Hydrogen effect on fracture toughness of thin film/substrate interfaces

The effect of hydrogen on the interface fracture toughness of two nano-film/substrate structures, Ni/Si and Cu/Si, were evaluated using four-point bend specimens with and without hydrogen charging. Hydrogen typically decreases the fracture toughness of materials. However, we found in this study that the interfacial toughness between the Ni film and the Si substrate increased due to the presence of hydrogen, while that of Cu/Si decreased. Nanoindentation experiments for the Ni and Cu films revealed that local plasticity in the Ni and Cu films is promoted by the charged hydrogen. The critical stress intensity at the Ni/Si interface crack considering the plasticity of Ni, namely the true fracture toughness, is scarcely influenced by the existence of hydrogen. The apparent increase in fracture toughness of the Ni/Si interface is due to the large stress relaxation near the crack tip caused by softening due to the presence of hydrogen. Although the promotion of plastic deformation of Cu relaxes the stress intensity at the Cu/Si interface crack, the apparent interfacial toughness still decreases because of the significant decrease in the true toughness due to the presence of hydrogen.     

Internal hydrogen effects on thresholds for crack growth in the iron-based superalloy IN903

This study of internal hydrogen-induced crack growth in the iron-based superalloy IN903 shows that slow crack growth thresholds are significantly lower than fracture toughness values at the same prechargsd hydrogen concentrations. However, failure in all precharged samples occurred by slip band fracture which differed only in the extent of local surface plasticity. Quantitative fractography of these surface fracture features indicates that the crack tip hydrogen concentrations at threshold were higher than in fracture toughness samples. These higher concentrations are due to crack tip stress enhancement when sufficient time exists for hydrogen redistribution. In addition, continuum models based on mechanisms of failure demonstrate that the matrix carbides control crack growth susceptibility in slow crack growth and fracture toughness samples by establishing the characteristic distance that the crack tip stresses and strains must span to initiate fracture.     

Effect of nano-metal particles on the fracture toughness of metal–ceramic composite

A theoretical model is proposed to study the influence of nano-metal particles (NMPs) on the fracture toughness of metal–ceramic composites (MCC). In the framework of the model, the crack tip intersects the grain boundary of the NMPs. Stress concentration at crack tip initiates edge dislocations which makes a shielding effect on the crack and leads to fracture toughness of the MCC. The dependence of critical crack intensity factors on grain size of the NMPs was calculated. The calculation suggested that the existence of the NMPs lead to an increase of critical crack intensity factors by 14%.     

Effect of loading rate on dynamic fracture initiation toughness of brittle materials

Numerical simulation is carried out to investigate the effect of loading rate on dynamic fracture initiation toughness including the crack-tip constraint. Finite element analyses are performed for a single edge cracked plate whose crack surface is subjected to uniform pressure with various loading rate. The first three terms in the Williams’ asymptotic series solution is utilized to characterize the crack-tip stress field under dynamic loads. The coefficient of the third term in Williams’ solution, A ₃, was utilized as a crack tip constraint parameter. Numerical results demonstrate that (a) the dynamic crack tip opening stress field is well represented by the three term solution at various loading rate, (b) the loading rate can be reflected by the constraint, and (c) the constraint A ₃ decreases with increasing loading rate. To predict the dynamic fracture initiation toughness, a failure criterion based on the attainment of a critical opening stress at a critical distance ahead of the crack tip is assumed. Using this failure criterion with the constraint parameter, A ₃, fracture initiation toughness is determined and in agreement with available experimental data for Homalite-100 material at various loading rate.     

