Ermüdungsrißwachstum in Kerben

Fatigue Crack Growth in Notches Nowadays it is wellknown that an important part of the fatigue life time, usually differenciated in crack initiation and crack growth, is often controlled by fatigue crack growth of cracks in notches. An elastic-plastic on the J-integral based crack growth model considering the crack opening and closure phenomenon will be described to determine crack growth of cracks in notches between crack initiation and failure. Experimental results and finite element analysis were used to verify the developed model.     

Numerical modeling the effects of overloading and underloading in fatigue crack growth

In this paper, the effects of overloading and underloading on fatigue crack growth were investigated. Numerical modeling was done by using finite element software. In this software, without using the remeshing technique, effect of crack tip plasticity in fatigue crack growth life was analyzed. Plasticity effects were considered by using three methods: COD method, U correction factor and J-integral. Calculated results for crack growth rates were compared with experimental data in literature. Results were obtained by COD method and U correction factor have good agreement but results form J-integral have not. We also study the effects of stress ratio (R) in plane stress and plane strain conditions. With increasing R, the fatigue life was increased. The extent of crack retardation is greater under plane stress than plane strain conditions. Underloading has not significant effects on fatigue crack growth rate. Underloading cause a little variation in plastic zones and so little effects on fatigue life.     

A survey of failure criteria and parameters in mixed-mode fatigue crack growth

From the present survey of the mixed-mode crack growth criteria based on the fracture toughness K _Ic (critical J-integral), it follows that this concept is very extensively and variously used by different authors. The criteria discussed in the work are based on the parameters K, δ, W, and J. The most extensively applied models include the mixed mode I + II described by the stress intensity factor K. The criteria presented in the work are based on the factors affecting the fatigue crack growth during testing, namely stress, crack-tip displacement, or energy dissipation. In the case of mixed-mode cracking, special attention should be paid to the energy approach (application of the J-integral and strain energy density), which seems to be very promising for elastoplastic materials. Under mixed-mode cracking, two things should be taken into account: the rate and direction of fatigue-crack growth. Moreover, the nonproportional loading, crack closure, or overloads strongly affect the process of fatigue crack growth in the case of mixed-mode cracking.     

Effect of thermomechanical loads on the propagation of crack near the interface brittle/ductile

The purpose of this paper is to understand the combined effect of thermal and mechanical loading on the initiation and behaviour of sub-interface crack in the ceramic. In this study a 2D finite element model has been used to simulated mixed mode crack propagation near the bimaterial interface. The assembly ceramometalic is subjected simultaneously to thermomechanical stress field. The extent of a plastic zone deformation in the vicinity of the crack-tip has a significant influence on the rate of its propagation. The crack growth at the joint specimen under four-point bending (4PB) loading and the influence of residual stresses was also evaluated by the maximum tensile stress criterion. The J-integral at the crack tip is generally expressed by the thermomechanical local stresses. The results obtained show the effect of the temperature gradient ΔT, the size of the crack and the applied stresses on the J-integral.     

The J-integral at Dugdale cracks perpendicular to interfaces of materials with dissimilar yield stresses

The J-integral is applied to a Dugdale crack perpendicular to an interface of materials with equal elastic properties but different yield stresses. It is shown that the integral is path independend with certain limitations to the integration path. Three essentially different paths can be distinguished. The first integration path is totally within the first material, it provides the local crack driving force. Performing the integral around the plastic zone in both materials gives the global crack driving force. An interface force can be defined by evaluating the integral along both sides of the plastically deformed region of the interface. A comparison of these three integrals reveals that the global crack driving force is equal to the sum of the local crack driving force and of the interface force. The derived expression for the J-integral are compared with the crack tip opening displacement published recently. This reveals that the local J describes the plastic deformation at the crack tip. Therefore it represents the crack driving force in bimaterials as it does the conventional J-integral in case of homogeneous materials. The analyses are also extended to cyclic plasticity, where an out-of-phase effect is observed. Finally it is discussed how these results can be used to explain fatigue tests at bimaterial specimens.     

Electrical resistance change and crack behavior in carbon nanotube/polymer composites under tensile loading

This paper studies the electrical and mechanical responses of cracked carbon nanotube (CNT)-based polymer composites. Tensile tests were performed on single-edge cracked plate specimens of the nanocomposites at room temperature and liquid nitrogen temperature (77 K), and the electrical resistance change of the specimens was monitored. An analytical model based on the electrical conduction mechanism of CNT-based composites was also developed to predict the resistance change resulted from crack propagation. The crack induced resistance change was calculated, and a comparison of the analytical predictions against the experimental data was made to validate the applicability of the model. In addition, the fracture properties of the nanocomposites were assessed in terms of the J-integrals using an elastic-plastic finite element analysis.     

