Tunneling radial cracks in layered structures from contact loading

Glass/epoxy laminates glued onto a compliant substrate are indented with a hard ball. The damage is characterized by a set of transverse cracks which pop out from the subsurface of the glass layers due to flexure and propagate stably in the radial direction with load in a bell-shape front under a diminishing stress field. Compliant interlayers, even extremely thin ones, are effective in inhibiting crossover fracture. This leads to crack tunneling and crack multiplication in the hard layers, which enhances energy dissipation and reduces the spread of damage relative to the basic bilayer configuration. The experiments show that the fracture in a given layer is well approximated by a power-law relation of the form c^3/2K_C/P = δ, where P, c, and K_C are the indentation load, crack length and fracture toughness, in that order, and δ an implicit function of the layer position and material and geometric variables, derived with the aid of available tunnel crack solutions.The model specimen studied provides a useful insight into the fracture behavior of natural, biological and synthetic layered structures from concentrated loading. The analysis shows that the crack arrest capability of a thin interlayer increases in proportion to the modulus misfit ratio between the layer and interlayer, and that the spread of radial cracks in a laminate of given thickness reduces in proportion to n^1/3, where n is the number layers in the laminate.     

Multi-crack analysis of hydraulically pumped cone fracture in brittle solids under cyclic spherical contact

The evolution of surface damage in bilayers due to cyclic spherical indentation in the presence of incompressible lubricant is studied using an all-transparent glass/polycarbonate system as a model for more practical applications such as dental crowns and rolling contact fatigue. In situ observations and post-mortem material sectioning reveal that inner cone cracks evolve sequentially from the contact edge inward by slow growth in a process controlled by stress shielding from preceding cracks. The embryonic cracks are then accelerated by the action of fluid pressure into the flexural tensile stress at the lower part of the coating, where crossover fracture leading to delamination between the coating and substrate may ensue. A consistent FEM brittle fracture analysis incorporating multiple cracks, rate-dependent toughness and liquid pressure is used to follow the damage evolution in the coating. Crack trajectories are determined incrementally under the dual constraint K _I = K _II = 0, which maximize the tension at the crack tip upon the application of fluid pressure. The latter, evaluated at each increment with the aid of a fluid entrapment model, helps drive the leading crack past the compression zone beneath the contact via a hydraulic pump like action. In the early stages of fracture, the liquid pressure is reasonably well approximated by the Hertzian radial surface stress at the crack mouth. Fluid trapped in secondary cracks accentuate the compression beneath the contact. This helps squeeze more liquid into the tip of the leading crack in a zipping like action, which further enhance the crack driving force in the far field. The analytic predictions generally collaborate well with the tests.     

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.     

Vickers Indentation Fracture (VIF) modeling to analyze multi-cracking toughness of titania, alumina and zirconia plasma sprayed coatings

For massive brittle materials, the fracture toughness in mode I, K_IC, can be determined using various reliable techniques. Besides, Vickers Indentation Fracture (VIF) technique has been developed to locally determine fracture toughness. However, since the indentation test generates a complex three-dimensional crack system around the indent, fracture toughness, K_C, is calculated instead of K_IC. Consequently some authors rightly reject the VIF technique to determine standard fracture toughness by arguing that the literature counts numerous VIF crack equations thus revealing discrepancies of this technique. Nevertheless in some cases (e.g. brittle ceramic coatings) inclusive material techniques are not applicable since presence of the substrate and/or multi-crack network can modify the crack propagation into the coating.In this work, we employed VIF technique to study multi-cracking behavior of titania, alumina and zirconia ceramic oxide coatings obtained by plasma spraying. To calculate VIF toughness, we propose (i) to select two crack equations for radial-median and Palmqvist cracking modes respectively, (ii) to adjust the crack equation of Miranzo and Moya for intermediate cracking mode, (iii) to develop a mathematical approach to determine the cracking mode, (iv) to take into account the multi-crack network by defining an equivalent four-crack system and (v) to propose a universal crack equation applicable independently of the cracking mode.     