A comparative study on five approaches to evaluate double-K fracture toughness parameters of concrete and size effect analysis

The current paper presents a comprehensive comparison of double-K fracture toughness parameters of concrete evaluated using experimental method and four existing analytical methods. Fracture tests were carried out on compact tension wedge splitting specimens with various depths varying from 200 mm up to 1000 mm. In the analytical calculation, depending on the relationship between critical crack tip opening displacement and the abscissa value of turning point on bilinear softening curve, two different distributions of cohesive stress are considered along crack extension. Results show that four available analytical calculations yield almost the same values of double-K fracture toughness parameters and agree well with those obtained from the experiment, which confirms the consistency of five approaches. Size effect was discussed, including unstable fracture toughness, initiation fracture toughness, critical effective crack length, the length of critical fracture process zone and critical crack tip opening displacement.     

Modeling the brittle–ductile transition in ferritic steels: dislocation simulations

We present a model for the brittle–ductile transition in ferritic steels based on two dimensional discrete dislocation simulations of crack-tip plasticity. The sum of elastic fields of the crack and the emitted dislocations defines an elasto–plastic crack field. Effects of crack-tip blunting of the macrocrack are included in the simulations. The plastic zone characteristics are found to be in agreement with continuum models, with the added advantage that the hardening behavior comes out naturally in our model. The present model is composed of a macrocrack with microcracks ahead of it in its crack-plane. These microcracks represent potential fracture sites at internal inhomogeneities, such as brittle precipitates. Dislocations that are emitted from the crack-tip account for plasticity. When the tensile stress along the crack plane attains a critical value σ _F over a distance fracture is assumed to take place. The brittle–ductile transition curve is obtained by determining the fracture toughness at various temperatures. Factors that contribute to the sharp upturn in fracture toughness with increasing temperature are found to be: the increase in dislocations mobility, and the decrease in tensile stress ahead of the macrocrack tip due to increase in blunting, and the slight increase in fracture stress of microcracks due to increase in plasticity at the microcrack. The model not only predicts the sharp increase in fracture toughness near the brittle–ductile transition temperature but also predicts the limiting temperature above which valid fracture toughness values cannot be estimated; which should correspond to the ductile regime. The obtained results are in reasonable agreement when compared with the existing experimental data.     

Multi-scale simulation of hydrogen influenced critical stress intensity in high Co–Ni secondary hardening steel

Hydrogen embrittlement was an important and long-standing problem in the fields of steels, especially ultra-high strength steels. In order to simulate the ability of hydrogen embrittlement resistance for high Co–Ni secondary hardening steels, a multi-scale simulation method with four steps was used to calculate the critical stress intensity (K_IC) and hydrogen influenced critical stress intensity (K_ISCC). For the four steps: the atomic scale and nm scale simulation were mainly used to simulate the effect of stress-assisted hydrogen diffusion at the crack tip; the μm scale simulation was used to handle the effect of microstructure; the cm simulation was used to analyze the size effect. As the effect of hydrogen concentration at the crack tip, the simulation results of critical cohesive strength of the Fe(110) at the crack tip decreased by 82.3%. The μm scale simulation showed the improvement of fracture toughness with the help of austenite layer between martensite laths. Compared with the mechanical properties of 300 M and AerMet100 steels, the accuracy of this simulation method was proved.     

Toughness of glass fibres reinforced glass-ionomer cements

Two fracture toughness parameters, the critical stress intensity factor, K _c and the work of fracture, W _f have been used to characterise the toughness of conventional and resin-modified glass-ionomer cements reinforced with glass fibres. The critical stress intensity factor was determined from the peak load, and the work of fracture was determined as the energy required to extend an introduced crack through the respective glass ionomers. For both materials, crack propagation became more stable as the weight fraction of glass fibres was increased. Additionally, when the weight percent of glass fibres was increased the work of fracture increased. Fibre bridging at the crack tip resulted in the increase in the work of fracture. As the percentage weight of fibres was increased, the critical stress intensity factor decreased proportionally to the increase in porosity.     

