Experimental evaluation of hinge phenomenon in notched three point bend bars using laser speckle metrology

In elastic-plastic fracture, material behavior is often characterized by the J-integral or crack tip opening displacement (CTOD) parameters. In order to evaluate these parameters accurately, the location of the plastic hinge point, and subsequently the value of the plastic rotational factor, r_p, must be determined. Traditionally, hinge point location and r_p have been inferred through crack opening displacement (COD) measurements. However, this work indicates that laser speckle metrology can be used to analyse directly the hinging phenomenon. Using notched three point bend bars fabricated from a high stretch low alloy steel, a full-field map of in-plane displacements was generated over the course of each test. The results indicate the existance of a hinge region, rather than an explicit hinge point. The hinge region appears to contain the computed hinge point location using the range of cited r_p values. This indicates that it may be appropriate to use the centroid of the hinge region in subsequent CTOD and J-integral calculations.     

Influence of bending rotations on three and four-point bend end notched flexure tests

It has been experimentally observed that mode II critical energy release rate (G_IIC) values determined by four-point end notched flexure test and three-point end notched flexure test are different for the same material. At the present work correction factors related to bending rotations are introduced to explain the differences between values of G_IIC obtained by three point and four point end notched flexure tests. The bending angle leads to the contact zones between specimen and supports and specimen and load rollers changing in both test configurations. The present analysis has been carried out by the classical beam theory, neglecting shear effects and assuming the hypothesis of small rotated angles. Results show that the relative differences between corrected and uncorrected values of G_IIC are greater in the case of four-point end notched flexure than in the case of three-point end notched flexure test.     

Fracture toughness determination of bearing steel using chevron-notch three point bend specimen

Stress intensity factor formulas and dimensionless compliance formula of chevron-notch three point bend specimen obtained by use of straight-through-crack assumption (STCA) and Bluhm's slice model have been presented. Two stress intensity factor coefficient formulas have been compared with the experimental data of GCr 15 bearing steel. The comparison has shown that the formula obtained using slice model is in better agreement with experimental data. The plane-strain fracture toughness measurements by chevron-notch specimen and by ASTM E399 standard method have been compared and are in agreement. The effect of slot width of chevron notch on the measurements has been studied.     

Fracture assessment of U-notches under three point bending by means of local energy density

The main purpose of the paper is twofold. First, to provide a new set of experimental results on fracture of U-notched samples, made of two different materials; second, to apply a fracture criterion based on the strain energy density (SED) averaged over a control volume to assess the fracture load of blunt-notched components under three point bending. Two different materials are considered in the tests: a composite material (Al–15%SiC) tested at room temperature and a steel with a ferritic–pearlitic structure tested at −40 °C. All samples are weakened by U-notches characterized by different values of notch root radius and notch depth. The theoretical loads to failure as determined according to the SED criterion are compared with the experimental data from more than 40 static tests and with a SED-based scatter band recently reported in the literature for a number of materials exhibiting a brittle behaviour under static loads.     

Influence of local fracture energy distribution on maximum fracture load of three-point-bending notched concrete beams

The maximum fracture load of a notched concrete beam has been related to the local fracture energy at the cohesive crack tip region analytically in this paper, and then the correlation between the size effects on the maximum fracture loads and the RILEM specific fracture energy is established. Two extreme conditions have been established, namely zero crack-tip bridging with zero local fracture energy and maximum crack-tip bridging with the maximum size-independent fracture energy. It is concluded that the local fracture energy at the crack tip region indeed varies with the initial crack length and the size of specimen. The tri-linear model for the local fracture energy distribution is confirmed by using the proposed simple analytical solution.     

A model for calculating geometry factors for a mixed-mode I–II single edge notched tension specimen

In the present study, a novel approach is presented to obtain closed-form solutions for the geometry factors, which are used to determine the stress intensity factors for various configurations. A single edge notched tension specimen with an angled-crack is used as an example to demonstrate the applicability, simplicity and flexibility of the new approach. Several values for crack inclination angles, plate widths and crack lengths, including micro-cracks, are considered in the analysis. The new approach is validated through comparison with existing analytical and numerical solutions as well as experimental results.     

