弹性地基上的4ENF试件柔度分析

基于Timoshenko梁理论,考虑了剪切变形和裂纹尖端变形的影响,建立了双参数弹性地基上的II型加载末端切口四点弯曲试件(4-point bending end-notched flexure specimen,简称4ENF)的柔度和能量释放率模型(BEF)。4ENF柔度与裂纹长度成正比,柔度变化率、能量释放率与裂纹长度无关,因而4ENFII型断裂实验无需测量裂纹的扩展长度,根据临界荷载便可求得临界能量释放率,从而大大简化了实验手段。对FRP-木4ENF试件II型加载情况下的BEF模型、Timoshenko梁理论模型和有限元结果比较证明:BEF模型的4ENF柔度在裂纹扩展的一定范围内与有限元吻合很好;而Timoshenko梁理论模型的柔度小于有限元结果,精度较差。该模型可用于复合材料界面断裂分析、确定断裂参数以及作为断裂试验数据分析的依据。     

Novel beam analysis of end notched flexure specimen for mode-II fracture

A novel beam model of end notched flexure (ENF) specimen for mode-II fracture testing is presented. By applying the principle of superposition, the ENF specimen is modeled as two sub-problems: (1) an un-cracked beam under three-point bending; and (2) a skew symmetric cracked beam under shear traction on the crack surface. Due to skew-symmetry of sub-problem two, only the upper half of the beam is analysed, and based on compatibility of deformation, a shear compliance coefficient is introduced to establish beam deformation equation. Explicit and simple closed form solutions of compliance and strain energy release rate are obtained, and they compare well with existing finite element analyses. Compared to other available analytical methods of the ENF specimen, the present beam model is relatively simple and easy to use; further, it can be applied to other beam fracture specimen analysis (e.g., mixed mode fracture and bi-material interface specimen).     

Analysis of stitched laminated ENF specimens for interlaminar mode II fracture toughness

Two simple micromechanics based models are proposed to predict the effect of through-thickness reinforcement (stitching) on the improvement of delamination crack growth resistance in end-notched flexure (ENF) specimens. In the first model, it is assumed that stitches stretch elastically and then rupture when the load carried approaches the failure load. In the second model, it is assumed that stitches are discontinuous and that the stitch thread-matrix interface is completely frictional. Approximate closed form solutions for energy release rates are obtained, and the effects of stitch density, matrix-stitch thread interfacial shear stress, stitch thread diameter, volume fraction of stitches, critical energy release rate and Young's modulus are then examined. A simple design study for sizing the ENF specimen to minimise geometric nonlinear response is presented. The influences of interlaminar shear deformation and friction between the crack surfaces on the strain energy release rate are examined.     

Analysis of unidirectional (0°) fiber-reinforced laminated composite double cantilever beam specimen using higher order beam theories

Mathematical models, for the stress analysis of unidirectional (0°) fiber-reinforced laminated composite double cantilever beam (DCB) specimen using classical beam theory, first and higher order shear deformation beam theories, have been developed to determine the mode I strain energy release rate (SERR) for unidirectional composites. In the present study, appropriate matching conditions at the crack tip of the DCB specimen have been derived by using variational principles. SERR has been calculated using compliance method. In general, the performance of shear deformation beam models of DCB specimen with variationally derived matching conditions at the crack tip is good in determining the SERR for medium to long crack lengths. Performance of higher order shear deformation beam model (having quadratically varying transverse displacement over the thickness) of DCB specimen, with non-variationally derived matching conditions at the crack tip, is good in determining the SERR for all the crack lengths in comparison with the available theoretical and finite element solutions in the literature. Higher order shear deformation beam theories having varying transverse displacement over the thickness are more appropriate to analyze DCB specimen as they predict the appropriate nature of the interlaminar normal stress at the crack tip and its distribution ahead of the crack tip.     

Creep crack growth modeling and near tip stress fields

The problem of near tip stress fields in a cracked body subjected to Mode I loading at elevated temperatures is studied. Specifically, the superalloy, IN 718, is examined in the standard compact tension specimen geometry. The simulation is at 650°C. The specimen is assumed to be under dead load conditions. For a stationary crack, the near tip stress fields are calculated and compared with the asymptotic solutions available in the literature. While the results assuming small strains agree very well with the asymptotic solutions, the large strain analysis does not. The results indicate that both the amplitude and the asymptotic exponent are dependent on the applied load level which is in disagreement with the asymptotic predictions. In addition, the zone effected by creep deformation is larger when large strains are considered. An algorithm is developed and tested for the modeling of stable crack growth. Both convergence and stability are investigated. Explicit time integration is used for crack growth studies as it is demonstrated to be computationally more efficient. The algorithm is employed to study the near tip stress fields for a growing crack. The near tip stress fields for a growing crack (with constant velocity) are generated using the developed algorithm. The results demonstrate that the asymptotic behavior of the stress field is load dependent. Comparison is made with the limited analyses available. Recommendations for future research are discussed.     

