Thickness Normal Stress Research Articles

Prediction equation for flange thickness of aluminum alloy cylinder-shaped parts by pressure rate under the action of thickness normal stress

Prediction equation for flange thickness of aluminum alloy cylinder-shaped parts by pressure rate under the action of thickness normal stress

Influence of thickness reduction on forming limits of mild steel DC01

The Forming Limit Diagram (FLD) is an essential tool to assess sheet metal formability in sheet metal deep drawing. In FLDs/FLC (Forming Limit Curve) is representation of material formability limits at which material is not able to withstand higher deformation. In this work, different methodologies for FLC determination of mild steel DC01 are investigated. The Nakajima test is a well-known experiment for FLC determination but, however, contact conditions that can appear in the form of either friction or pressure may perturb the results. The former may cause the need for repetitions for different widths by altering the necking location, whereas the latter may be responsible for overestimation of the material formability. Another method for FLC determination without those effects is to use the cruciform specimen test under biaxial loading conditions. As the first step, Necking has to be induced at the center of cruciform specimen by thickness reduction or groove. Therefore, in this work, the cruciform geometry under biaxial loading is optimized using FEM through the comparative analysis. The goal of simulation was to induce the necking just in the thinner gauge, not adjacent zone. Thereupon, different loads on biaxial machine’s axes can provide different strain paths at the thinner gauge of the optimized specimen. After reviewing of various researches in connection with thickness reduction effect on sheet metal deformation, it was found that thickness reduction might not influence the material formability during uniaxial and plane strain tensions, but it was observed that there is gradual decrease of limit strains with decreasing the thickness for equi-biaxial tension.Manufacturing process like milling, cause small defects on material surface and local instability takes place at lower level of deformation. Besides, it was found that existence of through thickness normal stress leads to higher value of FLC. Deformation during Nakajima and cruciform experiments were captured by Digital Image Correlation (DIC) system. The execution and evaluation of those experiments are explained in detail and Time Dependent Method (TDM) was applied to detect the beginning time of instability. Experimental strain paths are compared with consideration of strain rates and, as it was expected, FLC from cruciform specimen is lower than Nakajima one, especially on the right hand side of FLD. The remarkable difference can be attributed to defects in the material and existence of through-thickness normal stress, which leads to overestimation of the material formability during Nakajima experiment.

Flow property of AA2B06 sheet using overlapping elliptical bulge test

A novel experimental approach was presented, namely the overlapping elliptical bulge test, which can load and research thickness normal stress. Theoretical analysis model of the overlapping elliptical bulging was described, the equivalent stress–strain curves of target sheets with different ellipticity ratios were determined experimentally, and influences of the material performance and thickness of overlapping sheets on the flow property of the target sheet were also researched. The results show that, in the overlapping hydraulic bulge test, the equivalent stress–strain curve can be determined up to larger strains before necking than in the no overlapping hydraulic bulge test. And as the die ellipticity ratio decreases, the flow stress curves tend to move away from the curve obtained by circular (b/a=1) bulging test. Meanwhile, the flow property of the target sheet can be improved by choosing higher strength coefficient K, larger work hardening exponent n and proper thickness of the overlapping sheet.

Theoretical investigation on the springback behavior of AA7B04 sheet in hydraulic bulge process

The derivation of theoretical formula about the amount of springback in the hydraulic bulge process using aviation aluminum alloy 7B04 was studied. Firstly, the traditional formula of plate bending theory was amended when the thickness normal stress was introduced into it. Based on it, the theoretical formula of amount of springback in hydraulic bulge process with thickness normal stress was deduced. Secondly, by using the numerical simulation and the experiment, the theoretical formula was proved to be correct. Thirdly, several classic analytical models for radius of curvature at the bulging vertex and bulging vertex thickness were verified by use of the hydraulic bulge experiments. When the cavity pressure was 30 MPa, the measured springback value of radius of curvature at the bulging vertex was 1.2 mm, while the result calculated by the theoretical formula was 0.8 mm and the theory error was 33.3 %. When the cavity pressure was 50 MPa, the measured springback value of radius of curvature at the bulging vertex was 3.13 mm, while the result calculated by the theoretical formula was 1.98 mm and the theory error was 36.7 %. According to the actual measurement, the predicted values of Hill’s model concerning radius of curvature at the bulging vertex agreed well with experimental values and the predicted values of the Jovane’s model concerning bulging vertex thickness agreed well with experimental values. The theoretical formula of amount of springback with the thickness normal stress which is obtained by the derivation is proved to be correct and reasonable by the plate hydraulic bulge experiment. In addition, the calculation of the springback value in sheet forming process which is in three-dimensional stress state can be guided by the theoretical formula.

