Effect of notch root radius on fracture toughness of Ti–18Al–8Nb alloy

Abstract

The effect of notch root radius on the mode I fracture toughness of Ti–18Al–8Nb alloy in beta solution treated and water quenched condition was investigated. The apparent fracture toughness K _IA was found to be independent of the notch root radius below a critical notch root radius ρ ₀ and subsequently increase linearly with the square root of notch root radius ρ^1/2 beyond ρ ₀. The critical notch root radius in this alloy was found to be ～50 μm. The results were explained on the basis of strain controlled fracture model.     

The effect of volume fraction of primary α phase on fracture toughness behaviour of Timetal 834 titanium alloy under mode I and mixed mode I/III loading

The effect of volume fraction of primary α phase on mode I and mixed mode I/III fracture toughness of Timetal 834 titanium alloy was investigated. The mode I and mixed mode I/III fracture toughness values for loading angle of 30° were found to initially decrease and subsequently increase with increase in volume fraction of primary α phase. On the other hand, mixed mode I/III fracture toughness for loading angle of 45° was found to monotonically decrease with increasing volume fraction of α phase. The fracture toughness was also found to marginally increase with increasing loading angle for the two lower primary α volume fractions, i.e. 6% and 15% whereas it marginally decreases with increasing loading angle for primary α volume fraction of 30%. The results were explained on the basis of the nature of stress field ahead of the crack tip under mixed mode I/III loading as well as the fracture mechanisms operative in this alloy for different α volume fractions.     

Fracture toughness of Ti-15Al-8Nb alloy under mixed mode I/III loading

The effect of mixed mode I/III loading on fracture toughness of Ti-15 at.% Al-8 at.% Nb alloy, which undergoes stress-induced martensitic transformation, was investigated for four different grain sizes. The fracture toughness under mixed mode I/III loading was found to be significantly higher than that under mode I loading in all cases. The results were explained on the basis of the stress and strain fields ahead of a mixed mode crack and its influence on the martensitic transformation zone.     

Mixed mode I/III fracture toughness in extruded magnesium alloys

Fracture toughness under mode I and mixed mode I/III loading were determined for magnesium (Mg) as well as binary Mg-Al and Mg-Zn alloys in as-extruded condition. It was found that in Mg and in Mg-1.25Zn alloy the fracture toughness under mixed mode I/III loading was higher than that under mode I loading whereas in binary Mg-1Al and Mg-3Al alloys it was lower than that under mode I loading. The results have been explained on the basis of the fracture mechanism and the nature of the stress fields ahead of the crack tip under mixed mode I/III loading.     

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.     

Fracture of U-notched specimens under mixed mode: Experimental results and numerical predictions

The first part of the paper gives an account of 153 fracture tests on blunted notched specimens (with notches of root radius ranging from 0.3 to 4.0 mm), loaded under mixed mode (ranging from almost pure mode I to mode II, and beyond). Maximum loads and initial crack angles were measured as a function of notch root radius and loading mixity. Such results can help in evaluating numerical models of the fracture of notched components. The second part of the paper deals with the suitability of the cohesive crack concept for predicting fracture loads under mixed mode. Use of local mode I was considered for numerical computations. Comparison of experimental results with numerical predictions was significantly accurate. Diagrams of fracture loci for notched components loaded under mixed mode are discussed.     

A two-parameter approach to assessing notch fracture behaviour in clay/epoxy nanocomposites

Fracture toughness and other mechanical properties of epoxy are known to be affected by the addition of nanoclays. Fracture toughness has been shown by many researchers to depend on the nanocomposite structure with well-dispersed and distributed nanoparticles resulting in improvements in this property by up to 50%. Notch fracture toughness depends on the acuity of the notch as well as on the structure of the nanocomposite. In the present work, a two-parameter fracture criterion based on a critical notch stress intensity factor, K_ρ,c, and effective T-stress, T_ef, was used to study the effect of notch severity and nanoclay addition on the fracture toughness of the epoxy matrix. The results show that the average value of K_ρ,c for neat epoxy increased with increasing notch radius while the absolute value of T_ef decreased with notch radius. The addition of nanoclay to pristine epoxy reduced the average value of K_ρ,c and increased the absolute value of T_ef. The critical notch radius was found to be around 1.0 mm and the notch sensitivity was higher for neat epoxy. SEM analysis of the fractured surfaces revealed that the lower K_ρ,c for nanocomposites in both mode I and mixed mode fractures was due to early crack initiation at clay clusters or voids at the notch root.     

