Local Mode Mixity Research Articles

Piecewise-linear generalizable cohesive element approach for simulating mixed-mode delamination

A cohesive element formulation is proposed that provides a general framework to approximate experimentally measured Traction–Separation Law (TSL) shapes. Unlike other approaches, it does not assume specific TSL shapes, such as bi-linear or exponential. The TSL shapes are defined generally, in a piecewise-linear fashion, and Mode I and shear (Mode II and Mode III) TSLs can have different shapes. Furthermore, it provides added generality by enabling coupling with most fracture criteria proposed in the literature. For each material point, the measured Mode I and shear TSLs are scaled based on the fracture criterion chosen and the calculated mode-mixity. If the mode-mixity at a material point changes between damage onset and complete fracture, the Mode I and shear TSLs are scaled such that: (i) energy is dissipated as determined by the mixed-mode fracture criterion, and (ii) artificial healing/damage is prevented. The approach is shown to accurately converge to Linear Elastic Fracture Mechanics for conditions approaching quasi-brittle fracture, confirming its soundness. For conditions approaching brittle–ductile planar fracture, the approach reproduces accurately the general TSLs used as input, under pure Mode I and shear loadings. For mixed-mode conditions, the specified mixed-mode fracture criterion is accurately reproduced ensuring the correct energy is dissipated. The mixed-mode TSL shapes are a function of the Mode I and shear TSLs used, the fracture criterion chosen, and the local mode-mixity. The adaptability of the approach, as evidenced by the preliminary results, suggests that it can be used to simulate a broad range of cohesive responses.

Macro- and micro-approach to locally multiaxial fatigue crack paths in oriented and non-oriented pearlitic microstructures

This paper offers a macro- and micro-approach to locally multiaxial fatigue crack paths in oriented and non-oriented pearlitic microstructures, addressing the important role of microstructural evolution (orientation and packing closeness) during the manufacture process by cold drawing in the posterior fatigue performance of the pearlitic steel wires. Results show that fatigue crack paths are globally uniaxial (they develop in global mode I) in both oriented and non-oriented pearlitic microstructures, whereas such fatigue crack paths are locally multiaxial (they develop in local mixed-mode with a zig-zag shape) in the two mentioned microstructures, the degree of packing closeness and orientation affecting the microstructural features (micro-length and micro-deflection angle) of the fatigue crack path, thereby determining their distinct fatigue performance.

Effect of weld angle on the creep rupture life of ferritic/austenitic dissimilar weld interfaces under remote mode I fracture

Dissimilar metal welded structures (DMWs) used extensively in conventional and nuclear power plants can suffer from in-service failures at the dissimilar interface with a much reduced life compared to similar metal weld counterparts at the same operating stress and temperature. This paper evaluates the effect of weld angle on the interface creep failure mode of two-dimensional DMW plates consisting of a ferritic steel P91 and an Inconel 82 filler metal within a finite element (FE) framework. A physical cavity growth damage zone model is developed to describe the damage accumulation at the interface, which naturally takes into account the local mode mixity. The material parameters are calibrated against standard 90° weld creep rupture data and used to predict the rupture life of DMWs with a range of axial loads and reduced weld angles (75°, 60°, 45° and 30°). The predicted results match reasonably well with the limited interface failure data for a 45° weld angle. This work also provides additional evidence and insights regarding the improvement of interface creep rupture life of DMWs in power plant pipelines, in particular: (1) Compared with a 45° weld angle, a 60° weld angle is more detrimental to the creep life and should be avoided in actual components – on the contrary, damage tolerance can be promoted by designing and adopting weld angles smaller than 45°, which can have lives exceeding that of standard 90° welded components; (2) A weld interface with alternating weld angles/paths is expected to enable a greater fraction of the creep rupture life to be taken up with crack propagation compared with a flat weld interface, which also increases the probability of damage detection; (3) A fully constrained boundary condition is beneficial to the creep rupture life compared with a free boundary condition; (4) For weld angles less than 90°, the diversion of the crack into the HAZ is less likely compared with a 90° weld angle. Type IV failure mode through the FGHAZ is also less likely to occur.

