Multiaxial Tube Expansion Tests Research Articles

Measurement of Biaxial Deformation Behavior and Material Modeling for HI-PVC Using Multiaxial Tube Expansion Test

This study investigates the biaxial deformation behavior of the High Impact Polyvinyl Chloride (HI-PVC) used as a water pipe material. Multiaxial tube expansion test (MTET) was performed on the HI-PVC circular tube, and the stress-strain curves were measured for nine linear stress paths. The contours of plastic work and the directions of the plastic strain rates were also measurd. The experimental results show that the test sample has a strong anisotropy. Anisotropic hardening behavior was also confirmed from the evolution of the work contours. It was confirmed that the Yld2000-2d yield function had a better agreement with the measued work contour than Hill’s quadratic and the von Mises yield functons. Moreover, it was found that the test sample follows the normality rule with the Yld2000-2d yield function.

Characterization of yield stress surface and strain-rate potential for tubular materials using multiaxial tube expansion test method

A combined experimental and computational method was developed to characterize the yield stress surface and the conjugate plastic strain-rate potential of the AA7075-O extruded tube under biaxial tension and biaxial tension-compression stress states based on the plastic work equivalency assumption. In all the previous experimental investigations, the focus was on developing tube bulging experimental setup with PID capability to control pressure and axial feed to generate real-time proportional deformation in the stress space. In this paper, a more practical method is introduced in which the PID control is implemented into a finite element model with the von Mises yield function to generate the necessary pressure and axial feed that result in any desired proportional strain path in the mid-section of the tube in the tube bulging simulation. As expected, the application of FEM + PID generated boundary conditions in the tube bulging experiments resulted in slightly different deformation paths. However, the plastic work equivalency assumption was used to construct the yield stress surface and the plastic strain-rate potential for the tube at different plastic work levels. Finally, the parameters of the Yld2004–18p yield function were calibrated for AA7075-O aluminum tube with the measured principal stress and plastic strain rate ratios for three levels of accumulated plastic work, and it was shown that this tubular material displays nearly isotropic plasticity under tension-compression, and anisotropic plasticity under tension-tension stress states.

Material Modeling in High Strain Range and Forming Limit Analysis for 6000 Series Aluminum Alloy Sheet

This study investigates the effects of material modeling in high strain range on the forming limit analysis of a 6000-series alloy sheet 6016-T4. A servo-controlled tension-internal pressure testing machine was used to measure the multiaxial plastic deformation behavior in a strain range from initial yield to fracture. Tubular specimens were fabricated with a weld line thicker than the sheet thickness to prevent fracture from occurring in the weld zone. Proportional loading in the first quadrant of the principal stress space was applied to the specimens to measure the forming limit curve (FLC) and forming limit stress curve (FLSC), in addition to the contours of plastic work and the directions of plastic strain rates. Moreover, forming limit strains were measured using a flat-headed punch stretching test (PST). From the multiaxial tube expansion test (MTET) data, although a differential hardening effect was observed, appropriate coefficients including the exponent of the Yld2000-2d yield function (Barlat et al, 2003) were determined and employed in the Marcińiak-Kuczyski (1967) forming limit analysis (M-K analysis). The calculated forming limit strains in the vicinity of equibiaxial tension were smaller than the measured ones. The M-K analysis predicted that the forming limit strain in the vicinity of equibiaxial tension becomes minimum when the inclination angle of the localized neck from the rolling direction (RD) is 45° (diagonal direction; DD) while the experimental fracture direction was the RD. With the additional MTET, the plastic deformation behavior in the DD was measured and compared with that calculated from the material model. The reason of the discrepancy in the fracture direction between the experiment and the M-K approach is discussed.

