This paper reviews the recent progress in sensitivity analysis applied to the nonlinear finite element method (FEM). The sensitivity analysis method has been successfully developed over the years as a convenient tool for use in linear FEM, and it is reasonable to say that today the framework of the methodology is nearly completed. Nonlinear FEM-based sensitivity analysis, however, has only received considerable research attention since the mid 80's. Regarding static nonlinear problems, path-dependent problems such as elastic-plastic problems have been investigated by a number of research groups, and several competitive methods exist. Sensitivity analysis is also practically important in nonlinear buckling and postbuckling problems, for which several methods have been proposed. The performance of the proposed methods in static and buckling/postbuckling problems are compared, and some numerical examples are introduced to clarify the characteristics of the sensitivity which are peculiar to nonlinear problems.

View full abstract

An analysis method for evaluating the sensitivity of buckling load in geometrically nonlinear finite element methods is developed. By searching for the pseudo critical point in the perturbed system on the surface of the hyper-cylinder where the original critical point exists, the sensitivity of buckling load is estimated. Compared with other methods, the present method can cope with both snap-through and bifurcation problems without an eigenvalue analysis. In addition, the load sensitivity at arbitrary points on the equilibrium path can be calculated under the total-displacement constraint condition. Two examples of sensitivity buckling analysis of shell structures are demonstrated to examine the validity of this method, and satisfactory results are obtained.

View full abstract

The macroscopic elastic-plastic constitutive relation of inhomogeneous material is affected not only by the characteristics of respective constituents, but also by the microscopic distribution of stress and strain in heterogeneous regions. In order to describe the deformation behaviour of inhomogeneous material, several parameters are defined. A plane model of inhomogeneous material with inclusions is used for numerical simulation, and the changes in the parameters during elastic-plastic deformation are calculated and compared. Uniaxial loading under the plane-strain condition is assumed. It is concluded that the initial aspect ratio has a marked influence on the deformation behaviour. One of the parameters, called the constraint ratio, remains nearly constant with increase in the applied strain or the degree of inhomogeneity. This characteristic seems to be important for estimating the deformation behaviour of inhomogeneous material. The constitutive relation of inhomogeneous material may also be estimated from the value of the constraint ratio.

View full abstract

A finite-element polycrystal model is proposed to predict plastic behaviors of polycrystal metals. Each element in FEM is assumed to be a crystal of cubic shape having its proper orientation, and microscopic plastic strains are assumed to be uniform within each crystal. For the determination of rate-independent slips, a new numerical scheme, the "Successive Accumulation Method", is proposed on the basis of Schmid's law. The numerical code of the present model is quite simple and can be applied to arbitrary loading paths. A stress-strain curve under simple tension is calculated for a non-work-hardening FCC metal and compared with those of other theories.

View full abstract

The distributions of stress induced by an applied stress σ₀ in five joint plate specimens (copper/silicon nitride) with different thicknesses were calculated using three-dimensional (3-D) FEM stress analysis and the results were compared with those obtained using two-dimensional (2-D) FEM stress analysis. Along the longitudinal center line perpendicular to the interface on the surface of the specimen, the 3-D FEM calculation predicted a maximum stress of approximately 1. 36σ₀ in the interfacial region in the silicon nitride, with a minimum stress of 0.9σ₀ appearing in the copper. On the other hand, the 2-D FEM predicted only slight change in the stress in the interfacial region, giving a value close to the applied stress σ₀. The maximum stress decreased more rapidly with decreasing thickness of the specimen, and the stress value agreed more closely with the value calculated by the 2-D FEM as the distance from the interface increased.

View full abstract

The aim of this study is the development of an image processing system for estimation of trabecular strength and to investigate the relationship between the loads and the trabeculae in the femoral head. The trabecular system is a useful source of information concerning the mechanical environment of bones which is important in orthopedic treatment. In this paper, the distribution of principal stress obtained by the finite-element model based on Pauwels' theory is compared with that of trabecular strength estimated using the image processing technique. It is found that the result of the finite-element method is similar to the configuration of trabeculae in both magnitude and direction. This result shows that unknown loads applied to bone may be estimated using the inverse finite-element method.

View full abstract

Since the critical size of defects in ceramics is usually very small, the conventional method of fracture mechanics prediction often becomes inapplicable. In the present study, the fracture strength of silicon nitride with small defects is evaluated on the basis of the R-curve method. The parameters of the R-curve of silicon nitride are determined from the experimental relationship between the fracture strength and the defect size. For penny-shaped cracks, the fracture strength is constant for small defects and the critical stress intensity factor is constant for large defects. The equivalent defect size is an excellent parameter to correlate the fracture strength to the size of elliptical cracks with an aspect ratio between 0.3 and 1. For small voids, the fracture strength is nearly the same as that for a penny-shaped crack. On the other hand, for large voids, the fracture strength approaches a constant value which is equal to that of materials without voids divided by the elastic stress concentration factor. When the tip radius of deep long notches is small, the critical stress intensity factor for fracture is independent of the tip radius. A Monte Carlo simulation of bending fracture of silicon nitride was performed by randomly distributing penny-shaped cracks having random sizes in a specimen by a computer. On the basis of twenty-five runs of fracture simulation, the relationship between the bending strength and the equivalent defect length, and cumulative distribution function of the fracture strength were successfully derived.

