Complex Stress-Strain Relations of Tubular Materials Studied With a Flexible Hydroforming System

Lin, Yanli; Chu, Guannan; Zhang, He; Yuan, Shijian; Yan, Yongda

doi:10.1520/jte20160067

Cited by 5 publications

(5 citation statements)

References 18 publications

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“…Nonlinear regression models have been widely used to describe the nonlinear behavior of materials. Currently, experimental stress-strain data are commonly reproduced using nonlinear regression models, such as power law, the second-order function model, the fourth-order function model, and so on [25][26][27][28][29][30][31]. But with the development of technology, many new materials have emerged, and many flow stress-strain data under biaxial stress state can be obtained using the new proposed test method.…”

Section: Introductionmentioning

confidence: 99%

A New Regression Model for the Prediction of the Stress–Strain Relations of Different Materials

Lin,

Su,

Zhao

et al. 2023

Materials

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Experimental flow stress–strain data under different stress states are often used to calibrate the plastic constitutive model of anisotropic metal materials or identify the appropriate model that is able to reproduce their plastic deformation behavior. Since the experimental stress–strain data are discrete, they need to be mathematically returned to a continuous function to be used to describe an equivalent hardening increment. However, the regression results obtained using existing regression models are not always accurate, especially for stress–strain curves under biaxial stress loading conditions. Therefore, a new regression model is proposed in this paper. The highest-order term in the recommended form of the new model is quadratic, so the functional relationships between stress–strain components can be organized into explicit expressions. All the experimental data of the uniform deformation stage can be substituted into the new model to reasonably reproduce the biaxial experimental stress–strain data. The regression results of experimental data show that the regression accuracy of the new model is greatly improved, and the residual square sum SSE of the regression curves of the new model reduced to less than 50% of the existing three models. The regression results of stress–strain curves show significant differences in describing the yield and plastic flow characteristics of anisotropic metal materials, indicating that accurate regression results are crucial for accurately describing the anisotropic yielding and plastic flow behaviors of anisotropic metal materials.

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Section: Introductionmentioning

confidence: 99%

A New Regression Model for the Prediction of the Stress–Strain Relations of Different Materials

Lin,

Su,

Zhao

et al. 2023

Materials

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show abstract

“…But with the development of technology, for many materials, the regression results cannot be accepted. 12,13 So several variations of regression models are proposed, such as Ludwik model σ¯=σ0+Kɛ¯n and Swift model σ=c(ɛ0+ɛ)q . However, for many experimental flow stress–strain relations under biaxial stress states, the regression results of these models are not ideal.…”

Section: Introductionmentioning

confidence: 99%

“…Compared with the SOF model, higher regression accuracy can be obtained by the FOF model. 12,13 However, the expression of the FOF model is an implicit function. Consequently, the flow stress–strain curves under different loading conditions cannot be converted, which results in that different flow stress–strain relations cannot be substituted into the plastic constitutive model to describe the anisotropy yielding and plastic flow characteristics of the material.…”

Section: Introductionmentioning

confidence: 99%

An optimized constitutive model for reproducing flow stress–strain relationships of anisotropic materials

Lin

Yan

2018

Proceedings of the Institution of Mechanical Engineers, Part C:

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Due to the strong anisotropic property of the advanced metal materials used in automobile, aviation, and aerospace, experimental flow stress–strain relations including different stress states are necessary to provide the information of anisotropic hardening and plastic flow for constructing a constitutive model. Therefore, reasonably reproducing the experimental stress–strain relations is the most fundamental work to substitute adequate flow stress–strain curves into the constitutive equation at the same time. However, accurate and stable regression results are difficult to obtain through the current regression models such as power exponent, second-order function model, fourth-order function model, and so forth. In this paper, an optimized model named as a least square quadratic regression model (ordinary least square model) was proposed based on the most useful second-order function model. The significant difference is that all experimental points are used to reproduce the experimental stress–strain relations in ordinary least square model in place of only three experimental points adopted in second-order function model, which results in good regression accuracy. Through comparison, it is found that the regression results by power function are poor with regard to some experimental results, and the results reproduced by second-order function model or fourth-order function model are very sensitive to the experimental points selected to do the regression. The sum of squares for error (SSE) increases sharply when the selected points are unreasonable. In addition, for second-order function and fourth-order function models, only limited experimental points are adopted to do the regression, the best regression accuracy cannot be obtained even if the selected points are reasonable. In contrast, SSE of the regression curve by ordinary least square model reduces to less than 50% of the best regressed result by second-order function model, the yielding behavior and variable strain increment ratio of the anisotropic materials can be reflected more accurately. This is very important for accurately describing the plastic flow behaviors of anisotropic materials.

