Normal Crack Opening Displacements Research Articles

An interlaminar fatigue damage model based on property degradation of carbon fiber-reinforced polymer composites

Interface delamination is a significant damage mechanism in fiber-reinforced polymer (FRP) laminated composites caused by interlaminar normal and shear stresses. This is due to the low interlaminar properties including interface stiffness and strength that continuously degrade to cause fatigue crack nucleation and growth. In this respect, an interlaminar fatigue damage model is proposed to accurately address the reliability aspect of the FRP composite materials and structures. The model considers a damage process that consists of two stages: (1) fatigue damage evolution due to interlaminar properties degradation to the onset of crack nucleation. A cyclic cohesive zone model with a bilinear softening behavior is introduced along with the fatigue life model to capture the mean stress effect of the interface. This is followed by (2) the crack nucleation process leading to the physical separation/debonding of the interface material point, as governed by the cycle-dependent fracture energy dissipation. The mechanical prediction of the interlaminar fatigue damage process is illustrated through finite element simulation of a mixed-mode flexural test of a carbon fiber-reinforced polymer (CFRP) composite beam subjected to fatigue loading. The results indicate that the interlaminar normal and shear crack opening displacement increases exponentially with the larger number of load cycles. In addition, the high-stress gradient is limited to the interface crack front zone with the normal and shear stress peaks at 69.2 and 16.5 % of the respective interlaminar strength. Moreover, controlled interlaminar crack growth is initially foreseen at 7.0 × 10-6 mm/cycle, followed by an abrupt crack “jump” at 287,000 load cycles.

On determining mixed-mode traction–separation relations for interfaces

Traction–separation relations can be used to represent the adhesive interactions of a bimaterial interface during fracture. In this paper, a direct method is proposed to determine mixed-mode traction–separation relations based on a combination of global and local measurements including load-displacement, crack extension, crack tip opening displacement, and fracture resistance curves. Mixed-mode interfacial fracture experiments were conducted using the end loaded split (ELS) configuration for a silicon-epoxy interface, where the epoxy thickness was used to control the phase angle of the fracture mode-mix. Infra-red crack opening interferometry was used to measure the normal crack opening displacements, while both normal and shear components of the crack-tip opening displacements were obtained by digital image correlation. For the resistance curves, an approximate value of the J-integral was calculated based on a beam-on-elastic-foundation model that referenced the measured load-displacement data. A damage-based cohesive zone model with mixed-mode traction–separation relations was then adopted in finite element analyses, with the interfacial properties determined directly from the experiments. With the mode-I fracture toughness from a previous study, the model was used to predict mixed-mode fracture of the silicon/epoxy interfaces for phase angles ranging from $$-42^{\circ }$$ to $$0^{\circ }$$ . Results from experiments using ELS specimens with phase angles that differed from those employed in parameter extraction were used to validate the model. Additional measurements would be necessary to further extend the reach of the model to mode-II dominant conditions.

Mixed-mode traction-separation relations between graphene and copper by blister tests

A blister test with associated analysis was developed to characterize the traction-separation relations associated with interactions between graphene and a copper substrate to which it had been transferred. Graphene grown by chemical vapor deposition was backed by a photoresist film and transferred to a highly polished copper substrate from its seed copper foil. The graphene/photoresist composite film was then pressurized with deionized water through a hole in the substrate. The blister profiles and normal crack opening displacements (NCOD) were measured by two microscopes with synchronized cameras. Different mixed-mode conditions were achieved by varying the thickness of the backing layers. The measured adhesion energy for the graphene/copper and photoresist/copper interfaces showed a strong dependence on the mode-mix. Cohesive zone models associated with traction-separation relations were then developed to study the damage initiation and crack propagation under various mixed-mode conditions. The numerical solutions for the resistance curves, pressure vs. deflection, and NCOD were in good agreement with measurements. The cohesive zone model was extended to a wider range of mode-mixes by making use of the asperity locking model which had provided a mechanism for the observed toughening effect. The interactions between graphene and copper were found to be stronger in all respects than those associated with photoresist and copper. Because the monolayer graphene was sandwiched between photoresist and copper, this result suggests that graphene was not transparent to interactions between photoresist and copper, but opaque. The use of pressure could provide another approach to transfer large-scale graphene.

