Computer simulation of martensitic textures

We consider a Ginzburg-Landau model free energy F(ε, e₁, e₂) for a (2D) martensitic transition, that provides a unified understanding of varied twin/tweed textures. Here F is a triple well potential in the rectangular strain (ε) order parameter and quadratic e₁², e₂² in the compressional and shear strains, respectively. Random compositional fluctuations η(r) (e.g. in an alloy) are gradient-coupled to ε, ˜ − ∑_rε(r)[(Δ_x² − Δ_y²)η(r)] in a “local-stress” model. We find that the compatibility condition (linking tensor components ε(r) and e₁(r), e₂(r)), together with local variations such as interfaces or η(r) fluctuations, can drive the formation of global elastic textures, through long-range and anisotropic effective ε-ε interactions. We have carried out extensive relaxational computer simulations using the time-dependent Ginzburg-Landau (TDGL) equation that supports our analytic work and shows the spontaneous formation of parallel twins, and chequer-board tweed. The observed microstructure in NiAl and Fe_xPd_{1 − x} alloys can be explained on the basis of our analysis and simulations.     

Experimental micromechanical evaluation of strength of granular materials: Effects of particle rolling

Biaxial compression tests have been performed on assemblies of oval cross-sectional rods, in an effort to evaluate the effects of interparticle friction, particle shape, and initial fabric on the overall strength of granular materials. The variation in the spatial arrangement of the particles (fabric) and particle rolling and sliding are monitored by taking photoelastic pictures at various stages during the course of deformation. Based on this, the following conclusions are obtained. (1) Particle rolling appears to be a major microscopic deformation mechanism, especially when interparticle friction is large. (2) There are relatively few contacts at which relative sliding is dominant, and this seems to be true even when the assembly reaches the overall failure state; this observation is in contradiction to the common assumption that particle sliding is the major microscopic deformation mode. (3) During the course of deformation and up to the peak stress, new contacts are continually formed in such a manner that the contact unit normals tend to concentrate more in a direction parallel to the maximum principal compression. This concentration of unit normals seems to be closely related to the formation of new column-like load paths which carry the increasing axial stress under constant lateral force. After the peak stress, such a column-like microstructure disappears and considerable rearrangement of the load paths takes place, leading to a more diffused (homogeneous) microstructure in the critical state. (4) If a fabric tensor F_ij, i, J = 1,2,3, is defined to be proportional to the volume average of the quantity m_im_j, where m_i are the rectangular Cartesian components of a unit vector along a vector that connects the centroids of two typical contacting granules, then it appears that the overall stress with components σ_ij tends to become coaxial with the fabric tensor F_ij, as the overall deformation continues. For two-dimensional granules the result σ_ij = _OF_ij + β_OF_jkF_kj (k summed) obtained by Mebrabadi, Nemat-Nasser and Oda (1980) by microchemical modeling is confirmed experimentally; _O and β_O are material parameters.     

Magneto-mechanical properties evolution of Fe–C alloy during precipitation process

Evolution of magneto-mechanical properties of 160 ppm Fe–C alloy due to carbides precipitation during isothermal annealing at 473 K (up to t=50×10³ s) was studied by means of classical Barkhausen noise (HBN) and mechanical Barkhausen noise (MBN) effects. The MBN was measured for the torsion mode of load with a torque motor. Also the B(H) hysteresis loop and the coercive field H_c were evaluated using a low-frequency magnetisation set. Magnetic hysteresis losses ΔW₁ were compared with the integral ΔW₂ of HBN intensity over one period of magnetisation and the integral ΔW₃ of MBN intensity over one period of the mechanical load. The internal stress distribution function and the resulting mean level of internal stress parameter σ_i were evaluated from the MBN ‘first load’ data. It was revealed that a correlated increase of ΔW₁ and ΔW₂ parameters exists. However, the relative increase of ΔW₃ is much lower than the relative increase of ΔW₁. The relationship between H_c and σ_i was found to be parabolic. This dependence explained by Néel’s model of the impact of the residual stress level on H_c. The presence of precipitates of type was confirmed by scanning electron microscopy.     

Weight function calculations for mixedmode fracture problems with the virtual crack extension technique

An efficient finite element method is presented for calculating the stress intensity factors (K_I and K_II) and the weight functions for mixed-mode cracks with one virtual crack extension. The computational efficiency is enhanced through the use of singular elements and the application of colinear virtual crack extension (VCE) technique to symmetric mesh in cracktip neighborhood. This symmetric mesh in crack-tip vicinity permits the analytical separation of strain energy release rate into G_I for Mode I and G_II for Mode II for the mixed fracture problems with the colinear virtual crack extension.

