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.     

Tensile and flexural creep rupture tests on partially-damaged concrete specimens

Three series of novel tensile and flexural creep tests on partially-damaged concrete specimens were carried out in order to gain some insight into creep crack growth and failure of strain-softening materials. In the tests, each specimen was initially loaded to a given point in the descending branch and thus had a lower load-carrying capacity than that at the peak-point. Then, the specimen was unloaded and reloaded to sustain a load which was from 70% to 95% of its current load-carrying capacity. Experimental creep curves display a three-stage process, consisting of primary, secondary and tertiary stages, with a decreasing, constant and increasing creep rate, respectively. The secondary stage dominates the whole failure lifetime, whereas both the secondary and tertiary stages are important in terms of creep deformation. Failure life-time seems to be more sensitive to the change of load level in flexural tests rather than in tensile tests. The decrease in load-carrying capacity due to damage tends to result in a shorter failure lifetime and a lower critical load level for creep rupture. The descending branch of the static load-deflection or load-CMOD curve may be used as an envelope criterion for creep fracture.     

FATIGUE CRACK GROWTH BEHAVIOUR IN MOLTEN-METAL PROCESSED Sic PARTICLE-REINFORCED ALUMINIUM ALLOYS

Fatigue crack initiation and subsequent short crack growth behaviour of 2014-5wt%SiC aluminium alloy composites has been examined in 4-point bend loading using smooth bar specimens. The growth rates of long fatigue cracks have also been measured at different stress ratios using pre-cracked specimens. The distributions of Sic particles and of coarse constituent particles in the matrix (which arise as a result of the molten-metal processing and relatively slow cooling rate) have been investigated. Preferential crack initiation sites were found to be Sic-matrix interfaces, Sic particles associated with constituent particles and the coarse constituent particles themselves. For microstructurally short cracks the dispersed SiC particles also act as temporary crack arresters. In the long crack growth tests, higher fatigue crack growth rates were obtained than for monolithic alloys. This effect is attributed to the contribution of void formation, due to the decohesion of Sic particles, to the fatigue crack growth process in the composite. Above crack depths of about 200 μm “short” crack growth rates were in good agreement with the long crack data, showing a Paris exponent, m= 4 in both cases. For the long crack and short crack growth tests little effect of specimen orientation and grain size was observed on fatigue crack growth rates, but, specimen orientation affected the toughness. No effect of stress ratio in the range R=0.2-0.5 was seen for long crack data in the Paris region.     

Numerical investigation on stable crack growth in plane stress

Large deformation finite element analysis has been carried out to investigate the stress-strain fields ahead of a growing crack for compact tension (a/W=0.5) and three-point bend (a/W=0.1 and 0.5) specimens under plane stress condition. The crack growth is controlled by the experimental J-integral resistance curves measured by Sun et al. The results indicate that the distributions of opening stress, equivalent stress and equivalent strain ahead of a growing crack are not sensitive to specimen geometry. For both stationary and growing cracks, similar distributions of opening stress and triaxiality can be found along the ligament. During stable crack growth, the crack- tip opening displacement (CTOD) resistance curve and the cohesive fracture energy in the fracture process zone are independent of specimen geometry and may be suitable criteria for characterizing stable crack growth in plane stress. This revised version was published online in August 2006 with corrections to the Cover Date.     

An iteration method for directly determining J-Resistance curves of nuclear structural steels

An iteration method has been developed for determining crack growth and fracture resistance curves (J-R curves) of nuclear structural steels from the load versus load-line displacement record only. In this method, the hardening curve, the load versus displacement curve at a given crack length, is assumed to be a power-law function, where the exponent varies with the crack length. The exponent is determined by an iterative calculation method with the assumption that the exponent varies linearly with the load-line displacement. The proposed method was applied to the static J-R tests using compact tension (CT) specimens, a three-point bend (TPB) specimen, and a cracked round bar (CRB) specimen as well as it was applied to the quasi-dynamic J-R tests using CT specimens. The J-R curves determined by the proposed method were compared with those obtained by the conventional testing methodologies. The results showed that the J-R curves could be determined directly by the proposed iteration method with sufficient accuracy in the specimens from SA508 and SA516 pressure vessel steels and their welds and SA312 stainless steel.     

