Accounting for porosity, time and temperature dependency in fracture mechanics concepts on polyvinylidene fluoride material

The polyvinylidene fluoride (PVDF) under study is a semi-crystalline polymer that exhibits sensitivity of mechanical properties to both strain rate and temperature. Furthermore, this material is subjected to a significant cavitation during deformation. A comprehensive experimental database was built in order to analyze the fracture behaviour in the ductile to brittle transition domain. Tensile tests were carried out on smooth and notched specimens at temperatures ranging from −50 °C to 20 °C. The results were used to determine temperature-dependent material parameters by using the mechanics of porous media. The obtained set of parameters was validated on two kinds of pre-cracked specimens, by using the local approach of fracture mechanics. With the help of a finite element code, both global and local approaches of fracture mechanics were shown to complement one another: whereas classical formulae of J-integral fail to characterize crack initiation for this PVDF, the present methodology allowed the plot of J_1C values with respect to temperature.     

Elastic-plastic fracture mechanics assessment of test data for circumferential cracked pipes

This paper presents experimental validation of two reference stress based methods for circumferential cracked pipes. One is the R6 method where the reference stress is defined by the plastic limit load. The other is the enhanced reference stress method, recently proposed by the authors, where the reference stress is defined by the optimised reference load. Using 38 published pipe test data, the predicted maximum instability loads according to both methods are compared with the experimental ones for pipes with circumferential through-thickness cracks and with part circumferential surface cracks. It is found that the R6 method gives conservative estimates of the maximum loads for all cases. Ratios of the experimental maximum load to the predicted load range from 0.54 to 0.98. On the other hand, the proposed method gives overall closer maximum loads than R6, compared to the experimental data. However, for part through-thickness surface cracks, the estimated loads were slightly non-conservative for four cases, and possible reasons are fully discussed.     

Elastic-plastic fracture mechanics analyses of circumferential through-wall cracks between elbows and pipes

The present work proposes a method for elastic-plastic fracture mechanics analysis of the circumferential through-wall crack in weldment joining elbows and attached straight pipes, subject to in-plane bending. Heterogeneous nature of weldment is not explicitly considered and thus, the proposed method assumes cracks in homogeneous materials. Based on small strain finite element limit analyses using elastic-perfectly plastic materials, closed-form limit loads for circumferential through-wall cracks between elbows and straight pipes under bending are given. Then applicability of the reference stress-based method to approximately estimate J and crack opening displacement (COD) is evaluated. It was found that the limit moments for circumferential cracks between elbows and attached straight pipes can be much lower than those for cracks in straight pipes, particularly for a crack length of less than 30% of the circumference; this result is of great interest in practical cases. This result implies that, if one assumes that the crack locates in the straight pipe, limit moments could be overestimated significantly, and accordingly, reference stress-based J and COD could be significantly overestimated. For the leak-before-break analysis, accurate J and COD estimation equations based on the reference stress approach are proposed.     

Effect of fracture path on the toughness of weld metal

The crack propagation direction may affect weld metal fracture behavior. This fracture behavior has been investigated using two sets of single edge notched bend (SENB) specimens; one with a crack propagating in the welding direction (B×2B) and the other with a crack propagating from the top in the root direction (B×B) of a welded joint. Two different weld metals were used, one with low and one with high toughness values. For Weld Metal A, two specimen types have been used (B×B and B×2B) both with deep cracks. The weld metal A (with high toughness values) has reasonably uniform properties between weld root and cap. The resulting J-R curves show little effect of the specimen type, are ductile to the extent that the toughness exceeds the maximum J_max, value allowed by validity limits and testing is in the large –scale yielding regime. In the case of weld metal B (with low toughness values) with two specimen types (B×B and B×2B) the B×B specimen has shallow cracks while the B×2B specimen has deep cracks. Both resulting J-R curves show unstable behavior despite the fact that the types of specimen and their constraints are different. The analysis has shown that crack propagation direction is most influential for a weldment with low toughness in the small scale yielding regime, whereas its influence diminishes due to ductile tearing during stable crack growth and large scale yielding. The results have shown that these effects are different in both the crack initiation phase and during stable crack growth, indicating a dependence on weld metal toughness and the microstructure of the weld metal. It can be concluded that, if resistance curves during stable crack growth do not show differences in both notch orientations, the fracture toughness values of the whole weld metal can be treated as uniform.     