A comparison of direct and iterative methods for determining traction-separation relations

Traction-separation relations have been used to represent the adhesive interactions at bimaterial interfaces for contact and fracture analyses. There are a variety of methods for determining these relations, which are broadly sorted into iterative and direct methods. Here we compare the traction-separation relations for a silicon/epoxy interface extracted by two such methods. Interferometric measurements of the normal crack opening displacements near the crack front in a double-cantilever beam specimen were exploited along with an augmented analytical solution for J-integral as an illustration of the direct method. As an example of the iterative method, we relied on comparisons of measured crack length and normal crack opening displacements with numerical simulations obtained from two types of candidate traction-separation relations. It was found that the shape of the traction-separation relation, in addition to the interfacial toughness and strength, was needed to bring the numerical solutions into optimal registration with the measurements. On the other hand, the direct method lived up to its name in terms of ease of parameter extraction while providing a reasonable set of parameters.

A High Vacuum Fracture Facility for Molecular Interactions

This paper describes the development of a high vacuum fracture rig for delaminating functionalized silicon surfaces. The main focus here is on examining molecular interactions by functionalizing the silicon surfaces with carboxyl and diamine terminated self-assembled monolayers (SAMs). However, many other interactions can be considered. The crack front location and normal crack opening displacements (NCOD) are measured by infrared crack opening interferometry (IR-COI). This allows the normal traction-separation relation of the interactions to be determined. Some mixed-mode fracture experiments were conducted on silicon/carboxyl/diamine/silicon sandwich specimens in ambient and high vacuum. Interesting differences in behavior were noted.

Characterizing delamination of fibre composites by mixed mode cohesive laws

A novel method is used for the determination of mixed mode cohesive laws and bridging laws for the characterisation of crack bridging in composites. The approach is based on an application of the J integral. The obtained cohesive laws were found to possess high peak stress values. Mixed mode cohesive stresses were found to depend on both the normal and tangential crack opening displacements. The bridging laws, which are to be used together with a mode mixity dependent crack tip fracture energy, were found to possess relative low bridging stresses; the peak normal bridging stress was approximately 2 MPa during pure Mode I and the maximum shear stress during pure Mode II was about 10 MPa.

Micromechanical model of cross-over fibre bridging – Prediction of mixed mode bridging laws

The fracture resistance of fibre composites can be greatly enhanced by crack bridging. In situ observations of mixed mode crack growth in a unidirectional carbon-fibre/epoxy composite reveal crack bridging by single fibres and by beam-like ligaments consisting of several fibres. Based on the observed bridging mechanism, a micromechanical model is developed for the prediction of macroscopic mixed mode bridging laws (stress-opening laws). The model predicts a high normal stress for very small openings, decreasing rapidly with increasing normal and tangential crack opening displacements. In contrast, the shear stress increases rapidly, approaching a constant value with increasing normal and tangential openings. The solutions for the bridging laws and the resulting toughening due to the bridging stresses are obtained in closed analytical form.

