An Investigation of the Effects of Crack Front Curvature on the Crack-Tip Opening Displacement of A707 Steel

This paper examines the effects of crack front curvature on the fracture toughness (crack-tip opening displacement) of A707 steel. Fracture mechanics specimens, in which the radii of curvature of the crack fronts are controlled in an effort to simulate potential variations in crack front profiles in fracture experiments, were produced by machining and fatigue pre-cracking. Three-point bend crack-tip opening displacements (CTOD_c) were measured in accordance with the ASTM E-1290 code. The results show that the critical CTOD_c increases with increasing crack front curvatures between 0.05 and 0.17 mm^–1. In all cases, stable crack growth and final catastrophic failure of the specimens are found to occur by transgranular ductile dimpled fracture, in which the ductile dimples are nucleated around MnS or Al₂(Mg)O₃ inclusions. The implications of the results are discussed for the measurement of critical CTOD_c in specimens with varying levels of crack front curvature.     

A comparative study on five approaches to evaluate double-K fracture toughness parameters of concrete and size effect analysis

The current paper presents a comprehensive comparison of double-K fracture toughness parameters of concrete evaluated using experimental method and four existing analytical methods. Fracture tests were carried out on compact tension wedge splitting specimens with various depths varying from 200 mm up to 1000 mm. In the analytical calculation, depending on the relationship between critical crack tip opening displacement and the abscissa value of turning point on bilinear softening curve, two different distributions of cohesive stress are considered along crack extension. Results show that four available analytical calculations yield almost the same values of double-K fracture toughness parameters and agree well with those obtained from the experiment, which confirms the consistency of five approaches. Size effect was discussed, including unstable fracture toughness, initiation fracture toughness, critical effective crack length, the length of critical fracture process zone and critical crack tip opening displacement.     

Further developments in <Emphasis Type="Italic">J</Emphasis> evaluation procedure for growing cracks based on LLD and CMOD data

Laboratory testing of fracture specimens to measure resistance curves (J − Δa) have focused primarily on the unloading compliance method using a single specimen. Current estimation procedures (which form the basis of ASTM E1820 standard) employ load line displacement (LLD) records to measure fracture toughness resistance data incorporating a crack growth correction for J. An alternative method which potentially simplifies the test procedure involves the use of crack mouth opening displacement (CMOD) to determine both crack growth and J. However, while the J-correction for crack growth effects adopted by ASTM standard holds true for resistance curves measured using load line displacement (LLD) data, it becomes unsuitable for J-resistance measurements based upon the specimen response defined in terms of load-crack mouth opening displacement (CMOD). Consequently, direct application of the evaluation procedure for J derived from LLD records in laboratory measurements of resistance curves using CMOD data becomes questionable. This study provides further developments of the evaluation procedure for J in cracked bodies that experience ductile crack growth based upon the eta-method and CMOD data. The introduction of a constant relationship between the plastic components of LLD (Δ _p ) and CMOD (V _p ) drives the development of a convenient crack growth correction for J with increased loading when using laboratory measurements of P-CMOD data. The methodology broadens the applicability of current standards adopting the unloading compliance technique in laboratory measurements of fracture toughness resistance data (J resistance curves). The developed J evaluation formulation for growing cracks based on CMOD data provides a viable and simpler test technique to measure crack growth resistance data for ductile materials.     

Loading‐rate dependence of mode I crack growth in concrete

Mode I crack propagation process of concrete under relatively low loading rates which cover four orders of magnitude (0.2 μm/s to 2.0 mm/s) is investigated with three‐point bending (TPB) beams. All measured material properties exhibit rate sensitivity and follow a log‐linear relationship with the loading rate. A rate‐sensitive softening curve is established. The complete load‐crack mouth opening displacement (P‐CMOD) curve, crack propagation length, and fracture process zone (FPZ) length are simulated based on crack growth criterion with the fitted material parameters under those loading rates. Results show that the simulated P‐CMOD curves agree well with those of experimental measurements. It is clear that the peak load increases with the loading rate and so is the critical crack mouth opening displacement. Moreover, under the same load level, the length of the FPZ and the cohesive stress at the initial crack tip also increase with the increasing loading rate.     

