Influence of specimen geometry on determination of double-K fracture parameters of concrete: a comparative study

Comparative study on analytical method, simplified method and weight function approach for determination the double-K fracture parameters using three-point bend and compact tension tests specimen geometries is presented in the paper. The input data required for numerical calculations are obtained using Fictitious Crack Model. The study reports that the double-K fracture parameters computed depends on factors such as initial-notch length/depth ratios, specimen geometry and size-effect. In addition, it is demonstrated that the use of weight function will further improve the computational efficiency without loss of accuracy.     

Influence of specimen geometry and size-effect on the <Emphasis Type="Italic">K</Emphasis><Subscript><Emphasis Type="Italic">R</Emphasis></Subscript>-curve based on the cohesive stress in concrete

Comparative study for determining the K _R -curves associated with the cohesive stress distribution for complete fracture process for two standard specimen geometries i.e., three-point bending test and compact tension test specimen geometries of concrete using analytical method and weight function approach is reported in the paper. The laboratory size specimen (100 ≤  D  ≤  400 mm) with initial-notch length/depth ratios 0.3 and 0.5 are considered in the investigation. The load-crack opening displacement curves for these specimens are obtained using well known version of Fictitious Crack Model (FCM). It is found from the numerical results that the weight function method improves computational efficiency without any appreciable error. The stability analysis on the K _R -curves and the influence of specimen geometry and the size-effect on the K _R -curves, the CTOD-curves and the process zone length during crack propagation of complete fracture process are also described.     

Determining double-K fracture parameters of concrete for compact tension and wedge splitting tests using weight function

The paper presents use of universal form of weight functions for determining the double-K fracture parameters and on compact test and wedge splitting test specimens. The proposed method enables to obtain a closed form expression of cohesion toughness of concrete specimens. A comparison with existing analytical method shows that the weight function method for determination of double-K fracture parameters yields results without any appreciable error. Significant influence of initial notch to depth (a₀/D) ratio on the double-K fracture parameters is not also observed. Finally, a possible definition of brittleness of concrete using double-K fracture parameters is proposed.     

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.     

A comparative study on five approaches to evaluate double-K fracture toughness parameters of concrete and size effect analysis

The current paper presents a comprehensive comparison of double-K fracture toughness parameters of concrete evaluated using experimental method and four existing analytical methods. Fracture tests were carried out on compact tension wedge splitting specimens with various depths varying from 200 mm up to 1000 mm. In the analytical calculation, depending on the relationship between critical crack tip opening displacement and the abscissa value of turning point on bilinear softening curve, two different distributions of cohesive stress are considered along crack extension. Results show that four available analytical calculations yield almost the same values of double-K fracture toughness parameters and agree well with those obtained from the experiment, which confirms the consistency of five approaches. Size effect was discussed, including unstable fracture toughness, initiation fracture toughness, critical effective crack length, the length of critical fracture process zone and critical crack tip opening displacement.     

The virtual crack extension method for evaluation of J- and

The equation for evaluating the nonlinear fracture mechanics parameters J- and Ĵ-integrals are derived using the virtual crack extension method. The validity of the equations derived here are checked by solving several numerical examples, that is, the J-integral analyses of compact tension specimen and three-point bend specimen, and the Ĵ-integral analysis of centrally cracked plate. Reasonably good agreement is found between the virtual crack extension method and the line integral method.     

Measurement of Specific Fracture Energy and Surface Tension of Brittle Materials in Powder Form

Studies of the influence of specimen geometry and size–effect on the K _R –curves and the related fracture parameters were carried out by the authors (Kumar and Barai 2008b). The present paper is a supplementary contribution and reports interesting results related to the effect of the loading condition and size–effect studies on the K _R –curves associated with the cohesive stress distribution for complete fracture process, the double–K fracture parameters, the CTOD–curves and the process zone length using two different loading conditions (i.e., three–point bending test and four–point bending test). The laboratory size specimen with initial–notch length/depth ratios 0.3 and 0.5 are considered in the work. The load–crack opening displacement curves for these loading conditions are obtained using well known version of fictitious crack model.     

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.     

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.     

