Biaxial Tension State Research Articles

Research on biaxial tensile fracture prediction of 5052 aluminum alloy on electromagnetic sheet bulging

High-speed deformation fracture prediction of aluminum sheet, especially for biaxial tension state deformation, was a major problem in the development of electromagnetic bulging process. In this study, the biaxial tension failure limit of the AA5052 sheet was tested by the electromagnetic high-speed biaxial tensile testing equipment and quasi-static Nakazima experiment. A Digital Image Correlation (DIC) system was used to measure failure strain. Based on the tested data, a failure model considered stress state and strain rate coupling effect was established, which available for electromagnetic bulging failure prediction. Electromagnetic free bulging experiments were conducted to verify the failure criteria effectiveness. Results showed that the strain rate effects of the failure strain were influenced by the loading path. The strain rate effect of the sheet failure strain under plain strain state was higher than the loading stress triaxiality of uniaxial and biaxial tension state. Compared with the fracture prediction criterion ignored stress state effect on strain rate influence factor, the modified fracture model considered stress state and strain rate coupling effect could well predict the failure of electromagnetic bulging, which would exhibit different failure models at the rounded corner or the top under different discharge energies.

Biaxial formability and microstructure of an Al-Mg-Si alloy sheet post solution heat treatment

Hot forming-quenching integrated process was developed to fabricate aluminum alloy complex-shaped components by taking advantage of the enhanced formability at the temperature close to solution temperature. But, it is very difficult to evaluate the formability under biaxial tension state and continuous cooling conditions. A measuring method was proposed to evaluate the biaxial formability by combining solution heat treatment and hot gas free bulging test. The effects of temperature and pressurizing rate on the bulging ability and thickness uniformity of an Al-Mg-Si alloy sheet were clarified. The deformation mechanism was revealed by microstructure observation. It is found that excellent formability can be obtained under the high temperature with less heat loss and rapid pressurizing conditions. The limiting strain under rapid pressurizing condition decreases from 1.13 at 500 ℃ to 0.81 at 400 ℃, being at a high strain level. Thickness uniformity can be obviously improved at a higher deformation temperature accompanied by rapid loading due to the remarkable strain-rate hardening effect. Dynamic recovery is the main restoration mechanism, resulting in numerous substructures and unchanged grain size. The obtained biaxial formability closer to actual forming condition can provide fundamental guidance for forming aluminum alloy complex-shaped component by hot forming-quenching integrated process.

Development of In-situ Observation Methods of Surface Roughening Behavior By Hand-size Stretching Test for Metal Foils

It is known that the surface roughness on the free surface increases with increasing plastic strain. When the size of material is scaling down in to micro scale, the ratio of surface roughness to the thickness becomes large in micro metal forming compared with macro-scale forming. Thus, the surface roughening behavior of metal foils is an important factor in micro metal forming. To clarify the surface roughening behavior of the metal foils, in-situ observation is required under bi-axial tension state. In this study, the method of in-situ observation of surface roughening during plastic deformation is developed. The hand-size stretching test is developed and installed on the confocal laser micro scope which can evaluate quantitative 3D profile of surface with high resolution. The effect of strain state such as equi-biaxial on surface roughening behavior is investigated experimentally. By using developed in-situ observation method, it became possible to evaluate the process of changing the surface under various strain states.

Cylindrical cup-drawing characteristics of aluminum-polymer sandwich sheet

Compared with conventional monolithic material, an aluminum-polymer sandwich sheet possesses advantageous strength/stiffness versus weight ratio and has received increasing attention in aeronautical, automotive, marine, and civil engineering industries. In the present study, limiting draw ratio (LDR) and other cylindrical cup-drawing characteristics of aluminum-polymer sandwich sheets were investigated by experiments and numerical simulations. Deformation behaviors of skin layer and core polymer layer were analyzed respectively. It was demonstrated that the deformation mode of exterior sheet tends to biaxial tension state and that of interior sheet tend to compression state. The LDR of aluminum-polyethylene sandwich sheet was well predicted, and influences of core layer thickness and mechanical properties of skin sheet on the LDR of sandwich sheet were analyzed. Research results show that the drawability of the aluminum-polymer sandwich sheet becomes poor with increasing the thickness of the polymeric core and the strength of core polymer. The LDR of the sandwich sheet mainly depends on the drawability of the skin sheet.

