Representation of the displacement rate between the loading points in terms of applied stress and temperature and its relation to creep crack growth rate, C, P and Q parameters

The displacement rate between the loading points in SUS 304 stainless steel has been experimentally obtained under several applied gross stress and high temperatures, and the equation for has been obtained experimentally as a function of applied gross stress σ_g and absolute temperature T. Then, the relation of δ to creep crack growth rate da/dt was clearly shown in terms of equation. Furthermore, the relation has been clarified between the energy rate line integral C^* as affected by , and P parameter. In this way, it is clearly shown why log (da/dt) data plotted against log C^* deviates in some systematic trend with the increase of temperature and gross stress, respectively, whereas log da/dt vs the P parameter becomes exactly the same and one straight line independent of temperature and gross stress. The discussion is made on that the similar relation will hold between the evaluation by C^* and that by _gQ or by Q^*.     

Effect of temperature gradients and stress levels on damage of C/SiC composites in oxidizing atmosphere

Strain response of a C/SiC composite, which is cycled with ΔT₁ of 500 °C at 50 MPa, ΔT₂ of 400 °C at 100 MPa and ΔT₃ of 300 °C at 150 MPa, was investigated. Measured thermo-elastic strain ranges are found to retain 0.209% for ΔT₁, 0.168% for ΔT₂, and 0.122% for ΔT₃, independent upon the applied stress level. Non-linear variations of thermal cycling creep strain can reflect damage evolutions of the composites by changing its rate, which depends on temperature gradient and applied stress. After 104 thermal cycles, strength, modulus, and failure strain of the composites retain 60.29%, 84.2%, and 59% of the initial properties, respectively. The coating cracks of the cycled specimens are observed to be perpendicular to the applied stresses and arranged at relatively regular spacing, through which the fibers are oxidized superficially.     

Fatigue crack initiation and growth under mixed mode loading in aluminum alloys 2017-T3 and 7075-T6

Fatigue crack initiation and growth characteristics under mixed mode loading have been investigated on aluminum alloys 2017-T3 and 7075-T6, using a newly developed apparatus for mixed mode loading tests. In 2017-T3, the fatigue crack initiation and growth characteristics from a precrack under mixed mode loading are divided into three regions—shear mode growth, tensile mode growth and no growth—on the ΔK_I-ΔK_II plane. The shear mode growth is observed in the region expressed approximately by ΔK_II > 3MPa√m and ΔK_II/ΔK_I > 1.6. In 7075-T6, the condition of shear mode crack initiation is expressed by ΔK_II > 8 MPa√m and ΔK_II/ΔK_I > 1.6, and continuous crack growth in shear mode is observed only in the case of ΔK_I/ΔK_II, 0. The threshold condition of fatigue crack growth in tensile mode is described by the maximum tensile stress criterion, which is given by Δσ_θmax √2πr 1.6MPa√m, in both aluminum alloys. The direction of shear mode crack growth approaches the plane in which K_I decreases and K_II increases towards the maximum with crack growth. da/dN-ΔK_II relations of the curved cracks growing in shear mode under mixed mode loading agree well with the da/dN-ΔK_II relation of a straight crack under pure mode II loading.     

On the calculation of closure-free fatigue crack propagation data in monolithic metal alloys

A computational method is described for the determination of ΔK_b, corresponding to a fatigue crack growth rate of b/cyc, where b is the Burgers vector for a monolithic metal alloy. ΔK_b is found to be numerically equal to E√b for the case of closure-free crack growth behavior. Given that the closure-free FCP rate of many monolithic metals varies with ΔK³, the growth rate of metal alloys at ΔK ΔK_b is given by da/dN = (ΔK/E)³(1/√b. Excellent agreement is found between experimental and computed FCP data for the case of monolithic metal alloys. The limits of these relations for metal-matrix composites and ceramics are discussed.     

