Debonding and crack kinking in foam core sandwich beams—I. Analysis of fracture specimens

Sandwich beam specimens, recently developed for the study of facing/core debond fracture, were analyzed using the finite element method. Peel fracture was approached using a modified double cantilever beam (DCB) sandwich specimen with a precrack between the facing and core, while shear fracture employed a modification of the ASTM block shear test to include a facing/core precrack. Complex and conventional stress intensity factors were calculated for bimaterial cracks located between facing and bondlayer and bondlayer and core over a large range of core moduli. Overall, much larger stress intensity factors were observed for an interfacial crack between the facing and bondlayer than for a crack between the bondlayer and core for both types of specimens. Crack kinking analysis of the DCB specimen revealed that the debond tends to remain interfacial for stiff core materials, but may deflect into the core for compliant core materials. In shear loading of a debonded sandwich beam it was demonstrated that crack kinking is possible for any core material.     

泡沫夹芯复合材料梁界面裂纹曲折扩展实验与数值模拟

采用双悬臂梁(DCB)试验研究了具有不同密度的PMI泡沫芯体的玻璃纤维增强复合材料夹芯梁界面裂纹曲折破坏路径。基于包含裂纹的物质点算法(MPM), 建立了与试验研究相适应的MPM模型, 在不同的面板/芯体模量比下计算了界面裂纹裂尖模态比和曲折破坏角, 并结合曲折破坏准则模拟了界面裂纹曲折破坏路径。数值模拟结果和试验现象吻合良好, 说明了本文中数值分析模型和方法的有效性。研究结果表明, 面板材料和芯体材料模量失配越严重, 界面裂纹发生曲折破坏时的破坏角越大; 裂纹折入芯体后, 在 Ⅰ 型为主的加载模式的支配下以基本平行于界面的方向扩展。      

Quantitative evaluation of the adhesion of metallic coatings using cylindrical substrate

This paper introduces an effective interfacial fracture toughness test based on interface fracture mechanics theory. This testing method uses a circumferentially notched tensile (CNT) specimen, which is ideally suited for determining the interfacial fracture resistance of coatings. Unlike other interfacial fracture tests, this test is simple to prepare, requires minimum test setup and is easy to model. An interfacial pre-crack was generated between a nickel coating and mild steel cylindrical substrate to evaluate adhesion strength. In situ acoustic and SEM analyses were used to determine the crack initiation or the critical load of failure. The critical energy release rate, critical stress intensity factors and phase angle were determined using the J integral which was determined by applying the critical load to the finite element model. A detailed finite element analysis was carried out to study the effect of different interface pre-crack positions and mode mixity on energy release rate for different notch angles and elastic modulus ratios. The cracking resistance of the interface was characterised by the notch angle of CNT specimens. The analysis showed an increase in interfacial fracture toughness as phase angle increases and was significant when the phase angle was large. The combined results of computational and experimental analysis showed that any defect or stress concentration at the interface could significantly weaken the adhesion of coating.     

The competition between the crack kinking away from the interface and crack propagation along the interface in elastic bicrystals

The problem analyzed is of the crack kinking away from the interface between the two different anisotropic materials. The attention is concentrated on the initiation of the crack kinking and the condition that the length of the crack segment that is leaving the interface is small in comparison to the crack segment that remains along the interface. The emphasis is placed to the application of the fracture mechanics concept for the interfacial crack that propagates dynamically between the two orthotropic materials. The simulations and calculations were done by application of the Mathematica ^® programming routine. The stress intensity factors and the energy release rate are obtained for the kinked crack, as functions of the corresponding values for the interfacial crack prior to kinking. The analysis was performed of the influence of anisotropy on the crack kinking versus crack propagating along the interface competition. Due to anisotropy the kinking is easier, i.e., it is easier for the crack to kink away from the interface into the “softer” of the two materials. The oscillatory index for the case of the dynamic crack growth along the interface between the two orthotropic materials increases with crack tip speed v and with increase of the difference in stiffnesses. The practical application of this analysis could be for the interface in the glued joints and protective coatings.     