Re-examination of the PKHS crack model in piezoelectric materials

Abstract In this paper, the PKHS crack model is re-examined in detail. Some novel features and better understandings are presented. It is found that the normal crack opening displacement jump (NCODJ) across the crack is always extremely small, whereas the electric potential drop (EPD) across the crack is very large for PZT-4 or PZT-5H under 20 MPa and a varying electric field from −0.5 MV/m to 0.5 MV/m. It is also found that the permittivities of the medium inside the crack gap influence the NCODJ and the EPD significantly. Of great significance is that the crack tip energy release rate (ERR) does not always show an even functional dependence on the applied electric field as previous researchers reported. Its variable tendencies (even or odd) depend on the mechanical loading levels, which are called as the load dependence feature here. In PZT-4, this load-dependence feature induced from the increasing mechanical loading may lead to a transformation of the crack tip ERR from an even functional dependence to an odd one when the applied electric loading varies within the range mentioned above, whereas in PZT-5H no such feature exists. This implies that different mechanical loading levels may yield different fracture behaviors when using the crack tip ERR as a fracture criterion. Moreover, the permittivities of medium inside the PKHS crack gap influence the variable tendencies of the ERR significantly. Thus, a useful addition to previous works is provided and a reasonable explanation for the fundamental discrepancy between previous theoretical predictions and experimental observations in piezoelectric fracture can be given. That is, previous experiments were performed for quite different piezoelectric materials, under quite different mechanical loading levels, and with quite different media inside crack gaps.

Mixed Mode Effects on the Interfacial Crack Propagation

Initiation and propagation of interfacial crack along bimaterial interface are considered in this study. A series of interfacial crack initiation and propagation experiments are conducted using the biaxial loading device for various mixed modes. Normal crack opening displacement (NCOD) is measured near crack front by a crack opening interferometry and used for extracting fracture parameters. From mixed mode interfacial crack initiation experiments, large increase in toughness with shear components is observed. Initial velocity of crack propagation is very dependent upon the mode-mixes. It increased with positive mode-mix due to the increase of stress singularities ahead of crack front and decreased with negative mode-mix resulting from the increase of the degree of compressive stress behind the crack front. Crack propagation was less accelerated with positive mode-mix than the negative mode-mix.

Interfacial crack propagation under various mode-mixes

Initiation and propagation of interfacial crack along bimaterial interface are considered in this study. A biaxial loading device for a single specimen is used for obtaining a wide range of mode-mixities. The specimen is an edge-cracked bimaterial strip of glass and epoxy; the biaxial loading device, being capable of controlling displacements in two perpendicular directions, is developed. A series of interfacial crack initiation and propagation experiments are conducted using the biaxial loading device for various mixed modes. Normal crack opening displacement (NCOD) is measured near crack front by a crack opening interferometry and used for extracting fracture parameters. From mixed mode interfacial crack initiation experiments, large increase in toughness with shear components is observed. The behavior of interfacial crack propagation analyzed as a function of mode-mix shows that initial crack propagation is delayed with increase of mode-mixity, and its velocity is increased with positive mode-mixity but decreased with negative case. However, it is found that crack propagation is less accelerated with positive mode-mixity than the negative mode-mixity, which may be caused by contact and/or effects of friction between far field and near-tip field along the interfacial crack.

Continuum simulations of directional dependence of crack growth along a copper/sapphire bicrystal interface. Part II: crack tip stress/deformation analysis

The goal of this work is to explain the directional dependence of fracture of interfacial cracks in a copper/sapphire bicrystal in terms of continuum stress and deformation fields. In Part I of this pair of papers, we briefly review the main results of experiments by Kysar (Acta Mater. 48 (2000) 3509) and discuss how the orientation of the directional dependence of fracture is contrary to predictions made on the basis of crack tip dislocation nucleation concepts. We then set the stage for a series of finite element analyses of the bicrystal specimen. In Part II the simulation results are presented. We first conclude that the assumptions which enter into the crack tip dislocation nucleation analyses are valid. Therefore, the orientation of the directional dependence is opposite that of the dislocation nucleation analyses, in spite of the fact that crack tip dislocation nucleation may occur as predicted. We then show that the directional dependence of fracture, at least for the copper/sapphire bicrystal specimen, can be explained by the fact that the quasistatically growing brittle crack has the propensity to generate a significantly higher normal opening stress along its prolongation than does the ductile crack. This conclusion is valid for a wide range of crack growth criteria as well as material constitutive models and parameters. We also present results of the simulated crack opening displacement profiles of the two crack and compare them to experimental measurements. The results do not satisfactorily explain the qualitative features of the normal crack opening displacement profile; however we discuss some possible reasons why the finite element method may not be able to accurately model the crack opening displacement profile.

