Effects of finite notch width on the fracture of chevron – notched specimens

The chevron notched three-point bend test specimen is often used for measuring the fracture toughness of brittle materials such as ceramics. Specimen sizes are often very restricted when testing advanced materials due to limited volume of material available or high material costs. Since the minimum chevron notch width is limited by the size of the cutting wheels or wire saw used to produce it, as the sample size gets small enough, the notch width becomes large in relation to the sample size. It is shown via finite element analysis that the notch width has an important effect on the stress intensity factors of short cracks. The minimum in the normalized stress intensity factor versus crack length is lost, rendering the usual analysis of the experimental results invalid and contributing greatly to decreased fracture stability of such specimens. Previous analytical and numerical studies do not take into account the width of the chevron notch. Based on the calculations, a guideline to permissible notch widths is introduced. This revised version was published online in July 2006 with corrections to the Cover Date.     

R-curve behavior in fracture of notched porous ceramics

Notched specimens of porous silicon carbide (SiC) with porosity 37% were fractured under four-point bending. A single edge notch with six depths ranging from 0.1 to 2.8 mm was introduced to the specimen with a height of 7 mm. The fracture of specimens with a notch depth of 0.1 mm did not start from the notch, but from the intrinsic defect. The size of the non-damaging notch is about 0.1-0.2 mm and roughly equal to the size of SiC particles. When the notch depth was larger than 0.4 mm, the fracture started from the notch for all specimens. The record of the strain gage glued on the compression surface of the specimen as a function of the load showed nonlinearity before reaching the maximum load. The critical stress intensity factor was nearly constant for crack initiation from the notch. The resistance curve was constructed by estimating the crack length from the compliance change of the specimen, and was used for determining the maximum load point in bending tests. Fractographic observations showed the fracture path along the binder phase between silicon particles.     

Size dependence of concrete fracture energy determined by RILEM work-of-fracture method

The paper analyzes the size dependence of the fracture energy of concrete obtained according to the existing RILEM recommendation proposed by Hillerborg and based on the work-of-fracture method of Nakayama, Tattersal and Tappin, in which the energy dissipated at the fracture front is evaluated from the measured load-displacement curve. The analysis is based on the size effect law proposed by Baant, which has been shown to be applicable to the size ranges up to about 1:20 and apply in the same form for all specimen geometries. The analysis utilizes the previously developed method for calculating the R-curve from the size effect, and the load-deflection curve from the R-curve. The R-curve is dependent on the geometry of the specimen. The results show that the fracture energy according to the existing RILEM recommendation is not size-independent, as desired, but depends strongly on the specimen size. This dependence is even stronger than that of the R-curve. When the specimen size is extrapolated to infinity, the fracture energy according to the RILEM recommendation coincides with the fracture energy obtained by the size effect method. It is also found that, in fracture specimens of usual sizes, the pre-peak contribution of the work of the load to the fracture energy is relatively small. Finally, as a by-product, the analysis also verifies the fact that, in three-point bend fracture specimens, the fracture energy according to the RILEM definition is dependent on the notch depth.     

Fracture toughness measurement by cylindrical specimen with ring-shaped crack

A method for measuring the plane strain fracture toughness of metals by means of cylindrical specimen in tension with axi-symmetrical ring-shaped crack is discussed. Owing to the fact that the crack tip of such a specimen is closer to ideal plane strain state, the K_1c value measured is effective and reliable. This investigation has fairly satisfactorily solved the problems of crack prefabrication, experimental technique, data processing and requirements for specimen dimensions.In both safety evaluation and life estimation of engineering components by linear elastic fracture mechanics, it is necessary to measure the fracture resisting parameter—fracture toughness under plane strain. According to the ASTM-E399-74 standard[1], when measuring the fracture toughness K_1c values of medium and low strength steels with a standard compact tension specimen or three-point bending specimen, it is necessary to use specimens of large dimensions, great tonnage fatigue testing machine and universal testing mechine. Naturally, this presents great difficulties to the investigation and application of fracture mechanics and it is precisely for the purpose of overcoming these difficulties that we have studied the method of measuring the plane strain fracture toughness by a cylindrical specimen in tension with axi-symmetrical ring-shaped crack. This method has fairly satisfactorily solved the problems of crack prefabrication, experimental technique, data processing and requirements for specimen size. Owing to the fact that the field around the crack tip of such a specimen is closer to ideal plane strain state, the results obtained are values smaller than those by using compact tension and three-point bending specimens and are more reliable fracture resisting constants for materials in linear elastic fracture mechanics analysis. Moreover, this method is more practical and economical because no expensive large fatigue testing machine is needed and the specimen size is small.     