Elevated temperature creep deformation of a single crystal superalloy through the small punch creep method

Small punch testing is now a widely recognised approach for obtaining useful mechanical property information of critical structural components, particularly in the nuclear industry. However, to date the utilisation of this method has been limited to isotropic materials such as aluminium alloys and steels. This paper will look to utilise the small punch (SP) test to assess the creep response of 〈001〉-orientated CMSX-411CMSX-4 is a registered trademark of Cannon-Muskegon Corporation. at temperatures above 950°C. An orthogonal rafting regime of the γ′ structure is observed in the post-test microstructure due to the biaxial tension state typically produced in a SP test. Interpretation of the SP results to correlate with uniaxial creep data is carried out by employing the ksp approach in order to provide a platform for future material assessment.

Error analysis of FLC experimental data at warm/hot stamping conditions

Forming limit curves(FLCs) are commonly used for evaluating the formability of sheet metals. However, it is difficult to obtain the FLCs with desirable accuracy by experiments due to that the friction effects are non-negligible under warm/hot stamping conditions. To investigate the experimental errors, experiments for obtaining the FLCs of the AA5754 are conducted at 250°C. Then, FE models are created and validated on the basis of experimental results. A number of FE simulations are carried out for FLC test-pieces and punches with different geometry configurations and varying friction coefficients between the test-piece and the punch. The errors for all the test conditions are predicted and analyzed. Particular attention of error analysis is paid to two special cases, namely, the biaxial FLC test and the uniaxial FLC test. The failure location and the variation of the error with respect to the friction coefficient are studied as well. The results obtained from the FLC tests and the above analyses show that, for the biaxial tension state, the friction coefficient should be controlled within 0.15 to avoid significant shifting of the necking location away from the center of the punch; for the uniaxial tension state, the friction coefficient should be controlled within 0.1 to guarantee the validity of the data collected from FLC tests. The conclusions summarized are beneficial for obtaining accurate FLCs under warm/hot stamping conditions.

Plastic damage of T-shape hydroforming

The Gurson-Tvergaard-Needleman model (GTN model) was employed to analyze bursting behavior in the hydroforming of stainless steel T-shape. A free-bulging test combined with simulation was conducted to determine the critical porosity and the failure porosity in GTN model. The effects of the forming pressure and the axial feeding on damage development were investigated and the influences of stress triaxiality and the plastic strain on porosity variation were also studied. The results show that a higher forming pressure or a less axial feeding will lead to bursting failure. The stresses of the top of protrusion are in bi-axial tension state, while the stresses of the side wall of main tube are in hoop tension state and axial compression state, respectively. The plastic strain has a more significant influence on the porosity than the stress triaxiality under the lower internal pressure; however, the stress triaxiality will govern the growth of porosity under the higher internal pressure. The simulation results give a good agreement with the experimentally determined thickness, and the maximum thickness-thinning rate is about 36%.

Forming limit and fracture mechanism of ferritic stainless steel sheets

In this work, the forming limit curves (FLCs) of two ferritic stainless steel sheets, AISI409L and AISI430, were predicted with the Marciniak–Kuczynski (MK) and Bressan–William–Hill (BWH) models, combined with the Yld2000-2d yield function and the Swift hardening law. Uniaxial tension, disk compression and hydraulic bulge tests were performed to determine the yield loci and hardening curves of both materials. Meanwhile, the strain rate sensitivity (SRS) coefficient was measured through uniaxial tension tests carried out at different strain rates. Out-of-plane stretching tests were conducted in sheet specimens to obtain the surface limit strains under different linear strain paths. Micrographs of the specimens fractured in different stress states were obtained by optical and scanning electron microscopy. The overall results show that the BWH model can predict the FLC better than the MK model, and that the SRS does not have much effect on the limit strains for both materials. The predicted FLCs and micrograph analysis both indicate that failure occurs by surface localized necking in uniaxial and plane strain tension states, whereas it occurs by localized shearing in the through thickness direction in balanced biaxial tension state.

