Direct Observation and Analysis of Indentation Cracking in Glasses and Ceramics

A review of the observations of indentation-induced fracture suggests that there is no simple generalization which may be made concerning crack initiation sequences. Here, we investigate the material dependence of the initiation sequence of indentation cracks (cone, radial, median, half-penny, and lateral) using an inverted tester allowing simultaneous viewing of the fracture process and measurement of the indeter load and displacement during contact. Two normal glasses, two anomalous glasses, and seven crystalline materials are examined. Key results include (i) direct evidence that the surface traces of cracks observed at indentation contacts are those of radial cracks, rather than median-nucleated half-penny cracks (at least for peak contact loads <40 N) and (ii) that, in crystalline materials, radial cracks form almost immediately on loading of the indenter, in anomalous glasses at somewhat greater loads, but in normal glasses during unloading. A detailed consideration of the stress fields arising during indentation contact predicts material-dependent initiation sequences, in agreement with observations, particularly those of radial crack formation on loading for materials with large modulus-to-hardness ratios. In addition, a new, unexplored crack system is demonstrated, the shallow lateral cracks, which appear to be responsible for material removal at sharp contacts.     

Mechanisms of Failure from Surface Flaws in Mixed-Mode Loading

Mechanisms of failure from surface cracks in combined tension and shear are identified by directly observing the cracks during failure testing. Under the combined influences of residual contact stresses and applied loading, indentation cracks propagate stably and realign normal to the principal applied tension prior to failure. Annealing of indentation flaws causes relaxation of the residual stresses and thereby leads to a change in the mechanics of fracture; unstable propagation occurs from the initial crack at a critical applied loading, with an abrupt change in fracture plane. Strengths of indentation flaws and machining damage in both the as-formed and annealed states are measured as a function of flaw orientation relative to an applied uniaxial tension. Strength variations of indentations and machining flaws are similar. The results are assessed in terms of various proposed mixed-mode fracture criteria, and the implications of the results for nondestructive testing using scattering of surface acoustic waves are discussed.     

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.     

Indentation Crack Length Anisotropy in Silicon Nitride with Aligned Reinforcing Grains

Vickers indentation was performed on surfaces of silicon nitride with an aligned microstructure in order to study the interaction between cracks and the microstructure. Although there was not much evidence of crack bridging, the transverse radial cracks were very short, resulting in high fracture toughness values. The longitudinal radial cracks tended to propagate along the grain boundary of the reinforcements and were much longer than the transverse cracks. As the sintering temperature increased, the lateral cracks on the casting surface led to spalling and consumed more energy for the crack formation, making the longitudinal cracks shorter. On the surface normal to the alignment direction, there was no spalling and the indentation cracks became longer as the sintering temperature increased.     

In Situ Cube-Corner Indentation of Soda–Lime Glass and Fused Silica

Indentation fracture with a cube-corner diamond pyramid on soda–lime silicate glass and fused silica is investigated during the entire indentation cycle in both silicone oil and ambient-air environments. Radial cracks form immediately on loading in all cases. The two-component, elastic-contact + elastic-plastic mismatch (residual) stress field model that has been used successfully to describe radial crack evolution at Vickers indentations fails to describe the fracture response with the cube-corner. The amplitudes of both elastic-contact and residual stress-intensity factors as deduced from these cube-corner experiments are up to a factor of 10 greater than have been previously observed.     

