Dynamic fracture mechanics analysis of failure mode transitions along weakened interfaces in elastic solids

Dynamic fracture mechanics theory was employed to analyze the crack deflection behavior of dynamic mode-I cracks propagating towards inclined weak planes/interfaces in otherwise homogenous elastic solids. When the incident mode-I crack reached the weak interface, it kinked out of its original plane and continued to propagate along the weak interface. The dynamic stress intensity factors and the non-singular T-stresses of the incident cracks were fitted, and then dynamic fracture mechanics concepts were used to obtain the stress intensity factors of the kinked cracks as functions of kinking angles and crack tip speeds. The T-stress of the incident crack has a small positive value but the crack path was quite stable. In order to validate fracture mechanics predictions, the theoretical photoelasticity fringe patterns of the kinked cracks were compared with the recorded experimental fringes. Moreover, the mode mixity of the kinked crack was found to depend on the kinking angle and the crack tip speed. A weak interface will lead to a high mode-II component and a fast crack tip speed of the kinked mixed-mode crack.     

Calculation of transient strain energy release rates under impact loading based on the virtual crack closure technique

This paper describes an interface element to calculate the strain energy release rates based on the virtual crack closure technique (VCCT) in conjunction with finite element analysis (FEA). A very stiff spring is placed between the node pair at the crack tip to calculate the nodal forces. Dummy nodes are introduced to extract information for displacement openings behind the crack tip and the virtual crack jump ahead of the crack tip. This interface element leads to a direct calculation of the strain energy release rate (both components G_I and G_II) within a finite element analysis without extra post-processing. Several examples of stationary cracks under impact loading were examined. Dynamic stress intensity factors were converted from the calculated transient strain energy release rate for comparison with the available solutions by the others from numerical and experimental methods. The accuracy of the element is validated by the excellent agreement with these solutions. No convergence difficulty has been encountered for all the cases studied. Neither special singular elements nor the collapsed element technique is used at the crack tip. Therefore, the fracture interface element for VCCT is shown to be simple, efficient and robust in analyzing crack response to the dynamic loading. This element has been implemented into commercial FEA software ABAQUS^® with the user defined element (UEL) and should be very useful in performing fracture analysis at a structural level by engineers using ABAQUS^®.     

Numerical simulation of crack deflection and penetration at an interface in a bi-material under dynamic loading by time-domain boundary element method

The hybrid time-domain boundary element method (BEM), together with the multi-region technique, is applied to simulate the dynamic process of crack deflection/ penetration at an interface in a bi-material. The whole bi-material is divided into two regions along the interface. The traditional displacement boundary integral equations (BIEs) are employed with respect to the exterior boundaries; meanwhile, the non-hypersingular traction BIEs are used with respect to the part of the crack in the matrix. Crack propagation along the interface is numerically modelled by releasing the nodes in the front of the moving crack tip and crack propagation in the matrix is modeled by adding new elements of constant length to the moving crack tip. The dynamic behaviours of the crack deflection/penetration at an interface, propagation in the matrix or along the interface and kinking out off the interface, are controlled by criteria developed from the quasi-static ones. The numerical results of the crack growth trajectory for different inclined interface and bonded strength are computed and compared with the corresponding experimental results. Agreement between numerical and experimental results implies that the present time-domain BEM can provide a simulation for the dynamic propagation and deflection of a crack in a bi-material.     

Crack arrest testing of high strength structural steels for naval applications

The crack arrest fracture toughness of two high strength steel alloys used in naval construction, HSLA-100, Composition 3 and HY-100, was characterized in this investigation. A greatly scaled-down version of the wide-plate crack arrest test was developed to characterize the crack arrest performance of these tough steel alloys in the upper region of the ductile-brittle transition. The specimen is a single edge-notched, 152 mm wide by 19 mm thick by 910 mm long plate subjected to a strong thermal gradient and a tensile loading. The thermal gradient is required to arrest the crack at temperatures high in the transition region, close to the expected service temperature for crack arrest applications in surface ships. Strain gages were placed along the crack path to obtain crack position and crack velocity data, and this data, along with the applied loading is combined in a “generation mode” analysis using finite element analysis to obtain a dynamic analysis of the crack arrest event. Detailed finite element analyses were conducted to understand the effect of various modeling assumptions on the results and to validate the methodology compared with more conventional crack arrest tests.Brittle cracks initiation, significant cleavage crack propagation and subsequent crack arrest was achieved in all 15 of the tests conducted in this investigation. A crack arrest master curve approach was used to characterize and compare the crack arrest fracture toughness. The HSLA-100, Comp. 3 steel alloy had superior performance to the HY-100 steel alloy. The crack arrest reference temperature was T_KIA = −136 °C for the HSLA-100 plate and T_KIA = −64 °C for the HY-100 plate.     

