Fracture toughness of concrete determined on large specimens

It has often been questioned whether linear elastic fracture mechanics can be applied to describe crack propagation and failure of concrete. An important argument is that most test results are obtained on specimens too small to be representative of a material with a composite structure such as concrete. Large specimens with four different geometries have been prepared and tested. Crack length was increased under controlled conditions to at least 250 mm. It was found that fracture toughness increases initially as a crack propagates, but that a length-independent value is reached asymptotically. Within the range of accuracy, asymptotic values obtained with the four different geometries were the same. It is concluded that failure of large size concrete elements can be predicted realistically on the basis of linear elastic fracture mechanics. For comparatively small specimens, however, an approach which takes total fracture energy into consideration (for instance the fictitious crack model) is more appropriate. It is pointed out that the role of subcritical crack growth on fracture toughness needs further investigation.     

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.     

Numerical modelling of fracture initiation in large steel specimens at impact

Dynamic mode I fracture initiation in impact loaded single edge bend specimens with a quarter notch is investigated by numerical modelling and the results are compared with sets of experimental data from two different steel qualities. The finite element analysis include 2D (two-dimensional) plane strain, 2D plane stress and 3D models. No crack growth is included in the calculations. The impact velocities are approximately 15, 30 and 45 m/s and the specimen size is 320×75 mm² with a thickness of 20 or 40 mm. Some specimens have side grooves. Details of the deflection of the specimens are accurately reproduced prior to crack initiation both by the 2D plane strain model and by the 3D model.The experiments were performed in the ductile to brittle transition region. It is assumed that cleavage fracture initiation can be predicted by the Ritchie-Knott-Rice (RKR) model, i.e. cleavage fracture initiates when the opening stress exceeds the macroscopic cleavage stress over a fixed, critical distance. At an impact velocity of 15 m/s, fracture initiation by void nucleation and growth is observed, though the RKR-conditions is seemingly fulfilled according to the computational results. Possible limitations in the use of the RKR model are discussed.     

Determination of impact fracture toughness of polyethylene using arc-shaped specimens

This paper describes a methodology for the determination of the impact radial fracture toughness, G_IC, of cylindrical polymeric molded parts using arc-shaped specimens. The proposed methodology is an extension of the ISO/DIS 17281 Standard which states that for brittle behavior, a basically linear relationship exits between the fracture energy, U; and the energy calibration factor, φ. This relationship allows calculating the critical strain energy release rate from the slope of the U vs. φ plot. An expression for the energy calibration factor, φ, for the arc-shaped specimen is proposed in this work, by combining tabulated functions and finite element results. The methodology is applied to test high density polyethylene arc-shaped specimens taken from cylinder walls.     

Evaluation of fracture toughness and impact toughness of laser rapid manufactured Inconel-625 structures and their co-relation

The present study involves evaluation of fracture toughness and Charpy impact toughness of Inconel 625 structures fabricated by laser based additive manufacturing. The results of crack tip opening displacement (CTOD) fracture toughness are close to those reported for the Inconel 625 weld metal. The nature of the load–time traces of instrumented Charpy impact tests revealed that the alloy Inconel 625 in laser fabricated condition was associated with fully ductile behavior with Charpy V-Notch impact energy in the range of 48–54 J. Stress relieving heat treatment at 950 °C for 1 h has resulted in marginal improvement in the impact toughness by about 10%, whereas no clear evidence of such improvement is seen in the CTOD fracture toughness. Fractographic examination of the Charpy specimens and the results of the instrumented impact tests imply that the mechanism of crack growth was propagation controlled under dynamic loading conditions. Dynamic fracture parameters were estimated from the instrumented impact test data and compared with the experimentally evaluated fracture toughness results.     

Validity requirements for fracture toughness measurements obtained from small circumferentially notched cylindrical specimens

The authors have earlier proposed a small cylindrical circumferentially notched and fatigue cracked specimen for estimating K_Ic Finite element studies carried out are discussed with specific attention to the comparison between K_Ic thus obtained to that obtained experimentally. The size of the plastic zone is of particular interest in respect of the validity of the results; the F.E. result is compared to that obtained using Von Mises and Irwin approximations. Validity requirements are proposed for this specimen considering general yield of the final ligament, final ligament size, plastic zone size and depth of fatigue crack.     