The use of ΔK when examining microstructural effects on small fatigue crack growth

The behaviour of small fatigue cracks has been studied in the Al---Li---Cu---Mg---Zr alloy 8090. It was found that the crack inclination normal to the surface of the specimen made crack deflections and kinking in the plane of the specimen surface irrelevant to the crack driving force. The low closure levels associated with small fatigue cracks reduce the effect of microstructure on crack growth but this does not affect the ability of ΔK (stress intensity factor range) to detect microstructural influences. The use of ΔJ (J-integral range) as a correlating parameter reduced the differences between the data for long and short fatigue cracks. However, there was no evidence that ΔJ was superior at identifying microstructural effects. Similarly the effect of the higher-order terms on the value of ΔK was found to be minor. It is concluded that the use of ΔK is not likely to bias the microstructural effects and so ΔK may be used when examining microstructural effects on small fatigue crack growth.     

Influence of R on effective stress range ratio and crack growth

The influence of stress ratio R and stress intensity range ΔK on crack closure and fatigue crack growth were studied. Crack closure and crack growth experiments were performed on 6063-T6 Al alloy. Crack closure stresses were measured using a surface-measurement technique with a COD gauge. The gauge was placed at different locations behind the crack tip, and it was found that the location of the gauge does not influence the closure load. The closure load was however found to be a function of R and ΔK. Fatigue crack growth rate is found to depend upon R, U and ΔK. A model for both U and da/dN has been developed.     

Crack growth resistance characterized by the strain energy density function

Stable ductile fracture of a typical metal alloy is found to be governed by the condition dS/da = const., i.e. the rate change of the strain energy density S with crack length 2a (or a) remained constant. Since fracture and/or yielding are load rate dependent, the incremental theory of plasticity is employed for analyzing crack growth where unloading in the material near the crack can take place. Attention is focused on the energy per unit volume, dW/dV, stored along the prospective path of crack growth. The nearest neighbor continuum element must necessarily be at a finite distance r from the crack front. This leads to the general relation dW/dV = S/R. The critical value (dW/dV)_c representing the area under the uniaxial true stress and strain curve is assumed to correspond with failure of material elements. If yielding and unloading occurred locally, a certain amount of irrecoverable energy will not be available for dissipation during macrocracking. Hence, the threshold energy density must be modified to read as (dW/dV)_c^* < (dW/dV)_c. The quantity (dW/dV)_c may be regarded as the crack growth resistance whose magnitude decreases with increasing distance from the crack tip at which point yielding is most intensified.

The results are displayed graphically and shown that the condition dS/da = const. provides a rational means of collating and interpreting ductile fracture data.     

A model for predicting fatigue crack growth behaviour of a low alloy steel at low temperatures

In the present study, a model to predict the fatigue crack growth (FCG) behaviour at low temperatures is proposed for a low alloy steel (16 Mn). The experimental results indicate that fatigue ductile-brittle transition (FDBT) occurs in 16 Mn steel and the FDBT temperature (T_FDBT) is about 130 K. When T > T_FDBT, the FCG mechanism in the intermediate region is the formation of ductile striation and the FCG rates decrease with decreasing temperature. When T ≈ T_FDBT, the FCG mechanism changes into microcleavage and the fatigue fracture toughness K_fc of the steel decreases sharply. The FCG rates tend to increase as the temperature is further reduced. The test data of the FCG rates are well fitted by the formula developed by Zheng and Hirt. An approximate method to predict ΔK_th of the steel at low temperatures is proposed and then a general expression of the FCG rates is given at temperatures ranging from room temperature to T_FDBT. By means of the expressions proposed in this paper, the FCG rates at low temperatures can be predicted from the tensile properties if the endurance limit σ₋₁ and δk_th, at room temperature are known. Finally, a model for FDBT is tentatively proposed. Using this model, one can predict T_FDBT from the ductile-brittle transition curve determined from impact or slow bending tests of cracked Charpy specimens.     

