An Analytic Solution for an Expanding/Contracting Strain-Hardening Viscoplastic Hollow Cylinder at Large Strains and Its Application to Tube Hydroforming Design

This paper presents a semi-analytic rigid/plastic solution for the expansion/contraction of a hollow cylinder at large strains. The constitutive equations comprise the yield criterion and its associated flow rule. The yield criterion is pressure-independent. The yield stress depends on the equivalent strain rate and the equivalent strain. No restriction is imposed on this dependence. The solution is facilitated using the equivalent strain rate as an independent variable instead of the polar radius. As a result, it reduces to ordinary integrals. In the course of deriving the solution above, the transformation between Eulerian and Lagrangian coordinates is used. A numerical example illustrates the solution for a material model available in the literature. A practical aspect of the solution is that it readily applies to the preliminary design of tube hydroforming processes.

In Situ Stress Effects on Smooth Blasting: Model Test and Analysis

Most of the roadway excavation is completed by the drilling and blasting method. With the increase of buried depth, the existence of ground stress will generate a significant impact on the rock blasting, especially on the smooth blasting. In this study, self-made homogeneous similar materials and digital image correlation methods were used to determine influence of ground stress on the smooth blasting under uniform explosive charge parameters and various in situ stress conditions. The results show that the crack outline after blasting changes from zigzag to straight in shape, and multifractal calculation results of the rupture section between blastholes show that the fracture surface becomes flatter as ground stress increases, which is conducive to roadway formation. The strain and equivalent strain rate obviously decrease as the distance between the blasthole and measuring points increases. The same trend occurs as the confining pressure goes up. Meanwhile, a postexplosion acoustic wave test indicates that confining pressure inhibits damage of the retained rock, which is consistent with strain and equivalent strain rate results. Finally, we discussed the crack propagation mechanism of rock in smooth blasting.

An An Analysis of Strain Rate Distribution Using Streamline Model and A Quick Stop Device in Metal Cutting

In this paper, a quick stop device technique and the streamline model were employed to study the chip formation in metal cutting. The behavior of chip deformation at the primary shear zone was described by this model. Orthogonal test of turning process over a workpiece of the 6061-T6 aluminum alloy at different cutting speeds was carried out. The results of the equivalent strain rate and cumulative plastic strain were used to describe the complexity of chip formation. Finite element analysis by ABAQUS/explicit package was also employed to verify the streamline model. Some behavior of formation and strain rate distribution differs from the experimental results, but the overall trend and maximum results are approximately close. In addition, the quick stop device technique is described in detail. Which could be used in other kinds of studies, such as the metallurgical observation.

Numerical Implementation of a Rheology Model for Fiber-Reinforced Composite and Viscous Layer Approach for Friction Study

A transverse isotropic viscous model accounting for the anisotropy exhibited in fiber-reinforced composite is integrated in the numerical platform of the software Rem3D®. Simulations under various mechanical loading are tested for volume fiber concentrations of 3.5% and 14.7%. Equivalent stresses and equivalent strain rate deformations given by the software were compared to the ones predicted by the model, finding very good agreements. As a second point developed on this paper, we comment on the slip condition between Die/Punch tool with the composite under compression. We noticed that the variation of the viscosity value on a small layer between the Die/Punch tooland the composite affects the nature of the contact. A viscous friction is then formulated as a technique to set slip/no-slip contact condition. We found that the slip condition is recovered at lower values of the viscosity in the interface Die/Punch with the reinforced composite, whereas the no slip condition stated for higher viscosity values.

Steady-State Creep Deformations and Stresses in FGM Rotating Thick Cylindrical Pressure Vessels

In the present study, a closed-form analytical solution for the steady-state creep stresses of rotating thick cylindrical pressure vessels made of functionally graded materials (FGMs) is carried out. Norton's law governs the creep response of the material. Exact solutions for stresses and strain rate are obtained under the plane strain condition. How different material parameters involved in Norton's law affect radial and circumferential stresses together with the equivalent strain rate in rotating thick-walled cylindrical vessels under internal pressure is investigated. The result obtained shows that the property of FGMs has a significant influence on the equivalent creep strain rate and stresses distributions along the radial direction.

Effect of Plastic Anisotropy on the Strain Rate Intensity Factor: A Simple Analytic Solution

Solutions for many rigid/plastic models are singular in the vicinity of maximum friction surfaces. In particular, the magnitude of the equivalent strain rate near such surfaces is controlled by the strain rate intensity factor. This factor is the coefficient of the leading singular term is a series expansion of the equivalent strain rate in the vicinity of maximum friction surfaces. Since the equivalent strain rate has a great effect of material properties, it is of important to reveal the dependence of the strain rate intensity factor on parameters characterizing material models. In the present paper, quite a general model of anisotropic plasticity under plane strain conditions is adopted. Then, using an analytic solution for instantaneous compression of a layer of plastic material between two parallel plates the effect of the shape of the yield locus on the asymptotic behavior of the equivalent strain rate in the vicinity of the friction surface is demonstrated.

Mathematical Modelling to Evaluate the Superplastic Material Constants by Bulge Test

The mechanical behaviour of a superplastic material is often modelled by the power law relationship between the equivalent flow stress, the equivalent strain and the equivalent strain-rate at least over a limited range of strain rates. This paper introduces an original mathematical modelling to determine the superplastic material constants m, n and K by means of experimental tests carried out using a standard forming die geometry.

Texture Formation in AA5182 Aluminum Alloy by Hot Extrusion

The behavior of texture formation in AA5182 aluminum alloy is investigated by hot extrusion tests under equivalent strain rates and temperatures ranging from 5.0×10-4 s-1 to5.0×10-2s-1 and from 723K to 823K, respectively. After the deformation, {001} (extrusion plane) and {111} double fiber texture is formed in all the deformation conditions. {001} texture develops after the deformation at 823K under equivalent strain rate of 5.0×10-3s-1 up to an extrusion ratio of 2.8. The size of {001} grains is larger than the mean grain size, suggesting that the {001} texture formation is attributed to grain boundary migration. Weakening of {001} texture is confirmed in the annealed section of the specimen.