Evaluation by indentation of fracture toughness of ceramic materials

A transition fracture mode from Palmqvist to median has been observed in a number of ceramic materials. A new expression to determine the fracture toughness (K _IC) by indentation is presented. The K _IC values calculated by this formula are independent of the crack profile (median or Palmqvist) and of the applied load. This formula has been obtained by modifying the universal curve of Evans and Charles to incorporate Palmqvist and median cracks over a wide range of loads in the case of brittle materials with different mechanical properties (elastic properties: E, v, K _IC).     

Permeability of cracked concrete

The goal of the research presented here was to study the relationship between cracking and water permeability. A feedback-controlled test was used to generate width-controlled cracks. Water permeability was evaluated by a low-pressure water permeability test. The factors chosen for the experimental design were material type (paste, mortar, normal and high strength concrete), thickness of the sample and average width of the induced cracks (ranging from 50 to 350 micrometers). The water permeability test results indicated that the relationships between permeability and material type differ for uncracked and cracked material, and that there was little thickness effect. Permeability of uncracked material decreased from paste, mortar, normal strength concrete (NSC) to high strength concrete (HSC). Water permeability of cracked material significantly increased with increasing crack width. For cracks above 100 microns, NSC showed the highest permeability coefficient, where as mortar showed the lowest one.     

New developments for fracture toughness determination by Vickers indentation

Abstract

Indentation is a traditional method used to determine the toughness of brittle materials. Different models are used for the calculation depending on the shape of the cracks that are initiated and developed as a result of the indentation. Recently it was observed that a transition between Palmqvist and median cracks is possible when increasing the indentation load. In the present study it is shown that this transition is not as sharp as is generally supposed, but is rather smooth. In these conditions standard calculation procedures cannot be applied. A new methodology is proposed here, which allows the calculation of a unique toughness value on the basis of the determination of the limits of the material cracking tendency.     

Effect of substrate roughness on the contact damage of thin brittle films on brittle substrates

The effect of substrate and surface roughness on the contact fracture of diamond-like carbon coatings on brittle soda-lime glass substrates has been investigated. The average surface roughness (R_a) of the examined samples ranged from 15 nm to 571 nm. Contact damage was simulated by means of spherical nanoindentation, and fracture was subsequently assessed by focused ion beam microscopy. It was found that, in the absence of sub-surface damage in the substrate, fracture occurs in the coating in the form of radial, and ring/cone cracks during loading, and lateral cracks during unloading. Increasing the surface roughness results in a decrease in the critical load for crack initiation during loading, and in the suppression of fracture modes during unloading from high loads. When sub-surface damage (lateral cracks) is present in the substrate, severe spalling takes place during loading, causing a large discontinuity in the load-displacement curve. The results have implications concerning the design of damage-tolerant coated systems consisting of a brittle film on a brittle substrate.     

Slow growth of microcracks in hydroxyapatite during aging

Hydroxyapatite (Ca₁₀(PO₄)₆(OH)₂ or HA) is a brittle material that is subject to environmentally assisted slow crack growth. While most slow crack growth studies are carried out after aging, this study examines the slow growth of radial cracks induced by Vickers indentation in dense HA (94 % of theoretical density) during aging in ambient air, where the observed crack growth is consistent with a process in which residual stress drives crack growth. For indentation loads of 0.98, 1.96, 2.94, and 4.91 N, the average radial crack length increased exponentially with time for indentation loads of 0.98, 1.96, 2.94, and 4.91 N, with crack lengths saturating within 1 h following indentation. However, no radial crack growth was observed for 9.81 N loads. The load dependence of radial crack growth is proposed to be linked to the partitioning of residual strain energy by the lateral crack growth, which has not been reported in the literature.     

Indentation fracture of WC-Co cermets

Indentation fracture of a series of well-characterized WC-Co cermets was studied with a Vickers diamond pyramid indenter. The resulting crack length-indentation load data were analysed in terms of relations characteristic of radial (Palmqvist) and fully developed radial/median (half-penny) crack geometries. The radial crack model gave a better fit to the data on all the alloys studied. Crack shapes determined by repeated surface polishing confirmed the radial nature of the cracks. An indentation fracture mechanics analysis based on the assumption of a wedge-loaded crack is shown to be consistent with the observed linear relation between the radial crack length and the indentation load. The analysis also predicts a simple relation among the fracture toughness (K _lc), the Palmqvist toughness (W) and the hardness (H) of the WC-Co alloys.     

Kinetics of shear-activated indentation crack initiation in soda-lime glass

The initiation of radial cracks in Vickers indentation of soda-lime glass is found to be strongly rate dependent. For long contact durations the radial cracks pop in during the indentation event, at a reproducible stage of the unloading half-cycle; for short contacts the pop-in occurs after the event, with considerable scatter in delay time. The phenomenon is interpreted in terms of an incubation time to develop a critical nucleus for the ensuing fracture. Increasing either the water content of the environment or the peak contact load diminishes the incubation time. Scanning electron microscopy of the indentation patterns indicates that the sources of the crack nuclei are constrained shear faults within the deformation zone. A qualitative model is developed in terms of a two-step process, precursor faulting followed by crack growth to pop-in instability. Moisture may influence both these steps, in the first by interfacial decohesion and in the second by slow crack growth. No definitive conclusion is reached as to which of the steps is ratecontrolling, although it appears that it is the shear across the fault and not the tension across the crack which is vital in driving the initiation. The implications of these results in connection with the basic mechanical properties of brittle solids, particularly strength, are considered.     