Influence of dynamic strain ageing on mixed mode I/III fracture toughness of Armco iron

Fracture toughness tests under mode I and mixed mode I/III loading were carried out at different test temperatures ranging from ambient to 673 K. The dynamic strain ageing (DSA) range in Armco iron was identified to be between 383 and 573 K. A marked increase in fracture toughness was observed in the DSA regime and this correlated with the increase in the strain hardening exponent. The magnitude of fracture toughness, however, decreased with increasing loading angle. The extent of decrease was high at temperatures below the DSA regime (≤383 K) which can be understood in terms of the nature of the stress field ahead of a mixed mode I/III as well as the operative fracture mechanism. However, at higher temperatures, the effect of mode III in this respect diminished in the DSA regime (383–573 K) due to DSA causing the opposite effect, that is fracture toughness to increase.     

Translaminar fracture toughness: The critical notch tip radius of 0° plies in CFRP

The relationship between translaminar fracture toughness measured at initiation and specimen initial notch root radius is investigated for the translaminar failure mode of cross-ply IM7/8552 carbon/epoxy laminates. Compact tension specimens with four sizes of notch root radii were tested; the true initiation toughness of the laminate was measured from specimens with notch tip radii of ρ ? 250 μm. Testing of specimens with larger notch root radii, ρ = 750 μm, yielded an apparent toughness that was found to be 30% higher than the true toughness of the laminate. The propagation toughness corresponding to the R-curve plateau was found not to be affected by the initial notch tip radius. Investigation of the fracture surfaces of failed specimens revealed that there is no interaction between the 0° and 90° ply failure mechanisms, and that the critical notch radius is a property intrinsic to the 0° plies of the laminate.     

Dynamic fracture toughness testing of epoxy resin filled with sio2 particles

The fracture behavior of epoxy resin used as one of electrical insulation materials is generally brittle compared with that of metals. Therefore, when epoxy resin is used as a structural material, the effect of impact loading must be taken into consideration in design. In the present study, the dynamic fracture toughness of epoxy resin filled with SiO₂ particles has been evaluated both by the absorbed energy method and by the impact load obtained from the instrumented Charpy type impact test. Therefore, the absorbed energy has been analysed to evaluate the real fracture toughness. Moreover, the influence of inertial loading on the impact load must be also considered; therefore, the dynamic fracture toughness has been evaluated by the formula taking the inertial loading effect into consideration. Thus both fracture toughness values evaluated from absorbed energy and from impact load have been compared; as a result, a good agreement has been ascertained.It is common to perform impact test on specimens with blunt notches since they are easy to be prepared. However, variation of fracture toughness with notch root radius in the brittle material cannot be ignored. Therefore, the influence of notch root radius on the fracture toughness has been examined. As a result, it has been ascertained that the variation of fracture toughness with notch root radius follows the formula presented by Williams.     

Interlaminar fracture characterization for plain weave fabric composites

For the analysis of laminated composite plates under transverse loading and drilling of composites, all the elastic, strength and fracture properties of the composite plates are essential. Interlaminar critical strain energy release rate properties in mode I, mode II, mixed mode I/II and mode III have been evaluated for two types of plain weave fabric E-glass/epoxy laminates. The double cantilever beam test and the end notch flexure test have been used for mode I and mode II loading. The mixed mode bending test and split cantilever beam test have been used for mixed mode I/II and mode III loading. It is observed that the plain weave fabric composite with lesser strand width has higher interlaminar fracture properties compared to the plain weave fabric composite with more strand width. Further, crack length versus crack growth resistance plots have been presented for mode III loading. In general, it is observed that total fracture resistance is significantly higher than the critical strain energy release rate.     

Effect of mixed mode I/II on fracture behaviour of laminated metal matrix composites

Abstract

The effects of mixed mode loading (I/II) on the fracture toughness and fracture behaviour of both 6090/SiC/20_p-6013 diffusion bonded laminates and 2080/SiC/20_p-2080 adhesive bonded laminates tested in the crack arrester orientation were investigated. The effects of layer thickness and volume fraction ratio on the fracture behaviour under the mixed mode were also studied. The fracture behaviour under mode I/II of available similar discontinuously reinforced aluminium (DRA) materials was additionally compared to that of the laminates. The fracture behaviour of laminates under mode I/II was dependent on the volume fraction ratio and generally different from that of the monolithic and DRA. The increase in the fracture toughness of DRA by lamination with ductile layers under mode I changes somewhat under increasing load mixity, for 75/25 and 50/50 diffusion bonded laminate and 60/40 adhesive bonded laminate ABL. This results from extensive interfacial separation and delamination between the layers.     

