Arc PVD method. To validate the results, the analytically calculated crack radius was compared with the experimental crack radius in the fracture load and the difference between the radiuses was in the acceptable range.     

Nonlinear Compliance Testing Applied to Indentation Cracking in Ceramics

Indentation cracking under sharp-pointed indenters is analyzed using compliance-based, nonlinear, fracture mechanics. The stress intensity factor, K , in linear elastic fracture mechanics is well known to be proportional to the load, P ; in this nonlinear analysis K is proportional to P ^3/4. The observed relation between indenter load-point displacement and crack length is based on similitude of crack lengths with load-point displacements as a strain-controlled fracture. The equations that relate load and a function of the crack length to the crack driving force, J , have been found for Vickers indentations. Analysis of the nonlinear load vs displacement assumes an equilibrium crack in the elastic material surrounding the indent. The hardness that describes the load vs load-point displacement during cracking is derived on a constant J line in load-displacement space. The crack length is shown experimentally to be proportional to the load-point displacement after crack initiation for several different indenters in ZnS. The measured loading curves are nonlinear and display crack initiation during loading. The K _Ic expressions found here are very similar to correlations that have been applied to indentation cracks.     

Analysis of the mechanical properties of TiN/Ti multilayer coatings using indentation under a broad load range

In this study, physical vapor deposition was used to prepare TiN/Ti multilayer coatings as well as the corresponding monolithic coatings for comparison. Nanoindentation using a large load range (5–4800 mN) and finite element method (FEM) simulations were conducted to investigate the influence of various multilayer structures on the mechanical behavior of multilayer coatings. The nanoindentation results show that the TiN/Ti multilayer coating has the maximum hardness and Young's modulus while retaining good crack resistance and fracture toughness. The FEM results show that increasing the number of layers in the multilayer coatings reduced the hardness and Young's modulus as well as the maximum stress, while it increased the equivalent plastic strain. As the layer thickness ratio increased, both the hardness and Young's modulus gradually increased, and the stress in the coating reached its maximum at the highest thickness ratio. In addition, to consider the effect of the indentation depth on the coating, the influence of the number of layers and the layer thickness ratio on the multilayer coating is combined into the indentation response of the multilayer coating. Therefore, we establish an expression describing the relationship between the number of layers and the ratio of the layer thickness to the mechanical properties of TiN/Ti multilayer coatings.     

Fracture of Brittle Materials under a Simulated Wear Stress System

Currently no data are available for fracture toughnesses associated with the compression/shear (mixed mode) stress distribution of the sliding-wear loading system. To provide such information, diametrically compressed disk specimens of electrical porcelain were tested and used to develop a fracture criterion for a body containing a crack which is subjected to mixed-mode loading. The role of applied shear loads in creating local tensile stresses near the crack tip is discussed. While these stresses are embodied in the maximum-hoop-stress theory of mixed-mode fracture, it was found that the toughness values had only a fair fit with theory. However, the direction of initial crack growth, which is out-of-plane, is consistent with theory. Since effects due to crack-face rubbing were limited by using a finite-thickness notch in the test specimen (instead of a crack), the data, although indicative, are not fully representative of debris formation during sliding wear. The paper concludes with the formulation of a simple model of the formation of a debris particle.     

Nanoindentation-based study of the mechanical behavior of bulk supercrystalline ceramic-organic nanocomposites

Bulk poly-supercrystalline ceramic-organic nanocomposites were produced and characterized with a nanoindentation-based study. These nanocomposites were processed using two different routines, to compare their properties with and without crosslinking the organic ligands interfacing the ceramic nanoparticles. Together with the expected material strengthening induced by crosslinking, a distinct response emerges when using Berkovich and cube-corner indenters. The supercrystalline materials are prone to compaction, cracking and chipping phenomena that become more severe when a sharper tip is employed, implying that a Berkovich indenter is more suitable for the evaluation of elastic modulus and hardness. The cube-corner tip, on the other hand, is employed for the investigation of fracture toughness, comparing two methods and multiple models available from the literature. The fracture toughness outcomes suggest that cracks evolve with a quarter-penny shaped profile at the indent’s corners, and that extrinsic toughening mechanisms, such as plastic-like deformation and crack deflection, play a significant role.     

Median Cracking of Brittle Solids Due to Scribing with Sharp Indenters

The process of moving a loaded hard indenter across the surface of a brittle solid to produce a median crack is referred to as "scribing." As a first step in predicting the depth of median cracking due to sharp indenters, an approximate plastic plane strain analysis is presented for the region under the indenter. This allows the horizontal force transverse to the scribing direction to be predicted. Taking this force and an approximate solution for the stress intensity factor for the crack geometry in scribing leads to a prediction for crack depth as a function of load. The residual stresses which arise on unloading are shown to be a strong function of indenter geometry and may act to extend or partially close the original median crack formed during loading. Reasonable agreement is found between prediction and experiment for six indenter configurations.     