J-INTEGRAL APPROACH TO MODE III FATIGUE CRACK PROPAGATION IN STEEL UNDER TORSIONAL LOADING

Mode III fatigue crack propagation tests were conducted on circumferentially cracked bars of a medium carbon steel under a constant value of the J-integral range. The ΔJ value was evaluated from the loading part of the hysteresis loop of the applied torque and the angle of twist. The fracture surface was macroscopically flat for all cases examined in the present study. The crack propagation rate decreased with crack extension, because of the shear contact of the crack faces. The crack propagation rate, without contact shielding, obtained by extrapolating the relation between the crack propagation rate and the crack length to the pre-crack length, was a power function of ΔJ irrespective of the initial notch depth.     

Fracture behaviour of cracked carbon nanotube‐based polymer composites: Experiments and finite element simulations

This paper studies the fracture behaviour of cracked carbon nanotube (CNT)‐based polymer composites by a combined numerical–experimental approach. Tensile tests were conducted on single‐edge cracked plate specimens of CNT/polycarbonate composites at room temperature and liquid nitrogen temperature (77 K), and the critical loads for fracture instabilities were determined. Elastic–plastic finite element simulations of the tests were then performed to evaluate the J‐integrals corresponding to the experimentally determined critical loads. Scanning electron microscopy examinations were also made on the specimen fracture surfaces, and the fracture mechanisms of the CNT‐based composites were discussed.     

J-integral analysis of the interaction between an interface crack and parallel subinterface cracks in dissimilar anisotropic materials

The J-integral analysis is presented for the interaction problem between a macro-interface crack and subinterface microcracks parallel to the former in the near-tip process zone in dissimilar anisotropic composite materials. Elementary solutions respectively considering an interface crack and a subinterface crack subjected to different loads are given from which the interaction problem is deduced to a system of integral equations with the aid of superimposing technique (i.e., the so called `Pseudo-Traction Method' abbreviated as PTM). After the integral equations are solved numerically, a consistent relation among three kinds of the J-integral values is obtained. They are induced from the macro-interface crack tip, the microcracks, and the remote field, respectively. This consistent relation of the J-integral can be used to confirm the numerical results derived by using whatever kind of technique. With the aid of J-integral analysis, the interaction behaviors between an interface crack and parallel subinterface cracks are investigated in detail, and some special physical phenomena are obtained.     

An approximation for the cyclic state of stress ahead of cracks and its implications under fatigue crack growth

Numerical methods are mostly used in the field of fatigue to derive the stress intensity factor (SIF) or J-integral solutions to be employed in damage tolerance analysis of cracked components. In this frame, simple assumptions about material properties are taken into account.More refined approaches try to describe the plasticity-induced crack closure in order to account for retardation effects under variable amplitude loading. In these approaches, the cyclic plasticity is used and cyclic finite element analyses are carried out.In the present work, a novel strategy is presented for the calculation of the relevant parameters to the fatigue crack growth, based on the evaluation of local field parameters (J-integral, T-stress) and cyclic material properties. It is demonstrated that, in case of mild steels and under the assumption of a stress ratio R = −1, the global constraint factor α_g widely employed in fatigue crack growth algorithms such as the strip-yield model, can be calculated in a closed-form on the basis of the expression of the crack-tip fields. Moreover, α_g provides a reasonable explanation of the fatigue crack growth behaviour of the A1N steel for different geometrical and loading configurations. Further investigations carried out on different medium and high strength steel grades show that the plastic radius ahead of small and long cracks at their fatigue limits can be considered as a constant for the material.     

Fatigue crack growth law of API X80 pipeline steel under various stress ratios based on J‐integral

Load‐controlled three‐point bending fatigue tests were conducted on API X80 pipeline steel to investigate the effects of stress ratio and specimen orientation on the fatigue crack growth behaviour. Because of the high strength and toughness of X80 steel, crack growth rate was measured and plotted versus ΔJ with stress ratio. The fatigue crack length is longer in the transverse direction, whereas the fatigue crack growth rates are nearly the same in different orientations. Finally, a new fatigue crack growth model was proposed. The effective J‐integral range was modified by ΔJ_p in order to correlate crack closure effect due to large‐scale yield of crack tip. The model was proved to fit well for fatigue crack growth rate of API X80 at various stress ratios of R > 0.     

