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.     

Fatigue crack propagation damaging micromechanisms in ductile cast irons

Ductile iron discovery in 1948 gave a new lease on life to the cast iron family. In fact, these cast irons are characterized both by a high castability and by high toughness values, combining cast irons and steel good properties. Ductile cast irons are also characterized by high fatigue crack propagation resistance, although this property is still not widely investigated.In the present work, three different ferritic–pearlitic ductile cast irons, characterized by different ferrite/pearlite volume fractions, and an austempered ductile cast iron were considered. Their fatigue crack propagation resistance was investigated in air by means of fatigue crack propagation tests according to ASTM E647 standard, considering three different stress ratios (R = K_min/K_max = 0.1; 0.5; 0.75). Crack paths were investigated by means of a crack path profile analysis performed with an optical microscope. Crack surfaces were extensively analysed by means of a scanning electron microscope both considering a traditional procedure and performing a quantitative analysis of 3D reconstructed surfaces, mainly focusing graphite nodules debonding.     

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.     

Threshold toughness of polymers in the ductile to brittle transition region by different approaches

The fracture behavior of polymers in the ductile-to-brittle region is neither completely brittle nor entirely ductile. Besides, scatter in toughness results impairs the situation. Consequently, conventional methods based exclusively either on linear elastic fracture mechanics theory (LEFM) or on non-linear elastic fracture mechanics theory (NLEFM) are not suitable. It was demonstrated previously, that Weibull statistical method could be successfully used to determine the toughness threshold of polymers displaying ductile-to-brittle behavior. The present study compares the threshold toughness value determined by the statistical approach with other critical values calculated following other different suitable approaches: Low temperature plane strain fracture toughness, Plastic zone corrected fracture toughness, Stable and unstable propagation combined model, J extrapolated at zero stable propagation value, and Quasi J-R curve. The analysis was carried out on data points taken from fracture tests performed on polypropylene homopolymer, PPH, and on a blend of PPH and an elastomeric polyolefin, PPH/POes. The results of this analysis indicate that statistical, stable and unstable propagation combined model, and the J extrapolated at zero stable propagation value methods yield to very similar toughness threshold values being practically equivalent. In this case, threshold value was slightly smaller than the minimum J displayed by the experimental replicas, suggesting that it is an actual representative material toughness. Among these methodologies, the Statistical Method is applicable even if stable crack growth is difficult to determine. On the other hand, the methodologies based on LEFM tended to underestimate the fracture toughness, being very conservative while Quasi J-R curve method based on NLEFM overestimated the PPH/POes toughness value.     

Numerical simulations to support the normalization data reduction technique

The normalization data reduction (NDR) technique is an analytical methodology for characterizing the upper shelf fracture toughness of steels in the ductile regime, both in terms of critical toughness (J_Ic) and resistance to ductile crack extension (J-R curve). It represents an alternative to the more commonly used multi-specimen or single-specimen (unloading compliance and potential drop) techniques.Finite element analyses of a growing crack are executed to evaluate the performance of the technique. This approach has the advantage to remove large uncertainties entailing experimental results. Results demonstrate the precision of the method.     

Numerical modeling of strain localization in engineering ductile materials combining cohesive models and X-FEM

The present work aims at numerically predicting the current residual strength of large engineering structures made of ductile metals against accidental failure. With this aim in view, the challenge consists in reproducing within a unified finite element-based methodology the successive steps of micro-voiding-induced damage, strain localization and crack propagation, if any. A key ingredient for a predictive ductile fracture model is the proper numerical treatment of the critical transition phase of damage-induced strain localization inside a narrow band. For this purpose, the strong discontinuity cohesive model and the eXtended Finite Element Method are combined. A propagation algorithm is proposed and studied in the context of ductile materials. Physics-motivated criteria to pass from the phase of more or less diffuse damage to strain localization and from strain localization to crack propoagation are proposed. Finally, a 2D numerical example is shown to study the performance of the failure analysis model when implemented into an engineering finite element computation code, namely Abaqus.     

