A fractographic criterion for subcritical crack growth boundaries at internal fracture origins in hot pressed silicon nitride

Using the elliptic integral method, stress intensity factors (K _I) were estimated at boundaries defined by fracture features observed at various distances from internal fracture origins in H.P. silicon nitride. The fracture origins are surrounded by regions of transgranular fracture. At the outer boundaries of these regionsK _I is less thanK _IC showing that these are regions of subcritical crack growth. Regions of hummocks and depressions were observed surrounding the regions of transgranular fracture.K _I was calculated at the elliptical boundary determined by the outer edge of the nearest of these features to the fracture origin. At this boundary,K _I K _IC. Therefore, these features can be used to locate the subcritical crack growth boundary.     

Short-rod elastic-plastic fracture toughness test using miniature specimens

The standard ASTM-E399 plane-strain fracture toughness (K _IC) test requires (1) the test specimen dimensions to be greater than a minimum size and, (2) fatigue precracking of the specimen. These criteria render many materials impractical to test. The short-rod elastic-plastic plane-strain fracture toughness test proposed by Barker offers a method of testing not requiring fatigue precracking and furthermore, it appears that test specimens smaller than that stipulated by ASTM can be used to obtain validK _IC values. In this study, the use of a modified miniature short-rod fracture toughness test specimen was investigated. Our miniature short-rod specimen is approximately 7 mm long and 4 mm diameter. These mini specimens are well suited for the purpose of testing biomaterials. The value of the minimum stress intensity factor coefficient (Y _m ^* ) for the mini short-rod specimens was determined experimentally using specimens machined from extruded acrylic rod stock. An elastic-plastic fracture toughness analysis using the mini specimens gave values ofK _IC for extruded acrylic (nominally PMMA) equal to 0.67 ± 0.06 MPa m^1/2. The problem of testing non-flat crack growth resistance curve materials (such as PMMA) using the short-rod fracture toughness test method is discussed. A modification to the test procedure involving the use of aY ^* value corresponding to a short crack length is suggested as a method of overcoming this difficulty.Nomenclature a crack length - a ₀ initial crack length - a ₁ length of the chevron notch on the mini short-rod specimen - a _m critical crack length — crack length atY _m ^* - C specimen compliance - C dimensionless specimen compliance = CED - D mini short-rod specimen diameter - E Young's modulus - K ₁ stress intensity factor - K _1C plane-strain fracture toughness - K _max fracture toughness calculated usingP _max - P load applied to the test specimen during a short-rod fracture toughness test - P _c load applied to the test specimen atY _m ^* - P _max maximum load applied to the specimen during a short-rod fracture toughness test - p plasticity factor - W mini short-rod specimen width - Y ^* stress intensity factor coefficient - Y _m ^* minimum of the stress intensity factor coefficient - dimensionless crack length =a/W - ₀ dimensionless initial crack length = ₀/W - ₁ dimensionless chevron notch length =a ₁/W - _m dimensionless critical crack length =a _m/W     

Comparative study of the fracture toughness determination of a polymer-bonded explosive simulant

In this paper, a comparative study was carried out by using three-point bending, semi-circular bending, and flattened Brazilian disc tests to measure the plane-strain fracture toughness of a polymer-bonded explosive simulant. The K_IC magnitudes are 0.53 ± 0.03 MPa m^1/2, 0.50 ± 0.02 MPa m^1/2, and 0.53 ± 0.01 MPa m^1/2 respectively, showing good consistency in the results measured by different methods. Considering the difficulties in the machining and pre-crack fabrication of brittle explosives, the flattened Brazilian disc test is recommended as an alternative method for measuring the K_IC of PBX and other explosives. In addition, real-time microscopic observation of test samples was conducted by using a scanning electron microscope (SEM) equipped with a loading stage, and the fracture surfaces of samples were examined. The damage modes and the corresponding failure mechanisms were analyzed.     

