A simple model of stress intensity range threshold and crack closure stress

The cyclic stress intensity threshold (Δ$\text{K}{}_{\mathrm{TH}}$) below which cracks will not propagate varies with length for short cracks. A model is proposed which relates Δ$\text{K}{}_{\mathrm{TH}}$ to the crack closure stress arising from fracture surface roughness. This is used to predict a variation in Δ$\text{K}{}_{\mathrm{TH}}$ with crack length for surface cracks in Ti 6Al-2Sn-4Zn-6Mo alloy, based upon measured values of crack opening displacement arising from roughness. The predicted variation in Δ$\text{K}{}_{\mathrm{TH}}$ with crack length is found to be similar to that obtained from the empirical model of Δ$\text{K}{}_{\mathrm{TH}}$ proposed by El Haddad et al.[5]. The application of the new model to estimate the value of crack closure stress arising from crack tip plasticity for short surface cracks is also discussed.     

Photoelectrochemical study of the layered compound In23Pse3

The layered compound $\text{In}{}_{\mathrm{<mtext>2</mtext><mtext>3</mtext>}}\text{PSe}{}_3$ is studied by photoelectrochemical technique. Two modes of transition, indirect ～ 1.55 eV, and direct ～ 1.80 eV are evidenced. An estimation of the hole diffusion length is given through the use of Gärtner model ($\text{L}\text{? 4 μ}\text{m}$). The flat band positions of the junction $\text{In}{}_{\mathrm{<mtext>2</mtext><mtext>3</mtext>}}\text{PSe}{}_3\text{-}\text{electrolyte}$ at different pH values are determined in an electrochemical scale.     

The use of small specimen strength ratio for measuring fracture toughness

The specimen strength ratio ($\text{R}{}_{\mathrm{s}}$), determined from small specimen tests was correlated with plane strain fracture toughness ($\text{K}{}_{\mathrm{Ic}}$) values for many heats of A533B-1 steel. A variety of loading rate and specimen size results suggest that $\text{K}{}_{\mathrm{Ic}}$ can be predicted from the small specimen strength ratio up to values of $\text{R}{}_{\mathrm{s}}$ near 2.0. Also, conservative estimates of cleavage-initiated, elastic-plastic fracture toughness can extend beyond $\text{R}{}_{\mathrm{s}}$ values of 2.0. The ASTM E399 size criterion appears to be too restrictive for the class of steel studied, and a more appropriate requirement would reduce the ASTM criterion by a factor of four.     

A unifying strain criterion for fracture of fibrous composite laminates

A general fracture toughness parameter $\text{Q}{}_{\mathrm{c}}$ which is independent of layup, was previously derived using a strain failure criterion for fibers in the principal load-carrying plies. It was verified to be a material constant for centrally cracked boron/aluminum composite specimens. The specimens were made with various proportions of 0° and $\text{±45°}$ plies. Moreover, a limited amount of data indicated that the ratio $\text{Q}{}_{\mathrm{c}}\text{/?}{}_{\mathrm{tuf}}$, where $\text{?}{}_{\mathrm{tuf}}$ is the ultimate tensile strain of the fibers, might be a constant for all composite laminates, regardless of material and layup. In that case, a single value of $\text{Q}{}_{\mathrm{c}}\text{/?}{}_{\mathrm{tuf}}$ could be used to predict the fracture toughness of all fibrous composite laminates from only the elastic constants and $\text{?}{}_{\mathrm{tuf}}$.To verify that $\text{Q}{}_{\mathrm{c}}\text{/?}{}_{\mathrm{tuf}}$ is indeed a constant, values of $\text{Q}{}_{\mathrm{c}}\text{/?}{}_{\mathrm{tuf}}$ are calculated and presented here for centrally cracked specimens made from graphite/polyimide, graphite/epoxy, E-glass/epoxy, boron/epoxy. and S-glass-graphite/epoxy materials with numerous $\text{[0}{}_{\mathrm{i}}\text{/±45}{}_{\mathrm{j}}\text{/90}{}_{\mathrm{k}}\text{]}$ layups. The data indicate that $\text{Q}{}_{\mathrm{c}}\text{/?}{}_{\mathrm{tuf}}$ is reasonably constant for all laminates that did not delaminate or split extensively in the 0° plies at the crack tips. But some elevation of $\text{Q}{}_{\mathrm{c}}\text{/?}{}_{\mathrm{tuf}}$ due to small-to-moderate crack-tip damage is evident.Using a single value of $\text{Q}{}_{\mathrm{c}}\text{/?}{}_{\mathrm{tuf}}$ for all the layups and materials, strengths were predicted for the test specimens. The predicted and test values agree well except, of course, for the laminates that delaminated or split extensively. Then, the predicted strengths are usually conservative. Layup affects the ratio of cracked to uncracked strengths more for the resin matrix specimens than the boron/aluminum specimens.     