Crack kinking from an initially closed, ordinary or interface crack, in the presence of friction

One theoretically studies crack kinking from an ordinary crack (in some homogeneous solid) or an interface crack (between two dissimilar materials), in the situation where this crack is closed prior to kinking but open after it. This problem was recently considered by the authors with the simplifying, but physically quite unrealistic hypothesis of absence of friction between the crack lips. Their work is extended here to account for possible friction governed by Coulomb’s law. Problems of elastic fracture mechanics with unilateral contact and friction between the crack lips being not only non-linear, but incremental in nature, the theoretical treatment becomes notably more involved than without friction. It is still based, however, on the same basic ingredients, namely “homogeneity” properties of the type of problems considered, changes of scale and some reasonable hypotheses. It is shown that whatever the geometry of the body and the crack and whatever the loading, the asymptotic expression of the stress intensity factors (SIF) at the tip of a vanishingly small kinked crack extension depends solely upon the initial (mode II) SIF prior to kinking, the kink angle, Dundurs’s famous parameters α and β and the friction coefficient. The (history-independent) functions involved in the general formulae established are determined numerically through finite element computations. From there, using Goldstein and Salganik’s famous principle of local symmetry to predict the crack path, one derives a theoretical value for the kink angle. This value depends upon the loading only through the sign of the initial stress intensity factor; it also depends on the mismatch of elastic properties and the friction coefficient. However, its range of variation is numerically found to be rather narrow. Experiments conducted by various authors seem to confirm these theoretical predictions.     

Stress intensity factors for penny-shaped cracks perpendicular to graded interfacial zone of bonded bi-materials

This paper examines the stress intensity factors that are associated with a penny-shaped crack perpendicular to the interface of a bi-material bonded with a graded interfacial zone. Elastic modulus of the graded interfacial zone is assumed to be an exponential function of the depth. The stress intensity factors are calculated numerically using a so-called generalized Kelvin solution based boundary element method. Three cases of normal or shear tractions acting on the crack surfaces are examined. Values of the stress intensity factors are examined by taking into account the effects of the following four parameters: (a) the crack front position; (b) the non-homogeneity parameter of the graded interfacial zone; (c) the crack distance to the graded interfacial zone; and (d) the graded interfacial zone thickness. The numerical results are compared well with existing solutions under some degenerated conditions. These results are useful to furthering our knowledge on fracture behavior of bi-material systems with or without a graded interfacial zone.     

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.     

Mixed-mode interfacial fracture toughness for thermal barrier coating

A new interfacial fracture test method was developed for measuring the mixed-mode interfacial fracture toughness of thermal barrier coated material over a wide range of loading phase angles. The principle of this developed method is based on peeling the coating from the substrate due to compressive loading to the coating edge, as forming a shear loading to the interface, and slinging loading such as beam bending, as normal loading to the interface. The complete closed form of the energy release rate and associated complex stress intensity factor for our testing method is shown. An yttria stabilized zirconia (YSZ) coating, which was sprayed thermally on Ni-based superalloy, was tested using the testing device developed here.The results showed that the energy release rate for the coating-interfacial crack increased with loading phase angle, which is defined by tan⁻¹ for a ratio of stress intensity factor K₂ to K₁. It was noticed that the interfacial energy release rate increasing with mode II loading could be mainly associated with the contact shielding effect due to crack surface roughness rubbing together.     

Crack propagation from a pre-existing flaw at a notch root – II: Detailed form of the stress intensity factors at the initial crack tip and conclusion.