A generalised notch stress intensity factor for U-notched components loaded under mixed mode

A novel notch stress intensity factor (NSIF) for U-notched specimens loaded under mixed mode is examined in this article. The concept is based on the averaged strain energy density criterion, or alternatively on the cohesive zone model, as well as the equivalent local mode approach. To a certain extent, it is a generalisation of Glinka’s NSIF for mode I, where σ_tip is replaced by σ_max.The applicability of a fracture criterion based on this new NSIF is checked against 171 fracture tests with PMMA (at −60 °C) performed on U-notched specimens, with different notch root radii and loaded under mixed mode. The asymptotic behaviour of the new NSIF as the notch becomes a crack (when the notch root radius tends to zero) or when the notch disappears (when the notch root radius tends to infinity) is also discussed.     

A STUDY OF SUPERIMPOSED FRACTURE MODES I, II AND III ON PMMA

A test apparatus has been developed to study the fracture behaviour of engineering materials subjected to superimposed tensile and shear (Mode I and II) loads using a single edge notch specimen. Stress intensity factors were calculated using finite element analysis. Test results for PMMA are reported. Results from circumferentially notched round bar specimens, subjected to combined tension and torsion (Mode I and III) loading are also reported. The Mode I/II results are consistent with the mixed mode fracture response of a wide range of brittle materials, although there is some evidence of non-linear behaviour. The fracture behaviour for superimposed Modes I and III indicates the strong influence of non-linear deformation which causes the mixed mode toughness to be dependent on the sequence and type of loading.     

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.     

A critical shear displacement criterion for ductile–brittle transition under mixed mode I and II loading

Abstract

Micromechanisms producing ductile and brittle damage operate in parallel at a crack tip. The dominant mode of failure depends upon which of the two (ductile or brittle) damage parameters first reaches its critical value. This has been shown by a study of ductile–brittle transition behaviour in HY100 steel under mixed mode I and II loading. The transition from ductile to brittle behaviour in HY100 steel was found to be affected by mixed mode I and II ratio (ratio of imposed tensile and shear loading) in a manner such that with increasing shear the transition temperature decreased. In the present paper, a criterion is proposed based on the shear strain ahead of a notch tip, to predict the fracture behaviour at any given temperature and mixed mode ratio.     

Effect of notch root radius on fracture toughness of polycrystalline cubic boron nitride

The fracture toughness of five grades of polycrystalline cubic boron nitride (PCBN) has been determined using Single Edge V-Notched Beam specimens. Both coarse and fine grade materials were considered, containing CBN grain sizes of between 1 μm and 22 μm. The influence of notch root radius on the measured fracture toughness was examined. The notch root radius was found to have a major effect for materials with smaller CBN grain sizes while only a small effect was noted for the material with large CBN grain sizes. A simple analytical model was developed to explain the effect of the notch root radius on the fracture toughness and was found to agree well with experiment for all the materials tested. It was shown that the effect of notch root radius is directly linked to the size of the CBN grain. It is proposed that this effect results from the interaction between the microstructure and the stress field around the notch tip.     

Influence of mixed mode I/III loading on fracture toughness of mild steel at various strain rates

Abstract

The effect of loading angle &phis; on the fracture toughness of mild steel at various strain rates has been studied. The fracture toughness was found to decrease with increasing loading angle (or increasing mode III component) at strain rates 10^-5 to 10⁰ s^-1 where ductile fracture was observed. Under impact conditions (strain rate 10² s^-1), fracture was by cleavage and the fracture toughness was found to increase with increasing loading angle. The results showed that the mixed mode fracture behaviour of mild steel changed from Class C in the strain rate range 10^-5 to 10⁰ s^-1 to a combination of Class A and B under impact conditions. In the strain rate range 10^-5 to 10^-2 s^-1, the fracture toughness behaviour with increasing strain rate was found to be similar for the three loading angles studied, namely &phis;= 0, &phis;= 30 and &phis;= 45°. At the strain rates 10^-2 to 10² s^-1, fracture toughness at &phis;= 0° decreased sharply, while for loading angles &phis;= 30° and &phis;= 45°, the fracture toughness increased with strain rate. The increase in mixed mode fracture toughness with strain rate in this strain rate regime has been attributed to the inertial effects which are known to reduce the T stress ahead of the crack.     

Sudden Fracture from U-Notches in Fine-Grained Isostatic Graphite Under Mixed Mode I/II Loading

The U-notched maximum tangential stress (UMTS) criterion, proposed originally and utilized previously by the author and his co-researcher for predicting mixed mode I/II fracture in plexi-glass (PMMA) and also pure mode II fracture in PMMA and soda-lime glass, was employed to estimate the experimental results reported in literature dealing with brittle fracture of many U-notched fine-grained isostatic graphite plates under combined tensile/shear loading conditions. By using the fracture curves of the UMTS criterion, which can predict the onset of brittle fracture in terms of the notch stress intensity factors (NSIFs) in the entire domain from pure mode I to pure mode II, the mixed mode fracture toughness (i.e. the load-bearing capacity) of U-notched graphite plates was successfully estimated.     

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.