Size-independent Fracture Toughness Research Articles

Determination and influential factors of fracture toughness in unidirectional laminated bamboo-composite using double cantilever beams and single-edge notched bend tests

This paper studied two testing methods for determining the matrix-dominate fracture toughness in the unidirectional bamboo laminate panels, using double cantilever beam tests and single-edge notched bend tests. For single-edge notched bend tests, an isotropic solution was proposed to calculate the fracture toughness in which only the load-CMOD curve is required. In this isotropic solution, when calculating the energy release rate G Ic by G Ic = (K Ic ) 2 /E, the modulus of elasticity E can be directly obtained from the experimental load-CMOD curves, the pre-determination of Young’s modulus E x , E y , shear modulus G xy and Poisson’s ratio υ xy , υ xy is unnecessary for orthotropic materials. The results of modulus of elasticity E, the stress intensity factor K Ic , and energy release rate G Ic using the isotropic solution were compared to those using an orthotropic solution; it revealed that the isotropic solution could be well applied to unidirectional bamboo laminate panels with errors under 2.7%. The isotropic solution for single-edge notched bend tests was also verified by comparing the results to those obtained from double cantilever beam tests; it turned out that the energy release rate values determined by the two testing methods agreed well with each other. Moreover, the influence of initial notch width, initial notch to depth, and specimen depth on the fracture toughness was investigated to put forward a practical testing method to obtain the size-independent fracture toughness of unidirectional bamboo laminate panels by single-edge notched bend specimens.

Critical assessment of the Rolfe-Novak CVN-KIC upper shelf correlation

The Rolfe-Novak correlation, was the first attempt to relate Charpy-V impact energy to a fracture mechanical material parameter. They tested 11 materials with variable yield strength, mainly in the range 1000–1300 MPa. This data was used to develop a correlation between Charpy-V notch energy and linear elastic fracture toughness KIc. The correlation is considered as base for high strength steel CVN-KIc correlations still today. The historic Rolfe – Novak fracture toughness data are here re-analyzed based on present understanding of fracture mechanics. It is shown that the original results were affected by different specimen sizes, shallow flaw effects, varying degree of plasticity and a non-systematic and non-standard engineering definition of fracture toughness KIc. The data has been re-evaluated in terms of the new size-independent fracture toughness definition KIsi, now described in ASTM E399. Based on the re-evaluation a new physically sound correlation between CVN and KIsi is determined. KIsi is shown to be close to KJIc according to ASTM E1820 for high strength steels.

An investigation of fracture properties and size effects of concrete using the ESPI technique

In order to study the size effect in concrete fracture, three-point bending tests are performed on five groups of geometrically similar concrete beams. The electronic speckle pattern interferometry (ESPI) technique is used to measure the full-field deformation of concrete beams. Crack opening displacement data, which is crucial for understanding crack initiation and the evolution mechanism, but which is not readily available through conventional measurement techniques, is obtained. Fracture parameters of five groups of concrete beams, including the critical crack opening displacements (i.e. CMODc and CTODc) and crack growth lengths (i.e. ac and ae) at the peak, fracture toughness (KIc), fracture energy (GF) and nominal strength (σN), are determined. The influences of beam depth on the fracture parameters of concrete are evaluated and discussed. The results show that the CMODc, CTODc, ac, ae, KIc and GF increase with the increase in beam depth, while σN has a decreasing trend that follows the size effect law. Size-independent fracture toughness and fracture energy are estimated and proposed.

