Effect of loading rate on dynamic fracture initiation toughness of brittle materials

Numerical simulation is carried out to investigate the effect of loading rate on dynamic fracture initiation toughness including the crack-tip constraint. Finite element analyses are performed for a single edge cracked plate whose crack surface is subjected to uniform pressure with various loading rate. The first three terms in the Williams’ asymptotic series solution is utilized to characterize the crack-tip stress field under dynamic loads. The coefficient of the third term in Williams’ solution, A ₃, was utilized as a crack tip constraint parameter. Numerical results demonstrate that (a) the dynamic crack tip opening stress field is well represented by the three term solution at various loading rate, (b) the loading rate can be reflected by the constraint, and (c) the constraint A ₃ decreases with increasing loading rate. To predict the dynamic fracture initiation toughness, a failure criterion based on the attainment of a critical opening stress at a critical distance ahead of the crack tip is assumed. Using this failure criterion with the constraint parameter, A ₃, fracture initiation toughness is determined and in agreement with available experimental data for Homalite-100 material at various loading rate.     

Bending modified J–Q theory and crack-tip constraint quantification

It is well known that the J–Q theory can characterize the crack-tip fields and quantify constraint levels for various geometry and loading configurations in elastic–plastic materials, but it fails at bending-dominant large deformation. This drawback seriously restricts its applications to fracture constraint analysis. A modification of J–Q theory is developed as a three-term solution with an additional term to address the global bending stress to offset this restriction. The nonlinear bending stress is approximately linearized in the region of interest under large-scale yielding (LSY), with the linearization factor determined using a two-point matching method at each loading for a specific cracked geometry in bending. To validate the proposed solution, detailed elastic–plastic finite element analysis (FEA) is conducted under plane strain conditions for three conventional bending specimens with different crack lengths for X80 pipeline steel. These include single edge notched bend (SENB), single edge notched tension (SENT) and compact tension (CT) specimens from small-scale yielding (SSY) to LSY. Results show that the bending modified J–Q solution can well match FEA results of crack-tip stress fields for all bending specimens at all deformation levels from SSY to LSY, with the modified Q being a load- and distance-independent constraint parameter under LSY. Therefore, the modified parameter Q can be effectively used to quantify crack-tip constraint for bending geometries. Its application to fracture constraint analysis is demonstrated by determining constraint corrected J–R curves.     

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.     

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.     

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 .     

Constraint effects on probabilistic analysis of cracks in ductile solids

This paper presents a method for evaluating constraint effects on probabilistic elastic–plastic analysis of cracks in ductile solids. It is based on fracture parameters J and Q , correlation between Q and J– resistance curve of the material, and J -tearing theory for predicting fracture initiation and instability in cracked structures. Based on experimental data from small-scale fracture specimens, correlation equations were developed for fracture toughness at crack initiation and the slope of the J– resistance curve as a function of constraint condition. The random parameters may involve crack geometry, tensile and fracture toughness properties of the material, and applied loads. Standard reliability methods were applied to predict probabilistic fracture response and reliability of cracked structures. The results suggest that crack-tip constraints have little effect on the probability of crack initiation. However, the probability of fracture instability can be significantly reduced when constraint effects are taken into account. Hence, for a structure where some amount of stable crack-growth can be tolerated, crack-tip constraints should be considered for probabilistic fracture-mechanics analysis.     

An engineering methodology to assess effects of weld strength mismatch on cleavage fracture toughness using the Weibull stress approach

This work describes the development of an engineering approach based upon a toughness scaling methodology incorporating the effects of weld strength mismatch on crack-tip driving forces. The approach adopts a nondimensional Weibull stress, [`(s)]_w{\bar{{\sigma}}_w}, as a the near-tip driving force to correlate cleavage fracture across cracked weld configurations with different mismatch conditions even though the loading parameter (measured by J) may vary widely due to mismatch and constraint variations. Application of the procedure to predict the failure strain for an overmatch girth weld made of an API X80 pipeline steel demonstrates the effectiveness of the micromechanics approach. Overall, the results lend strong support to use a Weibull stress based procedure in defect assessments of structural welds.     