The fracture toughness of medium density fiberboard (MDF) including the effects of fiber bridging and crack–plane interference

The fracture toughness of medium density fiberboard (MDF) as a function of crack length (R curve) was measured. Fracture toughness was determined from force–displacement and crack length data using a new energy analysis procedure that avoids the scatter of prior discrete analysis methods. Because crack lengths were difficult to observe, they were measured using digital image correlation (DIC). The R curves for two different densities of MDF, two thicknesses, and for both in-plane and through-the-thickness cracks all increased linearly with crack length. The increase was interpreted as the development of a fiber-bridging process zone. Numerical modeling methods were used to determine the cohesive stress of the fiber-bridging zone.     

Study of elastic-plastic fracture toughness determination

The elastic-plastic fracture toughness viaJ-integral and crack tip opening displacement (CTOD) has been obtained in two structural steels using several fitting equations representing the resistance curve of the material. The toughness is determined as the values corresponding to the critical stretched zone width (SZW) on theR-curves and with respect to 0.2 mm crack growth. The SZW measurements were performed by scanning electron microscopy. The various toughness values have been compared and the importance of using appropriateR-curves based on physical considerations has been pointed out. TheJ-CTOD relationship during the blunting process has been experimentally investigated from load-displacement records of the fracture test.     

Evaluation of the ISO <Emphasis Type="Italic">J</Emphasis> initiation procedure using the EURO fracture toughness data set

The multiple specimen J _0.2/BL initiation fracture toughness test procedure from the ISO standard, ISO 12135:2002, is evaluated using the EURO fracture toughness data set. This standard is also compared with the ASTM standard, ASTM E 1820, multiple specimen J _Ic procedure. The EURO round robin data set was generated to evaluate the transition fracture toughness methods for steels. However, many of the tests resulted in ductile fracture behavior giving final J versus ductile crack extension points. This is the information that is measured in a multiple specimen J initiation fracture toughness test. The data set has more than 300 individual points of J versus crack extension with four different specimen sizes. It may be the largest data set of that type produced for one material. Therefore, its use to determine J initiation values can provide an important evaluation of the standard procedures. The results showed that a J _0.2/BL value could be determined from the ISO standard for three of the four specimen sizes, the smallest size did not meet the specimen size requirement on J. The construction line slopes in this method are very steep compared with the ASTM construction line slopes. This resulted in low J initiation values, about a factor of two lower than the one from the ASTM method. Of the various criteria imposed to determine a valid J _0.2/BL value, the one limiting the maximum J value was the most questionable. It had an effect of eliminating small specimen data that was identical to acceptable large specimen data.     

A simplified method for determining double-K fracture parameters for three-point bending tests

A simplified method for determining the double-K fracture parameters K _Ic ⁱⁿⁱ and K _Ic ^un for three-point bending tests is proposed. Two empirical formulae are used to describe the crack mouth opening displacement CMOD and the stress intensity factor K _I ^c caused by the cohesive force (x) on the fictitious crack zone for three-point bending beams. It has been found that the two empirical formulae are accurate for a large practical region of a/D. Experiments carried out by many researchers showed that the new formula of CMOD for three-point bending beams can be directly used to predict the initial crack length for precracked beams, the notch depth and the critical effective crack length, as well as the crack length in the post-critical situation with a satisfactory accuracy. Further verification is demonstrated to determine the double-K parameters K _Ic ⁱⁿⁱ and K _Ic ^un. They are very close to those determined by the method proposed in our previous work. Using the simplified procedure, the experiments can be performed even without a closed-loop testing facility and the calculation can be carried out on a pocket calculator.     

A numerical investigation on the geometry dependence of the crack growth resistance in CT specimens

The influence of the specimen thickness B and the ligament length b on the J _R -curves is numerically investigated for CT specimens. The thickness effect is taken into account with 2-D analyses by dividing a plain sided specimen into a plane stress part and a plane strain part. The fracture process is controlled by experimentally determined critical values of the crack tip opening displacement for crack growth initiation (CTOD_i) and the crack tip opening angle for stable crack growth (CTOA_C). It is shown that for the global behaviour of a plain sided specimen, the B/b ratio is essential. The difference between the geometry dependence of the initiation value of the J-integral and the geometry dependence of the slope of the J _R -curves is also shown.     

