Bifurcation and propagation of a mixed-mode crack in a ductile material

The bifurcation and the propagation of a 2-D mixed-mode crack in a ductile material under static and cyclic loading were investigated in this work. A general methodology to study the crack bifurcation and the crack propagation was established. First, for a mixed-mode crack under static loading, a procedure was developed in order to evaluate the fracture type, the beginning of the crack growth, the crack growth angle and the crack growth path. This procedure was established on the basis of a set of criteria developed in the recent studies carried out by the authors [Li J, Zhang XB, Recho N. J-M^p based criteria for bifurcation assessment of a crack in elastic-plastic materials under mixed mode I-II loading. Engng Fract Mech 2004;71:329-43; Recho N, Ma S, Zhang XB, Pirodi A, Dalle Donne C. Criteria for mixed-mode fracture prediction in ductile material. In: 15th European conference on fracture, Stockholm, Sweden, August 2004]. A new criterion, by combining experimentation and numerical calculation, was developed in this work in order to predict the beginning of the crack growth. Second, in the case of cyclic loading, the crack growth path and crack grow rate are studied. A series of mixed-mode experiments on aluminium and steel specimens were carried out to analyse the effect of the mixed mode on the crack growth angle and the crack growth rate. On the basis of these experimental results, a fatigue crack growth model was proposed. The effect of the mixed mode on the crack growth rate is considered in this model. The numerical results of this model are in good agreement with the experimental results.     

The non-constant CTOD/CTOA in stable crack extension under plane-strain conditions

Contrary to the previous work that successfully applied the constant CTOD/CTOA fracture criteria to relatively thin structures, this paper demonstrates that the initial non-constant portion of the CTOD/CTOA plays an essential role in predicting fracture behavior under plane-strain conditions. Three- and two-dimensional finite element analyses indicate that a severe underestimation of the load would occur as the crack extends if a constant CTOD/CTOA criterion were used. However, the use of a simplified, bilinear CTOD/CTOA criterion to approximate its non-constant portion will closely duplicate the test data. Furthermore, using the experimental data from J-integral tests with various crack length to specimen width ratios (a/W), it is demonstrated that the critical CTOD/CTOA is crack tip constraint dependent. The initial high values of the CTOD/CTOA are in fact a natural consequence of crack growth process that is reflected by, and consistent with, the J-resistance (J-R) curve and its slope (tearing modulus).     

A new constraint based fracture criterion for surface cracks

A new methodology for predicting the location of maximum crack extension along a surface crack front in ductile materials is presented. Three-dimensional elastic-plastic finite element analyses were used to determine the variations of a constraint parameter (α_h) based on the average opening stress in the crack tip plastic zone and the J-integral distributions along the crack front for many surface crack configurations. Monotonic tension and bending loads are considered. The crack front constraint parameter is combined with the J-integral to characterize fracture, the critical fracture location being the location for which the product Jα_h is a maximum. The criterion is verified with test results from surface cracked specimens.     

On the path independent integral-Ĵ

The path independent integral, $\text{J}\text{?}$, is presented as the rate of energy flux during crack extension. This integral is an extension of the J-integral proposed by Rice and includes the existence of a fracture process region and the effect of plastic deformations, body forces, thermal strains and inertial of material.It is shown that the $\text{J}\text{?}\text{-}\text{integral}$ can include as special cases other fracture mechanics parameters such as J by Rice, $\text{G}\text{?}$ by Eftis et al., J¹ by Blackburn or f by Strifors.A definition of the $\text{J}\text{?}\text{-}\text{integral}$ in a three-dimensional problem is presented and possibility of applying the $\text{J}\text{?}\text{-}\text{integral}$ as fracture criterion is discussed.     

Finite element simulations of crack propagation in functionally graded materials under flexural loading

Cracks in stepped and continuously graded material specimens under flexural loading were investigated via finite element analysis. Calculation of mechanical energy release rates and propagation angles with crack-opening displacement correlation and the local symmetry (K_II = 0) criterion, respectively, provided results most efficiently and accurately, as compared with compliance and J-integral approaches and other deflection criteria. A routine was developed for automatic crack extension and remeshing, enabling simulation of incremental crack propagation. Effects of gradient profile and crack geometry on crack-tip stresses and crack propagation path are examined, and implications of these for optimal design of graded components against failure by fast fracture are discussed.     

