Fatigue analysis of brittle materials using indentation flaws

A two-part study has been made of the fatigue characteristics of brittle solids using controlled indentation flaws. In this part a general theory is developed, with explicit consideration being given to the role played by residual contact stresses in the fracture mechanics to failure. The distinctive feature of the formulation is a stress intensity factor for well-defined indentation cracks, suitably modified to incorporate the residual component. Taken in conjunction with a standard power-law crack velocity function, this leads to a differential equation for the dynamic fatigue response of a given material/ environment system. Reduced variables are then introduced to facilitate generation of universal fatigue curves, determined uniquely by the crack velocity exponent,n. A scheme for using these curves to evaluate basic fracture parameters from strength data is outlined. In this way the foundation is laid for lifetime predictions of prospective brittle components, as well as for reconstruction of the crack velocity function. One of the major advantages of the analysis is the manner in which the residual stress parameters are accommodated in the normalized fracture mechanics equations: whereas it is understood thatall strength data are to be taken from test pieces in their as-indented state, so making it unnecessary to have to resort to inconvenient stress-removal procedures between the contact and failure stages of testing,a priori knowledge of the residual stress level is not required. The method is proposed as an economical route to materials evaluation and offers physical insight into the behaviour of natural flaws.     

Dynamic fatigue of brittle materials containing indentation line flaws

A study is made of the dynamic fatigue response of brittle materials containing indentation-induced line flaws. The theoretical fracture mechanics of median crack evolution to failure under applied tension are first developed, with special emphasis on the role of residual contact stresses. In particular, it is shown that use of fatigue curves to evaluate the exponent in an assumed power-law crack velocity function may result in systematic error, by as much as a factor of two, if proper account is not taken of this residual contact contribution. Data from strength tests on soda-lime glass bars in water, using a tungsten carbide cutting wheel to introduce the median pre-cracks, confirm the basic predictions. The results suggest that extreme care needs to be exercised when using surfaces with a contact history, e.g. as with machining damage, in fatigue test programmes for materials analysis.     

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.     

On internal cone cracks induced by conical indentation in brittle materials

The conditions for cone cracks to develop due to a conical indentation are investigated. Axisymmetric numerical simulations, based on the finite element method, are conducted, assuming a linear-elastic, perfectly plastic material. A superposition scheme is employed to simulate a range of crack geometries, including various lengths and orientations. The results indicate that the class of cracks investigated is prone to develop internally in brittle materials. Based on a reversed analysis, a new technique is proposed for measuring the fracture toughness in bulk material and thick coatings through one simple indentation test when the cone crack appears.     

Fatigue damage in ceramic materials caused by repeated indentation

Indentation fatigue is the damage accumulation in the surface layer of ceramics caused by local cyclic loading. It has been found that there are two types of indentation fatigue behaviour, Types I and II. Type I is characterized by a slight increase in indentation-induced damaged zone with increased number of indentation cycles, followed by the abrupt chipping of the surface layer. On the other hand, Type II behaviour is characterized by pronounced enlargement of the damaged zone in early cycles. Lateral cracking behaviour during cyclic indentation in various ceramics was also studied by scanning electron microscopy and scanning acoustic microscopy. It was confirmed that a lateral crack zig-zag propagates with repeated indentation in silicon nitride of transgranular fracture type. The relations between lateral cracking, microcracks and the resultant damaged zone in alumina and magnesium oxide were investigated in detail and their indentation fatigue mechanism is discussed.     

Fracture mechanics model for subthreshold indentation flaws

In Part II of this two-part study we extend the shear-fault-microcrack model to non-equilibrium fracture, to allow for rate effects in the critical instability configurations in chemically interactive environments. The calibratedK-fields of Part I are combined with independently evaluated crack velocity functions to determine kinetic conditions for microcrack extension. The analysis enables evaluation of (i) a time delay in radial crack pop-in from a subthreshold flaw; (ii) a time dependence in the strength characteristics, in both the subthreshold and postthreshold domains. Comparisons with delayed pop-in and strength-stressing-rate literature data for silicate glasses in moist environments indicate that the analysis is capable of quantitative predictions of kinetic characteristics. In the strength data, the model accounts for the relatively high magnitudes, scatter and fatigue susceptibilities in the subthreshold region. Guest Scientists: On leave from the Department of Materials Science and Engineering, Lehigh University, Bethlehem, PA 18015, USA.     

Fracture mechanics model for subthreshold indentation flaws

A fracture mechanics model for subthreshold indentation flaws is. described. The model describes the initiation and extension of a microcrack from a discrete deformation-induced shear fault (shear crack) within the contact zone. A stress-intensity factor analysis for the microcrack extension in residual-contact and applied-stress fields is used in conjunction with appropriate fracture conditions, equilibrium in Part I and non-equilibrium in Part II, to determine critical instability configurations.In Part I, the K-field relations are used in conjunction with the Griffith requirements for crack equilibrium in essentially inert environments to determine: (i) the critical indentation size (or load) for spontaneous radial crack pop-in from a critical shear fault under the action of residual stresses alone; (ii) the inert strengths of surfaces with subthreshold or postthreshold flaws. The theory is fitted to literature data for silicate glasses. These fits are used to calibrate dimensionless parameters in the fracture mechanics expressions, for later use in Part II. The universality of the analysis in its facility to predict the main features of crack initiation and propagation in residual and applied fields will be demonstrated. Special emphasis is placed on the capacity to account for the significant increase in strength (and associated scatter) observed on passing from the postthreshold to the subthreshold domain.     