The J-integral fracture criterion under opening and tearing modes and unloading effects

Measurements of $\text{J}$ from certain formulae agree well with compliance measurements for a round notched bar specimen subjected to tensile (Mode I) and torsional (Mode III) loadings. Crack growth resistance curves ($\text{R-}\text{curves}$) obtained by a three parameter technique are compared with those obtained by two current approaches. The $\text{J}{}_{\mathrm{IC}}$ values (Mode I) at initial crack growth are in good agreement with the $\text{j}{}_{\mathrm{IIIC}}$ values (Mode III). In addition, the effect of unloading on fracture toughness is examined.     

Characterization of transition temperature behavior of HY130 steel by the JIc fracture toughness parameter

The objectives of this study were to determine whether the $\text{J-R}$ curve approach could be used to evaluate the ductile to brittle temperature performance of a high yield strength structural steel (HY130) and to demonstrate that the single specimen unloading compliance method is applicable to evaluate $\text{J}{}_{\mathrm{Ic}}$ values and $\text{J-R}$ curves for compact specimens tested at temperatures from ?192 to 150°C. The major conclusions of this work are that $\text{J}{}_{\mathrm{Ic}}$ and the complete $\text{J-R}$ curve can be obtained using the single specimen method over the above temperature range and that $\text{J}{}_{\mathrm{Ic}}$ does define a ductile to brittle transistion temperature for HY130 steel which should be more valuable for structural design than that found from Charpy $\text{V}$ or dynamic tear specimens because it is based on a fracture toughness parameter. The comparison of the ${}_{\mathrm{Ic}}$ transition temperature and that from Charpy $\text{V}$ specimens shows that the Charpy $\text{V}$ transition temperture is more conservative for the HY130 steel tested. In transitional $\text{J}{}_{\mathrm{I}}$ specimens which demonstrated a ductile crack tearing followed by a brittle failure, scanning microscope stereo pair fractography showed that the transition from ductile to brittle behavior was very gradual in comparison to the distinct crack tips obtained on ductile specimens broken in a brittle fashion at a cryogenic temperature.     

The influence of environment and stress ratio on fatigue crack growth at near threshold stress intensities in low-alloy steels

Fatigue crack propagation at low stress intensities has been studied in two low alloy steels in a variety of environments with particular emphasis being placed on the influence of stress ratio and strength level. It was found that fatigue crack growth rates are lower and threshold stress intensities ($\text{ΔK}{}_0$) are higher in vacuum than in humid, laboratory air but, in dry gaseous environments (argon, hydrogen and air) and at low stress ratio ($\text{R ~ 0.1}$), crack growth rates are faster and $\text{ΔK}{}_0$ values are lower than in laboratory air. However, the influence of stress ratio is considerably greater in laboratory air than in dry gaseous environments with the result that, at high stress ratio ($\text{R ~ 0.8}$) $\text{ΔK}{}_0$ values are similar in all environments examined. Increasing material strength level resulted in higher, near-threshold crack growth rates and a reduction in $\text{ΔK}{}_0$ in both dry and humid air environments. The results are discussed in terms of the influence of crack closure and environmental effects on fatigue crack growth behaviour. The importance of corrosion debris produced in fatigue cracks at low stress intensities is also discussed.     

Effect of plate temperature oscillations on free convection boundary layers along a vertical plate

The laminar free convection flow and heat transfer along a semi-infinite vertical plate is analysed when the plate temperature $\text{T}{}_{\mathrm{p}}$ takes the form $\text{T}{}_{\mathrm{p}}\text{=T}{}_{\mathrm{w}}\text{+α(T}{}_{\mathrm{w}}\text{?T}{}_{\mathrm{\infty }}\text{sin}\text{ω}\text{t}\text{?}$ where$\text{0 ? α < 1}$. Thus the plate temperature consists of a basic steady distribution $\text{T}{}_{\mathrm{w}}$ with a super-imposed oscillatory distribution $\text{α(T}{}_{\mathrm{w}}\text{?T}{}_{\mathrm{\infty }}\text{)}\text{sin}\text{ω}\text{t}\text{?}$. It is to be noted that the main difference between this and the earlier works is that here the magnitude of oscillations α is not required to be very small. The skin friction and the rate of heat transfer from the wall are caleulated by means of two asymptotic expansions. A regular expansion is obtained for small values of the frequency parameter $\text{? (x) = [x/gβ(T}{}_{\mathrm{w}}\text{?T}{}_{\mathrm{\infty }}\text{)]}\text{ω}$ while for large values of ?, a singular perturbation technique is developed. Numerical computations are made for various values of α and it is demonstrated that there are values of ? at which the small and large ? exppnsions for the skin friction and the rate of heat transfer overlap satisfactorily.     