Experimental and numerical investigations of mixed mode crack growth resistance of a ductile adhesive joint

Polymeric adhesive joints are extensively employed in various industrial and technological applications. It has been observed that in ductile adhesive joints, interface fracture is a common mode of failure which may involve stable crack propagation followed by catastrophic growth. The objectives of this paper are to investigate the effects of bondline thickness and mode mixity on the steady state energy release rate J_ss of such a joint. To this end, a combined experimental and numerical investigation of interfacial crack growth is carried out using a modified compact tension shear specimen involving two aluminium plates bonded by a thin ductile adhesive layer. A cohesive zone model along with a simple traction versus separation law is employed in the finite element simulations of crack growth. It is observed that J_ss increases strongly as mode II loading is approached. Also, it enhances with bondline thickness in the above limit. These trends are rationalized by examining the plastic zones obtained from the numerical simulations. The numerically generated J_ss values are found to agree well with the corresponding experimental results.     

Some comments on hysteretic plastic work and cyclic J-integral associated with fatigue cracking

The hysteretic plastic work for a unit area of fatigue crack, U, is compared with δJ, the cyclic J integral. In the range of crack propagation rates (10^?8–10^?4 m/cycle) for A533B and HY80 steels studied, the value of δJ is much smaller than that of U. While U is the plastic work absorbed in the plastic zone, ΔJ is associated with the energy to extend the fatigue crack. Most of the external energy supplied by the loading machine is absorbed in the plastic zone. During linear-elastic crack growth, the value of U is proportional to (ΔJ×E)^2-M/2 where m is the Paris exponent and E is Young's modulus. Interestingly, under the large-scale plasticity condition, U appears to be independent of the crack growth rate or ΔJ when the exponent of ΔJ is close to 2.     

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.     

Experitmental method for JIC computation on fracture of solid propellants under dynamic loading conditions

An experimental method is proposed for fracture characterization of solid propellants. Regarding non linear behaviour of such material, investigation is restricted to high loading rate conditions and J_Ic fracture criterion is computed. A tensile split Hopkinson bar device was set up and fitted to experiments up to strain rate of 300 s⁻¹. Axisymmetric samples of various crack length was tested allowing J_Ic computation using Begley-Landes method. Results are then analysed and special attention is given to validity of L.E.F.M. assumptions in this case.     

An alternative formulation of the Ritchie-Knott-Rice local fracture criterion

In the paper an alternative formulation of the RKR local fracture criterion is proposed. It is based on the features of the stress distribution in front of a blunted crack in an elastic-plastic material. The stress distribution is computed using the finite strain option in the finite element method. It is postulated that the opening stress in front of the crack should be greater than the critical one, σ_c, over the distance l ? l_c, where l_c is considered as a material parameter. The hypothesis is applied to estimate the influence of the in-plane constraint on fracture toughness. New formulas to compute the critical value of the J-integral are derived both for the small scale yielding and large plastic deformations in front of the crack. The results obtained are compared with the Sumpter and Forbes experimental results and with the O’Dowd analytical formula concerning the J_c = J_c(J_IC,Q) relation.     

J-Dominance in Mixed Mode Ductile Fracture Specimens

The asymptotic mixed mode crack tip fields in elastic-plastic solids are scaled by the J-integral and parameterized by a near-tip mixity parameter, M _{_p} . In this paper, the validity and range of dominance of these fields are investigated. To this end, small strain elastic-plastic finite element analyses of mixed mode fracture are first performed using a modified boundary layer formulation. Here, a two term expansion of the elastic crack tip field involving the stress intensity factor |K| the elastic mixity parameter M _{_e} as well as the T-stress is prescribed as remote boundary conditions. The analyses are conducted for different values of M _{_e} and the T-stress. Next, several commonly used mixed mode fracture specimens such as Compact Tension Shear (CTS), Four Point Bend (4PB), and modified Compact Tension specimen are considered. Here, the complete range of loading from contained yielding to large scale yielding is analyzed. Further, different crack to width ratios and strain hardening exponents are considered. The results obtained establish that the mixed mode asymptotic fields dominate over physically relevant length scales in the above geometries, except for predominantly mode I loading and under large scale yielding conditions. This revised version was published online in August 2006 with corrections to the Cover Date.     

