Onset Of Crack Initiation Research Articles

Tough-to-brittle transition in multiwalled carbon nanotube (MWNT)/polycarbonate nanocomposites

Morphology and fracture behaviour of polycarbonate (PC)/multiwalled carbon nanotubes (MWNT) composites have been studied by AFM and essential work of fracture approach (EWF). A maximum in the non-essential work of fracture was observed at 2 wt.% MWNT demonstrating enhanced resistance to crack propagation compared to pure PC. DMA analysis shows an increase in the T g and broadening of the tan δ peaks with the increase in the MWNT content suggesting confinement of the PC chain mobility. Fracture kinetics studies reveal that the crack growth mechanism is broadly dominated by crack propagation rather than crack blunting. Crack resistance curves ( R-curves) demonstrate a transition in the crack growth mechanism (depending on crack extension) from pure crack-tip blunting/crack initiation mode to mixed mode of crack blunting and crack initiation/propagation. Above 2 wt.% MWNT a tough-to-brittle transition has been observed which is also in agreement with the substantially higher (almost 10 times) speed of crack growth without any fracture instability before the failure. The time-resolved in situ strain field analysis revealed that the onset of crack initiation has been shifted to shorter time for nanocomposites with 4 wt.% MWNT than that of 2 wt.% MWNT and thus explaining the existence of a tough-to-brittle transition in these nanocomposites. Fracture surface investigation by SEM shows bridging of the nanotubes across the radial and transverse cracks imparting higher toughness at 2 wt.% of MWNT. The main conclusion of our study is that the resistance against crack initiation ( J 0.5, EWF) and the resistance against crack propagation ( T J, βw p) in these nanocomposites are structurally correlated with the matrix behaviour (state of percolation) and morphology (distance between MWNT and their dispersion) respectively.

EBSD-AFM Hybrid Analysis on Early Fatigue Damage in Austenitic Stainless Steel under Cyclic Torsional Loading

Both the electron backscatter diffraction (EBSD) and atomic force microscopy (AFM) methods were used to investigate the active slip systems and crack initiation behavior in an austenitic stainless steel, SUS316NG, fatigued to one-fourth of the fatigue life under cyclic torsional loading. Most of the active slip systems under torsional loading took place on the primary planes with the largest Schmid factor. Fatigue cracks observed on the surface were classified into four types : GB (grain boundary), TB (twin boundary), SB (slip band) and TC (transcrystalline) cracks. The density distribution of TC cracks was maximum, followed by those of GB, SB, and TB cracks. The development of the surface topography due to fatigue was studied by AFM examination of replicated surfaces of the specimen. On the basis of EBSD and AFM observations, the following four parameters were measured : h, the depth of intrusion vertical to the surface ; S, the slip displacement ; SA, the component of slip displacement parallel to the surface ; SB, the component of the slip displacement perpendicular to the surface trace. Both h and SB values showed a sharp increase at the onset of crack initiation. The critical values of h and SB at crack initiation were 160nm and 170nm, respectively.

Crack Toughness Behaviour of Multiwalled Carbon Nanotube (MWNT)/Polycarbonate Nanocomposites

AbstractSummary: The morphology and fracture behaviour of polycarbonate (PC)/multiwalled carbon nanotube (MWNT) composites have been studied by AFM and post‐yield fracture mechanics. The essential work of fracture (EWF) method has been used to distinguish between two terms representing the resistance to crack initiation and crack propagation. A maximum in the non‐essential work of fracture was observed at 2 wt.‐% MWNT, demonstrating enhanced resistance to crack propagation compared to pure PC. At 4 wt.‐% MWNT, a tough‐to‐brittle transition has been observed. The time‐resolved in‐situ strain field analysis revealed that the onset of crack initiation was shifted to a shorter time for nanocomposites with 4 wt.‐% MWNT compared to that with 2 wt.‐%, and thus explained the existence of a tough‐to‐brittle transition in these nanocomposites. magnified image

Energy Approach to the Evaluation of the Limiting Equilibrium State of Orthotropic Cracked Bodies

We propose an energy criterion of crack propagation in anisotropic bodies based on the equation of energy balance at the onset of crack initiation. In this case, unlike the other well-known energy approaches, parallel with the equation specifying the limiting equilibrium of an anisotropic cracked body, we also use an additional equation for finding the direction of initial crack growth. The formulated criterion is applied to establish the limiting equilibrium state of an infinite orthotropic plate containing a rectilinear crack.

