Cracked Brazilian disc specimen subjected to mode II deformation

The centrally cracked Brazilian disc specimen has been used by many researchers to study mode I and mode II brittle fracture in different materials. However, the experimental results obtained in the past from this specimen indicate that the fracture toughness ratio (K_IIc/K_Ic) is always significantly higher than the theoretical predictions. It is shown in this paper that the increase in the ratio K_IIc/K_Ic can be predicted if a modified maximum tangential stress (MTS) criterion is used. The modified criterion takes into account the effect of T-stress in addition to the conventional singular stresses. The fracture toughness ratio K_IIc/K_Ic is calculated for two brittle materials using the modified criterion and is compared with the relevant published experimental results obtained from fracture tests on the cracked Brazilian disc specimen. A very good agreement is shown to exist between the theoretical predictions and the experimental results.     

Comparison of Interlaminar Fracture Toughness in Unidirectional and Woven Roving Marine Composites

This paper investigates the effect of fibre lay-up and matrix toughness on mode I and mode II interlaminar fracture toughness (G_Ic and G_IIc) of marine composites. Unidirectional and woven roving fibres were used as reinforcements. Two vinyl ester resins with different toughness were used as matrices. Results from both modes showed toughness variation that is consistent with matrix toughness. Values of G_Ic were not significantly influenced by fibre lay-up except at peak load points in the woven roving/brittle-matrix composite. Each peak load point, caused by interlocked bridging fibres, signified the onset of unstable crack growth. For unidirectional specimens, crack growth was stable and G_Ic statistically more reliable than woven roving specimens, which gave fewer G_Ic values due to frequent unstable crack growth. Mode II tests revealed that, except for crack initiation, G_IIc was higher in woven roving composites. This was due to fibre bridging, perpendicular to the crack growth direction, which encouraged stable crack growth and increased energy absorption. Mode II R-curves were obtained for the woven roving specimens. These R-curves provide additional information useful for characterising delamination resistance. The paper concludes that composites with woven roving fibres show similar mode I delamination characteristics to the unidirectional composites; but their mode II delamination characteristics, after crack initiation, are quite different.     

Critical values of stress intensity factor in mode II fracture of cementitious composites

The problem of mode II of brittle matrix composites is considered. After a short discussion of the present knowledge and a review of test results, the importance of fracture toughness in mode II is stressed. The test results presented concern both modes of fracture, and obtained values of stress intensity factorsK _Ic andK _IIc are discussed, taking into consideration the results of observations on SEM micrographs. It is suggested that the fracture toughness of concretelike materials should be expressed as a combination of mode I and II characteristics.     

Experimental and numerical investigation of cracked chevron notched Brazilian disc specimen for fracture toughness testing of rock

The cracked chevron notched Brazilian disc (CCNBD) specimen has been suggested by the International Society for Rock Mechanics to quantify mode I fracture toughness (K_Ic) of rock, and it has also been applied to mode II fracture toughness (K_IIc) testing in some research on the basis of some assumptions about the crack growth process in the specimen. However, the K_Ic value measured using the CCNBD specimen is usually conservative, and the assumptions made in the mode II test are rarely assessed. In this study, both laboratory experiments and numerical modeling are performed to study the modes I and II CCNBD tests, and an acoustic emission technique is used to monitor the fracture processes of the specimens. A large fracture process zone and a length of subcritical crack growth are found to be key factors affecting the K_Ic measurement using the CCNBD specimen. For the mode II CCNBD test, the crack growth process is actually quite different from the assumptions often made for determining the fracture toughness. The experimental and numerical results call for more attention on the realistic crack growth processes in rock fracture toughness specimens.     