Off-axis Fatigue Crack Growth and the Associated Energy Release Rate in Composite Laminates

Stable matrix crack growth behaviour under mechanical fatigue loading hasbeen studied in a quasi-isotropic (0/90/-45/+45)_s GFRPlaminate. Detailed experimental observations were made on the accumulationof cracks and on the growth of individual cracks in +45° as well as 90° plies. A generalised plain strain finiteelement model of the damaged laminate has been constructed. This model hasbeen used to relate the energy release rate of growing cracks to the crackgrowth rate via a Paris relation.     

Observing ideal “self-similar” crack growth in experiments

We here report on a detailed experimental study whose goal is to investigate spontaneous crack propagation in bonded and intact materials subjected to quasi-static far-field tensile loading. The cracks nucleate from a tiny circular hole and are triggered by an exploding wire. They subsequently propagate under the action of a constant far-field load. Dynamic photoelasticity in conjunction with high speed photography is used to capture the real-time photoelastic fringe patterns (isochromatics) associated with crack propagation. Dynamic stress intensity factors of propagating cracks are determined and the results are successfully compared with Broberg’s classical model of self-similar mode-I crack growth.     

Finite element modelling of crack propagation in elastic-plastic media

Materials which are cyclically stressed by sliding indenters often undergo fatigue wear, as surface breaking vertical cracks and subsurface horizontal cracks propagate causing eventual loss of material. In this study, the authors model crack propagation in an elastic-plastic material using finite element techniques, and consider the influence of friction, elasticity, plasticity and degree of penetration on the J-integral at the tip of a vertical crack. Crack propagation directions are estimated using J-integral maxima as the determining variable. It is found that the J-integral values, as a measure of strain energy release rate, can be used to estimate the crack propagation angle. Its main advantage lies in the fact that it considers both modes (I, II) of crack propagation. Using the J-integral values, one finds that, in the absence of friction between the indenter and the material, the vertical crack is equally prone to propagation at both 45 and 135° angles. However, one notices that the vertical crack favours the direction opposite to the direction of rolling for non-zero values of friction, i.e. 135°. The effects of both the crack depth and the crack tip plasticity are also investigated. It is found that any experimental findings suggestive of crack orientations closer to the horizontal in the direction opposite to the sliding direction are probably a result of shallow vertical asperities or higher crack tip plasticity.     

A general weight function for inclined cracks at sharp V-notches

A general method for evaluating the Stress Intensity Factors of an inclined edge crack originated at the tip of a sharp V-notch in a semiplane is presented. An analytical Weight Function with a matrix structure was derived by extending a method developed for an inclined edge crack in an unnotched semi-plane. The effects of the principal geometrical parameters governing the problem were studied through a parametric finite element analysis, carried out for different reference loading conditions. The Weight Function can be used to produce efficient and accurate evaluations of the stress intensity factors for cracks with inclination angle in the range −72°, +72° emanating from V-notches with opening angle in the range from 18° to 144°. For a crack length up to the 10% of the characteristic notch dimension, the maximum estimated error of the Stress Intensity Factor is lower than 2% (typical errors less than 1%) in the whole ranges of the angular parameters. The capability of the proposed method to analyse cracked notches in finite-size bodies was also considered. The agreement between the results with those obtained by accurate Finite Element solutions suggests that the proposed Weight Function can be used as a general tool for evaluating the Fracture Mechanics parameters of a short crack at any V-notch tip.     