Influence of heat input on microstructure and fracture toughness property in different zones of X80 pipeline steel weldments

In this paper, microstructure observations and mechanical behaviour of fusion line and offsetting positions from fusion line by 1, 2 and 3 mm were analysed. For the welding of X80 pipeline steel plates, different magnitudes of heat inputs such as high heat input (HHI) 25 kJ/cm, medium heat input (MHI) 20 kJ/cm and low heat input (LHI) 15 kJ/cm were employed. Critical values of J‐integral (J_0.2) and crack tip opening displacement (CTOD_0.2) for predetermined regions in the X80 weldment were determined as per ASTM‐E1820a. M‐A constituents of different sizes such as small (1–2 μm), large >2 μm and slender (>4 μm) were observed in the microstructure of subzones of weldments for different heat inputs. Formation of granular bainite, M‐A constituents and inclusions of Ti, Si, Mo in the microstructure impaired fracture toughness property. In the X80 weldment, the fusion line (FL) for HHI was found weakest in terms of fracture resistance, which subsequently increases the risk of fracture.     

Prediction of J–R curves of thin-walled fuel pin specimens in a PLT setup

Recently, a Pin-Loading-Tension setup has evolved for evaluation of fracture behavior of thin-walled tubular specimens which are machined from nuclear reactor fuel pins. In this work, the geometric functions required for estimation of plastic component of J-integral from experimental load–load-line displacement data has been derived by carrying out a detailed 3D finite element analysis of the Pin-Loading-Tension test setup using the concept of limit load. The fracture resistance behavior (in terms of J–R curve) of the fuel pin specimens have been derived using: (a) multiple-specimen and (b) single specimen load-normalization technique.     

A numerical study on the crack growth behavior of a low and a high strength steel

Geometry and size effects on the crack growth resistance curves in CT-specimens of a low and high strength material are numerically investigated. The fracture process is controlled by experimentally determined critical values of the crack tip opening displacement (CTOD_i for crack growth initiation and the crack tip opening angle (CTOA_C) for stable crack growth. The results show that for the low and the high strength material the geometry and size effects are different. This is mainly due to the fact that the load vs. load line displacement records are basically different for the two materials which results from the large difference in the scaled fracture toughness parameters, CTOD_i/_O and CTOA_C/_O, of the two materials.Presented at the Far East Fracture Group (FEFG) International Symposium on Fracture and Strength of Solids, 4–7 July 1994 in Xi'an, China.     

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.     

Fracture toughness of ISO 3183 X80M (API 5L X80) steel friction stir welds

Friction stir welding (FSW) is a solid-state joining process with numerous advantages such as good dimensional stability and repeatability, which is widely used Al alloys and with a great potential for critical joining applications involving high melting temperature alloys. Twelve millimeter thick plates of ISO 3183 X80M (API 5L X80) steel was friction stir welded using two passes on both sides of the plate using ceramic tools. Different heat inputs were obtained using a fix travel (welding) speed in combination with several spindle speeds. The fracture toughness of the two-pass joints was evaluated at 25 °C using the critical crack tip opening displacement (CTOD_m), revealing that joints produced with lower spindle speeds presented higher toughness at the heat-affected zone (HAZ) and stir zone (SZ), which are comparable with the base metal (BM) toughness. On the other hand, joints produced using higher spindle speeds presented low fracture toughness at the SZ and elevated CTOD_m toughness at the HAZ. The joints produced with low spindle speeds showed CTOD_m-values above the offshore standard (DNV-OS-F101) requirements.     

Single and multi-specimenR-curve methods forJ IC determination of toughened nylons

For characterization of the fracture resistance of materials used in the upper shelf toughness regime,J-R curves are widely considered the most promising candidates. However, there still remain problems concerning both the generation and measurement ofJ-R curves as material characterizing parameters and their application in ductile fracture analyses for failure prediction in polymeric materials. This paper reports the results of investigations conducted on two rubbertoughened nylons at room temperature. Two different methods ofJ-R curve determination are covered, namely multi-specimen and single specimen test methods. The resultingJ-R curves have also been evaluated to obtain values of the initiation toughness,J _IC, following the extrapolation and interpolation schemes prescribed by ASTM E813-81 and ASTM E813-87 test procedures, respectively. The results show that the multiple specimen unloading method and the single specimen partial unloading compliance method can be used to generate comparable crack growth resistanceJ-R curves of the toughened nylons. The value ofJ _IC for the crystalline rubber-toughened nylon was approximately twice the value obtained for the amorphous rubber-toughened nylon. The former material also exhibited a greater resistance to ductile crack growth.     