Application of finite element method for determination of stress intensity factor and plastic zone geometry in an aluminium alloy sheet under uniaxial tension

High strength materials have gained prominence in the fields of aero-structures, space missiles, ship-building, pressure vessels etc. However, high strength materials are often characterised by low values of crack resistance or fracture toughness. Knowledge of stress intensity factor (SIF) is essential to predict their fracture toughness. SIF values can be obtained both theoretically and experimentally. Theoretical methods include analytical techniques as well as the finite element method (FEM). The former is used for simpler geometries and the latter for complicated geometries of engineering structures. The SIF as a function of crack size in an aluminium alloy 2024-T₃ (Al-4·5% Cu, 1·5% Mg, 0·6% Mn) sheet was determined by a computer method. These values were obtained directly from the stresses as well as indirectly from strain energy release rateG andJ integral. The results agree well with the normalised values obtained from an ASTM formula. The size and shape of the plastic zone at the crack tip have been determined as a function of nominal stress for a fixed crack length. The plastic zone has the form of two ellipsoids with their maximum spreads oriented around 69° to the crack axis.     

Estimations of creep fracture mechanics parameters for through-thickness cracked cylinders and finite element validation

This paper compares engineering estimation schemes of C* and creep crack opening displacement (COD) for cylinders with circumferential and axial through‐thickness cracks at elevated temperatures with detailed 3D elastic‐creep finite element results. Engineering estimation schemes include the GE/EPRI method; the reference stress (RS) method where the reference stress is defined based on the plastic limit load; and the enhanced reference stress (ERS) method where the reference stress is defined based on the optimised reference load, recently proposed by the authors. Systematic investigations are made not only on the effect of creep‐deformation behaviour on C* and creep COD, but also on effects of the crack location, the cylinder geometry, the crack length and the loading mode. Comparison of the finite element (FE) results with engineering estimations provides that for idealised power law creep, estimated C* and COD rate results from the GE/EPRI method agree best with FE results, suggesting that published plastic influence functions for plastic J and COD for through‐thickness cracked cylinders are reliable. For general creep‐deformation laws where either primary or tertiary creep is important and thus the GE/EPRI method is hard to apply, on the other hand, the ERS method provides more accurate and robust estimations for C* and COD rate than the reference stress method. As these two methods differ only in the definition of the reference stress, the ERS method maintains benefits of the reference stress method in terms of simplicity, but improves accuracy of the estimated J, C* and COD results.     

Welding mechanics for advanced component safety assessment

Numerical methods are nowadays a useful tool for the calculation of distortion and residual stresses as a result from the welding process. Modern finite element codes not only allow for calculation of deformations and stresses due to the welding process but also take into account the change of microstructure due to different heating and cooling rates. As an extension to the pure welding simulation, the field of welding mechanics combines the mechanics and the material behaviour from the welding process with the assessment of service behaviour of welded components. In the paper, new results of experimental and numerical work in the field of welding mechanics are described. Through examples from automotive, nuclear and pipe-line applications it is demonstrated that an equilibrated treatment and a close interaction of “process”, “properties” and “defects” are necessary to come up with an advanced fitness-for-service assessment of welded components.     

Investigation of fracture resistance of natural rubber/clay nanocomposites by J-testing

The present work is aimed at studying the fracture behavior of a series of vulcanized natural rubber/organoclay samples obtained by melt blending. A fracture mechanics approach based on J-testing was adopted to evaluate the material resistance to crack initiation and propagation from a J-resistance curve as experimentally obtained by a single specimen procedure. The basis of the method and the experimental procedure adopted are described. Further, the effect of the organoclay content within the elastomeric matrix on the fracture properties is analyzed. It is found that the capability of the organoclay to improve fracture resistance is rate dependent indicating the viscoelastic character of the fracture process in such filled systems.     

Fracture mechanics solutions to spot welds

Notch stress, stress intensity factors and J-integral at a spot weld are generally expressed by structural stresses around the spot weld. The determination of these parameters are then simplified as determining the structural stresses that can be calculated by a spoke pattern in finite element analysis. Approximate stress formulas for structural stress, notch stress and equivalent stress intensity factor are given for common spot-welded specimens. With the aid of the formulas, test data in terms of the original load can be easily transformed into the data in terms of the structural stress, notch stress or equivalent stress intensity factor at the spot weld. The formulas also facilitate the transfer of test data across different specimens. A measuring method is given for lap joints. The strain gauge technique developed for the tensile-shear specimen shows that all the structural stress, notch stress, stress intensity factors and J-integral at the spot weld can be determined by two strain gauges attached only to the outer surface of one sheet. The results presented here should be helpful for the analysis and testing of spot welds and for developing measuring methods for spot welds.     