A study of inclined impact in polymethylmethacrylate plates

The penetration and perforation of a polymethylmethacrylate (PMMA) plate is investigated experimentally and numerically. Two combined failure criteria are used in the numerical analyses: ductile failure with damage evolution and tensile failure. The measured mechanical properties of PMMA are input to the analysis. The determination of the damage evolution parameter in this material is calibrated by simulating and replicating shear localization results obtained in confined PMMA cylinders. The numerical simulation based on these parameters is tested by comparing the numerical trajectory prediction to actual trajectories of inclined impacts of projectiles. The first comparison is qualitative and shows that the numerical simulation predicts ricochet of a projectile impacting at an angle of inclination 30° as reported by Rosenberg et al. (2005) [1]. Additional successful comparison with experimental results of inclined impact of a 0.5″ AP projectile on 3 PMMA plates is reported. The contribution of each failure criterion to the projectile trajectory is studied, showing that the ductile failure criterion enforces a straight trajectory in the initial velocity direction while the tensile failure criterion controls the deflection and ricochet phenomenon. The numerical analyses are further used to study the effect of the angle of inclination on the trajectory and kinetic energy of the projectile. The effect of the projectile mass and impact velocity on the depth of penetration (DOP) was investigated too. It is found that the ricochet phenomenon happens for angles of inclination of 0° < α ≤ 30°. The projectile perforates the plate for 50° ≤α ≤ 90°, thus defining a failure envelope for this experimental configuration. For normal impact (α = 90°) the DOP scales linearly with the projectile's mass and can be fitted by a square polynomial with the impact velocity.     

Short cracks initiated in Al 6013-T6 with the focused ion beam (FIB)-technology

The fatigue crack growth behaviour of short corner cracks in the Aluminium alloy Al 6013-T6 was investigated. The aim was to determine the crack growth rates of small corner cracks at a stress ratio of R = 0.1, R = 0.7 and R = 0.8 and to find a possible way to predict these crack growth rates from fatigue crack growth curves determined for long cracks. Corner cracks were introduced into short crack specimens, similar to M(T) – specimens, at one side of a hole (Ø = 4.8 mm) by cyclic compression (R = 20). The precracks were smaller than 100 μm (notch + precrack). A completely new method was used to cut very small notches (10–50 μm) into the specimens with a focussed ion beam. The results of the fatigue crack growth tests with short corner cracks were compared with the long fatigue crack growth test data. The short cracks grew at ΔK-values below the threshold for long cracks at the same stress ratio. They also grew faster than long cracks at the same ΔK-values and the same stress ratios. A model was created on the basis of constant K_max-tests with long cracks that gives a good and conservative estimation of the short crack growth rates.     

Ermüdungsrißausbreitung bei gleichphasiger Mixed-Mode I+II Belastung

Fatigue crack propagation under in phase mixed mode I+II loading Stress intensity factors of kinked cracks are calculated by using the boundary-element-method (BEM). The results are compared to some analytical solutions. Referred to the crack deflection angles. The results of BEM calculation agree well with NUISMER's criterion and in addition with the experimental results. The growth rates of kinked cracks are compared to purely mode I loaded cracks. At R = 0.6 the crack growth rates don't show any difference. At R = 0.1 the angled cracks show slower growth rates. The reason is a significant -induced crack closure. When referring the crack growth rates to ΔK_eff, there is almost no difference between the propagation rates of angled cracks and straight cracks. This is in good agreement with the results, achieved at R = 0.6.     

Wear damage of MgO single crystals

Mechanisms of surface and sub-surface wear damage in MgO single crystals were investigated by scratching with two sintered alumina sliders, having tip radii of 60 and 120m, using a simple scratching apparatus in a controlled atmosphere. The degree of surface and sub-surface cracking is dependent on the shape of the slider and the normal contact load, which are related to the penetration into the crystal. The chevron crack on the (001) plane in the [100] sliding direction consists of cracks intersecting at an angle of 90°, and with a spread angle of about 120°, and the normal crack. The nature of the sub-surface damage is investigated; a parallel crack develops in front of the slider and an oblique crack propagates towards the front of the slider. Then an internal normal crack is formed between the oblique crack and the parallel crack. In the [110] direction, the oblique crack initiates from the top of the normal crack under the surface, and the parallel crack continues from the oblique crack. This wear damage is explained by the dislocation interactions occurring due to the distribution of resolved shear stresses during sliding. The wear caused by the chevron crack is a factor of 10 higher than that with plastic flow. Internal cracks do not have a direct influence on the increase of wear.     

