Crack closure in fibre metal laminates

GLARE is a fibre metal laminate (FML) built up of alternating layers of S2-glass/FM94 prepreg and aluminium 2024-T3. The excellent fatigue behaviour of GLARE can be described with a recently published analytical prediction model. This model is based on linear elastic fracture mechanics and the assumption that a similar stress state in the aluminium layers of GLARE and monolithic aluminium result in the same crack growth behaviour. It therefore describes the crack growth with an effective stress intensity factor (SIF) range at the crack tip in the aluminium layers, including the effect of internal residual stress as result of curing and the stiffness differences between the individual layers. In that model, an empirical relation is used to calculate the effective SIF range, which had been determined without sufficiently investigating the effect of crack closure. This paper presents the research performed on crack closure in GLARE. It is assumed that crack closure in FMLs is determined by the actual stress cycles in the metal layers and that it can be described with the available relations for monolithic aluminium published in the literature. Fatigue crack growth experiments have been performed on GLARE specimens in which crack growth rates and crack opening stresses have been recorded. The prediction model incorporating the crack closure relation for aluminium 2024-T3 obtained from the literature has been validated with the test results. It is concluded that crack growth in GLARE can be correlated with the effective SIF range at the crack tip in the aluminium layers, if it is determined with the crack closure relation for aluminium 2024-T3 based on actual stresses in the aluminium layers.     

Weight function for a single edge cracked geometry with clamped ends

A single edge cracked geometry with clamped ends is well suited for fracture toughness and fatigue crack growth testing of composites and thin materials. Analysis of fiber bridging phenomenon in the composites and determination of stress intensity factors due to non-uniform stress distributions such as residual and thermal stresses generally require the use of a weight function. This paper describes the development and verification of a weight function for the single edge cracked geometry with clamped ends. Finite element analyses were conducted to determine the stress intensity factors (K) and crack opening displacements (COD) due to different types of stress distributions. The weight function was developed using the K and COD solution for a constant stress distribution. K and COD predicted using this weight function correlated well with the finite element results for non-uniform crack surface stress distributions.     

A MODEL TO PREDICT THE FATIGUE LIFE OF FIBRE-REINFORCED TITANIUM MATRIX COMPOSITES UNDER CONSTANT AMPLITUDE LOADING

A model based on micro-mechanical concepts has been developed for predicting fatigue crack growth in titanium alloy matrix composites. In terms of the model, the crack system is composed of three zones: the crack, the plastic zone and the fibre. Crack tip plasticity is constrained by the fibres and remains so until certain conditions are met. The condition for crack propagation is that fibre constraint is overcome when the stress at the location of the fibre ahead of the crack tip attains a critical level required for debonding. Crack tip plasticity then increases and the crack is able to propagate round the fibre. The debonding stress is calculated using the shear lag model from values of interfacial shear strength and embedded fibre length published in the literature. If the fibres in the crack wake remain unbroken, friction stresses on the crack flanks are generated, as a result of the matrix sliding along the fibres. The friction stresses (known as the bridging effect) shield the crack tip from the remote stress, reducing the crack growth relative to that of the matrix alone. The bridging stress is calculated by adding together the friction stresses, at each fibre row bridging the crack, which are assumed to be a function of crack opening displacement and sliding distance at each row. The friction stresses at each fibre row will increase as the crack propagates further until a critical level for fibre failure is reached. Fibre failure is modelled through Weibull statistics and published experimental results. Fibre failure will reduce the bridging effect and increase the crack propagation rate. Calculated fatigue lives and crack propagation rates are compared with experimental results for three different materials (32% SCS6/Ti-15-3, 32% and 38% SCS6/Ti-6-4) subjected to mode I fatigue loading. The good agreement shown by these comparisons demonstrates the applicability of the model to predict the fatigue damage in Ti-based MMCs.     

