Micro‐indentation fracture from flat‐ended cylindrical indenter

Unlike a Hertzian ring crack induced by a spherical indenter in absence of a singular stress field, a ring crack generated by a rigid flat cylindrical indenter can be explicitly linked to a K‐dominant singular stress field at the perimeter of the flat indenter. This means microcrack initiation induced by a flat indenter and relevant properties such as the critical indentation load and fracture toughness can be formulated explicitly using the fracture mechanics approach. It is shown in this paper that the indentation stress intensity factor, , for such a stress field is similar to that of a mode I crack. Based on the energy‐releasing rate and the Griffith's theorem, a flat indentation cracking model has been proposed; the critical load and critical cracking angle for crack initiation are derived. A new concept of fracture toughness for negative mode I singular stress field,, has been defined and a relationship between and the traditional K_IC has been derived. The experimental investigation validates the existence of such , from which the K_IC value of the glass had been determined to be 0.772 ± 0.003 MPa m^1/2, agreeing well with the literature data. This analysis for indentation fracture or crack initiation due to surface contact of a flat indenter is particularly useful in determining K_IC of brittle materials with dimensions in micro/nanoscales, e.g. thin films and other microstructures as flat micro/nano‐indenters are available and can be used on various nano‐indentation machines.     

Application of artificial neural network for predicting plain strain fracture toughness using tensile test results

A back‐propagation neural network was applied to predicting the K_IC values using tensile material data and investigating the effects of crack plane orientation and temperature. The 595 K_IC data of structural steels were used for training and testing the neural network model. In the trained neural network model, yield stress has relatively the most effect on K_IC value among tensile material properties and K_IC value was more sensitive to K_IC test temperature than to crack plane orientation valid in the range of material data covered in this study. The performance of the trained artificial neural network (ANN) was evaluated by comparing output of the ANN with results of a conventional least squares fit to an assumed shape. The conventional linear or nonlinear least squares fitting methods gave very poor fitting results but the results predicted by the trained neural network were considerably satisfactory. This study shows that the neural network can be a good tool to predict K_IC values according to the variation of the temperature and the crack plane orientation using tensile test results.     

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).     

Crack resistance curves of alumina and zirconia at room temperature

Ceramic three-point bend specimens were pre-cracked in a displacement-controlled test in air at room temperature to form sharp cracks of different lengths. Critical stress intensity factors (K _IC were then measured as a function of sharp crack length in a fast-fracture, load-controlled test. Crack resistance curves (K _IC against crack length) were determined for three commercially pure aluminas of different grain size, a debased alumina containing a glassy phase, and a partially stabilized zirconia (PSZ) material. The crack resistance curves proved to be flat for the finer-grained and the debased alumina. A steeply rising crack resistance curve was, however, observed for a pure coarse-grained alumina material which is explained by friction effects of the cracked microstructure behind the measured crack front. The effect is influenced by the test procedure itself. Though crack branching takes place the crack resistance curve of PSZ is completely flat, which is attributed to fast fracture testing where only the most dangerous flaw is activated.     

Fracture toughness and crack morphology in indentation fracture of brittle materials

The relationship between the indentation fracture toughness, K _c, and the fractal dimension of the crack, D, has been examined on the indentation-fractured specimens of SiC and AIN ceramics, a soda-lime glass and a WC-8%Co hard metal. A theoretical analysis of the crack morphology based on a fractal geometry model was then made to correlate the fractal dimension of the crack, D, with the fracture toughness, K _IC, in brittle materials. The fractal dimension of the indentation crack, D, was found to be in the range 1.024–1.145 in brittle materials in this study. The indentation fracture toughness, K _c, increased with increasing fractal dimension, D, of the crack in these materials. According to the present analysis, the fracture toughness, K _IC, can be expressed as the following function of the fractal dimension of the crack, D, such that $$In K_{IC} = {1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}\{ In[2\Gamma E/(1 - \nu ^2 )] - (D - 1)In r_L \}$$ Where Γ is the work done in creating a unit crack surface, E is Young's modulus, v is Poisson's ratio, and r _L is r _min/r _max, the ratio of the lower limit, r _min, to the upper limit, r _max, of the scale length, r, between which the crack exhibits a fractal nature (r _min ?r?r _max). The experimental data (except for WC-8%Co hard metal) obtained in this study and by other investigators have been fitted to the above equation. The factors which affect the prediction of the value of K _IC from the above equation have been discussed.     