Slow crack propagation in a heavily-filled particle reinforced epoxide resin

The fracture properties of two proprietary composite dental restorative materials and a model composite system were studied to determine the effects of filler concentration, exposure to water, and particle/polymer adhesion on subcritical crack propagation. Particle content ranged from 36 to 60 volume percent. The double torsion (DT) test was used to measure relationships between the stress intensity factor (K₁) and the speed of decelerating cracks or the rate of loading in dry and wet materials in air at laboratory conditions. Materials with weak particle/polymer interfaces fractured by continuous crack growth in both dry and wet conditions. In dry and wet materials with strong interfaces, continuous cracking also occurred at the low end of the range of speeds observed (10⁻⁷ to 10⁻³ m/s), but under test conditions of high crack speeds unstable (stick-slip) crack propagation was found in dry specimens and in wet model composites with 41 percent vol, filler. Water had a corrosive effect lowering K_1c for continuous crack propagation. The exponential dependence of K_1c on crack velocity, representing the viscoelastic response of the materials, was positively correlated to the filler concentration and the plasticizing effect of water. Observations on fracture surfaces indicate that low velocity cracks (<10⁻⁵ m/s) propagate through regions of high stress concentrations (interfaces, corners, pores) while at higher crack velocities failure occurs by a combination of interparticle and transparticle fracture.     

Stability of crack propagation in epoxy resins

The propagation of cracks in epoxy resins has been studied using a linear elastic fracture mechanics approach and a double torsion testing geometry. Under constant crosshead displacement rate conditions cracks are found to propagate in an unstable ‘stick-slip’ manner at high temperatures and with low rates of testing whereas at lower temperatures and using higher rates of loading propagation is more stable and cracks propagate in a continuous manner. The presence of liquid water tends to cause a transition from stable to unstable propagation at room temperature. The influence of specimen geometry upon crack stability is also discussed.     

Crack propagation during Vickers indentation of zirconia ceramics

A quarter finite element model of 3 mol% yttria stabilized tetragonal zirconia polycrystal (3Y-TZP) ceramics undergoing Vickers indentation was established to simulate the evolution of stress and the propagation of cracks inside a sample. The indentation experiment was carried out on the Micro Vickers Hardness Tester. The results of the geometric characteristic parameters, such as the indentation diagonal half-length a, the crack length c and the maximum indent depth h_m, from the indentation simulation and experiment were similar. The types of indentation cracks under various loads were determined according to the Lawn-Evan model, which exactly correspond to the simulation results. In addition, the propagation of indentation cracks was discussed based on the maximum principal stress contour plots at various stages, and the conclusions were verified by the indentation analysis model proposed by Yoffe. As a result, the model developed in this paper can be used in indentation studies to solve the related problem.     

Lateral Cracks and Microstructural Effects in the Indentation Fracture of Yttria

The fracture properties of three polycrystalline Y₂O₃ materials: one fully cubic phase, one containing an Al₂O₃ grain-boundary phase, and one containing hexagonal phase, were examined by indentation over a wide range of contact loads. The two former microstructures displayed tendencies at large indentation loads to radial crack lengths shorter than those extrapolated from the ideal response at low loads. The deviations correlated with the development of lateral cracks at the larger contacts, rather than with any observable change in the interaction between the cracks and the microstructure. After taking the lateral crack influence into account, the toughness of all three materials was estimated to be constant over the range of crack lengths studied, in contrast to the phenomena observed in similar grain size noncubic materials and inferred from earlier fractographic studies. The toughness of the partially hexagonal material was estimated to be 50% greater than the cubic materials. The general phenomenon of partitioning energy into lateral cracks at the expense of radial cracks at large indentation loads has been characterized by a lateral crack development parameter, L_D , which varies from 0 to 1 as lateral cracks progressively develop and remove material.     

Mechanical response and crack propagation of oil well cement under dynamic and static loads

The dynamic mechanical properties and fracture mechanism of three types of oil well cement with different formulations were investigated using a Φ50?mm split Hopkinson pressure bar (SHPB) and quasi-static mechanical tests were conducted with a hydraulic universal testing machine. The stress-strain diagram, time-stress diagram, total energy absorption diagram, and the dynamic growth factor (DIF) under different strain rates were obtained. The crack propagation process of the oil well cement under dynamic loading is evaluated using high-speed photography to determine the fracture mechanism. The test results show that the strength of the cement increases under a dynamic impact. The compressive strength of the pure cement increases from 37?MPa to 184.80?MPa under static loading. However, the peak stress of the cement stone strengthened with cellulose fiber is lower under a dynamic load than a static load. Under dynamic loading, the absorption energy is higher for the pure cement stone than for the cement stone reinforced with whiskers and cellulose. Furthermore, the crack initiation, crack propagation, and fracture characteristics of the oil well cement are different under dynamic and static loads. Under a static load, the rupture of the cement is the result of the propagation of the tensile cracks. Under dynamic loading, there are fewer micro cracks on the cement surface and a composite fracture results from tensile and shear cracks.     