Determination of the fracture toughness by applying a structural integrity approach to pre-cracked Small Punch Test specimens

The Failure Assessment Diagram (FAD) is a procedure for evaluating the structural integrity of cracked components. The component’s failure conditions (load and crack size) are based on the material fracture properties (K_mat) considering its plastic behavior. In this paper, a new methodology that combines the FAD approach and the load–displacement curve obtained from pre-cracked Small Punch Test (SPT) specimens is presented, in order to estimate the fracture toughness of 15.5PH stainless steel. This research is based on Finite Element Modeling (FEM) of the pre-cracked specimen to determine both the plastic collapse load and the stress intensity factors during the loading process. A set of interrupted tests on pre-cracked SPT specimens are also conducted in order to identify the initiation point of the crack propagation. This set of numerical and experimental values allows the toughness ratio (K_r) and load ratio (L_r), at the instant the cracked specimen fails, to be determined. The only unknown variable in this process is the value of the material toughness, K_mat. The parameters in question are then combined with the FAD of the material generated from the different options available on the ASME-API 579 procedure, thus yielding an estimate for the value K_mat. Finally, to evaluate the accuracy of this methodology, predicted toughness values are compared to those from normalized tests of the material being analyzed.     

A New Procedure for Mode I Fracture Characterization of Cement‐Based Materials

Fracture characterization under mode I loading of a cement‐based material using the single‐edge‐notched beam loaded in tree‐point‐bending was performed. A new method based on beam theory and crack equivalent concept is proposed to evaluate the Resistance‐curve, which is essential to determine fracture toughness with accuracy. The method considers the existence of a stress relief region in the vicinity of the crack, dispensing crack length monitoring during experiments. A numerical validation was performed by finite element analysis considering a bilinear cohesive damage model. Experimental tests were performed in order to validate the numerical procedure. Digital image correlation technique was used to measure the specimen displacement with accuracy and without interference. Excellent agreement between numerical and experimental load–displacement curves was obtained, which validates the procedure.     

Microstructure and fracture in three dimensions

A high resolution three dimensional (3D) scanning technique called X-ray microtomography was used to measure internal crack growth in small mortar cylinders under compressive loading. Tomographic scans were made at different load increments in the same specimen. 3D image analysis was used to measure internal crack growth during each load increment. Load–deformation curves were used to measure the corresponding work of the external load on the specimen. Fracture energy was calculated using a linear elastic fracture mechanics approach using the measured surface area of the internal cracks created. The measured fracture energy was of the same magnitude that is typically measured in concrete tensile fracture. A nominally bilinear incremental fracture energy curve was measured. Separate components for crack formation energy and secondary toughening mechanisms are proposed. The secondary toughening mechanisms were found to be about three times the initial crack formation energy.     

Deformation und Versagen von StE460 und AlMg4,5Mn bei mehrachsig-proportionalen Beanspruchungen mit konstanten und variablen Amplituden

Deformation and failure behaviour of FeE460 and AlMg4.5Mn under multiaxial proportional loading with constant and variable amplitudes To calculate the fatigue life-to-crack initiation of engineering components under combined cyclic loading, experimentally secured knowledge on the cyclic deformation and failure behaviour of the materials used under the certain multiaxial cyclic stress and strain conditions are required. To obtain this, strain-controlled fully reversed experimental tests at tensional, torsional and combined loading with constant and variable amplitudes have been conducted using thin-walled tube specimens of FeE460 and AlMg4.5Mn. Experimental tests on standard uniaxially loaded hourglass specimens have also been conducted to study specimen form effects. Cyclic deformation behaviour can be uniformly described by the stabilised cyclic σ-ε-curve, if stresses and strains are expressed as equivalent values according to the von Mises criterion. Failure behaviour at constant and variable amplitude loading is characterized by the initiation and growth of short cracks at right angle to the direction of the greatest principal stress (mode I) in the case of tensional or combined loading and by short crack growing in both shear stress directions (mode II+III) in the case of torsional loading. At fully reversed constant amplitude loading, all three types of load can be described by one constant amplitude strain life-to-crack initiation curve. At variable amplitude loading (notch strain simulation with gaussian spectrum, H₀=10⁵), the experimental fatigue life-to-crack initiation values are lower than estimated values based on Miner-calculations using an equivalent stress-strain supported P_SWT-N-curve. The question of mean stresses and their evaluation is discussed.     