This paper pursues the study of crack kinking from a pre-existing crack emanating from some notch root. It was shown in Part I that the stress intensity factors at the tip of the small initial crack are given by universal (that is, applicable in all situations, whatever the geometry of the body and the loading) formulae; they depend only on the `stress intensity factor of the notch' (the multiplicative coefficient of the singular stress field near the apex of the notch in the absence of the crack), the length of the crack, the aperture angle of the notch and the angle between its bisecting line and the direction of the crack. Here we identify the universal functions of the two angles just mentioned which appear in these formulae, by considering the model problem of an infinite body endowed with a notch with straight boundaries and a straight crack of unit length. The treatment uses Muskhelishvili's complex potentials formalism combined with some conformal mapping. The solution is expressed in the form of an infinite series involving an integral operator, which is evaluated numerically. Application of Goldstein and Salganik's principle of local symmetry then leads to prediction of the kink angle of the crack extension. It is found that although the direction of the crack is closer to that of the bisecting line of the notch after kinking than before it, the kink angle is not large enough for the crack tip to get closer to this line after kinking, except perhaps in some special situations.     

Mixed Mode Brittle and Ductile Fracture of a High Strength Rotor Steel at Room Temperature

The mixed mode fracture of a high strength rotor steel has been investigated at room temperature using single edge notched specimens. In mode I, and for limited amounts of shear loading, the steel exhibited cleavage fracture. For conditions near mode~II ductile fracture occurred. A transition from brittle to ductile fracture occurred for mixed mode loading. Finite element analysis provided estimates of the extent of near crack tip yielding and elastic-plastic stress intensity factors. Test results agreed with the maximum tensile stress (MTS) criterion for small scale yielding for limited amounts of shear loading. The load for mode II fracture was lower than predicted from the MTS criterion, but higher than predicted from plastic collapse predictions. Observed fracture angles where in broad agreement with the predicted fracture mechanisms. The load for the transition from brittle to ductile fracture was found to agree approximately with the predicted load. This revised version was published online in July 2006 with corrections to the Cover Date.     

Application of the biaxial Iosipescu method to mixed-mode fracture of unidirectional composites

In this paper the biaxial Iosipescu test method has been used, employing specimens with a central precrack placed along the notch-root axis, to study the intralaminar failure properties of a unidirectional carbon/epoxy composite under mixed-mode (dominated by shear) loadings. A linear finite element analysis has been performed to determine the energy release rates and stress intensity factors for the central crack under various biaxial loading conditions. In addition, a series of simple and biaxial fracture experiments have been performed on the composite material. Numerical results indicate that the method is capable of generating a wide range of mixed-mode loading conditions at the crack tip for various loading angles and crack lengths. Using the numerical results, in conjunction with experimental data, the biaxial intralaminar failure process in the cracked Iosipescu specimens has been explained.     

Finite element calculation of stress intensity factors for interfacial crack using virtual crack closure integral

This paper presents a successful implementation of the virtual crack closure integral method to calculate the stress intensity factors of an interfacial crack. The present method would compute the mixed-mode stress intensity factors from the mixed-mode energy release rates of the interfacial crack, which are easily obtained from the crack opening displacements and the nodal forces at and ahead of the crack tip, in a finite element model. The simple formulae which relate the stress intensity factors to the energy release rates are given in three separate categories: an isotropic bimaterial continuum, an orthotropic bimaterial continuum, and an anisotropic bimaterial continuum. In the example of a central crack in a bimaterial block under the plane strain condition, comparisons are made with the exact solution to determine the accuracy and efficiency of the numerical method. It was found that the virtual crack closure integral method does lead to very accurate results with a relatively coarse finite element mesh. It has also been shown that for an anisotropic interfacial crack under the generalized plane strain condition, the computed stress intensity factors using the virtual crack closure method compared favorably with the results using the J integral method applied to two interacting crack tip solutions. In order for the stress intensity factors to be used as physical variables, the characteristic length for the stress intensity factors must be properly defined. A study was carried out to determine the effects of the characteristic length on the fracture criterion based the mixed-mode stress intensity factors. It was found that the fracture criterion based on the quadratic mixture of the normalized stress intensity factors is less sensitive to the changes in characteristic length than the fracture criterion based on the total energy release rate along with the phase angle.This work has been supported by ONR, with Dr. Y. Rajapakse as the program official.     