A review of the J and I integrals and their implications for crack growth resistance and toughness in ductile fracture

The application of the J and the I-integrals to ductile fracture are discussed. It is shown that, because of the finite size of the fracture process zone (FPZ), the initiation value of the J-integral is specimen dependent even if the plastic constraint conditions are constant. The paradox that the I-integral for steady state elasto-plastic crack growth is apparently zero is examined. It is shown that, if the FPZ at the crack tip is modelled, the I-integral is equal to the work performed in its fracture. Thus it is essential to model the fracture process zone in ductile fracture. The I-integral is then used to demonstrate that the breakdown in applicability of the J-integral to crack growth in ductile fracture is as much due to the inclusion in the J-integral of progressively more work performed in the plastic zone as it is to non-proportional deformation during unloading behind the crack tip. Thus J _R -curves combine the essential work of fracture performed in the FPZ with the plastic work performed outside of the FPZ. These two work terms scale differently and produce size and geometry dependence. It is suggested that the future direction of modelling in ductile fracture should be to include the FPZ. Strides have already been made in this direction.     

J-integral determination in riveted beams of a structural old steel by estimation methods*

This work deals with the application of the J-integral estimation method to cracked riveted beams of old puddle iron. The ductility of some of these materials makes it necessary to use elasto-plastic fracture criteria to assess damage tolerance. This requires a high computational effort because it involves the determination of the J-integral in beams with plates and angles that interact by means of redundant forces dependent on crack size. The J-integral estimation method proposed by the Electric Power Research Institute could reduce this effort provided it were shown to be valid for this type of beam. This work contributes to this end by comparing the J-integral values resultant from the estimation method and a complete finite element modelling of a riveted beam consisting of two angles and a cracked plate made of actual puddle iron from a road bridge more than a century old but still in service. A number of samples removed from the bridge showed that this material failed in a ductile manner when it was fracture tested with fatigue precracked compact specimens, even at temperatures as low as −20 °C. The two types of J-integral values found are in good agreement over the ranges of load and crack size explored.     

FRACTURE MECHANICS ANALYSIS OF FATIGUE RESISTANCE OF SPOT WELDED COACH-PEEL JOINTS

Resistance spot welding is the most widely used joining method in automobile manufacture. The number, location, and quality of welds are some of the factors that influence the performance of welded subassemblies, and body panel structures. Therefore, design optimization requires knowledge of not only sheet metal behavior, but also weld behavior under service loadings. A linear elastic fracture mechanics approach was employed in this study to estimate the fatigue lives of spot welds subjected to tearing loads in a coach-peel specimen. Using a finite element method (FEM), the initial J-integral values for five coach-peel joints, each with different geometries, were calculated. Fatigue tests conducted on the same weld geometries provided life data. The experimental data were used to derive a relationship between the initial elastic J-integral values (ΔJ_e) and the fatigue life. It was found that the total fatigue life (N_f) of a weld at one applied stress range is related to its range of J-integral value such that a ΔJ_e vs N_f log-log plot gives a straight line relationship. This relationship can be used to evaluate the effects of geometrical variables on the fatigue life of coach-peel joints. The results show that, within the dimension range studied here, the effects of geometrical variables on the fatigue resistance can be ranked in the following decreasing order: weld eccentricity, sheet thickness and weld nugget diameter.     

Finite element modelling of crack propagation in elastic-plastic media

Materials which are cyclically stressed by sliding indenters often undergo fatigue wear, as surface breaking vertical cracks and subsurface horizontal cracks propagate causing eventual loss of material. In this study, the authors model crack propagation in an elastic-plastic material using finite element techniques, and consider the influence of friction, elasticity, plasticity and degree of penetration on the J-integral at the tip of a vertical crack. Crack propagation directions are estimated using J-integral maxima as the determining variable. It is found that the J-integral values, as a measure of strain energy release rate, can be used to estimate the crack propagation angle. Its main advantage lies in the fact that it considers both modes (I, II) of crack propagation. Using the J-integral values, one finds that, in the absence of friction between the indenter and the material, the vertical crack is equally prone to propagation at both 45 and 135° angles. However, one notices that the vertical crack favours the direction opposite to the direction of rolling for non-zero values of friction, i.e. 135°. The effects of both the crack depth and the crack tip plasticity are also investigated. It is found that any experimental findings suggestive of crack orientations closer to the horizontal in the direction opposite to the sliding direction are probably a result of shallow vertical asperities or higher crack tip plasticity.     