Acoustic emission based tensile characteristics of sandwich composites

Sandwich composite static and fatigue testing results indicated the predominant failure to be the core damage followed by interfacial debonding, resin cracking and fiber rupture. Under static testing, crack was observed to initiate in the core and ensue planar propagation near the interface with the facesheets; whereas, onset of crack initiation in the facesheets served as a precursor to the catastrophic failure. Multiple failure initiation and propagation sites in the core and intermittent interfacial debonding were consistently observed under fatigue. An acoustic emission based stiffness reduction model is presented that seems to accurately identify the extent of damage in sandwich composites subjected to fatigue loading conditions.

Fracture Toughness Properties of High-Strength Martensitic Steel within a Wide Hardness Range

Fracture toughness tests were carried out on six grades of high-strength martensitic steel within the hardness range from 270 to 475 HB. Four types of tests were performed: (a) Charpy V-notch (CVN) impact over the temperature range −120 to 60 °C, (b) plane strain fracture toughness, K IC , near the onset of crack growth, (c) fracture toughness, J IC , near the initiation of slow crack growth, and (d) fracture toughness, J iC , and crack tip opening displacement (CTOD iC ) at the onset of slow crack growth using direct current potential drop (DCPD) technique. Further, true plane strain fracture toughness, K o , at the onset of crack initiation was determined. Fracture toughness behavior including the measured and determined values of CVN, K IC , K o , J IC , K iC , and CTOD iC have been interrelated over the entire hardness range using the various analytical and empirical correlations reported in the literature. The results indicate that the steel acquires the optimum fracture toughness properties at a hardness of 305 HB, corresponding to a tempering temperature of 630 °C. Further, the steel exhibits a slight 300 °C temper embrittlement phenomenon.

Measurement techniques for determination of ductile crack initiation on Charpy specimens

In the engineering practice it is of importance to know the effect of loading rate on the material behaviour including the fracture mechanics properties. Depending on the material behaviour under a given loading condition, different fracture mechanics parameters should be determined. The critical values of these parameters are usually related to the onset of crack initiation which can be determined easier in the case of brittle fracture. But in the case of ductile fracture additional measurement techniques are required. This paper presents some possibilities to characterise the fracture resistance against ductile fracture using instrumented impact testing. The magnetic emission technique will be introduced as a potential measurement method for determining the onset of ductile crack propagation in magnetizable metals.

Energy density theory formulation and interpretation of cracking behavior for piezoelectric ceramics

Any attempt made to separate energy into electrical and mechanical parts may lead to inconsistencies as they do not necessarily decouple. This is illustrated by application of the energy density function in the linear theory of piezoelasticity. By assuming that a critical energy density function prevails at the onset of crack initiation, it is possible to establish the relative size of an inner and outer damage zone around the crack tip; they correspond to the ligaments at failure caused by pure electric field and pure mechanical load. On physical grounds, the relative size of these zones must depend on the relative magnitude of the mechanical and electrical load. Hence, they can vary in size depending on the electromechanical material and damage resistance properties. Numerical results are obtained for the PZT-4, PZT-5H, and P-7 piezoelectric ceramics. These two ligaments for the two damage zones may coincide for appropriate values of the applied electrical field and mechanical load. Explicit expression of the energy density factor S is derived showing the mixed mode electromechanical coupling effects. The factor S can increase or decrease depending on the direction of the applied electric field with reference to the poling direction. This is in contrast to the result obtained from the energy release rate quantity, which remains unchanged for electric field in the direction of poling or against it.