Subsurface Indentation Damage and Mechanical Characterization of α-Sialon Ceramics

Two hot-pressed sintered α-sialon samples of differing microstructures, but identical chemical composition, were evaluated first, in terms of indentation hardness and modulus, by depth-sensing indentation (DSI) tests on planes parallel and normal to the hot-pressed surface. The surface and subsurface cracks created under the DSI tests have also been investigated in relation to the effect of microstructure. Subsequently, Vickers indentation tests were conducted to explore the deformation and fracture characteristics in the two samples. The effect of microstructure and grain orientation on the development of different types of cracks, in particular subsurface cracks, was revealed and analyzed. Additionally, it suggested that the focused ion beam (FIB) miller is a preferred tool, in comparison to the conventional cross-sectioning techniques, for examining subsurface crack formation and structural characteristics.     

Methodology for measuring fracture toughness of ceramic materials by instrumented indentation test with vickers indenter

Virtual crack closure technique and elastoplastic finite element method were employed to calculate the stress intensity factors (SIF) of ceramic materials on the tip of both half‐penny crack (HPC) and radial crack (RC) induced by Vickers indenter and the value of fracture toughness (K_IC) was extracted by the design of equi‐SIF contour of HPC and RC crack front. Through dimensional theorem and regressive analysis, a functional relationship between instrumented indentation parameters, crack length of Vickers impression and fracture toughness of ceramic materials was established, thus a novel methodology has been presented for measuring fracture toughness of ceramic materials by instrumented Vickers indentation. Both numerical analysis and experiments have indicated that this methodology enjoys higher measurement precision compared with other available indentation methods. The methodology is universally suitable for HPC, RC as well as transition cracks and capable of determining fracture toughness and elastic modulus in a single indentation test. In addition, it saves the effort of measuring the diagonal length of Vickers impression in case that the impression remains unclear.     

Kinetics of Indentation Cracking in Glass

The propagation of indentation radial cracks in soda—lime silicate glass is measured as a function of time after indentation. Rapid lift-off of the indenter from the specimen surface causes a step-function perturbation in the radial crack mechanical energy release rate, thus providing access to a large range of observable crack velocities in the indentation stress field. Analysis of the data shows distinct threshold, reaction-limited, and transport-limited behavior in the crack velocity responses, in agreement with measurements made using macroscopic crack geometries. Atomistic models of fracture kinetics in reactive environments are fit to the data and are deconvoluted to yield the underlying atomic-scale, bond-rupture parameters. These latter are used to calculate potential functions for activated fracture and predict crack velocity responses as a function of temperature and pressure.     

Crack Tip Morphology of Slowly Growing Cracks in Glass

We present atomic force microscopy (AFM) observations of crack tips in glass during subcritical propagation. These have been obtained by means of an AFM sample holder which has been specially designed to propagate indentation cracks in glass plates. Crack tips in soda–lime–silica glass are always preceded by a few nanometers deep deformation. In vitreous silica, no other surface deformation than the crack itself could be detected. For both materials, the crack opening is found to largely exceed the elastic solution.     

Mixed Mode I—Mode III Fracture in Ceramic Single Crystals

A recently reported method has been used to propagate stable mixed mode I-mode III cracks in thin slices of single-crystal α-quartz (low quartz, SiO₂) and single-crystal rutile (TiO₂). A bond-counting technique has been developed and used to isolate planes of weakness in the crystalline structures of both crystals. Good correlation has been obtained with observed crack planes. Mode III component (K_III) versus crack velocity (v) relations for specified mode I contributions have thus been determined for m {10 1 0} fracture in basal (0001) slabs and for {a+c} fracture in m {10 1 0} slabs of α-quartz and also for (110) fracture in basal (001) and (101) fracture in (010) slabs of rutile.     