Prediction of Free Surface Roughening by 2D and 3D Model Considering Material Inhomogeneity

A Finite element (FE) model considering mesoscopic material inhomogeneity due to a different flow stress for each crystal grain to predict free surface roughening is proposed. The effect of the standard deviation of the material inhomogeneity and grain size was investigated by the 2D FE model. In addition, to verify the model considering material inhomogeneity, the free surface roughening behavior is predicted under a bi-axial tension state using the 3D FE model. Furthermore, by comparison with experimental results, the validity of the FE model considering material inhomogeneity and its determination method is discussed. The standard deviation σsd of the material inhomogeneity parameter α in the model has a strong correlation with the rate of increase in the surface roughness, which increases with increasing grain size, is agreement with the conventional empirical equation. The surface roughness under bi-axial tension state is larger than that under uni-axial tension state. In addition, the experimental results are in good agreement with the simulation results. From these findings, we can verify the fundamental behavior and the validity of this model considering material inhomogeneity for the prediction of free surface roughening.

A modified Landau–Devonshire thermodynamic potential for strontium titanate

The range of reported values of the Landau energy coefficients of bulk SrTiO3 leads to uncertainty in not only the magnitude but also the direction of the calculated spontaneous polarization in SrTiO3 thin films in a state of biaxial tension. In this study, we use experimental results from strained SrTiO3 films together with phase-field simulations to refine the values of the Landau energy coefficients and report a modified thermodynamic potential for bulk strontium titanate. The transition temperatures and ferroelectric/antiferrodistortive domain stabilities predicted from this modified potential agree well with measurements on biaxially strained SrTiO3 thin films.

Abstract: 101 PROPOSED EFFICACY CRITERIA AND CHOLESTEROL TARGETS FOR LDL APHERESIS

Small punch testing is now a widely recognised approach for obtaining useful mechanical property information of critical structural components, particularly in the nuclear industry. However, to date the utilisation of this method has been limited to isotropic materials such as aluminium alloys and steels. This paper will look to utilise the small punch (SP) test to assess the creep response of 〈001〉-orientated CMSX-41 at temperatures above 950 °C. An orthogonal rafting regime of the γ′ structure is observed in the post-test microstructure due to the biaxial tension state typically produced in a SP test. Interpretation of the SP results to correlate with uniaxial creep data is carried out by employing the ksp approach in order to provide a platform for future material assessment.

Abstract: 107 EVALUATING THE IMPACT OF NEW MARKERS ON RISK PREDICTION

Small punch testing is now a widely recognised approach for obtaining useful mechanical property information of critical structural components, particularly in the nuclear industry. However, to date the utilisation of this method has been limited to isotropic materials such as aluminium alloys and steels. This paper will look to utilise the small punch (SP) test to assess the creep response of 〈001〉-orientated CMSX-41 at temperatures above 950 °C. An orthogonal rafting regime of the γ′ structure is observed in the post-test microstructure due to the biaxial tension state typically produced in a SP test. Interpretation of the SP results to correlate with uniaxial creep data is carried out by employing the ksp approach in order to provide a platform for future material assessment.

