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.     

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.     

CYCLIC LOADING AND FRACTURE TOUGHNESS OF STEELS

Abstract— The paper considers the effect of cyclic loading and loading rate upon fracture toughness characteristics of steels at room and low temperatures. It is shown that fracture toughness of a low-alloy ferrite-pearlite steel with 0·1% C (steel 1) and for 15G2AFDps steel of the same class (steel 2) are 2 to 2·5 times lower under cyclic loading (50 and 0·5 Hz) and dynamic loading (= 1·5 × 10⁶MPa √m s⁻¹) than under static loading (= 0·6 to 9 MPa √m s⁻¹). For quenched and low-tempered 45 steel at 293 K and for armco-iron at 77 K fracture toughness characteristics do not depend on the loading condition. Macro- and micro-fractographic investigations revealed a correlation between the plastic zone size and the length of brittle fracture areas which are formed in steels 1 and 2, and in armco-iron during unstable propagation of the fatigue crack. Dependence of the decrease of the critical stress intensity factor under cyclic loading on the number of load cycles are obtained for repeating ( R = 0) and alternating bending ( R =−1) of specimens with a crack. A model for the transition from stable to unstable crack propagation is proposed involving crack velocity in the zone ahead of the crack tip damaged by cyclic plastic deformation. A new approach is suggested to the classification of materials on the basis of the sensitivity of fracture toughness characteristics to cyclic conditions of loading.     

Effect of loading rate on crack velocities in HSC

This paper presents the recent results of an experimental program aimed at disclosing the loading rate (loading-point-displacement rate) effect on the crack velocity in high-strength concrete (HSC). Eighteen three-point-bend tests were conducted using either a servo-hydraulic machine or a self-designed drop-weight impact device. Four strain gauges mounted along the ligament of the specimen were used to measure the crack velocity. Six different loading rates were applied, from 10⁻⁴ mm/s to 10³ mm/s (average strain rate from 10⁻⁶ to 10⁻¹ s⁻¹), i.e., a low loading-rate range (5.50 × 10⁻⁴ mm/s, 0.55 mm/s and 17.4 mm/s) and a high loading-rate range (8.81 × 10² mm/s, 1.76 × 10³ mm/s and 2.64 × 10³ mm/s). At low loading rates, the crack propagates with increasing velocity. Under high loading rates, the crack propagates with slightly decreasing velocity, though the maximum crack speed reached up to 20.6% of the Rayleigh wave speed of the tested HSC. In addition, the loading-rate effect on crack velocities is pronounced within the low loading-rate regime, whereas it is minor under the high loading-rate range.     

Dynamic delamination fracture toughness in unidirectional polymeric composites

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

An assessment of mechanical behavior and fractography study of glass/epoxy composites at different temperatures and loading speeds

Effect of loading rate on fracture and mechanical behavior of autoclave cured glass fiber/epoxy prepreg composite has been studied at various loading (striking) rates (0.01-10³ mm/min). The maximum load carrying capacity and strain at yield continuously increases with increasing loading speed. The interlaminar shear strength (ILSS) value is high at low loading speed and becomes low at high loading speed with the transition of loading rate at approximately 300 mm/min. The formation of steps, welt interfacial failure and cleavage formation on matrix resin i.e. localized plastic deformation processes were dominating mechanisms for specimens tested at low loading rates, while brittle fracture of fiber, fiber pull-out and impregnation were dominating mechanisms for specimens tested at loading rates of 800 mm/min or higher.     

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.     

Rate effects in mode-II fracture of plastically deforming,adhesively bonded structures

Results from a combined experimental and numerical investigation into the effects of rate on mode-II fracture of a plastically deforming, adhesively bonded joint are presented. It is shown that a cohesive-zone model has to be modified to include coupling between normal and shear modes of deformation when there is extensive shear deformation of the adhesive layer. A suitable cohesive-zone modeling strategy is described, and the mode-II cohesive parameters determined from the model are presented as a function of loading rate. Previous studies of the same system showed that the effects of rate in mode-I were limited to the probability that a crack growing in a toughened quasi-static mode would spontaneously make a transition to a brittle mode of fracture. No such transitions were found for mode-II fracture. Crack growth always occurred in a quasi-static fashion. While there was some evidence that rate might affect the mode-II fracture parameters, these effects were very limited even up to crack velocities of about 1,000 mm/s. Any possible effects was limited to a very minor increase in toughness and strength with increased loading rates. However, the magnitude of these possible increases were comparable to the magnitude of the uncertainties in the measured values.     

