Size effect on fracture toughness of freestanding copper nano-films

We conducted fracture toughness experiments on freestanding copper films with thicknesses ranging from about 800 to 100 nm deposited by electron beam evaporation to elucidate the size effect on fracture toughness in the nano- or submicron-scale. It was found that initially, the crack propagated stably under loading, and then the crack propagation rate rapidly increased, resulting in unstable fracture. The fracture toughness K_C was estimated on the basis of the R-curve concept to be 7.81 ± 1.22 MPa m^1/2 for the 800-nm-thick film, 6.63 ± 1.05 MPa m^1/2 for the 500-nm-thick film and 2.34 ± 0.54 MPa m^1/2 for the 100-nm-thick film. Thus, a clear size effect was observed. The fracture surface suggested that the crack underwent large plastic deformation in the thicker 800-nm and 500-nm films, whereas it propagated with highly localized plastic deformation in the thinner 100-nm film. This size effect in fracture toughness might be related to a transition in deformation and fracture morphology near the crack tip.     

Pre-cracking technique for fracture mechanics experiments along interface between thin film and substrate

Utilizing the difference in interface strength due to fabrication process, a technique for producing a sharp pre-crack between a thin film and a substrate is proposed. A cracked specimen for examining fracture toughness of interface between a sputtered copper (Cu) thin film and silicon (Si) is made by the method. A vacuum-evaporated Cu thin film, which has poor adhesion to Si, is inserted between the sputtered Cu thin film and the Si substrate as a release layer. The release layer debonds from the Si substrate at very low load, and the sharp pre-crack is successfully introduced along the interface. Using the pre-cracked specimen, the interface fracture toughness test is conducted and the critical J-integral, J_C, is evaluated as about 1 J/m² for the sputtered Cu/Si interface.     

Effect of laser shock processing on fatigue crack growth of duplex stainless steel

Duplex stainless steels have wide application in different fields like the ship, petrochemical and chemical industries that is due to their high strength and excellent toughness properties as well as their high corrosion resistance. In this work an investigation is performed to evaluate the effect of laser shock processing on some mechanical properties of 2205 duplex stainless steel. Laser shock processing (LSP) or laser shock peening is a new technique for strengthening metals. This process induces a compressive residual stress field which increases fatigue crack initiation life and reduces fatigue crack growth rate. A convergent lens is used to deliver 2.5 J, 8 ns laser pulses by a Q-switched Nd:YAG laser, operating at 10 Hz with infrared (1064 nm) radiation. The pulses are focused to a diameter of 1.5 mm. Effect of pulse density in the residual stress field is evaluated. Residual stress distribution as a function of depth is determined by the contour method. It is observed that the higher the pulse density the greater the compressive residual stress. Pulse densities of 900, 1600 and 2500 pul/cm² are used. Pre-cracked compact tension specimens were subjected to LSP process and then tested under cyclic loading with R = 0.1. Fatigue crack growth rate is determined and the effect of LSP process parameters is evaluated. In addition fracture toughness is determined in specimens with and without LSP treatment. It is observed that LSP reduces fatigue crack growth and increases fracture toughness if this steel.     

A critical investigation of the use of a mandrel peel method for the determination of adhesive fracture toughness of metal-polymer laminates

The application of peel tests for the measurement of adhesive fracture toughness of metal-polymer laminates is reviewed and the merits of a mandrel peel method are highlighted. The mandrel method enables a direct experimental determination of both adhesive fracture toughness (G_A) and the plastic bending energy (G_P) during peel, whilst other approaches require a complex calculation for G_P. In this method, the peel arm is bent around a circular roller in order to develop a peel crack and an alignment load attempts to ensure that the peel arm conforms to the roller.The conditions for peel arm conformance are thoroughly investigated and the theoretical basis for conformation are established. Experimental investigations involve the study of the roller size (radii in the range 5-20 mm are used), the peel arm thickness (varied from 0.635 to 2.0 mm) and the magnitude of the alignment load. In addition, the plane of fracture is studied since fractures can vary from cohesive to interfacial and this has a profound influence on the value of G_A and on interpretation of results.A test protocol for conducting mandrel peel is developed such that the roller size for peel arm conformance can be established from preliminary fixed arm peel tests.The work is conducted on two epoxy/aluminium alloy laminates suitable for aerospace applications. Comparative results of adhesive fracture toughness from mandrel peel and multi-angle fixed arm peel are made with cohesive fracture toughness from a tapered double cantilever beam test.     

