Study of the residual stress field around Vickers indentations in a 3Y-TZP

Indentation cracks are often used as initial flaws in ceramics for different mechanical tests because of their unique advantages. The residual stresses around the indent due to the elastic/plastic contact must generally be relaxed, which can be conducted by heat treatment. The stress field around Vickers indentation and conditions of annealing have been analysed on a Y-TZP material. Different heat treatments from room temperature up to 1200 °C have been conducted. The residual stress field has been characterized by different methods. First, stable crack propagation in the residual stress field has been conducted by applying a bending stress to the indented specimens. The apparent toughness has also been measured by conducting fast fracture on indented specimens. Finally the residual stress present around the indentation has been measured by making micro-indentations and by measuring the crack lengths. The results show that at intermediate temperatures up to 600 °C an apparent stress relaxation occurs due to the tetragonal to monoclinic phase transformation which induced a superimposed compressive stress. The higher temperature of 1200 °C effectively leads to a real stress relaxation without healing the crack.     

Evaluation of the fracture toughness of Nb-40Al-8Cr-1W-1Y-0.05B intermetallic material by indentation techniques

The fracture toughness of an Nb-40Al-8Cr-1W-1Y-0.05B intermetallic material was evaluated by indentation techniques at room temperature. Two widely used indentation methods, crack size measurement and indent strength, yielded excellent agreement with a conventional fracture toughness technique using straight-through precracked specimens, despite the occasional formation of poorly configured cracks. However, the modified indentation technique, using dummy indent flaws, resulted in a low fracture toughness compared to that evaluated by the other methods. The material did not exhibit rising R-curve behaviour, as evaluated from the indentation strength data. These results indicate that indentation fracture principles are applicable to this brittle intermetallic material without modification of the residual contact stress term originally calibrated for ceramic materials.     

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.     

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.     

Vickers indentation behavior of several commercial glasses at high temperatures

The Vickers indentation behavior of five commercial glasses has been investigated as a function of temperature. The glasses included: (i) soda-lime-silica Float glass, (ii) lead-alkali silicate, (iii) 7740 Pyrex™ borosilicate, (iv) potassium phosphate, and (v) lanthanum borate. A recording microindentation system was constructed to allow Vickers indentation testing to be conducted at temperatures significantly above room temperature. The Vickers hardness was observed to decrease continuously with increasing temperature for all glasses, with the exception of the 7740 Pyrex™ glass. Decreases in hardness were attributed to decreases in elastic moduli and bond strength with increasing temperature. The lengths of median-radial cracks around indentations in several glasses were observed to first increase, and then decrease, with increasing temperature. The first of this behavior was attributed to initial increases of the crack driving force, characterized by the quantity (E/H), as well as to a decrease in fracture surface energy. Viscous flow at higher temperatures was believed responsible for a reduction in the crack driving force and crack tip stress, resulting in an eventual decrease in crack length. Viscoelastic behavior of the Float glass was characterized by a rate-dependent hardness and indentation crack pattern. Load–displacement traces indicated an increase in the work of indentation and residual indentation depth with increasing temperature for all glasses.     

Laser-induced fracture in silicon

Utilizing the scanning electron microscope, the laser-impact zone on irradiated P-type silicon wafers has been characterized by a central region of compressive stress which decreases to zero and becomes tensile in character with increasing radius from the impact centre, with symmetrical fracturing occurring around the impact centre at a point of maximum tensile stress. The effect of surface flaws on the fracture of brittle Si wafers and their interaction with the impact zone were observed to be small for scratch widths of 60 μm, and lengths of 1 cm. Direct observations of advancing crack tips were made in the transmission electron microscope, and shown to have associated arrays of partial and total dislocations. The presence of numerous precipitates in the P-type Si wafers possessing long-range strain fields which overlapped along the {111} cleavage planes was observed to have a direct influence on the fracture process. Fracture was observed to occur in wafers containing cleavage-oriented scratches or scratches deviating by ～ 5° from a cleavage-plane orientation, but little influence was noted for randomly oriented scratches or those which deviated from a cleavage-plane orientation by ～ 10° or greater.     

