Mixed-mode crack growth in ductile thin-sheet materials under combined in-plane and out-of-plane loading

Ductile thin-sheet structures, such as fuselage skin or automobile panels, are widely used in engineering applications. These structures often-times are subjected to mixed mode (I/II/III) loading, with stable crack growth observed prior to final fracture. To characterize specific specimen deformations during stable tearing, a series of mixed-mode I/III stable tearing experiments with highly ductile thin-sheet aluminum alloy and steel specimens have been measured by using three-dimensional digital image correlation (3D-DIC). Measurements include (a) specimen’s deformed shape and 3D full-field surface displacement fields, (b) load-crack extension response and (c) crack path during stable tearing, (d) angular and radial distributions of strains and (e) the mixed mode crack-opening displacement (COD, measured at 1-mm from crack tip along crack surface) variation as a function of crack extension. Results indicate that for both aluminum alloy and steel at all mixed-mode I/III loading conditions (Φ = 30°, 60° and 90°), the crack tip fields have almost identical angular and radial polar strain distributions. The mixed mode I/III fields were different from those observed for the nominal Mode I loading case (Φ = 0°). The effect of the Mode III loading component is that it lowers the magnitude of the dominant strain component ε _θθ ahead of the growing crack tip and increases the singularity of the strain as compared with that in the mode I case. In addition, measurements indicate that the average mixed mode I/III stable COD for AL6061-T6 (GM6208 steel) is 4×(3×) greater than the average Mode I stable COD.     

Modeling of mixed-mode crack growth in ductile thin sheets under combined in-plane and out-of-plane loading

This paper describes a modeling approach for analyzing mixed-mode crack growth events in ductile thin-sheet materials under large deformation and combined in-plane and out-of-plane loading conditions. The remote mixed-mode I/III loading leads to local mixed-mode I/II/III fields near the crack front. Making use of full-field surface deformation measurements, finite element models of mixed-mode I/III stable tearing events in thin-sheet specimens have been developed. Model predictions have been compared with experimental measurements (a) just prior to initial crack growth and (b) during stable tearing crack growth. Analyses of curvilinear crack growth events are carried out using a nodal release option or a local re-meshing option and using a generalized CTOD parameter with experimentally measured critical CTOD values. Results of this study suggest that the modeling approach can be employed to numerically re-construct experimental crack growth events in thin plate specimens. This offers a viable means of analyzing and understanding the mixed-mode crack growth events and provides a tool for further investigations of 3D crack front fields (which are otherwise unavailable experimentally) and for the study of fracture criteria for stable tearing events.     

Investigation of crack tunneling in ductile materials

Crack tunneling has been commonly observed in crack growth experiments on specimens made of ductile materials such as steel and aluminum alloys. The objective of this study is to investigate the crack tunneling phenomenon and study the effects of crack tunneling on the distribution of several mechanics parameters controlling ductile fracture. Three-dimensional (3D) elastic-plastic finite element analyses of stable tearing experiments involving tunneling fracture are carried out. Two model problems based on stable tearing experiments are considered. The first model problem involves a plate specimen containing a stationary, single-edge crack with a straight or tunneled crack front, under remote mode I loading. In the numerical analyses, the crack tip opening displacement, the von Mises effective stress, the mean stress, the stress constraint and the effective plastic strain around straight and tunneled crack fronts are obtained and compared. It is found that crack tunneling produces significant changes in the stress and deformation fields around the crack front. The second model problem involves a specimen containing a stably growing single-edge crack with a straight or tunneled crack front, under remote mode I loading. Crack growth events with a straight or tunneled crack front are simulated using the finite element method, and the effect of crack tunneling on the prediction of the load-crack-extension response based on a CTOD fracture criterion is investigated.     

Mixed-mode fracture of ductile thin-sheet materials under combined in-plane and out-of-plane loading

