On the influence of rubbing fracture surfaces on fatigue crack propagation in mode III

Fatigue crack growth has been studied under fully reversed torsional loading (R = ?1) using AISI 4340 steel, quenched and tempered at 200°, 400° and 650°C. Only at high stress intensity ranges and short crack lengths are all specimens characterized by a microscopically flat Mode III (anti-plane shear) fracture surface. At lower stress intensities and larger crack lengths, fracture surfaces show a local hill-and-valley morphology with Mode I, 45° branch cracks. Since such surfaces are in sliding contact, friction, abrasion and mutual support of parts of the surface can occur readily during Mode III crack advance. Without significant axial loads superimposed on the torsional loading to minimize this interference, Mode III crack growth rates cannot be uniquely characterized by driving force parameters, such as ΔK_III and ΔCTD_III, computed from applied loads and crack length values. However, for short crack lengths (?0.4 mm), where such crack surface interference is minimal in this steel, it is found that the crack growth rate per cycle in Mode III is only a factor of four smaller than equivalent behaviour in Mode I, for the 650°C temper at $\text{ΔK}{}_{\mathrm{III}}\text{= 45 MPa m}\text{1}\text{2}$.     

The strain intensity criterion for crack branching in ceramics

Using a fracture mechanics method, crack branching data from three investigations were put on a comparable basis and used to demonstrate a strong correlation between the stress intensity at crack branching and Young's modulus. This strong correlation suggests a strain intensity criterion for crack branching at sharp cracks in brittle materials fractured at room temperature. Crack branching in 20 ceramics and glasses occurs at a strain intensity close to $\text{3.3 × 10}{}^{\mathrm{?5}}\text{m}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$.     

Fatigue crack propagation from a crack inclined to the cyclic tensile axis

Cyclic stresses with stress ratio R = 0.65 were applied to sheet specimens of aluminium which have an initial crack inclined to the tensile axis at angles of 30°, 45°, 72° or 90°. The threshold condition for the non-propagation of the initial crack was found to be given by a quadratic form of the ranges of the stress intensity factors of modes I and II. The direction of fatigue crack extension from the inclined crack was roughly perpendicular to the tensile axis at stress ranges just above the threshold value for non-propagation. On the other hand, at stress ranges 1.6 times higher than the threshold values the crack grew in the direction of the initial crack. The rate of crack growth in the initial crack direction was found to be expressed by the following function of stress intensity factor ranges of mode I, K₁, and mode II, K₂: $\text{dc}\text{dN}\text{= C(K}{}_{\mathrm{eff}}\text{)sum}$, where $\text{K}{}_{\mathrm{eff}}\text{= [K}{}_1{}^4\text{+ 8K}{}_2{}^4\text{]}{}^{\mathrm{<mtext>1</mtext><mtext>4</mtext>}}$. This law was derived on the basis of the fatigue crack propagation model proposed by Weertman.     

Condition for stable growth of branched cracks

In order to clarify the reason why the stable growth of branched cracks occurs in delayed failure, while not in other subcritical crack propagation process such as fatigue, the stress intensity factor after crack branching in delayed failure was dropped to various values, and the propagation behavior of both cracks was investigated.The well balanced growth of branched cracks in delayed failure occurs only when the crack propagation velocity after crack branching belongs to the region II where the crack propagation velocity is constant independently of $\text{K}$. The fatigue cracks at the tips of artificially branched cracks, on the other hand, can not propagate stably, and only either crack propagates preferentially.The exponent in the crack propagation law ($\text{d}\text{a/}\text{d}\text{t =}\text{c}{}_1\text{K}{}^{\mathrm{<mtext>m</mtext>}}\text{or}\text{d}\text{a/}\text{d}\text{N =}\text{c}{}_2\text{(ΔK)}{}^{\mathrm{<mtext>m</mtext>}}$) expresses the degree of unbalance growth of branched cracks. The stable growth of branched cracks occurs only when the crack propagation velocity is constant independently of $\text{K}$ or $\text{ΔK}$, i.e. $\text{m}\text{= 0}$.     