The influence of weld strength mismatch on crack-tip constraint in single edge notch bend specimens

Previous work by Dodds and Anderson provides a framework to quantify finite size and crack depth effects on cleavage fracture toughness when failure occurs at deformation levels where J no longer uniquely describes the state of stresses and strains in the vicinity of the crack tip. Size effects on cleavage fracture are quantified by defining a value termed J _SSY: the J to which an infinite body must be loaded to achieve the same likelihood of cleavage fracture as in a finite body. In weld metal fracture toughness testing, mismatch between weld metal and baseplate strength can alter deformation patterns, which complicate size and crack depth effects on cleavage fracture toughness. This study demonstrates that there is virtually no effect of ±20 percent mismatch on J _SSYif the distance from the crack tip to the weld/plate interface (L _min) exceeds 5 mm. At higher levels of overmatch (50 to 100%), it is no longer possible to parameterize the departure of J _SSYfor a weldment from that for a homogeneous SE(B) based on L _min alone. Weld geometry significantly influences the accuracy with which J _SSYfor a welded SE(B) can be approximated by J _SSYfor a homogeneous specimen at these extreme overmatch levels.     

Corrected stress intensity factor solution for a British standard single edge notched tension (SENT) specimen

This paper revisits a complicated analytical solution of the stress intensity factor K adopted in a newly published British standard BS 8571:2014 for clamped single edge notched tension (SENT) specimens. Comparison with existing numerical results of K shows that the analytical K solution in BS 8571 is correct only for the crack length to specimen width ratio a/W ≤ 0.6, but incorrect for a/W > 0.6. A reinvestigation is thus performed using the crack compliance method, and a corrected K solution is obtained for the BS 8571 clamped SENT specimens over the full range of a/W. On this basis, a simple closed‐form solution of K is obtained using the best curve fitting with an accuracy within 1% for crack sizes up to a/W = 0.98. Results show that the proposed closed‐form solution of K agrees well with the numerical results of K for the clamped SENT specimens.     

Numerical verification of stress intensity factor solution for clamped single edge notched tension (SENT) specimens

Stress intensity factor solutions for clamped single edge notched tension (SENT) specimens, including a closed‐form function recently proposed by Zhu along with a function by CanmetMATERIALS referenced in the British Standard BS 8571, have been assessed. Solutions for an SENT specimen with a daylight‐to‐width ratio of 10 have been compared with new finite element results generated in this work to assess their accuracies. The results of this study show that the polynomial proposed by Zhu differs by no more than 0.23% compared with the numerical results over the range of 0.2 ≤a/W ≤ 0.7. The CANMET function differs by no more than 0.69% over the same range.     

Measurement of the fracture energy using three-point bend tests: Part 2—Influence of bulk energy dissipation

Avialable measures of the fracture energy G_F obtained with the procedure proposed by RILEM TC-50 provide values that appear to change with sample size, calling into question whether G_F can be considered as a material parameter. In a previous paper, possible sources of energy dissipation from the testing equipment and lateral supports were considered. In this paper new possible sources of energy dissipation in the sample, apart from the fracture crack itself, are considered. Such dissipation will take place inside the bulk of the most stressed regions of the specimen and, if it is not taken into account, higher values of G_F will be recorded than that strictly due to surface fracture energy. When this constribution and the possible energy dissipation analysed in previous work are considered, they are not enough to account for the measured size effect. If G_F is to be considered a material parameter, the evaluation of the results from the RILEM method should be analysed more carefully. In any case, the dissipated energy reported here represents a non-negligible amount of G_F and should be taken into account when performing measurements.     

The effect of crack front curvature and side-grooving on three point bend specimen fracture toughness measurements

Finite element simulations of the three point bend fracture toughness specimen have been performed to investigate the effect of crack front curvature and side-grooving. Even modest crack front curvature moves the position of maximum energy release rate from the center towards the free surfaces of the specimen. A 30 percent difference between the maximum and minimum crack length can double the maximum energy release rate compared to that calculated for a straight crack of the same average length. A correction curve has been derived from which the curved crack energy release rate can be obtained using two dimensional solutions. Deep side-grooving substantially increases the energy release rate at the root of the groove, but for groove depths no more than 30 percent of the section, an energy release rate can be estimated from the two dimensional ungrooved solution scaled by the ratio of ungrooved to grooved thicknesses.     

Determining the double‐K fracture parameters for three‐point bending notched concrete beams using weight function

Parameters of universal form of weight functions having four terms and five terms are derived for edge cracks in finite width of plate. The standard Tada Green's function is taken as the basis for the derivation. The shape of universal form of weight functions considered enables closed form expressions for cohesive toughness of three‐point bending test geometry of notched concrete beams due to linear cohesive stress distribution in the fictitious fracture zone. This solution provides a viable method to determine the double‐K fracture parameters: the initiation toughness, and the unstable toughness for mode I fracture of concrete beam. A comparison with existing analytical method shows that the weight function method for determination of the double‐K fracture parameters yields results without any appreciable error. The use of weight function will not only simplify the calculation to obtain the double‐K fracture parameters, and but also it will avoid the need of skilled numerical integration technique due to singularity problem at the integral boundary.