Prediction of fracture toughness for heat-resistant steels considering specimen dimensions. Report 2. Ductile fracture

A model of ductile failure of a body with a crack has been developed which enables predicting fracture toughness on the upper shelf of the fracture toughness temperature dependence taking into account the influence of the stress state. The model is based on the physical-mechanical model of ductile failure which is controlled by the critical value εf reached by plastic strain at the crack tip ε _i ^ρ . In this case it is assumed that both the ε _i ^ρ value, which precedes the crack growth onset by the mechanism of pore coalescence, and the critical strain εf are functions of specific stress state parameters, namely: the critical strain is a function of the stress state triaxiality σ _m /σ _n (σ _m is the hydrostatic stress, σ _i is the stress intensity), and ε _i ^ρ is a function of the parameter χ introduced, which is an explicit function of all three principal local stresses in the process zone at the crack tip and which defines the degree to which the stress state approaches the plane strain conditions for a body of specified thickness. The model developed has two modifications one of which enables predicting fracture toughness of large-size bodies from the results of testing only small cylindrical specimens without cracks (smooth and with a circular recess) and the other from the results of testing small cylindrical specimens and small specimens with a crack. Translated from Problemy Prochnosti, No. 2, pp. 5–19, March–April, 1997.     

Rate-dependent fracture toughness of pure polycrystalline ice

A series of three-point bend tests using single edge notched testpieces of pure polycrystalline ice have been performed at three different temperatures (–20°C, –30°C and –40°C). The displacement rate was varied from 1 mm/min to 100 mm/min, producing the crack tip strain rates from about 10^–3 to 10^–1 s^–1. The results show that (a) the fracture toughness of pure polycrystalline ice given by the critical stress intensity factor (K _IC) is much lower than that measured from the J—integral under identical conditions; (b) from the determination of K _IC, the fracture toughness of pure polycrystalline ice decreases with increasing strain rate and there is good power law relationship between them; (c) from the measurement of the J—integral, a different tendency was appeared: when the crack tip strain rate exceeds a critical value of 6 × 10^–3 s^–1, the fracture toughness is almost constant but when the crack tip strain rate is less than this value, the fracture toughness increases with decreasing crack tip strain rate. Re-examination of the mechanisms of rate-dependent fracture toughness of pure polycrystalline ice shows that the effect of strain rate is related not only to the blunting of crack tips due to plasticity, creep and stress relaxation but also to the nucleation and growth of microcracks in the specimen.     

Effects of thickness and environmental temperature on fracture behaviour of polyetherimide (PEI)

The fracture behaviour of a polyetherimide (PEI) thermoplastic polymer was studied using compact tension (CT) specimens with a special emphasis on effects of specimen thickness and testing temperatures on the plane strain fracture toughness. The results show that the valid fracture toughness of the critical stress intensity factor, K _IC, and strain energy release rate, G _IC, is independent of the specimen thickness when it is larger than 5 mm at ambient temperature. On the other hand, the fracture toughness is relatively sensitive to testing temperatures. The K _IC value remains almost constant, 3.5 MPa in a temperature range from 25 to 130°C, but the G _IC value slightly increases due to the decrease in Young's modulus and yield stress with increasing temperature. The temperature dependence of the fracture toughness, G _IC, was explained in terms of a plastic deformation zone around the crack tip and fracture surface morphology. It was identified that the larger plastic zone and extensive plastic deformation in the crack initiation region were associated with the enhanced G _IC at elevated temperatures.     