A numerical fracture analysis of indentation into thin hard films on soft substrates

In this paper, finite element simulations of spherical indentation of a thin hard film deposited on a soft substrate are carried out. The primary objective of this work is to understand the mechanics of fracture of the film due to formation of cylindrical or circumferential cracks extending inwards from the film surface. Also, the role of plastic yielding in the substrate on the above mechanics is studied. To this end, the plastic zone development in the substrate and its influence on the load versus indentation depth characteristics and the stress distribution in the film are first examined. Next, the energy release rate J associated with cylindrical cracks is computed. The variation of J with indentation depth and crack length is investigated. The results show that for cracks located near the indenter axis and at small indentation depth, J decreases over a range of crack lengths, which implies stability of crack growth. This regime vanishes as the location of the crack from the axis increases, particularly for a substrate with low yield strength. Finally, a method for combining experimental load versus indentation depth data with simulation results in order to obtain the fracture energy of the film is proposed.     

The effects of thin compressive films on indentation fracture toughness measurements

Thin compressive films have been shown to decrease the lengths of radial cracks produced by a Vickers indentation in a variety of non-metallic materials. The intrinsic stress of submicrometre thick films deposited by reactive ion beam sputtering was measured by a cantilever technique. The change in the apparent indentation fracture toughness of the coated material was correlated with film thickness and stress, indentation load, and the nature of the substrate.     

In situ observation of crack propagation in ESP (engineered stress profile) glass

Important features of the ESP (engineered stress profile) glasses are the crack arrest and multiple cracking phenomena that occur even in an unstable stress field. In this work a detailed “in situ” observation of crack observation and analysis was performed with the aim to examine crack propagation in detail and relate it to the residual stress field produced by ion exchange and to the final mechanical performances of the material. The results showed that the peculiar residual stress field with a maximum below the surface is responsible for the formation of a multitude of stable cracks on the tensile surface of the glass that evolved into through-thickness flaws. The propagation within the material is limited by the increasing compressive residual stress, which also leads to kinking of the cracks in a direction parallel to the surface. The observed fracture phenomena are also responsible for a shielding effect that makes the measured failure resistance of ESP glass larger than predicted by simplistic single crack models.     

Anrißerzeugung in WC-Co-Hartmetall-Proben für die Messung des kritischen Spannungsintensitätsfaktors KIC

Precracking of WC-Co-Hardmetal-Specimens for Fracture-Toughness Testing The determination of a valid critical stress intensity factor K_IC requires an extremely sharp, well defined initial crack. Methods producing such a crack are well known for metallic materials, but they often can not be used with brittle materials, like cemented carbides or ceramics. Their low fracture toughness makes a controlled crack growth under pure tensile stress nearly impossible. More useful are precracking methods, utilizing a stress gradient to stop the crack at defined depth. A very simple methods uses the indentation of a hardness tester to produce a semi-elliptical surface crack, interfered with residual stresses. For different areas of application and specimen geometries, bridge indentation, wedge indentation and composite bending method produce cracks with a straight front. Also under cyclic loading, under tensile as well as under compressive stress, the creation of a sharp precrack, applicable in K_IC measurement, is possible.     

Fracture mechanics analysis of thin coatings under spherical indentation

Spherical indentation of a thin, hard coating bonded to a thick substrate is investigated. The bending of the coating over the softer substrate induces concentrated tensile stresses on the lower and upper coating surfaces, from which transverse cracks may ensue. This work is primarily concerned with ring cracks originating from the top surface of the coating. In-situ indentation tests are carried out on a model glass/polycarbonate bi-layer, with the coating thickness and the indenter radius being the main test variables. As the coating thickness is decreased, the critical load to initiate ring cracks progressively departs from that associated with a critical surface stress, the effect that increases with increasing the indenter radius. A fracture mechanics approach in conjunction with the FEM technique is used to elucidate the onset of cylindrical ring cracks in thin-film bi-layer structures due to spherical indentation. The analysis, conducted as a function of the coating thickness and the indenter radius, reveals the existence of bending-induced compression stress regions ahead of the crack tip, which tend to shield the crack or increase the fracture resistance. The specific behavior is dictated by a complex interplay between the contact radius, a, the coating thickness, d, and the crack length, c. An interesting manifestation of this shielding mechanism is that when the coating surface contains flaws of various sizes, small flaws in this population may be more detrimental than large ones. Incorporation of this aspect into the analysis led to a good correlation with the experimental results. In the limit case of point-load, a closed-form, approximate solution for the stress intensity factors and the critical loads is obtained. This solution constitutes a lower bound for the critical loads, and is furthermore directly applicable to finite size indenters provided da. In the limit c/d/to0, a failure stress criterion may be used irrespective of the ball radius, r. The analysis in this case reveals that decreasing either d/r or the coating/substrate modulus ratio tend to favor ring cracking over radial type cracking. The transition between these two failure modes is identified explicitly as a function of the system parameters.     