Thermoplastic gas pressure forming of bulk metallic glass sheets under biaxial tension

The deformation behaviour and structural evolution of bulk metallic glass sheets were studied under biaxial tension in supercooled liquid state. The sheets were gas pressure formed into hemispherical and semi-ellipsoid domes using dies with aspect ratios of 1:1 and 3:2, respectively, at the optimum temperature of 676 K. The structural evolution of the metallic glass sheets was examined after deformation. The stress distributions of the bulging sheets are calculated employing a finite element model. It was found that the stress state of biaxial tension accelerates nanocrystallization, which leads to an increase in the hardness of metallic glass. The gas pressure applied, bulging time, and temperature are the principal factors involved in the formation of products.

Localized failure of fibre‐reinforced elastic–plastic materials subjected to plane strain loading

AbstractWe consider discontinuous bifurcations as the indicator of a localized failure for a class of composites that are characterized by elastic fibres reinforcing an elastic–plastic matrix. A macroscopic tangent stiffness tensor for the fibre‐reinforced composite is developed by consistently homogenizing the contribution of fibres in a spherical representative volume element. Analytical solutions are derived for the critical hardening modulus and corresponding bifurcation directions for the case of plane strain loading. Properties of the solutions are further illustrated on the example of the non‐associated Drucker–Prager model at onset of yielding. Results show that presence of fibres decreases the critical hardening modulus, thus inhibiting the onset of strain localization. The rate of decrease in the critical hardening modulus is the highest for pure shear, followed by uniaxial tension, uniaxial compression, biaxial tension and biaxial compression. The main fibre parameters that control the onset of strain localization are their volumetric content and their stiffness modulus whereby very stiff fibres can produce the most significant decrease in the critical hardening modulus, especially for the state of biaxial tension. The critical hardening modulus for the non‐associated Drucker–Prager model exhibits a full range of localization modes including compaction bands, dilation bands, and transition in the form of shear bands regardless of the presence of fibres. Presence of fibres affects bifurcation directions, except in the case when Poisson's ratio of the matrix is equal to 0.25. The results demonstrate stabilizing effects of fibres by which they provide the control against the onset of strain localization. Copyright © 2006 John Wiley & Sons, Ltd.

Fragmentation in biaxial tension

We have carried out an experiment that places a ductile stainless steel in a state of biaxial tension at a high rate of strain. The loading of the ductile metal spherical cap is performed by the detonation of a high-explosive layer with a conforming geometry to expand the metal radially outwards. Simulations of the loading and expansion of the metal predict strain rates that compare well with experimental observations. A high percentage of the high explosives loaded material was recovered through a soft capture process, and characterization of the recovered fragments provided high- quality data, including uniform strain prior to failure and fragment size. These data were used with a modified fragmentation model to determine a fragmentation energy.

Residual stresses in a welded superalloy disc: Characterization using synchrotron diffraction and numerical process modeling

The residual stress state in an electron-beam welded assembly of IN718 nickel-based superalloy has been studied both experimentally and using computer modeling. Diffraction measurements were made at the European Synchrotron Radiation Facility (ESRF), using the ID11 beamline. The assembly consisted of a 1.75-mm-thick web of rolled IN718 sheet, welded between two 14-mm-thick circular forgings. Four radial scans each of 400 measuring points were made across the web at 90-deg intervals. Diffraction patterns were recorded using a charge-coupled device (CCD) detector, which enabled the collection of information from several diffraction peaks and, thus, the determination of in-plane lattice strains; the macroscopic residual strain and stress fields were then estimated using appropriate values of the diffraction elastic constants. The experimental results were compared with the predictions from a sequentially coupled thermal-mechanical model based upon the finite-element (FE) method. The agreement between the experimental data and the results from the model is reasonable. It is shown that the residual strain/stress field is strongly influenced by the constraint imposed by the geometry of the assembly, i.e., by the inner and outer forgings, and that, as a result, the web is in a state of biaxial tension. The FE model predicts that a steady state is reached during welding and, thus, that there are systematic errors associated with the strain scanning measurements. These are considered to arise from the uncertainty associated with the positioning of the assembly and a sensitivity analysis for this effect is presented.

