On Influence of Non-Singular Stress States on Brittle Fracture

In the case of sufficiently brittle material the use of stress intensity factor as a fracture parameter alone is well justified within the Linear-Elastic Fracture Mechanics. This is because the singular stress field associated with the stress intensity factor is dominant near the crack tip. However, there are numerous experimental evidences that the critical stress intensity factor to cause fracture initiation (or fracture toughness) can be affected by the specimen geometry as well as loading conditions. To address this issue a number of twoparameter criteria have been proposed in the past, which often utilise non-singular terms of the classical asymptotic expansion of the stress field near the crack tip. Therefore, there is a problem of the selection of an appropriate parameter in addition to the stress intensity factor, which could account for various effects induced by the specimen geometry and loading on initiation of brittle fracture. This short paper demonstrates that brittle fracture conditions can be successfully predicted with various two-parameter criteria, and there are no clear advantages in the use of T-stress as the additional parameter in fracture criterion, in comparison with the next non-singular term, A ₁, of the asymptotic expansion.     

Constraint Loss under Dynamic Loading in Rate Independent Plastic Solids

The objectives of this paper are to examine the loss of crack tip constraint in dynamically loaded fracture specimens and to assess whether it can lead to enhancement in the fracture toughness at high loading rates which has been observed in several experimental studies. To this end, 2-D plane strain finite element analyses of single edge notched (tension) specimen and three point bend specimen subjected to time varying loads are performed. The material is assumed to obey the small strain J ₂ flow theory of plasticity with rate independent behaviour. The results demonstrate that a valid J–Q field exists under dynamic loading irrespective of the crack length and specimen geometry. Further, the constraint parameter Q becomes strongly negative at high loading rates, particularly in deeply cracked specimens. The variation of dynamic fracture toughness K _dc with stress intensity rate K for cleavage cracking is predicted using a simple critical stress criterion. It is found that inertia-driven constraint loss can substantially enhance K _dc for .     

Variation of fracture toughness with constraint

`Curving' could occur in Mode I brittle fracture and it can be attributed to the constraint. The variation of the apparent fracture toughness with constraint with or without crack curving is investigated. Using a critical opening or hoop stress as the fracture criterion, it is demonstrated that a fracture event can be quantified by two mechanics parameters, i.e. K and A₃ for fracture without curving and K and T for fracture with curving. K, T and A₃ are the first, second and third coefficient in the Williams' asymptotic series solution, respectively, and are used here to quantify the constraint level. Test data are used to validate the theory. It is shown that while the apparent fracture toughness increases with increasing T it decreases with T after curving occurs.     

Basic studies of ductile failure processes and implications for fracture prediction

Fracture of ductile materials has frequently been observed to result from the nucleation, growth and coalescence of microscopic voids. Experimental and analytical studies have shown that both the stress constraint factor and the effective plastic strain play a significant role in the ductile failure process. Experimental results also suggest that these two parameters are not independent of each other at failure initiation. In this study, a methodology for characterizing the effect of stress constraint A_m (which is defined to be the ratio of the mean stress and the effective stress A_m=σ_m/σ_e ) on ductile failure is proposed. This methodology is based on experimental evidence that shows the effective plastic strain at failure initiation has a one‐to‐one relationship with stress constraint. Numerical analyses based on plane strain and three‐dimensional unit‐cell models have been carried out to investigate failure initiation of the unit cell under different constraint conditions. Results from the numerical studies indicate (a) for each void volume fraction, there exists a local failure locus in terms of mesoscopic quantities, σ_m and σ_e, that adequately predict incipient local micro‐void link‐up, (b) the results are fully consistent with a failure criterion that maximizes mesoscopic effective stress for a constant level of stress constraint A_m, (c) for high to moderate constraint A_m, the link‐up envelope values for σ_m and σ_e are consistent with limit load conditions where the critical principal stress σ_1c corresponds to the maximum principal stress in the loading history and (d) for low constraint, the link‐up envelope values for σ_m and σ_e correspond to link‐up conditions having high levels of plastic strain and a principal stress σ₁ that is lower than the maximum value for this loading history. Thus, the results suggest that a two‐parameter ductile fracture criterion is plausible, such as critical crack opening displacement (COD) and stress constraint A_m, for predicting the process of stable tearing in materials undergoing ductile void growth during the fracture process.     