G̃c and R-curve fracture toughness values for aluminum alloys under plane stress conditions

The effect of specimen geometry and subcritical crack growth on the nonlinear energy fracture toughness, $\text{G}\text{?}{}_{\mathrm{c}}$, has been examined for thin, center-cracked sheets of 2024-T3 and 7075-T6 aluminum alloys. The procedure followed was to independently vary the specimen length, L, width, w, andd crack length-to-specimen width ratio and to determine the toughness both at the onset of subcritical crack growth and at the initiation of unstable fracture. Comparisons were also made with the R-curve toughness, G_R, evaluated at unstable fracture from which it was found that both $\text{G}\text{?}{}_{\mathrm{c}}$ and G_R displayed the same trend of change with geometrical variables, with $\text{G}\text{?}{}_{\mathrm{c}}$ consistently higher than G_R. When the nonlinear energy fracture toughness was evaluated at the onset of subcritical crack growth, it was found that the geometry dependence essentially disappeared.Scanning electron microscopic examination of some typical fracture surfaces showed that stable crack growth was accompanied by a gradual change of fracture mode from plane strain to plane stress. An analysis of possible errors in the experimental procedure showed that the scatter observed in $\text{G}\text{?}{}_{\mathrm{c}}$ values was not due to experimental errors, but apparently due to inhomogeneities in the materials. Several techniques were also introduced for the purpose of more directly incorporating crack growth into the $\text{G}\text{?}{}_{\mathrm{c}}$ determination, but it was found that they did not cause significant variation in the toughness values.     

Relationship between KIc and plane-strain tensile ductility and microscopic mode of fracture

In most structural steels, the critical plane-strain stress-intensity factor, K_Ic, increases markedly with increasing test temperature. Because of this transition behavior with temperature and the inherently high fracture toughness of many steels, very thick specimens must be tested to determine valid K_Ic values. The large size of these specimens and the cost of conducting the tests minimize the usefulness of this procedure as a research tool for analyzing the fracture behavior of steels under plane-strain conditions. Therefore, as part of a long-range program to obtain K_Ic values from small specimens and to extend linear-elastic fracture mechanics to the region of elastic-plastic fracture mechanics, the Research Laboratory investigated the relationship between K_Ic and ordinary tensile material properties for four steels ranging in yield strength from 80 to 250 ksi (552–1720 MN/m²).The results showed that, for these steels, the variation of K_Ic with temperature was similar to the variation of the plane-strain tensile ductility with temperature. Scanning electron micrographs showed that the increase in the plane-strain stress-intensity factor for unstable crack extension, K_Ic, with increasing temperature could be related to changes in the microscopic mode of fracture at the crack tip. That is, at temperatures below the fracture-toughness transition temperature, the mode of fracture was cleavage, whereas at temperatures well above the transition-temperature region, the fracture mode was ductile tear. In the transition-temperature region, a gradual change in fracture mode from cleavage to ductile tear occurred at the tip of the fatigue crack in the K_Ic specimens.Scanning electron micrographs of the fracture-initiation region in the plane-strain tensile-ductility specimens showed that the increase in plane-strain tensile ductility with increasing temperature for steels ranging in yield strength from 80 to 250 ksi was accompanied by a change in the microscopic mode of fracture. The change in the microscopic mode of fracture in the plane-strain tensile-ductility specimens was similar to the change observed in the crack-initiation region in the K_Ic specimens. That is, the microscopic mode of fracture in the plane-strain tensile-ductility specimens gradually changed from cleavage at cryogenic temperatures to ductile tear at room temperature. Thus, it is suggested that the increase in K_Ic with increasing temperature is caused by an increase in the plane-strain tensile ductility with increasing temperature and that this increase in ductility is related to a change in the microscopic mode of fracture from cleavage to ductile tear.     

Mode II fracture mechanics properties of wood measured by the asymmetric four-point bending test using a single-edge-notched specimen

Using a single-edge-notched specimen of spruce, an asymmetric four-point bending test was conducted to obtain the mode II fracture toughness G_IIc and critical stress intensity factor K_IIc, and the test method was numerically and experimentally analyzed. A three-point bend end-notched flexure test was also conducted and the results were compared with those of the asymmetric four-point bending tests. The crack length had a small influence on the load/loading-line displacement relationship in the asymmetric four-point bending test, so it was difficult to determine the value of G_IIc, which requires the measurement of loading-line displacement. In contrast, the value of K_IIc obtained by two tests was similar when the initial crack length ranged from 0.7 to 0.85 times the depth of the specimen. These results show that the asymmetric four-point bending test is a promising means of determining K_IIc.     