Inclusion-controlled high cycle fatigue behavior of a high V alloyed powder metallurgy cold-working tool steel

Axial loading fatigue tests were carried out to study the influence of inclusion on high cycle fatigue behavior of a high V alloyed powder metallurgy cold-working tool steel (AISI 11). The fatigue strength of 1538 MPa with endurance life of 10⁷ cycles were obtained by stair-case method. The fatigue specimens were also subjected to a constant maximum stress of 1650 MPa to investigate the relationship among inclusion origin size (10-30 μm), fish-eye size (70-130 μm) and fatigue life (10⁵-10⁷ cycles). The fatigue life was found to be dependent on the inclusion size and the crack propagating length. A compressive residual stress of 300-450 MPa turned out to be present at the specimen surface, and finally induced the interior failure mode. Further investigation into the correlation between stress intensity factors of inclusion origin and corresponding stages of fatigue crack growth and fatigue life revealed that the high cycle fatigue behavior was controlled by crack propagation. According to the fractographic investigation, two distinct zones were observed in fish-eye, representing Paris-Law and fast fatigue crack growth stage, respectively. Threshold stress intensity for crack propagation of 3.9 MPa√m was obtained from the well correlated line on the ΔK_I-log N_? graph. The fracture toughness can also be estimated by the mean value of stress intensity factor ranges for fish-eye.     

A non-contact, thermally-driven buckling delamination test to measure interfacial fracture toughness of thin film systems

Interfacial fracture toughness measurements of thin film-substrate systems are of importance in many applications. In the microelectronics industry, the interfacial adhesion between the dielectric-barrier-metal layers on a semiconductor chip is critical for chip reliability. In this paper, we propose a thermally-driven patterned buckling delamination test that does not use a pre-existing weak interface. The test relies on causing a patterned film to debond from its substrate by inducing a compressive stress due to heating of the film on a thick silicon substrate. The compressive stress causes the film to buckle and debond from the substrate. A model for the propagation of the buckling-induced debond is then developed to estimate interfacial fracture toughness. The efficacy of the thermally-driven buckling test is demonstrated on a model Al/SU8/Si film-substrate system wherein the Al film debonds along its interface to SU8. The interfacial toughness of the Al/SU8 interface is estimated using the proposed test and is compared to the toughness for the same system obtained using an alternative test with a weakened interface to validate the developed elastic-plastic model for buckling-induced debond propagation.     

Eine neue Methode zur Festigkeits- und Zähigkeitsbestimmung von dünnen Schichten

A New Method of Determining Strength and Fracture Toughness of Thin Films A method is presented for measuring strength and fracture toughness of thin films. The basic idea of this method is to use a compact steel specimen as a substrate, which is deeply precracked by means of fatigue loading prior to the coating process. Under bend loading of this composite crack opening occurs accompanied by straining the free-standing thin film which bridges the crack. Film rupture firstly occurs at the front face of the specimen followed by crack growth on both sides. The film properties can be derived by eliminating the substrate effect through determining the difference between the two load-displacement curves corresponding to the intact and the damaged film, respectively. The strength of the film can be calculated from the load difference at film rupture at the front face of the composite. The fracture toughness is evaluated from load and compliance change during successive crack growth on both sides of the specimen. First results on PACVD TiN-films are presented and compared with available bulk data, thus demonstrating the applicability of the proposed method.     

Crack arrest testing of high strength structural steels for naval applications

The crack arrest fracture toughness of two high strength steel alloys used in naval construction, HSLA-100, Composition 3 and HY-100, was characterized in this investigation. A greatly scaled-down version of the wide-plate crack arrest test was developed to characterize the crack arrest performance of these tough steel alloys in the upper region of the ductile-brittle transition. The specimen is a single edge-notched, 152 mm wide by 19 mm thick by 910 mm long plate subjected to a strong thermal gradient and a tensile loading. The thermal gradient is required to arrest the crack at temperatures high in the transition region, close to the expected service temperature for crack arrest applications in surface ships. Strain gages were placed along the crack path to obtain crack position and crack velocity data, and this data, along with the applied loading is combined in a “generation mode” analysis using finite element analysis to obtain a dynamic analysis of the crack arrest event. Detailed finite element analyses were conducted to understand the effect of various modeling assumptions on the results and to validate the methodology compared with more conventional crack arrest tests.Brittle cracks initiation, significant cleavage crack propagation and subsequent crack arrest was achieved in all 15 of the tests conducted in this investigation. A crack arrest master curve approach was used to characterize and compare the crack arrest fracture toughness. The HSLA-100, Comp. 3 steel alloy had superior performance to the HY-100 steel alloy. The crack arrest reference temperature was T_KIA = −136 °C for the HSLA-100 plate and T_KIA = −64 °C for the HY-100 plate.     