Analysis of beam-type fracture specimens with crack-tip deformation

A novel bi-layer beam model is developed to account for local effects at the crack tip of a bimaterial interface by modeling a bi-layer composite beam as two separate shear deformable beams. The effect of interface stresses on the deformations of sub-layers, which is referred to as the elastic foundation effect in the literature, is considered in this model by introducing two interface compliance coefficients; thus a flexible joint condition at the crack tip is considered in contrast to the rigid joint condition used in the conventional bi-layer model. An elastic crack tip deformable model is presented, and the closed-form solutions of local deformation at the crack tip are then obtained. By applying this novel crack tip deformation model, the new terms due to the local deformations at the crack tip, which are missing in the conventional composite beam solutions of compliance and energy release rate (ERR) of beam-type fracture specimens, are recovered. Several commonly used beam-type fracture specimens are examined under the new light of the present model, and the improved solutions for ERR and mode mixity are thus obtained. A remarkable agreement achieved between the present and available solutions illustrates the validity of the present study. The significance of local deformation at the crack tip is demonstrated, and the improved solutions developed in this study provide highly accurate predictions of fracture properties which can actually substitute the full continuum elasticity analysis such as the finite element analysis. The new and improved formulas derived for several specimens provide better prediction of ERR and mode mixity of beam-type fracture experiments.*Author for correspondence (E-mail address: qiao@uakron.edu)     

Effect of compressive transverse normal stress on mode II fracture toughness in polymeric composites

Effect of transverse normal stress on mode II fracture toughness of unidirectional fiber reinforced composites was studied experimentally in conjunction with finite element analyses. Mode II fracture tests were conducted on the S2/8552 glass/epoxy composite using off-axis specimens with a through thickness crack. The finite element method was employed to perform stress analyses from which mode II fracture toughness was extracted. In the analysis, crack surface contact friction effect was considered. It was found that the transverse normal compressive stress has significant effect on mode II fracture toughness of the composite. Moreover, the fracture toughness measured using the off-axis specimen was found to be quite different from that evaluated using the conventional end notched flexural (ENF) specimen in three-point bending. It was found that mode II fracture toughness cannot be characterized by the crack tip singular shear stress alone; nonsingular stresses ahead of the crack tip appear to have substantial influence on the apparent mode II fracture toughness of the composite.     

FRONT DEVELOPMENT OF A LONG FATIGUE CRACK DURING ITS GROWTH

Abstract— A 3-D elastic-plastic finite element analysis has been developed to simulate the deformation development along the front of a long mode I single edge crack in plates subjected to either monotonic or cyclic loading. Idealisations having both equal and unequal layers through the thickness of the plate were involved. Plane stress and plane strain 2-D finite element analyses were also performed and compared with the present 3-D solutions. The development of the monotonic and cyclic crack tip plastically deformed zones and opening displacements were traced and correlated to accommodate the effect of the plate thickness and the profile of the crack front. A previously developed crack tip deformation parameter was invoked to predict the effect of the specimen thickness on mode I fatigue crack growth and the associated change of crack front profile. Comparison of such a prediction and the experimental findings of the present work reflected the capability of that parameter in modelling fatigue crack growth through the plate thickness.     

Dynamic delamination fracture toughness in unidirectional polymeric composites

A modified end-notched flexure (ENF) specimen was used to determine Mode-II-dominated dynamic delamination fracture toughness of fiber composites at high crack propagation speeds. A strip of FM-73 adhesive film was placed at the tip of the interlaminar crack created during laminate lay-up. This adhesive film with its greater toughness delayed the onset of crack extension and produced crack propagation at high speeds. Dynamic delamination experiments were performed on these ENF specimens made of unidirectional S2/8553 glass/epoxy and AS4/3501-6 carbon/epoxy composites. Crack speed was measured by means of conductive aluminum lines created by the vapor deposition technique. A finite-element numerical simulation based on the measured crack speed history was performed and the dynamic energy release rate calculated. The results showed that the dynamic fracture toughness is basically equal to the static fracture toughness and is not significantly affected by crack speeds up to 1100 m/s.     