Fracture Prediction for Mild Steel Sheet and High-Strength Steel Sheet Subjected to Draw Bending Using Forming Limit Stress Criterion

Abstract A fracture criterion for sheet metal subjected to draw bending is proposed based on the concept of the forming limit stress criterion. An experimental apparatus that is capable of draw bending sheet specimens with forming speeds (approximately 100 mm·s−1) comparable to those for commercial press forming machines was designed and built. The test materials were an ultralow-carbon steel sheet and a high-strength (590 MPa) steel sheet. Specimens underwent bending and unbending under tension when passing over a die. The magnitude of the true stress, σ D B , at which the stretch-drawn specimens fractured was precisely determined from the measured drawing force and the cross-sectional area of the specimen after fracture. Moreover, multiaxial tube expansion tests were performed to measure the forming limit stress, σ P T , for the test materials under plane-strain tension. It is found that σ D B is consistent with σ P T when the strain rate is properly taken into account in evaluating σ P T .

Measurement of differential hardening of pure titanium sheet based on multiaxial tube expansion testing and hole expansion forming simulation

Measurement of differential hardening of pure titanium sheet based on multiaxial tube expansion testing and hole expansion forming simulation

Fracture Prediction for High-strength Steel Sheet Subjected to Draw-bending Using Forming Limit Stress Criterion

A fracture criterion for sheet metals subjected to draw-bending is investigated using the concept of the forming limit stress criterion. The test material used is a 1.0-mm-thick high- strength steel sheet with a tensile strength of 590MPa. The specimen undergoes bendingunbending under tension when passing over the die profile. The drawing speed was set to 5-100 mm • s-1. The magnitude of true stress σDB when a specimen fractured has been precisely determined. Moreover, multiaxial tube expansion tests of the test material are performed to measure the forming limit stress σPT of the test material under plane-strain tension. It is found that σDB is larger than σPT by 2.8-6.3%. Therefore, it is concluded that the forming limit stress criterion is effective as a fracture criterion in draw-bending.

Fracture Prediction for Ultralow Carbon Steel Sheet Subjected to Draw-Bending Using Forming Limit Stress Criterion

A fracture criterion for sheet metals subjected to draw-bending is investigated using the concept of forming limit stress criterion. The test material used is a 1.0-mm-thick ultralow carbon steel sheet. Draw-bending experiment of a wide specimen is performed for a die profile radius of 4mm. A specimen undergoes bending-unbending under tension when passing over the die profile radius. The drawing speed was set to 5mm/s. The magnitude of true stress when a specimen fractured has been precisely determined from the measured data of a drawing force and the cross sectional area of the draw-bent specimen after fracture. Moreover, multiaxial tube expansion tests of the test material are performed to measure the forming limit stress of the test material under plane strain tension. It is found that the is larger than by approximately 10 %. Therefore, it is concluded that the forming limit stress criterion is effective as a fracture criterion for a mild steel sheet subjected to draw-bending.

Effect of Equivalent Stress-Strain Relation and Differential Hardening on Accuracy of Forming Limit Analyses

Multiaxial tube expansion tests (MTETs) were performed to measure the multiaxial plastic deformation behavior of a cold rolled interstitial-free (IF) steel sheet for a range of strain from initial yield to fracture. The testing machine is capable of applying arbitrary principal stress or strain paths to tubular specimens using an electrical, closed-loop servo-control system for an axial force and an internal pressure. Tubular specimens with an inner diameter of 44.6 mm were fabricated from a cold rolled IF steel sheet with a thickness of 0.7 mm by roller bending and laser welding. Many linear stress paths in the first quadrant of stress space were applied to the tubular specimens to measure the forming limit strains and forming limit stresses of the as-received sheet sample, in addition to the contours of plastic work and the directions of the plastic strain rates. It was found that the shapes of the measured work contours changed with increasing plastic work. The observed differential hardening behavior was approximated by changing the material parameters and the exponent of the Yld2000-2d yield function (Barlat et al, 2003) as functions of the reference plastic strain. The hydraulic bulge tests were also conducted to measure the forming limit strain and forming limit stress for equibiaxial tension and to determine the equivalent stress-equivalent plastic strain relation for a larger strain range. The forming limit curve and forming limit stress curve were calculated using the Marciniak-Kuczyński-type approach. The calculated results were in fair agreement with the measurement.