Continuum Shape Sensitivity analysis of a mode-I fracture in functionally graded materials

This paper presents a new method for conducting a continuum shape sensitivity analysis of a crack in an isotropic, linear-elastic, functionally graded material. This method involves the material derivative concept from continuum mechanics, domain integral representation of the J-integral and direct differentiation. Unlike virtual crack extension techniques, no mesh perturbation is needed to calculate the sensitivity of stress-intensity factors. Since the governing variational equation is differentiated prior to the process of discretization, the resulting sensitivity equations are independent of approximate numerical techniques, such as the meshless method, finite element method, boundary element method, or others. In addition, since the J-integral is represented by domain integration, only the first-order sensitivity of the displacement field is needed. Several numerical examples are presented to calculate the first-order derivative of the J-integral, using the proposed method. Numerical results obtained using the proposed method are compared with the reference solutions obtained from finite-difference methods for the structural and crack geometries considered in this study.     

A crack propagation criterion based on ΔCTOD measured with 2D‐digital image correlation technique

The fatigue cracks growth rate of a forged HSLA steel (AISI 4130) was investigated using thin single edge notch tensile specimen to simulate the crack development on a diesel train crankshafts. The effect of load ratio, R, was investigated at room temperature. Fatigue fracture surfaces were examined by scanning electron microscopy. An approach based on the crack tip opening displacement range (ΔCTOD) was proposed as fatigue crack propagation criterion. ΔCTOD measurements were carried out using 2D‐digital image correlation techniques. J‐integral values were estimated using ΔCTOD. Under test conditions investigated, it was found that the use of ΔCTOD as a fatigue crack growth driving force parameter is relevant and could describe the crack propagation behaviour, under different load ratio R.     

Calculation of J-integrals using experimental and numerical data: Influences of ratio (a/W) and the 3D structure

Contrary to J-integral values calculated from the 2D numerical model, calculated J-integrals [1] from 3D specimen in the numerical and experimental cases are not very close with J-integral used in the literature and two distinct points are present. The first one is according to (a/W) and can be reduced, when this ratio is inferior to 0.2. The second is a structure problem and can be explain by local three-dimensional effects surrounding the crack tip. Two applications using polymer materials for large and minor deformations are experimented. A grid method is used to experimentally determine the in-plane displacement fields around a crack tip in a Single-Edge-Notch (SEN) tensile polyurethane and PMMA specimens. This indirect method composed of experimental in-plane displacement fields and of two theoretical formulations, allows the experimental J-integral to be determined and the results obtained by the numerical simulations to be confirmed.     

Fracture of aluminium alloy 2024 under biaxial and triaxial loading

Previous studies on multi-axial fracture of metals have shown that the critical J-integral at fracture may be less than the fracture toughness measured in a standard test. This gives rise to the question: what is the minimum critical J-integral and how can it be obtained? To answer this question a series of uniaxial, biaxial and triaxial tests were carried out. Conducting biaxial and triaxial tests allows the effects of stress state in the fracture of metallic materials to be investigated, particularly when the plasticity is highly constrained. The primary purpose of this paper is to report the experimental findings of the tests performed on specimens fabricated from aluminium alloy 2024. Results of finite element analyses are then used to study further the detailed stress state near the crack tip and to evaluate the intensity of the plastic deformation and relate it to the critical J-integral variation. It was found that indeed high triaxial loading, corresponding to limited plastic deformation prior to the fracture, decreases the critical J-integral even below the values obtained from the biaxial tests, which are already less than the standard uniaxial value.     

THE EFFECTS OF CRACK DEPTH ON THE J-INTEGRAL AND CTOD FRACTURE TOUGHNESS FOR WELDED BEND SPECIMENS

This work deals with the influence of crack depth on the fracture toughness at initiation of crack growth and the constraint factor in relationship between the J-integral and the crack tip opening displacement (CTOD). A series of tests were performed on high strength low alloyed HT80 steel welds, and the critical J-integral and CTOD were determined using the load versus load point displacement record from three-point bend specimens with 0.05 < a/W < 0.5. It was found that the fracture toughness for shallow cracks at the onset of crack growth was larger than that for deep cracks for the steel welds tested, but it is felt that there is no fixed relationship between these values in the welds tested. The constraint factor is also a function of crack depth, and values of the factor increase from 0.5 to 1.5 when a/W increases from about 0.05 to 0.5. The factors are not very sensitive to the crack tip materials (HAZ or weld metal) in the welds tested.