Crack-opening interferometry at interfaces of transparent materials and metals

Crack-opening interferometry is a technique whereby one can directly measure the normal opening displacement of a crack that exists in a transparent material. Here, wer extend the techique to situations in which the crack lies along the interface between a stransparent material and a highly reflective metal. We discuss how the intensity distribution and the placement of the fringes vary with reflectivity of the metal. However, because the fringe spacing is not affected, the fringes can still be interpreted in terms of normal crack-opening displacement profile. The paper reports experimental measurements of crack-opening displacement profile of an interface crack in a copper-sapphire bircystal. The results show the crack-opening displacement profile to be that of a constant opening angle.

Asymmetric Shielding Mechanisms in the Mixed-Mode Fracture of a Glass/Epoxy Interface

An asymmetric increase in the apparent values of the interfacial fracture toughness with increasing mode II component of loading has been observed by several investigators. In this study, cracks were grown in a steady-state manner along the glass/epoxy interface in sandwich specimens in order to determine the mechanisms responsible for the shielding effect. Finite element analysis using a hydrostatic stress and strain rate dependent plasticity model for the epoxy and a cohesive zone model for the interface shows that plastic dissipation in the epoxy accounts for the asymmetric shielding seen in these experiments which cover a wide range of mode mix. Numerical predictions of normal crack-opening displacements yielded results that were consistent with measured values which were made as close as 0.3 μm from the crack tip.

Experiments and Simulations of Directionally dependent Fracture along Copper/Sapphire Interfaces

AbstractTo test the hypothesis that the brittleness and ductility of crystalline materials are controlled by a competition between dislocation nucleation and cleavage failure at a crack tip, Riceet al.[1] designed a four-point bend copper/sapphire bicrystal which has two cracks that propagate along the interface in opposing directions. They predicted, on the basis of the Rice-Thomson model [2], that the specimen would exhibit a directionally dependent fracture behavior; that is, one crack would propagate more readily than the other. Beltz and Wang [3] carried out the experiments and reported that the specimen exhibits a directionally dependent fracture behavior in accordance with the predictions. In the present work, these experiments are repeated independently and it is shown thatthe orientation of the experimentally observed directionally dependent behavior is opposite that of the predicted orientation.Furthermore, we show that Beltz and Wang incorrectly measured the orientation of the directional dependence in their experimental results. A correct interpretation of their results is consistent with the present work.Taking advantage of the transparent sapphire, the normal crack opening displacement (NCOD) profile of both cracks is measured with optical interferometry. The measurements show that, away from the very tip of the crack, the NCOD takes the form of a constant angle, irrespective of load level. The opening angle of the apparently brittle crack is smaller than that of the apparently ductile crack. Complementary measurements of the very tip of the crack with Atomic Force Microscopy show that the near-tip crack opening profiles of the brittle and ductile cracks differ significantly.The specimen is analyzed with the Finite Element Method, taking into account the elastic and plastic properties of the single crystal constituents. Since the very essence of the observed phenomenon is one of crack growth, the two cracks are simulated as they grow quasistatically along the interface. The asymptotic deformation fields, characteristic of single crystals, of the growing interfacial cracks are identified. The stress and strain fields, as well as the NCOD, are calculated. We present a plausible explanation of the directional dependence of fracture on the basis of the continuum plastic fields surrounding the quasistatically growing cracks.