Effects of thermomechanical processing on strength and toughness of Fe - 12Ni reactive metal alloys at 77 K

Thermomechanical processing (TMP) was evaluated as a method of strengthening normally tough iron-12 nickel-reactive metal alloys at cryogenic temperatures. Five iron-12 nickel alloys with reactive metal additions of aluminium, niobium, titanium, vanadium, and aluminium plus niobium were investigated. The primary evaluation was based on the yield strength and fracture toughness at 77 K. At 77 K, a yield strength of 1.3 GPa (187 ksi) with a corresponding K_Icd toughness of 243 MPa m^{$\text{1}\text{2}$} (221 ksi in^{$\text{1}\text{2}$}) was achieved with an iron-12 nickel-0.5 aluminium alloy which had undergone a 300 K rolling followed by annealing at 800 to 900 K. This represents the highest combination of cryogenic strength and toughness observed in iron-nickel alloys.     

Investigation of wood fracture toughness using mode II fracture (shearing)

The test results of fracture toughness for three wood species, such as pine, alder and birch are presented. Examination of fracture toughness is carried out using mode II fracture (shearing). Values of the stress intensity factor,K _IIc, are determined for the three main anatomic directions of wood. Microstructural tests of particular wood species, performed on specimens along the three main anatomic directions of wood, are discussed. Qualitative relationships are found to exist between the microstructure of wood and the obtained values of the stress intensity factor,K _IIc.     

A review of fatigue crack growth in high strength aluminum alloys and the relevant metallurgical factors

The results of 22 different investigations of cyclic crack growth, principally on the 2024-T3 and 7075-T6 alloys, but including results for unalloyed and other 2-, 5-, 6-, and 7-thousand series alloys have been examined and compiled with a view to separating metallurgical effects from other factors. The various crack growth measurements show good agreement when the comparisons involve the same $\text{R-}\text{value}$, environment and cyclic frequency. Both the 2024-T3 and 7075-T6 alloy can display widely different rates of growth for the same $\text{ΔK-}\text{value}$. The highest growth rates are for tests in humid air, the lowest growth rates for tests in dehydrated air with high cyclic frequencies. These extremes point to a moisture assisted corrosion process capable of producing a 20-fold increase in the growth rate at low $\text{ΔK-}\text{levels}$.Crack growth rate-$\text{ΔK}$ measurements have also been converted into S-N curves for cracked members. These curves illustrate the influence of flaw size, stress range, $\text{R}$ and $\text{K}{}_{\mathrm{c}}$ on the cyclic life of the 7075-T6 and 2024-T3 grades. The S-N curves show that the cyclic life of 2024-T3 is about 3 × that of 7075-T6 in laboratory air, about 5 × that of 7075-T6 in humidified air, and 10 × that of 7075-T6 if $\text{ΔK}$ is in proportion to the yield strength. Finally, recent studies of the mechanisms of cyclic growth and other observations bearing on the contribution of metallurgical factors are examined. Effects associated with composition, heat treatment, small amounts of cold work, hard particles and inclusions, grain boundaries, the dislocation substracture produced by cyclic straining, and slip offsets are discussed.     

Fatigue crack propagation from a crack inclined to the cyclic tensile axis

Cyclic stresses with stress ratio R = 0.65 were applied to sheet specimens of aluminium which have an initial crack inclined to the tensile axis at angles of 30°, 45°, 72° or 90°. The threshold condition for the non-propagation of the initial crack was found to be given by a quadratic form of the ranges of the stress intensity factors of modes I and II. The direction of fatigue crack extension from the inclined crack was roughly perpendicular to the tensile axis at stress ranges just above the threshold value for non-propagation. On the other hand, at stress ranges 1.6 times higher than the threshold values the crack grew in the direction of the initial crack. The rate of crack growth in the initial crack direction was found to be expressed by the following function of stress intensity factor ranges of mode I, K₁, and mode II, K₂: $\text{dc}\text{dN}\text{= C(K}{}_{\mathrm{eff}}\text{)sum}$, where $\text{K}{}_{\mathrm{eff}}\text{= [K}{}_1{}^4\text{+ 8K}{}_2{}^4\text{]}{}^{\mathrm{<mtext>1</mtext><mtext>4</mtext>}}$. This law was derived on the basis of the fatigue crack propagation model proposed by Weertman.     