Single crystal cleavage of brittle materials

Cleavage of brittle single crystals is reviewed and the historical criteria for the phenomenon are critically examined. Previously proposed criteria, including those based on crystal structure (crystal growth planes, the planes bounding the unit cell, and planar atomic packing) and crystal properties (ionic charge of possible cleavage planes, bond density, elastic modulus, and surface free energy), are found to be applicable only to particular crystals or to isostructural groups, but each lacks universal application. It is concluded that the fracture toughness (K _Ic) of the crystallographic planes is the most appropriate criterion. Measurements reveal that the cleavage toughnesses of brittle single crystals are usually about 1 MPa m^1/2 or less.Measurements of the fracture toughnesses of brittle polycrystalline aggregates are then compared to the single crystal cleavage values in those instances where reliable results are available for the same crystal structures. Polycrystalline toughnesses are consistently higher, in part because of the lack of continuity of cleavage cracks through the polycrystalline aggregates. However, the increment of toughness increase is only 1–2 MPa m^1/2. The role of grain texture or preferred crystal orientation is also addressed. It is concluded that polycrystalline aggregate toughnesses are often highly anisotropic and that the values for intensely oriented microstructures may approach those for single crystal cleavage.     

Thermodynamical approach to the brittle fracture of dry plasters

The evolution of the fracture toughness, K _lc, and fracture energy, G _lc, of set plasters was determined on notched beams as a function of sample porosity, P, and characteristic size, W. Toughness was found to decrease with decreasing crack width. For set plasters of 57.7% porosity, the lowest toughness measured was K _lc=0.13 MPa m^1/2 for a crack width of 0.2 mm. For this crack width, fracture toughness and fracture energy linearly changed with porosity: K _lc=0.5 1–1.3 P) MPa m^1/2 and G _lc= 13.47 (1–1.12 P) Jm^–2. Dense plasters were more difficult to break than porous ones. The fracture energies were affected by the velocity of the fracture propagation, which induces damaging and multicracking of the material, so that the roughly calculated chemical surface energy of set plaster was too high. After correction it was estimated to be 0.4 J m ^–2. Finally, because toughness increased with increasing sample size, it was concluded that fracture toughness and energy were not intrinsic parameters of the material. On the other hand, for our sample porosities and sizes, the reduced rupture force, F _rupt W ^–0.65 is a constant and seems to be a characteristic parameter of the mechanical resistance of set plaster beams.     

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 initiation under impact

In the first part of this paper the influence of temperature T and loading rate K_I upon the fracture toughness K_IC of structural steels is considered. A review of experimental results is presented over a wide range of loading rate and temperature in the form of the cross-sections of the constitutive surface K_INC = f(K_I,T). The hypothesis is proposed that both yield stress σ_y in uniaxial tension and fracture toughness K_IC are controlled by the same process of thermally activated movements of dislocations. Consequently, an introduction of the characteristic time t_c leads to the master plot K_IC (σ_y) in double logarithmic coordinates which is temperature and rate-independent. Such an approach provides a simple method for estimating the value of K_IC under a given set of imposed conditions (T,K?_I)₁ provided it is known for another set of imposed conditions (T,K?_I)₂.In the next part of this paper an attempt is presented to model the effect of T and K?_I on fracture toughness K_IC [15]. A model is discussed which combines correlations between critical cleavage stress σ_F, yield stress σ_y and the concept of thermally activated plastic flow from side and the local fracture criteria from the other [15]. It has been demonstrated that this approach can be useful in the proper predictions of changes of K_IC as a function of loading rate and temperature. For some steels, however, a minimum of fracture toughness is observed and typically occurs for $\text{K}{}_{\mathrm{I}}\text{? 1×10}{}^4$ MPa/pv/m/s at room temperature. The last part of this study deals with this important phenomenon [34]. It is concluded that the behavior of the constitutive surface K_IC = f(K_I,T) is highly nonlinear for steels.     

Environmental stress intensity for maraging steel

Stress intensity, K, values for 18 Ni 1800 MPa maraging steel stressed to 90% of its K _IC level and exposed to water, hydraulic oil (servo 317) and water inhibited with 0.5, 1.0, 1.5 and 2% dichromate (pH about 7.5) for various durations were determined using the modified wedge opening loading (WOL) technique. Experiments revealed that there is no appreciable deterioration in K in oil and water inhibited with 1.5% and 2% dichromate even after 25 days exposure. The threshold stress intensity is reached after 15 days in 0.5% dichromate inhibited water at 40 MPa m^1/2. Stress corrosion crack growth rate in water is about 40 times the rate in hydraulic oil. Crack path characteristics of the WOL-tested maraging steel specimens in different environments are briefly mentioned.     