Rice's displacement derivative representation of weight function vector for symmetric crack has been extended to the mixed fracture mode at nodal location (x_i,y_i) with crack length (a) and inclination angle (β) as h_I(II)(x_i, y_i, a, β) = (H/2K_I(II)(∂U_I(II)(x_i, y_i, a, β/∂a).

This equation permits explicit determination of weight functions for the entire structure of a given asymmetric crack geometry with colinear VCE technique. The explicit weight functions for mixed fracture mode depend strongly on the constraint conditions. The method of obtaining the required stress intensity factors of a given asymmetric crack geometry, from the weight function concept under the selected constraint conditions, which are different from constraint conditions used in the available weight functions for the same crack geometry, is also presented in this paper. This is accomplished by combining the predetermined explicit weight functions with the self-equilibrium forces at their application locations. These self-equilibrium forces include both the applied surface tractions and the reaction forces induced from the constraint conditions.     

Growth mechanism of stress corrosion cracking in high strength steel

Stress corrosion crack growth rates are measured at sveral stress intensity levels for low-tempered 4340 steel in 0.1N H₂SO₄ solution. The characteristics of the growth rates are divided into three regions of stress intensity factors: Region I near K_1SCC; Region III near unstable fracture toughness, K_1SC; and Region II, which lies between the two. K_1SCC is the value of K at which no crack growth can be detected after 240 hr.

In order to explain these experimental results, the crack initiation analysis reported in a previous paper is extended to the growth rates. A detached crack initiates and grows at the tip of an already existing crack. When the detached crack reaches the tip of the main crack, the process repeats as a new existing crack.

A relationship between crack growth rate, v, and stress intensity factor, K, is obtained as a function of b/a and a = b + d, where b is the distance from the tip of the main crack to the detached crack, and d is the ydrogen atom saturated domain.

The experimental data are in good agreement with the theoretical values in Region II when a = 0.02 mm, b/a = 0.8, c₁/c₀ = 2.8 for 200°C tempered specimens and a = 0.015 mm, b/a = 0.7, c₁/c₀ = 3.0, ρ_b = 0.055 mm for 400°C tempered specimens, where ρ_b is a fictitious notch radius. The plateau part in Region II for 400°C tempered specimens is also successfully explained by the present theory. For Region III, the value of b/a will be almost equal to 1 because v → ∞ for b/a → 1. On the other hand, for Region I, b/a will be zero, since the value of v becomes negligibly small and no crack growth is observable.     

Driver age, car mass and accident exposure— A synthesis of available data

The tendency of younger drivers to be more likely than older drivers to drive smaller cars has been an important consideration in a number of prior investigations of the relation between car size and traffic safety. The purpose of the present study is to quantify this effect on a firmer basis than hitherto by fitting data from seven independent sources to a unified general model. More specifically, when the exposure measures “per unit distance of travel” or “per registered car” are used in studies of car mass effects on traffic safety, the exposure information often does not contain the variable driver age. This work develops a general procedure for disaggregating such exposure data into three driver (or owner) age categories; A₁: 16–24; A₂: 25–34; and A₃: 35 years. Data from the seven sources are fined to the equation

f(i,m) = H_i[1 + G _i(m/900 − 1)]

where m is the ear mass in kg, and f(i,m) is the fraction of cars of mass m which are driven (owned) by persons in the A_i, (i = 1, 2, 3) age category. The form of this equation permits easy comparison of 900 and 1800 kg cars. Those particular masses that have been chosen for illustrative comparisons in earlier work. The seven sets of data are used to derive overall average values of the parameters H₁ and G₁. The data from all seven sources show consistent effects which are summarized in one analytical expression which is well suited for use in future studies of car size effects because it reflects a synthesis of much prior data and it permits sensitivity analyses to be performed conveniently.     