Image analysis studies of water transport and dimensional changes occurring in the early stages of hydration in cross-linked amylose matrices

The purpose of this work was to monitor and quantify water transport and dimensional changes occurring in the early stages of hydration in cross-linked amylose (CLA) matrices using image analysis technique. Samples were prepared by direct compression of CLA-6 powder to obtain matrices of 0.17 cm thickness and 1.295 cm in diameter. A surface gel layer was formed quasiinstantaneously. The gel expansion was then constrained and the material continuity caused the outer gel layer to be in a state of biaxial compression and the internal core in a state of biaxial tension. A diffusion front preceded the gel–glass interface even in the early stages of hydration. A delayed stress-release occurred through a radial expansion of the tablet interior. This relaxation coincided with the time at which the axial diffusion fronts met. The dimensional changes had a marked impact on the kinetics of water uptake in CLA-6 tablets in early stages of hydration.

The energetics of the relaxation of misfit strain in thin epitaxial films by means of twinning

Exact solutions for the interaction energy between infinitely long parallel twins of alternating orientation terminating at a distance h below the free surface in an elastically isotropic half-space have been obtained through the summation of pairwise interaction energies between the partial dislocations making up the twins. The results are compared with those obtained when the elastic interaction between parallel twins is approximated by the interaction between parallel dislocations of Burgers vector mb, where m is the number of partial dislocations making up the twin and b is the Burgers vector of the partial dislocations. It is shown that for twins lying on {111} planes in a half-space for which the surface normal is (001) there is an excellent agreement between the two solutions except for extremely small values of the twin spacing which are never encountered in practice. It is also shown that for this geometry the use of the approximate solution for the elastic interaction between alternating twins in calculations of the energetics of the relaxation of misfit strain via twinning gives rise to virtually the same results as the exact solution. Additional calculations are performed in order to compare the energetics of an array of alternating twins relieving misfit strain in a thin Si0.5Ge0.5 film on a Ge(001) substrate with those of an array of 60° perfect dislocations relieving misfit strain in the same film. The role played by the twin boundary energy in the evolution of twin morphology with increasing film thickness is illustrated through an examination of the relaxation process via twinning in thin Ag(001) and Pt(001) epitaxial films which are in a state of biaxial tension. A solution is also provided for the energetics of the relaxation of misfit strain in a linear isotropic elastic half-space by means of twin-like defects in which the defect thickness is allowed to vary continuously, allowing for the determination of effective average twin thicknesses and spacings which themselves vary continuously during the relaxation process.

Structural and Electrical Properties of Heteroepitaxial HgCdTe/CdZnTe/GaAs/Si

ABSTRACTThe structural and electrical properties of heteroepitaxial HgCdTe/CdZnTe/GaAs/Si were evaluated using high-resolution x-ray diffraction techniques and Hall-effect measurements as a function of temperature. Significant tilting of the layers was found for both {100} and {111} CdZnTe layers grown on misoriented {100}GaAs/Si substrates, consistent with the interpretation of a low-angle tilt boundary being formed at the interface to relieve the large lattice mismatch between the layers. The GaAs layer is in a state of biaxial tension before and after the growth of the CdZnTe layers. The x-ray FWHM of HgCdTe layers grown by LPE on these substrates was found to be reduced from that of the MOCVD-grown CdZnTe buffer layer due to both an annealing effect during LPE growth and to the increased distance of layer surface from the defective CdZnTe/GaAs interface. Hall-effect mobility for {100}HgCdTe layers was nearly identical to that of layers grown on bulk CdZnTe substrates. High-quality heterojunction infrared detectors have been fabricated using these materials.

Internal stresses in the cranial bone tissue

The presence of a plane internal stress field in the bone tissues of the cranium has been established. Values have been obtained for the Poisson's ratio and modulus of elasticity of the cranial bone. The outer surface of the cranium is in a state of biaxial tension, the inner surface in a state of biaxial compression.