Modelling the constitutive behaviour of thin metal sheet using strain gradient theory

Micheľ, J.; Picart, Philippe

doi:10.1016/s0924-0136(02)00370-9

Cited by 12 publications

(7 citation statements)

References 6 publications

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“…There is a distinct phenomenon in tensile tests wherein the flow stress decreases with decreasing specimen size and increasing grain size. This effect has been confirmed by several researchers using different materials [4][5][6][7][8][9][10] and explained by the surface layer model and Hall-Petch relation [11]. However, for bending tests, the result is different.…”

Section: Introductionsupporting

confidence: 53%

“…However, for bending tests, the result is different. If the grain size is smaller than the sheet thickness, the flow stress decreases with decreasing specimen size and increasing grain size, which is the same as tensile test; however, if the grain size is larger than the sheet thickness, the flow stress increases with increasing grain size [4][5][6][7][8][9][10].…”

Section: Introductionmentioning

confidence: 99%

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Size effects on flow stress of C3602 in cylinder compression with different lubricants

et al. 2009

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Micro parts are more difficult to be formed than macro parts because of size effects. The size effects on the flow stress of copper alloy C3602 with different lubricants were studied. Specimens were heat treated at 350°C for 1 h and 700°C for 3 h in nitrogen atmosphere, respectively. The initial diameters of the specimens were varied from 5 to 1 mm with a height-to-diameter ratio h 0 /D 0 = 1.5. Cylinder compression was carried out in the lubrication condition with talc powder, without lubricant, with petroleum jelly, and with vegetable oil. The experiment was carried out at room temperature on a universal testing machine INSTRON 5569 with a strain rate of ε = 0.0025 /s. The results show that with the same lubricant, the yield strength decreases with a decrease in specimen size for the specimens annealed at 350°C for 1 h; however, it increases with a decrease in specimen size for the specimens annealed at 700°C for 3 h. The yield strength decreases with an increase in grain size. The influences of lubricants on yield strength become larger with miniaturization of the specimens.

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Section: Introductionsupporting

confidence: 53%

Section: Introductionmentioning

confidence: 99%

Size effects on flow stress of C3602 in cylinder compression with different lubricants

et al. 2009

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“…Such results have encouraged researchers to adapt conventional models when approaching experimental results. One study proposed and implemented in numerical simulation for a modified model based on the experimental results of tensile tests which takes into account the grain size effect [7,8]. The material parameters associated with this model were identified by the reverse method.…”

Section: Introductionmentioning

confidence: 99%

Grain Size Effect in the Micro-V-Bending Process of Thin Metal Sheets

Chen¹,

Jiang

2011

Materials and Manufacturing Processes

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The aim of this study is to develop a micro-V-bending testing system and to investigate the grain size effect of 99.5% Ferrum sheet plate in the micro-V-bending process. In this study, two experiments have been conducted. They attempt to explain the characteristic of thickness variation at a constant average grain size of 29.93 m with a standard deviation (SD) of 2.4 and the different average grain sizes at a constant mean thickness of 490.63 m with a SD of 11.3. A laser displacement sensor is employed to monitor the real position of punch movement and to verify the effective stroke. In the micro-V-bending test, the thickness/average grain size (T/D) ratio is used to discuss material behavior such as punch force, springback, and spring-forward. According to the results, the conventional concept of V-bending deformation cannot be applied to different average grain sizes at a constant thickness in the micro-V-bending test particularly when the T/D ratio is less than 2. IntroductionMiniaturization is a trend in product development [1,2]. This trend encourages researchers to verify the feasibility of applying conventional macroscale analysis methods to microscale metal forming process. To date, many studies have focused on first-order size effects which can be accounted for by using conventional models. Studies have also explored second-order size effects that cannot be accounted for using conventional models. In the studies of first-order size effects, the influencing factors include grain size effect, grain boundary effect, free surface effect, grain statistics effect, and processing induced size effect [3,4]. For example, the contribution of frictional force to total force is significant when miniaturizing the deep drawing process. In a study on second-order size effects, all important process dimensions were scaled down due to the observance of geometric similarity. A length scale was designated corresponding to sheet thickness between 1 and 0.1 mm in the tensile test. As a result, the occurrence of second-order size effects was found to be expressed by the decrease in flow stress, vertical strain anisotropy, and ductility [5].It has been demonstrated that grain size effect influences deformability in tensile and air bending testing [6]. Tensile tests have also shown that yield strength decreases with the decrease of specimen thickness at a constant grain size. The material used was Al 2S. However, the experimental results of bending show that yield strength increases with decreasing grain size. The studies mentioned above show the influence of grain size effect on the constitutive behavior

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“…As a decisive parameter for the occurrence of either of the above described size effects, the ratio of foil thickness t 0 to mean grain size L G has been identified by [9]. In literature, various approaches of the strain gradient plasticity theory can be found [3,10,11]. These approaches do not only consider the strains but also their gradients.…”

Section: Introductionmentioning

confidence: 99%

Size effects in bending processes applied to metal foils

Diehl

Engel

Merklein

et al. 2009

Prod. Eng. Res. Devel.

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Ongoing development in the miniaturisation field leads to an increasing understanding interest in the forming behaviour of thin metal sheets since forming technology is well suited in particular for mass production. In case of micro forming, i.e. reducing the sheet thickness to the order of micrometers, established know-how of conventional sheet metal forming cannot directly be transferred to metal foil forming due to the phenomenon known as size effect. In this paper a bending concept, which enables the investigation of the two contrary size effects originating from the share of surface grains and the strain gradient via scaled experiments, is introduced. The forming behaviour is characterised by the spring-back angle which gives an indirect measure of the present bending moment and is an important factor for production accuracy. The experimental results are compared with analytical solutions and an approach to implement strain gradient dependent material behaviour in the analytical description of bending processes is presented.

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Modelling the constitutive behaviour of thin metal sheet using strain gradient theory

Cited by 12 publications

References 6 publications

Size effects on flow stress of C3602 in cylinder compression with different lubricants

Size effects on flow stress of C3602 in cylinder compression with different lubricants

Grain Size Effect in the Micro-V-Bending Process of Thin Metal Sheets

Size effects in bending processes applied to metal foils

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