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.     

Determination of double-Determination of double-K criterion for crack propagation in quasi-brittle fracture Part I: experimental investigation of crack propagation

The results of experimental investigations using laser speckle interferometry on small size three-point bending notched beams and using photoelastic coating and the strain gauges on very large size compact tension specimens of concrete are presented in detail. The investigations showed that there exists a stage of stable crack propagation before unstable fracture occurs. The results are in agreement with other researchers' investigations using moire interferometry, holographic interferometry, dye-impregnation method and microscope. Further detailed study shows that the three different states, i.e., crack initiation, stable crack propagation and unstable fracture can be distinguished in the fracture process in concrete structures. In order to predict the crack propagation during the fracture process in quasi-brittle materials a double-K criterion is proposed. The double-K criterion consists of two size-independent parameters. Both of them are expressed in terms of the stress intensity factors. One of them reflects the initial cracking toughness, denoted with Kⁱⁿⁱ, which can be directly evaluated by the initial cracking load, P_ini, and the precast crack length, a₀, using a formula of LEFM. The other one refers to the unstable fracture toughness, denoted with K^un, which can be obtained inserting the maximum load, P_max, and the effective crack length, a, into the same formula of LEFM. The values of the two parameters, K _Ic ⁱⁿⁱ and K _Ic ^un , obtained from the small size three-point bending notched beams and the large size compact tension specimens show that K _Ic ⁱⁿⁱ and K _Ic ^un are size-independent. Evaluating with the K-resistance curves obtained from the same test data, it is found that the proposed double-K criterion is equivalent to it in basic principle, but, the double-K criterion can be applied more easily than the K-resistance curve. Finally, as a practical example, the application of the double-K criterion to the prediction of the crack propagation in a concrete dam is discussed.     

A new method to estimate the plane strain fracture toughness of materials

Although the testing method for fracture toughness K_IC has been implemented for decades, the strict specimen size requirements make it difficult to get the accurate K_IC for the high‐toughness materials. In this study, different specimen sizes of high‐strength steels were adopted in fracture toughness testing. Through the observations on the fracture surfaces of the K_IC specimen, it is shown that the fracture energy can be divided into 2 distinct parts: (1) the energy for flat fracture and (2) the energy for shear fracture. According to the energy criterion, the K_IC values can be acquired by small‐size specimens through derivation. The results reveal that the estimated toughness value is consistent with the experimental data. The new method would be widely applied to predict the fracture toughness of metallic materials with small‐size specimens.     

Effect of size on plasticity and fracture toughness

The effect of thickness and width of CT specimens on the plastic zone size has been investigated. The investigation also examines the applicability of the various approaches to fracture toughness measurements such as ASTM E399 K_Ic, J_Ic, R-curve and a new procedure of K_Ic determination proposed recently, to a steel which has medium strength and which undergoes pop-in type unstable crack extension during the toughness testing. The results show that in CT specimens with a constant aspect ratio prepared from a given material and loaded to a given stress intensity factor, the plastic zone size decreases, as the specimen width increases; on the other hand, the thickness has only a comparatively small effect on the plastic zone size. The new procedure of K_Ic determination is verified with experiments on specimens with width to thickness ratio of about 50 and it gives a size independent K_Ic value in specimens whose thickness is 4.5 times less than that required by ASTM E399. The new procedure gives a meaningful value of K_Ic in a situation where all other methods such as ASTM E399 K_Ic, J_Ic and R-curve approach are observed to be inapplicable.     

On the fracture toughness evaluation in weldments of a maraging steel rocket motor case

Fracture toughness of the weld joints of the maraging steel rocket motor case obtained from the limited Compact Tension (CT) specimens are found to be invalid due to the measured crack lengths through the thickness of the specimens exceeding 10% of the initial crack length. This paper proposes an indirect method to evaluate the pre-crack length of the CT specimen from the recorded load versus crack mouth opening displacement data. The Chauvenet’s criterion is applied. After confirming the initial crack size and other validity conditions, the evaluated fracture toughness is designated as the plane-strain fracture toughness (K_IC).     