Lifetime prediction of brittle materials having spatial variations in fracture properties K IC and v versus K 1

The lifetimes of brittle materials under conditions of subcritical crack growth are analysed to indicate the effects of spatial variations of K _IC and v versus K _I and methods for studying the variations are suggested.     

Limitations of elastic definitions in Al-Si-Mg cast alloys with enhanced plasticity: linear elastic fracture mechanics versus elastic-plastic fracture mechanics

Linear elastic fracture mechanics describes the fracture behavior of materials and components that respond elastically under loading. This approach is valuable and accurate for the continuum analysis of crack growth in brittle and high strength materials; however it introduces increasing inaccuracies for low-strength/high-ductility alloys (particularly low-carbon steels and light metal alloys). In the case of ductile alloys, different degrees of plastic deformation precede and accompany crack initiation and propagation, and a non-linear ductile fracture mechanics approach better characterizes the fatigue and fracture behavior under elastic-plastic conditions.To delineate plasticity effects in upper Region II and Region III of crack growth an analysis comparing linear elastic stress intensity factor ranges (ΔK_el) with crack tip plasticity adjusted linear elastic stress intensity factor ranges (ΔK_pl) is presented. To compute plasticity corrected stress intensity factor ranges (ΔK_pl), a new relationship for plastic zone size determination was developed taking into account effects of plane-strain and plane-stress conditions (“combo plastic zone”). In addition, for the upper part of the fatigue crack growth curve, elastic-plastic (cyclic J based) stress intensity factor ranges (ΔK_J) were computed from load-displacement records and compared to plasticity corrected stress intensity factor ranges (ΔK_pl). A new cyclic J analysis was designed to compute elastic-plastic stress intensity factor ranges (ΔK_J) by determining cumulative plastic damage from load-displacement records captured in load-control (K-control) fatigue crack growth tests. The cyclic J analysis provides the true fatigue crack growth behavior of the material. A methodology to evaluate the lower and upper bound fracture toughness of the material (J_IC and J_max) directly from fatigue crack growth test data (ΔK_FT(JIC) and ΔK_FT(Jmax)) was developed and validated using static fracture toughness test results. The value of ΔK_FT(JIC) (and implicitly J_IC) is determined by comparing the plasticity corrected elastic fatigue crack growth curve with the elastic-plastic fatigue crack growth curve. A most relevant finding is that plasticity adjusted linear elastic stress intensity factor ranges (ΔK_pl) are in remarkably good agreement with cyclic J analysis results (ΔK_J), and provide accurate plasticity corrections up to a ΔK corresponding to J_IC (i.e. ΔK_FT(JIC)). Towards the end of the fatigue crack growth test (above ΔK_FT(JIC)) when plasticity is accompanied by significant tearing, the cyclic J analysis provides a more accurate way to capture the true behavior of the material and determine ΔK_FT(Jmax). A procedure to decouple and partition plasticity and tearing effects on crack growth rates is given.Three cast Al-Si-Mg alloys with different levels of ductility, provided by different Si contents and heat treatments (T61 and T4) are evaluated, and the effects of crack tip plasticity on fatigue crack growth are assessed. Fatigue crack growth tests were conducted at a constant stress ratio, R = 0.1, using compact tension specimens.     

Physical meaning of ΔKRP and fatigue crack propagation in the residual stress distribution field

Previous papers have shown ΔK_RP to be a useful parameter describing fatigue crack propagation behavior, where ΔK_RP is an effective stress intensity factor range corresponding to the excess RPG load (re-tensile plastic zone's generated load) in which the retensile plastic zone appears under the loading process. In this paper, the relationship between ΔK_RP and the zone size ( ) (which is smaller between the tensile plastic zone at maximum load and the compressive plastic zone at minimum load) was investigated using a crack opening/closing simulation model so as to consider a physical meaning of ΔK_RP. As a result, it becomes clear that ΔK_RP dominates the zone size where fatigue damage mostly occurs. This result supports the following crack propagation equation