Dynamic crack initiation toughness of 4340 steel at constant loading rates

Determination of fracture toughness for metals under quasi-static loading conditions can follow well-established procedures and ASTM standards. The use of metallic materials in impact related applications requires the determination of dynamic crack initiation toughness for these materials. There are two main challenges in experiment design that must be overcome before valid dynamic data can be obtained. Dynamic equilibrium over the entire specimen needs to be approximately achieved to relate the crack tip loading state to the far-field loading conditions, and the loading rate at the crack tip should be maintained near constant during an experiment to delineate rate effects on the values of dynamic crack initiation toughness. A recently developed experimental technique for determining dynamic crack initiation toughness of brittle materials has been adapted to measure the dynamic crack initiation toughness of high-strength steel alloys. A Kolsky pressure bar is used to apply the dynamic loading. A pulse shaper is used to achieve constant loading rate at the crack tip and dynamic equilibrium across the specimen. A four-point bending configuration is used at the gage section of the setup. Results are presented which show a monotonically increasing rate dependence of crack initiation toughness for 4340 high-strength steel.     

Partially stiffened elastic half-plane with an edge crack

A technique, using the Brazilian disk specimen, for measuring the fracture toughness of unidirectional fiber-reinforced composites, over the entire range of crack-tip mode mixities, was developed. The fracture toughness of a graphite/epoxy fiber-reinforced composite was measured, under both mode-I and mode-II loading conditions. We found that for certain material orientations the mode-II fracture toughness is substantially higher than the mode-I toughness. The complete dependence of the fracture toughness on the crack-tip mixity was determined for particular material orientations and the phenomenological fracture toughness curves were constructed. Using the Brazilian disk specimen, together with a hydraulic testing machine, the fracture toughness of the composite under moderate loading rates was measured. We observed that the mode-I fracture toughness was not sensitive to the loading rate at the crack tip, K, while the mode-II ‘dynamic’ fracture toughness increased approximately 50 percent over the quasi-static fracture toughness. A qualitative explanation of the dependency of fracture toughness on crack-tip loading rate is discussed. Finally, a mechanical fracture criterion, at the microscopic level, which governs the crack initiation under mixed-mode loading conditions is presented; these theoretical predictions closely follow the trend of experimental measurements. This revised version was published online in August 2006 with corrections to the Cover Date.     

Numerical determination of stretch zone width (SZW) using tensile test data

There is an increasing effort to use critical stretch zone width (SZW) for the evaluation of initiation fracture toughness that is considered as geometry independent material property. The existing numerical SZW evaluation method is based on crack tip opening displacement measurement, which is evaluated using various definitions. This numerical method also does not define the critical stage for critical SZW measurement. This work attempts to establish a procedure for numerical determination of SZW, its critical value (SZW_c) and initiation fracture toughness using tensile test data. The proposed methodology also tries to explain the mechanism involved in the creation of stretched zone and thus defines the stage to calculate critical SZW. Numerical analyses have also been carried out to understand the role of crack tip constraint in standard fracture specimen during the blunting process and the tensile test sample.     

Three‐dimensional analyses of in‐plane and out‐of‐plane crack‐tip constraint characterization for fracture specimens

Three‐dimensional elastic–plastic finite element analyses have been conducted for 21 experimental specimens with different in‐plane and out‐of‐plane constraints in the literature. The distributions of five constraint parameters (namely T‐stress, Q, h, T_z and A_p) along crack fronts (specimen thickness) for the specimens were calculated. The capability and applicability of the parameters for characterizing in‐plane and out‐of‐plane crack‐tip constraints and establishing unified correlation with fracture toughness of a steel were investigated. The results show that the four constraint parameters (T‐stress, Q, h and T_z) based on crack‐tip stress fields are only sensitive to in‐plane or out‐of‐plane constraints. Therefore, the monotonic unified correlation curves with fracture toughness (toughness loci) cannot obtained by using them. The parameter A_p based on crack‐tip equivalent plastic strain is sensitive to both in‐plane and out‐of‐plane constraints, and may effectively characterize both of them. The monotonic unified correlation curves with fracture toughness can be obtained by using A_p. In structural integrity assessments, the correlation curves may be used in the failure assessment diagram (FAD) methodology for incorporating both in‐plane and out‐of‐plane constraint effects in structures for improving accuracy.     