Cracks in thin structures often are subjected to combined in-plane and out-of-plane loading conditions leading to complex mixed mode conditions in the crack tip region. When applied to ductile materials, large out-of-plane displacements make both experimentation and modeling difficult. In this work, the mixed-mode behavior of thin, ductile materials containing cracks undergoing combined in-plane tension (mode I) and out-of-plane shear (mode III) deformation is investigated experimentally. Mixed-mode fracture experiments are performed and full, three-dimensional (3D) surface deformations of thin-sheet specimens from aluminum alloy and steel are acquired using 3D digital image correlation. General characteristics of the fracture process are described and quantitative results are presented, including (a) the fracture surface, (b) crack path, (c) load-displacement response, (d) 3D full-field surface displacement and strain fields prior to crack growth, (e) radial and angular distributions of the crack-tip strain fields prior to crack growth and (f) singularity analysis of the crack-tip strains prior to crack growth. Results indicate that the introduction of a mode III component to the loading process (a) alters the crack tip fields relative to those measured during nominally mode I loading and (b) significantly increases the initial and stable critical crack-opening-displacement. The data on strain fields in both AL6061-T6 aluminum and GM6208 steel consistently show that for a given strain component, the normalized angular and radial strains at all load levels can be reasonably represented by a single functional form over the range of loading considered, confirming that the strain fields in highly ductile, thin-sheet material undergoing combined in-plane tension and out-of-plane shear loading can be expressed in terms of separable angular and radial functions. For both materials, the displacement and strain fields are (a) similar for both mixed-mode loading angles Φ = 30° and Φ = 60° and (b) different from the fields measured for Mode I loading angle Φ = 0°. Relative to the radial distribution, results indicate that the in-plane strain components do not uniformly exhibit the singularity trends implicit in the HRR theory.     

Three-dimensional stress and deformation fields around flat and slant cracks under remote Mode I loading conditions

This paper investigates the phenomenon of slant fracture observed in stable tearing tests of many ductile materials, where an initially flat crack, loaded under remote Mode I conditions, tends to grow into a slant crack and stay in the slant configuration until final fracture. In an effort to identify potential reasons why cracks prefer to grow in a slant manner, three-dimensional finite element analyses of crack-front stress and deformation fields in Arcan-type specimens containing a flat or slant crack are performed under elastic–plastic and remote Mode-I loading conditions. In particular, the crack-tip opening displacement (COD) at a position behind the crack tip, the mean stress, the effective stress, and a constraint factor (defined as the ratio of the mean stress and effective stress) are studied and compared for the two types of cracks. Analysis results reveal several stress/deformation field variations around flat and slant cracks under identical remote loading conditions. First, close to the crack front, the COD of a slant crack is greater than that of a flat crack. Second, at the specimen’s mid-plane, a flat crack leads to a higher constraint value ahead of the crack than a slant crack. Third, the effective stress ahead of a slant crack is greater than that ahead of a flat crack, especially close to the crack front. The above results seem to suggest that slant fracture may be preferred because a slant crack enhances the driving force in the form of a higher near-tip COD value and because a shearing type of failure is promoted in the case of a slant crack compared to a tensile type of failure in the case of a flat crack.     

Three-dimensional finite element simulations of mixed-mode stable tearing crack growth experiments

Mixed-mode stable tearing crack growth events in Arcan plate specimens made of aluminum alloy 2024-T3 are simulated using three-dimensional (3D) finite element methods. A modeling/simulation procedure utilizing a mixed-mode CTOD fracture criterion and the custom 3D crack growth simulation software, CRACK3D, with an automatic local re-meshing option is demonstrated. Simulation predictions of the load-crack extension curve and the in-plane curvilinear crack growth path are compared with experimental measurements for various mixed-mode loading cases. Issues such as the effects of near-tip finite element size and crack extension increment size on simulation predictions are investigated.     

The effect of specimen dimensions on mixed mode ductile fracture

The results from a series of experiments are presented to determine the effect of specimen dimensions on the ductile tearing resistance of A508 Class 3 forged steel at ambient temperature. Single edge notch tension specimens were subjected to Mode I, Mode II and combination of Modes I and II. Mode I tests on various specimen sizes reveal characteristic features found in earlier work, such as decreasing slope of the tearing resistance with increasing constraint (or specimen size). In contrast, for Mode II the tearing resistance is shown to be independent of specimen size, although dependent on initial crack length. The tests show that there is a competition between void growth and shear localisation as mechanisms for ductile crack extension. The dominance of one mechanism over the other is shown to be related to the local Mode I and Mode II components of the J-integral.     