Orientation dependence of fracture toughness measured by indentation methods and its relation to surface energy in single crystal silicon

Fracture toughness of silicon crystals has been investigated using indentation methods, and their surface energies have been calculated by molecular dynamics (MD). In order to determine the most preferential fracture plane at room temperature among the crystallographic planes containing the 〈001〉, 〈110〉 and 〈111〉 directions, a conical indenter was forced into (001), (110) and (111) silicon wafers at room temperature. Dominant {110}, {111} and {110} cracks were introduced from the indents on (001), (011) and (111) wafers, respectively. Fracture occurs most easily along {110}, {111} and {110} planes among the crystallographic planes containing the 〈001〉, 〈011〉 and 〈111〉 directions, respectively. A series of surface energies of those planes were calculated by MD to confirm the orientation dependence of fracture toughness. The surface energy of the {110} plane is the minimum of 1.50 Jm⁻² among planes containing the 〈001〉 and 〈111〉 directions, respectively, and that of the {111} plane is the minimum of 1.19 Jm⁻² among the planes containing the 〈011〉 direction. Fracture toughness of those planes was also derived from the calculated surface energies. It was shown that the K _IC value of the {110} crack plane was the minimum among those for the planes containing the 〈001〉 and 〈111〉 directions, respectively, and that K _IC value of the {111} crack plane was the minimum among those for the planes containing the 〈011〉 direction. These results are in good agreement with that obtained conical indentation.     

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.     

CYCLIC LOADING BEHAVIOUR OF SODA-LIME SILICATE GLASS USING INDENTATION CRACKS

Abstract— Cyclic loading behaviour of soda-lime silicate glass was studied using Vickers indentation flaws. Glass bars were indented in air using a load of 9.8 N. Some samples were annealed in order to remove the indentation residual stress field. Both as-indented and annealed specimens were subjected to static and cyclic bending tests in a water environment using a four-point bending configuration. The influence of maximum stress on lifetime was considered. Crack propagation was examined by fractography and fracture patterns were similar to those observed in static fatigue. Characteristic fracture markers were seen on samples subjected to cyclic load. Experimental results were compared with theoretical predictions which were obtained on the basis of typical sub-critical crack growth behaviour. Precise determination of crack shape and residual stress factors were shown to play an important role in lifetime predictions.     

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.     

Residual stress effects in sharp contact cracking

A detailed strength analysis for brittle surfaces containing dominant flaws produced under elastic-plastic indentation loading is presented. The condition for failure is formulated in terms of stress intensity factors representing driving forces associated with applied tension and residual indentation fields. Incorporation of the second of these components depresses the equilibrium applied stress-crack size function; this depression is accentuated at small crack size, such that the function passes through a maximum. Depending on the relative intensity of the residual indentation field, the starting size of the median cracks, as determined from Part 1 of this study, may lie on either side of this maximum: large cracks, i.e. those starting beyond the maximum, fail spontaneously from an unstable branch of the applied stress curve; small cracks undergo precursor stable growth to a critical depth at the stress maximum before failing. Observations of median crack growth in annealed and tempered soda-lime glass discs taken to failure in biaxial flexure confirm the existence of an energy barrier to crack instability. The important implications of these manifestations of the residual indentation field in predicting strength degradation characteristics for prospective adverse contact conditions are discussed for test pieces subjected to various imposed surface stress states.     