A cumulative model of fatigue crack growth

A model of fatigue crack growth based on an analysis of elastic/plastic stress and strain at the crack tip is presented. It is shown that the fatigue crack growth rate can be calculated by means of the local stress/strain at the crack tip. The local stress and strain calculations are based on the general solutions given by Hutchinson, Rice and Rosengren. It is assumed that a small highly strained area existing at the crack tip is responsible for the fatigue crack growth. It is also assumed that the fatigue crack growth rate depends mainly on the width, x¹, of the highly strained zone and on the strain range, $\text{Δ?}{}^1$, within the zone. A relationship between stress intensity factor K and the local strain and stress has been developed. It is possible to calculate the local strain for a variety of crack problems. Then, the number of cycles N¹ required for material failure inside the highly strained zone is calculated. The fatigue crack growth rate is calculated as the ratio $\text{x}{}^1\text{N}{}^1$.The calculated fatigue crack growth rates were compared to the experimental ones. Two alloys steels and two aluminium alloys were analyzed. Good agreement between experimental and theoretical results is obtained.     

Growth of fatigue cracks in metals and polymers

Empirical data on the propagation of tensile fatigue cracks in metals and thermoplastics have been examined. It was found that a cyclic crack propagation relationship, based on the stress intensity factor concept, exists which can be successfully utilised for both types of materials.The proposed equation has a form $\text{/.a}{}_{\mathrm{x}}\text{= MA}{}^{\mathrm{n}}$ where $\text{A}$ is a function of$\text{ΔK}$ and mean $\text{K}$. The analysis of results suggests that this equation incorporating the influence of mean stress intensity factor provides an excellent fit to the investigated data. The possible modified forms of such a relationship in terms of strain energy release rate, the crack tip yielding and the crack opening displacement concepts are also indicated.     

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.     

The effect of temperature and R ratio on fatigue crack growth in A612 grade B steel

Fatigue-crack propagation rates in ASTM$\text{A612}$ Grade B steel were investigated at room temperature and ?100°F (?73°C) with $\text{R}\text{ratio}\text{= ?0.1}\text{and}\text{+0.67}$. The data were evaluated in terms of the crack propagation rates ($\text{d}\text{a/}\text{d}\text{N}$) as a function of the alternating stress intensition ($\text{ΔK}$), according to $\text{d}\text{a/}\text{d}\text{N = e+(v ? e)(? 1}\text{n}\text{(1 ?}\text{Δ}\text{K/K}{}_{\mathrm{b}}\text{))}{}^{\mathrm{t/k}}$. It was found that crack growth rates were increased due to increasing $\text{R}$ ratio. Also the dependence of crack growth rates on $\text{R}$ ratio is strongest at the lowest crack growth rates where a $\text{ΔK}$ fatigue threshold is established. Crack growth rates were decreased due to decreasing test temperature in the slow crack growth region. However, it was found that crack growth rates were increased due to decreasing test temperature in the fast crack growth region near the upper instability asymptote. Decreased test temperature and increased $\text{R}$ ratio interact synergistically to increase crack growth rates for the entire range of $\text{ΔK}$.     

An analysis of reported fatigue crack growth rate data with special reference to Ti-6A1-4V

A review of the published literature on fatigue crack growth suggests that power-law growth in Ti-6A1-4V is sensitive to microstnictural changes which result in variations in the fatigue mechanism. Microstnictures which promote secondary cracking along α/β interfaces display slow growth rates while microstructures which promote dimpled rupture display fast growth rates. Examples of similar effects are found in other alloy systems.Typically, the power-law growth are found in other alloy systems. It is also suggested that the power-law regime begins at $\text{ΔK ～- 13 MNm}{}^{\mathrm{<mtext>?</mtext><mtext>case3</mtext><mtext>2</mtext>}}$, coinciding with the lower limit of striation formation on the fracture surface. The upper limit occurs at about $\text{K}{}_{\max }\text{= 1/2K}{}_{\mathrm{c}}$. At higher growth rates, the Forman equation appears to be adequate.The normalized stress intensity factor, $\text{ΔK/E}$, required to produce a given growth rate in Ti-6A1-4V is on the order of that for other Ti-base alloys, ferritic steels, martensitic steels and aluminum alloys. Austenitic steels, which deform by planar slip are much more resistant to crack growth over much of the stress intensity range normally encountered.     

