Failure assessment of notched polycrystalline graphite under tensile-shear loading

The fracture load and the fracture initiation angle were experimentally measured for a V-notched specimen made of polycrystalline graphite under combined tensile-shear loading. The experimental results were obtained for several specimens with different notch angles and various notch tip radii. The experimental observations showed that for a constant notch tip radius, the fracture load in pure tensile loading conditions decreases as the notch angle increases. Moreover, for a constant notch angle, as the notch tip radius increases the fracture load in graphite specimens enhances in the entire domain between pure tensile and pure shear loading conditions. A recently developed failure criterion was then used to estimate the experimental values of the notch fracture resistance and the fracture initiation angle for the tested graphite specimens. The experimental results could be estimated very well by using the results of the proposed criterion.     

Failure initiation at a blunt V-notch tip under mixed mode loading

A criterion to predict crack onset at a sharp V-notch tip in homogeneous brittle materials under a mixed-mode loading was presented and validated by experimental observations in a previous paper by the authors. This criterion slightly underestimates the experimental loads causing failure which is attributed to a small notch tip radius that blunts the sharp corner. This discrepancy is rigorously analyzed mathematically in this paper by means of matched asymptotics involving 2 small parameters: a micro-crack increment length and the notch tip radius. A correction is brought to the initial prediction and a better agreement is obtained with experiments on PMMA notched specimens.     

Short fatigue crack growth behavior under mixed-mode loading

Mixed-mode loading represents the true loading condition in many practical situations. In addition, most of the fatigue life of many components is often spent in the short crack growth stage. The study of short crack growth behavior under mixed-mode loading has, therefore, much practical significance. This work investigated short crack growth behavior under mixed-mode loading using a common medium carbon steel. The effects of load mixity, crack closure, and load ratio on short crack growth behavior were evaluated by conducting experiments using four-point bending specimens with several initial K _II /K _I mixed-mode ratios and two load ratios. Cracks were observed to grow along the paths with very small K _II /K _I ratios (i.e. mode I). The maximum tangential stress criterion was used to predict the crack growth paths and the predictions were found to be close to the experimental observations. Several parameters including equivalent stress intensity factor range and effective stress intensity factor range were used to correlate short crack growth rates under mixed-mode loading. Threshold values for short cracks were found to be lower than those for long cracks for all the mixed-mode loading conditions. Crack closure was observed for the entire crack length regime with all load mixity conditions at R ≈ 0.05 and for short crack regime under high load mixity condition at R = 0.5. Several models were used to describe mean stress effects and to correlate crack growth rate data.     

Applications of normal stress dominated cohesive zone models for mixed-mode crack simulation based on extended finite element methods

In conventional cohesive zone models the traction-separation law starts from zero load, so that the model cannot be applied to predict mixed-mode cracking. In the present work the cohesive zone model with a threshold is introduced and applied for simulating different mixed-mode cracks in combining with the extended finite element method. Computational results of cracked specimens show that the crack initiation and propagation under mixed-mode loading conditions can be characterized by the cohesive zone model for normal stress failure. The contribution of the shear stress is negligible. The maximum principal stress predicts crack direction accurately. Computations based on XFEM agree with known experiments very well. The shear stress becomes, however, important for uncracked specimens to catch the correct crack initiation angle. To study mixed-mode cracks one has to introduce a threshold into the cohesive law and to implement the new cohesive zone based on the fracture criterion. In monotonic loading cases it can be easily realized in the extended finite element formulation. For cyclic loading cases convergence of the inelastic computations can be critical.     

The effect of tip plastic energy on mixed-mode crack initiation

An approach to the fracture initiation prediction of a ductile crack with mixed-mode loading (mode I and II) conditions is presented. The tip plastic energy around the crack tip is applied for evaluating the crack initiation load and the plastic zone shape. It is proposed that a mixed-mode crack will initiate as the tip plastic energy reaches a critical value. Numerical results for various loading conditions are illustrated. These results indicate that the predicted crack initiation loads correlate well with the experimental data available. This revised version was published online in August 2006 with corrections to the Cover Date.     