The toughness of epoxy-poly(butylene terephthalate) blends

Blends containing 5% poly(butylene terephthalate) (PBT) in an anhydride-cured epoxy with three different PBT morphologies were studied. The three morphologies were a dispersion of spherulites, a structureless gel and a gel with spherulites. The average fracture toughnesses, K _Ic, and fracture energies, G _Ic, for those morphologies were 0.83, 2.3 and 1.8 MPa m^1/2 and 240, 2000 and 1150 J m^–2, respectively. These values should be compared with the values of 0.72 MPa m^1/2 and 180 J m^–2, respectively, for the cured epoxy without PBT. The elastic moduli and yield strengths in compression for all three blend morphologies remained essentially unchanged from those of the cured epoxy without PBT, namely, 2.9 GPa for the modulus and 115 MPa for the yield strength. The fracture surfaces of the cured spherulitic dispersion blends indicate the absorption of fracture energy by crack bifurcation induced by the spherulites. The fracture surfaces of the cured structureless gel blends indicate that fracture energy was absorbed by matrix and PBT plastic deformation and by spontaneous crack bifurcation. But phase transformation of the PBT and anelastic strain of the matrix below the fracture surfaces may account for most of the large fracture energy of the cured structureless gel blends.     

On the applicability of linear elastic fracture mechanics to environmental stress cracking of low-density polyethylene

The primary aim of this work was to re-examine the range of applicability of linear elastic fracture mechanics (LEFM) to environmental stress cracking of low-density polyethylene. By use of a number of specimen types and a range of specimen dimensions and loads it is shown that theK _I-c relationship is unique only at lowK _Is. The material studied showed a region of constant crack velocity which was not caused by plasticity effects or the failure of LEFM. However, crack arrest, which occurred at highK _Is or loads, was shown to be caused by ductile yielding causing the crack to blunt.     

Microstructures and fracture toughness of directionally solidified Mo-ZrC eutectic composites

Microstructures and fracture toughness of arc-melted and directionally solidified Mo–ZrC eutectic composites were investigated in this study. Two kinds of directionally solidified composites were prepared by spot-melting and floating zone-melting. Microstructure of the arc-melted composite (AMC) consists of equiaxed eutectic colonies, in which ZrC particles are dispersed. The spot-melted composite (SMC) exhibits spheroidal colony structure, which is rather inhomogeneous in size and morphology. ZrC fibers in the eutectic colonies are aligned almost parallel to the growth direction. Well aligned, homogeneous columnar structure with thin ZrC fibers evolves in the floating zone-melted composite (FZC). Texture measurement by X-ray diffractometry revealed that the growth direction of Mo solid solution (Mo_SS) in FZC is preferentially 〈100〉, while that of SMC is scattered. Fracture toughness K_q evaluated by three point bending test using the single edge notched beam method is >13 MPa m^1/2 for AMC, 20 MPa m^1/2 for SMC and 9 MPa m^1/2 for FZC. Intergranular fracture along colony boundaries is often observed in AMC. In contrast, transgranular fracture is dominant in SMC and FZC, although significant gaps caused by intergranular fracture are occasionally observed in SEM micrographs of SMC. Fracture surface in FZC is wholly flat. Pull-out of ZrC occurs owing to Mo/ZrC interfacial debonding in intergranularly fractured regions of AMC and SMC.

Coarse elongated colonies in SMC and FZC induce transgranular fracture instead of intergranular fracture. Intergranular fracture and interfacial debonding in AMC and SMC causes frequent crack deflection accompanied by ligament formation and crack branching, which is responsible for the high fracture toughness of the composites. Preferred 〈100〉 growth of Mo_SS phase in FZC leads to brittle 〈100〉 cleavage fracture associated with low fracture toughness.     