An examination of mixed fatigue-tensile surface crack growth in rails

The fracture instability associated with alternating periods of fatigue and tensile growth of surface cracks was investigated in steel rails. Three different steels were tested. The instabilities commenced when the maximum stress intensity factor $\text{K}$ exceeded the fracture toughness $\text{K}{}_{\mathrm{IC}}$ and resulted in crack jump or total rail failure. The conditions for the establishment of fatigue-tensile crack jump and arrest are described. The load level, residual stresses, crack geometry and fracture toughness effects are analysed. The fatigue surface cracks were penetrated in both stress relieved and stress unrelieved rails. The effective stress intensity factors including the contribution of the applied load and residual stresses were calculated. For both the fatigue-tensile and tensile-fatigue transitions the stress intensity factors were almost the same with the value for the tensile-fatigue transition being slightly lower. Both calculated stress intensity factors were close to the fracture toughness $\text{K}{}_{\mathrm{IC}}$.     

A cumulative model of fatigue crack growth and the crack closure effect

A model of fatigue crack growth based on an analysis of elastic/plastic stress and strain at the crack tip is presented. It is shown that the fatigue crack growth rate can be calculated using the local stress/strain at the crack tip by assuming that a small highly strained area $\text{x}{}^1$, existing at the crack tip, is responsible for the fatigue crack growth, and that the fatigue crack growth may be regarded as the cumulation of successive crack re-initiations over a distance $\text{x}{}^1$. It is shown that crack closure can be modelled using the effective contact zone g behind the crack tip. The model allows the fatigue crack growth rate over the near threshold and linear ranges of the general da/dN versus ΔK curve to be calculated. The fatigue crack growth retardation due to overload and fatigue crack arrest can also be analysed in terms of g and $\text{x}{}^1$.Calculated fatigue crack growth rates are compared with experimental ones for low and high strength steel.     

Creep of mild steel at low temperatures

Creep data for mild steel at low temperatures (360–400°C) have been analysed and it has been found that the creep behaviour is similar to that at higher temperatures. The variation of secondary creep rate with stress and temperature, in the temperature range (360–538°C) may be described by two equations with a transition stress. This transition stress is 410 MPa at 360°C. For low stresses the creep equation is given by $\text{ε}{}_{\mathrm{<mtext>s</mtext>}}\text{= 250 σ}{}^{3.7}\text{exp}\text{{?(2.17 × 10}{}^5\text{/}\text{RT}\text{)}}$. Material response to stress is highly dependent on the amount of cold work; secondary creep rate decreases with increasing prior deformation.     

Fracture toughness and fatigue crack propagation in high strength steel from room temperature to −180°c

Fracture toughness under tensile test and fatigue test on high strength steel at temperature ranging from room temperature to ?180°C were experimentally studied. The value of fracture toughness under fatigue test is considerably tower than that obtained under tensile test.Within the range from room temperature to ?100°C the following results were obtained: the power coefficient δ of the fatigue crack propagation rate $\text{[(dc)/(dN)] = AΔK}{}^5$ is related with [(1)/($\text{T}$)] as: $\text{δ = b}{}_1\text{+ [(a}{}_1\text{)/(kT)]}$. $\text{[(dc)/(dN)]}$ shows Arrhenius type, and, however, different equation from usual stress dependent rate process equation. The trend is in good agreement with the dislocation dynamics theory of fatigue crack propagation.     

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.     

Prediction of threshold and ultra-low fatigue crack growth rates

A model was derived to predict the true threshold value for fatigue crack growth in the absence of crack closure. The model, based only on the tensile and cyclic properties of the material, was successfully verified against a set of experimental data on medium and high strength steels and one aluminium alloy. Good agreement with experimental results was also obtained for Region I of the $\text{d}\text{a/}\text{d}\text{N vs ΔK}$ curve using a fatigue crack growth rate equation based on the same model.Fatigue crack growth data obtained from the medium strength steel CK45 in the normalized state and two heat-treated conditions were analysed. Good data correlation was shown using a previously developed normalizing parameter, $\text{φ = (ΔK}{}^2\text{?ΔK}{}^2{}_{\mathrm{<mtext>th</mtext>}}\text{)/(K}{}^2{}_{\mathrm{<mtext>c</mtext>}}\text{?K}{}^2{}_{\mathrm{<mtext>max</mtext>}}\text{)}$, in the entire range of fatigue crack growth rates and for stress ratios ranging from 0.1 to 0.8.     

