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.     

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.     

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.     

Equivalence between stress intensity factor and energy approach based fracture parameters of concrete

The paper presents numerical study and relationship between the double-K fracture parameters and the double-G fracture parameters using two standard tests. The data required for calculation is obtained using cohesive crack model. It is observed that both the corresponding parameters of the double-K fracture model and the double-G fracture model at the onset of crack initiation and unstable fracture are equivalent. This observation agrees well with experimental results available in literature. It is also found that the fracture parameters of double-K fracture criterion and double-G fracture criterion are influenced by initial notch-length/depth ratio, specimen shape, size and softening function.     

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.     

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.     

Determination of the Fracture Toughness of a Low Alloy Steel by the Instrumented Charpy Impact Test

An attempt to establish a non-empirical relationship between the Charpy V-notch energy CVN and the fracture toughness K _Ic is presented. We focus our study on the lower shelf of fracture toughness and on the onset of the ductile-to-brittle transition of a A508 Cl.3 low alloy structural steel. The methodology employed is based on the `local approach'. Brittle cleavage fracture is modelled in terms of the Beremin (1983) model, whereas the ductile crack advance preceding cleavage in the transition region is accounted for with the GTN model (Gurson, 1977; Tvergaard, 1982; Tvergaard and Needleman, 1984. Mechanical testing at different strain rates and temperatures allowed the establishment of the constitutive equations of the material in a rate dependent formulation. Numerous fracture tests on different specimen geometries provided the large data set necessary for statistical evaluation. All specimen types were modelled with finite element analysis. Special consideration was taken in order to handle the dynamic effects in the Charpy impact test in an appropriate way. The fracture toughness could be predicted from Charpy impact test results, on the lower shelf, by applying the `local approach'. In the transition region the parameters of the Beremin model were found to deviate from those established on the lower shelf. Detailed fractographic investigations showed that the nature of `weak spots' inducing cleavage fracture changes with temperature. It is concluded that the Beremin model must be refined in order to be applicable in the ductile-to-brittle transition region.     

Measuring the Size‐Independent Fracture Energy of Concrete

Abstract: The fracture energy of concrete is an important parameter in the analysis of the mechanical behaviour of concrete structures, so it is considered as a material property. However, the most universal test method for measuring the specific fracture energy of concrete (RILEM work‐of‐fracture) has been a subject of intense debate among researchers. The values have been found to vary with the size and shape of the test specimen. In this study, an experimental comparative analysis of the size‐independent fracture energy obtained by two main methods has been carried out. One of these is based on the local fracture energy model of Hu et al. The second is based on the curtailment of the tail of the P–δ curve by Elices et al. Therefore, the relationship between both methods is highlighted. It is shown that both methods give almost identical results.     

Proposal of a new concept on creep fracture remnant life for a precracked specimen

Abstract

The creep life time of a smooth specimen can be predicted using existing laws for creep deformation and steady state creep rate. When crack growth behaviour is involved, it is necessary to construct a law of creep crack growth rate to predict creep fracture life. Creep fracture life can be measured by integrating the law of creep crack growth rate. One example is the creep crack growth rate, represented by the parameter Q*. In this study, we investigated the applicability of this prediction method to creep fracture remnant life for a cracked specimen. The Ω criterion is proposed to predict creep fracture remnant life for a smooth specimen for creep ductile materials. In this study, the correlation between Q*_L derived from the paremeters Q* and Ω is investigated. The correlation between Q_L* and Ω provided a unified theoretical prediction law of creep fracture remnant life for high-temperature creep-ductile materials in the range from smooth to precracked specimens.     

Impact of particle packing mix design method on fracture properties of natural and recycled aggregate concrete

The fracture properties of four types of concrete prepared using natural coarse aggregate and recycled coarse aggregate and conventional and particle packing method (PPM) of mix design approaches are studied. The three‐point bending (TPB) test is performed using three different sizes of single edge notched beam. The fracture energy is calculated from the load‐CMOD curve obtained in the TPB test, and in this process the load‐CMOD curve is curtailed at 2% of the depth of the beam. Based on CTOD_c and w₁ relationship, appropriate softening function is used to estimate the double‐K fracture parameters. The fracture energy and fracture toughness parameters of recycled aggregate concrete (RAC) is inferior to the natural aggregate concrete (NAC). The PPM mix design improves the fracture properties of concrete in comparison to the conventional mix design approach. The fracture properties of PPM mix designed RAC are comparable to that of NAC prepared using conventional method.     

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.     