Fracture toughness evaluation for short glass fibre reinforced composites

Valid plane-stress fracture toughness evaluation of short fibre reinforced composites relies essentially on the successful separation of the energy absorbed in the localized crack-tip region out of the total energy absorbed by the cracked material body at large. Three different experimental techniques, all stemming from the energetic interpretation of theJ integral, are utilized and their relative merits in the characterization of fracture initiation in short glass fibre reinforced injection-moulded nylon 6.6 examined. Various theoretical aspects concerning these experimental methods are outlined. The rationale behind using a single-edge-notched tension type specimen for theJ _c test is presented. TheJ _c value obtained from the compliance calibration method and the quasistatic energy method agree closely and can be considered to be independent of pre-crack length and specimen geometry when the pre-crack length to specimen width ratio (a/w) is larger than 0.45. The extrapolation method fails nevertheless to yield a physically consistentJ _c value, possibly due to its questionable theoretical representation. As no constraint on boundary conditions is necessitated during the course of crack extension, the quasistatic energy is physically more appealing.     

Effect of residual stresses on crack behaviour in single edge bending specimens

Residual stresses due to manufacturing processes, such as welding, change the load bearing capacity of cracked components. The effects of residual stresses on crack behaviour in single edge bending specimens were investigated using Finite element analyses. Three parameters (J, Q and R) were used to study the crack behaviour. The J‐integral predicts the size scale over which large stresses and strains exist, the constraint parameter Q describes the crack‐tip constraint as a result of geometry, loading mode and crack depth and the constraint parameter R is used to describe the constraint resulting from residual stresses. To carry out a systematic investigation on the effect of residual stresses on the J‐integral and crack‐tip constraints, models under different combinations of residual stresses and external loads with different crack depths were analysed. It has been shown that the crack‐tip constraint R increased by tensile residual stresses around the crack‐tip. On the other hand, the constraint parameter R decreased and tended to zero at high external load levels.     

CONSTRAINT EFFECTS ON DUCTILE CRACK GROWTH IN CLADDED COMPONENTS SUBJECTED TO UNIAXIAL LOADING

Abstract A two-parameter approach based on the J-integral and the parameter h, the ratio of the hydrostatic stress to the effective stress, was examined for ductile crack growth in cladded specimens. A series of cracked specimen configurations were tested and analysed by FEM to study the crack-tip constraint in different geometries. The test program consisted of homogeneous SEN specimens of a base material (A533-B steel), homogeneous SEN specimens of a cladding material (stainless steel weldment) and cladded specimens containing surface cracks through the cladding. Some issues concerning the cladding/base interface were also discussed from the basis of metallographical and fractographical examinations. While the crack growth initiation of the investigated materials appeared to be insensitive to the crack-tip constraints, the propagation of ductile crack growth was significantly influenced by crack-tip constraints. The crack-tip constraints in different specimen configurations could successfully be characterized by the parameter h. Prediction of crack growth along the crack fronts in two cladded specimens using the developed resistance laws accounting for constraint effects gave promising results.     

Quantifying Tstress controlled constraint by the master curve transition temperature T0

Specimen size, crack depth and loading conditions may effect the materials fracture toughness. In order to safeguard against these geometry effects, fracture toughness testing standards prescribe the use of highly constrained deep cracked bend specimens having a sufficient size to guarantee conservative fracture toughness values. One of the more advanced testing standards, for brittle fracture, is the master curve standard ASTM E1921-97, which is based on technology developed at VTT Manufacturing Technology. When applied to a structure with low constraint geometry, the standard fracture toughness estimates may lead to strongly over-conservative estimate of structural performance. In some cases, this may lead to unnecessary repairs or even to an early “retirement” of the structure. In the case of brittle fracture, essentially three different methods to quantify constraint have been proposed, J small scale yielding correction, Q-parameter and the T_stress. Here, a relation between the T_stress and the master curve transition temperature T₀ is experimentally developed and verified. As a result, a new engineering tool to assess low constraint geometries with respect to brittle fracture has been obtained.     