Crack growth behavior in dissimilar welded Ti based alloys under biaxial fatigue loading

This study aims at describing fatigue crack growth in dissimilar welding of Ti based alloys under macroscopic multiaxial loading. The proposed methodology involves the experimental analysis of fatigue crack behavior under equibiaxial tension and macroscopic combination of mode I and II for Ti17, Ti6242 and laser welded specimen of both base metals. Based on these experiments, crack path, fatigue crack growth rate and crack interaction with microstructure have been addressed. The 3D finite element analysis of cracks shapes has enabled to derive stress intensity factor (SIF) investigated for opening, in-plane and out-of-plane shear modes based on linear elastic fracture mechanics assumptions. Finally, an equivalent SIF has been proposed to take into account the local mode mixity induced by both macroscopic shear and 3D crack shape. As a conclusion, the dissimilar welding of Ti based alloys increase the fatigue crack growth rate (FCGR) for any macroscopic loading - with or without shear. Moreover, the microstructure of Ti6242 alloy, is well known to inhibit FCGR by multiples local bifurcation of crack path induced by the coarse microstructure of this alloy. This point was confirmed during equibiaxial tension but anomalous and very high FCGR was observed for macroscopic mode I + II loading. For the welded material, the fatigue crack to microstructure interactions have shown that the FCGR was clearly limited by coarse α needles inducing local bifurcation and conversely that in both fusion zone and heat-affected zone, local refinement of α needles could not slow down the crack propagation.

Mode mixity analysis of face/core debonds in a single cantilever beam sandwich specimen

The single cantilever beam sandwich specimen has been proposed, as a fracture test standard for mode I peel loading. Critical parameters, including specimen dimensions, determine whether the crack propagates along the face/core interface in mode I during the fracture test. This paper outlines a parametric study based on a numerical method to examine local mode mixity conditions for a wide array of sandwich systems by varying several geometrical and material parameters. The thickness and modulus of the face sheet were seen to influence the mode mixity for most sandwich systems. Core Poisson’s ratio was shown to influence the local mode mixity and has the capability of driving the crack along the interface or into the core. The effect of the intact specimen length was analyzed and presented from a mode mixity perspective based on various elastic foundation modulus expressions. Reinforcement of the single cantilever beam specimen with stiff layers was also investigated numerically and compared with a similar analysis in the literature. The analysis presented in this paper shows that, despite reducing the global shear component, the local mode mixity condition deviated away from the mode I regime for several sandwich specimens. An appropriate foundation model along with a minimum loading rod length was one of the recommendations provided from the analyses, which may supplement the ASTM International standardization efforts.

The Double Drum Peel (DDP) test: A new concept to evaluate the delamination fracture toughness of cylindrical laminates

Standard delamination tests of monolithic composites prescribe configurations where the crack is a symmetry plane for both overall geometry and stacking sequence, ensuring a controlled mode ratio. These normalized configurations do not enable testing of curved specimens, like those manufactured by filament winding. Here, we propose a new concept for the delamination testing of cylindrical laminates, the Double Drum Peel, related to the peel tests used for adhesives or thin-films debonding. A global energy analysis, including all sources of energy release and dissipation, provides the expression of the critical strain energy release rate. As in the classical peel test, the energy dissipated by mechanisms other than delamination should be accounted for to determine intrinsic interface properties. The local mode mixity is evaluated based on analytical results on the classical peel test. Tests using carbon-peek rings manufactured by laser assisted tape placement are presented to illustrate the potential of the DDP.