Resistance Against the Intrinsic Rate of Fracture Mechanics Parameters for Polymeric Materials Under Moderate Impact Loading

This study contributes towards understanding crack toughness as resistance against the intrinsic rate of fracture mechanics parameters. Up to now only few investigations have been done under moderate impact loading conditions. Based on experimental investigations using the crack resistance (R) concept, it has been shown that the stop block method combined with the multiple-specimen technique is a unique method for polymers under impact loading conditions in comparison with different R-curve methods. Other methods for the determination of R curve such as the low-blow technique are normally not applicable for polymers due to their time-dependent mechanical properties. The crack-tip opening displacement (CTOD) rate is a measurement of the rate sensibility of stable fracture process depending on the type of deformation, which can provide deep insights into the micromechanics and activation mechanisms during the fracture processes. In the polymeric materials mostly investigated, one can understand the stable crack propagation with three-stage processes; crack-tip blunting/crack initiation, non-stationary stable crack growth and steady-state stable crack growth (an equilibrium state). In this stable crack propagation, the values of normalized CTOD rate converge rapidly to a ‘matrix’-specific threshold. The stop block method in the multiple-specimen technique assures the criteria of the time-independent strain field around the crack tip and constant crack speed therewith and the J-integral is a valid toughness parameter.     

Mode I plane stress crack-tip constraint for elastic-plastic materials with different strain hardening

Finite element analyses and simulations have been undertaken to investigate the triaxial constraint in the crack-tip regions of a stationary crack and a steady-state growing crack under mode I plane stress for elastic-plastic materials with different strain hardening. The results show that the triaxial constraint in the crack-tip region is independent of specimen geometry, and material strain hardening, both for a stationary and an extending crack quasi-statically. The triaxial constraints for the various configurations examined are in better accordance with those required by the HRR solution for a stationary crack, which defines the low and similar constraints in crack-tip regions for different material strain hardening in the plane stress case. Along the entire ligament ahead of a crack tip, the constraint level transites gradually from that defined by the HRR solution within the near tip zone to that characterized by the stress intensity factor K _I in the far field.     

DAMAGE MECHANICS APPROACH TO REMOVE THE CONSTRAINT DEPENDENCE OF ELASTIC–PLASTIC FRACTURE TOUGHNESS

It is now generally agreed that the applicability of a one-parameter J-based ductile fracture approach is limited to so-called high constraint crack geometries, and that the elastic-plastic fracture toughness J_1c, is not a material constant but strongly specimen geometry constraint-dependent. In this paper, the constraint effect on elastic-plastic fracture toughness is investigated by use of a continuum damage mechanics approach. Based on a new local damage theory for ductile fracture(proposed by the author) which has a clear physical meaning and can describe both deformation and constraint effects on ductile fracture, a relationship is described between the conventional elastic-plastic fracture toughness, J_1c, and crack tip constraint, characterized by crack tip stress triaxiality T. Then, a new parameter J_dc (and associated criterion, J_d=J_dc) for ductile fracture is proposed. Experiments show that toughness variation with specimen geometry constraint changes can effectively be removed by use of the constraint correction procedure proposed in this paper, and that the new parameter J_dc is a material constant independent of specimen geometry (constraint). This parameter can serve as a new parameter to differentiate the elastic-plastic fracture toughness of engineering materials, which provides a new approach for fracture assessments of structures. It is not necessary to determine which laboratory specimen matches the structural constraint; rather, any specimen geometry can be tested to measure the size-independent fracture toughness J_dc. The potential advantage is clear and the results are very encouraging.     

