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.     

Some problems in the J-integral

For a blunt crack the j-integral is path dependent on contours which are very close to the crack tip even for elastic material. Using the incremental J-integral theory we introduce a new parameter J_t, characterizing the behavior of a crack tip and prove that the J-integral is almost path independent on contours whose radii are greater than several COD if σ_ij,1Δε_ij — ε_ijΔσ_ij = 0 in plastic regions for elasto-plastic material.     

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.     

The stationary value of the third stress invariant as a local fracture parameter (Det.-criterion)

In this paper the stationary value of the third stress invariant as a local fracture parameter is studied. The third stress invariant [Det(σ_ij)] is calculated along a circle around the crack-tip. This circle, which defines the core-region around the crack-tip, is the initial curve of the caustics. This distribution of the Det(σ_ij) presents a positive maximum. The crack propagates in the direction of the maximum value of the Det(σ_ij) and the fracture will initiate when the Det(σ_ij) on the core-region boundary reaches a critical maximum value which is a material property. This condition of initiation of the crack is proposed as Det.-criterion of fracture.     

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.     

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.     

Use of tensorial polynomial strength function for strength prediction in laminated polymeric composites

It has been shown recently that a strength function, expressed by a tensorial polynomial for an anisotropic material, can be only of the form

F₄(σ) + F₂(σ) + F₁(σ) ≤ 1

where F_i(σ) are the respective polynomials of order i of the σ tensor components. Some further work in this field is now presented. It will be seen that a notable simplification has been achieved, bringing down the initial number of components of an 8th rank tensor from 3⁸ = 6561 to a more managable number of 42 for orthotropic materials and 11 for the planar case. It is also shown that the three F_i(σ) polynomials cannot exist simulataneously, leading either to the known Tsai and Wu proposal or a new tensorial form. Some considerations to strength theory for isotropic materials are given as well. Finally, applicability of strength theories for composite laminates is discussed, with some suggestions for practical use.     

Influence of stress ratio at baseline loading on delayed retardation phenomena of fatigue crack growth in A553 steel and A5083 aluminium alloy

The delayed retardation phenomena of fatigue crack growth following a single application of tensile overload were investigated under the baseline loading with the stress ratio, R = σ_min/σ_max, ranging from −1 to 0.5 for A553 steel and A5083 aluminium alloy. Two different overload cycles were applied; the one is the case that the ratio of peak stress range to baseline stress range, r = Δσ₂/Δσ₁, is equal to two and the other is the case that the ratio of maximum peak stress to maximum baseline stress, σ_2max/σ_1max, is equal to two. The retardation took place stronger in aluminium than in steel. Under the condition of r = 2 the normalized number of cycles, N_D/N_C, (N_D: the number of cycles during retardation, N_C: the number of cycles required for propagation through the overload-affected-zone size) decreased slightly as the R ratio increased from −1 to 0.5, while under the condition of σ_2max/σ_1max = 2 the N_D/N_C-values increased drastically as the R ratio increased from −1 to 0 (or the overload ratio, r, increased from 1.5 to 2) in both the materials. These retardation behaviors were expressed theoretically according to the model proposed by Matsuoka and Tanaka [1, 3] by using four parameters: the overload ratio, r, the exponent in Paris equation, m, the overload-affected-zone size, ω_D, and the distance at the inflection point, ω_B.     

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.     

Stress relaxation in the interface between creep particle and elastic matrix-strengthening mechanism

The effect of a power law creep particle on interface behavior between the particle and elastic matrix is investigated by stress analysis. Using the results obtained through the stress analysis, the forces due to interaction of an applied stress and stress concentration with an edge dislocation are determined. The direct interaction between the edge dislocation and the creeping particle is studied under fully relaxed stress conditions. Through the investigation the following results are derived. Stress relaxation in the interface can be caused by power law creep along or by diffusion, or a combination of both mechanisms. The degree of stress relaxation caused by diffusion can be defined in terms of the relaxation time for both boundary diffusion and volume diffusion. The amount of stress relaxation caused by the power law creep particle is characterized by the quantity ₂ which is a function of Γ₀ = 2(1/√3)^{1 + m} × (σ_∞/2μ)^m(σ₀/σ_∞t^m), where m is strain rate hardening exponent, σ_∞ is applied stress, μ is the shear modulus, σ₀ is the material constant of the power law creep particle, and t is elapsed time. The value ₂ = 1.0 corresponds to the fully relaxed condition and ₂ = −0.6 corresponds to the initial state. The time to reach a fully relaxed condition is very sensitive to the strain rate exponent, with the smaller m values leading to longer times. The stress state of complete relaxation in the elastic matrix is equivalent to the solution of a void in an elastic matrix superposed on the solution of positive surface traction on the void. This result is identical to that obtained by Srolovitz et al. [Acta. Metall.32, 1979 (1984)]. When the stress is completely relaxed in the particle, all stress components (σ_r, σ_θand σ_rθ) are relaxed, while in the matrix relaxations are observed only for σ_rand σ_θ. The critical resolved shear stress and critical stress to climb the dislocation in the neighborhood of the particle exceed the Orowan stress. Also, the particle attracts the dislocation. Therefore the strengthening of a power law creep particle in an elastic matrix is caused by the Orowan mechanism and by attraction of the dislocation.     