Non-linear fracture mechanics analyses of part circumferential surface cracked pipes

This paper provides engineering estimates of non-linear fracture mechanics parameters for pipes with part circumferential inner surface cracks, subject to internal pressure and global bending. Solutions are given in the form of two different approaches, the GE/EPRI approach and the reference stress approach. For the GE/EPRI approach, the plastic influence functions for fully plastic J solutions are tabulated based on extensive 3-D FE calculations using deformation plasticity, covering a wide range of pipe and crack geometries. The developed GE/EPRI-type fully plastic J estimation equations are then re-formulated using the concept of the reference stress approach for wider applications. The proposed reference stress based estimates are validated against detailed 3-D elastic-plastic and elastic-creep FE results. For a total of 26 cases considered in this paper, agreement between the proposed reference stress based J and C ^* estimates and the FE results is excellent. An important aspect of the proposed estimates is that they not only are simple and accurate but also can be used to estimate J and C ^* at an arbitrary point along the crack front.     

Method of constraint loss correction of CTOD fracture toughness for fracture assessment of steel components

This paper presents a procedure for transferring the CTOD fracture toughness obtained from laboratory specimens to an equivalent CTOD for structural components, taking constraint loss into account. The Weibull stress criterion is applied to correct the CTOD for constraint loss, which leads to an equivalent CTOD ratio, β, defined as β = δ/δ_WP, where δ and δ_WP are CTODs of the standard fracture toughness specimen and the structural component, respectively, at the same level of the Weibull stress. The CTOD ratio β is intended to apply to the fracture assessment of ferritic steel components to stress levels beyond small-scale yielding. Nomographs are given to determine the β-value as a function of the crack type and size in the component, the yield-to-tensile ratio of the material and the Weibull shape parameter m. Examples of the fracture assessment using β are shown within the context of a failure assessment diagram (FAD). An excessive conservatism observed in the conventional procedure is reduced reasonably by applying the equivalent CTOD ratio, β.     

Crack opening analysis of complex cracked pipes

Based on the reference stress approach, two sets of the crack opening displacement (COD) estimation equations are proposed for a complex cracked pipe. One set of equations can be used for the case when full stress-strain data are known, and the other for the case when only yield and tensile strengths are available. To define the reference stress, a simple plastic limit analysis for the complex cracked pipe subject to combined bending and tension is performed, considering the crack closure effect in the compressive-stressed region. Comparison with ten published test data and the results from the existing method shows that the present method not only reduces non-conservatism associated with the existing method, but also provides consistent and overall satisfactory results. These results provide sufficient confidence in the use of the present method to estimate the COD (and thus the leak rate) for the Leak-before-Break (LBB) analysis of complex cracked pipes. Finally, the J-estimation equations are also provided for complex cracked pipes, for the LBB analysis of complex cracked pipes.     

Scratch test model for the determination of fracture toughness

We revisit the scratch test within the framework of linear elastic fracture mechanics. In the analysis, we employ an Airy stress function approach to determine stresses and displacement in the vicinity of the scratch-blade–material interface, which serve as input for the evaluation of the energy release rate by means of the J-Integral. In contrast to previous models, the energy release rate thus found scales with the sum of the applied forces squared. This entails a linear relation between the applied forces and , where w is the scratch width and d the scratch depth. This analytical scaling is validated using experimental scratch data on cement paste and sandstone, which shows that the proposed approach provides a convenient way to determine the fracture toughness from scratch tests carried out with different scratch widths and depths.     

Monotonic vis-à-vis cyclic fracture behaviour of AISI 304LN stainless steel

This investigation is aimed to examine the monotonic and cyclic fracture behaviour of AISI 304LN stainless steel and its weldments, in order to assess their integrity under seismic loading conditions. The monotonic fracture resistance of the steel has been determined using standard J-integral technique; whereas the cyclic fracture resistance has been evaluated using periodic unloading to different extents fixed by pre-determined R-ratio. Comparison of the fracture toughness values of the steel estimated under monotonic and cyclic loading indicates that the latter could be as low as one-fifth of the former. The observed degradation in cyclic fracture resistance has been attributed to crack tip re-sharpening during cyclic loading.     

An indirect boundary element method for three-dimensional dynamic fracture mechanics

Indirect boundary element methods (fictitious load and displacement discontinuity) have been developed for the analysis of three-dimensional elastostatic and elastodynamic fracture mechanics problems. A set of boundary integral equations for fictitious loads and displacement discontinuities have been derived. The stress intensity factors were obtained by the stress equivalent method for static loading. For dynamic loading the problem was studied in Laplace transform space where the numerical calculation procedure, for the stress intensity factor K_I(p), is the same: as that for the static problem. The Durbin inversion method for Laplace transforms was used to obtain the stress intensity factors in the time domain K_I(t). Results of this analysis are presented for a square bar, with either a rectangular or a circular crack, under static and dynamic loads.     