Fracture toughness modification by using a fibre laser surface treatment of a silicon nitride engineering ceramic

Surface treatment of a silicon nitride (Si₃N₄) engineering ceramic with fibre laser radiation was conducted to identify changes in the fracture toughness as measured by K_1c. A Vickers macro-hardness indentation method was adopted to determine the K_1c of the Si₃N₄ before and after fibre laser surface treatment. Optical and a scanning electron microscopy (SEM), a co-ordinate measuring machine and a focus variation technique were used to observe and measure the dimensions of the Vickers indentation, the resulting crack lengths, as well as the crack geometry within the as-received and fibre laser-treated Si₃N₄. Thereafter, computational and analytical methods were employed to determine the K_1c using various empirical equations. The equation K_1c = 0.016 (E/Hv)^1/2 (P/c^3/2) produced most accurate results in generating K_1c values within the range from 4 to 6 MPa m^1/2. From this it was found that the indentation load, hardness, along with the resulting crack lengths in particular, were the most influential parameters within the K_1c equation used. An increase in the near surface hardness of 4% was found with the Si₃N₄ in comparison with the as-received surface, which meant that the fibre laser-treated surface of the Si₃N₄ became harder and more brittle, indicating that the surface was more prone to cracking after the fibre laser treatment. Yet, the resulting crack lengths from the Vickers indentation tests were reduced by 37% for the Si₃N₄ which in turn led to increase in the K_1c by 47% in comparison with the as-received surface. It is postulated that the fibre laser treatment induced a compressive stress layer by gaining an increase in the dislocation movement during elevated temperatures from the fibre laser surface processing. This inherently increased the compressive stress within the Si₃N₄ and minimized the crack propagation during the Vickers indentation test, which led to the fibre laser-radiated surface of the Si₃N₄ engineering ceramic to have more resistance to crack propagation.     

Effect of annealing on the fracture behavior of La0.58Sr0.4Co0.8Fe0.2O3‐δ, a potential energy material for oxygen separation

The perovskite material La_0.58Sr_0.4Co_0.8Fe_0.2O_3‐δ, offers high oxygen permeability at elevated temperature and is considered as a potential material for oxygen separation membranes. It can enhance the efficiency of oxy‐fuel combustion at high temperatures (> 800 °C) and hence due to the high reliability demands, required by the long term operation at elevated temperatures, it requires a thorough investigation from the view point of structural stability. Aiming towards long term stability, the present work is a detailed and systematic study on the effect of annealing on the mechanical behavior of dense La_0.58Sr_0.4Co_0.8Fe_0.2O_3‐δ. The study reveals that the indentation fracture toughness of the material increases with increase in annealing temperature. In most of the indentation loads, the subsurface crack profile was Palmqvist in nature with low value of the ratio of crack length versus indentation size (c/a). A consistent pattern of variation of c/a and indentation fracture toughness (K_IC) at all indentation loads was observed. Systematic drop in c/a and subsequent increase in fracture toughness in the as prepared test pieces has been attributed to residual stress accumulation during preparation.     

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.     

Critical evaluation of indentation fracture toughness measurements with Vickers indenter on yttria‐stabilized zirconia dental ceramics

The purpose of this study was to investigate and analyze fracture toughness (K_Ic) of yttria stabilized tetragonal zirconia (Y‐TZP) dental ceramics by the Vickers indentation fracture test. In order to determine fracture toughness, the Vickers indenter was used under the load of 294.20 N (HV30). The cracks, which occur from the corners of a Vickers indentation, were measured and used for fracture toughness determination, through five mathematical models according to (I) Anstis, (II) Evans and Charles, (III) Tanaka, (IV) Niihara, Morena and Hasselman and (V) Lankford. Morphology of indentation cracking was determined by scanning electron microscope. The most adequate model for determination of fracture toughness (K_Ic) of yttria stabilized tetragonal zirconia dental ceramics by the Vickers indentation fracture test is Lankford model.     