where C and m are material constants.Simulation and fatigue crack propagation tests were then carried out for compact tension (CT), center cracked tension (CCT) and four points bend (4PB) specimens under constant amplitude loading to obtain C and m values for HT-50 steel. Fatigue crack propagation tests were also carried out under constant amplitude loading using CCT specimens with residual stress distribution due to flame gas heating at the center line or edge lines. The T specimen introduced tensile residual stress at the tip of a notch, and the C specimen introduced compressive residual stress. It therefore becomes clear that tensile residual stress leads to a decrease in RPG load, while compressive residual stress leads to increase in RPG load, and that the simulation results are in good agreement with the experimental RPG load. It also becomes clear that simulated crack growth curve using the simulated and the above equation is in good agreement with the experimental curve. It is understood that tensile residual stress creates only a slight increase in crack propagation rate and compressive residual stress create a big decrease a crack propagation rate.     

Carbon nanotubes: do they toughen brittle matrices?

The development of a model CNT-brittle matrix composite system, based on SiO₂ glass containing well-dispersed CNTs at up to 15 wt%, allows a direct assessment of the effect of the nanoscale filler on fracture toughness (K _IC). Samples were prepared by colloidal heterocoagulation followed by spark plasma sintering. Detailed K _IC measurements, using both indentation and notched beam techniques, show a linear improvement with CNT content, with up to a twofold increase of fracture toughness at maximum loading. The results from the two methods used in this study show equivalent trends but differing absolute values; the relative merits of these two approaches to measuring nanocomposite toughness are compared. Possible toughening mechanisms associated with CNT pull-out, crack bridging, and crack deflection are identified, and discussed quantitatively, drawing on conventional short-fibre composite theory and the potential effects of scaling fibre diameter.     

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.     

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.     

State‐of‐the‐art review on extended stress intensity factor concepts

The stress intensity factor concept for describing the stress field at pointed crack or slit tips is well known from fracture mechanics. It has been substantially extended since Williams' basic contribution (1952) on stress fields at angular corners. One extension refers to pointed V‐notches with stress intensities depending on the notch opening angle. The loading‐mode‐related simple notch stress intensity factors K₁, K₂ and K₃ are introduced. Another extension refers to rounded notches with crack shape or V‐notch shape in two variants: parabolic, elliptic or hyperbolic notches (‘blunt notches’) on the one hand and root hole notches (‘keyholes’ when considering crack shapes) on the other hand. Here, the loading‐mode‐related generalised notch stress intensity factors K_1ρ, K_2ρ and K_3ρ are defined. The concepts of elastic stress intensity factor, notch stress intensity factor and generalised notch stress intensity factor are extended into the range of elastic–plastic (work‐hardening) or perfectly plastic notch tip or notch root behaviour. Here, the plastic notch stress intensity factors K_1p, K_2p and K_3p are of relevance. The elastic notch stress intensity factors are used to describe the fatigue strength of fillet‐welded attachment joints. The fracture toughness of brittle materials may also be evaluated on this basis. The plastic notch stress intensity factors characterise the stress and strain field at pointed V‐notch tips. A new version of the Neuber rule accounting for the influence of the notch opening angle is presented.     

Dynamic fatigue behaviour of a steatite ceramic

Dynamic fatigue of a low dielectric loss steatite was investigated. To this end, the values of n and B, the so‐called subcritical crack growth (SCG) parameters were experimentally determined. The steatite exhibited the expected dynamic fatigue behaviour, so that the stress corrosion susceptibility parameter, n, of 24 was obtained. In addition, the material/environment parameter B, which is a constant for a given test environment, was also attained. These parameters are instrumental in predicting the lifetime of components under stress. When the applied load is such that the resulting strength equals half of the inert strength (σ_i), defined as the strength of a sample tested in an inert environment or at a fast stress rate, i.e. where no subcritical crack growth occurs, the time to failure (t_f) of the material was found to be ～140 h. Measurement of the fracture toughness of steatite is also of upmost importance and so it was determined using three test methods. A value of K_Ic = 1.91 ± 0.29 MPa m^1/2 was attained by the indentation fracture method through measurement of the cracks emanating from the Vickers indentation. This value is in good agreement with those determined using the K_Isc (surface crack in flexure) test method (2.21 ± 0.07 MPa m^1/2) and fractography analysis test method (2.00 ± 0.44 MPa m^1/2). Differences in test procedure and analysis causing the values from each test method to be different are discussed.     