Fracture behavior of stitched warp-knit fabric composites

Pilot studies are conducted to characterize the macroscopic fracture resistance behavior using linear elastic fracture mechanics and attempt to quantify the fracture parameters in which may govern the fracture and failure patterns of stitched warp-knit fabric composites. Methods based on the J-integral method and Betti's reciprocal theorem in extracting the fracture parameters, critical stress intensity factors, T-stress, and the second term of _y(r,0) near the crack tip prior to fracture initiation are formulated. Two fracture criteria, [_c,r _c] and [_c,r _c] are attempted to characterize the failure initiation for the fiber-dominated failure mode and self-similar crack extension in a given thickness of the laminate. Based on linear elastic fracture mechanics principle, these criteria are transformed into crack-driving forces [K _Q,T] and [K _Q,g ₃₂]. The two-parameter fracture criteria, [K _Q,T] and [K _Q,g ₃₂] provide a good correlation for the CCT and SENT specimens, but not for the high constraint CT specimens. With the limited experimental data, the results tend to show that the large tensile T-stress and large magnitude of negative g ₃₂ may inhibit the crack extension in the same crack plane and promote crack kinking.     

Boundary element analysis of three‐dimensional cracks in anisotropic solids

This paper presents a boundary element analysis of linear elastic fracture mechanics in three‐dimensional cracks of anisotropic solids. The method is a single‐domain based, thus it can model the solids with multiple interacting cracks or damage. In addition, the method can apply the fracture analysis in both bounded and unbounded anisotropic media and the stress intensity factors (SIFs) can be deduced directly from the boundary element solutions. The present boundary element formulation is based on a pair of boundary integral equations, namely, the displacement and traction boundary integral equations. While the former is collocated exclusively on the uncracked boundary, the latter is discretized only on one side of the crack surface. The displacement and/or traction are used as unknown variables on the uncracked boundary and the relative crack opening displacement (COD) (i.e. displacement discontinuity, or dislocation) is treated as a unknown quantity on the crack surface. This formulation possesses the advantages of both the traditional displacement boundary element method (BEM) and the displacement discontinuity (or dislocation) method, and thus eliminates the deficiency associated with the BEMs in modelling fracture behaviour of the solids. Special crack‐front elements are introduced to capture the crack‐tip behaviour. Numerical examples of stress intensity factors (SIFs) calculation are given for transversely isotropic orthotropic and anisotropic solids. For a penny‐shaped or a square‐shaped crack located in the plane of isotropy, the SIFs obtained with the present formulation are in very good agreement with existing closed‐form solutions and numerical results. For the crack not aligned with the plane of isotropy or in an anisotropic solid under remote pure tension, mixed mode fracture behavior occurs due to the material anisotropy and SIFs strongly depend on material anisotropy. Copyright © 2000 John Wiley & Sons, Ltd.     

Comparison of CTOD standards: BS 7448-Part 1 and revised ASTM E1290

Crack tip opening displacement (CTOD) has been calculated using the plastic hinge model with an assumed rotational center since the British Standards Institution (BS) standardized BS5762 in 1979. The American Society for Testing and Materials (ASTM) accepted the plastic hinge model and standardized E1290 in 1989. However, ASTM revised E1290 in 2002, and has proposed a conversion from J to CTOD. CTOD-based fracture toughness evaluation has been widely used for the defect assessment of many welded structural components, and two different CTOD calculations could lead to confusion for Fitness-for-Service. In this study, the effects of CTOD testing methodologies on CTOD values were investigated according to round robin tests conducted by the Japan Welding Engineering Society (WES), and the concept of CTOD as a fracture parameter is discussed.     

Reference Stress Approximations for J and COD of Circumferential Through-Wall Cracked Pipes

Reference stress approximations for the J integral and crack tip opening displacement (COD) for circumferential through-wall cracked pipes under tension and under bending are reported. The proposed J estimation equation is fully compatible with the existing reference stress based J estimation, currently embedded in the R6 assessment procedure, but involves a slightly different definition of the reference stress, using an optimised reference load instead of the limit load. This modification enhances the accuracy of the J estimation for circumferentially cracked pipes. Confidence in the proposed equation is gained from the significantly reduced hardening dependence of the plastic influence functions in the GE/EPRI method. The proposed COD estimation equation includes two further modifications. One is the use of a power-law fit to the plastic portion of the stress strain data, instead of the use of the actual stress strain data. In this context, a robust estimation equation for the strain hardening index is given. The other modification is to the plasticity correction term in contained yielding. A lower bound COD estimation equation is also given, similar to the R6 option 1 Jestimation curve, which is suitable when only limited tensile properties are available. The resulting estimation equations are simple to use. Comparisons with experimental pipe test data show that the proposed COD estimation equations provide overall good agreement, which gives confidence in applying them to Leak-before-Break (LBB) analyses.