Measurement and Analysis of the Differential Hardening of Ultralow Carbon Steel Sheets

Multiaxial tube expansion tests were performed to precisely measure the work hardening behavior of mild steel sheets with different r-values for a range of strain from initial yield to fracture. The testing machine is capable of applying an arbitrary linear stress path to a tubular specimen using an electrical, closed-loop servo-control system for the axial force and internal pressure applied to the tubular specimen. Tubular specimens with an inner diameter of 44.6 mm were fabricated from the as-received sheet sample by roller bending and laser welding. Nine linear stress paths, σx(rolling direction) :σy (transverse direction) =1:0, 4:1, 2:1, 4:3, 1:1, 3:4, 1:2, 1:4, and 0:1, in the first quadrant of the principal stress space were applied to the tubular specimens to measure the contours of plastic work and the directions of the plastic strain rates. It was found that the shapes of the measured work contours changed with increasing plastic work, or equivalently with increasing the reference plastic strain ; the test materials exhibited differential hardening (DH). The general trend of the DH appeared to be affected by the average r-value, or equivalently by the texture, of the materials.

Fundamental Investigation for Tensile Test Using Conical Cupping Die

A number of researches have conducted in order to evaluate the ductile fracture occurrence by using forming limit diagram. However, specimen shape and testing machine for obtaining forming limit diagram of sheet metal have some problems. The problem about specimen shape is occurring at the specimen edge. In uniaxial tensile test, the specimen edge may cause a defused neck in width direction and may have influence on fracture occurrence. In biaxial tensile test by using a cruciform specimen, a uniform biaxial deformation is not obtained because uniaxial tensile stress occurs at the specimen edge. Tensile test by using a specimen which does not have such edges should carry out, for example, in bulge test and multi-axial tube expansion test, specimens without edge are used. However, these methods need special machines. Therefore, new biaxial tensile testing method is required. By this method, materials deform depending on biaxial strain state by using popular pressing machines.

Forming Simulation Considering the Differential Work Hardening Behavior of a Cold Rolled Interstitial-Free Steel Sheet

The multiaxial plastic deformation behavior of a cold rolled interstitial-free steel sheet with a thickness of 0.65 mm was measured using a servo-controlled multiaxial tube expansion testing machine for the range of strain from initial yield to fracture. Tubular specimens were fabricated from the sheet sample by roller bending and laser welding. Many linear stress paths in the first quadrant of stress space were applied to the tubular specimens to measure the contours of plastic work in stress space up to an equivalent plastic strain of 0.289 along with the directions of plastic strain rates. The test material exhibited differential hardening (DWH). A material modeling method for reproducing the DWH in a finite element simulation has been developed. Hydraulic bulge forming simulation results based on the DWH model had a closer agreement with the experimental results than those calculated using the isotropic hardening models with selected yield functions.

21112 冷延IF鋼板の異方硬化挙動の定式による成形シミュレーションの高精度化

The deformation behavior of cold-rolled IF steel sheet under biaxial tension was investigated for a strain range from initial yielding to fracture. The test material was bent and laser welded to fabricate a tubular specimen. Multiaxial tube expansion tests were performed using a servo-controlled tension-internal pressure testing machine. Many linear stress paths in the first quadrant of stress space were applied to the tubular specimens to measure the counters of plastic work and the directions of the plastic strain rates. It was found the shapes of the work counters changed with an increase in ε^P_0 and the Yld2000-2d yield function could reproduce the differential work hardening behavior (DWH) of the test material by changing the material parameters and exponent as functions of ε^P_0. Finite element analysis of hydraulic bulge forming has verified the effectiveness of proposed DWH model based on Yld2000-2d yield function for improving the accuracy of the FEA.