A general method for determining mixed-mode stress intensity factors from isochromatic fringe patterns

A general method is presented for determining mixed-mode stress intensity factors K_I and K_II from isochromatic fringes near the crack tip. The method accounts for the effects of the far-field, non-singular stress, σ_ox. A non-linear equation is developed which relates the stress field in terms of K_I, K_II, and σ_ox to the co-ordinates, r and θ, defining the location of a point on an isochromatic fringe of order N.

Four different approaches for the solution of the non-linear equation are given. These include: a selected line approach in which data analysis is limited to the line θ = π and the K---N relation can be linearized and simplified, the classical approach in which two data points at (r_m, θ_m) are selected where r_m/θ = 0; a deterministic method where three arbitrarily located data points are used; and an over-deterministic approach where m (>3) arbitrarily located points are selected from the fringe field.

Except for the selected line approach, the method of solution involves an iteractive numerical procedure based on the Newton-Raphson technique. For the over-deterministic approach, the method of least squares was employed to fit the K-N relation to the field data.

All four methods provide solutions to 0.1% providing that the input parameters r, θ, and N describing the isochromatic field are exact. Convergence of the iterative methods is rapid (3–5 iterations) and computer costs are nominal. When experimental errors in the measurements of r and θ are taken into consideration, the over-deterministic approach which utilizes the method of least squares has a significant advantage. The method is global in nature and the use of multiple-point data available from the full-field fringe patterns permits a significant improvement in accuracy of K_I, K_II, and σ_ox determinations.     

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.     

Fracture angle and strain-energy-density-factor of a crack at hole at an arbitrary angle

For both the maximum stress criterion and strain-energy-density-factor (S) theory, fracture angle (the initial angle of crack growth) − θ_o is predicted by using opening and sliding mate stress intensity factors, k₁ and k₂. These theoretical predictions are consistent with experimental fracture angles.

For the S theory, the crack spreads in the negative θ_o-direction in a plane for which S is a minimum, S_min. This quantity was obtained analytically. The experimental data of the critical S (S_cr) on plexiglass fracture specimens remains essentially constant.     

A comparison on the effect of the ratio a/w on the fracture behaviour between ductile and brittle materials

The effect of the ratio a/W on the fracture behaviour of ductile and brittle materials has been studied by measuring the crack-opening displacement and J-integral for ductile material and the stress intensity factor for brittle material in three-point bend specimens with shallow and deep notches. It is shown that, for ductile material, the values of δ_i and J_i, for specimens with shallow notches are larger than those of deep notches. On the contrary, for brittle material, the values of K_IC for specimens with shallow notches are smaller than those of deep notches. The reason for this is explained.     

Stress intensity factors and energy release rates of delaminations in composite laminates

Due to the oscillatory characteristics of stresses near interface crack tips, the stress intensity factor K_i, i = I, II, III, should be modified and the energy release rate G_i, i = 1, 2, 3, of each fracture mode calculated by the virtual crack closure method may not exist. Based upon a near-tip solution for interface cracks between dissimilar anisotropic media, a proper definition for the stress intensity factors and energy release rates for general anisotropic bimaterial interface cracks is provided in this paper, which is applicable for the delaminated composites. Moreover, this definition can be reduced to the classical definition for a crack tip in homogeneous media when the two materials become the same. A simple quadratic relation between K_i and _Gi is derived, which is further reduced explicitly for orthotropic bimaterials. The influence of fiber orientation and the coupling among opening, shearing and tearing mode fracture are studied numerically. The results show that the classical stress intensity factors and energy release rates are still the dominant stress intensity and energy release rate of the mixed mode condition induced by the interface.     

Characteristics of brittle fracture under general combined modes including those under bi-axial tensile loads

In this paper, the brittle fracture initiation characteristics under general combination of the opening mode (Mode I), sliding mode (Mode II) and tearing mode (Mode III) were investigated both theoretically and experimentally.

First, the perfectly brittle fracture tests were conducted on specimens of PMMA (Polymethylmethacrylate) for all possible combinations of the fracture modes including respective pure modes. The experimental fracture strengths were compared with those predicted by the fracture criteria which are represented in terms of: (1) maximum tangential stress, [σ_gq]_max, extended to general combined modes, (2) maximum energy release rate at the propagation of a small kinked crack, [G^k(γ)]_max, and (3) newly derived maximum energy release rate at the initiation of a small kinked crack, [G(γ)]_max. It was found that the [G^k(γ)]_max or [G(γ)]_max criterion was very effective to predict both the direction of initial crack propagation and the fracture strength. These energy release rates are expressed in closed forms, and the interaction curves of the brittle fracture strength under arbitrary combinations of Modes I, II and III were derived.

