Fracture mechanics of sharp scratch strength of polycrystalline alumina

The strength of a polycrystalline alumina containing controlled scratches introduced by translated sharp contacts is investigated and described by a multiscale fracture mechanics model. Inert strength measurements of samples containing quasi‐static and translated Vickers indentation contacts showed that scratches degraded the strength at normal contact loads an order of magnitude less than those for quasi‐static indentation. The fracture mechanics model developed to describe strength degradation by scratches over the full range of contact loads included toughening effects by crack‐wake bridging at the microscale and lateral crack‐based residual stress relaxation effects at the mesoscale. A critical element of the model is the nonlinear scaling of the residual stress field of a scratch with the normal contact load acting during scratch formation. The similarities and differences in the scratch model in comparison with prior indentation‐strength fracture mechanics models are highlighted by parallel development of both. Central to the scratch model is the use of easily controlled normal contact load as the scratch‐strength measurement variable. Scratch length and orientation are shown to have significant effects on strength. The distributions of scratch widths controlling the intrinsic strengths of as‐received samples are determined and agreement with the observed scratch dimensions is demonstrated.     

Measurement of nanoindentation properties of polymers considering adhesion effects between AFM sharp indenter and material

Abstract

Nanomechanical properties of polymer samples were calculated using an adhesive contact model appropriate for AFM indentation problems. A series of Polydimethylsiloxane (PDMS) samples were indented by the sharp indenter in the air by using an AFM, and dozens of the force–displacement curves of each sample were obtained. An adhesive contact model suitable for sharp indentation with adhesion was established based on the same assumptions of the JKR model which is only suitable for spherical indentation at small penetration depth. Differences between sharp indentation problems with and without adhesion were discussed, and the limitations of the traditional adhesion model were given. The elastic modulus was obtained by fitting experimental force–displacement curves with theoretical ones, and results were compared to those macroscopic values in literature. The adhesion energy between the indenter and the sample surface was accurately calculated using the adhesion model based on the calculated elastic modulus. The influence of the indenter tip angle on the calculation results of the elastic modulus was also discussed theoretically. In this study, the mechanical properties of polymer samples were calculated at the nanoscale considering the adhesion effect.     

Nanoindentation behavior of ultrathin polymeric films

Measurement of the mechanical properties of nanoscale polymeric films is important for the fabrication and design of nanoscale layered materials. Nanoindentation was used to study the viscoelastic deformation of low modulus, ultrathin polymeric films with thicknesses of 47, 125 and 3000 nm on a high modulus substrate. The nominal reduced contact modulus increases with the indentation load and penetration depth due to the effect of substrate, which is quantitatively in agreement with an elastic contact model. The flow of the nanoscale films subjected to constant indentation loads is shear-thinning and can be described by a linear relation between the indentation depth and time with the stress exponent of 1/2.     

Experimental Measurement of Residual Stress Field around Sharp Indentation in Glass

A new technique is developed to measure the residual stress field around Vickers indentations in glass and ceramics. This technique uses a small indentation as a microprobe to measure the residual stress at a specific position near a large indentation. The approach is based on the observation that the crack lengths of the small indentation are changed under the influence of the residual stress field created by the large indentation. A simple fracture mechanics model is derived to calculate the residual stress from the measurement of the changes of the crack lengths of the small indentation. The results show that the residual stress around Vickers indentations is a nonequal biaxial field; both tensile and compressive stresses exist around a sharp indentation and decrease as the distance from the center of indentation increases. This technique can be easily extended to many other cases of residual stress in ceramics and composites.     

ADHESION FORCES OF SPHERICAL ALUMINA PARTICLES ON CERAMIC SUBSTRATES

Adhesion forces of spherical alumina particles on ceramic substrates were studied. Results of direct force measurements using an atomic force microscope (AFM) were compared with theoretical results of a new rod model and with molecular dynamic computer simulation. Spherical alumina particles were produced by a flame process. The particles were glued to cantilevers, and interaction forces were measured by the AFM. A significant reduction of adhesion forces due to adsorbed layers was observed. The interaction volumes were determined by AFM scanning using a soft cantilever. The measured interaction forces were compared with calculated forces using the Hamaker concept including an adsorbed surface layer and the determined interaction volume (rod model). It turned out that calculated adhesion forces, neglecting deformation, are smaller than measured ones. This problem can be overcome if deformation according to Hertz is included in the rod model. Even for such a hard material as alumina, deformation occurs in the contact zone, which was also observed in a molecular dynamic computer simulation.     

Determination of young's modulus of elastomers by use of a thermomechanical analyzer

This work used a conventional thermomechanical analyzer (TMA) to measure the depth of indentation at room temperature of elastomers and Finkin's equation to calculate Young's moduli of elastomers, which have been measured by Drutowski, from the radius of contact of an indentor on thin sheets of sample. Data obtained from the TMA are compared with those measured by radius of contact and Hertz contact theory and are found in good agreement. Measurements of Young's modulus as a function of temperature at different heating rates by TMA were made for an acrylic elastomer. The results are compared with theory and the deviations from theory are discussed.     

