Wall thinning, as one of the key defects in tube bending determined the forming quality and limit, is more easily to occur due to the specific properties of high strength 0Cr21Ni6Mn9N stainless steel tube (0Cr21Ni6Mn9N-HS tube). To achieve tube accuracy numerical control (NC) bending forming, the wall thinning characteristics of the 0Cr21Ni6Mn9N-HS tube should be clarified. An analytical model was proposed to reveal the essential relation between tube parameters and wall thickness distribution. Considering the varied elastic modulus, a finite element (FE) model was applied to explore the wall thinning under different geometrical and process parameters. Using the modified multi-parameter sensitivity analysis method combined with FE simulation, the sensitivity of the wall thinning to geometrical and process parameters was carried out. The experiments of NC tube bending were conducted to validate the analytical and simulate results. The results show that the varied elastic modulus can enhance the wall thinning degree, but has no obvious effect on wall thinning characteristics. The wall thinning characteristics under different geometrical and process parameters are revealed and the reasonable parameters ranges for the 0Cr21Ni6Mn9N-HS tube in NC bending are obtained. The most sensitive parameter on wall thinning is the relative bending radius, while the bending angle is the least one.

Self-demagnetization due to strongly magnetic bodies can seriously affect the interpretation of magnetic anomalies. Conventional numerical methods often neglect the self-demagnetization effects and limit their use to low susceptibilities ([Formula: see text]). We have developed a novel iterative method based on the integral equation and the Gauss-fast Fourier transform (FFT) technique for calculating the magnetic field from finite bodies of high magnetic susceptibility and arbitrary shapes. The method uses a segmented model consisting of prismatic voxels to approximate a complex target region. In each voxel, the magnetization is assumed to be constant, so that the integral equation in the spatial domain can reduce to a simple form with lots of merit in numerical calculation after the 2D Fourier transform. Moreover, a contraction operator is derived to ensure the convergence of the iterative calculation, and the Gauss-FFT technique is applied to reduce numerical errors due to edge effects. Our modeling results indicate that this new iterative scheme performs well in a wide range of magnetic susceptibilities (1–1000 SI). For lower susceptibilities ([Formula: see text]), the iterative algorithm converges rapidly and indicates very good correlation with the analytical solutions. At higher susceptibilities ([Formula: see text]), our method still performs well, but the numerical accuracy improves with a relatively slow speed. In the extreme case ([Formula: see text]), an acceptable result is also obtained after sufficient iterative computation. A further improvement in the numerical precision can be achieved by increasing the number of prismatic voxels, but at the same time, the computational time increases linearly with the size of the voxels.

Elastic modulus is one of the most crucial mechanical property parameters that affects the plastic forming quality of bent parts, especially for springback. Elastic modulus practically varies with plastic deformation, and its precise description is necessary to enhance simulation precision for tube bending and gain steady, high-precision bent components by actual bending. Using repeated loading-unloading tensile tests (RLUTTs), the variation of elastic modulus of high strength 21-6-9 stainless steel tube (21-6-9-HS tube) in terms of plastic strain has been obtained, which its decreases rapidly at the beginning, then decreases tardily and tends to be stable in the end with increasing the plastic strain. The variation can be expressed as a first order exponential decay function. By embedding the variation of elastic modulus with the plastic strain into ABAQUS software to simulate numerical control (NC) rotary draw bending of the 21-6-9-HS tube, the prediction precision for the springback angle, springback radius, maximum cross section distortion ratio and maximum wall thinning ratio can be improved by 11.98%, 7.62%, 35.53% and 11.55%, respectively.

Wall thinning, as one of the key defects determined directly the usability of the bent tube, should be strictly controlled. Elastic modulus changes with the plastic deformation and its influence the plastic forming quality of tube bending. To precisely predict the wall thinning of tube bending, a finite element (FE) model for numerical control (NC) bending of high strength 21-6-9 stainless steel tube (21-6-9-HS tube) was established considering the variation of elastic modulus. Using the model, the effects of process parameters on wall thinning of the 21-6-9-HS tube in NC bending were investigated. The results show that the variation of elastic modulus has no obvious effect on the change tendency of the wall thinning degree, but only increases the value of the wall thinning degree. The wall thinning degree enhances sharply at first, then occurs a platform deforming characteristics, and finally reduces abruptly from the bending section to the initial bending section, and it increases with the increase of the clearance of tube-bending die, the friction coefficient of tube-bending die and the friction coefficient of tube-wiper die or with the decrease of the clearance of tube-wiper die, but the increased degree is not significant in all conditions.

No abstract