Forming Limit Analyses of Cold Rolled IF Steel Sheet Using Differential Work Hardening Model

A servo-controlled multiaxial tube expansion testing machine was used to measure the multiaxial plastic deformation behavior of a cold rolled IF steel sheet for a range of strain from initial yield to fracture. The testing machine is capable of applying arbitrary principal stress or strain paths to a tubular specimen using an electrical, closed-loop servo-control system for an axial force and an internal pressure. Tubular specimens with an inner diameter of 44.6mm were fabricated from a cold rolled interstitial-free steel sheet with a thickness of 0.7mm by roller bending and laser welding. Many linear stress paths in the first quadrant of stress space were applied to the tubular specimens to measure the forming limit curve and forming limit stress curve of the as-received sheet sample, in addition to the contours of plastic work and the directions of the plastic strain rates. It was found that the shapes of the measured work contours changed with increasing plastic work. The observed differential work hardening behavior was approximated by changing the material parameters and the exponent of the Yld2000-2d yield function (Barlat et al., 2003) as a function of the equivalent plastic strain. The forming limit curve and forming limit stress curve were calculated using the Marciniak-Kuczyński-type approach and the differential work hardening model. The calculated results were in fair agreement with the measurement.

Material Modeling of High Strength Steel Sheet Using Multiaxial Tube Expansion Test with Optical Strain Measurement System

Material Modeling of High Strength Steel Sheet Using Multiaxial Tube Expansion Test with Optical Strain Measurement System

二軸バルジ試験法による高強度鋼板の加工硬化特性の測定と材料モデリング

The deformation behavior of high strength steel sheets with a tensile strength of 590 MPa under biaxial tension was investigated for a strain range from initial yielding to fracture. The test material was bent and laser welded to fabricate a tubular specimen with an inner diameter of 44.6mm, a wall thickness of 1.2mm, and an axial length of 200mm. Multiaxial tube expansion tests were performed using a servo-controlled tension-internal pressure testing machine. Many linear stress paths in the first quadrant of stress space were applied to the tubular specimens to measure the forming limit curve (FLC) and forming limit stress curve (FLSC) of the as-received sheet material, in addition to the contours of plastic work and the directions of plastic strain rates from initial yielding to fracture. Results calculated using the Yld2000-2d yield function with exponents of 6 to 8 provided the closest agreement with the measured work contours and directions of plastic strain rates for a reference plastic strain range of 0.002 ＜ε0p＜ 0.20. It was concluded that the multiaxial tube expansion test is effective for measuring the multiaxial deformation behavior of sheet metals for a wide range of plastic strains.

OS0404 二軸バルジ試験による純チタン板の加工硬化挙動の測定と材料モデリング

OS0404 二軸バルジ試験による純チタン板の加工硬化挙動の測定と材料モデリング

金属板材の大ひずみ二軸応力－ひずみ曲線の連続測定を可能とする二軸バルジ試験機の開発

金属板材の大ひずみ二軸応力－ひずみ曲線の連続測定を可能とする二軸バルジ試験機の開発

Multiaxial tube expansion test method for measurement of sheet metal deformation behavior under biaxial tension for a large strain range

A servo-controlled multiaxial tube expansion testing machine was developed to measure the multiaxial plastic deformation behavior of sheet metals for the range of strain from initial yield to fracture. The testing machine is capable of applying arbitrary principal stress or strain paths to a tubular specimen using an electrical, closed-loop servo-control system for axial force and internal pressure, in addition to having a novel strain measurement apparatus for tubular specimens. Tubular specimens with an inner diameter of 44.6mm were fabricated from cold rolled interstitial-free steel sheet with a thickness of 0.7mm by roller bending and laser welding. Many linear stress paths in the first quadrant of stress space were applied to the tubular specimens to measure the forming limit curve (FLC) and forming limit stress curve (FLSC) of the as-received sheet material, in addition to contours of plastic work and directions of plastic strain rates. Results calculated using the Yld2000-2d yield function with an exponent of 6 provided the closest agreement with the measured work contours and directions of plastic strain rates for an equivalent plastic strain range of 0.005–0.36. Moreover, a Marciniak–Kuczyński-type forming limit analysis was performed using the most appropriate yield function with the assumption of isotropic hardening; the calculated and measured FLC and FLSC were in fair agreement. Therefore, the multiaxial tube expansion test is effective to measure the multiaxial deformation behavior of sheet metals for a large range of plastic strain.

二軸バルジ試験による冷延IF鋼板の加工硬化特性の測定と材料モデリング

二軸バルジ試験による冷延IF鋼板の加工硬化特性の測定と材料モデリング