Validity requirements of circumferentially notched tensile specimens for the determination of the interfacial fracture toughness of coatings

A simple method was developed for evaluating the interfacial fracture toughness of coatings on substrates using circumferentially notched tensile (CNT) specimens. Mild steel cylindrical substrates of 0°, 15°, 30°, 45° and 60° notch angles with electroplated nickel were tensile tested. A well defined pre-crack was introduced at the interface for the quantitative evaluation of adhesion. In situ acoustic signals and scanning electron microscope were used to analyze the crack initiation and propagation. Finite element analyses were used to evaluate the critical interface energy release rate. The size of the plastic zone was determined for different notch angles to validate application of the linear elastic approach in determining the interfacial fracture toughness. The validity requirements have been proposed for this specimen, considering the yield strength of the coating and substrate, pre-crack position, notch angle and plastic zone size. The obtained interfacial fracture toughness values using CNT specimens was found to be very close to the values obtained by others using standard specimens.     

Determination of the fracture properties of metallic materials using pre‐cracked small punch tests

In this paper, the use of pre‐cracked small punch test (p‐SPT) miniature specimens to obtain the fracture parameters of a material is presented. The geometry of the specimens used was square of 10 × 10 mm with a thickness of 0.5 mm. An initial crack‐like notch was created in the SPT specimens by means of a laser micro‐cutting technique. In order to obtain the fracture parameters from p‐SPT specimens three different approaches have been considered here. The first approach is based on the crack tip opening displacement concept, the second is based on the measure of the fracture energy using the area under the load–displacement curve for different crack sizes, and the third approach is based on the direct numerical simulation of the p‐SPT specimen and the numerical calculation of the J‐integral. In order to study the crack initiation in these p‐SPT specimens, several interrupted tests and the subsequent scanning electron microscope analysis have been carried out. The results indicate that p‐SPT specimens can be used as an alternative method for determining the fracture properties of a material in those cases where there is not enough material to undertake conventional fracture tests. For these p‐SPT specimens, the multi‐specimen method for the determination of the fracture energy is the most promising approach. The results indicate that this small specimen size allows the value of the material toughness, under low constraint conditions to be obtained.     

纯Ⅰ型加载条件下有机玻璃中心切口圆盘断裂的尺寸相关性

采用直槽式和尖槽式中心切口圆盘试件,对有机玻璃在纯Ⅰ型准静态加载条件下的断裂行为进行了实验研究.结果表明,中心切口圆盘试件的切口形状对断裂行为和断裂韧度的测试结果有显著的影响.直槽切口偏离理想裂纹,裂纹起裂始于切口端部的角点,实测的断裂韧度值偏高且具有尺寸相关性;尖槽切口接近理想裂纹,裂纹起裂始于尖角的顶点,实测的断裂韧度不存在尺寸相关性,即是材料常数.     

Notch fracture toughness of high-strength Al alloys

In this study, the notch fracture toughness (NFT) of high-strength Al alloys was examined by a non-standardized procedure. The NFT is defined as the critical notch stress-intensity factor (NSIF) K_ρ,c, which is determined by using several methods of analysis and computing. A set of specimens with different notch root radii made from overaged 7xxx alloy forging was selected. The influence of the notch radius on the fracture toughness of the material was considered. It was found that the notch radius strongly affects the fracture behavior of forged 7xxx alloy in overaged condition. The notch fracture toughness was higher than the fracture toughness of a cracked specimen and increased linearly with notch radius. The critical notch radius was related to the spacing of intermetallic (IM) particles which promote an intergranular or transgranular fracture mechanism according to their size. It appeared that ductile transgranular fracture generated by the formation of dimples around dispersoids and matrix precipitates was predominant which indicates that intense strains are limited to a much smaller zone than the coarse IM particles spacing. This double mechanism is also operate for crack propagation of ductile fatigue. The nature and morphology of IM particles exert significant effects on the rate of fatigue crack growth and fracture toughness properties.     

Instrumented impact testing of polyethersulphone

The impact behaviour of polyethersulphone has been studied using a specially constructed instrumented impact testing machine. This machine is of the pendulum type and the samples are fractured in three-point bend loading. It is shown that accurate force/deformation curves can be obtained, in spite of complications due to flexural vibrations of the test sample. Measurements were made on both sharp-notched and blunt-notched specimens over a range of crack lengths. It was found that the sharp-notched samples could be analysed in terms of fracture toughness, G _C, whereas the blunt-notched samples corresponded to a constant critical stress at the root of the notch. The importance of multiple crazes at the crack tip in bluntnotched specimens is emphasized. It is also shown that ageing reduces the fracture toughness, while on the other hand, the critical stress observed in blunt-notched specimens, which has been associated with the craze initiation stress, is not affected by ageing.     