Size effects in concrete fracture – Part II: Analysis of test results

This paper presents an analysis of the extensive experimental program aimed at assessing the influence of maximum aggregate size and specimen size on the fracture properties of concrete. Concrete specimens used were prepared with varying aggregate sizes of 4.75, 9.5, 19, 38, and 76mm. Approximately 250 specimens varying in dimension and maximum aggregate size were tested to accomplish the objectives of the study. Every specimen was subjected to the quasi-static cyclic loading at a rate of 0.125mm/min (0.005in./min) leading to a controlled crack growth. The test results were presented in the form of load-crack mouth opening displacement curves, compliance data, surface measured crack length and crack trajectories as well as calculated crack length, critical energy release rate, and fracture toughness (G ₁). There is a well pronounced general trend observed: G ₁ increases with crack length (R-curve behavior). For geometrically similar specimens, where the shape and all dimensionless parameters are the same, the R-curve for the larger specimens is noticeably higher than that for the smaller ones. For a fixed specimen size, G ₁ increases with an increase in the aggregate size (fracture surface roughness). For the same maximum aggregate size specimens, the apparent toughness increases with specimen size. It was clear that the rate of increase in G ₁, with respect to an increase of the dimensionless crack length (the crack length normalized by the specimen width), increases with both specimen size and maximum aggregate size increase. The crack trajectory deviates from the rectilinear path more in the specimens with larger aggregate sizes. Fracture surfaces in concrete with larger aggregate size exhibit higher roughness than that for smaller aggregate sizes. For completely similar specimens, the crack tortuosity is greater for the larger size specimens. The crack path is random, i.e., there are no two identical specimens that exhibit the same fracture path, however, there are distinct and well reproducible statistical features of crack trajectories in similar specimens. Bridging and other forms of crack face interactions that are the most probable causes of high toughness, were more pronounced in the specimens with larger maximum size aggregates.     

Plastic eta factor and blunting line for characterization of fracture toughness of dissimilar metal weld

This paper addresses the fracture toughness evaluation procedure of different zones of dissimilar metal weld (DMW). Experiments have been conducted on compact tension specimens from DMW joint having initial notch in centre of weld and fusion boundaries. Plastic eta factors (η_p) and slope of blunting line (bl) for above specimens have been evaluated numerically. Experimental load, load line displacement, and crack growth data along with numerically evaluated η_p and bl have been used for calculation of fracture resistance curve and initiation fracture toughness, and finally, it has been compared with that evaluated as per ASTM E1820 and ESIS standard.     

R-curve behavior in notched beam tests of rocks

The R-curve for sandstone is obtained from the load-crack mouth opening response of notched specimens subjected to three-point-bending. This approach is used to analyze the fracture behavior under monotonic and cyclic loading. The asymptotic limit of the R-curve compares well with the fracture toughness determined through an effective crack model. The analysis of the relaxation observed before the unloading-reloading cycles in the cyclic tests leads to the conclusion that the fracture toughness remains practically constant while the crack propagates slightly during the load drop.     

SIMPLE Jc, ESTIMATION FORMULAE FOR THREE-POINT BEND SPECIMENS

This report reviews some simple methods for determining J_c at the onset of cleavage fracture in a three-point bend crack tip opening displacement test. It is concluded that acceptable estimates of J, can be made from specimen mouth opening displacement without precise measurement of crack length.     

Crack propagation in quasi-brittle two-dimensional isotropic lattices

Materials with cellular structure are gaining prominence in recent years due to improvements in production processes, that enable the manufacture of new materials, and biomechanics, that requires mechanical analysis of cellular structures such as bones. The possibility to use the Fracture Mechanics tools developed for the continua to the fracture of cellular materials is analyzed in the present paper. As proposed by Maiti et al. the fracture toughness of cellular solids can be obtained through two procedures: taking into account the stress at crack tip or the fracture toughness of the base material. Both procedures are analyzed and the equivalent R-curve and a cohesive law is obtained in function of the cell size and structure morphology. A critical truss length exists from which crack propagation goes from being governed by the energy dissipated to being governed by the stress field.