DETERMINATION OF FRACTURE TOUGHNESS OF CONCRETE AND ROCK USING UNNOTCHED SPECIMENS

It presents a theoretical model and its associated analytical expression for determining the fracture toughness of concrete and rock using unnotched specimens. The important influence of the size of concrete aggregates and rock particles is fully considered in the proposed model, and only the peak load of small-scale unnotched specimens of concrete or rock is required. Size-independent fracture toughness can be directly determined. Furthermore, a series of fracture tests on the rock specimens with different notch lengths is conducted. Experimental results show that the fracture toughness of unnotched rock specimens obtained using the proposed model is consistent with that determined from the prefabricated specimens with a notch of 1 mm length. The fracture toughness of unnotched specimens is also consistent with that of the notched specimens based on the regression analysis method. The test results of the unnotched and notched rock and concrete specimens from other studies are further analyzed using the proposed model. The rationality and applicability of the proposed model and associated method are also verified. It provides new insights into the determination of the size-independent fracture toughness of concrete and rock by using small-scale unnotched specimens in a laboratory.

Size-dependent fracture toughness of tungsten

In order to understand the size-dependent fracture behaviour of tungsten at the microscale, micro-cantilever tests were performed on single crystalline and ultrafine grained tungsten. The elastic-plastic fracture behaviour and crack tip plasticity were found to be strongly influenced by the sample size. The smallest cantilevers with dimensions below one micron failed by pure cleavage fracture at a fracture toughness of 1.5 MPa m1/2, which agrees well with the Griffith theory for brittle fracture. With increasing specimen size crack tip plasticity was observed, leading to a successive increase in fracture toughness and crack resistance behaviour. Using scanning transmission electron microscopy and electron backscatter diffraction, dislocation densities were analysed and measured. Pronounced plastic strain gradients were found at the crack tip for an intermediate specimen size, which also showed the highest crack resistance. When further increasing the specimen size, large plastic zones were still observed but the gradients in plastic strain vanished, leading to a reduction in the crack resistance behaviour. For those samples, a size independent fracture toughness of ca. 7 MPa m1/2 was found, which is close to macroscopic literature data. Increasing the initial dislocation density in the single crystals through plastic pre-straining led to a reduced stable crack growth behaviour but did not affect the fracture toughness. Furthermore, the effect of grain boundaries on the fracture behaviour was studied by means of ultrafine grained tungsten. A fracture toughness lower than the one reported in literature was found, which is explained by the higher susceptibility to failure once a crack propagates at the micro-scale.

On the understanding of the effects of sample size on the variability in fracture toughness of bulk metallic glasses

High strength in combination with improvements in failure characteristics and associated gains in fracture toughness have placed bulk metallic glasses (BMGs) among the most damage-tolerant materials to date. Recent studies show, however, that there can be large variabilities in the mechanical performance of these alloys, particularly in their toughness, which are likely associated with sample-size effects or structural variations from differences in processing. Here, we examine the variation in fracture toughness of the Pd-based metallic glass Pd77.5Cu6Si16.5, using single-edge notched bend specimens but in two different sizes. Although all toughness results on this glass were “valid” in terms of the nonlinear-elastic fracture mechanics J-standard, i.e., one would expect a single value of the fracture toughness for this alloy, marked differences were apparent in the toughness values and failure characteristics of the differently-sized samples. Specifically, significantly larger variations in toughness values were measured in larger-sized samples, which all essentially failed catastrophically, whereas none of the smaller-sized samples failed catastrophically yet displayed far less scatter in their measured toughness. Additional in situ tests on the smaller-sized samples in a scanning electron microscope revealed stable crack growth and progressive resistance to crack extension, i.e., rising crack-resistance (R-curve) behavior. Overall, this marked transition from brittle catastrophic failure in large samples, where a size-independent fracture toughness can be measured, to non-catastrophic, more ductile (R-curve), behavior in smaller samples, the latter associated with higher toughness, is related to the distinct size-dependent bending ductility and strain-softening behavior in BMGs.