Measurement of mode I and mode II rock dynamic fracture toughness with cracked straight through flattened Brazilian disc impacted by split Hopkinson pressure bar

In order to find an effective and convincing method to measure rock dynamic fracture toughness for mode I and mode II, cracked straight through flattened Brazilian disc specimens of marble, which were geometrically similar for three size, were diametrically impacted by split Hopkinson pressure bar on the flat end of the specimen with three load angle respectively. History of stress intensity factors (K_I(t) for opening mode I, and K_II(t) for sliding mode II), mode mixture ratio (K_I(t)/K_II(t)), as well as mode I and mode II dynamic fracture toughness at crack initiation (K_Id and K_IId) were determined with the experimental–numerical method. It is found that there is a unique size effect for dynamic fracture test with the specimens, the mode mixture ratio is not solely determined by load angle (the angle between load direction and crack line) as in the static loading; the pure mode II load angle is 19° for the ?50 mm specimen, however it is 10° for the ?130 mm and ?200 mm specimens; the mode II load angle decreases with increment of specimen size. Realization of pure mode II is justified by the mode mixture ratio approaching zero, it can be realized under certain load angle and loading rate for the specimen of specified size. K_IId is generally greater than K_Id. Both K_Id and K_IId increase with increment of specimen size, and this trend for K_IId is more remarkable than that for K_Id.     

Numerical Analysis of the Three Point Bend Impact Test for Polymers

The three point bend impact test is analysed by employing the finite volume method. Numerical modelling was necessary to enhance understanding of the test and to obtain dynamic correction functions, which are convenient to calculate K and G from measured time to fracture. A simple model of the three point bend test and a more sophisticated model, which included contact effects, were analysed. A good fit with experiments was found when using the contact model. The anvils were found to be important only at a late stage in the test. Several test parameters were varied to investigate their influence on the dynamic correction function. The contact stiffness was found to have an important influence on the shape of the dynamic correction function. Due to the nonlinear contact stiffness the impact velocity also affects the dynamic correction function. For a polymer specimen and a steel striker the specimen width and the specimen material were found to have only a small influence on the dynamic correction function. The dynamic correction function for G was found to exhibit higher oscillations than the dynamic correction function for Kas expected, and hence the former is a more sensitive parameter.     

Evaluation of the two‐parameter fracture criterion for various crack configurations made of 7075‐T6 aluminium alloy using finite‐element fracture simulations

For many years, a two‐parameter fracture criterion (TPFC) has been used to correlate and predict failure loads on cracked metallic fracture specimens. The current study was conducted to evaluate the use of the TPFC on a high‐strength aluminium alloy, using elastic‐plastic finite‐element (FE) analyses with the critical crack‐tip‐opening angle (CTOA) fracture criterion. In 1966, Forman generated fracture data on middle‐crack tension, M(T), specimens made of thin‐sheet 7075‐T6 aluminium alloy, which is a quasi‐brittle material. The fracture data included a wide range of specimen half‐widths (w) ranging from 38 to 305 mm. A two‐dimensional FE analysis code (ZIP2D) with a “plane‐strain core” option was used to model the fracture process with a critical CTOA chosen to fit the M(T) test data. Fracture simulations were then conducted on other M(T), single‐edge‐crack tension, SE(T), and bend, SE(B), specimens over a wide range in widths (w = 19‐610 mm). No test data were available on the SE‐type specimens. The results supported the TPFC equation for net‐section stresses less than the material proportional limit. However, some discrepancies in the FE fracture simulations results were observed among the numerical analyses made on the three specimen types. Thus, more research is needed to improve the transferability of the TPFC from the M(T) specimen to both the SE(T) and SE(B) specimens for quasi‐brittle materials.     

High yield four-point bend thin film adhesion testing techniques

Novel four-point bend specimen geometries are proposed for improved test yield over standard four-point bend specimens when measuring high-strength and ultra-thin film structures. The fracture energies of both a Cu/SiN dielectric diffusion barrier interface and a high-k/metal gate (HfO₂/Pt–Ti metal bilayer) interface are reported. Four novel specimen types were evaluated and result in significantly increased test yield as compared to the standard four-point bend specimens. The modified four-point bend specimens were fabricated by altering the crystallographic orientation, width, and thickness of the beams which make up the specimen. The mechanics of the four-point bend test are discussed for each different specimen type. The increased test yield is explained in terms of the stresses which develop in the specimen during testing, the phase angle of loading experienced for each specimen type, and the anisotropic fracture properties of single crystal silicon.     