Endurance of brittle solids under cyclic loads with local overheating

This article describes a method of calculating the endurance of brittle solids under cyclic loads with local over-heating of the material at the crack tips when no spontaneous heating of the material takes place during fracture. The method is applicable when the number of cycles to fracture is sufficiently large and when the loading frequency is relatively high so that other manifestations of the relaxation phenomena may be neglected. The method was used to carry out an approximate calculation of the endurance of polymethylmethacrylate under loading conditions corresponding to experimental data.     

Strength of poly(methyl methacrylate) with indentation flaws

Controlled flaws were introduced into poly(methyl methacrylate) samples in the presence of liquid acetone using a Vickers indenter over a range of indentation loads from 100 to 1400 N. Due to the large plastic zone underneath the indenter, the radial crack formed by indentation consisted of two halves, known as Palmqvist cracks, instead of a single semicircular crack. The strengths of the samples were measured in air either immediately following indentation or after a stress-relief anneal. The strength of the as-indented samples was about 6% less than that of the annealed samples; however, the dependence of strength on indentation load was similar for both sets of samples. These results were interpreted in terms of an indentation fracture mechanics model. The analysis is consistent with poly(methyl methacrylate) having a rising fracture toughness with increasing crack size.     

Sliding microindentation fracture of brittle materials: Role of elastic stress fields

An analytical model of the stress field caused by sliding microindentation of brittle materials is developed. The complete stress field is treated as the superposition of applied normal and tangential forces with a sliding blister approximation of the localized inelastic deformation occurring just underneath the indenter. It is shown that lateral cracking is produced by the sliding blister stress field and that median cracking is caused by the applied contact forces. The model is combined with measurements of the material displacement around an indentation to show that the relative magnitude of tensile stresses governing lateral crack and median crack growth varies with the magnitude of the applied load. The model also predicts a range of loads at which the lateral crack will grow only after the indenter is removed from the surface. These predictions are consistent with observations of the different regimes of cracking observed under a sliding pyramidal indenter in soda–lime glass and other brittle solids.     

Evolution of subsurface radial cracks in bi-material structures undergoing indentation loading

Mathematical modelling is used to study the evolution of damage caused by indentation loading on curved bilayers consisting of brittle shells filled with polymer support material. Such loads are pertinent to all-ceramic crown structures on tooth dentin in occlusal function. The aim is to develop tools to assist in the design of such structures to ensure both high damage resistance and high damage tolerance. Specifically, the initiation and propagation of a radial crack emanating from the interface is studied using the boundary element method (BEM) in three dimensions. The system that is analysed consists of a spherical indenter and both flat and convex bi-material samples. A semi-circular intrinsic flaw/crack is assumed to lie on the axis of indentation at the interface of the two materials, in the coating. Upon application of an indentation load, the mode I stress intensity factor distribution along the crack front is determined and the crack front is propagated using a small increment. By repeating this process, the critical load for propagation of the crack is obtained as a function of crack size. The results compare well with experimental crack propagation studies in bi-materials, as well as observed damage in porcelain crowns that have been used to repair teeth. The convex models show that radial cracks can exist in the brittle coating, without leading to catastrophic failure, up to a critical crack length. An increase in the applied load, causing the crack to grow beyond this length, causes the coating to fail in an unstable way. The results show that there is an optimum combination of design parameters for maximising the damage resistance. It is shown that larger convex radii of curvature lead to higher damage tolerance.     

Mode I stress intensity factor estimate for a half-penny shaped crack in a trilayer structure by reduction to a bilayer model

The stress intensity factor (SIF) of a half-penny shaped crack normal to the interface in the top layer of a three-layer bonded structure is obtained by the finite element method for a wide range of parameters. To obtain a simple estimate of the SIF, the method of reduction of an idealized cracked trilayer domain to that of a corresponding bilayer domain has been introduced based on the notion of an equivalent homogeneous material substitution for the two bottom layers. The results obtained are utilized in estimating the SIF of a small crack at the interface in a trilayer structure subjected to an indentation load based on the stress calculations in a corresponding uncracked structure. The simplification method may be useful in predicting brittle failure initiating from interfacial flaws in layered structural components with complex geometries that would normally require extensive computational modeling.     

Electron microscopy of microcracking about indentations in aluminium oxide and silicon carbide

Transmission electron microscopy is used to examine the nature of microcracking about small-scale indentations in two highly brittle solids, sapphire and carborundum. The observed crack geometry is discussed in terms of an earlier model of indentation fracture beneath a point force, in which both loading and unloading half-cycles contribute to the crack growth. The residual interfaces are generally found to exhibit moiré fringe contrast, and occasionally to contain dislocation networks. These observations are discussed in relation to spontaneous closure and healing mechanisms, and the associated “lattice mismatch” is estimated at about one part in a thousand. It is suggested that cleavage steps comprise the main source of obstruction to lattice restoration across the interfaces. Mechanical and thermal treatments of the indented specimens are found to influence the extent of the residual cracking. Some practical implications concerning the strength degradation of brittle solids are discussed.     