The crack tip opening angle (CTOA) of the plane stress moving crack

Recently, Crack Tip Opening Angle (CTOA) was proposed by C.F. Shih et al. to describe the instability criterion of ductile crack propagation during plane strain (flat crack) conditions, and was derived by J. R. Rice analytically by means of the slip line field theory and the incremental theory of plasticity. CTOA appears to be applicable in (some or most) cases, but does not accurately describe the plane stress growing crack (slant crack).Unstable ductile crack propagation of the plane stress crack is widely studied for the safe design of highly pressurized gas pipelines. The impact absorption energy of the Charpy test is well correlated to the fracture arresting properties of the structures, but the mechanics of the fracture are not yet well established.In this paper, CTOA of the plane stress growing crack is derived from the plane stress plasticity of perfectly plastic materials by Sokolovsky's approach. Our proposed modification of CTOA expressed as follows: $\text{CTOA}\text{= (α/δ}{}_0\text{)(}\text{d}\text{J/}\text{d}\text{l) + β(δ}{}_0\text{/E)}\text{ln}\text{(eR/r)}$ where $\text{β = 1.40}$ under the plane stress conditions.CTOA in the Dugdale model is also defined and compared with the results of laboratory test. The results show that $\text{α = 0.5}$, and $\text{β = 1.27}$ for plane stress crack growth. These analyses give similar results to those obtained by Rice et al. for CTOA under plane strain conditions, that is, $\text{α = 0.65}$ from the experimental results and $\text{β = 5.08}$ from the slip line theory.The CTOA obtained for plane stress ductile crack growth is applied to the wide plate tensile crack growth test. The results of the present analysis coincide well with those of the plane stress finite element method (FEM) computed by T. Kanazawa et al. The phenomena of plane stress ductile crack propagation are also explained by the CTOA criterion under plane stress conditions.     

A mechanical model to predict elastic-plastic fracture toughness in high strength materials

A mechanical model of crack initiation and propagation, which is based on the actual mechanism of ductile fracture in high strength materials, is proposed. Assuming that a crack initiates when the equivalent stress at a distance ρ from the crack tip reaches a critical value $\text{}\text{?}$gsf, an equation for predicting fracture toughness J_IC is obtained. From comparison between the predicted values and the experimental results, it is found that the distance ρ corresponds to the spacing of micro-inclusions. The temperature dependence of fracture toughness J_IC estimated according to the derived equation is given in an Arrhenius form of equation and is nearly consistent with the experimental results.     

Notch fracture toughness of high-strength Al alloys

In this study, the notch fracture toughness (NFT) of high-strength Al alloys was examined by a non-standardized procedure. The NFT is defined as the critical notch stress-intensity factor (NSIF) K_ρ,c, which is determined by using several methods of analysis and computing. A set of specimens with different notch root radii made from overaged 7xxx alloy forging was selected. The influence of the notch radius on the fracture toughness of the material was considered. It was found that the notch radius strongly affects the fracture behavior of forged 7xxx alloy in overaged condition. The notch fracture toughness was higher than the fracture toughness of a cracked specimen and increased linearly with notch radius. The critical notch radius was related to the spacing of intermetallic (IM) particles which promote an intergranular or transgranular fracture mechanism according to their size. It appeared that ductile transgranular fracture generated by the formation of dimples around dispersoids and matrix precipitates was predominant which indicates that intense strains are limited to a much smaller zone than the coarse IM particles spacing. This double mechanism is also operate for crack propagation of ductile fatigue. The nature and morphology of IM particles exert significant effects on the rate of fatigue crack growth and fracture toughness properties.     

Micromechanical analysis of mechanical heterogeneity effect on the ductile tearing of weldments

The objective of this study is determination of the effect of mechanical heterogeneity on ductile crack initiation and propagation in weldments using micromechanical approach. Welded single-edge notched bend (SENB) specimens were experimentally and numerically analysed. Material properties of welded joint zones were estimated using a combined experimental and numerical procedure; strains on a smooth tensile specimen were determined using ARAMIS stereometric measuring system in order to obtain true stress – true strain curves. High-strength low-alloyed steel was used as base metal, in quenched and tempered condition. J–R curves and crack growth initiation values of fracture mechanics parameter were experimentally and numerically obtained for specimens with a pre-crack in the heat-affected zone (HAZ) and weld metal (WM). The complete Gurson model (CGM) was used in prediction of J–R curves and crack growth initiation. It is shown that the resistance to crack initiation and growth can be predicted using micromechanical analysis, and that the results are significantly affected by mechanical heterogeneity of the weldment.     

Analysis of low temperature impact fracture data of thermoplastic polymers making use of an inverse methodology

In this work room and low temperature impact fracture data toughness of rubber modified polypropylene, polyethylene and rubber toughened polymethylmetacrylate have been assessed. In order to minimize the well-known dynamic effects a previously developed inverse methodology was used to treat force-time traces. Fracture parameters, such as K_IQ and J_C were estimated and the benefits of the inverse methodology were evaluated. The suitableness of energetic and force based toughness parameters for estimating a brittle to ductile transition was evaluated. The employment of the inverse methodology allowed us to infer the values of the crack tip loading rate, dK/dt, without the need of cushioning.     