Comparison between rectangular and trapezoidal bonded composite repairs in aircraft structures: A numerical analysis

The optimization of the patch shape of bonded composite repair in aircraft structures is a good way to improve the repair performance. In this study, the three-dimensional finite element method is used to compare the repair performance of patches with rectangular and trapezoidal shapes in aircraft structures. The comparison is done by analysing the stress intensity factor (SIF) at the tip of repaired crack and the distribution of the adhesive stresses for the two patch shapes. The obtained results show that, when the crack length is ranged from 5 to 20 mm, the trapezoidal shape presents lower stress intensity factor at the crack tip, which is beneficial for the fatigue life and lower adhesives stresses, which is beneficial for the repair durability. These advantages disappear when the crack length reaches the value of 40 mm. It is also shown that the use of the trapezoidal shape reduce the mass of the patch, which can reduce the repair cost.     

Crack opening displacements of Vickers indentation cracks

Vickers indentation cracks are an appropriate tool to determine the crack-tip toughness K_I0 and, possibly, the bridging relation of ceramics with an R-curve behaviour from the total crack opening displacements. Two contributions to the total crack opening displacement field are addressed. First, the residual stresses occurring in the uncracked body are considered and then, the contact stresses generated by preventing crack face penetration are computed. The COD solution resulting from the superposition of residual and contact displacements is given and an analytical expression is provided. Near-tip displacements are represented by the first terms of series expansions. As an example of application, an evaluation of the actual stress intensity factor is presented for a window glass 1 h after Vickers indentation.     

Computation of Stress Intensity Factors by Using Global Crack-Line Displacement Fitting Procedure

A global crack-line displacement fitting procedure to extract the stress intensity factors (SIFs) is proposed in this paper. The proposed procedure uses the entire crack opening displacement (COD) data and its numerical calculation only involves in displacement fields. The post processing is greatly reduced and no new contour and remeshing are needed. The procedure can be easily applied to mixed mode crack problems with arbitrary crack shapes. In addition, the errors of the obtained SIFs can be estimated from the error information of COD data by this procedure. The procedure has been applied to several test examples of crack problems with their COD data being calculated by using a constant element boundary element method with two special crack tip elements. The results verified that the proposed procedure is reliable, accurate and easily implementing to extract SIFs. This revised version was published online in July 2006 with corrections to the Cover Date.     

Crack propagation in cylindrical shells

Results of a theoretical study of dynamic steady crack propagation in a circular cylindrical shell are presented. Equations of thin circular cylindrical shells are utilized for theoretical investigation. The semi-analytic crack tip stress solutions to shell equations are obtained by the perturbation method as well as an iterative method. Plots of internal stresses in the shell with a stationary as well as a steadily running crack are presented. These results are compared with those related to flat plates. It is concluded that the shell curvature has a pronounced effect on increasing the values of crack tip stresses. It would also qualitatively affect the variation of stress field around the crack tip. In some cases, the curvature action is shown to be even more pronounced than the inertia effects.     

Determination of the Parameters of the Two-Parametric Fracture Mechanics along the Crack Front Based on the Digital Image Correlation Data

A mathematical processing technique and an algorithm for the numerical correction of experimental displacement fields on the specimen surface in the vicinity of a crack tip with consideration of the displacement of a body as a rigid whole under its loading and the actual position of a crack tip were proposed. The initial experimental displacement fields in the vicinity of a fatigue crack tip of a compact specimen were determined by digital image correlation. This approach was successfully used for a compact specimen and the possibility of its expansion to obtain the distributions of the stress intensity factors and the nonsingular T stresses along the spatial crack front was shown.     

Calculation of Near-Tip Non-Singular Stresses Under Mixed-Mode Crack Surface Tractions

When the crack surfaces are subjected to nonuniform mixed-mode surface tractions, there exist at the tip additional constant stress components other than the T-stress and the influence from the higher order non-singular stress terms may become more significant. In this work, an effective numerical approach is proposed to calculate the corresponding non-singular stresses. By introducing the concept of mixed-mode auxiliary stress fields, a de-singularized loading system is established for the calculation. The proposed scheme is applicable for 2-D problems subjected to arbitrarily distributed nonuniform crack surface tractions.     