The discharge of a I12TaSe4 cathode for lithium battery

The discharge process was investigated on a lithium battery using $\text{I}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{TaSe}{}_4$ as cathode. The battery works as primary battery. The potential gradually decreased from 2.1V to 1.8V upto a discharging of $\text{Li}\text{I}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{TaSe}{}_4\text{≈0.5}$. Then it was almost constant at 1.8V until the discharging of about 2.0. Iodine is partially removed out of $\text{I}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{TaSe}{}_4$, keeping the host TaSe₄ chain structure as it was in the first step of discharge. The new product has tetragonal crystal lattice having lattice parameters of $\text{a}\text{=9.532}\text{A}\text{?}$ and $\text{c}\text{=25.31}\text{A}\text{?}$, which is twice of c-parameter of $\text{I}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{TaSe}{}_4$.     

Synthesis of a new perovskite Pb(Li14Nb34)O3

A high-pressure technique was adopted to obtain perovskite-type $\text{Pb(Li}{}_{\mathrm{<mtext>1</mtext><mtext>4</mtext>}}\text{Nb}{}_{\mathrm{<mtext>3</mtext><mtext>4</mtext>}}\text{)}\text{O}{}_3$. A new perovskite $\text{Pb(Li}{}_{\mathrm{<mtext>1</mtext><mtext>4</mtext>}}\text{Nb}{}_{\mathrm{<mtext>3</mtext><mtext>4</mtext>}}\text{)}\text{O}{}_3$ was characterized to have a cubic symmetry with $\text{a}{}_{\mathrm{<mtext>o</mtext>}}\text{= 4.069}\text{A}\text{?}$; Li and Nb ions in the B-site of perovskite lattice may be in a random arrangement.     

Experimental determination of Jc data using different types of specimen

$\text{J}{}_{\mathrm{c}}$ values for two medium-strength steels have been experimentally determined from tests on different types of specimen. Evaluation of test records was performed utilizing a digital computer. Two independent electrical methods were employed to determine critical points. Results indicate independence of $\text{J}{}_{\mathrm{c}}$ on specimen configuration and hence support the suggestion that the $\text{J-}\text{integral}$ be a relevant parameter for onset of crack growth. Present results compare favourably with previously published data.     

A comparison of the geometry dependence of several nonlinear fracture toughness parameters

A number of fracture toughness tests on compact tension specimens have been performed for the purpose of comparing several nonlinear fracture toughness methods; including the nonlinear energy ($\text{G}\text{?}{}_{\mathrm{I}}$), J-integral ($\text{J}{}_{\mathrm{I}}$), COD ($\text{G}{}_{\mathrm{\delta }}$), and linear (–$\text{G}{}_{\mathrm{I}}$) approaches. The effect of variations in specimen thickness ($\text{B}$) and width ($\text{w}$) on the fracture toughness was examined for 7075-T651, 2124-T851, 2048-T35I, and 2048-T851 aluminum alloys, Ti-6Al-4V, and 4340 steel. Fracture toughness values were evaluated at both the initiation of stable crack growth and the onset of unstable fracture (peak load).It was found that the peak load toughness values are quite geometry sensitive at thicknesses below the requirement for plane strain fracture. At the initiation of stable crack growth, the toughness values are constant over a much larger range of specimen thickness. However, the nonlinearity of the load displacement curve is quite limited at this point and the associated fracture toughness is only 30–50% of the peak-load values.     

The effects of load ratio on environmentally assisted fatigue crack growth

A modification to the model of Weir et al. for surface reaction and transport controlled fatigue crack growth has been developed to explicitly account for the effect of load ratio on environmentally assisted fatigue crack growth. Load ratio was found to affect principally gas transport to the crack tip, and therefore affected only transport controlled crack growth response. Experimental verification of the modified model was made by studying the room temperature fatigue crack growth responses at different load ratios for a 2219-T851 aluminum alloy exposed to water vapor.The results show that the effects of load ratio can be attributed to two different sources—one relating to its effect on local deformation at the crack tip and is reflected through the mechanical component, (d$\text{a}$/d$\text{N}$)₀ and the other on its role in modifying environmental effect and is manifested through the corrosion fatigue component, $\text{(da/dN)}{}_{\mathrm{cf}}$ Furthermore, the results show that the saturation value of corrosion fatigue component, $\text{(da/dN)}{}_{\mathrm{cf,s}}$, is essentially independent of $\text{R}$, and that the exposure needed to produce “saturation response” ($\text{P}{}_0\text{/2f)}{}_{\mathrm{s}}$, as a function of load ratio can be predicted from the modified model. The modified model, therefore, allows one to predict the corrosion fatigue crack growth response for any load ratio on the basis of measurements made at a single load ratio, provided that the values of ($\text{da/dN}$), are known.     