Influence of the matrix constituent on mode I and mode II delamination toughness in fiber-reinforced polymer composites under cyclic fatigue

Mode I and mode II fracture behaviour under static and dynamic loading was analyzed in two composites made up of the same reinforcement though embedded in two different matrices. Specifically, the delamination energy under static and dynamic loading was obtained for both materials and both fracture modes, i.e. the number of cycles necessary for the onset of fatigue delamination. Subsequently, the crack growth rate (delamination rate) was obtained for different percentages of the critical energy rate. The main goal of the study was to ascertain the influence of the matrix on the behaviour of the laminate under fatigue loading.From the experimental results for the onset of delamination, similar fatigue behaviour was observed at a low number of cycles for both matrices and both fracture modes, while in fatigue at a high number of cycles, a higher fatigue limit was obtained in the composite with the modified resin (higher toughness) for both fracture modes. From the point of view of crack growth rate, both materials behaved similarly for different levels of stress under fatigue and the two fracture modes for small crack lengths (initial growth zone < 5 mm), although the growth rate increased for large crack lengths. This behaviour was the same in both loading modes.     

Hybrid spectral/finite element analysis of dynamic delamination of patterned thin films

A combined spectral and finite element analysis is performed to investigate the dynamic edge delamination of patterned thin films from a substrate. The analysis is motivated by an emerging experimental technique in which high-amplitude laser-induced stress waves initiate progressive interfacial debonding of thin film interfaces. The numerical method relies on the spectral representation of the elastodynamic solutions for the substrate and the finite element model for the thin film. A cohesive model is introduced along the interface of the bimaterial system to capture the decohesion process. The important role of the film inertia on the crack extension and the appearance of the mixed-mode failure are demonstrated by observing the traction stress evolution at various points along the bond line. Parametric studies on the effect of film thickness, interface fracture toughness, loading pulse shape and amplitude on the debonding process are performed. A semi-analytical investigation on the inertial effect is carried out to predict the final crack length as a function of the film thickness and pulse amplitude.     

The effect of initial notch shape of compact specimen on fatigue pre-cracking and fracture toughness testing

The circular notched compact specimens, along with standard specimens having straight or chevron notch are provided for fatigue and fracture toughness testings in order to study the crack observation capability during fatigue pre-cracking, skewness of the crack front, and the resulting fracture toughness K_Q. The test results indicated that circular notched specimens significantly facilitate the crack observation during fatigue testing as the cracks initiate on both surfaces of the specimen. No remarkable differences were observed on geometries of the fatigue crack front obtained and the resulting fracture toughness among these three types of specimen. The macroscopic observation of beach marks on the fracture surfaces revealed that, in the present material Ti-6Al-4V (ELI), the advance of only 1.3% of the whole crack length corresponded to the load level at which fracture toughness K_Q was evaluated.     

Statistical analysis of fatigue crack growth behavior for grade B cast steel

Tests for fatigue crack growth rate (FCGR) and crack-tip opening displacement (CTOD) were performed to clarify the fatigue crack growth behavior of a railway grade B cast steel. The threshold values of this steel with specific survival probabilities are evaluated, in which the mean value is 8.3516 MPa m^1/2, very similar to the experimental value, about 8.7279 MPa m^1/2. Under the conditions of plane strain and small-scale yielding, the values of fracture toughness for this steel with specific survival probabilities are converted from the corresponding critical CTOD values, in which the mean value is about 138.4256 MPa m^1/2. In consideration of the inherent variability of crack growth rates, six statistical models are proposed to represent the probabilistic FCGR curves of this steel in entire crack propagation region from the viewpoints of statistical evaluation on the number of cycles at a given crack size and the crack growth rate at a given stress intensity factor range, stochastic characteristic of crack growth as well as statistical analysis of coefficient and exponent in FCGR power law equation. Based on the model adequacy checking, result shows that all models are basically in good agreement with test data. Although the probabilistic damage-tolerant design based on some models may involve a certain amount of risk in stable crack propagation region, they just accord with the fact that the dispersion degree of test data in this region is relatively smaller.     