View full abstract

Tests to determine the growth of load-controlled fatigue cracks were carried out on two kinds of structural steels under constant-amplitude and repeated two- and three-step loadings in the postyield region. Crack growth increment and crack closure were measured by the computer-aided unloading elastic compliance method. A fracture mechanics parameter, ΔJ/(1-J_max/C), was found to be a good parameter for expressing the crack growth rates under constant-amplitude loadings irrespective of the stress ratios, where ΔJ, J_max and C are the J integral range, the maximum J integral and a constant related to apparent fracture toughness of the specimen used, respectively. One-directional cyclic deformation was observed to occur under load cycles with high mean stresses. Moreover, it was found that crack closure and plastic deformation under variable amplitude loadings were affected by load variation pat-terns and load sequences. However, fatigue crack growth rates under varying loadings where both one-directional and cyclic plastic deformation were observed to be significant could be well estimated by the linear summation rule of crack growth using ΔJ^*/(1-J_max/C), where ΔJ^* is the J integral range-pair taking account of the above mentioned one-directional deformation.

View full abstract

In this investigation, singular fields of stresses and heat fluxes at the tip of a crack in a nonhomogeneous body, or functionally gradient material (FGM), are studied under both elastic and plastic conditions. It is found that the crack tip fields have the same forms as those in the homogeneous material, provided that the material properties of FGM are continuous. The heat fluxes have a square-root singularity at the crack tip, and the elastic crack tip stress field is characterized by the K-field of linear fracture mechanics and the plastic singular field is the HRR field for a power-law material. The relationship between stress intensity factors and the path-independent integral J^^^ proposed by Aoki, Kishimoto and Sakata is discussed.

View full abstract

In the present work, static and fatigue residual bending strengths of carbon fiber reinforced plastic (CFRP) laminates having impact damage are evaluated with four-and three-point bending tests. A steel ball was launched from an air gun and impacted upon CFRP laminates to generate impact damage. The delamination growth during fatigue tests and the fracture surface are observed with a scanning acoustic microscope and scanning electron microscope, respectively. The residual strengths determined by the four-point bending test are reduced, particularly when the impacted side is compressed. The degree of reduction is influenced by the propagation of surface cracks near the impact impression. The residual strengths determined by the three-point bending test are almost the same whether the impacted side is the top or the bottom. It is determined that the degree of reduction of strength is governed by the slide of the transverse cracks due to the shear force.

View full abstract

A reliability analysis of the Shinkansen vehicle axle using probabilistic fracture mechanics is presented. Failures of the axles are assumed to occur as the result of the growth of cracks originating from fretting corrosion in a wheelseat. Cracks are considered to be randomly distributed in size, and cyclic stresses induced during train operation are used in conjunction with the crack growth characteristics of the material to predict the variation of the crack size with the distance travelled. The probability of failure is considered to equal the probability of having a crack larger than the corresponding critical size. The effects of in-service inspections are evaluated for two different induction-hardened axles. Finally, a series of calculations were performed in order to assess the influence of various factors on these probabilities.

View full abstract

In this paper we discuss an analysis, with an atom probe, of nanometer-scale microstructural changes that occur during thermal aging of the ferritic phase of duplex stainless steel. The changes in electrochemical behavior and the magnetic hysteresis loop are examined and related to the microstructural changes. Cast duplex stainless steel containing 12.5% ferritic phase with a nominal composition of Fe-19%Cr-10%Ni-2%Mo was aged at 475°C for 443 h. By analysis, it is found that aging promotes a significant phase separation of the ferrite into Cr-rich and Fe-rich regions with spatial durations of 10-20 nm. An electrochemical reactivation peak observed in the polarization curve of aged steel is thought to be related to the Fe-rich region with a Cr concentration below 14 at% (13% in weight). Nanometer-scale microstructural changes are shown to cause hardening and increase the loss in magnetic hysteresis.

View full abstract

The attenuation of surface acoustic waves is a useful parameter for estimating grain size, porosity and microstructure, which are closely related to electrical and mechanical properties of materials. In the present paper, a novel method for the determination of ultrasonic attenuations in the surface layer of materials using an ultrasonic spectroscopic technique is proposed. The method is based on absolute measurement of the reflection coefficient of the materials and analysis of its spectral behavior. The attenuations are determined by detecting the frequency of least reflection and by estimating a locus of zero points of the reflection coefficients in the complex plane. An experiment with annealed carbon steel was demonstrated. The reflection coefficient calculated with the attenuations estimated by the present method indicated a frequency dependence similar to the experimental result. This reveals that the estimated attenuations are good approximations of the actual acoustic response of materials.

View full abstract