A model for predicting the influence of warm pre-stressing and strain ageing on the cleavage fracture toughness of ferritic steels

A micromechanistic model of warm pre-stressing is extended to predict the combined effects of warm pre-stressing and strain ageing on the cleavage fracture toughness of ferritic steels. The crack tip stress distribution after a cycle of pre-straining and strain ageing is estimated by superposition of the appropriate monotonic loading stress distributions. The Ritchie, Knott and Rice model of cleavage fracture and its associated fracture criterion are employed in conjunction with the crack tip stress distribution to predict the critical stress intensity factor after warm pre-stressing and strain ageing. Illustrative calculations are presented, based upon the published material's properties of a high nitrogen mild steel. Available experimental data for pressure vessel steels bear out the form of the predictions. At low temperatures, and after heavy pre-loads, the benefits of warm pre-stressing dominate strain ageing induced embrittlement and the toughness is apparently enhanced. At higher temperatures, or after small pre-loads, however, strain ageing dominates and the apparent toughness is reduced. Various assumptions and approximations inherent in the model are discussed. These generally tend to render the predictions conservative. Finally it is noted that the model should be equally applicable to the prediction of the combined effect of warm pre-stressing and neutron irradiation on the cleavage fracture toughness of ferritic steels.     

Plane strain fracture toughness of modern ferritic structural steels

Abstract

The temperature dependence of the plane strain fracture toughness of a low carbon, fine grain, ferritic steel for structural applications is investigated. The ductile–brittle transition is found to occur in the interval between 160 and 184 K. The experimental results are interpreted by an analytical model which permits calculation of the plane strain fracture toughness K _1c in the brittle domain as a function of the tensile properties and the cleavage fracture stress, making use of a piecewise approximation for the distribution of tensile stress on the crack axis and applying a deterministic fracture criterion at the stress peak. A similar criterion, which consists of equating the severest strain on the crack axis to a critical strain for cavity nucleation, provides the upper shelf fracture toughness. A relatively simple figure for predicting the transition temperature of steels in this family as a function of material properties can be obtained in this way.     

Plastic deformation around the tip of a stopped brittle crack in the Robertson test with a temperature gradient

Robertson tests with imposed temperature gradients were carried out to investigate crack stopping in structural steels. Macroscopic fracture toughness in plane strain and plane stress conditions were evaluated using linear elastic fracture mechanics to study the effect of various testing conditions. Both values were expected to be almost equal. On the other hand, microscopic fracture toughness was then deduced from the concept of maximum plastic deformation ahead of the stopped crack tip. The macroscopic and the microscopic fracture toughness agreed well.

The fracture toughness for arrest is shown to depend on extent of plastic deformation at some distance ahead of the stopped crack tip. In consequence, the shear lip on the fracture surface is likely to play only a secondary role in causing arrest.     

THE CRACK INITIATION TOUGHNESS FOR BRITTLE FRACTURE OF SUPER DUPLEX STAINLESS STEEL

Abstract— The occurrence of brittle stable crack growth before unstable fracture was demonstrated with the aid of heat-tinting, for a ferritic matrix super duplex stainless steel which had been age-hardened at 475°C. The critical crack tip opening displacement for stable crack growth, i.e. the crack initiation toughness, was measured using the direct-current-potential drop crack monitoring technique. A quantitative model for the effect of temperature and age-hardening on the brittle crack initiation toughness is described.     

Instrumented impact testing of polyethersulphone

The impact behaviour of polyethersulphone has been studied using a specially constructed instrumented impact testing machine. This machine is of the pendulum type and the samples are fractured in three-point bend loading. It is shown that accurate force/deformation curves can be obtained, in spite of complications due to flexural vibrations of the test sample. Measurements were made on both sharp-notched and blunt-notched specimens over a range of crack lengths. It was found that the sharp-notched samples could be analysed in terms of fracture toughness, G _C, whereas the blunt-notched samples corresponded to a constant critical stress at the root of the notch. The importance of multiple crazes at the crack tip in bluntnotched specimens is emphasized. It is also shown that ageing reduces the fracture toughness, while on the other hand, the critical stress observed in blunt-notched specimens, which has been associated with the craze initiation stress, is not affected by ageing.     