Fixtureless superlayer-driven delamination test for nanoscale thin-film interfaces

A fixtureless delamination test has been developed to measure the interfacial fracture toughness of patterned nanoscale thin films on a substrate. The driving energy for delamination propagation is supplied by a highly stressed superlayer deposited on top of the nanoscale thin film. The amount of energy available for delamination propagation is changed by depositing an etchable thin release layer with varying width between the nanoscale thin-film strip and the substrate. By designing a decreasing area of the release layer, it is possible to arrest the delamination at a given location, and the interfacial fracture toughness or critical energy release rate can be found at the location where the delamination ceases to propagate. For titanium film with a thickness of 90 nm, the results show that the interfacial fracture toughness of titanium/silicon ranges from 3.45 J/m² to 5.70 J/m² when the mode mixity increases from 6.8° to 38.4°. The methodology presented in this paper is generic in nature, and can be used to measure the process-dependent interfacial fracture toughness of various micro and nanoscale thin films on a substrate.     

Toughening boron/epoxy bonded joints using the resin film infusion technique

Bonded boron/epoxy repairs to aircraft can be susceptible to fatigue damage and crack propagation at high levels of in-service loading. In an effort to improve the fatigue tolerance of these repairs, an attempt has been made to improve the mode I fracture toughness. Two techniques for toughening boron/epoxy plies for use in bonded composite repairs were investigated. Firstly, the resin film infusion technique was used with dry boron fibres and the rubber-toughened film adhesive FM73 to produce a toughened boron/epoxy ply. The second technique involved co-curing a boron/epoxy laminate with FM73 adhesive. Bonded joints, comprising various toughened and un-toughened boron/epoxy adherends and FM73 adhesive, were made into fracture toughness specimens and tested. The fracture toughness for crack initiation increased from 328 J/m² for the un-toughened specimens to 1600 and 3100 J/m², respectively, for the two toughened specimens. The second technique, however, produced unstable fractures. Fractography revealed that the boron fibre-to-resin interface was the preferred failure path in all cases.     

Influence of interfacial delamination on channel cracking of elastic thin films

Channeling cracks in brittle thin films have been observed to be a key reliability issue for advanced interconnects and other integrated structures. Most theoretical studies to date have assumed no delamination at the interface, while experiments have observed channel cracks both with and without interfacial delamination. This paper analyzes the effect of interfacial delamination on the fracture condition of brittle thin films on elastic substrates. It is found that, depending on the elastic mismatch and interface toughness, a channel crack may grow with no delamination, with a stable delamination, or with unstable delamination. For a film on a relatively compliant substrate, a critical interface toughness is predicted, which separates stable and unstable delamination. For a film on a relatively stiff substrate, however, a channel crack grows with no delamination when the interface toughness is greater than a critical value, while stable delamination along with the channel crack is possible only in a small range of interface toughness for a specific elastic mismatch. An effective energy release rate for the steady-state growth of a channel crack is defined to account for the influence of interfacial delamination on both the fracture driving force and the resistance, which can be significantly higher than the energy release rate assuming no delamination.     

Effect of loading type on fatigue properties of high strength bearing steel in very high cycle regime

Very high cycle fatigue tests under axial loading at frequencies of 95 Hz and 20 kHz were performed to clarify the effect of loading type on fatigue properties of a high strength bearing steel in combination with experimental result of this steel under rotating bending. As a result, this steel represents the single P-S-N (probabilistic-stress-life) curve characteristics for surface-induced fracture and interior inclusion-induced fracture, just like that under rotating bending. However, fatigue strength is lower, where the run-out stress at 10⁹ cycles is evaluated to be 588 MPa, less than that under rotating bending with about 858 MPa. Occurrence probability of larger and deeper inclusion-induced fracture is much higher than that under rotating bending. Furthermore, the formation process of fine granular area (FGA) is independent of the type and frequency of loading, which is very slow and is explained as the crack nucleation process under the special dislocation mechanism. The stress intensity factor range at the front of FGA, ΔK_FGA, is approximately regarded as the threshold value controlling the stable propagation of interior crack. For the control volume of specimen under axial loading, the estimated value of fatigue limit by FGA is similar to experimental run-out stress value at 10⁹ cycles, but that by inclusion is larger. However, the corresponding estimated results under rotating bending are all conservative.     