Equilibrium penny-like cracks in indentation fracture

A study is made of the mechanics of two basic types of indentation fracture, cone cracks (“blunt” indenters) and median cracks (“sharp” indenters). The common feature which forms the central theme in this work is that both crack types, in their well-developed stages of growth, may be regarded as essentially “penny-like”. On this basis a universal similarity relation is derived for equilibrium crack dimension as a function of indentation load. Experimental measurements confirm the general form of this relation. A more detailed fracture mechanics analysis is then given, to account for additional, contact variables evident in the data. Notwithstanding certain analytical limitations, the study serves as a useful basis for investigating a wide range of contact-related problems, both fundamental and applied, in brittle solids.     

Cone cracks around Vickers indentations in fused silica glass

Surface and subsurface deformation and cracking around Vickers identations in fused silica have been studied. The indentations were sectioned by making the Vickers indents on and near the tip of a pre-existing crack. The characteristic median and lateral cracks around the impression and shallow cracks within the surface of the indentation were observed on the specimen surface. The subsurface deformation showed compacted or densified zones, devoid of any flow line rosettes. The dominant cracks, similar to the Hertzian cone cracks observed around purely elastic spherical indentations, occurred outside the compacted zones. These cone cracks make angles of 30 to 40° with the specimen surface. Multiple cone cracks with shallower angles often formed outside the major cone cracks. It has been suggested that the expansion of the boundary of the compacted zone as the indenter load is increased can cause median cracks during loading while the mismatch of strain at this boundary may give rise to lateral cracks during unloading.     

A technique for studying interacting cracks of complex geometry in 2D

A method for studying brittle fracture in an infinite plate containing interacting cracks of complex shape under general loading conditions is developed and studied for accuracy and potential applications. This technique is based on superposition and dislocation theory and can be used to determine the full stress and displacement fields in a cracked body. In addition, stress intensity factors at both crack tips and wedges, created by crack kinking and branching, are calculated so that crack growth and initiation can be analyzed at these locations of possible crack propagation. Such information can then be used to study damage accumulation in structures containing a large number of interacting cracks.     

Approximate weight function method for elliptical arc through cracks in mechanical joints

Mechanical joints such as bolted, riveted or pinned joints are widely used to join the constituent parts of structural components. Reliable stress intensity factor analysis of arbitrary cracks in mechanical joints is required for the safety evaluation or fracture mechanics design. It has been reported that cracks in mechanical joints usually nucleate as the corner crack and grow as the elliptical arc through crack. The weight function method is a useful technique to calculate the stress intensity factor using the appropriate weight function for a cracked body and the stress field of an uncracked body. In this paper, the weight function method for the two surface points of elliptical arc through cracks in mechanical joints is developed to analyze the mixed-mode stress intensity factors. Unknown coefficients included in the weight function are determined using the reference stress intensity factors obtained from finite element analysis.     

Single particle impact damage of fused silica

Single-impact damage of fused silica by spherical and conical tungsten carbide (WC) projectiles of velocities up to 200 m sec⁻¹ has been investigated with a high-speed framing camera photographing at a rate of up to 1.7×10⁶ frames per second. For spherical particles the Hertzian cone cracks, which for higher impact velocities are accompanied by median and radial cracks, form during the loading part of the impact; some growth of all these cracks also occurs during unloading. With the conical particles the Hertzian cone cracks do not form; only radial and median cracks form during the loading; in this case both radial and median cracks grow during the unloading. In both cases “lateral” cracks form during unloading. From these experiments values of the static equivalent of the dynamic stress-intensity factor for high-velocity cracks are also obtained; these are found to be considerably lower than those obtained from quasi-static indentation experiments. Finally, the extent of the damage produced by a single impact has been discussed.     

维氏压痕对常压固相烧结碳化硅陶瓷材料力学性能的影响

为了研究维氏压痕裂纹对常压固相烧结碳化硅陶瓷(SSiC)材料力学性能的影响, 通过扫描电镜观察了0.1~100 N的压痕载荷下产生的表面裂纹及裂纹剖面的状况, 并测试了相应载荷下的力学性质, 探讨了压痕法测量SSiC材料硬度、韧性等力学性质的适当压力载荷. 结果表明, SSiC材料压痕裂纹起始的临界压力载荷介于0.1~0.2 N; 当压痕载荷小于0.5 N时, 裂纹尺寸小于5 μm, SSiC材料的平均弯曲强度受影响程度较小. 此外, 当压痕载荷为10 N以上时, 压痕法测得的维氏硬度值趋近定值, 且所得到的裂纹是半圆形裂纹, 因此, 10 N为采用压痕法准确测量SSiC材料硬度及韧性的最低压痕载荷值.