On the use of an anti‐symmetric four‐point bend specimen for mode II fracture experiments

The edge‐cracked beam specimen subjected to anti‐symmetric four‐point bend (ASFPB) loading has been conventionally used in the past for investigating the pure mode II fracture experiments in many engineering materials. However, it is shown through finite element analysis that the ASFPB specimen sometimes fails to produce pure mode II conditions. For anti‐symmetric loads applied close to the crack line, there are considerable effects from K_I and T‐stress in the ASFPB specimen. Pure mode II is provided only when the applied loads are sufficiently far from the crack plane.     

Crack resistance curves of alumina at high temperatures

Ceramic three-point bend specimens were pre-cracked in a displacement-controlled test in air at room temperature to form sharp cracks of different lengths. Critical stress intensity factors (K _lc) were then measured as a function of sharp crack length in a fast-fracture, load-controlled test at 900, 1000 and 1100° C. By means of these fast fracture tests, crack resistance curves (K _lc against crack length) were determined for two commercially pure aluminas of different grain size and for a debased alumina containing a glassy phase. The crack resistance curve for the pure, fine grained alumina proved to be flat at 900° C, as was found for room temperature. A steeply rising crack resistance was, however, observed for the pure coarse-grained alumina at 1100° C and for the debased alumina at 1000 and 1100° C. This rise in KR curves is explained by friction effects of the cracked microstructure behind the crack front for the coarse grained alumina and by adhesive forces caused by the second phase behind the crack front for the debased alumina. These facts are proved by comparison to experiments on notched specimen and by annealing experiments. From the annealing experiments the size of the adhesive zone is estimated for the debased material.The death of Dr R. F. Pabst is sadly recorded. (On leave of absence from Max-Planck-Institut für Metallforschung, Seestraße 92, 7000 Stuttgart 1, Federal Republic of Germany).     

Determination of crack tip parameters for ASCB specimen under mixed mode loading using finite element method

In this paper, a new asymmetric semicircular bend specimen (ASCB) is presented. Having more geometric parameters in asymmetric bend elements gives the opportunity of covering a wider range of K_?, K_?? and T-stress in comparison with classical SCB specimens. Finite element method is used to obtain these parameters from pure mode I to pure mode II. Extensive numerical calculations are made to get a wide range data for crack tip parameters of this specimen. It is observed that for ASCB specimens with specified geometries under pure mode II loading, one of the bottom supports can move horizontally without significant variation in Y_I. The complete sets of numerical results are obtained and can be used for verification and interpretation of future experimental results.     

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.     

Effects of notch length,specimen thickness,ply thickness and type of defect on the fracture behaviour of angle-ply graphite-epoxy composites

An experimental study was carried out on the effects of notch length, specimen thickness, ply thickness and type of defect (centre-notch or hole) on the fracture toughness of graphite-epoxy composites with lay-up sequences of 0/±45°/0 and 0/90°. Three fracture-mechanical concepts were applied: the Waddoups-Eisenmann-Kaminski (WEK) model, the Whitney-Nuismer model (point and average stress cirteria) and the K _R-curve method. An increase of notch length as well as an increase of ply thickness led to a higher toughness, whereas a change in specimen thickness did not noticeably affect the toughness. Furthermore, the hole caused a smaller strength reduction than a notch. The applicability of the above-mentioned concepts is probably restricted mainly because of the fact that they do not, or do only insufficiently, regard the damage zone near the border of the defect, if a large damage zone usually leads to larger material parameters of the investigated concepts, namely the inherent flaw size, the characteristic lengths of the point and average stress criterions and the K _R -value at fracture.     

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.     

Energy absorption and damage propagation in 2D triaxially braided carbon fiber composites: effects of in situ matrix properties

Results from an experimental program to investigate the propagation of damage and energy dissipation in 2D triaxially braided carbon fiber textile composites (2DTBC) under static conditions are reported. A methodology is presented in which classical concepts from fracture mechanics are generalized to address damage growth in an orthotropic and heterogeneous structural material. Along with results from the experimental program, a novel numerical technique that employs ideas from cohesive zone modeling, and implemented through the use of finite-element analysis, is also presented. The inputs that are required for the discrete cohesive zone model (DCZM) are identified. Compact tension specimen fracture tests and double notched tension tests were carried out to measure the fracture energy (G _Ic), and the maximum cohesive strength (σ _c), of the 2DTBC. The DCZM modeling strategy was independently verified by conducting single edge notched three-point bend tests using a modified three-point bend test fixture. The experimental and numerical analyses were carried out for two different types of 2DTBC made from the same textile architecture but infused with two different resin systems to validate the proposed methodology.