Fatigue crack growth characteristics of rotor steels

Room temperature fatigue crack growth rate data were generated for Ni-Mo-V (ASTM A469, Cl-4), Cr-Mo-V (ASTM A470, Cl-8) and Ni-Cr-Mo-V (ASTM A471, Cl-4 and a 156,000 psi yield strength grade) rotor forging steels. Testing was conducted with WOL type compact toughness specimens and the results presented in terms of fracture mechanics parameters. Data show that the Ni-Cr-Mo-V steels exhibit slower fatigue crack growth rates at a given stress intensity range (ΔK) than do the Ni-Mo-V steels. In addition, the Cr-Mo-V steel was found to exhibit slower growth rates than the other alloys at ΔK levels below 40 ksi √in but somewhat foster rates at ΔK levels in excess of 45 ksi √in. The fatigue crack growth rate properties of the alloys studied conform to the generalized fracture mechanics crack growth rate law where da/dN = C₀ΔK^R. It was noted that the fatigue crack growth rate parameters n and C₀ tend to decrease and increase, respectively, with increasing material toughness, K_ic.     

Evaluation of fatigue crack growth behavior of GLARE3 fiber/metal laminates using a compliance method

The objectives of this study were to investigate the effectiveness of a compliance method for analyzing the fatigue crack growth of GLARE3 fiber/metal laminates. The materials tested were GLARE3-5/4 (2.6 mm thick) and GLARE3-3/2 (1.4 mm thick). Centrally notched specimens with two kinds of notch length and two kinds of fiber orientation were fatigue tested under constant amplitude loading. The expression of the experimental stress intensity factor, K_exp, for the 2024-T3 aluminum-alloy layers of a GLARE3 is formulated and K_exp were obtained from the relationship between crack length and specimen compliance. The test results clarified the following: (1) da/dN–ΔK_exp relationships roughly show the linear relationship independent of the maximum stress level, specimen thickness, notch length, and fiber orientations, (2) the da/dN–ΔK_exp relationships approximately agree with the linear part and its extension of Paris–Erdogan’s law obtained for the da/dN–ΔK relationship of the 2024-T3 aluminum-alloy, (3) the compliance method is effective for analyzing fatigue crack growth in GLARE3 laminates.     

The growth of fatigue cracks through particulate sic reinforced aluminum alloys

Crack growth rates for large fatigue cracks in 12 variations of particulate silicon carbide reinforced aluminum alloy composites have been measured. Composites with seven different matrix alloys were tested, four of which were of precipitation hardening compositions, and those were tested in both as-extruded and peak aged conditions. Five of the materials were made by casting, ingot metallurgical methods and two of the alloys by mechanical alloying, powder metallurgical methods. For both manufacturing methods, primary fabrication was followed by hot extrusion. The fatigue crack growth curves exhibited an approximately linear, or Paris law, region, fitting the function da/dN = BΔK^s, and a threshold stress intensity factor, ΔK_th. As has been found for other materials, the coefficients B and s are correlated; for these composites In B= −16.4−2.1s. A correlation was also found between ΔK_th and s, and it was found possible to compute the magnitude of ΔK_th using a simple model for the threshold together with yield stress and SiC size and volume fraction. These results were explained using a relationship between ΔK_th and crack closure determined previously for unreinforced aluminum alloys. The path of fatigue crack growth is through the matrix for these composites, and SiC has the effect of altering the slip distance, therefore, the plasticity accompanying fatigue cracks. It was shown that all the crack growth rate curves were reduced to one equation having the form da/dN = B'ΔK_eff^s' where B' = 6.5 × 10^-9m/cy and s' = 1.7. A partly theoretical method for predicting fatigue crack growth rates for untested composites is given. Fatigue crack surface roughness was measured and found to be described by a fractal dimension, but no correlation could be obtained between surface roughness parameters and ΔK_th.     

Fatigue crack-growth characteristics of two magnesium alloys

Magnesium alloys are being increasingly used for engineering applications. Fatigue crack-growth data have therefore been obtained for a high strength magnesium-Zr alloy and a medium strength, weldable magnesium-Mn alloy. The results of tests on sheet material are presented in terms of the range of stress intensity factor ΔK. Critical values of ΔK necessary for fatigue crack growth ΔK_c were also obtained. The behaviour of the two alloys was similar; both rates of crack growth and ΔK_c were sensitive to mean stress. Fatigue crack growth was entirely on a 90° plane with no sign of the transition to crack growth or 45° planes usually observed in sheet materials. This was ascribed to the effects of preferred orientation of the crystal structure.     