Coupled influence of microstructure and atmosphere environment on fatigue crack path in new generation Al alloys

The fatigue crack propagation behavior of new generation Al alloys developed for aeronautical applications is studied at moderate ΔK and in the near threshold domain. The crack growth rate and the crack path are shown to depend on alloy composition, aging condition and atmosphere environment, and to be governed by the slip morphology. In absence of environment assistance, a crystallographic (1 1 1) faceted cracking leads to a slow stage I-like propagation in Al-Li-Cu alloys and underaged Al-Cu-Mg alloys with microstructure consisting of shareable precipitates or solute cluster structures that promote heterogeneous slip-band formation, which is in contrast with a ductile transgranular featureless stage II crack path in overaged Al-Cu-Mg. In air at moderate ΔK, an adsorption assisted propagation mechanism is assumed to prevail in both Li and Mg bearing materials, water vapor assistance inducing a transgranular stage II regime associated to homogeneous slip generating a flat-facet and step-like features; in the near threshold domain, the same mechanisms is operating for Al-Cu-Mg alloys while even more accelerated growth rates and lower effective threshold for Al-Cu-Li alloys are attributed to an assistance of hydrogen produce from the dissociation of adsorbed water vapor.     

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.     

Effect of residual stresses on ductile crack growth resistance

It is well known that residual stresses influence the ductile fracture behaviour. In this paper, a numerical study was performed to assess the effect of residual stresses on ductile crack growth resistance of a typical pipeline steel. A modified boundary layer model was employed for the analysis under plane strain, Mode I loading condition. The residual stress fields were introduced into the finite element model by the eigenstrain method. A sharp crack was embedded in the center of the weld region. The complete Gurson model has been applied to simulate the ductile fracture by microvoid nucleation, growth and coalescence. Results show that tensile residual stresses can significantly reduce the crack growth resistance when the crack growth is small compared with the length scale of the tensile residual stress field. With the crack growth, the effect of residual stresses on the crack growth resistance tends to diminish. The effect of residual stress on ductile crack growth resistance seems independent of the size of geometrically similar welds. When normalized by the weld zone size, the ductile crack growth resistance collapses into one curve, which can be used to assess the structural integrity and evaluate the effect of residual stresses. It has also been found that the effect of residual stresses on crack growth resistance depends on the initial void volume fraction f₀, hardening exponent n and T-stress.     

Fracture characterisation of a nuclear vessel steel under dynamic conditions in the transition region

The Master Curve (MC) methodology, originally proposed by Kim Wallin, is a standardised engineering tool for analysing the fracture toughness of ferritic steels in the ductile to brittle transition (DBT) region by means of the reference temperature T₀. This temperature is normally estimated from quasi-static fracture toughness tests, nevertheless, it has been recently extended to the determination of dynamic fracture toughness. The aim of the present contribution is to characterise the fracture resistance in the DBT region under high strain rate conditions by applying the MC methodology to the steel of the Santa María de Garoña Spanish nuclear power plant (NPP). In this sense, 15 Charpy instrumented tests were performed on pre-cracked specimens from the surveillance program of the plant. The dynamic reference temperature, T_0,dyn, was obtained and compared with the quasi-static reference temperature, T_0,sta. The reliability of a semi-empirical formula proposed by Wallin to obtain T_0,dyn from T_0,sta has been analysed for this material.     

Identification of CTOA and fracture process parameters by drop weight test and finite element simulation

This paper presents a new technique that is able to predict ductile fracture propagation occurrences in large metallic structures, by means of an appropriate application of the finite element modelling. This technique takes account of a cohesive zone in the vicinity of the crack tip, where a nodal release technique is implemented. Two parameters, governing the process zone of the material under investigation, have to be determined: the process zone dimension (named “Δ distance”) and the critical value of crack tip opening angle (CTOA). CTOA_C can be determined through an experimental laboratory procedure two specimen CTOA test (TSCT) that is already known and used by researchers who study fracture propagation on pipelines [Demofonti G, et al. Step-by-step procedure for the two specimen CTOA test. In: Proceedings of the Second International Conference on Pipeline Technology, Ostend, vol. II. 1995]. The second parameter required, Δ distance, is determined minimizing the differences of Finite Element results towards experimental data of an instrumented impact test (drop weight tear test). Some interesting improvements, concerning distinction between the initiation energy and the propagation energy accounted in TSCT procedure, are also discussed, in order to successfully extend its use to both high strength and high toughness steels.     

Study of the fatigue failure of an anti-return valve of a high pressure machine

This paper presents a study of the fatigue failure of an anti-return valve, designed to work in the high pressure system (500 MPa) of a high pressure processing machine. To do this, the crack propagation has been simulated by means of the linear-elastic fracture mechanics approach under mixed-mode loading conditions. From an initial crack, which size is related with the microstructure and superficial finish, the crack growth has been simulated using the stress intensity factors K_I and K_II of the cracked valve axisymmetric geometry. The crack propagation path has been obtained step by step, applying the criterion of the maximum circumferential stress at the crack tip. The experimental and simulated crack propagation paths have been compared and, as a consequence of the reliable results obtained, the fatigue life of the valve has been calculated using the Paris law of the material with an effective stress intensity factor K_eff. The good agreement with experimental fatigue life allows to perform new improved designs using the methodology presented.