Akio Takimoto

Nonlinear Optimization Using Multilayer Neural Network : Application to Optimizing Condition of Heat Treatments

Optimization method for various phenomena on nonlinear problems is presented by using multilayer neural network in this paper. The each gradients of objective function for the output signals of the network is assumed in order to define the effects of learning on back propagation, and then it comes to derive optimum design variables on the problems including inelastics by self-teaching. Furthermore, it is also presented that the idea of probability can realize efficient optimization by adding fluctuation to the network. The results of the presentation are applied to the reduction problem of residual stress of welding by use of thermo-elasto-plastic analysis and show its applicability to the problems.

The variation of fracture surface marks in brittle plastic sheet specimens during a primary crack propagation. In the case of an intermediate-length central crack.

We have reported that fracture surface marks in brittle plastic sheet specimens having short (≤ 5mm) and long (≥ 40mm) central primary cracks are well expressed by equations under the fracture conditions of a constant load (or stress) and a constant deflection (or strain), respectively. Here, we discuss the velocity and the marks in the specimens having an intermediate-length central crack. The crack velocity is measured and expressed by an equation where the velocity is presumed to be composed of both constant stress and strain components. In this case, a fracture starts with a constant stress condition which changes gradually to a constant strain condition as the crack propagates, and we call this a fracture in a mixed condition. This velocity expression, combined with the existing relation between crack velocity and a dynamic stress-intensity factor, gives the variations of the dynamic stress-intensity factor and a dynamic strain energy release rate both of which excellently predict the experimental variations of the fracture surface marks in those specimens such as the number of marks, the relative interference appearing distance (e/Co2) and the relative critical distance (d/Co2).

Discussion of thn linking and cracking processes of two neighboring holes in a thin sheet metal and their fracture ductility under tension.

The linking and cracking processes of two neighboring holes in a thin sheet metal were investigated in detail to get quantitative information about the deformation behavior of voids in a ductile fracture. The holes deform into elliptical holes and crack with come intruding and/or protruding under tension, depending on the experimental variables of the inter-hole distance ξo/2ro (ro: radius), the two-hole arrangement angle φ0 and the plastic strain. The complicated shape of the deformed hole is qualitatively measured and analyzed. The deformation of two holes having various arrangements of ξo/2ro and φ0 has also been analyzed by an elastic-plastic FEM, and the results are in qualitative agreement with the experimental data. Fracture ductility for the linking or cracking of two holes is approximately expressed by applying McClintocks fracture model for each volume which contains a hole at its center. The values of linking strain eZ, cal. and fracture strain ef, cal. by the equations are consistent with the experimental linking strain eZ, exp. and cracking strain eC, exp. where cracking strain is, of course, a few percentages smaller than the fracture strain in a ductile fracture.

Relationship between sharply notched fracture strength and fracture surface marks in a brittle plastic in tension. (In the case of an inside loading)

The fracture strength was varied by changing an inter-grip distance (which we call a gage length here) of a sharply center-notched tensile sheet specimen of unsaturated polyester resin, where the specimen width, thickness, crack length and loading method were kept constant. The loading method is such that the main load works on a central-line parallel to the axis of loading which crosses perpendicularly the central crack length. We call this an inside loading in contrast to an outside loading (1). The number, density, area ratio of fracture surface marks vary with the fracture strength of the material. The total number of marks increases with the fracture strength. The density and area ratio marks increase at each different rate with respect to fracture strength. These results are discussed with the analytical relations of the fracture strength, the dynamic stress-intensity factor and the dynamic strain-energy-release rate by employing the reported relations. The fracture surface marks are examined by the two-dimensional equation of fracture surface marks, and the analytical area ratio of the marks is also calculated.

The variation and comparison of fracture surface marks on an unsaturated polyester resin due to primary crack propagation conditions.

The conditions for crack propagation were varied from a constant load (or stress) condition to a constant elongation (or strain) condition while increasing a central crack length (2Co1) from 6mm to 200mm in thin sheet plastic (Unsaturated Polyester Resin) specimens of 240mm width (2W), which were fractured under tension at room temperature. Numbers and various dimensions of fracture surface marks of both end close type (abbreviated BECM) and one end opened type (abbreviated OEOM) were measured under optical and scanning electron microscopes and analyzed. The marks observed in specimens fractured under a constant strain condition are excellently approximated by the equation of fracture marks proposed previously by us. Fracture strength and average values of their dimensions for each crack length decrease in a hyperbolic curve similar to the relative crack propagation distance at fracture W/Co1 as the crack length increases. The experimental results for specimens having Co1≒5.1mm, 23.85mm and 58.42mm are compared. Their dimensions and their gradients decrease as the length of the primary crack increases, and all these relations are predicted well by the equation of fracture marks.

The variation of the strain-hardening exponent due to grain-size distributions in engineering metallic sheet materials.

Grain-size distributions of commercially pure aluminum, copper and 6·4 brass are approximated well with a log-normal distribution function, and it is shown that the median and the standard-deviation of distributions increase the strain-hardening exponent of sheet specimens of copper and 6·4 brass under tension. Both the simple equal-strain and equal-stress models of a composite flow curve are introduced, which are based on the flow stress rule of nth-power curve relation, connecting with the distribution function whose upper grain-size is bounded with 3·5 times the mean-grain diameter. The equal-strain model gives the lower flow stress limit, and the equal-stress model yields the upper one, and the experimental flow stress appears in between or closely around these two neighboring limits. Both models prove analytically that the median and the standard-deviation of distributions increase the strain-hardening exponent of a sheet metal under tension. The former model predicts the upper bound of the strain-hardening exponent and the latter one predicts the lower one, and experimental data on 6·4 brass are shown to appear in between them.