Microscale characterization of granular deformation near a crack tip

This paper presents a study of microscale plastic deformation at the crack tip and the effect of microstructure feature on the local deformation of aluminum specimen during fracture test. Three-point bending test of aluminum specimen was conducted inside a scanning electron microscopy (SEM) imaging system. The crack tip deformation was measured in situ utilizing SEM imaging capabilities and the digital image correlation (DIC) full-field deformation measurement technique. The microstructure feature at the crack tip was examined to understand its effect on the local deformation fields. Microscale pattern that was suitable for the DIC technique was generated on the specimen surface using sputter coating through a copper mesh before the fracture test. A series of SEM images of the specimen surface were acquired using in situ backscattered electronic imaging (BEI) mode during the test. The DIC technique was then applied to these SEM images to calculate the full-field deformation around the crack tip. The grain orientation map at the same location was obtained from electron backscattered diffraction (EBSD), which was superimposed on a DIC strain map to study the relationship between the microstructure feature and the evolution of plastic deformation at the crack tip. This approach enables to track the initiation and evolution of plastic deformation in grains adjacent to the crack tip. Furthermore, bifurcation of the crack due to intragranular and intergranular crack growth was observed. There was also localization of strain along a grain boundary ahead of and parallel to the crack after the maximum load was reached, which was a characteristic of Dugdale–Barenblatt strip-yield zone. Thus, it appears that there is a mixture of effects in the fracture process zone at the crack tip where the weaker aspects of the grain boundary controls the growth of the crack and the more ductile aspects of the grains themselves dissipate the energy and the corresponding strain level available for these processes through plastic work.     

Modeling of hydrogen embrittlement in single crystal Ni

A large-scale molecular dynamics simulation by the embedded atom method was carried out on hydrogen embrittlement of a single crystal containing 1,021,563 nickel atoms. The details of the deformation in the specimen were identified by a new method of the deformation analysis. Plenty of slip deformation occurred around the crack tip and in the bulk of the hydrogen-free specimen. Hydrogen embrittlement was most serious in the specimen hydrogen-charged in the notched area. Serious embrittlement was also observed in the specimen hydrogen-charged in the slip planes, in which dislocation emission was localized at the crack tip and enhanced on the planes where hydrogen atoms were located. It is considered that the fracture process is due to the hydrogen-enhanced decohesion mechanism.     

Application of the effective crack method to mode I and mode II interlaminar fracture of carbon/epoxy unidirectional laminates

This paper describes an experimental study involving double cantilever beam (DCB), end-notched flexure (ENF) and four-point end-notched flexure (4ENF) tests on carbon/epoxy unidirectional specimens. The main purpose was to evaluate the so-called effective crack method (ECM), which avoids operator crack position monitoring. Extensive fibre bridging in DCB tests made the ECM inappropriate, as shown in subsequent finite element analyses. On the other hand, the ECM gave very consistent results from ENF tests, despite the usually unstable initiation. The present results confirmed some dependence of perceived initiation toughness values on ENF specimen geometry predicted in recent numerical studies. Differences between results of ENF and 4ENF tests could be explained by friction effects in the latter.     

The influence of cross-sectional thickness on fatigue crack growth

For thin structures, fatigue crack growth rates may vary with the structure's thickness for a given stress intensity factor range. This effect is mainly due to the change in the nature of the plastic deformation when the plastic zone size becomes comparable with, or greater than, the cross-sectional thickness. Variations in the constraint affect both the crack tip plastic blunting behaviour as well as the fatigue crack closure level. Approximate expressions are constructed for the constraint factor based on asymptotic values and numerical results, which are shown to correlate well with finite element results. It is demonstrated that the present results not only permit predictions of the specimen thickness effects on fatigue crack propagation under spectrum loading, but also eliminate the need to determine the constraint factor by curve-fitting crack growth data.     

FINITE ELEMENT ANALYSIS OF STABLE CRACK GROWTH IN THREE SIZES OF COMPACT SPECIMENS OF A508 STEEL

Abstract— Plane strain, elastic-plastic, finite element analyses have been undertaken to simulate stable crack growth in an A508 forging steel for three different sizes of compact tension specimen and for small scale yielding by enforcing the same experimentally-measured deformation theory J resistance curve. The results show that path-dependence of the numerically calculated J -integral occurs from the very beginning of crack growth, and the degree of path-dependence is not strongly related to the amount of crack growth expressed as a proportion of the uncracked ligament. Crack tip stresses and strains are only mildly sensitive to changes in specimen size for the range of crack extension investigated. Small specimens appear to produce more intense deformation than small scale yielding and therefore cause more damage. For a tough steel such as A508 the parameter bσ_f/J_d , appears to be the most important in limiting the validity of J -characterized fields of deformation ahead of the growing crack.     