Mixed mode stable tearing of thin sheet?AI 6061-T6 specimens: experimental measurements and finite element simulations using a modified Mohr-Coulomb fracture criterion

In this investigation, a combined experimental and computational approach with a Modified Mohr Coulomb (MMC) fracture criterion employing post-initiation element softening is used to simulate stable crack propagation under Mode I, Mode III and combined Mode I/III loading conditions. Results from the studies demonstrate that good correlation exists between the measured load-displacement and the numerically predicted response when the stiffness of the specimen fixture is included in the FE model. The numerical results were able to capture most of the experimentally observed features during crack propagation, such as through-thickness slant fracture, necking, tunneling and local specimen twist, thus confirming that the MMC criterion is suitable for predicting in-plane and out-of-plane tearing of sheets. It was found that in order to predict correctly the load-displacement curve as well as the fracture plane, different amount of softening is needed for Mode I and Mode III loading cases. This observation can be justified on the micro-mechanical level, while there is a competition between the mechanisms of dimple and shear fracture.     

MODE II STABLE CRACK GROWTH

Abstract Mode II stable crack extension has been examined for an aircraft grade aluminium alloy D16AT. Both theoretical and experimental results are presented. The experimental observations include load displacement diagrams, plastic wake, crack front tunnelling and scanning electron micrographs of the fracture surfaces. The crack shows a tendency for in-plane extension, and the fracture surface is very flat, smooth and free of any dimples. The crack front advances with neghgible tunnelling at all stages of extension. The span of mode II stable crack growth (SCG) is longer than in the case of mode I SCG reported earlier for the same material and there is also more extensive plastic deformation. In the presence of a slight mode I load, the crack grows out-of-plane and the fractured surface facets resemble that of a mode I or mixed-mode dimpled fracture. The theoretical study is based on a finite element analysis using small deformation theory and incremental plasticity. Some of the experimental results have been theoretically predicted using the COA criterion as the governing criterion. The theoretical results include load-displacement diagrams, crack edge displacement curves, plastic zones and the J resistance curves. There is good agreement between the load-displacement diagrams. The initiation and maximum loads differ by less than 15%. The J resistance curve has a constant slope over the whole span of stable crack growth.     

The fatigue crack direction and threshold behaviour of mild steel under mixed mode I and III loading

As part of a programme to investigate the mixed mode fatigue crack growth threshold behaviour of mild steel, tests were carried out on three-point bend specimens with spark machined initial slits inclined to give mixed Mode I and III displacements. Overall the expected tendency to Mode I crack growth showed as an initial directional discontinuity followed by a smooth rotation of the crack front until it was almost perpendicular to the specimen sides. At a smaller scale, initial crack growth was by the formation of Mode I branch cracks which developed into a ‘twist’ fracture surface consisting of narrow Mode I facets separated by cliffs. The facets eventually grew out and the fracture surface became smooth. The result in the initiation it was necessary to distinguish between the threshold conditions which result in the initiation of crack growth, specimen failure and crack arrest. An envelope based on Mode I branch crack growth provides a reasonable lower bound to the results for crack initiation and specimen failure. The crack arrest threshold results and some of the crack growth threshold results could not be analysed in detail because of lack of appropriate stress intensity factors.     

Dynamic ductile crack growth and transition to cleavage – a cell model approach

The fracture behavior of ferritic steel in the transition regime is controlled by the competition between ductile tearing and cleavage. Many test specimens that failed by catastrophic cleavage showed significant amounts of ductile tearing prior to cleavage fracture. The transition from ductile tearing to cleavage has been attributed to the increase in constraint and sampling volume associated with ductile crack growth. This work examines the role of dynamic ductile crack growth on the fracture mode transition by way of a cell model of the material. The cell model incorporates the effects of stress triaxiality and strain rate on material failure characteristics of hole growth and coalescence. Loading rate and microstructure effects on the stress fields that evolve with rapid (ductile) crack growth are systematically studied. The stress fields are employed to compute the Weibull stress which provides probability estimates for the susceptibility to cleavage fracture. A center-cracked panel subjected to remote tension is the model problem under study. The computational model uses an elastic-viscoplastic constitutive relation which incorporates enhanced strain rate hardening at high strain rates. Adiabatic heating due to plastic dissipation and the resulting thermal softening are also accounted for. Under dynamically high loading rate, our model shows the crack speed achieves its peak value soon after crack initiation and quickly falls off to slower speeds with further crack growth. Remarkably, the Weibull stress follows a similar pattern which suggests that the transition to the cleavage fracture is most likely to occur, if at all, at the peak speed of ductile crack growth. Key words: Dynamic fracture, ductile tearing, crack growth, transition regime, cleavage fracture, cell model, finite element.     

