The formation of fracture process zones in polygranular graphite as a precursor to fracture

The initiation and growth of fracture process zones are explored in polygranular Pile Grade A reactor core moderator graphite subjected to four-point bending. Digital image correlation is combined with resistance strain gauge measurements to evaluate both the localised and the global strains during tests on graphite. The experiments, performed on plain and notched rectangular beam specimens, show non-linear load–displacement characteristics prior to peak load. This behaviour is shown to be mainly dominated by the presence of localised strains (or process zones) extending up to about 3 mm from the tensile surface of the specimen. At peak load, a macrocrack propagates rapidly along an irregular path controlled by the direction of the applied load and the microstructure of the graphite. These cracks arrest prior to complete separation of the specimen. Once cracks are formed, localised tensile displacements extend for distances of up to about 3 mm ahead of the tips of these cracks. It is also demonstrated that failure load is not sensitive to the presence of the notch. The results are discussed with respect to the role of process zones on the non-linear load–displacement response of the graphite prior to the peak load and during macrocrack propagation post peak load.     

Mechanical behaviour of graphite in fracture of austempered ductile iron

Abstract

An investigation was carried out to examine the mechanical behaviour of graphite in the fracture of austempered ductile iron (ADI) by in situ tensile testing with an SEM. The results indicate that the graphite in ADI cannot be regarded as voids with no strength because graphite–matrix (G–M) interface cracking and the internal fracture of graphite were observed. Under tensile testing, microcracks always initiated at and propagated along the G–M interface first. Graphite nodules do not cause micronotch stress concentration thermselves in advance of the G–M interface cracking. The propagation of interfacial cracks along the G–M interface resulted in crack deflection. When the main crack propagated to a graphite nodule whose G–M interface had cracked and formed a void, it was obviously blunted. Graphite–matrix interface cracking occurred ahead of a propagating crack. The G–M interfaces and graphite nodules have a certain strength.     

Fluid jet erosion of tension-softening materials

Fluid jets are increasingly used to process and machine tension-softening materials. Typical applications are drilling, cutting, fragmentation, hydrodemolition and 3D-machining. Tension-softening materials, such as concrete, reinforced ceramics, most rocks and solidified impurities, are quasi-brittle behaving materials characterised by a so-called fracture process zone. Therefore, linear elastic fracture mechanics does not suitably cover these materials. It is also known that conventional strength parameters, such as compressive strength, cannot describe the resistance of this group of materials against fluid jet erosion. In this paper, the behaviour of cement paste, mortar and concrete during the erosion by high-speed waterjets with velocities up to 470 m s^–1 is investigated. The results of SEM-studies are presented that clearly illuminates features of quasi-brittle behaviour, including grain bridging, microcracking and crack branching. It is also found that the erosion process is strongly determined by the size of the aggregate (inclusions) in the material. It is concluded that a non-linear fracture resistance parameter may be suitable to estimate the erosion resistance of the material. It is found that the brittleness B _M – the inverse of the characteristic length of a material – is a suitable resistance parameter. A very good relationship between the brittleness and the volumetric erosion rate estimated from 24 different types of concrete could be obtained.     

Correlation between fracture and damage for quasi-brittle bi-material interface cracks

Fracture at a bi-material interface is essentially mixed-mode, even when the geometry is symmetric with respect to the crack and loading is of pure Mode I, due to the differences in the elastic properties across an interface which disrupts the symmetry. The linear elastic solutions of the crack tip stress and displacement fields show an oscillatory type of singularity. This poses numerical difficulties while modeling discrete interface cracks. Alternatively, the discrete cracks may be modeled using a distributed band of micro-cracks or damage such that energy equivalence is maintained between the two systems. In this work, an approach is developed to correlate fracture and damage mechanics through energy equivalence concepts and to predict the damage scenario in quasi-brittle bi-material interface beams. The study is aimed at large size structures made of quasi-brittle materials failing at concrete-concrete interfaces. The objective is to smoothly move from fracture mechanics theory to damage mechanics theory or vice versa in order to characterize damage. It is concluded, that through the energy approach a discrete crack may be modeled as an equivalent damage zone, wherein both correspond to the same energy loss. Finally, it is shown that by knowing the critical damage zone dimension, the critical fracture property such as the fracture energy can be obtained.     