Nonlinear dynamic response of symmetric laminated composite beams under combined in-plane and lateral loadings using full layerwise theory

The nonlinear dynamic responses of symmetric laminated composite beams subjected to combined in-plane and lateral loadings are studied in this paper. The composite laminates are modelled using the full layerwise theory (FLWT) based on the advanced first order shear deformation theory (AFSDT). The nonlinear governing differential equations of the laminated composite beams are derived using Hamilton's principle. The partial discretization based on Galerkin method is used to obtain the nonlinear ordinary differential equations (ODEs); in addition, the obtained nonlinear ODEs are solved numerically using step-by-step Newmark-Beta algorithm. In this study, the effects of two different cross-ply lay-up sequences and in-plane loading on the dynamic responses of composite beams are investigated. Moreover, the normal and interlaminar shear stress distributions are obtained. The results of present study are compared with the results of Partial Layerwise theory (PLWT) and validated with the exist results in this field of subject. Furthermore, the obtained results are compared with those obtained from finite element method (FEM) of analysis, which are in good agreement. Beside these, the number of used degrees of freedom in the present method is remarkably less than the FEM, leading to a significant computational cost reduction. Moreover, because of using FLWT, the present method is capable of predicting through the thickness normal stress and strain distributions.

Residual stresses in high temperature corrosion of pure zirconium using elasto-viscoplastic model: Application to the deflection test in monofacial oxidation

The paper is devoted to modeling residual stresses and strains in an oxide film formed during high temperature oxidation. It describes the deflection test in isothermal high-temperature monofacial oxidation (DTMO) of pure zirconium. The model incorporates kinetics and mechanism of oxidation and takes into account elastic, viscoplastic, growth and chemical strains. Different growth strains models are considered, namely, isotropic growth strains given by Pilling–Bedworth ratio, anisotropic growth strains defined by Parise and co-authors and physically based model for growth strain proposed by Clarke. Creep mechanisms based on dislocation slip and core diffusion, are used. A mechanism responsible for through thickness normal stress gradient in the oxide film is proposed. The material parameters are identified using deflection tests under 400°C, 500°C and 600°C. The effect of temperature on creep and stress relaxation is analyzed. Numerical sensitivity study of the DTMO experiment is proposed in order to investigate the effects of the initial foil thickness and platinum coating on the deflection curves.

Investigation on the effect of through thickness normal stress on forming limit at elevated temperature by using modified M-K model

The formability can be improved in warm/hot sheet hydroforming due to two important factors of temperature and through thickness normal stress. An extension of the M-K model was presented in this paper with the liquid pressure induced through thickness normal stress taken into account. The through thickness normal stress was introduced by using the general form of the Hill48 criterion. The combined effect of temperature and through thickness normal stress on the increase of FLD0 is achieved by applying a proposed temperature dependent constitutive equation for 5A06 aluminum alloy (a Chinese designation of Al-Mg alloy, corresponding to the ASTM designation of 5056 aluminum alloy) into the M-K approach. The Newton–Raphson method is used in the numerical procedure and it is proved to be stable and correct. The yield loci show a significant dependence on temperature and through thickness normal stress. Both size shrinking caused by the elevated temperature and location shifting due to the increasing thickness normal stress of the yield loci are observed. Comparison of the experimental FLDs of AISI-1012 low carbon steel (an AISI designation of steel) at plane stress and room temperature, STKM-11A steel (a Japanese designation of Steel Tube Kozo Machine) for tube hydroforming at room temperature and 5A90 aluminum alloy (a Chinese designation of Al-Li alloy) at plane stress and elevated temperature with the theoretical results show good agreements. The effect of key parameters, such as inhomogeneity factor f0, n value, m value and initial thickness T0, grain size d, initial surface roughness R0, show a strong dependence on FLDs and increase of FLD0. The increase of FLD0 is formulized in a full quadratic form, which is a function of temperature and through thickness normal stress. The left quadrant of FLD was determined by the cylindrical warm hydromechanical cup deep drawing, which shows a good accordance with the predicted results by using the modified M-K model.

Effect of through thickness normal stress on forming limit at elevated temperature investigated by using modified M–K model

The formability can be improved in warm/hot sheet hydroforming due to two important factors of temperature and through thickness normal stress. An extension of M–K model is presented in this paper with consideration of the liquid pressure induced through thickness normal stress. The through thickness normal stress is introduced by using the general form of Hill48 yield criterion. The effects of temperature and through thickness normal stress on the formability improvement can be predicted by using the modified M–K model with the combination of a proposed temperature dependent constitutive equation. The Newton–Raphson method is used and the numerical procedure is approved stable and correct. The yield loci show a significant dependence on temperature and through thickness normal stress. Size shrinking caused by the elevated temperature and location shifting due to the increasing thickness normal stress are observed. Comparison of the experimental FLDs of AISI1012 at plane stress and room temperature, STKM-11A for tube hydroforming at room temperature and 5A90 at plane stress and elevated temperature with the theoretical results show good agreements. The key parameters, such as inhomogeneity factor f0, n value, m value and initial thickness T0, grain size d, initial surface roughness R0, show a strong dependence on FLDs and increase of FLD0. The increase of FLD0 is formulized in a full quadratic form, which is a function of temperature and through thickness normal stress. The cylindrical cup warm hydromechanical deep drawing was carried out and the effects of temperature and through thickness normal stress on formability can be observed.