Small punch and uniaxial creep fracture behaviours of modified SUS304H steel at various temperatures

Commercial austenitic stainless steel SUS304H with small amount of vanadium addition was used in this study. Small punch (SP) creep and uniaxial tensile creep tests were conducted at 650, 700, and 750 °C to measure creep lives and the minimum displacement rates or the minimum creep strain rates. The measured parameters were compared between the two test methods, seeking empirical relationships among the parameters using Larson-Miller Parameter and Monkman-Grant relation. Magnitude of the applied stress (MPa) in the uniaxial tensile creep test was approximately equal to the applied load value (N) in the SP creep test at all test temperatures. It was shown that during the creep deformation of the SP creep specimen, crack initiation and accompanying crack growth occur simultaneously. Competing failure mechanisms of creep deformation and crack growth may affect the SP creep life and consequently determine the proportionality function, α, in the relation between the SP load and the tensile creep rupture stress in creep tests.     

Near tip damage and subcritical crack growth in a participate composite material

In this study, pre-cracked sheet specimens were used to conduct constant displacement rate crack propagation tests at room temperature. The effects of microstructure on damage accumulation and fracture processes near the crack tip and crack growth behavior were investigated and the results are discussed.     

Viscoplastic analyses of a compact tension specimen in mode I loading

Finite element analyses of stationary cracks in a compact tension specimen, subjected to Mode I loading into the large-scale yielding regime, are presented in an extension of earlier studies of small-scale yielding. Significant time dependence of the inelastic deformation of structural metals at room temperature under quasistatic loading rates has been observed in uniaxial tests and so the theory of viscoplastidty based on total strain and overstress is employed. The material properties of annealed AISI Type 304 Stainless Steel are used in the analyses, but the results are expected to be of general applicability because the properties of other important structural metals have been found to be qualitatively similar to those of AISI Type 304 Stainless Steel. The compact tension specimen model is loaded in load control at two rates varying by two orders of magnitude in the quasistatic range followed by subsequent sustained loading periods. For these loadings, significant time dependence of the crack-tip fields and of the overall specimen deformation are predicted by the analyses. The trends of the results are completely consistent with those of the earlier small-scale yielding analyses. When the results are interpreted with two different fracture criteria, it is predicted that the load at which crack growth is initiated is loading-rate dependent and that strain-induced crack growth could be initiated during sustained loading. These results are in full support of the earlier contention that time-dependent deformation should be considered in design against fracture, even at room temperature. Furthermore, the previously proposed design approaches based on the special features of the viscoplastidty model employed are supported by the results.     

Microstructure‐oriented characterisation of the cyclic deformation behaviour of Ti‐6Al‐4V

In this paper, the cyclic deformation behaviour of the titanium alloy Ti‐6Al‐4V is characterised in uniaxial stress‐ and total‐strain‐controlled load increase and constant amplitude tests at ambient temperature by means of mechanical stress‐strain hysteresis and temperature measurements. The measured physical values obviously show a pronounced interrelation with the underlying fatigue processes and represent the actual fatigue state. In selected experiments the influence of elevated temperatures on the cyclic deformation behaviour was investigated. Using the plastic strain amplitude and the change of the specimen temperature with the physically based lifetime calculation “PHYBAL” an excellent accordance with experimentally determined lifetimes could be realised. Microstructural changes were evaluated by transmission electron microscopy in defined fatigue states, additionally, the fracture surface was analysed by scanning electron microscopy.     