Determination of double-K criterion for crack propagation in quasi-brittle fracture, Part II: Analytical evaluating and practical measuring methods for three-point bending notched beams

In this paper, an attempt is made to determine the double-K fracture parameters K _Ic ⁱⁿⁱ and K _Ic ^un using three-point bending notched beams. First, based on the knowledge from extensive investigations which showed that the nonlinearity of P-CMOD curve is mainly associated with crack propagation, a linear asymptotic superposition assumption is proposed. Then, the critical effective crack length a is analytically evaluated by inserting the secant compliance c into the formula of LEFM. Furthermore, an analytical result of a fictitious crack with cohesive force in an infinite strip model was obtained. The double-K fracture parameters K _Ic ⁱⁿⁱ and K _Ic ^un as well the critical crack tip opening displacement CTOD_c were analytically determined. The experimental evidence showed that the double-K fracture parameters K _Ic ⁱⁿⁱ and K _Ic ^un are size-independent and can be considered as the fracture parameters to describe cracking initiation and unstable fracture in concrete structures. The testing method required to determine K _Ic ⁱⁿⁱ and K _Ic ^un is quite simple, without unloading and reloading procedures. So, for performing this test, a closed-loop testing system is not necessary.     

Investigation of fatigue and fracture behaviour of sensitized marine grade aluminium alloy AA 5754

In the present study, fatigue and fracture characteristics of sensitized marine grade Al‐Mg (AA 5754) alloy are experimentally evaluated. Received alloy is sensitized at temperatures of 150°C (SENS50) and 175°C (SENS75) for 100 hours. Fracture parameters, K_Ic and J_Ic, are experimentally evaluated. Slow strain rate tensile tests at a crosshead speed of 0.004, 0.006, and 0.01 mm/min; fatigue crack growth tests at load ratios (R = P_min/P_max) of 0.1, 0.2, and 0.5; and low cycle fatigue tests at four strain amplitudes of (0.3‐0.6)% are performed for SENS50 and SENS75 alloys. Relatively lower magnitude of fracture toughness values are observed for SENS75 specimen. Severe degradation in tensile properties, fatigue crack growth characteristics, and low cycle fatigue lives are observed for SENS75 samples. Extended finite element method is adopted to simulate the elasto‐plastic crack growth during fracture toughness evaluation. Scanning electron microscopy (SEM) is used to understand the failure mechanism of sensitized alloys.     

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.     

On the use of Brazilian disc specimen for calculating mixed mode I-II fracture toughness of rock materials

The centrally cracked Brazilian disc specimen has been used frequently in the past for investigating mixed mode I-II fracture toughness in rock materials. However, a review of the available test results reveals that the conventional fracture criteria like the maximum tangential stress criterion always underestimate the mixed mode I-II fracture toughness data obtained from the Brazilian disc specimen. In this paper, a generalized maximum tangential stress criterion which takes into account the effects of the three fracture parameters K_I, K_II and T-stress is used for predicting the mixed mode fracture toughness data available in the literature for several types of rock materials tested with the Brazilian disc specimen. It is shown that the generalized maximum tangential stress criterion provides significantly improved predictions for the experimental results.     

Fracture-induced photon emission of aluminium oxide and its application to fracture mechanical investigations

Mechanically-stimulated luminescence is generated during sub-critical crack growth prior to macroscopic bending fracture of sintered alumina, fusion-cast Al₂O₃, sapphire, and ruby. At similar toughness, K _Ic, the measured intensity increases with the hardness of the tested specimens, it does not depend on the macroscopic fracture strength.     

An insight into mode II fracture toughness testing using SCB specimen

The effect of friction forces between the test specimen and its bottom supports on the mode II fracture toughness values obtained using the semicircular bend (SCB) specimen is investigated. First, a number of experiments were conducted on SCB specimen in order to determine the mode II fracture toughness of polymethyl methacrylate (PMMA) according to the conventional approaches available in the literature. Three different types of supports that have been frequently employed by researchers in recent years were used to evaluate the effect of support type on the fracture loads. It was found that the friction forces between the supports and the SCB specimen have a significant effect on the value of mode II fracture toughness measured using the SCB samples. Then, the specimen was simulated using finite element method for more detailed investigation on the near crack tip stress field evolution when friction forces increase between the supports and the SCB specimen. The finite element results confirmed that the type of support affects not only the stress intensity factors K_I and K_II but also the T‐stress. The experimental and numerical results showed that the use of the crack tip parameters available in literature for frictionless contact between the supports and the SCB specimen can result in significant errors when the mode II experiments are performed by using the fixed or roller‐in‐grove types of supports.     

Ein einfaches Verfahren zur Bestimmung gültiger Bruchzähigkeitswerte von Hartmetallen

A Simple Method of Determining Valid Fracture Toughness Data of Cemented Carbides From a comparison of published data it follows that a valid determination of the fracture toughness of cemented carbides depends on the use of samples containing sharp cracks. It is shown that using the technique of controlled fracture experiments sharp cracks of a given length can be introduced easily and reproducibly into bend specimens. A new evaluation method permits the fracture toughness to be calculated without knowing the crack length if the compliance of the pre-cracked specimen is measured. The K_Ic values determined in this way are characterized by a very small scatter and agree well with data from the literature which were obtained from specimens of similar composition. A comparison of the flaw size calculated from K_Ic and the bend strength to the failure size detected in fractographic studies shows very good agreement.     