Study on cleavage fracture criteria of the quasi-brittle and micro-inhomogeneous materials

On the bases of recent achievements on the micro-mechanism of cleavage this paper analyses the inherent deficiencies of the stress intensity factor K _I which is used to evaluate the fracture toughness of quasi-brittle and micro-inhomogeneous materials. The K _I parameter can uniquely determine the field intensity ahead of a crack tip in the condition of elastic and small scale yielding (SSY). However, the K _I cannot uniquely determine the critical condition triggering the cleavage fracture in a quasi-brittle and inhomogeneous steel where the cleavage fracture process is not a direct extension of the precrack but is initiated at a variable distance from the precrack tip. The variable distances of cleavage initiations invoke varied critical values of K _I. On the bases of authors' experiments, this paper analyses the physical meaning of the local fracture stress _f, its stability and the feasibility to be used as an engineering parameter for assessing the fracture toughness.     

Fracture toughness measurement with fatigue-precracked single edge-notched beam specimens of WC-Co hard metal

The plain-strain fracture toughness of WC-8%Co hard metal, K _IC, was measured using single edge-notched beam (SENB) specimens with fatigue precrack. The fatigue precrack was introduced with compressive fatigue cycling in four-point bending at room temperature. Since stable fatigue-crack propagation was obtained from the notch tip, it was easy to control the fatigue-precrack length. A reasonable K _IC value of 13.3 MPa m^1/2 was obtained with the fatigue-precracked SENB specimens in four-point bending. The compressive fatigue-precracking technique in four-point bending was simple and convenient, and is therefore applicable to precracking in a variety of brittle materials prior to fracture-toughness measurements.     

Fracture study of a polyacetal resin

Fracture experiments have been carried out with unnotched and notched tensile specimens of a polyacetal resin at room temperature at various rates of extension. An increase of approximately 13% in yield stress was observed in the unnotched tests with increased deformation rates from 1–1000 mm min^–1, whilst strain to failure was reduced from about 85% to approximately 0.05%. In all specimens, failure appeared to have taken place by initiation of a microscopic flaw upon yielding, and this flaw then slowly grew into a critical size when catastrophic fracture set in. In the slow-growth region, the mechanism of failure was by void growth whereby the lamellar texture was transformed into a fibrillar one. However, on the rapid fracture surface, there was evidence of lamellar texture being retained, but with small voids in the stacks of lamellae, In notched fracture specimens containing sharp razor cut, a fracture toughness, K _lc, of approximately 5 MPa m^1/2 was obtained between crosshead speeds of 0.5 and 50 mm min^–1. At speeds of 500 and 1000 mm min^–1, the K _lc was reduced to 4 MPa m^1/2. In the absence of a starter crack, blunt notch fracture toughness of about 6.3 MPa m^1/2 was observed at all test speeds. In specimens with a razor cut, the slow-growth region decreased as test speed increased; this can be used to construct an R-curve.     

Microstructure and mechanical properties of hot-pressed SiC-TiC composites

Hot-pressed SiC-TiC composite ceramics with 0–100 wt% TiC have been investigated to determine the effect of composition (amount of TiC) on the elastic modulus, hardness, flexural strength and fracture toughness,K _IC. The composites exhibited superior mechanical properties compared to monolithic SiC and TiC, especially in fracture toughness,K _IC, value for 30–50 wt% TiC composite. The maximum values ofK _IC and room-temperature flexural strength were 6 MPa m^1/2 for a 50 wt % TiC and 750 MPa for a 30 wt% TiC composite, respectively. The observed toughening could be attributed to the deflection of cracks due to dispersion of the different particles. Although no third phases were detected by both TEM and XRD studies, an EDAX study and resistivity measurements indicated some possibility of solid solutions being present. The composites containing more than 30 wt% TiC, exhibited resistivity lower than 10^–3 cm which is favourable for electro-discharge machining of ceramics.     

