A numerical model for calculation of stress intensity factors in particle-reinforced metal–matrix composites

A two-dimensional finite element model was developed to study effects of particle diameter, mechanical properties of the fiber and matrix materials and loading conditions (Mode 1 and Mixed-Mode). A theoretical model was proposed to calculate the stress intensity factor for an interface crack in Particle-Reinforced Metal–Matrix Composites. The displacement Correlation Method was used to calculate the stress intensity factors K ₁ and K ₂. In the present model the fiber and matrix materials were modeled in linear elastic conditions. The interface crack was considered between the fiber and matrix, without the presence of the interphase. Obtained results show that the key role on the stress intensity factors played by the relative elastic properties of the fiber and matrix. The results also show that K ₁ and absolute K ₂ values increase for both Mode 1 and mixed-mode loading condition once Young’s modulus of the fiber material increases. The values of K ₁ and K ₂ stress intensity factors decrease when the fiber volume fraction increases for Mode 1 loading.     

Effect of the chemical composition of welds of pipelines on their resistance to crack propagation in hydrogen-sulfide environments

We investigate the influence of the chemical composition of a weld metal on the long-term crack resistance under static loading in NACE hydrogen-sulfide solution. The effect of C, S, P. Mn, Si, Ni, Cu, V, Zr, Co, B, and Mo on corrosion-mechanical properties of welds is established. Welds containing about 0.11–0.14% C are shown to have the highest crack resistance. The optimum concentrations of manganese (∼0.6%) and silicon (∼0.3%), at which the maximum values ofK _1ssc are obtained, are found. The admissible manganese and silicon contents are 0.39–1.0% and 0.2−0.5%, respectively. The susceptibility to cracking increases with sulfur and phosphorus contents. The highest values ofK _1ssc were obtained at a sulfur content of 0.004 to 0.014% and at a phosphorus content of 0.014 to 0.023%. The adverse influence of these elements in welds is manifested to a lesser extent than in the rolled metal. Alloying with boron is inexpedient and dangerous. Joint alloying with 0.4–0.54% Cu and 0.1–0.3% Ni improves the crack resistance. The influence of molybdenum is analogous (K _1ssc increases by 29–50%). Alloying with 0.5% Co and 0.05% Zr results in the formation of nonequilibrium structures. In this case,K _1ssc is close to those of welds made with carbon steel electrodes. On alloying with 0.2% V, the fine structure forms, andK _1ssc decreases by 20–30%. Alloying with vanadium in these amounts is inadmissible. Preference should be given to complex microalloying. Karpenko Physicomechanical Institute, Ukrainian Academy of Sciences, L'viv. Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 35, No. 1, pp. 95–102, January–February, 1999.     

Crack significance evaluation with special reference to welded structures

Fracture mechanics parameters (stress intensity factorK _I and its critical valueK _Ic , crack opening displacement, and the contourJ integral) are originally defined for static and quasistatic loading conditions. On the basis of theoretical background, standard test methods for the experimental determination of their specific values were developed. Structural integrity analysis requires the extension of application of these parameters to other types of loading. We propose new parameters for stress corrosion (stress corrosion cracking thresholdK _1sco ), for cyclic loading (stress intensity factor range ΔK and fatigue threshold ΔK _th), and for creeping at elevated temperatures (C ^* andC _t integrals). The structural integrity of welded structures is mainly affected by cracks in welded joints. We demonstrate the practical application of fracture mechanics parameters to the evaluation of structural integrity under the above-mentioned loading conditions. Faculty of Technology and Metallurgy, University of Belgrade, Yugoslavia. Faculty of Mechanical Engineering, University of Belgrade, Yugoslavia. Published in Fizyko-Khimichna Mekhanika Materialiv, Vol. 32, No. 2, pp. 107–118, March–April, 1996.     

A Study of Specific Heat Capacity Functions of Polyvinyl Alcohol–<Emphasis Type="Italic">Cassava</Emphasis> Starch Blends

The specific heat capacity (C _sp) of polyvinyl alcohol (PVOH) blends with cassava starch (CSS) was studied by the differential scanning calorimetry method. Specimens of PVOH–CSS blends: PPV37 (70 mass% CSS) and PPV46 (60 mass% CSS) were prepared by a melt blending method with glycerol added as a plasticizer. The results showed that the specific heat capacity of PPV37 and PPV46 at temperatures from 330 K to 530 K increased from (2.963 to 14.995)  J· g⁻¹ · K⁻¹ and (2.517 to 14.727)  J · g⁻¹· K⁻¹, respectively. The specific heat capacity of PVOH–CSS depends on the amount of starch. The specific heat capacity of the specimens can be approximated by polynomial equations with a curve fitting regression > 0.992. For instance, the specific heat capacity (in J · g⁻¹ · K⁻¹) of PPV37 can be expressed by C _sp = −17.824 + 0.063T and PPV46 by C _sp = −18.047 + 0.061T, where T is the temperature (in K).     