The transition between stress corrosion crack growth and plastic fracture—II. The effect of loading pattern

The paper addresses the problem of predicting the onset of plastic fracture at the tip of a growing stress corrosion crack, using data from laboratory fracture mechanics tests. A theoretical analysis for a particular model: namely that of the place strain deformation of a solid with two symmetrically situated deep cracks, and with tension of the small remaining ligament, shows that plastic fracture occurs at a $\text{J}$ value that is not constant, but depends on whether the loading is load or displacement control. This result, which is valid for materials for which the onset of crack extension and unstable fracture are coincident in a rising load fracture mechanics test, provides valuable support for the view that great care must be exercised when using fracture mechanics procedures to predict the transition between stress corrosion crack growth and plastic fracture in such materials.     

Procedure to predict ultimate fracture failure history for plane stress plasticity problems

A finite element solution procedure is presented to predict the load-displacement history up to ultimate fracture failure for a structural system. Incremental plasticity theory for the von Mises yield criterion and isotropic strain hardening are used to march along the uniaxial stress-strain curve of the material up to fracture. When an element fractures its strain energy is distributed into the unfractured elements using an element nodal release method. If another element fractures during this redistribution process, then unstable crack growth is said to occur, and the total load at this stage is termed the ultimate fracture failure load of the structural system. The analysis steps to automate the solution procedure are described. Numerical results obtained for a center pre-cracked panel tension specimen are reported and compared with experimental results available in the literature.     

Verfahren zur vollständigen Ermittlung der R‐Abhängigkeit des Rissausbreitungsverhaltens mit nur einer Probe

Procedure for the determination of the complete R‐dependency of the crack growth behaviour with only one specimen A new concept for fatigue crack propagation tests has been developed. Using a single specimen, it is possible to determine fatigue crack growth curves (da/dN ‐ ΔK) for every stress ratio between R = 0.9 and R = ‐1. Additionally, the new concept also provides threshold values for fatigue crack growth for different values of R and K_max. In combination with a continuous crack length measurement tool (such as the DC potential drop method) this testing procedure can be performed with minimal effort of personnel and time. The test procedure consists of a sequence of K_max‐constant tests with decreasing crack growth rates. As the applied K_max is increasing stepwise there should be no load history effects. According to the procedures described in the ASTM Standard E 647, the results using this new testing procedure fit very well to the da/dN ‐ ΔK curves generated with different specimens. The tests also fulfil all the requirements of ASTM Standard E 647.     

Transferability of specimen J–R curve to straight pipe with circumferential surface flaw

Specimen J–R curve is extensively used for structural integrity of large components. It is well known that J–R curve heavily depends on constraint level ahead of crack tip in remaining ligament. In earlier work, it was demonstrated that J–R curve from Three Point Bending (TPB) specimen is transferable to straight pipe with circumferential through wall crack. In this paper, the transferability of J–R curve is investigated from TPB specimen to pipe with circumferential surface crack. A 16 in. diameter pipe with circumferential surface crack and TPB specimen machined from same piping material (SA333Gr6 Steel) are tested. Consequently, 3D finite element analysis (FEA) has been performed on surface cracked pipe and TPB specimen. Crack‐initiation load is also predicted for surface cracked pipe by FEA and compared with experimental result. J–R curve is calculated for the pipe using experimental data, that is, load, load line displacement and crack growth. J–R curve of pipe is compared with TPB specimen and it is found that the pipe is predicting much higher J–R curve than TPB. This difference of J–R curve is investigated by evaluating stress triaxiality in remaining ligament for both cases. Stress triaxiality is quantified using triaxiality factor (h) ahead of crack tip for pipe and TPB specimen. It is found that the TPB specimen has considerably higher constraint level than pipe with surface crack, which is well supported by trend of J–R curves for specimen and pipe. A study has also been carried out to investigate the effect of internal pressure on the stress triaxiality. It is found that there is negligible difference in stress triaxiality because of internal pressure. The stress triaxiality is re‐established as a qualitative parameter to assess the transferability of J–R curve from specimen to component.     