Delamination Fracture of Multidirectional Carbon-Fiber/Epoxy Composites under Mode I, Mode II and Mixed-Mode I/II Loading

The purpose of the present study was to characterize the delamination fracture of continuous carbon fiber/epoxy multidirectional-laminates under Mode I, Mode II and Mixed-Mode I/II loading conditions. The present study considers the variation of the interlaminar failure energy, G C, with the extent of crack jumping, and ensuing fiber bridging, which arises during the growth of the delamination in the multidirectional-laminates under the various modes of loading. The main type of laminate which was studied was a multidirectional fiber composite prepared from 24 ply lay-ups of (-45°/0°/+45°)2S (+45°/0°/-45°)2S. The initial delamination was located at the +45°/-45° mid-plane of the specimen. It has been found that when the values of the interlaminar fracture energy, G c, are ascertained as a function of the length of the propagating crack, a, then very complex relationships are observed. This was the case for all the different modes of loading, and these observations reflected the complex failure paths which occurred as the delamination propagated through the multidirectional fiber composites. It was, however, possible to define clearly the onset of crack initiation. These results also revealed that the values for the interlaminar fracture energy, G C-(initiation), at crack initiation for the (-45°/O°/+45°)2S (+45°/O°/-45°)2S multidirectional laminates were always significantly greater than that for the corresponding unidirectional (i.e., 0°/0°) laminates.

Intergranular Crack Nucleation in Bicrystalline Materials Under Fatigue

During cyclic deformation of polycrystalline materials, as substantiated by many experimental observations, due to existence of high stress concentration at the interfaces the preferential site of crack nucleation is intercrystalline. Accordingly, it is assumed that the highly localized cyclic deformation persistent slip band (PSB) occurs along the grain boundary (GB) which results in intergranular crack initiation. In the present work the irreversible accumulation of dislocations are used to characterize PSB by means of double pile-up which are composed of vacancy and interstitial dipoles. We shall give the mechanism and a quantitative remedy of ratcheting of plastic deformation peculiar to fatigue deformation. In a manner conceptually analogous to Griffith theory (1921), the critical number of cycles to failure and hence the S-N curves for crack initiation is obtained by considering the free energy of the system. The Gibbs free energy change ΔG increases with the fatigue cycle number due to cyclic increment of elastic strain energy which in turn stems from cyclic pile-up of dislocations along the slip planes. The Gibbs free energy change attains its maximum value at a critical cycle number beyond which the state of dislocation dipole accumulation becomes energetically unstable. In our theory we postulate that this critical state is the onset of crack initiation. We shall give a quantitative value for the fatigue limit and analyze the dependence of the S-N curve on several important physical parameters such as grain size; surface energy; yield strength; width of the PSB; and the ratio of the shear modulus of the bicrystalline material.

Predicting ductile crack initiation near notch tip under mode I loading by the damage theory

In this paper, the new ductile damage theory previously developed by the authors is employed to study the onset of crack initiation near the notch tip under mode I loading in the spirit of the slip-line field theory.

Fracture toughness of PC/PBT blend based on J‐integral methods

AbstractThe fracture toughness of a polycarbonate/poly(butylene terephthalate) (PC/PBT) blend was determined using three different J‐integral methods, ASTM E813‐81, E813‐87, and hysteresis energy. The critical J values (J1c) obtained are largely independent of the cross‐head speed (range from 0.5 to 50 mm/min). ASTM E813‐81 and hysteresis energy methods result in comparable J1c values, while the E813‐87 method estimates J1c to be 60–80% higher. The critical displacement determined from the plots of hysteresis (energy and ratio) and the true crack growth length vs. displacement is very close. This indicates that the critical displacement determined by the hysteresis energy method is indeed the displacement at the onset of crack initiation and the corresponding J1c represents a physical event of crack initiation. © 1995 John Wiley & Sons, Inc.