Experimentally determined key curves for fracture specimens

Crack extension during fracture toughness tests of ferritic structural steels cannot be determined from measurements of unloading compliance or electric potential change when the specimen is dynamically tested. Measurements of crack extension in fracture toughness tests are also very difficult when the test temperature is high or the test environment is aggressive. To circumvent this limitation, researchers for years have been developing key curve and normalization function methods to estimate crack extension in standard elastic-plastic fracture toughness test geometries. In the key curve method (Ernst et al., 1979; Joyce et al., 1980) a load-displacement curve is measured for a so-called `source' specimen that is sub size or has a blunt notch so that the crack will not initiate during elastic-plastic loading. The load and displacement are then converted to normalized stress-strain units to obtain a key curve that can be used to predict crack extension in geometrically similar `target' specimens of same material loaded at similar loading rates and tested under similar environmental conditions. More recently Landes and coworkers (Herrera and Landes, 1990; Landes et al., 1991) proposed the normalization data reduction technique – Annex A15 of ASTM 1820 specification – that presents an alternative to the standard E1820 unloading compliance procedure. Although the normalization method works well in many cases, it has serious drawbacks: the load, displacement and crack length at the end of the test must be measured; the prescribed functional form that is fitted to the initial and final data may not be accurate for all materials; and the iterative method of inferring crack length from the combination of the data and the normalization function is complex. The compliance ratio (CR) method developed in this paper determines key curves for predicting crack extension as follows. First, a statically loaded source specimen with the unloading compliance procedure specified in ASTM 1820. Second, the so-called CR load-displacement curve is calculated for the source specimen, which is the load-displacement record that would have been obtained if the crack had not extended. Third, non-dimensionalizing the CR load by the maximum load and the displacement by the elastic displacement at the maximum load, P ^* _i/P _max and v _i/v _{el max} from the source specimen yields the adjusted key curve. Analysis of extensive data shows that the key curve is independent of notch type, initial crack length and temperature. But it is dependent on specimen size and steel type. Assuming that the key curves of the source and target specimens are one and the same, the compliance of the target specimens are calculated with a reverse application of the compliance ratio method, and the crack length is obtained using the equations in ASTM E1820. The CR Method is found to be much simpler than the normalization method described in the Annex A15 of ASTM 1820. With the compliance ratio method, Joyce et al. (2001) successfully predicted crack extension in dynamically loaded specimens using a key curve of a statically loaded specimen.     

Thickness effect on the mode III fracture resistance and fracture path of rock using ENDB specimens

Study of the thickness effect in predicting the crack growth behavior and load bearing capacity of rock‐type structures is an important issue for obtaining a relation between the experimental fracture toughness of laboratory subsized samples and the real rock structures with large thickness. The fracture of rock masses or underground rock structures at deep strata may be dominantly governed by the tensile or tear crack growth mechanism. Therefore, in this research, a number of mode I and mode III fracture toughness experiments are conducted on edge notch disc bend (ENDB) specimen made of a kind of marble rock to investigate the effect of specimen thickness on the corresponding K_Ic and K_IIIc values. It is observed that the fracture toughness of both modes I and III are increased by increasing the height of the ENDB specimen. Also, the ratio of K_IIIc/K_Ic obtained from each thickness of the ENDB specimens is compared with those predicted by some fracture criteria, and it was shown that the minimum plastic radius (MPR) criterion is the main suitable criterion for investigating the fracture toughness ratio K_IIIc/K_Ic . Also, the effect of ENDB height on fracture trajectory of tested samples is assessed. It is shown that the crack grows curvilinearly in thicker ENDB samples and cannot extend along the crack front in small specimens.     

Determination of r‐curves of steel fiber reinforced concrete from size effect tests

Abstract

A developed size effect law for blunt fracture is used to determine the R‐Curves and related parameters of steel fiber reinforced concrete. Geometrically similar single‐edge notched beams of different sizes made of cementitious mixes at various fiber volume fractions and different maximum aggregate sizes were used for the tests. Fracture energy of concrete is identified by linear regression using the size effect law. From the experimentally calibrated size effect law, the R‐curve is obtained as the envelope of the family of fracture equilibrium curves for different specimen sizes.     

The influence of material mismatch on the evaluation of time-dependent fracture mechanics parameters

The influence of material mismatch on the stress field of uniaxial specimens and the time-dependent fracture mechanics parameters is studied in the present work. The applicability of the conventional C^* equation based on the load line displacement is re-examined by using the finite element method. It is found that under the extensive creep condition the C^* value of hard weld/soft parent metal specimen can be significantly higher than that of a single weld metal specimen, and the material mismatch has little influence on C(t) in small scale creep in the studied cases. It is proposed that the C^* formula based on the load line displacement recommended by ASTM E1457 needs to be modified to interpret the CCG behaviour of welded specimens. Candidate modification factors have been proposed.     