Correlation of fracture behavior in high pressure pipelines with axial flaws using constraint designed test specimens--Part I: Plane-strain analyses

This work presents a numerical investigation of crack-tip constraint for SE(T) specimens and axially surface cracked pipes using plane-strain, nonlinear computations. The primary objective is to gain some understanding of the potential applicability of constraint designed fracture specimens in defect assessments of pressurized pipelines and cylindrical vessels. The present study builds upon the J-Q approach using plane-strain solutions to characterize effects of constraint on cleavage fracture behavior for the analyzed fracture specimens and cracked pipes. Under increased loading, each cracked configuration follows a characteristic J-Q trajectory which enables comparison of the corresponding driving force curve in the present context. A key outcome of this investigation is that toughness data measured using SE(T) specimens appear more applicable for cleavage fracture predictions of pressurized pipelines and cylindrical vessels than standard, deep notch fracture specimens under bend loading. The results provide a strong support for use of constraint-designed SE(T) specimens in fracture assessments of pressurized pipes and cylindrical vessels.     

Constraint-modified J−R curves and its application to ductile crack growth

The concept of J-controlled crack growth is extended to J–A ₂ controlled crack growth using J as the loading level and A ₂ as the constraint parameter. It is shown that during crack extension, the parameter A ₂ is an appropriate constraint parameter due to its independence of applied loads under fully plastic conditions or large-scale yielding. A wide range of constraint level is considered using five different types of specimen geometry and loading configuration; namely, compact tension (CT), three-point bend (TPB), single edge-notched tension (SENT), double edge-notched tension (DENT) and centre-cracked panel (CCP). The upper shelf initiation toughness J _IC, tearing resistance T _R and J–R curves tested by Joyce and Link (1995) for A533B steels using the first four specimens are analysed. Through finite element analysis at the applied load of J _IC, the values of A ₂ for all specimens are determined. The framework and construction of constraint-modified J–R curves using A ₂ as the constraint parameter are developed and demonstrated. A procedure of transferring the J–R curves determined from standard ASTM procedure to non-standard specimens or practical cracked structures is outlined. Based on the test data, the constraint-modified J–R curves are presented for the test material of A533B steel. Comparison shows the experimental J–R curves can be reproduced or predicted accurately by the constraint-modified J–R curves for all specimens tested. Finally, the variation of J–R curves with the size of test specimens is produced. The results show that larger specimens tend to have lower crack growth resistance curves.     

A transferability model for brittle fracture including constraint and ductile tearing effects: a probabilistic approach

This study describes a computational framework to quantify the influence of constraint loss and ductile tearing on the cleavage fracture process, as reflected by the pronounced effects on macroscopic toughness (J _c , _c). Our approach adopts the Weibull stress _w as a suitable near-tip parameter to describe the coupling of remote loading with a micromechanics model incorporating the statistics of microcracks (weakest link philosophy). Unstable crack propagation (cleavage) occurs at a critical value of _w which may be attained prior to, or following, some amount of stable, ductile crack extension. A central feature of our framework focuses on the realistic numerical modeling of ductile crack growth using the computational cell methodology to define the evolution of near-tip stress fields during crack extension. Under increased remote loading (J), development of the Weibull stress reflects the potentially strong variations of near-tip stress fields due to the interacting effects of constraint loss and ductile crack extension. Computational results are discussed for well-contained plasticity, where the near-tip fields for a stationary and a growing crack are generated with a modified boundary layer (MBL) formulation (in the form of different levels of applied T-stress). These analyses demonstrate clearly the dependence of _w on crack-tip stress triaxiality and crack growth. The paper concludes with an application of the micromechanics model to predict the measured geometry and ductile tearing effects on the cleavage fracture toughness J _c of an HSLA steel. Here, we employ the concept of the Dodds-Anderson scaling model, but replace their original local criterion based on the equivalence of near-tip stressed volumes by attainment of a critical value of the Weibull stress. For this application, the proposed approach successfully predicts the combined effects of loss of constraint and crack growth on measured J _c -values.     