Prototype evaluation of transformation toughened blast resistant naval hull steels: Part II

Application of a systems approach to computational materials design led to the theoretical design of a transformation toughened ultratough high-strength plate steel for blast-resistant naval hull applications. A first prototype alloy has achieved property goals motivated by projected naval hull applications requiring extreme fracture toughness (C _v > 85 ft-lbs or 115 J corresponding to K _Id≥ 200 ksi.in^1/2 or 220 MPa.m^1/2) at strength levels of 150–180 ksi (1,030–1,240 MPa) yield strength in weldable, formable plate steels. A continuous casting process was simulated by slab casting the prototype alloy as a 1.75′′ (4.45 cm) plate. Consistent with predictions, compositional banding in the plate was limited to an amplitude of 6–7.5 wt% Ni and 3.5–5 wt% Cu. Examination of the oxide scale showed no evidence of hot shortness in the alloy during hot working. Isothermal transformation kinetics measurements demonstrated achievement of 50% bainite in 4 min at 360 °C. Hardness and tensile tests confirmed predicted precipitation strengthening behavior in quench and tempered material. Multi-step tempering conditions were employed to achieve the optimal austenite stability resulting in significant increase of impact toughness to 130 ft-lb (176 J) at a strength level of 160 ksi (1,100 MPa). Comparison with the baseline toughness–strength combination determined by isochronal tempering studies indicates a transformation toughening increment of 65% in Charpy energy. Predicted Cu particle number densities and the heterogeneous nucleation of optimal stability high Ni 5 nm austenite on nanometer-scale copper precipitates in the multi-step tempered samples was confirmed using three-dimensional atom probe microanalysis. Charpy impact tests and fractography demonstrate ductile fracture with C _v > 80 ft-lbs (108 J) down to −40 °C, with a substantial toughness peak at 25 °C consistent with designed transformation toughening behavior. The properties demonstrated in this first prototype represent a substantial advance over existing naval hull steels. Achieving these improvements in a single design and prototyping iteration is a significant advance in computational materials design capability.     

Size effect in beams with rounded-tip V-notch

Stresses and strains in a beam with a single-edge rounded-tip V-notch subjected to bending were analyzed by the method of finite elements by using nonconforming quadrilateral elements under the assumption that the material is linearly elastic. We studied the influence of the depth of the notcha, its radius of curvature ρ, the angle of the notch ω, and the height of the beamh on the stress intensity factorK _t . It is established that the relative depth of the notch ζ=a/h causes practically no influence if the notch angle ω lies within the range 0°–135°. The influence of the notch rapidly weakens as the relative radius of curvature ρ _d =ρ/h increases from 0.01 to 1.0 and becomes insignificant for ρ _d ≤ 1. For small ρ _d (ρ _d ≤ 1), the quantityK _t attains its maximum value provided that ζ lies within the range 0.1–0.3. As the height of the beam increases, the quantityK _t first remains practically constant, then increases, and finally, ash infinitely increases, approaches a certain constant value. Dipartimento di Ingegneria Civile, Universita di Parma Viale delle Scienze, 43100 Parma, Italy. Published in Fizyko-Khimichna Mekhanika Materialiv, Vol. 32, No. 3, pp. 73–79, May–June, 1996.     

Ferroelectric and piezoelectric properties of new NaNbO<Subscript>3</Subscript>–Bi<Subscript>0.5</Subscript>K<Subscript>0.5</Subscript>TiO<Subscript>3</Subscript> lead-free ceramics

New lead-free ceramics (1–x)NaNbO₃–xBi_0.5K_0.5TiO₃ have been fabricated by the conventional ceramic sintering technique, and their ferroelectric and piezoelectric properties have been studied. The results of X-ray diffraction reveal that Bi_0.5K_0.5TiO₃ diffuses into the NaNbO₃ lattices to form a new perovskite-type solid solution with orthorhombic symmetry. The addition of a small amount of Bi_0.5K_0.5TiO₃ (x ≥ 0.025) transforms the ceramics from antiferroelectric to ferroelectric. The ceramic with x = 0.10 possesses the largest remanent polarization P _r and thus exhibits the optimum piezoelectric properties, giving d ₃₃ = 71 pC/N, k _p = 16.6% and k _t = 39.7%. The ceramics with low doping level of Bi_0.5K_0.5TiO₃ are normal ferroelectrics and the ferroelectric-paraelectric phase transition becomes diffusive gradually with the doping level x of Bi_0.5K_0.5TiO₃ increasing. Our results show the (1–x)NaNbO₃–xBi_0.5K_0.5TiO₃ ceramics is one of the good candidates for lead-free piezoelectric and ferroelectric materials.     