Growth and coalescence of two collinear indentation cracks in glass

Subcritical growth and coalescence of two collinear cracks of different lengths were investigated using small Knoop indentation cracks in glass. Indentation cracks subjected to bending in water showed anomalous crack growth in terms of the stress intensity factor, K_I. The crack growth velocity, dc/dt, was initially high, decreased and thereafter increased with increasing K_I. The effective stress intensity factor, K_I,eff, was calculated by adding a term describing the state of residual stress to explain this anomalous growth. Before crack coalescence, a large crack showed a crack velocity higher than expected from the coalescent crack. The coalescent crack velocity increased with K_I,eff and the slope of dc/dt−K_I,eff curves differed from that for a single crack, depending on the crack length.     

Crack tip constraint correction applied to probabilistic fracture mechanics analyses of floating production, storage and off-loading vessels

Revision 4 of the British Energy R6 document: “Assessment of the integrity of structures containing defects” provides methods to allow for loss of crack tip constraint for shallow weld flaws. The document also provides methods to estimate upper-bound values of the through thickness residual stress distribution for a range of common weld joint configurations. The present paper presents approaches to modify the R6 Option 1 failure assessment diagram (FAD) for loss of crack tip constraint pertaining to primary and non-uniform residual stress. The modified FAD was formulated for probabilistic fracture mechanics analyses of semi-elliptical surface cracks located at transverse deck welds of floating production, storage and off-loading vessels designed to operate in the North Sea. The objective was to study the influence on the failure probability of modifying the FAD for constraint and allowing for non-uniform residual stress. Another objective was to study the influence of constraint correction on the combined fatigue and fracture failure probability for the vessels subjected to wave loading.The results demonstrate clearly the importance of correcting for crack tip constraint pertaining to both primary and secondary stress and to allow for non-uniform residual stress for shallow surface flaws of known crack heights. However, in combination with fatigue crack growth the effects become less prominent as the failure probability is governed by the uncertainty in the parameters of the crack growth relationship and the long-term stress distribution.     

Fracture and fracture toughness of stoichiometric MgAl2O4 crystals at room temperature

The fracture toughness and path of stoichiometric spinel (MgAl₂O₄) crystals were determined at 22 °C for key low-index planes by double cantilever beam, as well as fractography of flexure specimens failing from either machining or indentation flaws. These results are compared with other single and polycrystalline MgAl₂O₄ fracture toughness values measured by various techniques, as well as single crystal versus polycrystal results for other materials. Evaluation of experimental and theoretical results shows (1) the fracture toughness of the spinel {110} plane is only a limited amount (e.g. 6%) higher than for the {100} plane (1.2 MPa m^1/2), (2) fractography of machining flaw fracture origins was the most effective source of K _IC results, and (3) caution must be used in applying fracture toughness techniques to single crystals. Cautions include accounting for possible effects of elastic anisotropy (especially for double cantilever beam and probably double torsion tests), the nature of failure-initiating flaws (especially for notch-beam tests), and the frequent lack of symmetric plastic deformation and fracture (especially for indentation techniques).Retired.     

Application of an indentation method to the fracture mechanics study of a polycrystalline graphite

None of the conventional indentation techniques are applicable to carbon and graphite materials for determining fracture mechanics parameters because of the difficulty in introducing well-defined median/radial cracks. A novel indentation method is proposed in this work for fracture mechanics studies and then applied to a polycrystalline graphite fracture. The most prominent advantage of the indenter designed is that the residual stresses beneath the indentation impression, which prevail in conventional indentation methods (Knoop and Vickers indentations) and lead to crucial difficulties in fracture mechanics analysis, are negligibly small. This makes possible a quantitative study on the microstructural interaction between the indentation-induced micro-flaw and the natural intrinsic flaws of the material. The dependence of flexural strength of a polycrystalline graphite on the indentation-induced surface flaw size is also discussed by examining the microstructural scaling transition of fracture origin from the indentation-induced to the intrinsic flaws with diminishing indentation surface flaw. An important role of the Mrozowsky micro-crack system in the scaling transition is emphasized.