Toughening polymeric composites using nanoclay: Crack tip scale effects on fracture toughness

Fracture behavior of vinyl ester resin and the methods that can be used to toughen vinyl ester resin were studied. Neat resin, 5% by weight nanoclay, 5% by weight core shell rubber (CSR) and hybrid system (3% nanoclay and 2% CSR by weight) were the material systems considered for comparing fracture toughness. Three types of cracks were used to determine the stress intensity factors at failure, viz., sharp crack, blunt crack and notch. The critical stress intensity factor in the case of sharp cracks improved significantly when compared to neat resin. In the case of notched and blunt cracked specimens, a reduction in stress intensity factors (at failure) was observed for reinforced systems. However, for notched and blunt cracked specimens, it was shown from the morphology of the fracture surface that the stress intensity factor calculated by assuming a notch or a blunt crack as an ideal crack was not the controlling parameter for fracture. A method for quantifying the crack tip sharpness using fracture surface roughness has been proposed.     

Cohesive layer models for predicting delamination growth and crack kinking in sandwich structures

There are potentially two types of fracture that sandwich structures with strong and stiff facing sheets and lightweight cores are liable to suffer. These are the delamination growth at the face-sheet core interface and crack kinking into the sandwich core, respectively. The paper proposes computational models to simulate these failure mechanisms. The models employ the cohesive layer concept and are so constructed as to ensure that the crack advance is controlled by the critical value of strain energy release rate in mode I fracture. Of these, the first model can treat only delamination along a predetermined plane and is designated as CLD (cohesive layer delamination model). The performance of this model is thoroughly investigated in the light of experimental results. The influence of the key parameters of the model, viz. the thickness of the cohesive layer and the strength and stiffness of the cohesive layer material, have been studied. It is found that the model, as developed in this study, is fairly robust and is not sensitive to changes in parameters other than the critical strain energy release rate. The second model can track crack growth which is not predetermined in its direction. This it does by identifying the element in which the maximum principal tensile stress exceeds a critical value; once a crack is nucleated, the stress across the crack is relieved so that the right amount of energy is released when the crack is fully developed - much in the same manner as in a cohesive layer model. This model is designated as CLDK (Cohesive Layer Delamination and Kinking) model as it deals with interfacial delamination and crack kinking- whichever is the preferred mode of fracture. Experimental results of three sandwich specimens, viz. bottom restrained beams with 0° and –10° tilt angle, respectively, and a compressed beam, were used for comparison. The results indicate that the both the models are able to capture the initiation and track the growth of the interfacial delamination. The CLDK model is capable in addition to track the crack kinking into the core, and its subsequent return to the face sheet-core interface.     

Effects of T-stresses on fracture initiation for a closed crack in compression with frictional crack faces

This paper studies crack extension resulting from a closed crack in compression. The crack-tip field of such a crack contains a singular field relative to K _II and non-singular T-stresses T _x and T _y parallel and perpendicular to the crack plane, respectively. Using a modified maximum tensile stress criterion with the singular and non-singular terms, the kinking angle at the onset of crack growth is determined by a two parameter field involving the mode-II stress intensity factors and T-stresses, and at fracture initiation a wing crack may be created at an arbitrary angle from 0° to 90°. A compressive T _y increases the kinking angle and reinforces apparent mode-II fracture toughness, while a compressive T _x decreases the kinking angle and enhances apparent mode-II fracture toughness. The direction and resistance of fracture onset is strongly affected by T-stresses as well as frictional stress. The von Mises effective stress is determined for small-scale yielding near the crack tip. The effective stress contour shape exhibits a marked asymmetrical behavior unless 2T _x  = T _y  ≤ 0 for plane stress state. Coulomb friction between two crack faces generally increases the kinking angle, shrinks the size enclosed by the effective stress contour and enhances apparent fracture toughness. Field evidence and experimental observations of many phenomena involving the growth of closed cracks in compression agree well with theoretical predictions of the present model.     