Fatigue crack growth rate under full yielding condition for 15CDV6 steel

Strain fatigue crack growth rate was studied using center cracked specimens for 15CDV6 steel tempered at 200°C after quenching by means of the method which deflections were controlled to a sloping load vs deflection line. Cyclic $\text{J-}\text{integral}$ values estimated from load vs deflection hysteresis loops are correlated with the growth rate. The relationship between them can be expressed by a simple power function $\text{da/dN = 2.5 × 10}{}^{\mathrm{?4}}\text{(ΔJ)}{}^{1.38}$ The plastic portion Δ$\text{J}{}_{\mathrm{p}}$ in $\text{J-}\text{integral}$ is exponentially increased as the deflection increases, while the peak value of the elastic portion Δ$\text{J}{}_{\mathrm{e}}$ appears as the deflection varies. These relations may provide a convenient way to use $\text{J-}\text{integral}$ in engineering practice. A concept is proposed that “high strain rate induces cleavage”. The critical value of the strain rate for the steel tested is 10^?4/sec. If the strain rate is higher than this value, cleavage predominates on the fracture surface. On the other hand, if it is lower than this value, dimples will prevail.     

An experimental study of crack tip plastic flow in mild steel

The paper deals with an experimental study on the nature of plastic flow at the root of a crack in mild steel beams, for the non-valid $\text{K}{}_{\mathrm{IC}}$ test regime, under three point hending loads. Photoelastic coating technique has been used to measure the plasticity spread ahead of the tip in relation to the load-COD record. It is observed that in all cases there is a sudden increase in specimen compliance near the maximum linear load due to an abrupt increase in plastic zone size on some preferential planes ahead of the crack tip. This abrupt increase in plastic flow was seen to occur along the 45° planes (with respect to the plane of the crack) for thicker beams and/or with longer cracks. In contrast, the plastic zone extended more on the plane of the crack for thin section beams with relatively shorter cracks. The stress intensity factor required to cause this sudden loss of resistance to localized deformation is found to be remaining constant beyond a certain crack length for a given specimen thickness. These observations suggest that a critical stress intensity factor () concept can be introduced to describe the abrupt flow localization ahead of the crack tip. This () can be taken as a new parameter in addition to those commonly used in characterising the overall “fracture” behaviour of large scale yielding materials like mild steel, especially in the non-valid $\text{K}{}_{\mathrm{IC}}$ test regime.     

Liquid phase epitaxial growth of gallium arsenide on an etched substrate

A method is described for etching the surface of GaAs substrates with a Ga solution $\text{in}$$\text{situ}$ immediately prior to epitaxial layer growth from the liquid phase. Layers grown by this procedure show excellent surface morphologies and electrical properties ($\text{μ～5100}\text{cm}{}^2\text{v-sec}$ at 300°K for $\text{n～ 7.8×10}{}^{16}\text{cm}{}^3$). Advantages of the method and its applicability to epitaxial growth of other III-V compounds are 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.     

Etude des proprietes structurales et electrioues d'un nouveau conducteur anionique: PbSnF4

Three allotropic varieties of PbSnF₄ - α, β and γ - have been detected by DTA and X-ray diffraction. The α ai β and β ai γ transitions are reversible and occur at 80 and 355°C respectively. The high temperature form γ - PbSnF₄ is cubic and of fluorite type. The structures of the tetragonal β - PbSnF₄ and the orthorhombic α - PbSnF₄ forms are derived from the same structural type. PbSnF₄ has a high anionic conductivity ($\text{σ200°C ? 10}{}^{\mathrm{?1}}\text{Ω}{}^{\mathrm{?1}}\text{cm}{}^{\mathrm{?1}}$). The temperature dependence of the conductivity indicates the existence of a break in the activation energy at 90°C.