Effects of serrated grain boundaries on the crack growth in austenitic heat-resisting steels during high-temperature creep

The effect of serrated grain boundaries on creep crack growth is investigated using an austenitic 21Cr-4Ni-9Mn steel principally at 700° C. The relationship between the microstructure of specimens and the crack growth behaviour is discussed. The creep crack growth rate in the specimens with a surface notch is relatively reduced by serrated grain boundaries especially in the early stage of crack growth. The life of crack propagation in the specimens with serrated grain boundaries is longer compared with that of the specimens with straight grain boundaries. It is confirmed in the surface crack growth of smooth round bar specimens crept at 700° C that serrated grain boundaries are effective in retarding the growth of a grain-boundary crack less than about 4×10^–4 m long, and that this effect decreases with increasing crack length. It is suggested that crack deflection due to serrated grain boundaries caused a decrease in the stress intensity factor of the grain-boundary crack and resulted in a decrease of the crack growth rate in the steel. The crack arrest at the deflection points and the circumvention of crack path on the serrated grain-boundaries may also contribute to the retardation of the grain-boundary crack growth during creep. Further, it is deduced from the experimental results on the notched specimens that the creep fracture is caused by the linkage of the main crack to many microcracks and voids on the grain-boundary at 900°C.     

Fatigue cracks emanating from sharp notches in high-strength aluminium alloys: The effect of loading direction, kinking, notch geometry and microstructure

The effect of notch geometry on the propagation of fatigue cracks emanating from sharp V-shaped notches was investigated. To this purpose, an experimental campaign has been conducted on Al-7075–T651 specimens carrying notches with aperture angles of 45°, 90°, and 135°. In order to investigate the role of microstructure texture, specimens were extracted from the plates with the main axis either in the longitudinal rolling direction (L-samples) or in the transversal direction (T-samples), or 45° inclined with respect to both directions (LT-samples). The effect of stress amplitude was investigated by performing tests at two load levels. Three loading directions θ = 0°, 45° and 90° were considered. Some specimens experienced pure Mode I loading condition, whereas the remaining ones were subjected to combined Mode I and Mode II loading condition. The crack deflection induced by the variation in loading direction was determined by measuring the kinking angle. A linear elastic fracture mechanics approach was adopted for the analysis of experimental results. Stress intensity factors (SIF) of straight cracks were calculated using an appropriate weight function set up for studying inclined edge cracks emanating from sharp V-notches. On the contrary, a finite element model has been built up to derive the SIFs at the tip of the kinked cracks. The influence of K_II on the crack propagation was discussed on the basis of theoretical and semi-empirical models. It has been found that (i) the crack initiation at the notch root occurred in mixed mode conditions, (ii) a decreasing Mode II component with growing crack length was observed under initial loading direction θ₀ = 45° and θ₀ = 90°, (iii) a crack deflection was observed after 45° rotation of the initial loading direction; a good prediction of the kinking angle was obtained using the maximum tangential stress criterion, and (iv) a fairly good rationalization of all the collected crack growth rate data is obtained if the driving force for crack propagation is expressed in terms of K_I.     

Determination of dynamic crack resistance of ductile cast iron using the compliance ratio key curve method

The compliance ratio method is an analytical approach for instantaneous crack length determination in dynamic single-specimen J-R curve testing of ferritic ductile cast iron (DCI). Comparison testing at room temperature and −40 °C was applied to PCVN and SE(B)15 specimens to examine their performance and suitability for the dynamic key curve method for DCI. An experimental reference database of dynamic crack resistance curves was set up by low-blow multiple-specimen tests and used to validate the results of the CR method. The influence of test temperature, microstructure, loading rate and specimen geometry on fracture behavior of the tested DCI was investigated in great detail and these parameters were linked to fracture mechanical properties. The results obtained show that the CR method is suited to establish valid dynamic crack resistance curves for both types of specimen. Nevertheless, SE(B)15 specimens are preferred for dynamic J-R curve determination of DCI based on their advantages such as higher accuracy.     