Application of the ac potential drop technique to the determination of R curves of tough ferritic steels

The suitability of the AC potential drop (ACPD) technique for detecting crack initiation and monitoring crack extension during slow stable growth has been investigated using side-grooved Charpy size specimens tested in three point bending. For ferritic steels with widely differing initiation and growth characteristics, the potential drop (PD) vs clip gauge opening displacement (CGOD) trace shows consistent behaviour, the most important feature being the occurrence of a minimum around the point of crack initiation. At low current frequency (150 Hz), there is close agreement between $\text{δ}{}_{\min }$, the COD corresponding to the minimum of the PD/CGOD trace and $\text{δ}{}_{\mathrm{i}}$ estimated by the recommended multispecimen technique for $\text{δ}{}_{\mathrm{i}}$ ranging from 0.02 to 0.37mm. In steels with $\text{δ}{}_{\mathrm{i}}$ less than about 0.1 mm, the minimum occurs at the same value of δ for both low (150 Hz) and high (4.7 kHz) frequencies. However, for steels with higher toughness, the minimum shifts to lower δ values as the frequency is increased. It appears that for any steel, there is a maximum frequency below which the minimum corresponds to $\text{δ}{}_{\mathrm{i}}$. It is demonstrated that the ACPD method can be employed to determine $\text{R}$ curves from single specimens.     

A study of the size-effect on plastic energy dissipation and toughness in 2024-T3 aluminum alloy sheets

The plastic energy dissipation before crack growth initiation and during stable crack growth was determined in centercracked thin sheet specimens of 2024-T3 aluminum alloy with different width and crack length-to-width ratios. The plastic energy dissipation rate versus stable crack growth curve was found to be approximately linear, but the slope decreased considerably with increase in crack length. No correlation was observed between plastic energy dissipation rate and the linear toughness ($\text{G}\text{?}{}_{\mathrm{c}}$), the nonlinear energy toughness ($\text{G}\text{?}{}_{\mathrm{c}}$) or the $\text{R-}\text{curve}$ toughness ($\text{G}{}_{\mathrm{R}}$). The role of net section yielding on the decrease in stable crack growth and toughness values in small specimens is discussed.     

Studies on crack growth rate under high temperature creep,fatigue and creep-fatigue interaction—II: On the role of fracture mechanics parameter aeffσg

For high temperature creep, fatigue and creep-fatigue interaction, several authors have recently attempted to express crack growth rate in terms of stress intensity factor $\text{K}{}_{\mathrm{I}}\text{= α}\text{aσ}{}_{\mathrm{g}}$, where a is the equivalent crack length as the sum of the initial notch length a₀ and the actual crack length $\text{a}{}^1$, that is, $\text{a = a}{}_0\text{+ a}{}^1$. On the other hand, it has been shown by Yokobori and Konosu that under the large scale yielding condition, the local stress distribution near the notch tip is given by the fracture mechanics parameter of $\text{aσ}{}_{\mathrm{g}}\text{?(σ}{}_{\mathrm{g}}$), where a is the cycloidal notch length, σ_g is the gross section stress and $\text{?(σ}{}_{\mathrm{g}}$) is a function of σ_g. Furthermore, when the crack growth from the initial notch is concerned, it is more reasonable to use the effective crack length a_eff taking into account of the effect of the initial notch instead of the equivalent crack length a. Thus we believe mathematical formula for the crack growth rate under high temperature creep, fatigue and creep-fatigue interaction conditions may be expressed at least in principle as function of $\text{a}{}_{\mathrm{eff}}\text{σ}{}_{\mathrm{g}}\text{, σ}{}_{\mathrm{g}}$ and temperature.In the present paper, the geometrical change of notch shape from the instant of load application was continuously observed during the tests without interruption under high temperature creep, fatigue and creep-fatigue interaction conditions. Also, the effective crack length a_eff was calculated by the finite element method for the accurate estimation of local stress distribution near the tip of the crack initiated from the initial notch root. Furthermore, experimental data on crack growth rates previously obtained are analysed in terms of the parameter of $\text{a}{}_{\mathrm{eff}}\text{σ}{}_{\mathrm{g}}$ with gross section stresses and temperatures as parameters, respectively.     