Effects of T-stresses on fracture initiation for a closed crack in compression with frictional crack faces

This paper studies crack extension resulting from a closed crack in compression. The crack-tip field of such a crack contains a singular field relative to K _II and non-singular T-stresses T _x and T _y parallel and perpendicular to the crack plane, respectively. Using a modified maximum tensile stress criterion with the singular and non-singular terms, the kinking angle at the onset of crack growth is determined by a two parameter field involving the mode-II stress intensity factors and T-stresses, and at fracture initiation a wing crack may be created at an arbitrary angle from 0° to 90°. A compressive T _y increases the kinking angle and reinforces apparent mode-II fracture toughness, while a compressive T _x decreases the kinking angle and enhances apparent mode-II fracture toughness. The direction and resistance of fracture onset is strongly affected by T-stresses as well as frictional stress. The von Mises effective stress is determined for small-scale yielding near the crack tip. The effective stress contour shape exhibits a marked asymmetrical behavior unless 2T _x  = T _y  ≤ 0 for plane stress state. Coulomb friction between two crack faces generally increases the kinking angle, shrinks the size enclosed by the effective stress contour and enhances apparent fracture toughness. Field evidence and experimental observations of many phenomena involving the growth of closed cracks in compression agree well with theoretical predictions of the present model.     

COMPENDIUM OF T-STRESS SOLUTIONS FOR TWO AND THREE DIMENSIONAL CRACKED GEOMETRIES

Conventional theories of fracture assume that the state of stress and strain in the vicinity of a crack tip, and so the onset of failure, is characterised by a single parameter. The physical extent of these single-parameter fields is determined by the geometry, size and mode of loading of the engineering structure or test specimen containing the crack. It is now recognised that fracture toughness is a material property characterised by a single parameter J only in special circumstances which involve a high degree of constraint at the crack-tip. In general the apparent toughness of a material changes according to the shape and size of the cracked configuration and the mode of loading imposed. Recent analytical, numerical and experimental studies have attempted to describe fracture in terms of both J and a second parameter. The reason for the second parameter is to provide further information, which J on its own is unable to convey, concerning how the structural and loading configuration affects the constraint conditions at the crack-tip. One particular candidate parameter is the elastic T-stress which is directly proportional to the load applied to the cracked geometry. This paper brings together published solutions for the T-stress for a range of two and three-dimensional cracked geometries and presents some new results calculated at AEA Technology. The application of two-parameter fracture mechanics is a subject of ongoing development and users of the data in this paper are recommended to seek expert advice regarding applications to specific structural integrity assessments.     

Effect of strength mis-match and dynamic loading on ductile fracture initiation

It has been well known that ductile fracture of steels is accelerated by triaxial stresses. The characteristics of ductile crack initiation in steels are evaluated quantitatively using a two-parameter criterion based on equivalent plastic strain and stress triaxiality.The present study focuses on the effects of geometrical discontinuity, strength mis-match, which can elevate plastic constraint due to heterogeneous plastic straining, and loading rate on the critical condition for ductile fracture initiation using a two-parameter criterion. Fracture initiation testing has been conducted under static and dynamic loading using circumferentially notched round-bar specimens. In order to evaluate the stress/strain state in the specimens, especially under dynamic loading, a thermal elastic-plastic dynamic finite element (FE) analysis considering the temperature rise due to plastic deformation has been carried out.The tensile tests on specimens with an undermatching interlayer showed that the relationship between the critical equivalent plastic strain to initiate ductile fracture and stress triaxiality was equivalent to that obtained on homogeneous specimens under static loading. Moreover, the two-parameter criterion for ductile fracture initiation is shown to be independent of the loading rate. It was demonstrated that the critical global strain to initiate ductile fracture in specimens with strength mis-match under various loading rate can be estimated based on the local criterion, that is two-parameter criterion obtained on homogeneous specimens under static tension, by mean of FE-analysis taken into account accurately both strength mis-match and dynamic loading effects on stress/strain behaviors.     