Exploring the fracture toughness KIE and KIC of a medium-Strength steel plate using the surface-flaw test

The fracture toughness of a 30 CrMnSiA steel plate of three thicknesses (10,8 and 5 mm) and three widths (110,80 and 56 mm) has been investigated by using surface-flaw method under room temperature. It is not easy to compute the value of K_IE by the maximum applied load. But the values of K_IE and K_IC could be obtained easily, if the computation of the conditional applied load P₁₀ and P₅ based on the relative effective extension Δa/a₀ = 10% and 5% were adopted, together with the conditions of P_max/P₁₀ 1.2 and P_max/P₅ 1.3. The K_R — Δ_a curve, i.e. the resistance-curve described by the parameter K, has been plotted. The values of K_IC and K_IE are then the resistances corresponding to the real extensions of flaws of Δ/a₀ = 2 and 7%, respectively. These values so obtained are in good agreement with the computed values of K_IC and K_IE by using the conditional applied loads. The values of K_IC and K_IE so obtained are also in agreement with the value of K_IC converted from the J-integral and the effective value of K_IE computed by the maximum applied load, respectively.

An approximate relation between K_IC and K_IE has been found to be: K_IC = (0.85˜0.95)K_IE.

The requirements for the dimensions of specimens are: Thickness of plate: B 1.0(K_IC/σ_0.2)² or 1.25(K_ICσ_0.2)²]; Width of plate: 8 W/B 10, 4 W/2c 5; Effective length: l 2W.     

Growth of lithium doped silver niobate single crystals and their piezoelectric properties

Lithium doped silver niobate (Ag_1−xLi_xNbO₃, 0 < x < 0.1) is one of the candidate materials for lead-free piezoelectric materials. In this study, Ag_1−xLi_xNbO₃ single crystals were successfully grown by a slow cooling method. Crystal structure was assigned to perovskite-type orthorhombic (monoclinic) phase. Dielectric properties were measured as a function of temperature. As a result, with increasing lithium contents, the phase transition at around 60 °C was shifted to lower temperature while the phase transition at around 400 °C was shifted to higher temperature. On the basis of these peak shifts, the lithium contents in Ag_1−xLi_xNbO₃ single crystals were determined. Moreover, P–E hysteresis measurement revealed that pure silver niobate crystal was weak ferroelectrics with P_r of 0.095 μC/cm² while Ag_0.9Li_0.1NbO₃ (ALN10) crystal was normal ferroelectrics with P_r of 10.68 μC/cm². About this ALN10 crystal, polling treatment was performed and finally piezoelectric properties were measured. As a result, high electromechanical coupling coefficient k₃₁ over 70% was observed.     

Statistical investigation of surface fatigue cracks in large-sized turbine rotor shaft steel

Distribution properties of an initiation life N_i and a propagation life N_p of surface cracks, statistical characteristics of a crack growth rate dl/dN, and a relationship between a scatter of the distributions and a gradient a of S-log N curves in rotating bending fatigue tests were investigated for Ni-Cr-Mo-V steel, using for a large-sized turbine rotor shaft. The distributions of N_i and N_p were expressed as Weibull distributions, and the scatter of them for smooth specimens and for lower stress amplitude σ_a tests were larger than those for notched ones and for higher σ_a tests, respectively. The statistical properties of crack propagation rate were almost similar in both smooth and notched specimens. The relationship between the a and a coefficient of variation η for the distributions of N_i, N_p and a final fracture life N_f was expressed as η = c(a)^−b, where c and b are constants.     

A theoretical study on the second-order nonlinear optical susceptibilities of lithium formate monohydrate crystal, HCOOLi·H2O

Ab initio calculations of the first hyperpolarizabilities of (HCOOLi·H₂O)_2n supermolecules, as the building-blocks of lithium formate monohydrate (LFM) crystal with extended system, were performed for the first time. The dependence of the static β_ijk⁰ values on chain length was explored, and the frequency dependence of β_ijk(−2ω;ω,ω) was measured, and the influences of electron correlation and basis set on β_ijk⁰ were evaluated. Finally, we predicted the second-order nonlinear optical coefficients of LFM crystal. The β_ijk⁰ value of (HCOOLi·H₂O)_2n is linearly dependent on the chain length of supermolecule, which is quite unusual for an extended system connected by the O–Li bonds with ionic characters. Although the static component of β_zzz⁰ tensor is the static largest in these three components under study, the absolute value of frequency-dependent β_zyy(−2ω;ω,ω) element, transforming the smallest into the largest, is the most sensitive to frequency. After the fundamental wavelength is smaller than 500 nm, it is found that the β_ijk(−2ω;ω,ω) value is resonantly enhanced to a great extent due to the double frequency lies in the region of resonance. In addition, the β_zxx⁰ value goes from negative to positive with changes of electron correlation and basis set. Obviously, it is very necessary to take into account the effect of electron correlation, if the hyperpolarizability tensor components must be accurately calculated. Moreover, it is also very important whether it is adopted a complete basis set with diffuse and polarization functions. The calculated nonlinear coefficients at high level suggest that the scaled set reported by Robert seem more reasonable.     