Analysis of applicability of small-sized specimens to prediction of temperature dependence of fracture toughness

The paper addresses the use of small-sized specimens of various types, including those with deep (50%) side grooves, for the purpose of fracture toughness prediction. The experimental data for numerous (more than 500) small-sized specimens prepared from materials of various degrees of embrittlement are compared to the test results for full-sized specimens of C(T) type. The concepts of Master Curve and Unified Curve are applied for the processing of experimental data. To handle the test results for small-sized deep-grooved specimens a calculation procedure has been elaborated, which adjusts the calculation method specified in the ASTM Standard E 1921. We provide recommendations of how to use precracked Charpy type deep-grooved (50%) specimens for prediction of a representative temperature dependence of fracture toughness. Translated from Problemy Prochnosti, No. 2, pp. 5–26, March–April, 2009.     

Weibull master curves and fracture toughness testing Part III Master curves for the evaluation of dynamic Charpy impact tests

The existence of specimen-size-independent quasi-static Weibull master curves for macroscopically homogeneous solids characterizing strength and failure of both purely brittle materials and rather tough materials, which undergo an amount of stable crack growth prior to failure, has already been proved in earlier publications. In this paper, the concept of Weibull master curves is extended to the case of dynamic testing conditions, being typical for Charpy impact tests performed in the ductile-to-brittle transition temperature-range of ferritic-martensitic steels. Dynamic Weibull master curves can be constructed, if the stress-distributions, which are built up in the process zone of the specimens during the Charpy impact tests, can be described with a dynamic quasi-equilibrium approach. In this case, the dynamic Weibull master curves can be related to the quasi-static Weibull master curves with the help of the toughening exponent , characterizing the rate of toughness increase with increasing crack length. Characteristic magnitudes, being most convenient to estimate the capacity of the tested materials to undergo stable crack growth, microcracking and crack-tip shielding prior to rupture, can be derived as well from dynamic Weibull master curves as from quasi-static Weibull master curves.     

Fracture toughness of silicon nitride determined by cyclic-fatigue-cracked specimens

An experimental technique for determining fracture toughness has been developed. In this method, a fatigue precrack is introduced in single-edge notched beam specimens by cyclic fatiguing in four-point bend at an elevated temperature. The resulting fatigue precracks satisfy all conditions required by the ASTM Standard Test for plane-strain fracture toughness of metallic materials. The applicability of this technique to provide reproducible fracture toughness values is demonstrated by experimental results obtained for silicon nitride sintered in two different ways in comparison with those obtained by means of the indentation technique for the same materials.     

Physics of deformation and fracture at impact loading and penetration

The structure, dislocation substructure, and mechanical properties of the targets made of four aluminum alloys after a impact loading by kinetic energy projectile have been investigated. The formula for approximation of the ballistic limit velocity by indentation technique is proposed. It has been shown that the maximum nonequiaxiality of the grain shape, increase of dislocation density, and decrease of dislocation cell size correspond to the 40–70% of plastic deformation at static compression for the investigated aluminum alloys.     

Estimation of fracture toughness using miniature chevron-notched specimens

An approach for determining fracture toughness of materials using miniature chevron‐notched specimens is reported here for the first time. An outline of the principle and the experimental procedure for the test is depicted using results generated on eutectoid steel. Fracture toughness values of soft annealed and fully annealed eutectoid steels with inter‐lamellar spacing 167 nm and 549 nm are found to be 76 and 56 , respectively. The estimated fracture toughness values from miniature specimens are found to be in good agreement with the ones reported for similar bulk materials.     

Determination of fracture toughness from thin side-grooved specimens

Methods of determining fracture toughness from specimens of thickness lower than that required by ASTM Standard, E399 were studied using aluminum and titanium alloy specimens. In thin specimens in which crack growth initiation is clearly marked by a sudden change in the slope of the load-displacement curve, the stress intensity at the crack growth initiation point was found to be the same as the standard fracture toughness value. Crack growth initiation was more easily identifiable in the aluminum alloys than in the titanium alloy, although the latter was more brittle. Side grooves enable identification of crack growth initiation in thinner specimens, reducing considerably the thickness requirement for fracture toughness testing. A nearly straight crack front was found to be essential for obtaining reproducible results. Sharp and deep side grooves produced fatigue cracks leading at the edges.     

Effect of loading rate on fracture toughness of bonded joints

Feasibility studies in using adhesive bonding to replace conventional fastening methods have been proved successful. At this stage it is essential to furnish the designer with the data required for such type of fabrication. One of the main factors affecting the bonded joint strength is the loading rate. Therefore, the objective of this study is to investigate the role of loading rate on fracture toughness of bonded joints. Cleavage strength tests were carried out at different loading rates using epoxy resin as an adhesive material and two adherend materials, namely aluminium and brass. Tests were carried out to cover seven different loading rates. The results indicate a significant role of the strain rate on the fracture strength.