Effect of loading and geometry on the subsonic/intersonic transition of a bimaterial interface crack

An experimental investigation was conducted to study the nature of intersonic crack propagation along a bimaterial interface. A single edge notch/crack oriented along a polymer/metal interface was loaded predominantly in shear by impacting the specimen with a high velocity projectile fired from a gas gun. The stress field information around the propagating crack tip was recorded in real time by two different optical techniques--photoelasticity and coherent gradient sensing, in conjunction with high speed photography. Intersonic cracks on polymer/metal interfaces were found to propagate at speeds between the shear wave speed (c_s) and of the polymer. The nature of the crack tip fields during subsonic/intersonic transition and the conditions governing this transition were examined. Experimental observations showed the formation of a crack face contact zone as the interfacial crack speed exceeds the Rayleigh wave speed of the polymer. Subsequently, the contact zone was observed to expand in size, shrink and eventually collapse onto the intersonic crack tip. The recorded isochromatic fringe patterns showed multiple Mach wave formation associated with such a scenario. It is found that the nature of contact zone formation as well as its size and evolution differ substantially depending on the sign of the opening component of loading.     

Finite element analysis of postbuckling and delamination of composite laminates using virtual crack closure technique

The two-dimensional and three-dimensional parametric finite element analysis (FEA) of composite flat laminates with two through-the-width delamination types: 0₄/(±θ)₆//0₄ and 0₄//(±θ)₆//0₄ (θ = 0°, 45°, and “//” denotes the delaminated interface) under compressive load are performed to explore the effects of multiple delaminations on the postbuckling properties. The virtual crack closure technique which is employed to calculate the energy release rate (ERR) for crack propagation is used to deal with the delamination growth. Three typical failure criteria: B-K law, Reeder law and Power law are comparatively studied for predicting the crack propagation. Effects of different mesh sizes and pre-existing crack length on the delamination growth and postbuckling properties of composite laminates are discussed. Interaction between the delamination growth mechanisms for multiple cracks for 0₄//(±θ)₆//0₄ composite laminates is also investigated. Numerical results using FEA are also compared with those by existing models and experiments.     

Dynamic crack propagation in large steel specimens

Dynamic fracture experiments on crack initiation and crack growth in single edge bend specimens are performed. The impact velocity is in the range of 14 to 50 m/s and the specimen size is 320×75 mm with a thickness varying from 18 to 40 mm. The experiments are recorded by high speed photography.Two different steel qualities are investigated and their constitutive characterisation are obtained from uni-axial tension tests and shear tests with strain rates in the range 10⁻⁴ to 10³ s⁻¹ and tension tests at temperatures between −196 and 600°C.One of the materials exhibits a transition from a ductile dimple fracture to a brittle cleavage fracture as the loading velocity increases and as the specimen thickness increases. Scanning electron microscope fractographs show that the density of plastic bridges within cleavage ligaments decreases with increasing impact velocity and with increasing specimen thickness. It is also noted that the local crack propagation direction deflects from the global one in cleavage fracture areas with a high density of plastic bridges.The other material fails in a ductile mode in all the investigated cases.     

Modeling of fatigue crack closure in inclined and deflected cracks

A 2-dimensional, elastic-plastic finite element model has been developed to simulate plasticity induced crack closure in slanted and deflected cracks growing outside the small scale yielding (SSY) regime. The finite element model allows for contact between deformable surfaces to capture the complex contact interaction between the crack faces. Coulomb's friction law has been used to model friction between the crack faces and has been incorporated in the finite element model. This paper examines the mode I and mode II behavior of slanted cracks subjected to remote mode I, constant amplitude cyclic loading. Two possible types of mode II crack face interaction have been identified: (a) complete slip in mode II before mode I opening and, (b) mode I crack opening before the crack faces undergo mode II displacements. Both types of interactions were observed in slanted cracks. The finite element study also reveals a clear dependence of mode I and mode II crack opening levels for a slanted crack on R ratio and maximum stress, S_max/₀. The crack opening levels for a slanted crack are found to be significantly higher than the stable opening values for a straight crack growing in pure mode I. The mode I and mode II crack opening levels are also found to depend on the friction between the crack faces. A four-fold increase in friction coefficient resulted in almost 50% increase in normalized mode I and mode II opening values. This paper also describes the effect of crack deflection on closure. Deflection of a fatigue crack from 45° inclination to pure mode I caused a decrease in mode I opening level, but, an increase in mode II opening level. This difference in opening behavior is attributed to the transition of the nature of crack interaction from complete slip before opening to opening in mode I before mode II shear offset. Final stable opening levels for a deflected crack are found to be close to the stable value for straight cracks.