Effect of a hard artificial asperity on the crack closure behavior in an annealed SAE 1015 steel

The load-crack opening displacement (COD) curves and deformation characteristics in the vicinity of a hard artificial asperity in an annealed SAE 1015 steel were studied. The artificial asperity was found to have a significant effect on the trend of the load-COD curves. The lower portion of the load-COD curves in the unloading phase exhibited a convex shape without the asperity, but a concave shape with the asperity. The concave shape, signifying the acceleration in the COD decrease, was further verified by varying the size of the asperity, conducting special compression tests and elastic-plastic load-COD tests. The plastic deformation in the vicinity of both asperity and crack tip was studied via microhardness tests, etching techniques, and finite element analysis. Based on the experimental observations, a modified crack closure process model was proposed, where three stages of the unloading curve was defined: (i) the asperity does not contact the upper crack face, (ii) a process where both the asperity and the specimen material deform elastically, and the elastic-wedge model is applicable, and (iii) the plastic deformation of the specimen material adjacent to the asperity occurs, thus resulting in the concavely shaped load-COD curves. An equation was proposed to estimate the COD values, in which the plastic deformation both at the crack tip and at the asperity was considered. The residual COD calculated from the proposed equation was found to be consistent with the experimental results.     

APPLICATION OF FRACTURE MECHANICS TECHNIQUES TO THE ENVIRONMENTALLY ASSISTED CRACKING OF ALUMINIUM 2024

Abstract— Stress corrosion cracking of 2024 T351 aluminium alloy in an aqueous 3.5% sodium chloride solution was investigated using three fracture mechanics based testing techniques: constant load, constant displacement, and constant displacement rate. In spite of their different loading characteristics, all three test methods yielded approximately the same K _lscc value. Crack growth rates in the plateau region, as measured from bolt loaded DCB specimens and from CT specimens tested at low constant displacement rates are similar. The tests at constant displacement rate not only provide results in a much shorter time, but produce additional information in terms of crack growth resistance curves as a function of the displacement rate. Linear elastic as well as elastic-plastic fracture mechanics test evaluation procedures are applied and discussed in view of an assessment of criteria for the accelerated evaluation of SCC parameters such as K _lscc, J _lscc, and δ_lscc.     

Cyclic loading and fatigue in ice

Isotropic polycrystalline ice was subjected to cyclic loading in uniaxial compression at ?5°C, with stress limits 0–2 and 0–3 MPa, and frequencies in the range 0.043 to 0.5 Hz. Stress-strain records showed hysteresis loops progressing along the strain axis at non-uniform rates. The effective secant modulus, which was about half the true Young's modulus, decreased during the course of a test. The elastic strain amplitude and the energy dissipated during a loading cycle both increased with increase of time and plastic strain. Strain-time records gave mean curves which were identical in form to classical constant-stress creep curves, with a small cyclic alternation of recoverable strain about the mean curve. The inflection point of the “creep curve”, marking the transition from strain hardening to strain softening, occurred at a plastic strain of 1% (±0.1%), which is about the same as the “ductile failure strain” found in constant stress creep tests and in constant strain-rate tests on ice of the same type at the same temperature. The dissipation of strain energy up to this “failure point” was much higher for the cyclic tests than for corresponding quasi-static tests ? 100 to 600 kPa (or kN-m/m³) in comparison to about 30 kPa. The number of cycles taken to reach the “failure point” was of no direct significance, varying greatly with stress amplitude and with frequency. The results of the tests suggest that maximum resistance under compressive cyclic loading occurs at an axial plastic strain of about 1%, which is essentially the same as the failure strain for ductile yielding under constant stress and under constant strain-rate.