用圆孔内单边裂纹平台巴西圆盘和实验-数值-解析法确定砂岩的动态起裂和扩展韧度

在I型(张开型)动态断裂实验中,利用大直径(?100 mm)分离式霍普金森压杆径向冲击圆孔内单边裂纹平台巴西圆盘试样。考虑了材料惯性效应和裂纹扩展速度对动态应力强度因子的影响,用实验-数值-解析法确定了高加载率和高裂纹扩展速度情况下,砂岩的动态起裂韧度和动态扩展韧度。由动态实验获取试样的动荷载历程,采用裂纹扩展计(Crack Propagation Gauge,CPG)测定试样断裂时刻和裂纹扩展速度,获得裂纹扩展速度对应的普适函数值。然后将动荷载历程带入到有限元软件中进行动态数值模拟,求出静止裂纹的动态应力强度因子历程,再用普适函数值对其进行近似修正。最后根据试样的起裂时刻和穿过CPG中点的时刻,由相应的动态应力强度因子历程分别确定砂岩的动态起裂和动态扩展韧度,它们分别随动态加载率和裂纹扩展速度的提高而增加。     

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.     

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.     

Fracture toughness and fracture mechanisms of PBT/PC/IM blend

The static and impact fracture toughnesses of a polybutylene terephthalate/polycarbonate/impact modifier (PBT/PC/IM) blend were studied at different temperatures. The static fracture toughness of the blend was evaluated via the specific fracture work concept and the J-integral analysis. A comparison of these two analytical methods showed that the specific essential fracture work, W _e, was equivalent to the obtained by the ASTM E813-81 procedure, representing the crack initiation resistance of the material. The discrepancy between W _e and of ASTM E813-89 was caused by the extra energy component in consumed by a 0.2 mm crack growth. Impact fracture toughness was also analysed using the specific essential fracture work approach. When the fracture was elastic, W _e was equivalent to the critical potential energy release rate, G _IC, obtained via LEFM analysis. Temperature and strain-rate effects on the fracture toughness were also studied. The increase in impact toughness with temperature was attributed to two different toughening mechanisms, namely, the relaxation processes of the rubbery particles and the parent polymers in a relatively low-temperature range and thermal blunting of the crack tip at higher temperatures. The enhancement in static fracture toughness at temperatures below — 60 °C was thought to be caused by plastic crack-tip blunting, but the monotonic reduction in yield stress was largely responsible for the toughness decreasing with higher temperatures. The temperature-dependent fracture toughness data obtained in static tests could be horizontally shifted to match roughly the data for the impact tests, indicating the existence of a time-temperature equivalence relationship.     

Experimental Determination of Dynamic Crack Initiation and Propagation Fracture Toughness in Thin Aluminum Sheets

An experimental investigation was undertaken to characterize the dynamic fracture characteristics of 2024-T3 aluminum thin sheets ranging in thickness from 1.63–2.54 mm. Specifically, the critical dynamic stress intensity factor Kdc was determined over a wide range of loading rates ( expressed as the time rate of change of the stress intensity factor KdI ) using both a servo- hydraulic loading frame and a split Hopkinson bar in tension. In addition, the dynamic crack propagation toughness, KD, was measured as a function of crack tip speed using high sensitivity strain gages. A dramatic increase in both Kdc and KD was observed with increasing loading rate and crack tip speed, respectively. These relations were found to be independent of specimen thickness over the range of 1.5 to 2.5 mm.     

Effect of Strain Rate and Preloading on the Fracture Toughness of ZrO2-Based Ceramics

We study the variation of the fracture toughness K_Ic ofZrO₂ - Y₂ O₃ ceramics (density 98%) as a function of the testing machine crosshead speed (0.005–50 mm/min) and preloading at K_I < K_c. The fracture toughness is shown to be practically constant in the speed range from 0.05 to 5 mm/min. At a loading rate of 50 mm/min, the quantity K_Ic substantially decreases (by a factor of more than two), whereas at a rate of 0.005 mm/min it slightly increases. Preloading leads to a 1.5-fold increase in K_Ic. Variation of the fracture toughness is associated with structural transformations.     