In situ observation of crack nuclei in poly-granular graphite under ring-on-ring equi-biaxial and flexural loading

Fracture tests of graphite are known to exhibit sensitivity to stress state, such as a difference between their flexural and tensile strengths. Bi-axial tensile and flexural loading are representative of the stress states in some regions of graphite components in nuclear fission reactors, where loading develops from fast neutron irradiation-induced dimensional change and thermal strains. Study of the behaviour of the inherent defects that determine strength variability requires in situ observation of crack nucleation. To this end, digital image correlation can be used to monitor the evolution of displacement fields and hence the cracks on the surface of large samples whilst under load. In this study, a ring-on-ring flexural test setup was developed to apply equi-biaxial tensile stress to large disc specimens of graphite along with the conventional four-point-bend test. A 17% reduction in mean flexural strength was observed for the equi-biaxial loading, relative to uniaxial loading. DIC was used to characterise the observed fracture nuclei. Linear elastic fracture mechanics analysis was shown to be inadequate to explain the strength reduction. It is suggested that fictitious crack models, originally developed to simulate the behaviour of concrete structures, can be utilised to explain the behaviour.     

Load history effects in ductile cast iron for wind turbine components

Fracture-mechanics experiments were carried out on samples of ductile cast iron to investigate the fracture behaviour under cyclic and random loading. Under cyclic loading, the crack growth rate was described well by the ESACRACK model. Fatigue crack growth behaviour depends on the graphite particle size. Increasing particle size leads to higher threshold-values ΔK_th, lower da/dN values and higher transition to static fracture K_fc. The investigation of load history effects with low–high and high–low transitions shows that crack growth acceleration is independent of the transition type. The computation of the a–N curves based on different load history models yields non-conservative results.     

Development of hypoeutectoid graphitic steel for wires

Abstract

Hypoeutectoid graphitic steels with BN as prime nucleating site for graphite nucleation were developed for improvement of drawability of wires. Al₂O₃ also acted as nucleation site for graphite. The steel chemistry has played an important role for BN formation and thus dictated the behaviour of graphite formation and tensile properties after graphitising annealing. The steels are with a low yield ratio of ～0·5 while percentage elongation is in the range of 23–25% and percentage reduction in area is in the range of 45–51%.     

Fracture behaviour of a magnesium–aluminium alloy treated by selective laser surface melting treatment

Fracture behaviour of AZ91D magnesium alloy is dominated by the brittle fracture of the β-Mg₁₇Al₁₂ phase so its modification is required to improve the toughness of this alloy. The novel laser treatment named as Selective Laser Surface Melting (SLSM) is characterized by the microstructural modification of the β-Mg₁₇Al₁₂ phase without altering the α-Mg matrix. We have studied the effect of the selected microstructural modification induced by the laser treatment in the fracture behaviour of the alloy has been studied using in situ Scanning Electron Microscopy bending test. This test configuration allows the in situ observation of the crack progression and the record of the load–displacement curve. It has been observed that the microstructural modification introduced by SLSM causes an increase of 40% of the fracture toughness of the treated specimen. This phenomenon can be related with the transition from brittle to ductile fracture behaviour of the laser modified β-phase.     

A new expression for crack opening stress determined based on maximum crack opening displacement under tension–compression cyclic loading

The maximum crack opening displacement is introduced to investigate the effect of compressive loads on crack opening stress in tension–compression loading cycles. Based on elastic–plastic finite element analysis of centre cracked finite plate and accounting for the effects of crack geometry size, Young's modulus, yield stress and strain hardening, the explicit expression of crack opening stress versus maximum crack opening displacement is presented. This model considers the effect of compressive loads on crack opening stress and avoids adopting fracture parameters around crack tip. Besides, it could be applied in a wide range of materials and load conditions. Further studies show that experimental results of da/dN ? ΔK curves with negative stress ratios could be condensed to a single curve using this crack opening stress model.     

Cyclic fracture behaviour of 304LN stainless steel under load and displacement control modes

Attempts have been made to understand cyclic fracture behaviour of AISI 304LN stainless steel used for nuclear piping materials under load vis‐à‐vis displacement controlled fracture tests; the former closely simulate the seismic loading conditions. The load controlled tests indicate that a material fails in a limited number of cycles even when the load amplitudes are sufficiently below the maximum load in a monotonic J–R test. The displacement controlled tests, on the other hand, show that the energy absorbing ability of a material gets severely reduced under cyclic loading conditions. The obtained results on standard laboratory specimens have been compared with similar available results on components in order to provide guidelines for maximum load bearing capability of engineering components under cyclic loading.     

On the transfer of specimen J–R curve to piping components with throughwall circumferential flaw

Transferability of the specimen J–R/J–T curve to the component level is an important issue in the field of fracture mechanics. Towards this goal, fracture experiments have been carried out on single‐edge bend (SE(B)) and compact tension (CT) specimens and throughwall circumferentially cracked straight pipes/elbows of 200 mm nominal bore (NB) diameter. The pipe material is SA 333 Gr 6 steel (low strength and high toughness material) and specimens are machined from the pipes. Subsequently, elastic–plastic finite‐element analyses have been carried out on these cracked components/specimens in order to evaluate the stress triaxiality levels. It is found that the triaxial levels for these cracked components are similar. Hence, similar fracture behaviour is expected for these components. Consequently, one of the pipe J–R curves is used as a reference J–R curve to consider the crack growth in the analysis and the load deformation behaviour of other pipes/elbows is predicted. The load deformation behaviour of the piping components is also predicted using an extrapolated J–R curve from a specimen that exhibits the similar triaxiality level to that of the cracked components. The predicted results are in good agreement with the experiments.     