A size effect law for notched tensile strength of woven carbon/epoxy laminates

Specimen-size effect and notch-size effect on the tensile strength of woven fabric carbon/epoxy laminates are evaluated and modeled. For two different layups of [(0/90)12] and [(±45)2/(0/90)5]S, respectively, static tension tests were performed on two-dimensional geometrically similar unnotched and double-edge notched specimens scaled to three different sizes. Experimental results demonstrate that the notched strength of the woven CFRP laminates depend on the size of specimen as well as the size of notch. The ratio of notched strength to unnotched strength decreases as the length of notch increases, regardless of the size of specimen. For a given size of notch, the notch strength ratio becomes larger with decreasing size of specimen. A notch-size effect law is derived by means of the Neuber interpolation method. A specimen-size effect is embedded into the notch sensitivity parameter involved by the notch-size effect law to establish a size effect law that can cope with these two kinds of size effect. The engineering size effect law proposed can adequately describe the specimen-size effect as well as notch-size effect on the tensile strength of the woven CFRP laminates. It is also demonstrated that the size effect law allows determining the size independent fracture toughness on the basis of notched strengths of small specimens that fail in a quasi-brittle manner.

Fracture Toughness Evaluation Based on Tension-softening Model and its Application to Hydraulic Fracturing

This paper discusses the applicability of the tension-softening model in the determination of the fracture toughness of rocks, where the fracture toughness evaluated based on the tension-softening model is compared with the crack growth resistance deduced from laboratory-scale hydraulic fracturing tests. It is generally accepted that the fracture process is dominated by the growth of a fracture process zone for most types of rocks. In this study, the J-integral based technique is employed to determine the fracture toughness of Iidate granite on the basis of the tension-softening model, where compact tension specimens of different dimensions were tested in order to examine the specimen size effect on the measured fracture toughness. It was shown that the tension-softening relation deduced from the J-integral based technique allowed us to determine the specimen size independent fracture toughness K c of Iidate granite.Laboratory-scale hydraulic fracturing tests were performed on cubic specimens (up to a 10 m sized specimen), where cyclic pressurization was conducted using a rubber-made straddle packer to observe the extent of the hydraulically induced crack. The experimental results of pressure and crack length were then used to construct the crack growth resistance curve based on the stress intensity factor K. The crack growth resistance obtained from the hydraulic fracturing tests was observed to initially increase and then level off, giving a constant K value for a long crack extension stage. The plateau K value in the crack growth resistance curve was found to be in reasonable agreement with the fracture toughness K c deduced from the tension-softening relation. It was demonstrated that the tension-softening model provides a useful tool to determine the appropriate fracture toughness of rocks, which may be applicable for the analysis of the process of large-scale crack extension in rock masses.

An engineering approach to remove the specimen geometry constraint dependence of elastic-plastic fracture toughness

Constraint effects on fracture have been the subject of a number of recent studies. In this paper, the effects of constraint changes on the elastic-plastic fracture toughness values J lc are investigated and an engineering approach for constraint correction is proposed. A relationship between the conventional elastic-plastic fracture toughness, J lc, and crack tip constraint characterized by crack tip stress triaxiality, T, is derived from a modified damage criterion for ductile fracture. Then, a new parameter J sc and associated J-like criterion, J s = J sc, for ductile fracture are proposed, in which both the crack tip deformation characterized by the J-integral and the crack tip constraint characterized by stress triaxiality are included. Several experiments show that the toughness variation with specimen geometry constraint changes can effectively be removed by use of the constraint correction procedure proposed in this paper and that the new parameter J sc is a material constant independent of specimen geometry (constraint). This parameter can serve as a new parameter to differentiate the elastic-plastic fracture toughness of engineering materials, which provides a new approach to the fracture assessments of structures. It is not necessary to determine which laboratory specimen matches the structural constraint; rather, any specimen geometry can be tested to measure the size independent fracture toughness J sc. The potential advantage is clear and the results are very encouraging.