Effects of thickness and environmental temperature on fracture behaviour of polyetherimide (PEI)

The fracture behaviour of a polyetherimide (PEI) thermoplastic polymer was studied using compact tension (CT) specimens with a special emphasis on effects of specimen thickness and testing temperatures on the plane strain fracture toughness. The results show that the valid fracture toughness of the critical stress intensity factor, K _IC, and strain energy release rate, G _IC, is independent of the specimen thickness when it is larger than 5 mm at ambient temperature. On the other hand, the fracture toughness is relatively sensitive to testing temperatures. The K _IC value remains almost constant, 3.5 MPa in a temperature range from 25 to 130°C, but the G _IC value slightly increases due to the decrease in Young's modulus and yield stress with increasing temperature. The temperature dependence of the fracture toughness, G _IC, was explained in terms of a plastic deformation zone around the crack tip and fracture surface morphology. It was identified that the larger plastic zone and extensive plastic deformation in the crack initiation region were associated with the enhanced G _IC at elevated temperatures.     

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.     

Densification and mechanical properties of WC particulate reinforced Cr3C2 matrix composites

The mechanical properties of Cr₃C₂ can be improved by adding 14–25 vol % of WC particulates through a hot-pressing process. The Cr₃C₂-20 vol % WC composite exhibits a fracture strength and fracture toughness of 883 MPa and 6.8 MPa m^1/2, respectively, which is a better than 60% increase over the monolithic Cr₃C₂(_f = 526 MPa, K _IC = 4.1 MPa m^1/2). The possible strengthening and toughening mechanisms are disscussed in terms of microstructures, fracture modes (intergranular or transgranular) and micromechanics. The microstructural evolution and fractography which were studied by scanning electron microscopy (SEM) and transmission electron microscopy (TEM) will be discussed.     

Fracture toughness of Si3N4 measured with short bar chevron-notched specimens

The short bar chevron-notched specimen was used to measure the plane strain fracture toughness of hot-pressed Si₃N₄. Specimen proportions and chevron-notch angle were varied, thereby varying the amount of crack extension to maximum load (upon which K_ic was based). The measured toughness (4.68 ± 0.19 MN m^3/2) was independent of these variations, inferring that the material has a flat crack growth resistance curve.Nomenclature a crack length - a _A crack length at arrest of unstable crack advance - a ₁ length of chevron notch at specimen surface (distance from line of load application to point of chevron emergence at specimen surface) - a ₀ initial crack length (distance from line of load application to tip of chevron) - a _R crack length at ending of stable crack extension (conversely, crack length at onset of abrupt, unstable crack advance) - B specimen thickness - H specimen half-height - K _1A stress intensity factor at arrest of unstable crack advance - K _IR stress intensity factor at end of stable crack extension (crack growth resistance) - K _IC plane strain fracture toughness - P _max maximum applied load in fracture toughness test - W specimen width - Y ^* dimensionless stress intensity factor coefficient for chevron-notched specimen - Y ^* _m minimum value ofY ^* as a function of - a/W - ₀ a ₀/W - ₁ a ₁/W     

Fracture mechanics behaviour of austenitic compacted graphite cast iron

The fracture mechanics behaviour of high-nickel austenitic compacted graphite cast iron was studied and the effects of graphite morphology, alloying elements and specimen thickness on the mechanical properties, plane stress fracture toughness, and fatigue crack growth rate were evaluated. It was found that the graphite morphology, i.e. the percentage of compacted graphite present, was the major determinant of all properties of the materials investigated. The irons with a greater amount of compacted graphite (the balance was nodular graphite in austenitic matrix) resulted in lower tensile strength, yield strength, elongation and K _c fracture toughness but higher crack-growth index values (poorer crack-growth resistance). For 25 mm thick specimens, K _c values of the austenitic compacted graphite cast irons in this study were in the range of 58–64 MPa m^1/2. This is higher than ferritic/pearlitic ductile iron of 43–53 Mpa m^1/2, and is compatible to Ni-resist austenitic ductile iron of 64.1 Mpa m^1/2. The addition of cobalt not only contributed to slightly higher values of mechanical properties, but also higher plane stress fracture toughness and better crack growth resistance. Optical microscopy, scanning electron microscopy and X-ray diffraction techniques were applied to correlate the microstructural features to the properties attained.