EFFECTS OF CRACK LENGTH, NOTCH ROOT RADIUS AND GRAIN SIZE ON FRACTURE TOUGHNESS OF FINE CERAMICS

Generally, fracture toughness and fracture stress of ceramics depend on crack length, notch root radius and grain size. These three parameters are most important when assessing the integrity of structural ceramic members and developing high-performance ceramics. A new failure criterion called the process zone size failure criterion, has been proposed based on the existence of a crack-tip process zone. Using this criterion, it is shown that theoretical values are in good agreement with many test results quoted from many papers. It is concluded that this failure criterion is useful when evaluating crack length and notch root radius problems. The effect of grain size on both the fracture toughness and on the toughening mechanism is also considered.     

Fracture measurements on cement paste

This paper describes an investigation into the fracture behaviour of hardened cement paste. Notched specimens of the material were tested to failure in flexure and tension. In the initial flexural tests on beams of fixed overall depth, the stress intensity factor at failure as calculated from linear-elastic fracture mechanics appeared to be a material constant. However, further investigation showed that this factor varied with specimen size, and suggested that linear-elastic fracture mechanics and the concept of fracture toughness are not readily applicable to hardened cement paste, which would appear to be a relatively notch insensitive material whose strength is not greatly reduced by the presence of flaws. A “tied crack” model explains semi-quantiatively the observed behaviour.     

Environmental stress cracking of PVC and PVC-CPE

The fracture toughness of Polyvinylchloride (PVC) and PVC modified with 10% chlorinated polyethylene (PVC-CPE) was studied in vapour and in liquid environments by crack growth measurements on single-edge notch specimens under three-point bending at 23°C. In addition, some results obtained in air at lower temperatures are presented. The fracture toughness is quantified by a stress intensity factor leading to failure after a given loading period. It is shown that for a given slow crack growth rate at 23 °C, the environment hardly affects the fracture toughness of PVC. In contrast, the slow crack growth in PVC-CPE at 23 °C is accelerated by the presence of benzene vapour, n-octane/benzene mixtures and gas condensate. A decrease in temperature results in an increase in fracture toughness, both for PVC and for PVC-CPE. A Dugdale model to describe the craze ahead of the crack was used to analyse the observed changes in fracture toughness.     

The fracture mechanics of some graphite fibre-reinforced epoxy laminates part 2: (± 45) ns laminates

The fracture behaviour of (± 45)_ns laminates of T300/934 graphite fibre-reinforced epoxy was studied using compact tension specimens of several widths and thicknesses, centre-notched tension, and three-point bend specimens. The process of damage initiation and propagation was studied and is discussed in detail. The critical stress intensity factor was evaluated and its variation with specimen size and type is shown. On the basis of these investigations, a suitable specimen for the evaluation of meaningful fracture toughness is suggested.     

A criterion for brittle fracture in U-notched components under mixed mode loading

A failure criterion is proposed for brittle fracture in U-notched components under mixed-mode static loading. The criterion, called UMTS, is developed based on the maximum tangential stress criterion and also a criterion proposed in the past for mode I failure of rounded V-shaped notches [Gomez FJ, Elices M. A fracture criterion for blunted V-notched samples. Int J Fracture 2004;127:239-64]. Using the UMTS criterion, a set of fracture curves are derived in terms of the notch stress intensity factors. These curves can be used to predict the mixed mode fracture toughness and the crack initiation angle at the notch tip. An expression is also obtained from this criterion for predicting fracture toughness of U-notched components in pure mode II loading. It is shown that there is a good agreement between the results of UMTS criterion and the experimental data obtained by other authors from three-point bend specimens.     

Prediction of intrinsic fracture toughness for brittle materials from the apparent toughness of notched-crack specimen

In this investigation, fracture process zone model is used to establish a new relationship to predict the intrinsic fracture toughness from the apparent fracture toughness of a notched-crack specimen. The parameters needed in the proposed model are very rare, such as, the fracture process zone size of materials, the notch radius. Specimens made up of two kinds of polycrystalline alumina and one soda-lime glass with notch radii as small as a few micrometer are used to verify the predictions of this model. Besides, the results also show that fracture toughness of ceramics decreases with the decreasing of notch root radius. Under condition of the radius of crack tip is not greater than the averaged grain size, the apparent toughness can be approximately regarded as the fracture toughness of the materials.     

