Study on wood fracture parallel to the grains based on fractal geometry

The fracture toughness (K _IC ) parallel to the grains of five kinds of wood was tested by compact tension specimen and the profile contour analysis method was employed to measure fractal dimensions D _s of their fracture surfaces. The results show that fracture toughness parallel to the grains of various woods is different because of their textural diversity and such differences are also shown on the morphology of fracture surfaces. Furthermore, the fractal dimension D _s and fracture toughness ${K_{IC}^{TL} }$ parallel to the grains have evident direct proportional relation, and this helps to reveal the inherent relationship between fracture toughness of wood and its microstructure.     

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.     

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.     

A model for the static fracture toughness of ductile structural steel

Fracture of ductile structural steels generally occurs after void initiation, void growth and void coalescence. In order for ductile fracture of structural steels to occur, energy must be spent to induce void initiation and void growth. Therefore, fracture toughness for ductile fracture should be contributed from void initiation and void growth. On the basis of this suggestion static fracture toughness (K_IC) of ductile structural steels is decomposed into two parts: void nucleation-induced fracture toughness (denoted as K_IC.n) and void growth-induced fracture toughness (K_IC.g). K_IC.n, defined as the stress intensity factor at which voids ahead of a crack begins to form, is calculated from crack tip strain distribution and void nucleation strain distribution. In contrast, K_IC.g is determined by the void growth from the beginning of void nucleation to void coalescence. Therefore, K_IC.g relates to the void sizes and void distribution. In this paper, the expression for K_IC.g is given from the void sizes directly from fracture surfaces. The relationship between K_IC.n, K_IC.g and K_IC is expressed in the form (K_IC)²=(K_IC.n)²+(K_IC.g)². The newly developed model was applied to the fracture toughness evaluation of three structural steels (SN490, X65 and SA440), and the theoretical calculation agrees with the experimental results.     

A model for the static fracture toughness of ductile structural steel

Fracture of ductile structural steels generally occurs after void initiation, void growth and void coalescence. In order for ductile fracture of structural steels to occur, energy must be spent to induce void initiation and void growth. Therefore, fracture toughness for ductile fracture should be contributed from void initiation and void growth. On the basis of this suggestion static fracture toughness (K_IC) of ductile structural steels is decomposed into two parts: void nucleation-induced fracture toughness (denoted as K_IC.n) and void growth-induced fracture toughness (K_IC.g). K_IC.n, defined as the stress intensity factor at which voids ahead of a crack begins to form, is calculated from crack tip strain distribution and void nucleation strain distribution. In contrast, K_IC.g is determined by the void growth from the beginning of void nucleation to void coalescence. Therefore, K_IC.g relates to the void sizes and void distribution. In this paper, the expression for K_IC.g is given from the void sizes directly from fracture surfaces. The relationship between K_IC.n, K_IC.g and K_IC is expressed in the form (K_IC)²=(K_IC.n)²+(K_IC.g)². The newly developed model was applied to the fracture toughness evaluation of three structural steels (SN490, X65 and SA440), and the theoretical calculation agrees with the experimental results.     

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

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

Fracture toughness KIC analysis of Co-doped 7YSZ

Abstract

Co-doped samples of 7YSZ with Yb³⁺, Ce⁴⁺ and Nb⁵⁺ having high porosity are subject to Vickers hardness testing. Fracture toughness K_IC values are obtained by measuring linear and non-linear crack geometries. Three separate means are used to calculate the fracture toughness and to investigate the associated trends. It is confirmed that high amounts of retained tetragonal zirconia improve fracture toughness, while elevated amounts of monoclinic zirconia lower overall fracture toughness. The experimental trend for increasing K_IC is Nb:7YSZ<Yb:7YSZ<7YSZ<Ce:7YSZ; however, this trend is qualitative as the Young’s modulus values for different samples are corrected for porosity using an equation that does not generally apply to indentation techniques.     

Correlation between crack tortuosity and fracture toughness in cementitious material

This paper proposes a new technique for the evaluation of fractal dimension (D) of fracture surface and a quantitative correlation between D and fracture toughness of cementitious materials. The experimental program has been performed on compact tension (CT) specimens (600 × 525 × 125 mm) with three different aggregate sizes (d _max=4.7 mm, 18.8 mm and 37.5 mm). The fractal geometry concept is utilized in the evaluation of fracture surface roughness. To avoid indirect or destructive experimental procedures that are prohibitively laborious and time consuming, a new non-destructive technique is presented. Results of the analysis indicate that the concept of fractal geometry provides a useful tool in the fracture surface characterization. The results also suggest that the fracture toughness can be correlated with the fractal dimension of fracture surface.     