Crack spacing statistics and spalling area fractions for indented silica-coated bismaleimide (BMI)

Indentation loading of thin, continuous silica coatings adhered to Bismaleimide (BMI) polymeric substrates induces a concentric array of cracks in the silica coating. For Vickers indentation, the array consists of diamond-shaped concentric cracks, while Hertzian indentation gives circular concentric cracks. This paper characterizes the indentation-induced crack damage in the coating in terms of: (1) f _s, the area fraction of the coating (within the indentation-cracked region) that spalls off the substrate due to the indentation and (2) the spacing between the cracks in the crack array. For a given indentation crack field, the crack spacing was uniform as a function of radial distance outward from the center of the indentation. One of the key results of this study was that the curing temperature for the coating dramatically affected both the coating spalling area fraction, f _S, and the manner in which the crack spacing changed as a function of the applied indentation load.     

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.     

Crack-Tip Stress-Strain Fields During Cyclic Loading and Effect of Overload

Finite-deformation elastoplastic analysis of a plane-strain crack subjected to mode I cyclic loading under small scale yielding was performed. The influence of the load range, load ratio and overload on the crack tip stress-strain field is presented. Two independent parameters of cyclic loading, such as ΔK and K _max, both substantially affect the near tip evolutions of cyclic stresses and plastic strains, in agreement with typical experimental trends of fatigue cracking. This implies that the behaviour of cracks is governed by stress and strain fields ahead of the tip, via their control over the key process variables (damage accumulation and rupture, i.e., bond-breaking), so that the coupled process becomes a two-parameter one in terms of fracture mechanics variables ΔK and K _max.     

Substrate dependent cracking behavior of CrAlN coatings

The present study investigated the effect of substrate deformation behavior on crack resistance of CrAlN coatings under quasi-static and cyclic loads using nanoindentation. (Cr₄₇Al₅₃)N coatings were deposited on cemented carbide WC-Co and high-speed steel HS652C substrates through physical vapor deposition (PVD) und characterized. In order to study the coating cracking behavior, the coated substrates were subjected to quasi-static nanoindentations with indentation force F_max = 1 N, F_max = 1.5 N and F_max = 2 N. Moreover, the crack resistance under cyclic loading with frequency f = 0.16 Hz was analyzed at F = 1 N and F = 1.5 N after n = 900 cycles. A conical diamond indenter was used for the tests. At the end, the indentation imprints were analyzed by scanning electron microscopy (SEM). The substrate dependency was apparent in cracking behavior of the coating. Albeit the lower indentation depth compared to the variant with HS6-5-2C substrate, the CrAlN coating on WC-Co substrate showed surface cracks under quasi-static and cyclic loading. These cracks on the coated surface were absent in the variant with HS6-5-2C substrate. This could be related to higher resistance of cemented carbide substrates against plastic deformation, prompting earlier crack initiation in CrAlN coating for effective energy dissipation during indentation.     

Assessment of the toughness of thin coatings using nanoindentation under displacement control

Various indentation models have been developed to measure the toughness of bulk materials and coatings. Most of them are based on the formation of well-developed cracks. However, in order to eliminate the influence of elastic–plastic deformation in the substrate, it is preferable to perform small indentations in thin coatings and thus the cracks may not be well-developed compared to the indentation size. Relatively little work has been done to investigate this kind of small cracks. The ultra small cracks (< 500 nm in length) in thin coatings (∼ 500 nm in thickness) confined to indentation zone are investigated here. A new method to assess the toughness of the main components of solar control coatings such as SnO₂, TiO_xN_y and ITO deposited on soda–lime glass is proposed here. This method is able to separate the energy contributions from other deformation mechanisms from that dissipated in the fracture event. The energy release rate of these ceramics coating are in the range 15–45 J/m² by this method.     