Optimum regression model and data-window on J-integral method based on hysteresis on PC/PBT blend

The J-Integral fracture mechanics based on an hysteresis approach has been previously demonstrated to be viable and simple experimentally. However, the optimum procedure to construct the J-R curve in terms of regression model and data-window has not yet been well defined. In this study, the fracture toughness of the PC/PBT blend has been investigated using the previously developed hysteresis method by seven regression models and three data-window ranges. The second order polynomial model results in the best data-fitting capability and moreconsistent Jc values than those higher order polynomial models or the linear regression model. The critical J values obtained from this second polynomial model using the same data-window as ASTM E813-81 standard are comparable to those obtained from the ASTM standards. The trend clearly shows thathigher Jc values are obtained when the range of data-window is increased. The close Jc values obtained from this hysteresis method and the ASTM E813-81 indicate that the determined critical displacement from this hysteresis method is indeed the onset of crack initiation.

Precrack hysteresis energy in determining its ductile–brittle transition. III. Effect of temperature

AbstractA temperature variable has been used to correlate the precrack hysteresis energy and the corresponding ductility in terms of ductile–brittle transition behavior for polycarbonate. When the precrack plastic zone exceeds a critical value, crack extension thereafter will be effectively contained within the domain of the plastic zone and result in ductile fracture. Whether a specimen will fail in a ductile mode or a brittle mode is actually already being decided before the onset of crack initiation. The precrack elastic storage energy, total input energy minus hysteresis energy, is the major driving force to strain the crack tip for crack initiation. A higher testing temperature with lower yield stress converts a greater fraction of the input energy into the precrack hysteresis energy and relieves the storage strain energy available for crack initiation. A polycarbonate‐toughening mechanism of incrasing temperature is very similar to the presence of rubber by reducing yield stress and increasing the precrack plasticity. © 1994 John Wiley & Sons, Inc.

Determination of Dynamic Fracture-Initiation Toughness Using a Novel Impact Bend Test Procedure

A novel impact bend test procedure is described/or determining the dynamic fracture-initiation toughness, KId, at a loading rate (stress intensity factor rate), K˙I, of the order of 106MPam/s. A special arrangement of the split Hopkins on pressure bar is adopted to measure accurately dynamic loads applied to a fatigue-precracked bend specimen. The dynamic stress intensity factor history for the bend specimen is evaluated by means of a dynamic finite element technique. The onset of crack initiation is detected using a strain gage attached on the side of the specimen near a crack tip. The value of KId is determined from the critical dynamic stress intensity factor at crack initiation. A series of dynamic fracture tests is carried out on a 7075-T6 aluminum alloy, a Ti-6246 alloy and an AISI 4340 steel. The KId values obtained for the three structural materials are compared with the corresponding values obtained under quasi-static loading conditions.

Plasticity and fracture initiation in rubber‐toughened poly(methyl methacrylate)

AbstractThe deformation behavior of rubber toughened poly(methylmethacrylate), RT‐PMMA, has been investigated in terms of the ability of the material to nucleate plasticity. Work‐hardening rate parameter K measurements in the early stages of the nonelastic response in a constant strain‐rate test are used to probe the development of micro shear zones as a function of rubber volume fraction. The results reveal the existence of a sharp transition from difficult to easy shear band nucleation for a critical rubber volume fraction Vc. This abrupt change in mechanical behavior also shows in the evolution of the critical stress intensity factor K measured at the onset of crack initiation. These findings are discussed in terms of the morphological parameters of the blends.