Dependence of electrical and thermal conductivity on temperature in directionally solidified Sn–3.5 wt% Ag eutectic alloy

Sn–3.5 wt% Ag alloy was directionally solidified upward with a constant growth rate (V = 16.5 μm/s) and a temperature gradient (G = 3.3 K/mm) in a Bridgman-type growth apparatus. The variations of electrical resistivity (ρ) with temperature in the range of 293–476 K for the directionally solidified Sn–3.5 wt% Ag eutectic alloy was measured. The measurements indicate that the electrical resistivity of the directionally solidified Sn–Ag eutectic solder increases with increasing temperature. The variations of thermal conductivity of solid phases versus temperature for the same alloy was determined from the Wiedemann-Franz and Smith-Palmer equations by using the measured values of electrical conductivity. From the graphs of electrical resistivity and thermal conductivity versus temperature, the temperature coefficient of electrical resistivity (α _TCR ) and the temperature coefficient of thermal conductivity (α _TCT ) for the same alloy were obtained. According to experimental results, the electrical and thermal conductivity of Sn–Ag eutectic solder linearly decrease with increasing the temperature. The enthalpy of fusion (ΔH) and the change of specific heat (ΔC _P ) during the transformation at the studied alloy were determined from heating curve during the transformation from eutectic solid to eutectic liquid by means of differential scanning calorimeter (DSC).     

A new heat transfer model of inorganic particulate-filled polymer composites

Thermal conductivity is an important parameter for characterization of thermal properties of materials. Various complicated factors affect the thermal conductivity of inorganic particulate-filled polymer composites. The heat transfer process and mechanisms in an inorganic particulate-filled polymer composite were analyzed in this article. A new theoretical model of heat transfer in these composites was established based on the law of minimal thermal resistance and the equal law of the specific equivalent thermal conductivity, and an relevant equation of effective thermal conductivity (K _eff) for describing a relationship between K _eff and filler volume fraction as well as other thermal parameters were derived based on this model. The values of K _eff of aluminum powder-filled phenol–aldehyde composites and graphite powder-filled phenol–aldehyde composites were estimated by using this equation, and the calculations were compared with the experimental measured data from these composites with filler volume fraction from 0 to 50% in temperature range of 50–60 °C and the predictions by Maxwell–Eucken equation and Russell equation. The results showed that the predictions of the K _eff by this equation were closer to the measured data of these composites than the other equations proposed in literature.     

Cyclic fatigue-crack propagation in a silicon carbide whisker-reinforced alumina composite: role of load ratio

The characteristics of subcritical crack growth by cyclic fatigue have been examined in a silicon carbide whisker-reinforced alumina composite, with specific reference to the role of load ratio (ratio of minimum to maximum applied stress intensity, R=K _min/K _max); results are compared with similar subcritical crack-growth data obtained under constant load conditions (static fatigue). Using compact-tension samples cycled at ambient temperatures, cyclic fatigue-crack growth has been measured over six orders of magnitude from ∼10⁻¹¹–10⁻⁵ m cycle⁻¹ at load ratios ranging from 0.05–0.5. Growth rates (da/dN) display an approximate Paris power-law dependence on the applied stress-intensity range (ΔK), with an exponent varying between 33 and 50. Growth-rate behaviour is found to be strongly dependent upon load ratio; the fatigue threshold, ΔK _TH, for example, is found to be increased by over 80% at R=0.05 compared to R=0.5. These results are rationalized in terms of a far greater dependency of growth rates on K _max(da/dN ∞ K _max ³⁰ ) compared to ΔK(da/dN ∞ ΔK ⁵), in contrast to fatigue behaviour in metallic materials where generally the reverse is true. Micromechanisms of crack advance underlying such behaviour are discussed in terms of timedependent crack bridging involving either matrix grains or unbroken whiskers.     