Effect of residual stress on cleavage fracture toughness by using cohesive zone model

This study presents the effect of residual stresses on cleavage fracture toughness by using the cohesive zone model under mode I, plane stain conditions. Modified boundary layer simulations were performed with the remote boundary conditions governed by the elastic K‐field and T‐stress. The eigenstrain method was used to introduce residual stresses into the finite element model. A layer of cohesive elements was deployed ahead of the crack tip to simulate the fracture process zone. A bilinear traction–separation‐law was used to characterize the behaviour of the cohesive elements. It was assumed that the initiation of the crack occurs when the opening stress drops to zero at the first integration point of the first cohesive element ahead of the crack tip. Results show that tensile residual stresses can decrease the cleavage fracture toughness significantly. The effect of the weld zone size on cleavage fracture toughness was also investigated, and it has been found that the initiation toughness is the linear function of the size of the geometrically similar weld. Results also show that the effect of the residual stress is stronger for negative T‐stress while its effect is relatively smaller for positive T‐stress. The influence of damage parameters and material hardening was also studied.     

Crack tip reinforcement by bridging elements: modelling the fracture of the matrix material

There is a wide range of physical situations where the faces of a crack in a matrix material with limited ductility are restrained from opening, a phenomenon known as crack reinforcement. In quantifying this phenomenon, the simplest way of modelling the behaviour of the matrix material ahead of a crack tip is to assume that it deforms in accord with the laws of linear elasticity with the crack extending when the stress intensity at the crack tip (the leading edge of the restraining region) attains a critical value,K _IC, the fracture toughness of the matrix material; i.e. the details of the matrix deformation and fracture behaviour are ignored. The viability of thisK-matrix assumption is examined for the case of a semi-infinite crack in a remotely loaded infinite solid, for which the restraining stress between the crack faces increases linearly with crack opening until the attainment of a critical opening when the restraining stress falls to zero. The analysis defines the range of material parameters for which theK-matrix assumption is adequate with regard to the determination of (a) the applied value ofK required for the crack tip and restraining zone to propagate through the solid, and (b) the size of the restraining zone when propagation occurs. TheK-matrix assumption always gives an overestimate of the appliedK, but the overestimation is small when the matrix toughness contribution is small or is dominant. However, when the contributions from the matrix toughness and the toughness provided by the restraining material are roughly equivalent, theK-matrix assumption leads to a significant overestimate of the appliedK, and in this situation the matrix material behaviour should be modelled more precisely.     

Measurement of the temperature field induced by dynamic crack growth in Beta-C titanium

The temperature increase at the tip of a dynamically propagating crack may have a significant effect on a material's mechanical properties, and hence on its dynamic fracture toughness. In order to start to understand this phenomena, measurements of the temperature field at the tip of a dynamically growing crack in Beta-C titanium alloy were performed using a linear array of high speed infrared detectors. The results show that a maximum temperature of 450°C is reached at the crack tip. In addition, the dynamic fracture toughness was measured for crack speeds from 0 to 500 m/s. In this speed range, the toughness appears to be constant. Estimates of the crack tip energy release rate and plastic strain rate are made using analysis of the experimental data.     

The cohesive zone model in a problem of delayed hydride cracking of zirconium alloys

The crack tip model with the cohesive zone ahead of a finite crack tip has been presented. The estimation of the length of the cohesive zone and the crack tip opening displacement is based on the comparison of the local stress concentration, according to Westergaard's theory, with the cohesive stress. To calculate the cohesive stress, von Mises yield condition at the boundary of the cohesive zone is employed for plane strain and plane stress. The model of the stress distribution with the maximum stress within the cohesive zone is discussed. Local criterion of brittle fracture and modelling of the fracture process zone by cohesive zone were used to describe fracture initiation at the hydride platelet in the process zone ahead of the crack tip. It was shown that the theoretical K _IH-estimation applied to the case of mixed plane condition within the process zone is qualitatively consistent with experimental data for unirradiated Zr-2.5Nb alloy. In the framework of the proposed model, the theoretical value of K ^H _IC for a single hydride platelet at the crack tip has been also estimated.