Experimental investigations of three-dimensional effects near a crack tip using computer vision

An experimental study of the near tip deformation fields for a Single Edge-Cracked specimen (SEC) has been completed. The surface deformation fields for a thin SEC plexiglas specimen have been obtained in the region 0.15 <- r/t <- 0.60, where r is radial distance from the crack tip and t is the specimen thickness, by using a novel computer vision method. The results of the study indicate that the value of the J-Integral obtained from the measured surface deformation, and under the assumption of plane stress linearly elastic behavior, is essentially path independent over a region that is considered to be within the crack tip three-dimensional zone by researchers who have performed tests on other materials.However, the near-tip, in-plane displacement field does show a deviation from the traditional linear elastic crack tip singularity over the same region, suggesting the need for further studies to address this inconsistency.     

Surface effects on mode-I crack tip fields: A numerical study

Surface energy often significantly influences the deformation and failure behavior of materials and devices at the nanoscale. However, how it alters the local deformation around a crack tip remains unclear. In the present paper, we investigate the surface effects on the near-tip fields of a mode-I blunt crack (or notch). The theory of surface elasticity is incorporated into the finite element method. It is found that when the curvature radius of the crack root shrinks to nanometers, surface effects considerably affect the local stress distributions near the crack tip. We also calculate the J-integral, which is almost independent of surface effects except when the integral path approaches the crack tip. This demonstrates that surface effects are localized in a small zone around the crack tip, where the classical fracture mechanics solutions neglecting surface effects should be modified.     

Finite deformation finite element analyses of tensile growing crack fields in elastic-plastic material

Finite deformation finite element analyses of plane strain stationary and quasi-statically growing crack fields in fully incompressible elastic-ideally plastic material are reported for small-scale yielding conditions. A principal goal is to determine the differences between solutions of rigorous finite deformation formulation and those of the usual small-displacement-gradient formulation, and thereby assess the validity of the (nearly all) extant studies of ductile crack growth that are based on a small-displacement-gradient formulation. The stationary crack case with a significantly blunted tip is studied first; excellent agreement in stress characteristics at all angles about the crack tip and up to a radius of about three times the crack tip opening displacement is shown between Rice and Johnson's [1] approximate analytical solution and our numerical solution. Outside this radius, the numerical results agree very well with Drugan and Chen's [2] small-displacement-gradient analytical characteristics solution in the region of principal plastic deformation. Thus we identify accurate analytical representations for the stress field throughout the plastic zone of a blunted stationary crack. For the growing crack case, the macroscopic difference in crack tip opening profiles between previous small-displacement-gradient solutions and the present results is shown to be negligible, as is the difference in the stress fields in plastic regions. The stress characteristics again agree very well with analytical results of [2]. The numerical results suggest—in agreement with a recent analytical finite deformation study by Reid and Drugan [3]—that it is the finite geometry changes rather than the additional spin terms in the objective constitutive equation that cause any differences between the small-displacement-gradient and the finite deformation solutions, and that such differences are nearly indistinguishable for growing cracks.     

Determination of T-stress from finite element analysis for mode I and mixed mode I/II loading

The elastic T-stress has been recognised as a measure of constraint around the tip of a crack in contained yielding problems. A review of the literature indicates that most methods for obtaining T are confined to simple geometry and loading configurations. This paper explores direct use of finite element analysis for calculating T. It is shown that for mode I more reliable results with less mesh refinement can be achieved if crack flank nodal displacements are used. Methods are also suggested for calculating T for any mixed mode I/II loading without having to calculate stress intensity factors. There is good agreement between the results from the proposed methods and analytical results. T-stress is determined for a test configuration designed to investigate brittle and ductile fracture in mixed mode loading. It is shown that in shear loading of a cracked specimen T vanishes only when a truly antisymmetric field of deformation is provided. However this rarely happens in practice and the presence of T in shear is often inevitable. It is shown that for some cases the magnitude of T in shear is much more than that for tension. The effect of crack length is also investigated. This revised version was published online in August 2006 with corrections to the Cover Date.     

Mode II Brittle Fracture Assessment Using ASFPB Specimen

The four-point bend specimen subjected to anti-symmetric loading (ASFPB) is frequently used for determining pure mode II fracture resistance of rock materials. It is shown in this paper that, when the applied loads are close to the crack plane, the ASFPB specimen does not provide pure mode II condition, since the effect of mode I also appears in crack tip deformation. A set of fracture test were also conducted on a type of marble using ASFPB configuration. The test results showed that fracture resistance is strongly dependent on the loading distance from the crack plane. The effective fracture toughness increases when the distance between the loading points and the crack plane decreases. It is shown that the enhanced fracture resistance of marble samples could be mainly because of very large negative T-stresses that exist for the mentioned loading situations.