Lateral cracks during sliding indentation on various optical materials

A series of static and sliding indentation (ie, scratching) was performed and characterized on a wide range of optical workpiece materials [single crystals of Al₂O₃ (sapphire), SiC, Y₃Al₅O₁₂ (YAG), CaF₂, and LiB₃O₅ (LBO); a SiO₂–Al₂O₃–P₂O₅–Li₂O glass ceramic (Zerodur); and glasses of SiO₂:TiO₂ (ULE), SiO₂ (fused silica), and P₂O₅–Al₂O₃–K₂O–BaO (Phosphate)] at various applied loads using various indenters (Vickers, 10 µm conical, and 200 µm conical). Despite having different load dependencies, the lateral crack depth formed during sliding indentation quantitatively scales with that formed during static indentation, explaining why static indentation has been historically effective in describing various grinding parameters. Depending on the indenter geometry, the amount of residual trench damage (plastic deformation and local fracturing) during sliding indentation was often enhanced by more than an order of magnitude compared with static indentation. A simple ploughing scratch model, which considers both tangential and normal stresses (where the tangential stress is amplified by relatively small tangential contact area), explains this enhancement and other observed trends. Accounting for the high correlation between residual trench depth and volumetric fracturing, the model is extended to estimate the amount of fracture damage as a function of the material properties of the workpiece, indenter geometry, and applied load. Such a model has utility in the design of optimized grinding processes, particularly the abrasive geometry. Finally, at higher loads (>1 N), lateral cracks were often observed to preferentially propagate in the forward scratching direction, as opposed to perpendicular to the scratch as typically observed. High-speed imaging of the scratch process confirms that these cracks propagate ahead of the sliding indenter during the scratching event. Finite element stress analysis suggests the ploughing frictional forces increase the mode I tensile stresses at the leading edge of the sliding indenter explaining the direction of crack propagation of such cracks.     

Contact damage tolerance of alumina-based layered ceramics with tailored microstructures

This work demonstrates how to enhance contact damage resistance of alumina-based ceramics combining tailored microstructures in a multilayer architecture. The multilayer system designed with textured alumina layers under compressive residual stresses embedded between alumina–zirconia layers was investigated under Hertzian contact loading and compared to the corresponding monolithic reference materials. Critical forces for crack initiation under spherical contact were detected through an acoustic emission system. Damage was assessed by combining cross-section polishing and ion-slicing techniques. It was found that a textured microstructure can accommodate the damage below the surface by shear-driven, quasi-plastic deformation instead of the classical Hertzian cone cracking observed in equiaxed alumina. In the multilayer system, a combination of both mechanisms, namely Hertzian cone cracking on the top (equiaxed) surface layer and quasi-plastic deformation within the embedded textured layer, was identified. Further propagation of cone cracks at higher loads was hindered and/or deflected owed to the combined action of the textured microstructure and compressive residual stresses. These findings demonstrate the potential of embedding textured layers as a strategy to enhance the contact damage tolerance in alumina ceramics.     

Indentation densification of fused silica assessed by raman spectroscopy and constitutive finite element analysis

Inelastic deformation of anomalous glasses manifests in shear flow and densification of the glass network; the deformation behavior during indentation testing is linked strongly to both processes. In this paper, the indentation densification field of fused silica is investigated using depth-resolved Raman spectroscopy and finite element simulations. Through affecting the size of the indent, the normal load and the Raman laser spot size determine the spatial sampling resolution, leading to a certain degree of structural averaging. For appropriate combinations of normal load (indent size) and laser spot diameter, a maximum densification of 18.4% was found at the indent center. The indentation behavior was modeled by extended Drucker-Prager-Cap (DPC) plasticity, assuming a sigmoidal hardening behavior of fused silica with a densification saturation of 21%. This procedure significantly improved the reproduction of the experimental densification field, yielding a maximum densification of 18.2% directly below the indenter tip. The degree of densification was found to be strongly linked to the hydrostatic pressure limit below the indenter in accordance to Johnson's expanding cavity model (J. Mech. Phys. Solids, 18 (1970) 115). Based on the good overlap between FEA and Raman, an alternative way to extract the empirical correlation factor m, which scales structural densification to Raman spectroscopic observations, is obtained. This approach does not require the use of intensive hydrostatic compaction experiments.     