Essential work of fracture analysis of the tearing of a ductile polymer film

The fracture behaviour of a 0.5 mm thick ethylene-propylene block copolymer, previously evaluated using the essential work of fracture method, has been analyzed again in more detail, using different plots, allowing the determination of the crack initiation displacement and stress. In such plots is evidenced that the specific essential work of fracture, w_e, corresponds to the energy just up to crack initiation value that can be related with J₀. Also, it has been found a novel relationship between the plastic term, βw_p and the crack initiation stress, σ_i.     

Fractal modeling of the J-R curve and the influence of the rugged crack growth on the stable elastic-plastic fracture mechanics

In this paper, fractal geometry is used to modify the Griffith-Irwin-Orowan classical energy balance. Crack fractal geometry is introduced in the elastic-plastic fracture mechanics by means of the Eshelby-Rice J-integral and the influence of the ruggedness of the crack surface on the quasistatic crack growth is evaluated. It is shown that the rising of the J-R curve correlates to the topological ruggedness dimension of the crack surface. Results from fracture experiments are shown to be very well fitted with the proposed model, which is shown to be a unifying approach for fractal models currently used in fracture mechanics.     

Fatigue crack propagation in a ductile superalloy at room temperature and extensive cyclic plastic flow

Fatigue crack propagation experiments under both force and displacement control have been performed on the wrought superalloy Haynes 230 at room temperature, using a single edge notched specimen. The force controlled tests are nominally elastic, and the displacement controlled tests have nominally large plastic hysteresis at the beginning of the tests, but saturates towards linear elastic conditions as the crack grows. As some tests are in the large scale yielding regime, a non-linear fracture mechanics approach is used to correlate crack growth rates versus the fracture parameter $\mathrm{\Delta }$J. It is shown that crack closure must be accounted for, to correctly model the crack growth seen in all the tests in a unified manner. For the force controlled small scale yielding tests the Newman crack closure model was used. The Newman equation is however not valid for large nominal cyclic plasticity, instead the crack closure in the displacement controlled tests is extracted from the test data. A good agreement between all tests is shown, when closure is accounted for and effective values of $\mathrm{\Delta }$J are used.     

Verification of brittle fracture criteria for elements with V-shaped notches

In this paper an analysis of crack initiation in plane elements with V-shaped notches under biaxial loading (mode I and II) was presented. The following fracture criteria were used to evaluate the critical loads and directions of crack initiation: strain energy release rate criterion; strain energy density criterion; modified McClintock's stress criterion; non-local stress criterion.Results of numerical analysis obtained using the boundary element method and path independent H and J integrals were compared with experimental data.     

Mixed-mode fracture angle and fracture locus of materials subjected to compressive loading

The incipient fracture angle and fracture loci of prenotched brittle-like material subjected to compressive loading are investigated analytically and experimentally.The analysis of the problem includes parameters whose effects on fracture were pronounced via laboratory tests, namely: notch-tip curvature, subcritical microcracks emanating from the notch and crack closure process. Such considerations, jointly with the well-established fracture criteria in tensile loading (like the critical energy release rate, the critical energy density, J-integral and critical maximum stress used in this work) yielded an associated fracture locus for each criterion. Due to the mixed mode nature of the situation (K₁ and K₂) preevaluation of the fracture angle was instrumental.Data on critical (far-field) compressive load along with measured fracture angles performed on PMMA and Tungsten Carbide specimens are used to depict the most suitable fracture locus and thus to distinguish between the various fracture criteria when extended to fracture under compressive loading. An exact expression for the threshold load for complete closure of 2D elliptical cracks is used to delimit the fracture locus.     