SEMI-ELLIPTICAL FATIGUE CRACK GROWTH UNDER ROTATING OR REVERSED BENDING COMBINED WITH STEADY TORSION

Abstract— An analysis of the influence of steady torsion loading on fatigue crack growth rates under rotating or reversed bending is presented. Mixed-mode (I + III) tests were carried out on cylindrical specimens in DIN Ck45k steel and results are compared for two different testing machines: rotary bending and reversed bending obtained by cyclic Mode I (Δ K ₁) with or without superimposed static Mode III ( K _III) loading, simulating the real conditions on power rotor shafts where many failures occur. The growth and shape evolution of semi-elliptical surface cracks, starting from a chordal notch on the cylindrical specimen surface, was measured for several Mode III/ Mode I ratios. Results have shown that the steady Mode III loading superimposed on the cyclic mode I leads to a significant reduction in the crack growth rates. It is suggested that this retardation is related to an increase of plastic zone size near the cylindrical surface in association with the interlocking of rough fracture surfaces, friction and fretting debris, leading to a decrease of the ΔK effective at the crack tip profile due to the "crack closure effect". This work provides a contribution to a better understanding of crack growth rates under mixed-mode load conditions thereby allowing one to predict remaining lifetimes and to estimate the risks of pre-cracked rotor shafts.     

Plane stress finite element prediction of mixed-mode rubber fracture and experimental verification

This study demonstrates through experimental validation, that one can predict critical loads of arbitrarily shaped cracked rubber specimens of the mixed-mode type (mode I and II) using a plane stress finite element method and utilizing material constants that characterize the mechanical and fracture properties of SBR (Styrene Butadiene Rubber) material determined from experimental tests on a mode I specimen. Conversely, the finite element method can be used to extract useful critical tearing energy information from complicated, arbitrarily shaped cracked rubber specimens. The predicted critical loads or critical tearing energies for crack growth initiation and final fracture, as well as the crack growth initiation direction are compared to the experimental data with good agreement.     

Ductile–brittle fatigue and fracture behaviour of aluminium/PMMA bimaterial 3PB specimens

Fracture toughness and fatigue crack growth tests and numerical simulations on 3PB specimens were carried out to study the behaviour of a crack lying perpendicular to the interface in a ductile/brittle bimaterial. Polymethylmethacrylate acrylic (PMMA) and aluminium alloy 2024 T531 were joined together using epoxy resin. A precrack was introduced into the ductile material and tests were carried out to obtain fracture toughness and fatigue properties. The body force method and elastic–plastic finite-element analyses were used to simulate the experimental stress intensity K_I and cracking behaviour under monotonic and cyclic loads. It was found that the bimaterial fatigue crack growth rate is higher than that for monolithic aluminium 2024 but lower than the rate for a monolithic PMMA. This agreed with the trend for the fracture toughness values and was consistent with the numerical method results. The initial Mode I stable ductile cracking in the aluminium appears to ‘jump’ the interface and continues under mixed fracture Mode (I and II) in the PMMA material up to the final failure. A consistency between the simulation methods has indicated that the bimaterial fatigue crack growth is dominantly elastic with a small plastic zone near the crack tip.     

Experimental study of crack growth in thin sheet 2024-T3 aluminum under tension-torsion loading

To assess the viability of using a critical COD criterion for flaws in 2024-T3 aluminum experiencing tension stresses (S _P) and torsion stresses (S _T), the enclosed work presents (a) a complete set of measurements for critical COD during crack growth under nominal tension-torsion loading, (b) the evolution of crack path with crack growth and (c) crack surface shape as a function of loading. Data from this work will provide an important experimental database for use in assessing the predictive capability of advanced, three-dimensional, crack growth simulation tools. Results for COD during crack growth under tension-torsion loading indicates that the measured critical COD for tension-torsion loading is constant during crack growth. In addition, the value of COD measured using image correlation methods is approximately 8% larger than observed for in-plane tension-shear, with much of the increase apparently due to specimen deformations in the crack tip vicinity. In addition, crack path evolution data for the range of S _T/S _P considered in this work show that the crack experiences both tunneling and slant fracture during loading, with tunneling rapidly decreasing (a) as crack growth progresses for all S _T/S _P values or (b) as S _T/S _P increases. Furthermore, results indicate that tearing during tension-torsion loading always occurs in a manner so that the crack surfaces tend to interfere during growth. Finally, crack surface shape data indicates that, with the exception of a small secondary transition, the direction of crack growth remains stable along a straight line oriented along the initial fatigue crack direction for the range of S _T/S _P being considered.     