Fracture toughness characterization of several aluminum alloys in semi-brittle fracture

A method has recently been developed for determining a nonlinear fracture toughness parameter defined by the relation $\text{G}\text{?}{}_{\mathrm{c}}\text{=}\text{C}\text{?}\text{G}{}_{\mathrm{c}}$ where G_c is the critical elastic strain energy rate as defined by Irwin. The $\text{C}\text{?}$ term is a function of the nonlinearity of the load-displacement test record and has been evaluated using the three parameter Ramberg-Osgood approach, although other curve fitting techniques could be applied as well. The method is quite straightforward and is applicable to plane stress, plane strain and mixed mode testing although only plane stress conditions are considered in this paper. For the case of a linear load-displacement record $\text{C}\text{?}\text{→ 1}$ and $\text{G}\text{?}{}_{\mathrm{c}}$ reduces to the linear elastic result.The toughness parameter $\text{G}\text{?}{}_{\mathrm{c}}$ has been evaluated for a number of high strength aluminum alloys and compared with published G_c values for these materials. The tests were conducted on center-cracked sheets of 2014-T6, 2024-T81, 7075-T6 and 7475-T61 aluminum alloys under conditions of varying specimen geometry and displacement gage length. It was found that the values of $\text{G}\text{?}{}_{\mathrm{c}}$ obtained from displacement readings with a gage length of 2 in. generally agreed with published values of $\text{G}{}_{\mathrm{c}}\text{=}\text{K}{}_{\mathrm{c}}{}^2\text{E}$. The $\text{G}\text{?}{}_{\mathrm{c}}$ values were found to vary inversely with gage length and a/w ratios. The variation in values for $\text{G}\text{?}{}_{\mathrm{c}}$ is of the same order of magnitude as the scatter in published values for G_c. However, $\text{G}\text{?}{}_{\mathrm{c}}$ appears to be less sensitive than G_c to changes in a/w.     

The prediction of KIc from tensile data

A theory of fracture toughness is developed which is based on the Dugdale crack model. Work hardening is considered. By using the stress-strain curves as input data, $\text{K}{}_{\mathrm{Ic}}$ values are predicted for a wide range of materials including uranium alloys, beryllium, aluminum, a nickel-cobalt alloy, and a titanium alloy. The calculated values agree exceptionally well with the experimental values. Plastic-zone size (including a qualitative estimate of shape) and stress and strain in the plastic zone are also predicted.     

A study of the size-effect on plastic energy dissipation and toughness in 2024-T3 aluminum alloy sheets

The plastic energy dissipation before crack growth initiation and during stable crack growth was determined in centercracked thin sheet specimens of 2024-T3 aluminum alloy with different width and crack length-to-width ratios. The plastic energy dissipation rate versus stable crack growth curve was found to be approximately linear, but the slope decreased considerably with increase in crack length. No correlation was observed between plastic energy dissipation rate and the linear toughness ($\text{G}\text{?}{}_{\mathrm{c}}$), the nonlinear energy toughness ($\text{G}\text{?}{}_{\mathrm{c}}$) or the $\text{R-}\text{curve}$ toughness ($\text{G}{}_{\mathrm{R}}$). The role of net section yielding on the decrease in stable crack growth and toughness values in small specimens is discussed.     

Fracture behavior of as-cast pearlitic nodular iron

The fatigue crack propagation and fracture toughness behavior of an ASTM A536, as-cast, pearlitic nodular iron with a bull's-eye structure was studied. The material had an ultimate strength of 76 ksi, a yield strength of 59 ksi, and an elongation of 1.6%. Fracture toughness tests were conducted on compact tension specimens with thicknesses of 0.30, 0.50, 0.70, and 1.00 inches. The conditional fracture toughness, K_Q, was found to be insensitive to the specimen thickness in the above range and to have a value of approximately 30 ksi-in^1/2. The dependence of the fatigue crack growth rate, da/dN, on the stress intensity factor, δK, was determined for stress ratios of 0.1, 0.3, 0.5, and 0.7. At the same °K level, the da/dN rates were higher for the higher stress ratios. The parameters, C and n, of the Paris equation, da/dN=C(δK)ⁿ were determined for each stress ratio. Near-threshold tests were also conduced for the stress ratio of 0.1. The threshold stress intensity factor, δK_TH, was found to be in the range of 6.3 to 7.7 ksi-in^1/2. A statistical model was used to calculate the agreement of the results of two duplicate fatigue crack growth tests.     