Two parameter fracture mechanics: Fatigue crack behavior under mixed mode conditions

The fatigue crack path has been studied on a tensile specimen with holes. The experimental crack path trajectories were compared with those calculated numerically. To incorporate the influence of constraint on the crack curving, we predicted the fatigue crack path by using the two-parameter modification of the maximum tensile stress (MTS) criterion. The values of the mixed-mode stress intensity factors K_I, and K_II as well as the corresponding constraint level characterized by T-stress were calculated for the obtained curvilinear and reference crack path trajectories. It is shown that in the studied configuration the effect of T-stress on the crack path is not significant. On the other hand the effect of constraint on the fatigue crack propagation rate is more pronounced.     

Indentation-induced subsurface tunneling cracks as a means for evaluating fracture toughness of brittle coatings

When a plate glued to a compliant substrate is subject to indentation, cracks may initiate from its subsurface due to flexure. Upon increasing the load, the damage develops into a set of tunnel radial cracks which propagate stably under a diminishing stress field. This phenomenon is utilized here to extract fracture toughness K _C for brittle materials in the form of thin plates or films. Experiments show that the SIF at the tip of the subsurface radial cracks is well approximated as K ~ P/c ^3/2, where P is the indentation load and c the mean length of the crack fragments. Using a transparent substrate, c can be easily determined after unloading, from which K _C is found. This simple and economic concept is applied to a wide variety of thin ceramic coatings, yielding toughness data consistent with literature values. Because the tip of the tunneling cracks are well removed from the contact site, the method circumvents certain complications encountered in common top-surface radial cracking techniques such as the effect of plastic deformation, residual stresses and crack extension after unloading. Although the present tests are limited to coating thicknesses >150 μm, it is believed that thinner coatings may be studied as well provided that the indenter radius is kept sufficiently small to insure that subsurface radial cracking dominates over all other failure modes.     

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.     

Static Tensile and Transient Dynamic Response of Cracked Aluminum Plate Repaired with Composite Patch – Numerical Study

In this study, the central cracked aluminum plates repaired with two sided composite patches are investigated numerically for their response to static tensile and transient dynamic loadings. Contour integral method is used to define and evaluate the stress intensity factors at the crack tips. The reinforcement for the composite patches is carbon fibers. The effect of adhesive thickness and patch thickness and configuration in tensile loading case and pre-tension, pre-compression and crack length effect on the evolution of the mode I stress intensity factor (SIF) (K_I) of the repaired structure under transient dynamic loading case are examined. The results indicated that K_I of the central cracked plate is reduced by 1/10 to 1/2 as a result of the bonded composite patch repair in tensile loading case. The crack length and the pre-loads are more effective in repaired structure in transient dynamic loading case in which, the 100 N pre-compression reduces the maximum K_I for about 40 %, and the 100 N pre-tension reduces the maximum K_I after loading period, by about 196 %.     

Methods for calculating stress intensity factors in anisotropic materials: Part I—z = 0 is a symmetric plane

The problem of a crack in general anisotropic material under LEFM conditions is presented. In Part I, three methods are presented for calculating stress intensity factors for various anisotropic materials in which z = 0 is a plane of symmetry. All of the methods employ the displacement field obtained by means of the finite element method. The first one is known as displacement extrapolation and requires the values of the crack face displacements. The other two are conservative integrals based upon the J-integral. One employs symmetric and asymmetric fields to separate the mode I and II stress intensity factors. The second is the M-integral which also allows for calculation of K_I and K_II separately.All of these methods were originally presented for isotopic materials. Displacement extrapolation and the M-integral are extended for orthotropic and monoclinic materials, whereas the J_I- and J_II-integrals are only extended for orthotropic material in which the crack and material directions coincide. Results are obtained by these methods for several problems appearing in the literature. Good to excellent agreement is found in comparison to published values. New results are obtained for several problems.In Part II, the M-integral is extended for more general anisotropies. In these cases, three-dimensional problems must be solved, requiring a three-dimensional M-integral.