Slow crack growth in cellulose fibre cements

Slow stable crack growth is a prominent feature of the fracture behaviour of cellulose fibre cements. It is shown that this characteristic can be described by crack growth resistance against crack extension curves based on linear elastic fracture mechanics. Double-cantilever-beam specimens with side grooves are used to obtain such crack resistance curves for a commercial cellulose cement containing approximately 8% mass fraction of bleached fibres. Both dry and wet samples are tested. Compliances measured during slow crack growth by the unloading/reloading technique at successive crack increments are less than those obtained for saw-cut notches with similar crack lengths. Residual displacements due to either mismatch fracture surfaces or a large inelastic process zone at the crack tip are also observed at zero load. A modified elastic potential energy release rate (G _R ^* ), and hence its equivalentK _R ^* [= (EG _R ^* )^1/2], must be used to include this residual displacement effect in order to yield the true crack growth resistance curves. This is found to be necessary for the wet samples due to their large residual displacements. The crack growth resistances of the wet samples are superior to those of the dry samples: this is explained in terms of the improved ductility and toughness of the wet cellulose fibres.     

Fracture toughness parameters and elasticplastic analysis of non-moderate fracture conditions using finite element methods

Non-moderate fracture conditions of load and geometry, in which plastic zones remain neither constant in size nor uniform in shape as load or crack progress, were simulated using two dimensional elasticplastic finite element calculations. Comparison of conventional crack extension energy rate G, as determined by elastic fracture mechanics and by a compliance method suitable for non-linear deformation, is made with Rice's ‘J integral’, with crack opening displacement, and also with plastic strain energy. The relationship of crack opening displacement to crack extension force can be linearised by selecting values of crack opening displacement at locations which nominally follow the calculated location of the elastic-plastic boundary on the crack face. The relatively large plastic zones associated with high loading are shown, and the field determined in the usual manner from incremental load increases is compared with the field resulting when only two steps are used to reach the same load. Some insight is gained into the use of finite element calculations for determining, from among the various fracture indicators, a single parameter capable of describing nonmoderate fracture conditions.     

Deformation and fracture in Al–Li-base alloys

Abstract

Aluminium–lithium-base alloys are of considerable interest because of their low density and high modulus. However, they have been shown to have low ductility and poor fracture toughness. This has been attributed to a variety of factors, including intense shear band formation, segregation to grain boundaries, and weakened grain boundaries due to precipitation and precipitate-free zones. The authors have investigated the deformation structures observed in binary and more complex commercial alloys. As would be expected, considering the microstructure of the alloys, extensive strain localization and shear band formation occurs in these alloys. However, it is shown that the commercial alloys are less sensitive to strain localization than the model binary alloy systems investigated. The stresss–train behaviour has been investigated. The alloys exhibit jerky flow, which is indicative of negative strain rate sensitivity, and strain rate change tests showed this to be the case. This is consistent with the deformation structures observed. The effect of weakened grain boundaries due to precipitation and precipitate-free zones has been studied by comparing the fracture characteristics of aged and unaged material. It is shown that the mode of failure is identical under appropriate conditions. It is concluded that segregation to grain boundaries is the major cause of the lower ductility and toughness of Al–Li alloys. This possibility has been investigated using in situ fracture surface analysis techniques. Results are presented on grain boundary segregation, and methods of reducing its influence on fracture behaviour are indicated.

MST/570     

Caustic stress corrosion cracking of a spheroidal graphite cast iron: laboratory investigation

Abstract

This paper presents the results of an experimental investigation into the stress corrosion cracking (SCC) of an engineering cast iron (namely a spheroidal graphite (SG) cast iron), in a highly caustic solution (namely synthetic Bayer liquor (SBL)) at high temperature. In order to ascertain experimental conditions under which plain iron - carbon materials may fracture predominantly by SCC in a caustic environment, slow strain rate testing (SSRT) was performed on carbon steel specimens, employing various combinations of strain rates and temperatures, in SBL and an inert environment of liquid paraffin. Under the conditions identified to be most conducive for caustic SCC of mild steel, specimens of the SG cast iron were subjected to SSRT in SBL and liquid paraffin, and the fracture behaviour was investigated by detailed fractography and microstructural characterisation.     