Mixed-mode crack propagation through reinforced concrete

This paper presents the results of a very recent experimental research program aimed at investigating mixed-mode fracture of reinforced concrete. The tests were designed so that only one single mixed-mode crack generates and propagates through the specimen, as opposed to the usual dense crack pattern found in most of the tests in scientific literature. The specimens were three-point-bend beams of three different sizes. They were notched asymmetrically and reinforced with various ratios of longitudinal and inclined reinforcement. These experiments may help to understand the mechanisms of crack initiation and propagation through reinforcing bars under mixed-mode load conditions.     

Modeling of delamination using a discretized cohesive zone and damage formulation

Delamination initiation and growth are analyzed by using a discrete cohesive crack model. The delamination is constrained to grow along a tied interface. The model is derived by postulating the existence of a maximum load surface which limits the adhesive forces in the process zone of the crack. The size of this maximum load surface is made dependent on the amount of dissipated crack opening work, such that the maximum load surface shrinks to zero as a predefined amount of work is consumed. A damage formulation is used to reduce the adhesive forces. Mode I, II and III loading or any combined loading is possible. An analytical solution is obtained for a single mode opening and the implications of this result on the governing equations is discussed. The delamination model is implemented in the finite element code LS-DYNA and simulation results are shown to be in agreement with experimental results.     

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

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

Adhesive power measurements of bonds between old and new concrete

A simple procedure for measuring the adhesive bond of cement-bonded materials is introduced and tested with an old-new concrete bond. Cubic or cylindrical specimens with a notch and the interface in their middle are split under stable crack growth conditions. The load is recorded as a function of the crack opening displacement. From this curve, the maximum load (notch tensile stress) and the fracture energy (G _F) can be determined. The course of the curve characterizes the mechanical behaviour of the material bond in the crack opening mode and is an important basis for a numerical treatment of interface problems. Different pre-treatments of the old concrete surface have an important influence on the adhesion of the material compound. Good adhesive properties have been measured after sand-blast treatment and poorer properties after a dispersion emulsion treatment.     

FATIGUE STRENGTH OF A ROTOR STEEL SUBJECTED TO TORSIONAL LOADING SIMULATING THAT OCCURRING DUE TO CIRCUIT BREAKER RECLOSING IN AN ELECTRIC POWER PLANT

Abstract— The fatigue strength of notched specimens of a rotor steel was examined under variable torsional loading which simulates turbine-generator oscillations resulting from the high speed reclosing of transmission-line circuit breakers. The local stress-strain response at a notch root was analysed using Neuber's rule and the resulting complex strain sequences applied to smooth specimens. Using the rain flow analysis and the linear summation rule, fatigue lives of the smooth specimens were successfully predicted from constant amplitude fatigue life data in association with the cyclic stress-strain curve obtained by the incremental step method. Experimental crack initiation lives for notched specimens subjected to variable torsional loading were in excellent agreement with the theoretical curves derived from results on smooth specimens. According to the view that fatigue damage is equated to crack length, the propagation life of a mode II crack along the notch root was predicted to be actually coincident with the life to crack initiation at the notch root denned in this study, i.e. the life at the stage of finding a continuous circumferential crack.     

A criterion for brittle fracture in U-notched components under mixed mode loading

A failure criterion is proposed for brittle fracture in U-notched components under mixed-mode static loading. The criterion, called UMTS, is developed based on the maximum tangential stress criterion and also a criterion proposed in the past for mode I failure of rounded V-shaped notches [Gomez FJ, Elices M. A fracture criterion for blunted V-notched samples. Int J Fracture 2004;127:239-64]. Using the UMTS criterion, a set of fracture curves are derived in terms of the notch stress intensity factors. These curves can be used to predict the mixed mode fracture toughness and the crack initiation angle at the notch tip. An expression is also obtained from this criterion for predicting fracture toughness of U-notched components in pure mode II loading. It is shown that there is a good agreement between the results of UMTS criterion and the experimental data obtained by other authors from three-point bend specimens.     