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“…State of the art which can improve control precision for the ratio of axial compressive stress to hoop tension stress and obtain more accurate experimental results. A series of studies [81][82][83][84] on evaluating the yield function and forming limit diagrams under the large ratio of the tensile to compressive stress for several different tubular materials are performed on this machine. However, isotropic material plastic flow behaviors are not considered in these studies.…”

Section: Deformed Tube Locking Gasketmentioning

confidence: 99%

“…The above equations 2.1 and 2.2 lay the foundation to calculate the circumferential and longitudinal stress components and fit the flow stress curve, which are first derived by Woo et al [50] and then used in many studies [23,56,66,[88][89][90][91][92][93]. Fuchizawa et al [53] improve this stress model by taking into account the wall thickness of metal tubes, and following re-searchers [54,55,58,59,63,71,72,81,87,[94][95][96][97][98][99][100] recommend this new formula because it is more in line with the actual situation. Obviously, no matter in which formula to calculate the stress component proposed by Woo [50] or Fuchizawa [53], the internal pressure, expanding diameter, axial feeding force if necessary, meridional curve radius and pole thickness are required where the first three indicators are easy to record online in the experiment.…”

Section: Analytical Modelmentioning

confidence: 99%

The automatic optimization of metal forming processes: Inverse identification of constitutive parameters for tubular materials based on hydraulic bulge test

Zhang¹

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Tube hydroforming process is an advanced manufacturing technology for complex thin-walled tubular components applied in the aerospace, aviation and automotive industries. The fluid medium is used as a pressure source to deform tubular materials into the desired shape in this process. Finite element model is a popular method to describe and analyze this innovative process. A successful tube hydroforming operation and reliable finite element simulation depend heavily on the accurate characterization of mechanical properties of the incoming tubular materials. As a result, it is critical to determine these material parameters utilizing suitable experimental tests and evaluation procedures.This thesis presents the development of an automatic inverse parameter identification framework combining finite element models with gradientbased algorithms and its utilization in determining material parameters for thin-walled metallic tubes. The main principle of the inverse framework is the minimization of the objective function defined as the least square error between simulated results and experimental observations. Finite element methods are used to describe and analyze the experimental testing process and gradient-based optimization techniques adjust the input material parameters in the model until the calculated results have a good agreement with the experimental measurements.The feasibility and performance of this proposed inverse framework are demonstrated through applying it to different tube hydraulic bulge tests with fixed and forced end-conditions to identify the flow stress data of thin-walled aluminium tubes. The bulge height, axial compressive force and pole thickness are measured during the experiment and input into the inverse strategy. Based on the obtained material values, finite element simulated models of hydroforming processes are established and used to predict the shape properties of final products. The comparison between simulated predictions and experimental data shows that the developed inverse strategy provide a robust and effective method to determine material properties for thin-walled metallic tubes.Furthermore, a theoretical analysis is integrated into the inverse frameiii work, and the two are recombined into a hybrid strategy to avoid local minimums in the parameter identification process. The new strategy is tested by the experimental data from fixed and forced tube hydraulic bulge tests. As a result of this research, it is possible to conclude that the novel hybrid strategy does not depend heavily on the initial points and can improve the computation robustness and identify more accurate constitutive parameters for tubular materials.

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Complex Stress-Strain Relations of Tubular Materials Studied With a Flexible Hydroforming System

Cited by 5 publications

References 18 publications

A New Regression Model for the Prediction of the Stress–Strain Relations of Different Materials

A New Regression Model for the Prediction of the Stress–Strain Relations of Different Materials

An optimized constitutive model for reproducing flow stress–strain relationships of anisotropic materials

The automatic optimization of metal forming processes: Inverse identification of constitutive parameters for tubular materials based on hydraulic bulge test

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