Prediction of mode I crack growth resistance based on a comparative investigation of J-integral and energy dissipation rate concept

An energy dissipation rate concept is employed in conjunction with the J-integral to calculate crack growth resistance of elastic-plastic fracture. Different from Rice’s J-integral, the free energy density is employed in place of the stress working density to define an energy-momentum tensor, which yields that the slightly changed J-integral is path dependent regardless of incremental plasticity and deformational plasticity. The J-integral over the remote contour is split into the plastic influence term and the J _FPZ-integral over the fracture process zone which is an appropriate estimate of the separation work of fracture. Finite element simulations are carried out to predict the plane strain mode I crack growth behavior by an embedded fracture process zone. It can be concluded that J-integral characterization is in essence a stress intensity-based fracture resistance similar to the K criterion of linear elastic fracture, and energy dissipation rate fracture resistance can be taken as an extension of the Griffith criterion to the elastic-plastic fracture.     

Evaluation of the elastic-plastic mixity parameters on the base of different crack propagation criteria. Part 1. Preliminary analysis

In order to evaluate the mechanical behavior around small-scale yielding crack tip for both plane strain and plane stress, the asymptotic governing equations and their boundary conditions by considering fracture mechanisms are formulated. A total deformation theory of plasticity with a power-law hardening is used. The analysis of the near-tip fields is carried out for both the maximum tensile and shear stress crack growth direction criteria, as well as for the complete range of mixity parameters and various strain-hardening levels. The new scheme of mixed-mode problem solution is proposed. Realationships between elastic and plastic mixity parameters are given as functions of the crack growth direction criterion and the strain-hardening exponent.Translated from Problemy Prochnosti, No. 1, pp. 60–75, January–February, 2005     

Creep-fatigue crack propagation in lead-free solder under cyclic loading with various waveforms

Crack propagation tests of lead-free solder were conducted using center-notched plate specimens under cyclic tension-compression of three load waveforms: pp waveform having fast loading and unloading, cp-h waveform having a hold time under tension, and cc-h waveform having a hold time under tension and compression. In the case of fatigue loading, i.e. pp waveform, the path of crack propagation was macroscopically straight and perpendicular to the maximum principal stress direction, showing tensile-mode crack propagation. The introduction of the creep components by hold time in cc-h and cp-h waveforms promoted shear-mode crack propagation. For fatigue loading of pp wave, the crack propagation rate was expressed as a power function of the fatigue J integral and the relation was identical for load-controlled and displacement-controlled conditions. The creep component due to the hold time greatly accelerates the crack propagation rate when compared at the same values of the fatigue J integral or the total J integral (the sum of fatigue J and creep J integrals). The creep crack propagation rate was expressed as a power function of the creep J integral for each case of cp-h and cc-h waveforms. The crack propagation rate for cp-h waveform is higher than that for cc-h waveform. The predominant feature of fracture surfaces was striations for pp waveform and grain boundary fracture for cp-h waveform. Grain fragmentation was abundantly observed on the fracture surface made under cc-h waveform.     

Elastic-plastic J and COD estimation schemes for throughwall circumferentially cracked elbow under in-plane closing moment

Leak-before-break (LBB) assessment of primary heat transport piping of nuclear reactors involves detailed fracture assessment of pipes and elbows with postulated throughwall cracks. Fracture assessment requires the calculation of elastic-plastic J-integral and crack opening displacement (COD)¹ for these piping components. Analytical estimation schemes to evaluate elastic-plastic J-integral and COD simplify the calculations. These types of estimation schemes are available for pipes with various crack configurations subjected to different types of loading. However, no such schemes are available for throughwall circumferentially cracked elbow (or pipe bend), an important component for LBB analysis. In this paper, simple J and COD estimation schemes are proposed for throughwall circumferentially cracked elbow subjected to closing bending moment. The ovalisation of elbow cross-section has a significant bearing on its fracture behavior. Therefore, unlike conventional deformation theory plasticity analysis, incremental flow theory is adopted considering both material and geometric non-linearities in the development of the proposed estimation schemes. Although it violates Ilyushin’s theorem, it has been shown that the resulting estimation schemes is still reasonably accurate for engineering purposes. Finally, experimental/numerical validation has been provided by comparing the J-integral and COD between numerical/test data and predictions of the proposed estimation schemes.