Effects of weld strength undermatch on fracture toughness of HAZ notched weldments in a HSLA steel

In the present work the effects of weld strength undermatch on fracture toughness of heat affected zone (HAZ) have been studied. In the investigation a high strength low alloyed steel (HSLA) with 800 MPa strength class was used, and the undermatched welded joints were made with two weld strength mismatch levels. Three-point bending test specimens with crack depth to specimen width ratio a/W ranging from 0.05 to 0.5 were extracted from the welded joints. The test results show that strength mismatching gives an obvious influence on the fracture toughness of coarse grained HAZ for the undermatched joints. The lower the weld strength mismatching, the higher the fracture toughness of the HAZ. In addition the tendency of fracture toughness change with crack depths is much the same as in previous studies on base metals or weld metals, that is, fracture toughness of the HAZ is increased with reduction of crack depths. From the measured results it shows that the macroscopically mechanical heterogeneity of the welds may have more important influence on the fracture toughness of the HAZ than the meso-heterogeneity in the reheated coarse grained HAZ. Furthermore, numerical verification indicates that the stress triaxiality at crack tip may be the essential reason for the change of fracture toughness of HAZ. It is also shown that the yield strength of HAZ determined by the limit load in the three-point bend test represents the combinative effects of HAZ and its surrounding materials. This revised version was published online in August 2006 with corrections to the Cover Date.     

The effect of initial notch shape of compact specimen on fatigue pre-cracking and fracture toughness testing

The circular notched compact specimens, along with standard specimens having straight or chevron notch are provided for fatigue and fracture toughness testings in order to study the crack observation capability during fatigue pre-cracking, skewness of the crack front, and the resulting fracture toughness K_Q. The test results indicated that circular notched specimens significantly facilitate the crack observation during fatigue testing as the cracks initiate on both surfaces of the specimen. No remarkable differences were observed on geometries of the fatigue crack front obtained and the resulting fracture toughness among these three types of specimen. The macroscopic observation of beach marks on the fracture surfaces revealed that, in the present material Ti-6Al-4V (ELI), the advance of only 1.3% of the whole crack length corresponded to the load level at which fracture toughness K_Q was evaluated.     

Effect of compressive transverse normal stress on mode II fracture toughness in polymeric composites

Effect of transverse normal stress on mode II fracture toughness of unidirectional fiber reinforced composites was studied experimentally in conjunction with finite element analyses. Mode II fracture tests were conducted on the S2/8552 glass/epoxy composite using off-axis specimens with a through thickness crack. The finite element method was employed to perform stress analyses from which mode II fracture toughness was extracted. In the analysis, crack surface contact friction effect was considered. It was found that the transverse normal compressive stress has significant effect on mode II fracture toughness of the composite. Moreover, the fracture toughness measured using the off-axis specimen was found to be quite different from that evaluated using the conventional end notched flexural (ENF) specimen in three-point bending. It was found that mode II fracture toughness cannot be characterized by the crack tip singular shear stress alone; nonsingular stresses ahead of the crack tip appear to have substantial influence on the apparent mode II fracture toughness of the composite.     

An experimental study of the critical stress intensity factor in laminated structures at high loading rates

A method for the determination of the critical stress intensity factor at high loading rates is introduced. Reflexions of stress waves, which disturb the measurement when conventional types of specimens are used, can be avoided almost entirely for a specimen made in the form of a ring. A small notch constitutes the only deviation from full circular symmetry. The ring is subjected to an interior pressure, obtained through the action of electromagnetic forces, arising from a current induced in the ring itself. As an illustration of the use of the ring-shaped specimen, an experiment is performed for determining the fracture toughness and the energy absorption before crack growth of laminated material. The ring was laminated in the radial direction. It is shown that this lamination improves the apparent fracture toughness of the ring and increases its energy absorption, in comparison with a ring of homogeneous material.     

A new method for evaluating fracture toughness of brittle materials

A new testing procedure is suggested for measuring the fracture toughness of brittle materials as superconductors and ceramics. The idea is to perform a compression test on a subcompact square specimen which contains a central hole. The presence of the hole induces a tensile stress at a certain small region attached to the hole. In this region an artificial notch is introduced such that the fracture path satisfies a pure tensile opening mode (mode I) to which the linear fracture mechanics rules apply. The stress distribution on the fracture plane guarantees a certain amount of stable crack extension. The relationship between the critical compressive load and the stress intensity factor is formulated via an available Green function along with a numerical solution (FEM with ANSYS code). The testing procedure is demonstrated with specimens made of two types of tungsten carbide which differ by their grain size only. Test results are examined via fracture toughness and strength values produced by other conventional methods and the agreement is very good. The geometry and loading direction enable the fracture toughness results to be relatively insensitive to the notch tip radius and the crack length, thereby relaxing the requirements for accurate measurements.The small size of the suggested specimen (12.70mm×12.70mm×5mm) and the avoidance of gripping interfaces provide the major cost-wise advantages.