Mixed mode fracture criterion of interface crack between dissimilar materials

This study presents an application of fracture mechanics to the interface crack between dissimilar materials. In this study, a concept of the stress intensity factors of an interface crack is discussed, and various types of specimens are tested experimentally for investigating the mixed mode fracture toughness criterion of an interface crack. The fracture toughness based on the stress intensity factors of an interface crack is decided by the fracture test and the boundary element analysis using the contour integral method. The mixed mode fracture toughness criterion is successfully characterized by the stress intensity factors of an interface crack.     

Dislocation modeling of quasi-static crack propagation in an elasto-plastic medium

A dislocation model for simulating two-dimensional quasi-static crack propagation is presented. The crack and plastic flow along slip planes are described using dislocation dipoles. A stationary crack can be modeled as well as a propagating crack along a straight line inclined at an arbitrary angle to a free surface of a semi-infinite medium. Cracks are also allowed to kink. A superdipole algorithm is introduced to save simulation time without loosing important information and necessary geometric details. It reduces the number of dislocation dipoles on slip planes in the plastic wake. The paper gives results on crack shapes for stationary and advancing cracks as well as it describes how the size of the plastic zone depends on crack inclination angles. Results on stress intensity factors (SIF) are given using two different approaches as well as kinking cracks are introduced and SIF at kinked crack tips are calculated.     

Dual boundary element method and finite element method for mixed‐mode crack propagation simulations in a cracked hollow shaft

Three‐dimensional mixed‐mode crack propagation simulations were performed by means of the dual boundary element method code BEASY and 2 finite element method‐based crack propagation codes: ZENCRACK (ZC) and CRACKTRACER3D (CT3D). The stress intensity factors (SIFs) along the front of an initial semielliptical crack, initiated from the external surface of a shaft, were calculated for 4 different load cases: bending, press fit, shear, and torsion. The methods used for the SIF assessment along the crack front were the J‐integral for BEASY and ZC and the quarter point element stress method for CT3D. Subsequently, crack propagation simulations were performed, with the crack growth rate evaluated by using Paris' law, calibrated for the material at stake (American Society for Testing and Materials A469 steel). The kink angles were evaluated by using the minimum strain energy density and maximum tangential stress criteria for BEASY, the maximum energy release rate and maximum tangential stress for ZC, and the maximum principal asymptotic stress for CT3D. The results obtained in terms of SIFs and crack propagation life show very good agreement among the 3 codes. Also, the shape of the propagated crack, which is significantly out‐of‐plane for the shear and torsion loading, matched very well.     

FE analysis of stresses and stress intensity factors of interfacial cracks in a CTS specimen

A plane stress finite element analysis was implemented to understand the stress fields for a crack lying at an aluminium/epoxy interface of a compact tension and shear specimen. The interaction integral method was used to separate the mixed-mode stress intensity factors at the interfacial crack-tip under different loading modes, which can have important implications for characterisation of interfacial crack growth.     

Mechanics of two-stage crack growth in fretting fatigue

Motivated by experimental observations, we carry out a numerical analysis of the two-stage crack growth under fretting fatigue by using an efficient and accurate boundary element method. To start with, the variation of stress field during a loading cycle is analyzed. Various values of friction coefficient in the contact zone are considered, which is shown to considerably affect the stress field. Then, by assuming crack initiation to occur in the shear mode, a surface-breaking crack is introduced to the specimen at the location of highest shear-stress amplitude. The crack-tip stress intensity factors (SIFs) are calculated for various crack lengths and at various crack angles ranging from 25° to 45° about the contact surface. It is shown that, for a loading ratio of 0.5, the cyclic mode-II SIF amplitude decreases with increasing crack length, whilst its mean value increases. It suggests that the (first-stage) shear crack would sooner or later become dormant, or switch to another mode that can provide continuous support of growth. Then, the first-stage shear crack is manually kinked into a second-stage opening crack, and the follow-on driving force is analyzed. It is shown that the kinking event is only favored after the first-stage crack has grown to a certain length. The present study thus provides insights in the mechanics of two-stage crack growth that has been frequently observed in a typical dovetail joint under fretting fatigue. It also suggests an improved experimental setup to quantitatively investigate the fretting fatigue in dovetail joints.