Failure criteria for mixed mode delamination in glass fibre epoxy composites

Critical strain energy release rate of glass/epoxy laminates using the virtual crack closure technique for mode I, mode II, mixed-mode I + II and mode III were determined. Mode I, mode II, mode III and mixed-mode I + II fracture toughness were obtained using the double cantilever beam test, the end notch flexure test, the edge crack torsion test and the mixed-mode bending test respectively. Results were analysed through the most widely used criteria to predict delamination propagation under mixed-mode loading: the Power Law and the Benzeggagh and Kenane criteria. Mixed-mode fracture toughness results seem to represent the data with reasonable accuracy.     

Investigation of sub-critical fatigue crack growth in FRP/concrete cohesive interface using digital image analysis

The cohesive stress transfer during the sub-critical crack growth associated with the debonding of FRP from concrete under fatigue loading is experimentally investigated using the direct shear test set-up. The study focused on high-amplitude/low-cycle fatigue. The fatigue sub-critical crack growth occurs at a load that is smaller than the static bond capacity of the interface, obtained from monotonic quasi-static loading, and is also associated with a smaller value of the interfacial fracture energy. The strain distribution during debonding is obtained using digital image correlation. The results indicate that the strain distribution along the FRP during fatigue is similar to the strain distribution during debonding under monotonic quasi-static loading. The cohesive crack model and the shape of the strain distribution adopted for quasi-static monotonic loading is indirectly proven to be adequate to describe the stress transfer during fatigue loading. The length of the stress transfer zone during fatigue is observed to be smaller than the cohesive zone of the interfacial crack under quasi-static monotonic loading. The strain distribution across the width of the FRP sheet is not altered during and by fatigue loading. A new formulation to predict the debonding crack growth during fatigue is proposed.     

Grain boundary microstructure and fatigue crack growth in Allvac 718Plus superalloy

The correlation between grain boundary microstructure and fatigue crack growth with hold-times was investigated for two conditions of the superalloy Allvac 718Plus; a Standard condition with the recommended distribution of grain boundary phases and a Clean condition with virtually no grain boundary phases. Fatigue testing was performed at 704 °C using 10 Hz cyclic load with intermittent hold-times of 100 s at maximum tensile load. Microstructural characterization and fractography were conducted using scanning- and transmission electron microscopy techniques. Auger electron- and X-ray photoelectron spectroscopy techniques were used for oxide analyses on fracture surfaces. It was found that in the Standard condition crack growth is mostly transgranular for 10 Hz loading and intergranular for hold-times, while for the Clean condition crack growth is intergranular in both load modes. The lower hold-time crack growth rates in the Standard condition are attributed to grain boundary δ-phase precipitates. No effect of δ-phase was observed for 10 Hz cyclic loading crack growth rates. Two different types of oxides and oxide colours were found on the fracture surfaces in the Standard condition and could be correlated to the different loading modes. For cyclic loading a bright thin Cr-enriched oxide was dominate and for hold-times a dark and slightly thicker Nb-enriched oxide was dominant These oxide types could be related to the oxidation of δ-phase and the matrix respectively. The influence of δ-phase precipitates on crack propagation is discussed.     

Probability of cleavage fracture for a crack propagating by fatigue

Standard fracture toughness tests use fatigue pre-cracked specimens loaded monotonically from zero to failure. Scatter in toughness (cleavage) occurs because steel is metallurgically inhomogeneous, and because each specimen has its crack tip in a different local microstructure. A probability of fracture toughness distribution can be obtained by conducting multiple repeat tests on the same steel. This is often used to make probabilistic structural fracture predictions for combinations of crack length and applied load. However, it is likely the true structural situation involves gradual extension of a fatigue crack under a cyclic load. The question then arises as to how often the probability of fracture for the structure needs to be re-calculated. It could be argued that each fatigue load cycle moves the crack tip to a new position and gives a different instantaneous probability of fracture. But if this were the case, the predicted cumulative probability of fracture would quickly tend to unity. This paper describes cold temperature, wide plate fatigue tests designed to investigate this apparent contradiction. The steel is 15 mm thick, grade A, ship plate and the tests involve propagation of a fatigue crack from 300 mm to 650 mm length under a constant amplitude fatigue cycle of 10-100 MPa at −50 °C. The cold temperature fatigue tests do not show an obviously increased probability of fracture compared with the standard monotonic load tests. Nevertheless, in view of uncertainties surrounding the issue, a cumulative probability of fracture determined at 5 mm intervals through the steel is recommended for safe structural predictions.