Study of crack tip opening under cyclic loading taking into account the environment and R ratio

This study involves the R effect and environment effect on crack closure mode, in 7175 T 651 aluminium alloy. To obtain one of the selected objectives, it was necessary to use a clip gauge located at the notch of the compact specimen and a C.T.O.D. gauge located at the crack tip. The crack opening phenomena observed in our tests depends on the applied method which accounts for the differences in ΔK_eff found in the literature. The systematic use of the two methods allowed us to bring to light common features permitting the calculation of ΔK_eff according to Elber's criteria. The concept of ΔK_eff does not fully explain the influence of R ratio and the environment effect.     

A higher-order approximation for the T-criterion of fracture in biaxial fields

The T-criterion of fracture is based on the principle that crack propagates when the maximum value of the distribution of the dilatational component of strain energy density T_v, evaluated along contour lines of constant distortional energy density T_D around the crack tip, attains a limiting value T_vo The angle of this maximum defines also the direction of initiation of crack propagation. Then, the study of the distribution of T_v around the crack tip presents a special interest for understanding mechanisms of fracture.

In this investigation an exhaustive theoretical analysis of the distribution of t_v-component around the tip of crack under in-plane modes of loading was undertaken. The T_v-distribution was evaluated along the elastic-plastic boundary, developed around the crack tip for impending plasticity, according to the Mises yield condition (T_D = T_D0 = const.). The mode of loading of the cracked plate was assumed biaxial with different biaxiality ratios k and a two-term approximation for the respective complex stress function was considered, according to the studies of Liebowitz et al.[1], instead of only the singular term considered up-to-now.

It was found that the T_v-distribution along the Mises initial elastic-plastic boundary presents always a maximum in front of the crack tip, whose position and magnitude depend on the biaxiality factor k and the angle of loading β. The position and the magnitude of this maximum for the two-term approximation of φ(z) showed differences in some regions with the respective values for the singular solution.     

Threshold range and opening stress intensity factor in fatigue

The fatigue threshold, ΔK_th, is strongly influenced by the stress-ratio, ie by the loading conditions. Results for a Ti6A14V alloy show that a ΔK exists for non-propagating fatigue cracks which is independent of loading conditions. This ΔK is called the fatigue tolerance range and is denoted by ΔK^K. The fatigue tolerance range corresponds to that part of the ΔK_th during which the fatigue crack is open. Arguments that the fatigue tolerance range has to be explicitly incorporated in equations predicting fatigue crack growth rates are presented.     

Statistical evaluation of fatigue crack propagation properties including threshold stress intensity factor

The relationship between fatigue crack propagation rate, da/dn, and range of stress intensity factor, ΔK, including threshold stress intensity factor, ΔK_th, is analyzed statistically. A non-linear equation, da/dn = C{(ΔK)^m-(ΔK_th)^m}, is fitted to the data by regression method to evaluate the 99% confidence intervals. Several experimental results on fatigue crack propagation properties of welded joints are compared by using these confidence intervals.     

Finite element analysis of an interface crack with large crack-tip contact zones

There is considerable ambiguity regarding the limiting values of the strain energy release rate (SERR) components at the tips of a crack lying along the interface between two dissimilar isotropic media. In this paper this aspect is examined using finite element analysis and Modified Crack Closure Integral (MCCI) for a problem in which the material properties are chosen so as to cause a large size crack-tip contact zone. By careful choice of this problem, interpenetration of the crack faces in the crack-tip contact zones is observed for the first time in the finite element analysis. Earlier solutions primarily on remote mode 1 loading reported that SERR components do not converge as the virtual crack extension Δa → 0 and that these components show an oscillatory nature when Δa is less than the contact zone size r_c. In the present work, multipoint constraints are imposed on crack face normal displacements in the contact zone and meaningful results are generated for both remote tension and shear loading cases. The apparent nonconvergence of the SERR components as Δa → 0 can be explained if these components are considered as functions of Δa, and Δa is considered as the actual crack growth step size.     

