A method for calculating differential constitutive equation of linear viscoelastic composite model

The stress–strain behaviors of viscoelastic materials are often simulated using a model composed of various combinations of springs and dampers. With the increase in the number of springs and dampers, the viscoelastic characteristics of the model will approach those of the actual material. This study discusses how to obtain the differential constitutive equation of a viscoelastic model composed of any number of springs and dampers. First, the general viscoelastic model is regarded as the combination of various Kelvin units. The viscoelastic model is then transformed into a digraph. Based on the relationships between the independent path of the digraph and the strain equation of the viscoelastic model and between the closed enclosure and the stress equation, the derivation of the constitutive equation is transformed into operations involving the incidence matrix of the digraph. Finally, the coefficients of the linear differential operator of the constitutive equation of the viscoelastic model can be obtained by block matrix operations. This method is suitable for computer programming and has a certain significance for accurately constructing viscoelastic models of engineering materials.

A Minimum Creep Rate for 2-1/4Cr-1Mo Steel Consistent With the ASME Section III, Division 5 Rules

This technical note describes a minimum creep rate model for 2-1/4Cr-1Mo steel that is consistent with the current creep strain equation embedded in the ASME Boiler & Pressure Vessel Code Section III, Division 5, Subsection HB, Subpart B isochronous stress–strain curves. Minimum creep rate models for all the Section III, Division 5 Class A materials are required for the development of improved high temperature design methods. Of all the Class A materials, only 2-1/4Cr-1Mo does not have a readily identifying minimum creep rate term in the current isochronous stress–strain curve model.

Development of the External Pressure Charts for 2¼Cr-1Mo and Mod.9Cr-1Mo Steel at Elevated Temperature Design

For the required thickness estimation against buckling in the elevated temperature design, the external pressure chart for two kinds of ferritic steel, 2 1/4Cr-1Mo and Mod.9Cr-1Mo steel, was developed. On the basis of the guideline described in the ASME BPVC Section II, Part D, Mandatory Appendix 3 with mechanical and physical properties provided in the JSME fast reactor code, the external pressure charts for each material were constructed. The minimum stress-strain curve for evaluating the external pressure chart was applied the stress-strain equation with design yield strength, Sy, provided by the JSME fast reactor code. As a result, three external pressure charts with digital values were proposed for elevated temperature design. Moreover, the rationalization effect from the current alternative was evaluated by the sample problem. This proposal resolves two issues. One is alternative use of chart for lower strength material over the 150 °C. The other is the external pressure chart above 480°C for which ferritic steels are not available.

An Analytical Model for a Pneumatic Vibration Isolator with the Stiffness Effect of the Elastomeric Diaphragm

The elastomeric diaphragm is widely used in pneumatic vibration isolators, and the relevant model is often ignored due to its complexity. Considering that the ignored model of the elastomeric diaphragm in pneumatic vibration isolators plays an important role in the discrepancy between the predicted and practical behavior, this paper develops an analytical model for the elastomeric diaphragm using the Mooney-Rivlin modeling method and elastomeric theory. Specifically, the elastomeric diaphragm consists of several segments in the axial section. After considering the structural restriction, each segment can be simplified as uniaxial stretching, and the force-strain equation can be established for each segment. By combining the equations of all segments, an analytical model of the elastomeric diaphragm can be built and solved via numerical methods. The developed model is added to the standard model of pneumatic cylinders to supply a complete analytical model for pneumatic vibration isolators. The experimental results demonstrate that the analytically predicted behavior is similar to the practical behavior. The proposed analytical model can be used as a guide for the parameter design of pneumatic isolators in practice.

THIN-WALLED BARRELL SHELL DEFLECTIVE MODE ANALYSIS

The paper deals with the deflective mode of steel rotary shell with different form of outer surface that are loaded with axially symmetric load. The results show solution of shell voltage and strain equation under the load that is described by exponential law and based on efforts from temperature differentials. Besides, the paper represents design formulas for deflection analysis, running bending moments and running transverse forces in shells with different abutment to the basis. It was shown the basic function of deflection and maximum value of relevant parameters of the reaction. The analysis of aspects about efficiency of using corrugated wall for steel barrel shell is done. The results in analytical and graphical form are shown. According to resulting formulas, it was made comparative calculations of shells with constant and variable wall thickness.

Dynamic Recrystallization of Mg-8Gd-3Y-1Nd-0.5Zr Alloy during Hot Deformation

Uniaxial hot compression was conducted on Gleeble-3500 thermo simulation machine. Based on stress-strain curves, the constitutive relationship and the dynamic recrystallization kinetics model of Mg-8Gd-3Y-1Nd-0.5Zr were established. Simultaneously, dynamic recrystallization mechanism of this alloy under different deformation condition was investigated by SEM, EBSD and OM. The critical strain equation and the dynamic recrystallization kinetics model were obtained. The results showed that the dynamic recrystallization volume fraction increased with the increasing of the strain.The twin dynamic recrystallization (TDRX) was the mainly DRX mechanism at 350°C;the dynamiac recrysallization mechanism was dominated by continuous dynamic recrystallization (CDRX) at 400°C and 450°C. At higher temperature (500°C), the dynamic recrystallization was dominated by discontinuous dynamic recrystallization (DDRX) with a small amount of CDRX.

Non-Linear Analysis of Mode II Fracture in the end Notched Flexure Beam

Analysis is carried-out of fracture in the End Notched Flex- ure (ENF) beam configuration, taking into account the material nonlin- earity. For this purpose, the J-integral approach is applied. A non-linear model, based on the Classical beam theory is used. The mechanical be- haviour of the ENF configuration is described by the Ramberg-Osgood stress-strain curve. It is assumed that the material possesses the same properties in tension and compression. The influence is evaluated of the material constants in the Ramberg-Osgood stress-strain equation on the fracture behaviour. The effect of the crack length on the J-integral value is investigated, too. The analytical approach, developed in the present paper, is very useful for parametric analyses, since the simple formulae obtained capture the essentials of the non-linear fracture in the ENF con- figuration.