Correlation of material constraint with fracture toughness of interface regions in a dissimilar metal welded joint

In this work, the constraint parameter A_p based on crack‐tip equivalent plastic strain was calculated by finite element analyses for the cracks located at different locations in two interface regions in a dissimilar metal weld joint (DMWJ). The capabilities of the parameter A_p for characterizing material constraint and establishing correlation of material constraint with fracture toughness of the interface region cracks have been examined. The results show that the parameter A_p can characterize material constraint effect caused by material mismatch and initial crack positions in the interface regions. Based on the A_p, the correlation lines and formulae of material constraint with fracture toughness of the interface region cracks in the DMWJ can be established, and they may be used for obtaining material constraint‐dependent fracture toughness for the interface region cracks. The results in this work combining with those in the previous studies indicate that the parameter A_p may be a unified constraint parameter that can characterize both geometry constraint (including in‐plane and out‐of‐plane constraints) and material constraint, and it may be used in accurate fracture assessments of welded components with different geometry and material constraints.     

Method of Prevention of Fracture of Welded Metal Structural Elements Subjected to Single Dynamic Loading

We propose a method for the assessment of the fracture toughness of structural materials and their welded joints under conditions of single dynamic loading, which is based on the criterion of nonlinear fracture mechanics _cr ^D . The regularities of the loading rate effect defined by the parameter ' (the rate of the crack tip opening displacement) on the fracture toughness have been established. A procedure is recommended for prevention of fracture of welded structure elements under conditions of high strain-rate deformation.     

Initiation, propagation and arrest of an interface crack subjected to controlled stress wave loading

An experimental study has been conducted to investigate the initiation, propagation, and arrest of bimaterial interface cracks subjected to controlled stress wave loading in the form of a tensile dilatational stress wave pulse. The tensile pulse is generated by detonating lead azide explosive in a specially designed specimen. Dynamic loading of the bimaterial interface results in crack initiation, propagation, and arrest, all in the same experiment. This failure event is observed using photoelasticity in conjunction with high speed photography. Full field data from the experimentally obtained isochromatic fringe patterns is analyzed to determine time histories of various fracture parameters such as the crack tip speed, the dynamic complex stress intensity factor, the energy release rate, and the mixity. The experimental data is also used to quantify the values of the dynamic initiation and arrest toughness and to evaluate a recently proposed dynamic interface fracture criterion. This revised version was published online in August 2006 with corrections to the Cover Date.     

A framework to correlate a/W ratio effects on elastic-plastic fracture toughness (J c )

Single edge-notched bend (SENB) specimens containing shallow cracks (a/W < 0.2) are commonly employed for fracture testing of ferritic materials in the lower-transition region where extensive plasticity (but no significant ductile crack growth) precedes unstable fracture. Critical J-values J _c ) for shallow crack specimens are significantly larger (factor of 2–3) than the J _c )-values for corresponding deep crack specimens at identical temperatures. The increase of fracture toughness arises from the loss of constraint that occurs when the gross plastic zones of bending impinge on the otherwise autonomous crack-tip plastic zones. Consequently, SENB specimens with small and large a/W ratios loaded to the same J-value have markedly different crack-tip stresses under large-scale plasticity. Detailed, plane-strain finite-element analyses and a local stress-based criterion for cleavage fracture are combined to establish specimen size requirements (deformation limits) for testing in the transition region which assure a single parameter characterization of the crack-tip stress field. Moreover, these analyses provide a framework to correlate J _c )-values with a/W ratio once the deformation limits are exceeded. The correlation procedure is shown to remove the geometry dependence of fracture toughness values for an A36 steel in the transition region across a/W ratios and to reduce the scatter of toughness values for nominally identical specimens.     

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.     

The cohesive zone model in a problem of delayed hydride cracking of zirconium alloys

The crack tip model with the cohesive zone ahead of a finite crack tip has been presented. The estimation of the length of the cohesive zone and the crack tip opening displacement is based on the comparison of the local stress concentration, according to Westergaard's theory, with the cohesive stress. To calculate the cohesive stress, von Mises yield condition at the boundary of the cohesive zone is employed for plane strain and plane stress. The model of the stress distribution with the maximum stress within the cohesive zone is discussed. Local criterion of brittle fracture and modelling of the fracture process zone by cohesive zone were used to describe fracture initiation at the hydride platelet in the process zone ahead of the crack tip. It was shown that the theoretical K _IH-estimation applied to the case of mixed plane condition within the process zone is qualitatively consistent with experimental data for unirradiated Zr-2.5Nb alloy. In the framework of the proposed model, the theoretical value of K ^H _IC for a single hydride platelet at the crack tip has been also estimated.