Analysis of mixed-mode cracks in a rubbery particulate composite

The mixed-mode loading of a rubbery particulate composite is studied experimentally. Linear fracture mechanics concepts are used to determine the initiation of growth, the initial growth direction, and the subsequent growth rate for a range of mode mixities. The fracture toughness locus is determined to be elliptical, with the Mode II toughness being lower than its Mode I counterpart. The initial growth directions correlate with maximum strain energy density theories. The crack growth rates can be modeled effectively using an equivalent Mode I crack.     

Simulation of ductile crack propagation in dual-phase steel

The modified Mohr–Coulomb and the extended Cockcroft–Latham fracture criteria are used in explicit finite-element (FE) simulations of ductile crack propagation in a dual-phase steel sheet. The sheet is discretized using tri-linear solid elements and the element erosion technique is used to model the crack propagation. The numerical results are compared to quasi-static experiments conducted with five types of specimens (uniaxial tension, plane-strain tension, in-plane shear, 45° and 90° modified Arcan) made from a 2 mm thick sheet of the dual-phase steel Docol 600DL. The rate-dependent J ₂ flow theory with isotropic hardening was used in the simulations. The predicted crack paths and the force–displacement curves were quite similar in the simulations with the different fracture criteria. Except for the 45° modified Arcan test, the predicted crack paths were in good agreement with the experimental findings. The effect of using a high-exponent yield function in the prediction of the crack path was also investigated, and it was found that this improved the crack path prediction for the 45° modified Arcan test. In simulations carried out on FE models with a denser spatial discretization, the prediction of localized necking and crack propagation was in better accordance with the experimental observations. In four out of five specimen geometries, a through-thickness shear fracture was observed in the experiments. By introducing strain softening in the material model and applying a dense spatial discretization, the slant fracture mode was captured in the numerical models. This did not give a significant change in the global behaviour as represented by the force–displacement curves.     

Strain and stress fields near the blunted tip of a crack under mixed mode loading and the implications for fracture

The strain distribution in the vacinity of a blunted crack-tip is analysed by slip line theory under the conditions of plane-strain, small-scale yielding, and mixed-mode loading of Modes I and II. A generalized crack-tip opening displacement is introduced by which the strain and stress fields near the blunted crack-tip are determined uniquely over a wide range of Mode I and II combinations. Also, coupled experimental and finite-element analyses under the condition of large-scale yielding reveal that the initiation of stable crack growth occurs when the generalized crack-tip opening displacement attains a critical value which is constant for the material tested. The finite-element analysis is based on the finite deformation theory of elastic-plastic materials. The generalized crack-tip opening displacement criterion is found to be superior to the J-integral and the usual COD for the characterization of the initiation of stable crack growth. The plastic work in a small circular region at the crack-tip is found to be equivalent to the generalized crack-tip opening displacement, as a fracture criterion.     

A proposed mixed-mode fracture specimen for wood under creep loadings

A mixed-mode fracture specimen was designed in this paper. This geometry is a judicious compromise between a modified Double Cantilever Beam specimen and Compact Tension Shear specimens. The main objective is to propose a specimen which traduces a stable crack growth during creep loading taking into account viscoelastic behaviour under mixed-mode loadings. The numerical design is based on the instantaneous response traduced by a crack growth stability zone. This zone is characterized by a decrease of the instantaneous energy release rate versus the crack length. In order to obtain a mixed-mode separation, the paper deals with the use of the M-integral approach implemented in finite element software, according to energetic fracture criterions. In these considerations, a numerical geometric optimization is operated for different mixed-mode ratios. Finally, a common specimen which provides to obtain fracture parameters, viscoelastic properties and creep crack growth process for different mixed-mode configurations is proposed.     

An investigation into the mixed-mode delamination growth in unidirectional T800/924C laminates

This study presents the results of experimental investigations and numerical simulation on mixed-mode I/II delamination growth initiated from an artificial transverse notch. Specimens made of unidirectional carbon fiber epoxy (T800/924C) composite have been tested under three-point-bend condition. A finite element procedure has been introduced to model 3-D stable delamination growth in the specimen to generate numerical growth data including loads, displacements, delamination lengths, and the growing crack front shapes. The simulation method uses strain energy release rate criterion in conjunction with a moving mesh facility. It is shown that very good compatibility exists between experimental and numerical results. A finite element-based data reduction method is then described as an application of the simulation procedure. Based on the obtained results, it is stated that this bending specimen can effectively be used in practice to study the mixed-mode crack growth and to measure interlaminar fracture toughness of unidirectional laminates.