New method for extracting fracture toughness of ceramic materials by instrumented indentation test with Berkovich indenter

Applying finite element analysis, a method is proposed for evaluating fracture toughness of ceramic materials by instrumented indentation with Berkovich indenter. The crack-tip K_I (Stress intensity factor) of Berkovich-produced crack is numerically calculated by using virtual crack closure technique, in particular, three kinds of crack pattern, i.e., radial crack, transition crack and half-penny crack are identified and their crack fronts meet the equi-K_I requirement. The validity of the proposed method is verified by instrumented indentation tests on standard SRM2100 (Si₃N₄) and CRM156 (Fused Silica) samples. Comparison with six representative conventional indentation methods indicates that the proposed method has advantages including wide application range, high accuracy and applicability to different crack patterns. Additionally, it’s revealed that the conventional indentation fracture toughness formulae derived from Lawn-Evans-Marshall formula tend to exhibit larger test error when applied to materials of relatively high indentation work ratio W_e/W_t.     

Improving energy dissipation and damage resistance of CFRP laminates using alumina nanoparticles

ABSTRACT

In this paper, the effect of a toughened epoxy matrix on the damage evolution, energy dissipation, and permanent indentation of composite laminates under out-of-plane (transverse) loading is presented experimentally. The epoxy matrix was toughened by 3% alumina nanoparticles with sizes less than 200?nm. A quasi-static indentation test was exploited to characterise the damage modes and evaluate the dissipation of energy of the composite laminate. The dissipated energy was evaluated as the enclosed area between the loading and unloading curves, while the damage resistance was expressed as the number of delaminations and their size. The results showed that epoxy toughened by alumina nanoparticles, showed an improvement in the damage threshold load by 27.3% and higher ultimate load under indentation. Regarding the damage resistance, the toughened laminates showed lower number of delaminated interfaces and lower projected delamination area than untoughened laminates. This is due to the localised damage under the indenter, the matrix cracks at low indentation energy and fibre breakages occur at high indentation energy.     

Impact attrition of sodium chloride crystals

Impact attrition of cubic NaCl particles has been studied. The particles are produced by cleaving melt-grown ingots to about 1 mm in size, and standardised by chemical polishing and annealing. They are accelerated in an air eductor, and are impacted onto a target in the velocity range 15 – 30 ms⁻¹. The low velocity impact causes extensive plastic deformation on the impacting corner and removal of thin platelets from the faces adjacent to it. The process may be treated as indentation fracture: the ensuing 〈110〉 cracks resemble closely those produced by quasi-static indentation fracture and can be interpreted in the same way. Formation of platelets is attributed to sub-surface lateral cracks, which follow a pattern similar to impact damage of large targets.     

Peak stress intensity dictates fatigue crack propagation in UHMWPE

The majority of total joint replacements employs ultra-high molecular weight polyethylene (UHMWPE) for one of the bearing components. These bearings may fail due to the stresses generated in the joint during use, and fatigue failure of the device may occur due to extended or repeated loading of the implant. One method of analysis for fatigue failure is the application of fracture mechanics to predict the growth of cracks in the component. Traditional analyses use the linear elastic stress intensity factor K to describe the stresses near a loaded crack. For many materials, such as metals, it is the range of stress intensity, ΔK, that determines the rate of crack propagation for fatigue analysis. This work shows that crack propagation in UHMWPE correlates to the maximum stress intensity, K_max, experienced during cyclic loading. This K_max dependence is expected due to the viscoelastic nature of the material and the absence of crazing or other cyclic load dependent crack tip phenomena. Such a dependence on a non-cyclic component of the stress allows cracks to propagate under load with little or no fluctuating stresses. Consequently, traditional fatigue analyses, which depend on the range of the stress to predict failure, are not always accurate for this material. For example, significant static stresses that develop near stress concentrations in the component locking mechanisms of orthopedic implants make such locations likely candidates for premature failure due the inherent underestimate of crack growth obtained from conventional fatigue analyses.