Strength Degradation of Brittle Surfaces: Sharp Indenters

A theory of strength loss for brittle surfaces in contact situations, developed in a previous paper for "blunt" indenters, is extended to the case of "sharp" indenters. A prior fracture mechanics analysis of crack growth beneath ideal cone indenters serves as the basis for predetermining the prospective surface degradation of ceramic components in service. Compared to blunt indenters, sharp indenters can cause severe degradation at lower contact loads. However, at high loads, the extent of degradation becomes remarkably insensitive to details in the indenter geometry. Essential theoretical predictions are verified by bend tests on glass slabs. Effects of indenter "sharpness" and initial specimen surface flaw state are investigated systematically, along with some secondary rate effects in the contact process. The possibility of minimizing degradation via adjustment of material parameters (including hardness) or surface condition (e.g. residual stresses, frictional properties) is briefly discussed.     

Toughness measurement on ball specimens. Part I: Theoretical analysis

A new toughness test for ball-shaped specimens is presented. In analogy to the “Surface Crack in Flexure”-method the fracture toughness is determined by making a semi-elliptical surface crack with a Knoop indenter into the surface of the specimen. In our case the specimen is a notched ball with an indent opposite to the notch. The recently developed “Notched Ball Test” produces a well defined and almost uniaxial stress field.The stress intensity factor of the crack in the notched ball is determined with FE methods in a parametric study in the practical range of the notch geometries, crack shapes and other parameters. The results correlate well with established calculations based on the Newman-Raju model.The new test is regarded as a component test for bearing balls and offers new possibilities for material selection and characterisation. An experimental evaluation on several ceramic materials will be presented in a consecutive paper.     

The impact of densification on indentation fracture toughness measurements

The fracture toughness was measured by the Vickers indentation method and by chevron notch for a series of xCaO-xAl₂O₃-(100 − 2x)SiO₂ glasses. As the silica content was increased, the fixed ξ value Vickers indentation fracture toughness (IFT) values increased, while the chevron notch values decreased. Glasses with higher silica contents deform with more densification and less shear when indented with a Vickers tip, thus resulting in reduced residual stress in the region surrounding the indent. The reduction in residual stress for high silica glasses results in less median/radial crack extension and unreasonably high Vickers IFT values. This indicates that a fixed ξ value of 0.016 is not appropriate for the glasses in this series. By repeating the IFT method with a sharper 110° four-sided pyramidal diamond indenter, it is demonstrated that indentation toughness and chevron notch toughness values now trend in the same direction and are in good agreement with a fixed ξ value of 0.0297. With the sharper indenter tip, the densification component to the deformation is substantially reduced for all glass types such that it no longer has such a prominent influence on the residual stress field. This result suggests that a fixed ξ value IFT method may be appropriate for all glass types if a sharper indenter tip is substituted in the place of the Vickers tip.     

Surface damage resistance and yielding of chemically strengthened silicate glasses: From normal indentation to scratch loading

We report on surface elasticity, plastic deformation and crack initiation of chemically strengthened soda-lime silicate and sodium aluminosilicate glasses during lateral indentation and scratch testing. Instrumented indentation using a normal indenter set-up corroborated previous findings on the effects of chemical strengthening on surface Young's modulus, hardness, and indentation cracking. Using lateral indentation in the elastic-plastic regime, we find a pronounced increase in the scratch hardness as a result of chemical strengthening, manifest in higher work of deformation required for creating the scratch groove. Thereby, the glass composition is found to play a stronger role than the absolute magnitude of surface compressive stress. Using a blunt conical stylus for instrumented scratch testing reveals three distinct modes of scratch-induced surface fracture, which occur during scratching or after unloading. Occasional micro-cracking caused by pre-existing surface flaws at low scratching load can be completely suppressed through chemical strengthening. The intrinsic defect resistance to microcracking is reduced as a result of ion stuffing, depending on the initial glass composition, whereas the resistance to abrasive yielding is enhanced by several hundred MPa.     

Mechanical properties and indentation-induced phase transformation in 4H–SiC implanted by hydrogen ions

This paper aims to improve machining efficiency, suppress surface cracking, and reduce subsurface damage of silicon carbide (SiC). Hydrogen ions were implanted into SiC to study mechanical properties at nano and macro scales. Nanoindentation experiments were conducted using a Berkovich indenter. Firstly, the effect of ion implantation on the load-displacement curves at different indentation depths was investigated using molecular dynamics (MD) simulations. Elastic-plasticity at nanoscale was analyzed, and the values of material properties were obtained. Secondly, variability of surface morphology, phase transformation, and coordination number induced by nanoindentation with and without ion implantation was evaluated. Although ion implantation induced damage to the SiC model, the damage after nanoindentation was lower than that without ion implantation. Additionally, nanoindentation experiments were performed for small loads and high loads, respectively. The small load experiments were employed to derive material properties of the ion-implanted SiC. Improvement mechanisms of ion implantation on crack extension, fracture toughness, and elastic recovery rate were investigated under the high-load experiments. The results indicate that the amorphous structure induced by ion implantation can successfully prevent crack propagation and improve fracture toughness. The modification technology of SiC by ion implantation significantly improves the machining efficiency and the non-damage of its surface and subsurface.