Mixed-mode fracture characterization of adhesive joints

A novel load jig is presented which allows mixed-mode fracture testing of adhesive joints and composite laminates over the entire range from mode I to mode II, by using a single equal adherend double-cantilever-beam specimen. Experiments performed with the load jig showed that G_IIC was approximately three times higher than G_IC for the tested adhesive system consisting of FPL-etched 7075-T6 aluminium adherends bonded with Cybond 4523GB (American Cyanamid) epoxy adhesive. Experimental data showed that G_C was independent of crack length and that there was no dependence of G_IC on adherend thickness. Comparison of G_IIC values obtained by using the load jig to test conventional end notch flexure (ENF) specimens indicated that there are relatively small friction effects between crack faces in mode II testing of ENF specimens. The experimental data were also used to evaluate three different analytical techniques for the mode partitioning of unequal adherend specimens.     

EARLY DEVELOPMENT OF FATIGUE CRACKING AT MANUAL FILLET WELDS

Abstract— An experimental study within the Canadian Offshore Corrosion Fatigue Research Programme was performed on the early development of fatigue cracking along the wavy toe of manual fillet welds between structural steel plates. Stress relieved and as-welded cruciform joints were tested under R = −1 and R = 0 loading at different stress amplitudes. The depth and the opening level of cracks as small as 10–20 μm were monitored using miniature strain gauges installed along the toe apex, in combination with beach marking. Most of the "initiation life" (25% to 50% of total life), conventionally defined by a crack depth of 0.5 mm, is consumed in short crack propagation. Three types of short crack development for different combinations of local mean stress and stress range are identified and analyzed. Growth rates in as-welded specimens are faster than in stress relieved specimens, which results in shorter "initiation lives". This is associated with a higher effective stress range, particularly under R = - 1 loading where cracks are open over nearly the full stress range. The V-notch stress intensity factor is a promising parameter to rationalize the crack "initiation life". It takes into account the thickness effect experimentally observed. Under R = - 1 loading of as-welded joints, using R = 0 data and taking the whole stress range gives a reasonably conservative approximation of the crack "initiation life".     

Mixed mode failure criteria for brittle elastic V-notched structures

Three mixed mode failure initiation criteria at reentrant corners in brittle elastic materials are examined. Prediction of failure load and crack initiation angle are compared to experimental observations carried out on PMMA (polymer) and MACOR (glass ceramic) V-notched specimens. Since the mode mixity ratio influences greatly both the failure load and crack initiation angle, a detailed experimental procedure has been followed, focusing on obtaining a wide range of mode mixity ratios. It is demonstrated that by assuming a sharp V-notch tip some failure criteria predict reasonably well both the crack initiation angle and failure load.     

SEMI-ELLIPTICAL FATIGUE CRACK GROWTH UNDER ROTATING OR REVERSED BENDING COMBINED WITH STEADY TORSION

Abstract— An analysis of the influence of steady torsion loading on fatigue crack growth rates under rotating or reversed bending is presented. Mixed-mode (I + III) tests were carried out on cylindrical specimens in DIN Ck45k steel and results are compared for two different testing machines: rotary bending and reversed bending obtained by cyclic Mode I (Δ K ₁) with or without superimposed static Mode III ( K _III) loading, simulating the real conditions on power rotor shafts where many failures occur. The growth and shape evolution of semi-elliptical surface cracks, starting from a chordal notch on the cylindrical specimen surface, was measured for several Mode III/ Mode I ratios. Results have shown that the steady Mode III loading superimposed on the cyclic mode I leads to a significant reduction in the crack growth rates. It is suggested that this retardation is related to an increase of plastic zone size near the cylindrical surface in association with the interlocking of rough fracture surfaces, friction and fretting debris, leading to a decrease of the ΔK effective at the crack tip profile due to the "crack closure effect". This work provides a contribution to a better understanding of crack growth rates under mixed-mode load conditions thereby allowing one to predict remaining lifetimes and to estimate the risks of pre-cracked rotor shafts.     

Effect of adhesive thickness on fatigue and fracture of toughened epoxy joints – Part II: Analysis and finite element modeling

The effect of bondline thickness on the fatigue and fracture of aluminum adhesive joints bonded using a rubber-toughened epoxy adhesive was studied using finite element analysis. The fatigue data of Part I examined the dependence of the fatigue threshold and cyclic crack growth rate on the adhesive thickness under both mode-I and mixed-mode loading. The fracture data of Part I illustrated the relation between the adhesive thickness and the quasi-static crack initiation and steady-state critical strain energy release rates. These experimental trends are explained in terms of the effects of the adhesive thickness and the applied strain energy release rate on the stress distribution in the bondline, the stress triaxiality at the crack tip, and the plastic zone size in the adhesive layer.     