An experimental study on the crack initiation from notches connected to interfaces of bonded bi-materials

A systematic experimental study was conducted to investigate the interaction between cracks, notches and interfaces of bonded aluminum and polymer joints. Bi-material specimens with sharp V-notches with variation in notch angles (30°, 90° and 120°), bonding strengths and loading locations were tested under three-point bonding. The notch angle and the bonding strength have significant effect on the crack initiation load. For weakly bonded polymer/metal specimens, crack initiation load increases with the increase of the notch angle. The loading point locations also affect the crack initiation load due to change in local mode-mixity at the notch tip.

Near-threshold propagation of mode II and mode III fatigue cracks in ferrite and austenite

The near-threshold behavior of mode II and mode III long fatigue cracks in ferritic (ARMCO iron) and austenitic (X5CrNi18-10) steel were experimentally studied using various samples specially prepared to obtain the effective threshold values ΔKIIeff,th and ΔKIIIeff,th. In both investigated materials, the effective thresholds for mode III were ∼1.7 times higher than those for mode II. Three-dimensional topological data obtained by the examination of fracture surfaces using stereophotogrammetry were utilized to identify crack growth micromechanisms. In austenite, mode I branching of both the mode II and mode III cracks started at the very onset of crack growth. On the other hand, all cracks in ferrite propagated in crystallographically assisted local mixed mode I+II+III with mode II dominance. These experimental results can be understood in terms of crack growth micromechanisms according to a deformation model in ferrite and a decohesion model in austenite. The dissimilarity of growth mechanisms in ferrite and austenite may be attributed to a different number of available slip systems in body-centered cubic and face-centered cubic metals.

Modeling flat to slant fracture transition using the computational cell methodology

Macroscopic mode I ductile crack propagation in metallic sheets or plates often starts in mode I as a flat triangle (coplanar with the precrack) whose normal corresponds to the loading direction. After some limited extension, the crack becomes slanted and propagates under local mixed mode I/III. Modeling and understanding this phenomenon is challenging. In this work, the “computational cell” methodology proposed in [1], which uses a predefined crack path, is used to study flat to slant fracture transition. The energy dissipation rate is studied as a function of the assumed crack tilt angle. It is shown that a minimum is always reached for an angle equal to 45°. This correlates well with the variation of the crack tip opening angle (CTOA) or the mean plastic deformation along the crack path. Stress and strain states in the stable tearing region hardly depend on the assumed tilt angle. A parametric study shows that flat to slant fracture transition is less likely to occur in materials having high work hardening and favored if additional damage is caused by the local stress/strain state (plane strain, low Lode parameter) in the stable tearing region.

Constitutive mixed mode model for cracks in concrete

The scope of the paper is to set up a constitutive mixed mode model for cracks in concrete. The model is formulated at macro level and includes the most important micro scale effects. An associated plasticity model inspired by the modified Cam clay model is established. The hardening parameters are based on the standard Mode I tensile softening response and the response for Mode I crushing. The roughness of the crack is included through a topographic description of the crack surface. The constitutive behavior is based on the integration of local contributions. The local mixed mode ratio is determined from the topographic information and the constitutive model is thereby purely mechanically based. Using the actual topographic description the model is validated against experimental results for mixed mode crack openings.

Finite element modelling of crack propagation in carbohydrate extruded starch with open void structure

This study presents a new way of describing the void architecture of a of starch foam to allow the simulation of crack propagation in extruded starch material. In these materials, complex stress distribution takes place upon loading leading to a jagged crack extension. Based on the principle of stress intensity factors, the maximum energy release criterion is implemented and combined with a particular 2-D meshing of the material. The meshing is based on a modification of the element connectivity in a regular grid. A material property is assigned to each element based on grey level of acquired images of the carbohydrate material. The numerical results show that the void structure is responsible for the development of a local mixed mode. Crack propagation exhibits significant changes in the crack path because of the heterogeneous stress distribution. The comparison between numerical and observed crack paths well shows that the predictions are sensitive to grey level distributions and mesh refinement. Finally, the criterion is able to predict nicely the crack extension if the contrast between bright and dark regions is properly addressed.