Mechanical Properties and Residual Stresses in Oxide/Metal Multilayer Films Synthesized by Ion Beam Assisted Deposition

ABSTRACTFilms of Al, Al2O3 and Al/Al2O3 microlaminates were formed by ion beam assisted deposition (IBAD) at R ratios from 0.0025 to 0.5 and film thicknesses between 150 and 2600 nm. Oxide films were amorphous while metal layers were crystalline with small grains and texture for both PVD and IBAD conditions. The average stress in the oxide film is tensile at R=0 and becomes compressive, saturating at approximately 15 eV/atom. The residual stress in the Al films is tensile over all R ratios and the stress in the microlaminate roughly follows a rule of mixtures. Deformation of ductile substrates on which films had been deposited revealed that the critical strain to fracture was strongly dependent on residual stress. Large compressive stresses in monolithic films produced by ion beam assisted deposition delayed the onset of crack initiation while the presence of multiple layers, in general, lowered the crack density at saturation, suggesting a possible ductilizing effect.

新しい衝撃曲げ試験法による動的破壊じん性の評価

A novel impact bend test procedure is described for determining the dynamic fracture-initiation toughness, KId, at a loading rate KI of the order of 106MPa√m/s. The split Hopkinson pressure bar technique was used to measure dynamic loads applied to a fatigue-precracked bend specimen. The dynamic stress intensity factor history for the bend specimen was evaluated by means of a dynamic finite element code. The onset of crack initiation was detected using a strain gage near a crack tip. The KId value was determined from the critical dynamic stress intensity factor at crack initiation. A series of dynamic fracture tests were performed for a Ti-6246 alloy and a 7075-T6 aluminum alloy. The KId values obtained for both the alloys were compared with the corresponding values obtained under quasi-static loading conditions. The fracture surface morphology was examined with the help of a scanning electron microscope to rationalize the apparent differences in the measured fracture-initiation toughness in response to the change in loading rate. Furthermore, the validity of the KId determination was confirmed by measurements of the crack tip plastic zone size in the interior of the fracture specimens based on the microhardness tests.

亀裂開口変位（ＣＯＤ）制御によるモードＩＩ形層間破壊靭性試験

End-notched flexure (ENF) test is commonly accepted to determine the mode II interlaminar fracture toughness of composite laminates. As the crack propagation in the ENF specimen is unstable under displacement-control, the critical energy release rate, GIIC, is determined at the onset of crack initiation but not during the crack propagation. In order to estimate the mode II fracture toughness from the initiation to the stable crack propagation, a new test method has been proposed in the present paper. A special COD gauge has been developed for the measurement of the crack opening displacement (COD) of ENF specimen and applied to the mode II interlaminar fracture toughness test. The crack initiation in the ENF specimen can be detected with higher accuracy from the load-COD diagram than the load-displacement dia-gram. Moreover, the crack propagates in the stable manner under the COD-control test, though it is unstable when the conventional displacement-control test is applied. Analytical compliance method has been successfully applied to the ENF test and the relation between fracture tough-ness, GIIC, and crack length, a, can be obtained automatically by using a computer aided test-ing system. Applicabilities of the COD-control test and the analytical compliance method to the ENF test are confirmed in the present paper.

Mixed-mode crack growth predictions

The problem of slow stable growth of an inclined crack in a plate subjected to uniaxial tension is studied by the strain energy density criterion. The stable crack growth process is simulated by predicting a series of crack growth steps corresponding to a piecewise loading increase when material elements along the direction of crack extension absorb a critical amount of elastic strain energy density. Crack instability takes place when the last ligament of crack extension takes a critical value which is a material constant. The critical stress at the onset of crack initiation and unstable crack extension is determined for various crack inclination angles. Three different loading step increments corresponding to three different loading rates are considered and their effect on stable crack growth is analysed. Furthermore, the influence of loading history on the crack growth process for three different loading types is studied. The complete crack growth patterns for all types of load are determined and analysed. It is obtained that the amount of slow crack growth can be increased by lowering the rate of loading. The effect of the loading history on the failure load and the crack paths is established.