Forming characteristic of sheet hydroforming under the influence of through-thickness normal stress

Sheet hydroforming is different from conventional sheet forming due to the existence of liquid pressure. Through thickness normal stress induced by liquid pressure is derived by solving the normal force equilibrium equation. The theoretical prediction is in a good agreement with that determined by experimental data at cup wall. As the third principal stress, through thickness normal stress cannot be reflected in two dimensional yield locus. The variables of η and ω as new coordinates were introduced. Accompanied with stress triaxiality βav and effective strain ɛeq, they were used to describe the change of typical stress states in sheet hydroforming. As liquid pressure increases to infinity, sheet hydroforming covers the stress states from equi-biaxial tension to uniaxial compression. The numerical simulation in Marc shows that, the stress states of non-free bulging zones are away from plane stress in the (βav, ɛeq) and (η, ω) based spaces.

Double-sided high-pressure tubular hydroforming

It is generally understood that tensile stress loads lead to the shearing and/or expansion of micro voids in a metal specimen. Such deformation leads to stress concentrations that ultimately form the basis of the limiting strain capacity in a metal. Accordingly, a number of formability theories suggest that stress (not strain) is the key mechanism for ductile fracture. Motivated by such theories, an introduction to a special form of tubular hydroforming (THF) is put forth, where hydraulic pressure is introduced on both sides of the metal. Six different formability models are compared in light of their sensitivity to thickness normal stress ( σ 3) and other process variables associated with THF. It is shown that the models which capture the σ 3 effect are most suitable for formability assessment for the double-sided high-pressure (DSHP) process. The stress space forming limit model is then employed in the context of a solid finite element model of a plane-strain THF expansion. The presence of the DSHP boundary condition is shown to lead to increased formability relative to that observed for the traditional single-sided high-pressure (SSHP) process. Research of the DSHP process may lead to discoveries of various avenues towards greater formability. Consequently, the design space currently available to those employing the SSHP process may be significantly increased through the DSHP process. Ultimately, such design space increase may result in lower product cost, greater customer enthusiasm and increased market share for those manufacturers who invest in the DSHP process. This work represents a preliminary numerical investigation into the DSHP process only. Issues of cost, time and fixture design are left untouched.

An Experimental and Analytical Study of Delamination of Unidirectional Specimens with Cut Central Plies

The effect of various factors on delamination has been studied using uni directional glass fibre and carbon fibre-epoxy specimens with cut central plies. It is con cluded that the fracture energy is not a material constant. Among the various factors which affect the fracture energy, the specimen thickness and the through thickness normal stress are the two most significant ones. A simple model is proposed to take account of these two factors. The new model gives excellent correlation with experimental results and is able to account for the effect of through thickness compressive stresses in mode II fracture, which is ignored in conventional fracture mechanics calculations.

Effect of Through Thickness Tensile and Compressive Stresses on Delamination Propagation Fracture Energy

Strain energy release rate criteria are often used for predicting delamination. However, the fracture energy for delamination propagation is not a material constant, but varies depending on the through thickness normal stress. For tensile normal stresses this problem is usually overcome by using a mixed mode fracture criterion. However, the mixed mode approach fails to take into account compressive through thickness normal stresses. These can greatly increase the delamination stress and therefore cannot be simply ignored. A new approach is proposed in which it is assumed that the fracture energy for delamination propagation is a linear function of the average through thickness normal stress. Comparison with experimental results for unidirectional specimens with discontinuous plies shows excellent correlation, and accounts for a number of experimental observations that cannot be explained using the standard fracture mechanics approach.

Interface phase in Ti-6242 alloy

The paper is devoted to modeling residual stresses and strains in an oxide film formed during high temperature oxidation. It describes the deflection test in isothermal high-temperature monofacial oxidation (DTMO) of pure zirconium. The model incorporates kinetics and mechanism of oxidation and takes into account elastic, viscoplastic, growth and chemical strains. Different growth strains models are considered, namely, isotropic growth strains given by Pilling–Bedworth ratio, anisotropic growth strains defined by Parise and co-authors and physically based model for growth strain proposed by Clarke. Creep mechanisms based on dislocation slip and core diffusion, are used. A mechanism responsible for through thickness normal stress gradient in the oxide film is proposed. The material parameters are identified using deflection tests under 400 °C, 500 °C and 600 °C. The effect of temperature on creep and stress relaxation is analyzed. Numerical sensitivity study of the DTMO experiment is proposed in order to investigate the effects of the initial foil thickness and platinum coating on the deflection curves.