Next, for fracture accompanied by plastic deformation, tests were carried out on specimens of mild steel (SM 41) imposing bi-axial tensile loads at various low temperatures. Then, brittle fracture with plastic deformation occurs under a combination of Modes I and II. In the case of brittle fracture with small scale yielding, the [G(γ)]_max criterion predicts well the direction of initial crack propagation but estimates only lower fracture strength than the experimental one. In the cases of brittle fracture with large scale yielding and under general yielding, it was found from the fracture tests that the direction of initial crack propagation was nearly normal to the resultant vector of the crack opening displacements in the opening and sliding modes at the notch tip. To this type of fracture, the modified COD criterion predicts well the direction of initial crack propagation, but lower fracture strength.

When brittle fracture occurs under the influence of plastic deformation, in such cases as the last three mentioned above, the actual fracture strength is higher than what the most reliable criterion predicts and it increases as deformation in Mode II becomes larger.     

Relaxation of residual stress with fatigue loading

Investigations have been carried out to study the relaxation of the surface residual stress in 0.23% C steel due to the application of fatigue loading. The residual stress was induced in the specimen by pre-straining and was measured by X-ray back reflection method using Cr-K radiation. The surface residual stress induced, depends on the plastic strain and appears to bear a relation of the type σ_R = σ_o(e_p)^0.78. The decay of the residual stress appears to depend on log N, given by the relation σ_R1 = σ_RO−K log N, where N is the number of fatigue cycles. The constant K depends on the initial value of the residual stress.     

A curvilinear integral method for multiaxial fatigue life computing under non-proportional, arbitrary or random stressing

Some popular concepts for reducing three variable stress components σ_x(t), σ_y(t), τ_xy(t) to one equivalent amplitude spectrum, and the use of the linear damage accumulation hypothesis, have been evaluated as not fully correct when these components vary non-proportionally and arbitrarily. A different approach is suggested: computing damage accumulation by means of an integral directly on the non-radial arbitrary path, called the ‘trajectory’, described in the σ_x−σ_y plane when τ_xy(t) = 0, in the σ_x−τ_xy plane when σ_y(t) = 0, or in a special coordinate space where this trajectory is invariant of stress directions x, y. If the trajectory is random, it may be replaced by a statistical two-dimensional density of distribution. The integrand, called the R-function, is derived from various S−N fatigue curves under different determined loadings. Thus the traditional S−N function is replaced by the R-function for direct damage summation with differential analysis, which allows the loading to be arbitrary (non-cyclic, multiaxial and non-proportional). The method works by means of computer programs and is applicable to real structures.     

Development of Bi-oxide superconducting tapes and coils

We have developed Bi-2212 and 2223 tapes. For Bi-2212, two double stacked pancake type coils were fabricated using Bi-2212/Ag tapes prepared by a combination of the continuous dip-coating process and melt-solidification. A small coil (13 mm inner bore, 46.5 mm outer diameter) was inserted in a conventional superconducting magnet system. In a bias field of 20.9 T, the generated field of the coil was 0.9 T, at an I_c of 310 A (criterion 10⁻¹³ Ωm) at 1.8 K. Thus, the superconducting magnet system achieved the generation of a field of 21.8 T in the full superconducting state. A large coil (20 mm inner bore, 94 mm outer diameter) generated a field of 2.6 T (I_c = 385 A (10⁻¹³ Ωm)) at 4.2 K and 1.53 T (I_c = 225 A (10⁻¹³Ωm)) at 20 K in self-field. For Bi-2223, tapes were prepared by the powder-in-tube technique using Ag-10% Cu-x%M (x = 0–1.0, M = Ti, Zr, Hf or Au) alloy sheaths. The high J_c values of 5–7 × 10⁴ A cm⁻² at 4.2 K and 14 T were obtained for the tapes doped with x = 0.03–0.1 at.% Ti, 0.1 at.% Zr, 0.1 at.% Hf or 0.3% Au. These tapes have a modified Bi-2223 grain structure at the sheath/core interface and also a dense and more aligned microstructure, resulting in higher J_c values.     

Magnetoimpedance effect at various temperatures for manganite La0.7Ca0.3MnO3−δ

In the present work, the AC magnetoimpedance effect in La_0.7Ca_0.3MnO_3−δ at various temperatures are investigated. The peak of the metal–insulator transition occurs in the temperature dependence of impedance. Negative magnetoimpedance effect in the La_0.7Ca_0.3MnO_3−δ is obtained at frequencies f≤10 MHz. In the magnetoimpedance effect of manganites, the magnetic field not only decreases the permeability μ_t, but also reduces the resistivity ρ by aligning the local spins and varying the transfer integral t_ij. The AC magnetoimpedance participated by the DC colossal magnetoresistance (CMR) in manganites, should be connected with the combined effects of double exchange interaction, electron–phonon coupling and skin effect.