Multi-axial strain-stiffening elastic potentials with energy bounds:explicit approach based on uniaxial data

According to the well-known models for rubberlike elasticity with strain- stii^ening effects, the unbounded strain energy is generated with the unlimitedly growing stress when the stretch approaches certain limits. Toward a solution to this issue, an explicit approach is proposed to derive the multi-axial elastic potentials directly from the uniaxial potentials. Then, a new multi-axial potential is presented to characterize the strain-stiffening effect by prescribing suitable forms of uniaxia] potentials so that the strain energy is always bounded as the stress grows to infinity. Numerical examples show good agreement with a number of test data.

THE INTEGRAL AS A FUNCTION OF THE UPPER LIMIT AND AN ANALYTICAL SOLUTION TO PLANE STRAIN DRAWING AND EXTRUSION

A kinematically admissible velocity field which is different from Avitzur's is established in Cartesian Coordinates. An upper-bound analytical solution to strip drawing andextrusion is obtained by using the integral as a function of the upper limit in this paper.

An Isogeometric Cloth Simulation Based on Fast Projection Method

A novel continuum-based fast projection scheme is proposed for cloth simulation.Cloth geometry is described by NURBS,and the dynamic response is modeled by a displacement-only Kirchhoff-Love shell element formulated directly on NURBS geometry.The fast projection method,which solves strain limiting as a constrained Lagrange problem,is extended to the continuum version.Numerical examples are studied to demonstrate the performance of the current scheme.The proposed approach can be applied to grids of arbitrary topology and can eliminate unrealistic over-stretching efficiently if compared to spring-based methodologies.

Effect of consolidation parameters on mechanical properties of Cu-based bulk amorphous alloy consolidated by hot pressing

Cu50Zr40Ti10 bulk amorphous alloys were fabricated by hot pressing gas-atomized Cu50Zr40Ti10 amorphous powder under different consolidation conditions without vacuum and inert gas protection. The consolidation conditions of the Cu50Zr40Ti10 amorphous powder were investigated based on an L9（34） orthogonal design. The compression strength and strain limit of the Cu50Zr40Ti10 bulk amorphous alloys can reach up to 1090.4 MPa and 11.9 %, respectively. The consolidation pressure significantly influences the strain limit and compression strength of the compact. But the mechanical properties are not significantly influenced by the consolidation temperature. In addition, the preforming pressure significantly influences not the compression strength but the strain limit. The optimum consolidation condition for the Cu50Zr40Ti10 amorphous powder is first precompacted under the pressure of 150 MPa, and then consolidated under the pressure of 450 MPa and the temperature of 380 °C.

Analysis of complete plasticity assumption for solid circular shaft under pure torsion and calculation of shear stress

The distribution of shear stress on the cross-section of plastic metal solid circular shaft under pure torsion yielding, the applicability of complete plastic model assumption and the shear stress formula were researched. Based on the shear stress formula of circular shaft under pure torsion in elastic stage, the formula of torque in elastic stage and the definition of yield, it is obtained that the yielding stage of plastic metal shaft under pure torsion is only a surface phenomenon of torque-torsion angle relationship, and the distribution of shear stress is essentially different from that of tensile stress when yielding under uniaxial tension. The pure torsion platform-torsion angle and the shape of torque-torsion angle curve cannot change the distribution of shear stress on the shaft cross-section. The distribution of shear stress is still linear with the maximum shear stress ts. The complete plasticity model assumption is not in accordance with the actual situation of shaft under torsion. The experimental strength data of nine plastic metals are consistent with the calculated results of the new limiting strain energy strength theory （LSEST）. The traditional yield stress formula for plastic shaft under torsion is reasonable. The shear stress formula based on the plane assumption in material mechanics is applicable for all loaded stages of torsion shaft.

PREDICTION FOR FORMING LIMIT OF AL2024T3 SHEET BASED ON DAMAGE THEORY USING FINITE ELEMENT METHOD

This paper presents the application of anisotropic damage theory to the study of forming limit diagram of A12024T3 aluminum alloy sheet. In the prediction of limiting strains of the aluminum sheet structure, a finite element cell model has been constructed. The cell model consists of two phases, the aluminum alloy matrix and the intermetallic cluster. The material behavior of the aluminum alloy matrix is described with a fully coupled elasto-plastic damage constitutive equation. The intermetallic cluster is assumed to be elastic and brittle. By varying the stretching ratio, the limiting strains of the sheet under biaxial stretching have been predicted by using the necking criterion proposed. The prediction is in good agreement with the experimental findings. Moreover, the finite element cell model can provide information for understanding the microscopic damage mechanism of the aluminum alloy. Over-estimation of the limit strains may result if the effect of material damage is ignored in the sheet metal forming study.

Deformation and Densification Laws of Powder Cold Forging

The deformation and densification laws of preform upsetting and closed-die forging were researched based on experimental results of cold forging of deoxidized Fe powder sintering porous material under different initial conditions such as friction factor, ratio between height and diameter and relative density. The fracture limit criteria＂ for powder cold-forging upsetting and the limit strain curve were achieved. The effect of friction facto,, ratlt, between height and diameter and relative density on fracture strain limitation was emphatically analyzed. The limit process parameter curves for the deformation of upsetting were also confirmed. Laws of deformation, densification and density distribution for closed-die forging of powder perform during cold-forging were further analyzed and discussed with the help of experimental phase analysis. As a result, this experiment established theoretical foundations for the design of preform and die as well as optimization of technological process parameters.

Formability of the AMS 5596 Sheet in Comparison with EDDQ Steel Sheet

Some materials form better than others, moreover, a material that has the best formability for one stamping may behave very poorly in a stamping of another Configuration. The forming limit of a metal sheet is generally given in terms of the limiting principal strains under different loading conditions and represented by the so-called FLD （forming limit diagram）. In view of the difficulty to experimentally determine the forming limits, many researchers have sought to predict FLD. The formability of sheet metal has frequently been expressed by the value of strain hardening exponent and plastic anisotropy ratio. The stress-strain and hardening behaviour of a material is very important in determining its resistance to plastic instability. For these reasons, extensive test programs are often carried out in an attempt to correlate material formability with value of some mechanical properties. In this study, mechanical properties and the FLD of the AMS 5596 sheet metal was determined by using uniaxial tensile test and Marciniak＇s flat bottomed punch test respectively.

Limit Analysis of Defect-Free Pipe Elbow Under Internal Pressure With Mean Yield Criterion

With mean yield（MY）criterion,an analytical solution of the collapse load for a defect-free pipe elbow under internal pressure is first obtained.It is a function of ratio of thickness to radius t0/r0,strain hardening exponent n,curvature influence factor mand ultimate tensile strength.The collapse load increases with the increase of m,and it is the same as the burst pressure of straight pipe if m=1is assumed.The MY-based solution is compared with those based on Tresca,Mises and twin shear stress（TSS）yield criteria,and the comparison indicates that Tresca and twin shear stress yield criteria predict a lower bound and an upper bound to the collapse load respectively.However,the MY-based solution lies just between the TSS and Tresca solutions,and almost has the same precision with the Mises solution.