On the analysis of a mixed mode bending sandwich specimen for debond fracture characterization

The mixed mode bending specimen originally developed for mixed mode delamination fracture characterization of unidirectional composites has been extended to the study of debond propagation in foam cored sandwich specimens. The compliance and strain energy release rate expressions for the mixed mode bending sandwich specimen are derived based on a superposition analysis of solutions for the double cantilever beam and cracked sandwich beam specimens by applying a proper kinematic relationship for the specimen deformation combined with the loading provided by the test rig. This analysis provides also expressions for the global mode mixities. An extensive parametric analysis to improve the understanding of the influence of loading conditions, specimen geometry and mechanical properties of the face and core materials has been performed using the derived expressions and finite element analysis. The mixed mode bending compliance and energy release rate predictions were in good agreement with finite element results. Furthermore, the numerical crack surface displacement extrapolation method implemented in finite element analysis was applied to determine the local mode mixity at the tip of the debond.

Split singularities and the competition between crack penetration and debond at a bimaterial interface

For a crack impinging upon a bimaterial interface at an angle, the singular stress field is a linear superposition of two modes, usually of unequal exponents, either a pair of complex conjugates, or two unequal real numbers. In the latter case, a stronger and a weaker singularity coexist (known as split singularities). We define a dimensionless parameter, called the local mode mixity, to characterize the proportion of the two modes at the length scale where the processes of fracture occur. We show that the weaker singularity can readily affect whether the crack will penetrate, or debond, the interface.

Analytical modelling of the influence of local mixed mode displacements on roughness induced crack closure

Application of crack closure analytical modelling to predict the behavior of complex fatigue crack growth properties is limited partly due to restricted two-dimensional modelling approaches. An analytical model of roughness induced crack closure (RICC) is developed in the present paper considering a three-dimensional twisted and kinked crack path. Residual shear deformations at asperities in the crack wake affect the crack opening generating closure. These residual shear deformations are explicitly formulated from residual plastic deformation. The respective influence of the in-plane and out-of-plane deformation on RICC is discussed. The crack twisting is found to be a less significant effect on the RICC than the crack kinking, for similar deviation angles. However, these out-of-plane crack deflections are found to be non negligible particularly at low tilting angles. This analytical model is used to predict the closure stress intensity factor for a range of 2xxx aluminium alloys. Predictions are compared to experimental results obtained from low Δ K fatigue crack growth tests. Experimental results show that fatigue performance scale with closure level and roughness of the failed fatigue specimen surfaces. Comparison of estimated and measured closure stress intensity factor show similar trends.

Fundamental Criteria for the Propagation of Telephone Cord Buckles Beneath DLC Films on Glass Substrates

ABSTRACTThe topology of telephone cord buckles that form beneath compressed diamond-like carbon films (DLC) on glass substrates has been characterized with Atomic Force Microscopy (AFM) and with the Focused Ion Beam (FIB). Using AFM with 2nm resolution, the wavelength and amplitude of the buckles and their profiles have been measured. It has been found that, within each wavelength, the profile has symmetric and asymmetric segments. These changes have been related to differences in local mode mixity around the periphery of each repeat unit along the buckle, resulting in a fundamental rationale for the factors governing the wavelength. Sections made through various segments of the buckle by using the FIB imaging system result in local changes in the shape and size of the buckles that provide further insight into the buckle propagation criterion.

Quantitative Characterization of the Fracture Surface of Si Single Crystals by Confocal Microscopy

Experiments are conducted to study the dislocation nucleation conditions at the crack tip in {110}〈110〉 oriented Si single crystals. Specimens with surface cracks are first statically loaded at elevated temperatures for a prolonged period of time to initiate and move dislocations away from the crack tip, then cooled down to room temperature and loaded to fracture to measure the fracture toughness. Fractographic analysis of the fracture surfaces is performed. Distinct wavy patterns on the fracture surface at the initial cleavage crack front are observed, which is attributed to the existence of local mixed mode I/mode III stresses resulting from the inhomogeneous dislocation activity. Confocal microscopy is employed to quantify the fracture surface roughness. The results show that the increase of fracture toughness is directly associated with the increased area of the rough surface, which is characterized by the roughness number or the fractal dimension increment. Our results also demonstrate that dislocation nucleation can occur only at discrete sites. The spacing between these dislocation nucleation sources is of the order of 1 μm. A simple model is developed for the relationship between the fracture toughness and the surface roughness parameters, which is in good agreement with the experimental results.