Toughening mechanisms in mixed-mode interfacial fracture

A series of mixed-mode interfacial crack initiation experiments were conducted using thinner glass/epoxy specimens than had been used in the past [Liechti and Chai (1992, J. Appl. Mech.59, 295–304)]. Three-dimensional effects were eliminated in the sense that the crack front shapes were the same for all mode-mixes. Nonetheless, the thinner specimens were associated with an overall increase in toughness and a noticeable change in the distribution of toughness with mode-mix. Interferometric measurements of normal crack opening displacements (NCOD) revealed values that were lower than predictions based on rate independent and dependent plasticity and even elastic analyses. The lower NCOD were attributed to long range cohesive crack face tractions, possibly due to electrostatic effects. Shielding calculations suggested that the long range tractions were more important than plastic dissipation. Nonetheless, they did not fully explain the shear-induced toughness effect that has been noted for this and other interfaces.

Micromechanical Behavior Of Polymer Interface Reinforced With Copolymers

AbstractThe fracture toughness of interface reinforced with dps-b-dpmma copolymer between immiscible polymers of PS and PMMA is tested by asymmetric double cantilever beam. The local deformation field at the interfacial crack tip is determined by the technique of SIEM. Normal and tangential crack opening displacements are calculated. A weak singularity is shown to exist near crack tip. Direct observation on the fracture process inside an environmental scanning electron microscope shows the large effect of mode mixity.

Three-dimensional effects in interfacial crack propagation

The paper describes the use of crack-opening interferometry for examining the variation in normal crack-opening displacements (NCOD) along the front of an interfacial crack in an edge-cracked bimaterial strip under biaxial loading. For the glass/epoxy combination considered here, the crack front was concave in the direction of crack growth, in contrast to previous observations with a glass/polyurethane/glass sandwich specimen and cracks in homogeneous materials. The NCOD were greatest in the interior of the specimen for all mode-mixes considered and the exponents in a power-law fit of NCOD versus distance from the crack front decreased towards the free surface. The exponents varied with mode-mix, suggesting that interfacial crack-front geometries could be similarly affected.

Asymmetric Shielding in Interfacial Fracture Under In-Plane Shear

The toughness of a glass/epoxy interface was measured over a wide range of mode mixes. A toughening effect was associated with increasing positive and negative inplane shear components. Optical interference measurements of normal crack opening displacements near the crack front and complementary finite element analyses were used to examine near-front behavior during crack initiation. Estimates of the toughening based on plastic dissipation, bulk viscoelastic dissipation, and interface asperity shielding did not fully account for the measured values. The results suggest that the inelastic behavior of the epoxy, frictional, and, perhaps, three-dimensional effects should be considered.

The interfacial fracture characteristics of bimaterial and sandwich blister specimens

The interfacial crack initiation characteristics of bimaterial and sandwich strip blister specimens were compared. Interface cracks were grown along glass/epoxy interfaces and the corresponding loads, normal crack opening displacements (NCOD) and crack front geometries were measured. Finite element analyses were used to compare NCOD, extract fracture parameters and examine near front stress fields. On the small scale of crack extension that could be measured, the bimaterial specimens exhibited resistance curve behavior whereas none could be resolved in the sandwich specimens. The phase angle dependence of toughness in the bimaterial specimens was similar to that obtained in previous blister tests but was much steeper than has otherwise been measured. The toughness of the glass/epoxy interface in the sandwich specimen decreased with decreasing epoxy thickness in spite of the fact that it was never completely spanned by plastic zones.

Elastic wave scattering by a circular crack in a transversely isotropic solid

The scattering of arbitrary elastic waves by a circular crack in a tranversely isotropic solid is investigated. The symmetry axis of the solid and the normal to the crack are parallel. The problem is first divided into a symmetric and an antisymmetric part with respect to the plane of the crack. A Fourier-Hankel representation for the scattered field is then assumed and some manipulations using the conditions in the plane of the crack lead to an integral equation for the normal crack opening displacement for the symmetric part and two coupled integral equations for the tangential components of the crack opening displacement for the antisymmetric part. The crack opening displacements are expanded in series of Legendre functions which fulfil the correct edge conditions and the integral equations are projected on the same set of Legendre functions. The far field is calculated with the stationary phase method. Numerical results are given for crack opening displacements for incident quasi P and SV plane waves and compared with corresponding results for an isotropic solid.