A direct estimate of JIc from the load versus load-line displacement record

The purpose of this study is to examine the current standard fracture toughness test procedure to determine if there could be an easier method to get a J_Ic value from the test record. The current method for determining J_Ic involves a detailed computational and construction procedure. The objective in this study is to simplify the analysis for the determination of J_Ic. The results of this study show that the load and displacement record for a fracture toughness test can be used to directly estimate a J_Q value, a provisional value for fracture toughness, J_Ic. The J value taken at the maximum load point can be used along with an adjustment factor to estimate a J_Q value. This J_Q estimate is close to the one obtained from the construction procedure of ASTM Standard E 1820. When a unit‐sized specimen is tested, that is, a specimen with a width of 50 mm and a thickness of 25 mm the maximum load point provides a direct estimate of J_Q. Other sizes require a size adjustment factor, which is simply a square root relationship between the width of the test specimen and a unit width. The proposed new method of estimating J_Q is simple in concept and requires a minimum number of calculations. It appears to produce values of J_Q which are comparable to those obtained from the ASTM E1820 construction procedure and may produce less scatter.     

Numerical prediction of notch bluntness effect on fracture resistance of SM490A carbon steel

The present work investigates the notch radius effect on fracture resistance using the finite element (FE) damage analysis based on the multiaxial fracture strain model. The damage model was determined from experimental data of notched bar tensile and fracture toughness test data using a sharp‐cracked compact tension specimen. Then, the FE damage analysis was applied to simulate fracture resistance tests of SM490A carbon steel specimens with different notch radii. Comparison of simulated results with experimental data showed good agreement. Further simulation was then performed to see effects of the specimen size, thickness, and side groove on J‐R curves for different notch radii. It was found that effects of the specimen size and thickness became more pronounced for the larger notch radius. Furthermore, it was found that without side groove, tearing modulus for notched specimens was similar to that for cracked specimens, regardless of the notch radius.     

Estimation of high‐temperature fracture parameters for small punch specimen with a surface crack

An outline of a newly proposed methodology for evaluating creep crack growth (CCG) parameters using cracked small‐punch (SP) specimens is explained. Three‐dimensional finite element analyses were performed to calculate the stress intensity factor along the crack front for a surface crack formed at the centre of a SP specimen. Effects of crack ratio, (a/t); crack aspect ratio, (a/c); and thickness of the specimen, (t), on the fracture parameters were studied. It was observed that the minimum variation of K‐value along the crack front can be achieved when a/c was 0.50 except the location very near the intersection of the crack and free surface. This condition is similar to the case of constant K‐values along the crack front of the conventional compact tension specimen. Thus, it can be argued that the SP specimen with a surface crack is a suitable specimen geometry for CCG testing. The proposed CCG test method was found to be practically applicable for the crack geometry of 0.10 to 0.30 of a/t with constant aspect ratio of 0.50. An estimation of the K and C_t‐parameter under the small scale creep condition was derived. Future work for further development of the suggested CCG testing is discussed.     

Influence of water and accelerated aging on the shear fracture properties of glass/epoxy composite

The degradation of interlaminar shear strength and shear fracture toughness of glass/epoxy composites due to uptake of distilled water and sea water has been studied. The composites were immersed in water for up to eight months at temperatures up to 70 °C. Unreinforced matrix resin samples were also immersed for periods up to 2 years. Sea water was absorbed less rapidly than distilled water. Weight gains below 1% did not influence the shear strength while higher weight gains reduced shear strength up to 25%. The loss in apparent interlaminar shear strength was uniquely related to specimen weight gain. Mode II fracture toughness, G _IIc, also decreased with increasing immersion time after an initial incubation period, but the accelerated tests were found to reduce G _IIc less than the room temperature tests at comparable weight gains.     

CTOD-R curve construction from surface displacement measurements

The construction of a fracture resistance δ–R (or J–R) curve requires the appropriate measurement of crack-tip opening displacement (CTOD) as a function of crack extension. This can be made by different procedures following ASTM E1820, BS7448 or other standards and procedures (e.g., GTP-02, ESIS-P2, etc.) for the measurement of fracture toughness. However, all of these procedures require standard specimens, displacement gauges, and calibration curves to get intrinsic material properties. This paper deals with some analysis and aspects related to the measurement of fracture toughness by observing the surface of the specimen. Tests were performed using three-dimensional surface displacement measurements to determine the fracture parameters and the crack extension values. These tests can be conducted without using a crack mouth opening displacement-CMOD or load-line displacement gauge, because CMOD can be calculated by using the displacement of the surface points. The presented method offers a significant advantage for fracture toughness testing in cases where a clip gauge is not easy to use, for example, on structural components. Simple analysis of stereo-metrical surface displacements gives a load vs. crack opening displacement curve. Results show that the initiation of stable crack propagation can be easy estimated as the point of the curve’s deviation. It is possible to determine the deviation point if the crack opening displacement measurements are close to crack tip in the plastic zone area. The resistance curve, CTOD-R, is developed by the local measurement of crack opening displacement (COD) in rigid body area of specimen. COD values are used for the recalculation with the CMOD parameter as a remote crack opening displacement, according to the ASTM standard.