Residual stress induced crack tip constraint

This paper studies the effect of welding residual stresses on the near tip stress field in single edge notched bending and tensile specimens. A combined effect of mechanical stresses by the applied load and residual stress on the crack tip constraint is analyzed. Three initial residual stress distributions were considered. It has been shown that the crack tip stress field is strongly influenced by the residual stresses and a new parameter, R, is proposed to characterize the residual stress induced crack tip constraint. The results therefore suggest a three-parameter approach (CTOD, Q and R) to characterize the crack tip stress field in the presence of residual stress where CTOD sets the size scale over which large stresses and large strains develop, and the geometry constraint parameter Q and the new residual stress induced constraint parameter R control the actual crack tip constraint level. For the cases analyzed, R is in general positive, which indicates that residual stress can enhance the crack tip constraint. However, the results also indicate that the R decreases towards zero and the effect of residual stress on crack tip constraint can be neglected when a full plastic condition is approached in the specimen.     

Experimental Study of Self-Similar Crack Distributions

This paper presents laboratory experiments on polyester resin samples subjected to special regimes of curing under which multiple shrinkage cracks with wide distributions of sizes were produced. Loading these samples produced stress-strain curves that followed a power law within certain stress ranges. The results of the tests were analysed using the mechanics of materials with self-similar crack distributions. The analysis showed that the observed power law in the stress-strain relationship indicated that the crack distribution was approximately self-similar. Thus, the described experiments serve as a verification procedure for the proposed formation mechanism of multiscale self-similar crack distribution in brittle materials. This mechanism is based on: (1) the action of self-equilibrating stress fluctuations as initiators and propagators of cracks and (2) the size discriminating action of crack interaction. The concentration factors for the crack distributions have been retrieved from the experimental data.     

A crack in a linear-elastic material under mode II loading, revisited

A sharp crack in a two-dimensional infinite linear-elastic material, under pure shear (mode II) loading is re-examined. Several criteria have been proposed for the prediction of the onset and direction of crack extension along a path emanating from the tip of the initial crack. These criteria date back some three decades and are well documented in the literature. All the predictions from the different criteria are close and indicate that the crack extension takes a direction at an angle of ≈ −70° measured counterclockwise from the positive x -axis, in the case of a remotely applied positive shear stress. However, the possibility seems to have been overlooked that the crack extension may initiate not from the crack tip itself, but instead may initiate on the free surface at an infinitesimal distance behind the crack tip. The effect of crack tip plasticity on the relevant stresses in the region of the crack tip is investigated by the application of an elastic–plastic finite element program.     

Crack initiation in laminated metal-intermetallic composites

Several mechanisms have been proposed to describe crack initiation and propagation in ductile-brittle composites. This experimental study shows that the failure of metal intermetallic (metal-aluminides) composites was initiated by cracking initiation in the intermetallic layers. For metal layers that allowed shear deformation, crack initiation in adjacent intermetallic layers resulted from shear bands propagating from a crack tip in the intermetallic layer through the metal layer and producing stress concentration points at the interfaces of adjacent intermetallic layers. For metal layers that did not support shear deformation, crack initiation in the intermetallic layers resulted from the continued build up of stresses within the intermetallic layers, resulting in a relatively uniform distribution of cracks within the individual intermetallic layers. Prior to failure, lateral constraints produce lateral cracks in the intermetallic layers. The final fracture features of both failure mechanisms were similar for both metal-intermetallic systems.     

Crack growth prediction for underground high pressure gas lines exposed to concentrated carbonate–bicarbonate solution with high pH

A crack growth model for high pH stress corrosion cracking of pipeline steels is presented based on the assumption that the cracking is dominated by the repeated rupture of passive film at the crack tip. The model is validated by the experimental data available. It provides a reasonably good prediction to effects of various factors relating to materials, environment and loading conditions. Although the fatigue damage produced in operation of gas lines is negligible, the contribution due to cyclic load-promoted crack tip dissolution needs to be considered in remaining life prediction. Finally, the procedure for field application is discussed.     