Effect of geometry on the fracture behavior of lead-free solder joints

Copper bars were soldered along their length with a thin layer of lead-free Sn3.0Ag05.Cu alloy under standard surface mount processing conditions to prepare double cantilever beam (DCB) specimens. The geometry of the DCBs was varied by changing the thickness of the solder layer and the copper bars. These specimens were then fractured under mode-I and two mixed-mode loading conditions. The initiation strain energy release rate, G_ci, increased with the relative fraction of mode-II, but was unaffected by the changes in either the substrate stiffness or the solder layer thickness. However, the steady-state strain energy release rate, realized after several millimeters of crack growth, was found to increase with the solder layer thickness at the various mode ratios. The crack path was found to be influenced by mode ratio of loading and followed a path that maximizes the von Mises strain rather than maximum principal stress. Finally, some preliminary results indicated that the loading rate significantly affects the G_ci.     

Experimental studies on mixed‐mode dynamic fracture behaviour of aluminium alloy plates with narrow U‐notch

Mixed‐mode dynamic fracture behaviour of cast aluminium alloy ZL205A thin plates with narrow U‐notch was studied by split Hopkinson tensile bar apparatus. Specimens with different loading angles were designed to realize different fracture modes. The same loading condition was maintained during the tests. Recovery specimens show that crack propagates along the notch direction. Force–elongation relations show that with the loading angle increasing, the fracture force increases while the final elongation decreases. Deformation and fracture process was observed by a high‐speed camera. Displacement distribution around the crack was calculated through digital image correlation technique. Based on the photos and displacement results, initiation time of the crack was derived. Besides, two stress components (normal stress and shear stress) applied on the fracture surface were investigated. Results show that crack initiation stresses at different loading angles satisfy the ellipse equation. Pure mode I and II fracture stresses are 425.3 and 236.7 MPa, respectively. Furthermore, specific fracture energy of different specimens was calculated. The energy data vary with loading angle and located on an approximate upward parabolic curve. From the curve, the minimum specific fracture energy of the thin plate specimen is 42.0 kJ/m² under loading angle of 76.3°.     

Effect of an asymmetrical V-notch on the load carrying capacity of eccentrically loaded columns

In this paper theoretical and experimental investigations have been carried out to determine the effect of an asymmetrical V-shaped notch on the load carrying capacity of eccentrically loaded columns. The depth of the notch was kept constant whereas the notch angle, notch root radius; eccentricity of loading and length of the column was varied. It has been concluded that an asymmetrically placed V-notch decreases the load carrying capacity of the column. The load carrying capacity is not affected appreciably upto a notch angle of approx. 90°, but beyond 90° it increases. The load carrying capacity of the column also increases as the notch root radius increases but it decreases as the eccentricity of load and slenderness ratio increase.     

A hybrid method to assess interface debonding by finite fracture mechanics

Adhesive connections are potentially weak locations in many kinds of engineering structures. Since adhesive joints can be regarded locally as bimaterial notches, the assessment of the hazard of crack nucleation, initiation and propagation in the vicinity of bimaterial notches and the reliability of the junctions is an important problem. An essential requirement in this context is a sufficient criterion for crack nucleation. The present contribution proposes a modified approach based on Leguillon’s hypothesis in order to provide a feasible criterion. A crack at a notch is assumed to be initiated and to grow if and only if both the released energy and the local stresses exceed critical values. Thus, simulating virtual crack growth along an interface of two dissimilar bonded materials, the integrity of the bond is revisable. The approach enables the determination of characteristic lengths for freshly nucleated cracks forming the base for any further integrity assessment. As an example, the concept is applied to the analysis of an adhesive bond of metallic and ceramic materials under severe thermal loading conditions as they occur, among other examples, in high temperature fuel cell technology. It is shown that the failure hazard of the adhesive joint can be reduced significantly by an appropriate local design.