A new method to compute size independent fracture toughness values for brittle materials

Generally, linear elastic fracture mechanics (LEFM) is inadequate for fracture toughness ( K Ic ) characterizations of brittle or quasi-brittle materials such as ceramics, concretes, and rocks, because large process zones exist. In order to obtain a valid, size independent K Ic value (or to satisfy the small scale yielding criterion), huge specimen sizes are required. For this reason, a testing method based on the nonlinear tension-softening behavior has been proposed. A new computational scheme for determining size independent fracture toughness of brittle materials is presented in detail. This scheme is direct, accurate and it eliminates several numerical steps (including curve fitting and taking derivatives of fitted curves) and the associated errors from the original experimental technique. All theoretical concepts and the experimental technique of this new and more efficient method of deducing the tension-softening curve for brittle and quasi-brittle materials are presented. Results and comparisons of a fracture toughness investigation of sandstone and basalt using both tension-softening and LEFM concepts are also presented.

2. Size effect in the fracture toughness of Ogino tuff

Splitting tests were conducted using large specimens of Ogino tuff in order to investigate the process of fracture propagation and also to clarify the size effect in fracture toughness of the rock-including specifically the effects of thickness, width and height of specimen as well as that of crack length. Two types of stiff loading apparatus, a wedge type and a screw type, were used for controlling fracture propagation; and fracture toughness during the process of fracture propagation was determined with compliance calibration. From the results on size effects, a standard size of the specimen was proposed to obtain a specimen size-independent fracture toughness value in the splitting test.

A Fracture toughness criterion for concrete

Many have attempted to calculate the fracture toughness of concrete in Mode I by testing notched beam specimens. It has been observed that when K Ic is calculated from the measured values of the maximum load, the initial notch length and using the formulas developed from LEFM, its value is dependent on the dimensions of the beam. This size and geometry dependency can be attributed to slow crack growth and nonlinearity due to geometrical interlock effects. A method is suggested to calculate a size independent fracture toughness parameter. To calculate the value of K Ic according to the proposed method, inelastic displacements are extracted from the total displacements and the slow crack growth is included by incorporating crack closing-pressure. Using this constant K Ic criterion, the load vs crack mouth opening displacement and load vs deflection curves were accurately predicted for 40 beams of different sizes tested for this investigation as well as those reported by other investigators.

Determination of Fracture Toughness of a Material That Exhibits Pop-In Behavior

Abstract Fracture toughness of a material that undergoes pop-in crack extension was measured in two different heat treated conditions by a new procedure proposed in a recent publication. It is shown in this publication that the new procedure gives a size independent plane strain fracture toughness KIc value in thin and wide specimens prepared from relatively tough material. The present investigation examines the effect of width and the applicability of various approaches to fracture toughness measurement procedures, such as the new procedure, ASTM Test Method for Plane-Strain Fracture Toughness of Metallic Material (E 399), KIc, the ductile fracture toughness value JIc, and the crack growth resistance R curve, to a material that undergoes pop-in crack extension. The results show that whereas the new procedure can give a meaningful, reliable, and size independent fracture toughness even for a material that undergoes pop-in crack extension, the other methods, such as R curve, JIc, Kpop, or ASTM E 399 are inapplicable. The new procedure also shows that the K-KIc approach can be used in specimens whose thickness is 4.5 times less than that required by ASTM E 399.

A Measure for the Fracture Toughness of Cement Based Materials

It is frequently reported that the higher the strength of cement based materials, the more brittle is their behavior. It could he useful to quantitatively express the degree of brittleness. Many attempts [1–13] have been made to use linear elastic fracture mechanis (LEFM) to quantitatively express the degree of brittleness. For example, by testing notched beams one can calculate, using the formulas developed from LEFM, a quantity called fracture toughness and termedKICfrom the measured maximum load and the initial notch-length. Unfortunalely, it has been observed thatKthus calculated is dependent on the dimension of the beams. Many researchers have attempted to analyze this size dependency. Such approaches are usually quite cumbersome and are often based on expensive nonlinear finite element programs. In this paper a direct method is suggested to calculate two size-independent fracture toughness parameters from the experimental results. The method was developed based on tests on notched-beams of different mix proportions and different sizes.