Mode I weight functions for an orthotropic double cantilever beam

Approximate weight functions are proposed and validated numerically for an orthotropic double cantilever beam (DCB) loaded in mode I. They define the stress intensity factor at the crack tip due to a pair of point forces acting on the crack surfaces and have been deduced from the corresponding isotropic result using an orthotropy rescaling technique. The weight functions allow mode I large scale bridging problems in beams and plates to be formulated as integral equations, in terms of stress intensity factors at the crack tip, without the limitations imposed on accuracy by beam theory approximations. The proposed functions are applied to investigate the influence of the orthotropy of the material on the fracture behavior of DCBs in the presence of large scale bridging.     

Evaluation of Stresses in Reinforced-Concrete Beam Elements,Their Strength,and Crack Resistance

We develop a procedure for the evaluation of strength and crack resistance of reinforced-concrete beam elements based on the approaches of fracture mechanics. A model for the numerical analysis of stresses is proposed and the formulas for finding normal stresses in the reinforcement and compressed concrete fibers are deduced by taking into account the inelastic zones in the vicinity of the crack tip. The established relations are checked experimentally and compared with the formulas proposed by SNiP 2.03.01-84.     

Thermal effect of plastic dissipation at the crack tip on the stress intensity factor under cyclic loading

Plastic dissipation at the crack tip under cyclic loading is responsible for the creation of an heterogeneous temperature field around the crack tip. A thermomechanical model is proposed in this paper for the theoretical problem of an infinite plate with a semi-infinite through crack under mode I cyclic loading both in plane stress or in plane strain condition. It is assumed that the heat source is located in the reverse cyclic plastic zone. The proposed analytical solution of the thermo-mechanical problem shows that the crack tip is under compression due to thermal stresses coming from the heterogeneous stress field around the crack tip. The effect of this stress field on the stress intensity factor (its maximum and its range) is calculated analytically for the infinite plate and by finite element analysis. The heat flux within the reverse cyclic plastic zone is the key parameter to quantify the effect of dissipation at the crack tip on the stress intensity factor.     

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.     

Shielding Stresses for Soft PZT

Crack opening displacements (COD) were obtained on fully developed cracks in compact tension specimens manufactured from a commercial, soft lead zirconate titanate (PZT). The data were evaluated using the weight function method to provide crack closures stresses as a function of distance to the crack tip. As ferroelastic toughening in PZT shows time-dependent effects, data were taken at different stages of unloading. The peak closure stress was determined as 20 MPa.     

Experimentelle Charakterisierung und zweidimensionale Simulation der mikrostrukturbestimmten Ermüdungsrissausbreitung in einer β‐Titanlegierung

In this project the initiation and propagation of short fatigue cracks in the metastable β‐titanium alloy TIMETAL®LCB is investigated. By means of an interferometric strain/displacement gauge system (ISDG) to measure the crack opening displacement (COD) and the electron back scattered diffraction technique (EBSD) to determine the orientation of individual grains the microstructural influence on short crack initiation and growth can be characterized. Finite element calculations show a high influence of the elastic anisotropy on the initiation sites of cracks. Crack propagation takes place transgranulary along slip planes as well as intergranulary along grain boundaries. The crack growth rate depends strongly on the active mechanism at the crack tip which in turn is influenced by crack length, the applied stress and the orientation of the grains involved. The value of the steady state crack closure stress changes from a positive value at low applied stresses (roughness induced) to a negative one at higher applied stresses (due to plastic deformations at the crack tip). The crack growth simulation is realised by a two‐dimensional boundary element technique, which contains the ideas of Navarro und de los Rios. The model includes the sequence of the applied stress amplitude as well as the experimental measured roughness induced crack closure.