Thermal equation of state of natural chromium spinel up to 26.8 GPa and 628 K

A pressure–volume–temperature data set has been obtained for natural chromium spinel, using synchrotron X-ray diffraction with a resistance heated diamond-anvil cell (RHDAC). The unit cell parameter of the chromium spinel was measured by energy dispersive X-ray diffraction up to pressures of 26.8 GPa and temperatures of 628 K. No phase change has been observed. The observed P–V–T data were fit to the high-temperature Birch-Murnaghan equation of state, with V ₀ fixed at its experimental value, yields K ₀ = 209 ± 9 GPa, (∂K/∂T)_P = −0.056 ± 0.035 GPa K⁻¹, and α₀ = 7±1 × 10⁻⁵ K⁻¹. The temperature derivative of the bulk modulus (∂K/∂T)_P of chromium spinel is determined here for the first time. The obtained K ₀ is slightly higher than the previous results of synthetic spinel. We suggest that Fe²⁺–Mg²⁺ substitution is responsible for the high bulk modulus of chromium spinel.     

High thermal conductivity composites consisting of diamond filler with tungsten coating and copper (silver) matrix

Tungsten coatings with thickness of 5–500 nm are applied onto plane-faced synthetic diamonds with particle sizes of about 430 and 180 μm. The composition and structure of the coatings are investigated using scanning electron microscopy, X-ray spectral analysis, X-ray diffraction, and atomic force microscopy. The composition of the coatings varies within the range W–W₂C–WC. The average roughness, R _a, of the coatings’ surfaces (20–100 nm) increases with the weight–average thickness of the coating. Composites with a thermal conductivity (TC) as high as 900 W m⁻¹ K⁻¹ are obtained by spontaneous infiltration, without the aid of pressure, using the coated diamond grains as a filler, and copper or silver as a binder. The optimal coating thickness for producing a composite with maximal TC is 100–250 nm. For this thickness the heat conductance of coatings as a filler/matrix interface is calculated as G = (2–10) × 10⁷ W m⁻² K⁻¹. The effects of coating composition, thickness and roughness, as well as of impurities, on wettability during the metal impregnation process and on the TC of the composites are considered.     

Measurement of Specific Fracture Energy and Surface Tension of Brittle Materials in Powder Form

Studies of the influence of specimen geometry and size–effect on the K _R –curves and the related fracture parameters were carried out by the authors (Kumar and Barai 2008b). The present paper is a supplementary contribution and reports interesting results related to the effect of the loading condition and size–effect studies on the K _R –curves associated with the cohesive stress distribution for complete fracture process, the double–K fracture parameters, the CTOD–curves and the process zone length using two different loading conditions (i.e., three–point bending test and four–point bending test). The laboratory size specimen with initial–notch length/depth ratios 0.3 and 0.5 are considered in the work. The load–crack opening displacement curves for these loading conditions are obtained using well known version of fictitious crack model.     

Thermoelectric properties of <Emphasis Type="Italic">n</Emphasis>-Bi<Subscript>2</Subscript>Te<Subscript>2.7</Subscript>Se<Subscript>0.3</Subscript>〈I,In〉 crystals

n-Bi₂Te_2.7Se_0.3〈I〉 single crystals additionally doped with indium (0.1–2.0 mol % In₂Te₃) have been grown by Czochralski pulling through a floating crucible. As the In₂Te₃ content of the growth charge increases to 0.2 mol %, the thermoelectric figure of merit (Z) of the crystals increases from 0.0029 to 0.0031 K⁻¹ and Z _max shifts to higher temperatures by ∼30 K. Increasing the In₂Te₃ content to 2 mol % sharply reduces Z _max to 0.002 K⁻¹ and shifts the maximum to lower temperatures. This behavior of the thermoelectric figure of merit can be understood in terms of the nonmonotonic variation of electron mobility with indium and iodine concentrations in the crystals.     

The Effect of Sintering Temperature Variation on the Superconducting Properties of ErBa<Subscript>2</Subscript>Cu<Subscript>3</Subscript>O<Subscript>7−<Emphasis Type="Italic">δ</Emphasis></Subscript> Superconductor Prepared via Coprecipitation Method

The effect of heat treatment on the superconducting properties of ErBa₂Cu₃O_7−δ (ErBCO) ceramic materials has been studied. The nano-metal oxalate precursor was prepared using coprecipitation (COP) method. The prepared materials were subjected to calcination process at 900 °C for 12 h and then sintered under oxygen environment for 15 h at 920 °C, 930 °C, 940 °C, and 950 °C, respectively. All samples showed a metallic behavior and single-step transition in the R–T curves. The best zero critical current, T _C(R=0)=91.4 K, was for the sample sintered at 920 °C. XRD data showed single phase of an orthorhombic structure. As the sintering temperature increases, the formation of nonsuperconducting phases (impurities) was observed when the samples sintered above 920 °C. The formation of nano-oxalate powders via COP method is a very efficient procedure to produce high-quality superconductors with less processing temperature required.     