Development of the AASHTO fracture-toughness requirements for bridge steels

This paper describes the effects of temperature and strain rate on the fracture-toughness behavior of bridge steels. The test results showed the existence of a fracture-toughness transition that is an inherent material property rather than a behavior caused only by a change in the stress state. The effect of a slow loading rate, compared with impact loading rates, is to shift the fracture-toughness transition to lower temperatures. The magnitude of the temperature shift between stow loading ($\text{?≈ 10}{}^{\mathrm{?5}}\text{sec}{}^{\mathrm{?1}}$)and impact loading ($\text{/.? ≈ 10 sec}{}^{\mathrm{?1}}$) decreased with increased yield strength of the steel. The fracture-toughness behavior of bridge steels under strain rates that are encountered in actual bridge ($\text{/.? t~ 10}{}^{\mathrm{?3}}\text{sec}{}^{\mathrm{?1}}$) is closer to slow loading than to impact loading.Relationships are presented among fracture-toughness values determined by testing fracture-mechanics-type specimens, Charpy $\text{V-}\text{notch}$ (CVN) specimens, and nil-ductility-transition (NDT) specimens. Moreover, procedures are presented for using CVN impact-test results to predict $\text{K}{}_{\mathrm{IC}}$ values at slow or at moderate loading rates such as occur in actual bridges. The predicted $\text{K}{}_{\mathrm{IC}}$ values are shown to be close to those experimentally determined by testing $\text{K}{}_{\mathrm{IC}}$ specimens at various strain rates.The test results were used to develop fracture-toughness requirements for bridge steels. These toughness requirements have been approved by the Federal Highway Administration (FHWA) and by the American Association of State Highway and Transportation Officials (AASHTO) and are mandatory requirements on all Federal-aid highway programs in the United States.     

Copper doped zinc oxide Y2BaZnO5: ERS and optical investigation

In copper doped Y₂BaZnO₅ oxides, copper exhibits a distorted square pyramidal coordination which is consistant with the values of g and A tensors obtained from O band ERS spectrum for a sample containing about 1 % Cu. Three values for g and A are observed, g₁ = 2.049₅, g₂ = 2.051₅, g₃ = 2.275, $\text{¦}\text{A}{}_1\text{¦ = 13 10}{}^{\mathrm{?4}}\text{cm}{}^{\mathrm{?1}}$, $\text{¦}\text{A}{}_2\text{¦ = 10 10}{}^{\mathrm{?4}}\text{cm}{}^{\mathrm{?1}}$ and $\text{¦}\text{A}{}_3\text{¦ = 147.5 10}{}^{\mathrm{?4}}\text{cm}{}^{\mathrm{?1}}$. Since $\text{g}{}_1\text{?}\text{g}{}_2$ an approximate C_4v point symmetry can be assumed for copper. The electronic spectrum shows three bands at 11700, 14500 and 20500 cm^?1 which can be assigned to the transitions A₁ → B₁, B₂ → B₁ and E → B₁ respectively. The orbital reduction parameters are calculated and the bonding covalency is discussed.     

Crystal growth and characterization of In23PS3

Crystals of $\text{In}{}_{\mathrm{<mtext>2</mtext><mtext>3</mtext>}}\text{PS}{}_3$ were grown by chemical vapor transport of the elements from a charge zone maintained at 630°C. and a growth zone at 560°C. The crystals were characterized by chemical, x-ray, and densitometric techniques. $\text{In}{}_{\mathrm{<mtext>2</mtext><mtext>3</mtext>}}\text{PS}{}_3$ is structurally related to the M^IIPS₃ thiophosphides. The compound is an insulator and has an optical absorption edge of 3.1(1) e.V.     

An investigation of the blunting line

Experimental evidence obtained on 3-point SENB specimens of carbon steel (St52-3) is used to compare ways of determining the slope of the “blunting line” in $\text{J}{}_{\mathrm{Ic}}$ testing. The results demonstrate that the slope of the blunting line obtained by the stretched zone width (SZW) method is steeper than the blunting line predicted by the ASTM method. This results in lower values for both $\text{J}{}_{\mathrm{Ic}}$ and $\text{(Δa)}{}_{\mathrm{c}}$ as determined with the SZW method, compared with those obtained by the ASTM method. The increased conservatism compared to the ASTM approach and the experimental evidence underlying it recommend the SZW method for further study. The subsequent widespread use expected for any recognized $\text{J}{}_{\mathrm{Ic}}$ determination seems to justify the additional effort and expenses associated with the SZW method.