Some problems in experimental fracture mechanics

A standard procedure for the determination of fracture toughness K_IC is discussed. The insufficiency of the existing K_ic determination confidence criteria is stressed and the following criteria are proposed instead: φ_max ? 1.5%; $\text{σ}{}_{\mathrm{fr}}{}^{\mathrm{net}}\text{σ}{}_{\mathrm{0.2\; ?\; 0.8}}$, in conjunction with the old criterion $\text{P}{}_{\max }\text{P}{}_{\mathrm{Q}}\text{? 1.1}$. Determination of K_IC from P_max should be used instead of from P_Q.A method for the determination of a point on the “force-displacement” diagram corresponding to crack growth initiation is set forth. The method is based on specimen compliance tests under repeated load-relief cycles. The crack growth initiation point is used to determine both the critical crack opening and plane strain fracture toughness. The indefinite effect of the growing crack (in the ease of crack opening or Cherepanov-Rice integral calculations) is thereby eliminated. Necessity is emphasized to determine the share of the J-integral which contributes to fracture process. A method for plotting the elastic displacement diagram is proposed which allows on the basis of preliminary estimates to determine fracture toughness of small-sized specimens without using special setups. The area ratio between the plastic and elastic strain diagrams is proposed to be adopted as fracture type criterion. Certain experiments to determine crack resistance of material specimens are described and discussed.     

Fractal dimensions for fatigue fracture surfaces performed on micro- and meso-scale levels

A methodology was developed to use digital photograph fracture for calculating the integral fractal dimension and spectrum fractal dimensions for two perpendicular directions. The fractal dimension value, which was discovered by the variation of the pixel size up until the fractal dimension became unchangeable, i.e., where d _\min,d _\max are the borders of the scale level used. The effectiveness of the methodology performed showed the basis of the fracture surface analyses for Al-based alloys BS L65 and 2024 T351 (analogous to Al alloy D16T), specimens of which were tested by pull-push with imitation fretting corrosion damage of the sur- face and with four-point bending after the laser peening, respectively.     

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).     

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.     

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.     

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.     

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.     

Viscoelasticity of ceramics at high temperatures

The dependence of the fracture toughness, K _IC, on the loading rate has been calculated. On the basis of linear elastic fracture mechanics (LEFM) a strong dependence of the fracture toughness on the loading rate is obtained if subcritical crack growth is taken into account. If the subcritical crack growth parameters n and B are sufficiently small, which correspond to a high velocity of crack extension, the fracture toughness should decrease at lower loading rates. This behaviour is similar to the well-known decrease of bending strength. The experimental results for alumina containing glassy phase as a model material, however, show a maximum in a certain regime of loading rates. A model is established, which combines LEFM and the viscoelasticity, and leads to a maximum of K _IC at a certain loading rate dependent on the viscosity of the glassy phase.     

Study of the relationship between fracture toughness (J IC) and bulge ductility

A theoretical model relating fracture toughness expressed as J _IC and bulge ductility {ie71-1} for a material exhibiting linear elastic behavior at low temperature and elastic-plastic behavior at higher temperatures is proposed. This model shows a variation of J _IC with {ie71-2} for linear elastic behavior and J _IC with {ie71-3} for elastic-plastic behavior. The model contains three constants to be determined experimentally for a given material, specimen geometry and testing conditions. A case study on 1045 steel in the temperature range ?60 to 25°C confirms the validity of the model. The experimental results help in determining the size of the fracture zone ahead of the crack as well as the mechanisms for crack blunting and crack growth.     

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.     

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.     

Interaction between tensile strength failure and mixed mode crack propagation in concrete

Crack size and structure size transitions are illustrated which connect the two limit-cases of ultimate tensile strength failure (small cracks and small structures) and mixed-mode crack propagation (large cracks and large structures). The problem of mixed-mode crack propagation in concrete is then faced. By increasing the size-scale of the element the influences of heterogeneity and cohesive crack tip forces disappear and crack branching is governed only by the linear elastic stress-singularity in the crack tip region. It is proved in this way that the fracture toughness of the material is measured by a unique parameter (G_IF, G_IC or K_IC) even for the mixed-mode condition. The ratio of the sliding or Mode II fracture toughness (G_IIF, G_IIC or K_IIC) to the opening or Mode I fracture toughness depends only on the crack branching criterion adopted and not on the material features. Eventually, very controversial experimental results recently obtained on the shear fracture of concrete are explained on the basis of the above-mentioned size-scale transition.