Screening for fracture toughness using the sharp notch tension test

Correlations are shown between the plane strain fracture toughness, K_Ic, and the notch tensile/yield strength ratios, NTS/YS, for 2124-T851 alloy. Over 100 data points were available in each of the three conventional testing directions. Results indicate that the sharp notch tension test could have reduced by 50% the more expensive K_Ic testing with a high degree of confidence based on proposed minimum K_Ic values. Little difference was shown in examining the toughness in various locations within a large 2219-T851 plate. However, specimen size effects are shown in these alloys.     

A new method of determining the stress intensity factor K from isochromatic fringe loops

This paper describes the four parameter method of analysis for determining the stress intensity factor K. Dynamic photoelastic isochromatic fringe patterns associated with cracks propagating in centerpin loaded, eccentric-pin-loaded and crack-line-loaded SEN specimens of Homalite 100 were recorded. Data was obtained for tests over a range of crack velocities from arrest to the terminal velocity of 14,900 in. sec (378 m sec).Six measurements describing the size and shape of the experimental isochromatic loops were used to determine the stress intensity factor K by employing a comparison function to match analytical and experimental results. The analytical isochromatic loops were generated with a Westergaard stress function of the form $\text{Z(z) =}\text{K}\text{√2πz}\text{{1 + β(}\text{z}\text{a})}$ and a superimposed normal stress σ_Ox=αK|√2πz which acts parallel to the direction of crack extension. Results were obtained by the computer program (FRACTURE) for different values of the four parameters to give 8925 analytical fringe loops. Another computer program (SEARCH) was used to find a small group of solution which given very low values of the comparison function f_c. The final solution which contains the value of K was obtained from the small group by selecting the most consistent solution.The results obtained for Homalite 100 show that K_min and K_k are nearly the same and that ? increases abruptly from 0 to about 10,000 in./sec (254 msec) for modest increases in K above 400 psi √in. (4.4 × 10⁵$\text{Nm}{}^{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$). Further increases in crack velocity require significant increases in K until terminal velocity is     

Interlaminar shear fracture of chopped strand mat glass fibre-reinforced polyester laminates

The interlaminar shear fracture of chopped strand mat glass fibre-reinforced polyester laminates has been studied both experimentally and analytically. Lap shear (double-grooved) specimens were used to measure the interlaminar shear strength and the cracking mechanism was studied using photomicrography. The finite element method was used to calculate the stress distribution along the shear surface and the mixed-mode stress intensity factors K_I and K_II. The length of the shear surface was found to have a significant effect on the results. Based on the experimental and analytical results, the validity of the British Standard for GRP pressure vessels (BS4994, 1973) was evaluated and the critical stress intensity factors K_Ic and K_IIc for this material were estimated.     

Evaluation of Fracture Parameters by Double-G,Double-K Models and Crack Extension Resistance for High Strength and Ultra High Strength Concrete Beams

This paper presents the advanced analytical methodologies such as Double- G and Double - K models for fracture analysis of concrete specimens made up of high strength concrete (HSC, HSC1) and ultra high strength concrete. Brief details about characterization and experimentation of HSC, HSC1 and UHSC have been provided. Double-G model is based on energy concept and couples the Griffith's brittle fracture theory with the bridging softening property of concrete. The double-K fracture model is based on stress intensity factor approach. Various fracture parameters such as cohesive fracture toughness (K_Ic^c), unstable fracture toughness (K_Ic^un) and initiation fracture toughness (K_Icⁱⁿⁱ) have been evaluated based on linear elastic fracture mechanics and nonlinear fracture mechanics principles. Double-G and double-K method uses the secant compliance at the peak point of measured P-CMOD curves for determining the effective crack length. Bi-linear tension softening model has been employed to account for cohesive stresses ahead of the crack tip. From the studies, it is observed that the fracture parameters obtained by using double - G and double - K models are in good agreement with each other. Crack extension resistance has been estimated by using the fracture parameters obtained through double - K model. It is observed that the values of the crack extension resistance at the critical unstable point are almost equal to the values of the unstable fracture toughness K_Ic^un of the materials. The computed fracture parameters will be useful for crack growth study, remaining life and residual strength evaluation of concrete structural components.