3-D stress intensity factors for arrays of inner radial lunular or crescentic cracks in thin and thick spherical pressure vessels

Some spherical pressure vessels are manufactured from a series of double curved petals welded along their meridional lines. Such vessels are susceptible to multiple radial cracking along the welds. For fatigue life assessment and fracture endurance of such vessels, one needs to evaluate the stress intensity factors (SIF) distribution along the fronts of these cracks. In a recent paper by the authors, mode I SIF distributions for a wide range of lunular and crescentic internal, surface, radial cracks were evaluated for a typical spherical pressure vessel of an outer to inner radii ratio of η = R_o/R_i = 1.1. The present analysis is aimed to determine the influence of the spherical vessel geometry in terms of its outer to inner radii ratio η = R_o/R_i on the prevailing SIFs. Mode I SIF distributions for a wide range of lunular and crescentic crack array configurations are evaluated. The 3-D analysis is performed by means of the FE method, employing singular elements along the crack front, for five geometries representing thin, moderately thick, and thick spherical pressure vessels with outer to inner radius ratios of η = R_o/R_i = 1.01, 1.05, 1.1, 1.7, and 2.0. SIFs are evaluated for arrays containing n = 1–20 cracks; for a wide range of crack depth to wall thickness ratio, a/t, from 0.025 to 0.95; and for various ellipticities of the crack, i.e., the ratio of crack depth to semi crack length, a/c, from 0.2 to 1.5. The obtained results clearly indicate that the SIFs are affected considerably by the geometry of the spherical pressure vessel-η, and by the following parameters: the number of cracks in the array-n, the depth of the cracks-a/t, and their ellipticity-a/c.     

Analysis of three-dimensional interface cracks using enriched finite elements

Many important interface crack problems are inherently three-dimensional in nature, e.g., debonding of laminated structures at corners and holes. In an effort to accurately analyze three-dimensional interface fracture problems, an efficient computational technique was developed that utilizes enriched crack tip elements containing the correct interface crack tip asymptotic behavior. In the enriched element formulation, the stress intensity factors K _I, K _II, and K _III are treated as additional degrees of freedom and are obtained directly during the finite element solution phase. In this study, the results that should be of greatest interest are obtained for semi-circular surface and quarter-circular corner cracks. Solutions are generated for uniform remote tension and uniform thermal loading, over a wide range of bimaterial combinations. Of particular interest are the free surface effects, and the influence of Dundurs’ material parameters on the strain energy release rate magnitudes and corresponding phase angles.     

Mode II fracture testing method for highly orthotropic materials like wood

In this paper a mode II fracture testing method has been developed for wood from analytical, experimental and numerical investigations. Analytical results obtained by other researchers showed that the specimen geometry and loading type used for the proposed mode II testing method results in only mode II stress intensity and no mode I stress intensity at the crack tip. Experiments have been carried out to determine mode II fracture toughness K _IIC and fracture energy G _IIF from the test data collected from both spruce (pice abies) and poplar (populus nigra) specimens. It was found that there existed a very good relation between fracture toughness K_IIC and fracture energy G _IIF when the influence of orthotropic stiffness E _II ^* in mode II was taken into account. It verified that for this mode II testing method the formula of LEFM can be employed for calculating mode II fracture toughness even for highly orthotropic materials like wood. In the numerical studies for the tested spruce specimen, the crack propagation process, stress and strain fields in front of crack tips and the stress distributions along the ligament have been investigated in detail. It can be seen that the simulated crack propagating process along the ligament is a typical shear cracking pattern and the development of cracks along the ligament is due to shear stress concentrations at the crack tips of the specimen. It has been shown that this mode II fracture testing method is suitable for measuring mode II fracture toughness K _IIC for highly orthotropic materials like wood.     