Low-cyclic fatigue behaviour of an Al–Cu–Mg–Ag alloy under T6 and T840 conditions

The low-cyclic fatigue (LCF) behaviour of an AA2139 alloy belonging to the Al–Cu–Mg–Ag system was investigated under T6 and T840 conditions. The T840 treatment involves cold rolling with a 40% reduction prior to ageing, and this was effective in increasing the tensile strength of the alloy. Under cyclic loading at total strain amplitudes (ε_ac) of ±0.4 to ±1.0%, the mechanical behaviour is defined as the prevalence of elastic over plastic deformation processes under both the T6/T840 conditions. The initial weak hardening during one to two cycles of loading at ε_ac?>?0.55% and an insignificant softening upon following the cyclic loading to fracture was observed for the T6/T840 conditions. The LCF behaviour of the alloy under the T6/T840 conditions is described by the Basquin–Manson–Coffin relationship.

This paper is part of a Themed Issue on Aluminium-based materials: processing, microstructure, properties, and recycling.     

Influence of composition and processing parameters on mechanical properties and erosion response of Ni–TiB2 coatings

Abstract

Sputtered Ni–TiB₂ coatings have been shown to protect Ti–6Al–4V and Inconel 718 substrates from solid particle erosion. However, before new erosion resistant coatings can be efficiently designed, it is essential that the role of mechanical properties in determining erosion resistance be fully understood. In this investigation, nanoindentation techniques were used to quantify the effects of substrate preparation, coating composition, and sputtering process parameters on the elastic moduli and indentation hardness of thin coatings deposited on Ti–6Al–4V and Inconel 718 substrates. The influence of these parameters on coating adhesion was determined using a conventional scratch test. Elastic moduli, indentation hardnesses, and coating adhesion were correlated with erosion behaviour. The erosion resistance of the coatings that exhibited microscopic ductility is dependent on the nodule diameter and coating properties such as hardness, elastic modulus, and fracture toughness.

MST/1697     

Fracture mechanics of polymers. Critical evaluation for linear elastic behaviour at high speed testing

Over the last few years considerable effort has been made to obtain reliable stress intensity factor and strain energy release rate (K _IC andG _IC) data on polymeric materials. Experience has shown that a valuable method to minimize viscoelastic losses and plastic deformation is to work at high speed. However, some problems remain, for this kind of experimental method, which have to be solved before standard methods can be defined. On the basis of measurements done with 3-point bending geometry on poly(vinylchloride) (PVC) and poly(propylene) (PP) at room temperature and over a large range of notch depths, the present work demonstrates that the linearity of experimental data both in the load (F) and in the energy (U) against (2BW ²/3LYa) and (BW) plot is not a critical test for linear elastic behaviour, so that (K _IC andG _IC) values can be affected by large errors. Only the knowledge of the experimental curves, which can be obtained by means of instrumented pendula in optimized test conditions, allows a critical test to be applied for linear elastic behaviour, based on the comparison between experimental and predicted data for load, displacement and energy. These tests show that the linear elastic fracture mechanics, LEFM, criterion is satisfied for PVC, but not for PP. This conclusion is further supported by the morphologies of the fracture surfaces.     

Modelling complex cracks with finite elements: a kinematically enriched constitutive model

A continuum constitutive framework with embedded cohesive interface model is presented to describe the failure of quasi-brittle materials. Both cohesive behaviour for cracking inside the fracture process zone and elastic bulk behaviour are treated at integration points making implementation straightforward. In this sense, the proposed approach is simpler than existing ones that focus on element enrichments, such as the extended finite element method, while share similarities with smeared crack models, and offers the capability to correctly model quasi-brittle failure in post-peak regime at constitutive level. In this work, the formulation is introduced, numerical algorithms described and static and dynamic fracture simulations with complex crack patterns are conducted to demonstrate the capability and advantage of the proposed approach.     

Determination of the kink point in the bilinear softening model for concrete

The characterization of the softening curve from experimental results is essential for predicting the fracture behavior of quasi-brittle materials like concrete. Among various shapes (e.g. linear, exponential) to describe the softening behavior of concrete, the bilinear softening relationship has been extensively used and is the model of choice in this work. Currently, there is no consensus about the location of the kink point in the bilinear softening curve. In this study, the location of the kink point is proposed to be the stress at the critical crack tip opening displacement. Experimentally, the fracture parameters required to describe the bilinear softening curve can be determined with the “two-parameter fracture model” and the total work of fracture method based on a single concrete fracture test. The proposed location of the kink point compares well with the range of kink point locations reported in the literature, and is verified by plotting stress profiles along the expected fracture line obtained from numerical simulations with the cohesive zone model. Finally, prediction of experimental load versus crack mouth opening displacement curves validate the proposed location of the kink point for different concrete mixtures and also for geometrically similar specimens with the same concrete mixture. The experiments were performed on three-point bending specimens with concrete mixtures containing virgin coarse aggregate, recycled concrete coarse aggregate (RCA), and a 50-50 blend of RCA and virgin coarse aggregate. The verification and validation studies support the hypothesis of the kink point occurring at the critical crack tip opening displacement.