The Compelling Case for Indentation as a Functional Exploratory and Characterization Tool

The utility of indentation testing for characterizing a wide range of mechanical properties of brittle materials is highlighted in light of recent articles questioning its validity, specifically in relation to the measurement of toughness. Contrary to assertion by some critics, indentation fracture theory is fundamentally founded in Griffith–Irwin fracture mechanics, based on model crack systems evolving within inhomogeneous but well‐documented elastic and elastic–plastic contact stress fields. Notwithstanding some numerical uncertainty in associated stress intensity factor relations, the technique remains an unrivalled quick, convenient and economical means for comparative, site‐specific toughness evaluation. Most importantly, indentation patterns are unique fingerprints of mechanical behavior and thereby afford a powerful functional tool for exploring the richness of material diversity. At the same time, it is cautioned that unconditional usage without due attention to the conformation of the indentation patterns can lead to overstated toughness values. Limitations of an alternative, more engineering approach to fracture evaluation, that of propagating a precrack through a “standard” machined specimen, are also outlined. Misconceptions in the critical literature concerning the fundamental nature of crack equilibrium and stability within contact and other inhomogeneous stress fields are discussed.     

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。     

PARTICLE ADHESION AT THE NANOSCALE

This article attempts to connect macroscopic observations of particle adhesion with the known interatomic forces which bind particulate interfaces together by studying contact between a plane surface and a sphere of smaller and smaller diameter. The fracture of a contact between a plane and a macroscopic sphere depends on the nonuniform stress distribution across the contact spot, causing atomic attraction at the edges of the contact region. Interface atoms some distance inside the contact region do not contribute to the adhesion. In fact, these inner atoms are in compression and are pushing the particles apart rather than causing adhesion. When a smaller sphere adheres to a plane at the nanoscale, this nonuniform stress distribution cannot be possible and the stress across the contact must be more even. To prove this hypothesis, molecular dynamics (MD) simulations have been carried out to study the fracture behaviour of subnano sodium chloride crystals. The MD models show clean fracture across the contact junction, in agreement with the macroscopic fracture studies. The models included explicit interatomic potentials to calculate the adhesion forces and contact stress distributions during particle pulloff as sodium chloride particles were altered in size. The results show that there is stress concentration at the contact edge for the smallest particles with 16 atoms (4?×?4) in contact.     

PARTICLE ADHESION AT THE NANOSCALE

This article attempts to connect macroscopic observations of particle adhesion with the known interatomic forces which bind particulate interfaces together by studying contact between a plane surface and a sphere of smaller and smaller diameter. The fracture of a contact between a plane and a macroscopic sphere depends on the nonuniform stress distribution across the contact spot, causing atomic attraction at the edges of the contact region. Interface atoms some distance inside the contact region do not contribute to the adhesion. In fact, these inner atoms are in compression and are pushing the particles apart rather than causing adhesion. When a smaller sphere adheres to a plane at the nanoscale, this nonuniform stress distribution cannot be possible and the stress across the contact must be more even. To prove this hypothesis, molecular dynamics (MD) simulations have been carried out to study the fracture behaviour of subnano sodium chloride crystals. The MD models show clean fracture across the contact junction, in agreement with the macroscopic fracture studies. The models included explicit interatomic potentials to calculate the adhesion forces and contact stress distributions during particle pulloff as sodium chloride particles were altered in size. The results show that there is stress concentration at the contact edge for the smallest particles with 16 atoms (4 × 4) in contact.     

Hertzian Indentation Stress Field Equations

Indentation with hard spherical indenters (so called Hertzian indentation) is a well‐known technique to probe the mechanical properties of ceramics and other brittle materials. Using contact mechanics, it is possible to calculate the stress distribution in the sample and use it to express maximum tensile or compressive stresses as a function of load and contact radius. The equations describing the full stress distribution are not usually mentioned in the literature, and surprisingly most of the classical references disclosing them are either mistaken or incomplete. We recovered the full and detailed equations for the stress field distribution and numerically implemented them using the computer language Python. We point out the relationships between the different expressions that have been published, check the consistency with existing results, and discuss the sources of confusion.     

Extension of continuum mechanics to the nanoscale

This is an extension of continuum mechanics to the nanoscale (not the molecular scale). In the context of continuum mechanics, nanoscale problems always involve the immediate neighborhood of a phase interface or the immediate neighborhood of a three-phase line of contact or common line. While the presentation is new, it is based upon a long history of important developments beginning with that of Hamaker (Physica 4 (1937) 1058).We test this theory by using it to predict both the surface tensions of the n-alkanes and the static contact angles for the n-alkanes on PTFE and for several liquids on polydimethylsiloxane. In the case of surface tension and like the best previous theory, one adjustable parameter is required. For the contact angle predictions, no adjustable parameters are used. In both cases, the results are compared with previously published experimental data.The results for the contact angle analysis also provide a successful test of a previously derived form of Young's equation for the true, rather than apparent, common line.     