Intersonic shear crack growth along weak planes

Classical dynamic fracture theories predict the Rayleigh surface wave speed (c _R ) to be the limiting speed of propagation for mode-I cracks in constitutively homogeneous, isotropic, linear elastic materials subjected to remote loading. For mode-II cracks, propagating along prescribed straight line paths, the same theories, while excluding the possibility of crack growth in the speed regime between c _R and the shear wave speed, c _s , do not exclude intersonic (c _s <υ<c _l ) crack tip speeds. In the present study, we provide the first experimental evidence of intersonic crack growth in such constitutively homogeneous and isotropic solids, ever recorded in a laboratory setting. Intersonic shear dominated crack growth, featuring shear shock waves, was observed along weak planes in a brittle polyester resin under far-field asymmetric loading. The shear cracks initially propagate at speeds just above c _s and subsequently accelerate rapidly to the longitudinal wave speed (c _l ) of the solid. At longer times, when steady state conditions are attained, they propagate at speeds slightly higher than √2–c _s . The experimental results compare well with existing asymptotic theories of intersonic crack growth, and the significance of the preferred speed of √2–c _s is discussed. Received: 13 September 1999 / Reviewed and occerted: 19 November 1999     

A FRACTURE CRITERION FOR CRACKS UNDER MIXED-MODE LOADING

Abstract A fracture criterion is proposed, based on maximum energy release rates at the tips of short kinks when the main cracks are subjected to mixed mode loading. The criterion differs from existing energy based criteria in that the fracture toughness, g_c, is not independent of the stress mode prevailing in the region of the tip of the kink but is a function of the ratio of the mode II to mode I stress intensity factors at the tip of the kink, i.e., g_c is determined directionally by an elliptical region with major and minor axes equal to the fracture resistances of the material, K_Ir and K_IIr, for pure mode I and pure mode II, respectively. Points inside the elliptical region are considered safe. When K_IIr is equal to K_Ir the ellipse degenerates into a circle and the fracture criterion reverts to the existing familiar maximum energy release rate criterion based on a single value of the fracture toughness, irrespective of the active mode prevailing in the region at the tip of the kink. In this case, under pure shear (mode II) applied load, K_II, the angle of inclination of the fracture crack extension to the main crack, α, is in the region of ?76°, in general agreement with previous well established results. However, when the ratio r (=K_IIrK_Ir) is less than r′ (=0.82, approximately) a different pattern emerges and, in particular, under pure mode II load, the crack advance is co-planar with the main crack, i.e., in mode II. A lower transition value r″ (=0.582, approximately) was also detected under pure mode I applied load. Thus for values of r≥r″, the crack extension is in pure mode I and is co-planar with the main crack but when r < r″, the crack branches out at an angle (which can be positive or negative) in mixed modes I/II crack extension. Some implications of these results are discussed.     

Shear mode threshold for a small fatigue crack in a bearing steel

The fatigue behaviour of small, semi‐elliptical surface cracks in a bearing steel was investigated under cyclic shear‐mode loading in ambient air. Fully reversed torsion was combined with a static axial compressive stress to obtain a stable shear‐mode crack growth in the longitudinal direction of cylindrical specimens. Non‐propagating cracks less than 1 mm in size were obtained (i) by decreasing the stress amplitude in tests using notched specimens and (ii) by using smooth specimens in constant stress amplitude tests. The threshold stress intensity factor ranges, ΔK_IIth and ΔK_IIIth, were estimated from the shape and dimensions of non‐propagating cracks. Wear on the crack faces was inferred by debris and also by changes in microstructure in the wake of crack tip. These effects resulted in a significant increase in the threshold value. The threshold value decreased with a decrease in crack size. No significant difference was observed between the values of ΔK_IIth and ΔK_IIIth.     

Micro-defects Initiation Ahead of a Wedge-shaped Inhomogeneity

The problem of micro-defects that are initiated at the tip of a wedge-shaped inhomogeneity is investigated. Firstly, the elastic solution due to a screw dislocation near the tip of a semi-infinite wedge-shaped inhomogeneity is derived using the conformal mapping method. Then, a Mode III micro-crack initiated from the tip of the imhomogeneity is examined. The effects of the wedge angle, the crack location and the relative shear modulus of the inhomogeneity on the stress intensity factor of the micro-crack are studied. Finally, an interesting relationship between the critical stress intensity factor (K^*_III c for a line inhomogeneity and the fracture toughness of a crack (K_IIIc) in the same material is established for different shear modulus of the inhomogeneity.