Mechanical behaviour of poly(methyl methacrylate)

A series of tensile and three-point bending studies was conducted at various temperatures and loading rates using a commercial poly(methyl methacrylate) (PMMA). Tensile properties and fracture toughness data were obtained for the various conditions. In general, both tensile strength and fracture toughness increase with increasing loading rate and decreasing temperatur E. However, when the temperature reaches the glass transition region, the relationships between fracture toughness, loading rate, and temperature become very complex. This behaviour is due to the simultaneous interaction of viscoelasticity and localized plastic deformation. In the glass transition region, the fracture mechanism changes from a brittle to a ductile mode of failure. A failure envelope constructed from tensile tests suggests that the maximum elongation that the glassy PMMA can withstand without failure is about 130%. The calculated apparent activation energies suggest that the failure process of thermoplastic polymers (at least PMMA) follows a viscoelastic process, either glass or transition. The former is the case if crack initiation is required.Deceased.     

Quasi-static and dynamic fracture behaviour of rock materials: phenomena and mechanisms

An experimental investigation is conducted to study the quasi-static and dynamic fracture behaviour of sedimentary, igneous and metamorphic rocks. The notched semi-circular bending method has been employed to determine fracture parameters over a wide range of loading rates using both a servo-hydraulic machine and a split Hopkinson pressure bar. The time to fracture, crack speed and velocity of the flying fragment are measured by strain gauges, crack propagation gauge and high-speed photography on the macroscopic level. Dynamic crack initiation toughness is determined from the dynamic stress intensity factor at the time to fracture, and dynamic crack growth toughness is derived by the dynamic fracture energy at a specific crack speed. Systematic fractographic studies on fracture surface are carried out to examine the micromechanisms of fracture. This study reveals clearly that: (1) the crack initiation and growth toughness increase with increasing loading rate and crack speed; (2) the kinetic energy of the flying fragments increases with increasing striking speed; (3) the dynamic fracture energy increases rapidly with the increase of crack speed, and a semi-empirical rate-dependent model is proposed; and (4) the characteristics of fracture surface imply that the failure mechanisms depend on loading rate and rock microstructure.     

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.     

The fracture energy of metal fibre reinforced ceramic composites (MFCs)

A model is presented for prediction of the fracture energy of ceramic-matrix composites containing dispersed metallic fibres. It is assumed that the work of fracture comes entirely from pull-out and/or plastic deformation of fibres bridging the crack plane. Comparisons are presented between these predictions and experimental measurements made on a commercially-available composite material of this type, containing stainless steel (304) fibres in a matrix predominantly comprising alumina and alumino-silicate phases. Good agreement is observed, and it’s noted that there is scope for the fracture energy levels to be high (∼20 kJ m⁻²). Higher toughness levels are both predicted and observed for coarser fibres, up to a practical limit for the fibre diameter of the order of 0.5 mm. Other deductions are also made concerning strategies for optimisation of the toughness of this type of material.     

Effect of pre-strain on fracture toughness of ductile structural steels under static and dynamic loading

The ductile fracture process consists of void nucleation, growth and coalescence. The whole ductile process can be divided into two successive steps: (I) the initial state to void nucleation, followed by (II) void growth up to void coalescence. Based on this suggestion, resistance to ductile fracture could be divided into the resistance to stage I and stage II, and accordingly the whole fracture toughness could be regarded to be due to contributions from stages I and II. The fracture toughness contributed from the two steps is, respectively, denoted as void nucleation-contributed fracture toughness and void growth-contributed fracture toughness. The effect of plastic pre-strain on the fracture toughness of ductile structural steels under static and dynamic loading (4.9 m/s) within the ductile fracture range was evaluated by summing contributions due to void nucleation-contributed and void growth-contributed fracture toughness. The effect of strain rate on fracture toughness was also investigated by the same means. The results show that both plastic pre-strain and high-speed loading decrease the void nucleation-contributed fracture toughness while their effects on the void growth-contributed fracture toughness depend on the variations in strength and ductility. Moreover, fracture toughness of structural steels generally decreases with increasing strain rate.     

Effect of temperature on the mode I and mixed mode I/III fracture toughness of SA333 steel

The effect of temperature on tensile properties, mode I and mixed mode I/III fracture toughness of SA333 Grade 6 steel was investigated. The variation of ultimate tensile strength and strain hardening exponent with temperature as well as the appearance of serrations in the stress-strain plots indicated that dynamic strain aging regime in this steel is in the temperature range 175-300 °C at a nominal strain rate of 3 × 10⁻³ s⁻¹. Both mode I and mixed mode I/III fracture toughness values were found to exhibit a significant reduction in the DSA regime. The mixed mode I/III fracture toughness was found to be significantly lower than the mode I fracture toughness at all temperatures. However, the difference between the two toughness values was much higher prior to the onset of DSA. The results are explained on the basis of the nature of deformation fields under mode I and mixed mode I/III loading as well as the fracture mechanism prevalent in these steels at different temperatures.