A model for sliding mode crack closure part I: Theory for pure mode II loading

A physical model has been developed to quantify the sliding mode crack closure (SMCC) experienced in cyclic mode II loading conditions. Idealized crystallographic surface geometry and Coulomb friction behaviour were assumed in the model. The results reveal that faceted crack surfaces will generate a local wedging mode I component while frictional attenuation tends to reduce the effective mode II stress intensity factor range. It is found that asperity angle and friction coefficient are two fundamental factors influencing near-threshold fatigue crack growth behaviour during the entire fatigue cycle. The local stress-strain field is significantly altered due to the wedging mode I component and frictional attenuation of the nominal mode II component. It is concluded that ideal mode II loading may never be achieved in practice for polycrystalline materials due to the inevitable existence of local mixed mode loading conditions.

Mixed mode fatigue crack growth in the commercial AlLi alloy, 8090

Crystallographic fatigue crack propagation along planar slip bands has been recognized to occur over a particularly wide range of conditions in Al-Li alloys due to the presence of coherent, shearable [delta][prime] (Al[sub 3]Li) precipitates, in conjunction with the strong underlying crystallographic texture often developed in these materials during secondary processing. Such Stage 1 propagation typically produces a highly tortuous crack path during conventional mode 1 fatigue testing. While the net crack growth direction remains parallel to the nominal mode 1 direction, crack tortuosity has been generally recognized as beneficial to fatigue resistance, as both local mixed mode crack-tip loading conditions and roughness induced closure may significantly reduce the driving force for crack extension (i.e. crack shielding'' occurs). Recent investigations of commercial Al-Li plate in the damage tolerant condition have however shown that co-planar Stage 1 crack propagation along preferred [111]-plane orientations may give rise to sustained macroscopic crack deviation from the nominal mode 1 growth direction. Such crack growth raises a number of important questions with regard to conventional, nominally mode 1 based structure lifting and fatigue testing methods when applied to these materials. Work has therefore been carried out to characterized fatigue crack growth during sustained co-planar Stage 1more » propagation in a commercial Al-Li alloy, with particular reference to mixed mode loading conditions.« less

Delamination toughness computation for curved thermoplastic composites

The curved double cantilever beam (CDCB) test is a method used to characterize mode I delamination toughness of curved composite materials, fabricated by filament winding technology. A finite element model for this geometry is presented, that takes into consideration nonlinear deformational effects, orthotropic material properties and local mixed mode load at crack-tip. It can be used as the theoretical basis for analysis of experimental results. Especially for long cracks, compliant materials and thin samples large deflection should not become neclected in the modelling. In spite of its highly unsymmetrical geometry the crack tip loading state proved to be nearly pure mode I.

Finite element analysis of interleaved DCB specimen

Compliances, strain energy release rates, and stress intensity factors for homogeneous and interleaved double cantilever beam (DCB) specimens for mode I fracture characterization are investigated with finite element analysis. Interleaving refers to a thin layer of ductile polymer film being placed at the midplane of the beam. It was found that the introduction of the interleaf film reduced significantly the stress intensity factor in mode I as compared to the homogeneous orthotropic specimen. Finite element results for a wide range of interleaf thicknesses revealed that the asymmetry ofabimaterial interfacial crack had negligible influence on the compliance, whereas it caused some local mixed mode (mode I/II) crack-tip loading. The mode II contribution increased with increasing interleaf thickness, but was relatively independent of the elastic properties of the interlayer.