Flexural strength analysis of brittle materials

The relation between flaw density and strength of ceramic or brittle materials were derived and applied to a commonly used testing method of four-point bending for determining the strengths of ceramic or brittle materials. Previous analysis failed to include the failures outside or at the inner loading positions for four-point test data. The present approach elevates such a constrain so that the relation applies to failures occurs at any points between the outer loading positions for four-point test data.     

Calculation of penetration resistance of brittle materials using spherical cavity expansion analysis

In this paper, we show that the ‘target resistance’ of brittle materials can be calculated accurately using spherical cavity expansion analysis and a conventional brittle material model. The stress field ahead of the tip of the penetrator is assumed to have spherical symmetry. The brittle material is modeled as an elastic material which cracks under tension. The cracked material is considered to be pulverized when it fails in compression, which is then characterized as a Mohr-Coulomb material with pressure dependent shear strength. The target resistance value found from this analysis compares well with the reported experimental values for AD995 alumina (Al₂O₃) and aluminum nitride (A1N).     

Fractoemission during indentation fracture of brittle solids

Journal of Materials Science Letters -     

Finite element analysis of vickers indentation cracking processes in brittle solids using elements exhibiting cohesive post-failure behaviour

The cracking processes during the indentation test of brittle solids is simulated by means of the finite element method (FEM) using elements exhibiting cohesive post-failure behaviour and alumina as the model material. The results show that at low indentation loads, median cracks could nucleate at full loading but Palmqvist cracks only nucleate in the unloading stage and that they may not join up even after full unloading. Such cracks are stable as they are embedded in a region of high hydrostatic compression throughout the indentation test. At high indentation loads, both median and Palmqvist cracks nucleate early during the loading stage and coalesce to form a half-penny crack on further loading. Although the cracks are embedded in a region of high hydrostatic compression during loading, an annular tensile region eventually develops in between the cracked material beneath the indenter and the surrounding uncracked material during the unloading stage of the macro-indentation. This not only provides the driving force for existing cracks to grow but also new crack systems to form. The present work shows that for brittle solids with negligible plastic deformation, the mismatch in elastic recovery between the cracked and uncracked bodies on unloading plays an important role in indentation fracture processes.     

Applicability of Weibull analysis for brittle materials

Weibull analysis for the interpretation of strengths of brittle materials was previously justified for a particular flaw size distribution. The present results show that the Weibull distribution provides a close approximation to the distribution of failure stress for all the flaw size distributions considered. However certain reservations are noted in the interpretation of the Weibull modulus.     

Statistical failure analysis of brittle coatings by spherical indentation: theory and experiment

The mode of failure and failure probability of a brittle coating on a compliant substrate subjected to a static load through a spherical indenter is investigated experimentally and theoretically. We extend our recent study (2003, J Mat Sci 38:1589) of surface crack initiation in a monolithic solid to the layered system, and account for the multi axial stress state of the indentation in the failure probability analysis. Two modes of failure, a Hertzian cone crack initiating from the contacting surface and a half-penny-shaped crack initiating from the interface, are investigated and the probability of failure initiation for both surfaces are theoretically predicted and compared with experimental data.The effect of interface debonding on failure phenomena is investigated. For a given load the failure probability for debonded specimens is significantly higher than that of well-bonded samples. For the debonded case the theoretical failure probability curve falls within the 90% confidence interval of the experimental data, while the experimental values for the completely bonded case show somewhat lower failure probabilities than that predicted. This may be attributed to the possible bridging effect by the adhesive on interfacial surface defects in the ceramic that is not accounted for in our model.     

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.     

Fracture of ceramics with surface flaws introduced by Knoop indentation

The crack opening behaviour of surface flaws in ceramic materials, produced by Knoop indentation tests, was investigated. The damaged region below the indenter tip was replaced by a wedge. The influence of this wedge is reduced, if tensile stresses are acting at the damaged surface. For alumina the wedging force in moment of fracture was found approximately 50% of its value without additional bending.     

Probabilistic analysis of continuum damage mechanics of brittle materials

Uncertainty of material properties in solution of engineering problems is often a fundamental question. Statistical methods give a powerful tool for analysis of uncertainty. Monte Carlo simulations together with Gumbel distribution are used as a possible way to study influence of data dispersion on assessment of damage of brittle materials.     

Numerical analysis of brittle materials fractured by sharp indenters

Indentation can be used to determine the fracture properties of materials. A detailed investigation is here presented on the reliability of finite element simulations of sharp indentations on cracked specimens. Elastic analyses of the stress and deformation fields arising from Vickers, Berkovich and cube-corner indenters generated the stress intensity factor along the edge of penny-shaped or elliptical cracks. Various materials with a range of properties were analysed and the results compared with published experimental data. Additional measurements from tests on soda-lime glass provided further opportunities for experimental validation of numerical predictions. The variation of the stress intensity factor indicated trends for crack growth patterns, which were consistent with experimental observations. Particular attention was given to the evaluation of the geometry-dependent parameter appearing in the relation yielding the fracture toughness of cracked indented materials. The numerical predictions of this parameter were remarkably consistent with experimental data and results from other approximate methods.