Mechanics of the indentation test and its use to assess the adhesion of polymeric coatings

The indentation test provides a simple means by which the adhesion of coatings can be qualitatively assessed. On the way to establishing a quantitative measurement of the adhesion strength of coatings and films, it is important that the mechanics of this test are clearly understood. To investigate the influence of factors such as the coating thickness, the indenter radius, and friction during the test, numerical simulations of the indentation of a typical polymeric coating, polymethylmethacrylate (PMMA), bonded to a rigid substrate were conducted by using the finite element method. The stress generated during the indentation test were obtained by employing an accurate constitutive model of the elastic-viscoplastic behaviour of the polymeric coating under consideration. The results of this analysis illustrate the effects of the factors mentioned above on the deformation of the coating during indentation, its confinement, and interfacial shear, and the normal, shear, and hoop stress distributions occurring during indentation. These results provide insight into the possible failure mechanisms operative during the indentation of thin coatings and the important effects of the coating thickness during such tests.     

Adhesion Map of Spheres: Effects of Curved Contact Interface and Surface Interaction Outside Contact Region

In this work three dimensionless parameters are introduced in the debate concerning hard contact models. These parameters are related to the overall adhesive contact area, curved surface contribution and surface interaction forces outside the contact region. With the variations of these three parameters, the relations and transitions between the different hard contact models such as Hertz, Bradley, Johnson–Kendall–Roberts (JKR), Derjaguin–Muller–Toporov (DMT) and Maugis–Dugdale (MD) models are presented in a systematic way. The combination of the three parameters provides a new hybrid model. The influence of these three parameters on the contact between spheres has been studied. By analyzing the pressure profiles of contact region, two new instability jumps are proposed. The instability jumps together with the three parameters are used to explain some recent experimental and numerical observations which deviate more or less from those predicated by the classical hard contact models.     

A phase field model of pressure-assisted sintering

The incorporation of an efficient contact mechanics algorithm into a phase field sintering model is presented. Contact stresses on the surface of arbitrarily shaped interacting bodies are evaluated and built into the model as an elastic strain energy field. Energy relaxation through deformation is achieved by diffusive fluxes along stress gradients and rigid body motion of the deforming particles maintain contact between the particles. The proposed model is suitable for diffusion deformation mechanisms occurring at stresses below the yield strength of a defect-free material; this includes Nabarro-Herring creep, Coble creep and pressure-solution. The effect of applied pressure on the high pressure-high temperature (HPHT) liquid phase sintering of diamond particles was investigated. Changes in neck size, particle coordination and contact flattening were observed. Densification rates due to the externally applied loads were found to be in good agreement with a new theory which implicitly incorporates the effect of applied external pressure.     

Effect of Indenter Geometry on Controlled-Surface-Flaw Fracture Toughness

Fracture toughness values obtained using both Knoop and Vickers-indentation-produced controlled surface flaws were compared as a function of indentation load for a well-characterized glass-ceramic material. At the same indentation load, Knoop cracks were larger than Vickers. As-indented K_c values calculated from fracture mechanics expressions for surface flaws were higher for Knoop flaws than Vickers, but both types gave low K_c values due to indentation residual stress effects. Analysis suggested that theoretical formalisms for indentation residual stress effects based on fracture mechanics solutions for a center-loaded penny crack in an infinite medium should apply to both indentation types. K_c values calculated using the residual stress approach were identical for Knoop and Vickers controlled surface flaws when a "calibration" value for a constant term in the expression for K_c was used for both indentation types.     

A quantitative analysis of the indentation fracture of fused silica

It is unclear how the densification of fused silica influences the damage of its precision optics subjected to machining. This paper presents a quantitative analysis of the indentation fracture of fused silica involving densification with the embedded center of dilation (ECD) model. The Hertzian stress field and the ECD-induced stress field were superposed to provide the overall stress distribution in the loading stage. A new method was established to accurately determine the strength of the ECD-induced stress field with densification effects. With the aid of the ECD model, the starting locations, initiation stages and initiation sequence of crack morphologies were predicted by analyzing the stress fields. To quantitatively study the initiation of conical cracks in fused silica, the strain energy release rate was calculated by linear elastic fracture mechanics (LEFM). The predicted minimum threshold load leading to conical cracking was consistent with the measured values.     

A Critical Evaluation of Indentation Techniques for Measuring Fracture Toughness: I, Direct Crack Measurements

The application of indentation techniques to the evaluation of fracture toughness is examined critically, in two parts. In this first part, attention is focused on an approach which involves direct measurement of Vickers-produced radial cracks as a function of indentation load. A theoretical basis for the method is first established, in terms of elastic/plastic indentation fracture mechanics. It is thereby asserted that the key to the radial crack response lies in the residual component of the contact field. This residual term has important implications concerning the crack evolution, including the possibility of post indentation slow growth under environment-sensitive conditions. Fractographic observations of cracks in selected "reference" materials are used to determine the magnitude of this effect and to investigate other potential complications associated with departures from ideal indentation fracture behavior. The data from these observations provide a convenient calibration of the Indentation toughness equations for general application to other well-behaved ceramics. The technique is uniquely simple in procedure and economic in its use of material.