Structure and piezoelectric properties of new ternary K<Subscript>0.5</Subscript>Na<Subscript>0.5</Subscript>NbO<Subscript>3</Subscript>–LiSbO<Subscript>3</Subscript>–CaTiO<Subscript>3</Subscript> lead-free piezoceramics

New ternary (1−x)K_0.5Na_0.5NbO₃–x(0.80LiSbO₃–0.20CaTiO₃) lead-free ceramics were fabricated by a conventional ceramic technique and their structure and piezoelectric properties were studied. The results of X-ray diffraction reveal that LiSbO₃ and CaTiO₃ diffuse into the K_0.5Na_0.5NbO₃ lattices to form a new solid solution with a perovskite structure. After the addition of LiSbO₃ and CaTiO₃, the cubic-tetragonal and tetragonal-orthorhombic phase transitions shift to lower temperatures. Coexistence of the orthorhombic and tetragonal phases is hence formed in the ceramics with 0.03 < x < 0.07 at room temperature, leading to a significant enhancement of the piezoelectric properties. For the ceramics with x = 0.04–0.06, the piezoelectric properties become optimum: d ₃₃ = 172–253 pC/N, k _P = 49.9–55.5%, k _t = 49.2–52.1% and T _C = 348–373 °C. The ceramic with x = 0.04 also exhibits a good thermal stability of piezoelectric properties.     

Formation and properties of SnO–MgO–P<Subscript>2</Subscript>O<Subscript>5</Subscript> glasses

A new glass system SnO–MgO–P₂O₅ with low viscosity has been developed by a melt-quenching method. Formation, thermal properties, and chemical durability of these glasses have been investigated. For a constant P₂O₅ concentration, the glass formation ability is enhanced with the increasing Sn/(Sn + Mg) ratio. The glasses exhibit low glass transition temperature (T _g = 270–400 °C), low dilatometric softening temperature (T _DS = 290–420 °C), and high thermal expansion coefficient (CTE = 110–160 × 10⁻⁷ K⁻¹). With the increasing Sn/(Sn + Mg) ratio, T _g and T _DS decrease, and CTE increases. When Sn/(Sn + Mg) ratio is varied, the relationship between chemical durability and thermal properties of the present glasses is not consistent with what expected in general cases. It is noted that the glasses with 32–32.5 mol% P₂O₅ exhibit excellent chemical durability and tunable T _g, T _DS, and CTE (by varying Sn/(Sn + Mg) ratio).     

Crystallization characteristic and properties of some zinc containing soda lime silicate glasses

The crystallization behaviour of some soda lime silicate glasses modified by ZnO/CaO replacement to give the composition (Na₂O)₂·CaO_1−x ·(ZnO) _x ·3SiO₂ (x = 0, 0.2, 0.4, 0.6, 0.8 and 1.0) have been investigated using differential scanning calorimetry (DSC) and X-ray diffraction analysis (XRD). The thermal expansion coefficients and AC electrical properties in the frequency range 40 Hz–5 MHz of the obtained crystalline products were determined. Two forms of sodium calcium silicate (Na₄CaSi₃O₉ & Na₂Ca₂Si₃O₉), sodium metasilicate-Na₂SiO₃, two types of sodium zinc silicate (Na_1.31Zn_0.655Si_1.345O₄ & Na₂ZnSiO₄) and α-quartz phases were mostly developed in the crystallized glasses using various heat-treatment processes. The coefficient of thermal expansion of the obtained glass–ceramic materials are between 120 × 10⁻⁷°K⁻¹ and 168 × 10⁻⁷°K⁻¹ in the 25°–600 °C temperature range. The increase of frequency generally resulted in the increase of the conductivity and decrease the dielectric constant together with the loss tangent of the glass–ceramic materials.     

Thermal-lens study of thermo-optical properties of tellurite glasses

Mode-mismatched Thermal Lens (TL) measurements were performed in 70TeO₂–19WO₃–7Na₂O–4Nb₂O₅ (% mol) tellurite glasses doped with either Er³⁺ or Tm³⁺ and co-doped with Er³⁺/Tm³⁺ ions. Thermo-optical parameters (D, K, ds/dQ and ds/dT) were obtained in function of thulium concentrations (0.39–1.6) × 10 ²⁰ ions/cm³. For Er³⁺/Tm³⁺ co-doped tellurite glasses, D and K values are practically independent of the Tm³⁺ concentrations used in this study. The average values of D and ds/dT obtained for tellurite glasses are: (3.1 ± 0.2) × 10⁻³ cm²/s and (16 ± 3) × 10⁻⁶ K⁻¹, respectively.