Study of fracture toughness evaluation of FRP

Using the fibre reinforced plastics (FRP) laminates consisting of glass chopped strand mat and unsaturated polyester resin, experiments were conducted under various conditions in order to determine the fracture toughness for crack instability. Crack growth was judged not by cracking of the resin matrix but by break of the glass fibres. The crack front was considered to be located in the section which was cracked through the 90% of the specimen thickness. Crack extension resistance (R-curves) thus obtained did not significantly vary with specimen thickness and initial crack length, but depended greatly on specimen configurations, compact tension (CT) and centre-cracked tension (CCT) specimens. The R-curve for a CT specimen was steeper than the one for a CCT specimen, which is quite contrary to the tendency for metals. It was deduced that the instability fracture toughness calculated from the maximum load on a load-deflection diagram, K _max, was scarcely affected by specimen thickness, initial crack length and specimen geometry (i.e. loading configuration), and therefore could be regarded as a material constant of the FRP used.     

Numerical analysis of the Edge Crack Torsion test for mode III interlaminar fracture of composite laminates

A detailed numerical analysis of the Edge Crack Torsion test was performed to verify its adequacy for the mode III interlaminar fracture characterization of composite laminates. A new data reduction scheme based on specimen compliance was proposed. Three-dimensional finite element analyses including a cohesive damage model were performed in order to evaluate the accuracy of perceived G_IIIc values obtained with the proposed method. Despite some degree of crack length dependency of perceived G_IIIc, acceptable errors could be achieved within a certain crack length range, which is thus recommended for experimental tests.     

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.     

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.     

On Improvement of Methods for Experimental Determination of Strength Characteristics of NPP Component Materials

The methods for experimental determination of strength characteristics as per applicable standards have been reviewed. For some structural steels used in NPP facilities, the influence of loading parameters and specimen geometry are allowed for during the assessment of static fracture toughness (K_Ic, J_Ic). Recommendations are given on the setting of cycling conditions for fracture toughness testing of standard specimens with and without crack-guiding lateral grooves. The authors substantiate the applicability of the Master Curve method to determination of fatigue strength of small specimens with subsequent use of the results for calculating brittle fracture resistance of reactor pressure vessel materials in the welded joint.     

Determination of double-K criterion for crack propagation in quasi-brittle fracture, Part III: Compact tension specimens and wedge splitting specimens

This paper shows how the double-K fracture parameters K _Ic ⁱⁿⁱ and K _Ic ^un can be determined for concrete using CT-specimens and wedge splitting specimens. The experimental results collected from the fracture tests the very large size CT-specimens and small size wedge splitting specimens carried out by many researchers are utilized to investigate the characters of the obtained double-K fracture parameters K _Ic ⁱⁿⁱ and K _Ic ^un . It was found that the double-K fracture parameters K _Ic ⁱⁿⁱ and K _Ic ^un determined from fracture tests on the large size CT-specimens are size-independent. And the values of K _Ic ⁱⁿⁱ and K _Ic ^un determined from small size wedge splitting specimens with same dimensions are independent of the relative preformed notch length a₀/D. However, when the dimensions of small size wedge splitting specimens change from 150×150×150 mm³ to 450×450×450 mm³, the values of K _Ic ⁱⁿⁱ and K _Ic ^un slightly depend on the heights of the specimens and do not depend on the thickness of the specimens.     

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     

Deformation and fracture of cork in tension

Various properties related to the deformation and fracture of cork in tension were experimentally determined, including the Young's modulus, the stress and strain at fracture and the fracture toughnessK _Ic. The transverse isotropy of cork implies that there are three independent systems of mode I crack propagation andK _Ic was measured for each. The mechanisms of deformation and fracture were identified by SEM microscope observation ofin situ deformation and of the fracture surfaces and crack paths. Two fundamental mechanisms of fracture occur: crack propagation along the lateral cell walls in non-radial tension, withK _Ic = 94±16 kPam^1/2 and crack propagation by breaking the cell walls in radial tension withK _Ic=125±14 kPam^1/2. In radial tension, local fractures that do not propagate due to crack stopping were observed which lead to serrations in the tensile curves for that direction. The strain to fracture in this direction is considerably larger than in the perpendicular (non-radial) directions.