The effect of the stress ratio on fatigue crack growth in a 3% NaCl solution

Corrosion fatigue crack growth tests have been carried out at various stress ratios for a low alloy steel SNCM 2 and type 304 stainless steel.

Measurements of the effective stress intensity factor range ratio U were performed to explain the effect of stress ratio R.

The corrosive environment decreased da/dN at R = 0.1, 0.4 and little affected da/dN at R = 0.9 for SNCM 2 and increased da/dN at all R ratios for SUS 304.

It was confirmed that there exists a threshold stress intensity factor ΔK_thCF in 3% NaCl solution for both materials tested.

The corrosive environment decreased ΔK_thCF for all conditions tested except at R = 0.1 and 0.4 for SNCM 2, where ΔK_thCF-values were nearly equal to ΔK_th-values in air. ΔK_thCF/ΔK_th was 0.6 at R = 0.9 for SNCM 2 and 0.8, 0.5 and 0.7 at R = 0.1, 0.7 and 0.9 for SUS 304, respectively.

It was shown that the complicated effect of stress ratios on crack growth for SNCM 2 can be explained using effective stress intensity factor ΔK_eff.     

First principles calculations of thermal equations of state and thermodynamical properties of MgH2 at finite temperatures

We present the first principles calculations of the thermodynamical properties of magnesium hydride (MgH₂) over a temperature range of 0–1000 K. The phonon dispersions are determined within the density functional framework and are used to calculate the free energy of MgH₂ within the quasiharmonic approximation (QHA) at each cell volume and temperature T. Using the free energies the thermal equation of state (EOS) is derived at several temperatures. From the thermal EOS structural parameters such as the equilibrium cell volume (V₀) and elastic properties, namely, bulk modulus (K₀) and its pressure derivative are computed. The free energies are also used to calculate various thermodynamical properties within QHA. These include internal energy E, entropy S, specific heat capacity at constant pressure C_P, thermal pressure P_thermal(V, T) and volume thermal expansion ΔV/V (%). The good agreement of calculated values of S and C_P with experimental data exhibits that QHA can be used as a tool for calculating the thermodynamical properties of MgH₂ over a wide temperature range. P_thermal(V,T) increases strongly with T at all the volumes but it is a slowly varying function of volume for T = 298–500 K. According to Karki [B.B. Karki, Am. Miner. 85 (2000) 1447] such volume based variations can be neglected and so it is possible to estimate the thermal EOS only with the knowledge of the measured P_thermal(V, T) versus temperature at ambient pressure and isothermal compression data at ambient temperature. Temperature dependence of ΔV/V(%) shows that V₀ increased with increase in temperature. However, the percentage decrease in K₀ superseded this percentage increase in V₀ even at temperatures moderately higher than 298 K. Therefore, we suggest application of temperature (T > 298 K) as an approach to enhance the hydrogen storage capacity of MgH₂ because of its better compressibility at these temperatures.     

Polar nanodomains and relaxor behaviour in (1 − x)Pb(Mg1/3Nb2/3)O3–xPbTiO3 crystals with x = 0.3–0.5

Phase transitions and dielectric properties of the (1 − x)Pb(Mg_1/3Nb_2/3)O₃–xPbTiO₃ crystals with x = 0.3–0.5 are studied. The solid solutions in this composition range are shown to be relaxor ferroelectrics. The crystals with low x demonstrate a diffused maximum in the temperature dependences of the dielectric permittivity at T_m. T_m varies with frequency according to the Vogel–Fulcher law. The polarizing microscopy investigations reveal a first-order phase transition from the relaxor phase to the low-temperature ferroelectric phase at T_C, which is several degrees below T_m. The permittivity peak in the crystals with x = 0.5 is sharp, and T_m is equal to T_C and does not depend on frequency, as is typical of the transition from a ferroelectric to an ordinary paraelectric phase. Nevertheless, the relaxor, but not the paraelectric, phase is observed at T > T_m. This conclusion is confirmed by the observation of the temperature behaviour of complex dielectric permittivity at T > T_m, which is typical of relaxors and related to the existence of polar nanodomains.