Dendritic Microstructure Affecting Mechanical Properties and Corrosion Resistance of an Al-9 wt% Si Alloy

It has been reported that the mechanical properties and corrosion resistance of metallic alloys depend strongly on the solidification microstructural arrangement. The correlation of corrosion behavior and mechanical properties with microstructure parameters can be very useful for planning solidification conditions in order to achieve desired final properties. The aim of the present work is to investigate the influence of dendritic microstructural parameters of an Al-9 wt.% Si alloy on mechanical properties and corrosion resistance. The experimental results establish correlations between secondary dendrite arm spacings (λ₂) and ultimate tensile strength (σ_u), yield strength (σ_y), corrosion potential (E_Corr), and corrosion rate (i_Corr).     

Some experimental studies of fatigue slip bands and persistent slip bands during fatigue process of low-carbon steel

Initiation and propagation behaviours of fatigue slip bands and persistent slip bands in lowcarbon steel have been investigated: fatigue slip bands were expressed quantitatively as a volume fraction which was products of the slip bands area (Σ A_s/A₀), the depth (h_s/h₀) and the number of slipped grains (G_s/G₀).

It was shown that distributions of fatigue slip bands and persistent slip bands showed the maximum at the angle division of 0° ˜ 10° (at and near the normal to the stress axis) and decreased gradually with increasing of the angle. And the normalized volume fraction of fatigue slip bands increased linearly in proportion to the number of cycles independently of the stress amplitude σ_a and the angle θ. The increment in volume fraction of fatigue slip bands meant the increment in fatigue damage and the fatigue life decreased in proportion to the increment in volume fraction of fatigue slip bands until its value reached a certain content. Then, the initiation rates of fatigue slip bands, persistent slip bands and stage I microcracks showed the increasing tendency with increasing of stress amplitude σ_a, and the propagating rates from fatigue slip bands to persistent slip bands and from fatigue slip bands to stage I micro-cracks were also similar increasing tendency with stress amplitude.     

A fracture criterion for three-dimensional crack problems

A criterion for predicting the growth of three-dimensional cracks is developed on the basis of the strain energy density concept which has been used successfully for treating two-dimensional crack problems. Fracture is assumed to initiate from the nearest neighbor element located by a set of spherical coordinates (r, θ, φ) attached to the crack border. The new fracture surface is described by a locus of these elements whose locations correspond to the strain energy function, dW/dV, being a minimum. The function dW/dV is found to be singular of the type 1/r and is of quadratic form in the three stress intensity factors k₁, k₂ and k₃ expressed through the strain energy density factor S. It is postulated that unstable crack propagation initiates from a region where S reaches a critical value S_cr = r₀(dW/dV)_cr. The locations of failure lying on the fracture surface is determined by holding (dW/dV)_cr = S_min/r₀ constant. The quantity S_min stands for the value of S minimized with respect to θ and φ and r₀ is a radial distance measured from the crack border.

An example of failure prediction for an embedded elliptical crack subjected to both normal and shear loads is presented. According to the S-criterion, fracture initiation takes place at the ends of the minor axis. An unexpected result is that for a narrow elliptical crack and Poisson's ratio of 1/3 the lowest failure load occurs when the uniaxial tensile load makes an angle of approximately 60° with the crack surface and is in the plane of the major axis. This is in contrast to the expectation that the lowest critical load occurs when the uniaxial tension is perpendicular to the crack surface. In the limit as the elliptical crack becomes increasingly narrower, the result reduces to the two dimensional line crack case of Mode I and III loading. The S-criterion is also applied to the failure prediction of three dimensional cracks under compressive loads.     

Effects of oxygen partial pressure on lead content of PLZT thin films produced by excimer laser deposition

Excimer laser ablation has been used to produce thin films of lanthanum-modified lead zirconate titanate (PLZT), or Pb_1−xLa_x(Zr_1−yTi_y)_1−x/4O₃. PLZT is an interesting class of materials since it has a wide range of compositionally dependent electro-optical properties and strong non-linear optical characteristics. PLZT thin films of 7/0/100, 28/0/100 and 0/0/100 compositions have been deposited onto crystalline Si100 and amorphous fused silica substrates. Effects of oxygen backfill pressure on the Pb:(Ti + La) ratios were investigated. The results indicate that controlling the oxygen backfill pressure during laser deposition strongly influences the stoichiometry and crystal structure of PLZT thin films.     