J–R curves corrected by load-independent constraint parameter in ductile crack growth

The constraint effect on J–resistance curves of ductile crack growth is considered under the condition of two-parameter J–Q^* controlled crack growth, where Q^* is a modified parameter of Q in the J–Q theory. Both J and Q^* are used to characterize the J–R curves with J as the loading level and Q^* as a constraint parameter. It is shown that Q^* is independent of applied loading under large-scale yielding or fully plastic deformation, and so Q^* is a proper constraint parameter during crack growth. An approach to correct constraint effects on the J–R curve is developed, and a procedure of transferring the J–R curves determined from standard ASTM procedure to nonstandard specimens or real cracked structures is outlined.The test data of fracture toughness, J_IC, and tearing modulus, T_R, by Joyce and Link (Engng. Fract. Mech. 57(4) (1997) 431) for a single-edge notched bend specimen with various depth cracks are employed to demonstrate the efficiency of the present approach. The variation of J_IC and T_R with the constraint parameter Q^* is obtained, and then a constraint-corrected J–R curve is constructed for the test material of HY80 steel. Comparisons show that the predicted J–R curves can match well with the experimental data for both deep and shallow cracked specimens over a reasonably large amount of crack extension.Finally, the present approach is applied to predict the J–R curves of ductile crack growth for five conventional fracture specimens. The results show that the effect of specimen geometry on the J–R curves is generally much larger than the effect of specimen sizes, and larger specimens tend to have lower crack growth resistance curves.     

A numerical study on the crack tip constraint of pipelines subject to extreme plastic bending

This study investigates the fracture response and crack tip constraint of thick wall pipelines subject to large plastic bending. Such a circumstance frequently occurs during the installation of offshore pipelines (such as the reeling method), and accidental overloading, both inducing inelastic bending. The near-tip stress and strain fields are obtained through the fully nonlinear 3D finite element models constructed to examine the response of a practical range of cracked pipeline geometries and material properties. It is observed that throughout the loading history (up to the large scale yielding of the pipeline), by incorporation of the J–Q two parameter fracture theory, the near crack tip fields do indeed resemble those obtained from a K–T modified boundary layer formulation. This analogy provides sufficient proof for the applicability of the similitude concept inherent and fundamental to any fracture assessment procedure. All the pipelines considered in this study, which had realistic crack sizes, exhibited low constraint behavior (i.e. −1.4 < Q < −0.4). Additionally, Q was observed to decrease as a linear function of the global bending strain. Based on this correlation, simplified design equations are presented by which the constraint of such pipelines could be effectively estimated. The equations would be suitable for incorporation in the constraint-matched integrity assessment procedures that would in turn overcome the overt conservatism produced by the use of single parameter fracture mechanics approaches. Suitability of the low constraint laboratory specimens for fracture toughness measurements is also confirmed.     

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.     

Mechanical heterogeneity and validity of J-dominance in welded joints

Fracture criterion of the J-integral finds wide application in the integrity evaluation of welded components, but there exist some confused problems such as the dependence of the fracture toughness on the strength mis-matching and specimen geometry which need to be clarified. It is rough and unsuitable to attribute the variation of J-integral fracture parameter simply to the effect of mechanical heterogeneity. In the present paper, a two-dimensional finite element method is employed to analyze the distribution and variation of crack tip field of welded joints with different strength mis-matching in four kinds of specimen geometry, and then the validity of J-dominance in welded joints is investigated. It is found that the crack tip field of mis-matched joint is different from that of either the weld metal or base metal of which the joint is composed, but it is situated between those of weld metal and base metal. Under the plane strain, there is obvious difference in stress triaxiality for different strength mis-matched joints. The validity of J-dominance in welded joint can not be obtained by comparing whether the stress triaxiality meets that required by the HRR solution because of the existence of mechanical inhomogeneity. By ascertaining if the stress triaxiality of welded joint near the crack tip is dependent of specimen geometry, the conclusion can be arrived at: for plane stress the validity of J-dominance is valid, whilst for plane strain the validity of J-dominance is lost. Based on the above, attempt has been made to point out that the influence of mechanical heterogeneity on the fracture toughness of weldment arises from the variation of constraint intensity-crack tip stress triaxiality. Compared with the effect of mechanical heterogeneity on the stress triaxiality, the losing of validity of J-dominance in mis-matched joint under plane strain may play a more critical role in the variation of J-integral fracture parameter of weldment.