The theory of non-steady state fracture kinetics analysis—1: General theory of crack propagation

The kinetics theory of thermally activated time dependent crack propagation is extended to describe the crack size distribution in non-steady state. The distribution is represented by a series of n differential equations, each expressing the rate of crack tip concentration change over the system of n consecutive energy barriers. The general solution for the set of homogeneous linear first order differential equations developed in this report is of the form ρ_i = Σ_jc_i,je^{−λj_t + C_i}, where ρ_i is the crack tip concentration in the ith valley. The theory takes into consideration the discrete character of solids in contrast with the usual continuum models of fracture studies. The analysis is readily applicable to Regions I and II of stress corrosion cracking.     

Mechanical characterization of Ni1−xZnxFe2O4 prepared by non-conventional methods

The mechanical properties like hardness, H_v and compressive strength, σ of Ni_1−xZn_xFe₂O₄ (x = 0.2, 0.3, 0.4 and 0.5) prepared by the non-conventional flash combustion and citrate-gel decomposition techniques are studied and reported. It is observed that there is an increase in hardness with zinc content as well as sintering temperature. The hardness in the order of 2.0–3.63 GPa and compressive strength in the order of 150–240 MPa are obtained for Ni–Zn ferrites prepared by these non-conventional techniques. The influence of density, porosity and microstructure on hardness and compressive strength of Ni–Zn ferrites with respect to sintering temperature was studied.     

Effects of gage length and stress concentration on the compressive strength of a unidirectional CFRP

Compression tests for a unidirectional CFRP were carried out for a wide range of gage lengths, three different configurations of end tab edges and two different end tab materials under the conditions of constant specimen thickness. The relation of σ_c-L is to be divided into two parts, namely, a part where the compressive strength, σ_c, is nearly constant independent of gage length, L, and beyond that, a part where σ_c decreases with increasing L. The apparent compressive strength measured by Celanese test method was lower than the true compressive strength because of the stress concentration near the end tab edges of the specimen. The true compressive strength was obtained by using the specimen where the gage lengths of 3.2 mm and 6.4 mm, and the material of end tab is stainless steel.     

Determination of the E1 and E1+Δ1 energy bands by photoreflectance in AlxGa1−xAs in the region 0<x<0.55

The E₁ and E₁+Δ₁ energy bands of metal–organic chemical vapor deposition grown Al_xGa_1−xAs, with x in the range 0–0.55, have been determined using photoreflectance technique. The aluminum composition for each sample was determined using the energy of the room-temperature photoluminescence compensated peak value and a suitable fundamental band gap formula. The positions of the E₁ and E₁+Δ₁ peaks were determined from curve-fitting an appropriate theoretical model to our experimental data by a modified downhill simplex method. Using the results, we propose new E₁ and E₁+Δ₁ cubic expressions as functions of the aluminum composition, x, and compare them with the available reported expressions.     

On the buckling of a column in an elastic medium

One deals with the buckling of a cantilever column in an elastic medium by the aid of the differential eqns (2), (2′) with bilocal conditions (3), (3′). Introducing the conventional load (4), one considers the three cases P_cr < P₀, P_cr = P₀ and P_cr > P₀ and one determines the corresponding characteristics eqns (8″), (12), (15″). The reduced critical load P_cr/P₎ and the reduced critical length l_cr/l are listed in a table and plotted into diagrams for various values of an adimensional magnitude bl. One obtains also the asymptotic formulae (16), (16′).     

Spectroscopic ellipsometry analysis of GaAs1 − xNx layers grown by molecular beam epitaxy

In this work, we present the effect of nitrogen incorporation on the dielectric function of GaAsN samples, grown by molecular beam epitaxy (MBE) followed by a rapid thermal annealing (for 90 s at 680 °C). The GaAs_1 − xN_x samples with N content up to 1.5% (x = 0.0%, 0.1%, 0.5%, 1.5%), are investigated using room temperature spectroscopic ellipsometry (SE). The optical transitions in the spectral region around 3 eV are analyzed by fitting analytical critical point line shapes to the second derivative of the dielectric function. It was found that the features associated with E₁ and E₁ + Δ₁ transitions are blue-shifted and become less sharp with increasing nitrogen incorporation, in contrast to the case of E₀ transition energy in GaAs_1 − xN_x. An increase of the split-off Δ₁ energy with nitrogen content was also obtained, in agreement to results found with MOVPE GaAs_1 − xN_x grown samples.