Complex unloading behavior: Nature of the deformation and its consistent constitutive representation

Sun, Li; Wagoner, R. H.

doi:10.1016/j.ijplas.2010.12.003

Cited by 194 publications

(95 citation statements)

References 53 publications

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“…Therefore, considering elastic behaviour as a linear curve by using a single value for Young's modulus to describe the elastic region can potentially generate significant uncertainties in determination of springback. This is even more pronounced during unloading compared to loading [1,5,[7][8][9][13][14][15].…”

Section: Introductionmentioning

confidence: 93%

“…Earlier studies [1,7,8,10,11,[13][14][15][16][17] show a degradation in Young's modulus as a function of the level of plastic deformation for different alloys. This has usually been shown by comparing the initial elastic modulus, characterised using standard methods, at no plastic strain to those measured after various levels of plastic strain through interrupted tensile tests, consisting of a series of loading-unloading-loading steps on a same sample [5].…”

Section: Introductionmentioning

confidence: 99%

“…Different methodologies exist to study degradation in Young's modulus as a function of plastic deformation, such as interrupted uniaxial [1,7,8,[13][14][15]18] and biaxial loading-unloading-loading tensile tests [19,20], and pre-strained three-point bending tests [19,[21][22][23]. The former is the most reported method used for detailed characterisation of elastic modulus during plastic deformation [1,7,8,10,11,[13][14][15][16][17]. Despite the intensive application of interrupted tensile test technique, it has been argued that the pre-strained threepoint bending test provides measurement of degradation in elastic modulus during plastic deformation more accurately [19].…”

Section: Introductionmentioning

confidence: 99%

“…Springback is mainly known as elastic strain recovery, while various studies [5,8,9,14,18] conducted on steels and aluminium show springback as a combination of elastic and anelastic strain recoveries. It is a common practice to use the slope of the loading curve (i.e.…”

Section: Introductionmentioning

confidence: 99%

“…It is a common practice to use the slope of the loading curve (i.e. Young's modulus) in each loading-unloading loop, to investigate the degradation in Young's modulus, using interrupted tensile test procedure [14,15]. In this approach, the nonlinear strain recovery occurring during the unloading step was originally neglected; however, later studies considered the Chord modulus as a criterion to overcome this source of uncertainty for springback investigation [5-7, 9, 10, 13, 14, 24].…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Characterisation and modelling of in-plane springback in a commercially pure titanium (CP-Ti)

Khayatzadeh

Thomas

Millet³

et al. 2018

J Mater Sci

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Effective prediction of springback during sheet metal forming is critically important for automotive and aerospace industries, especially when forming metals with high strength-to-weight ratio such as titanium. This requires materials mechanical data during plastic deformation and their dependencies on parameters like strain, strain rate and sample orientation. In this study, springback is quantified experimentally as elastic strain recovery, degradation in Young's modulus and inelastic strain recovery on unloading in a commercially pure titanium type 50A (CP-Ti-50A). The results show strain rate-dependent anisotropic mechanical behaviours and a degradation in Young's modulus with increased level of plastic deformation. The level of degradation in Young's modules increases gradually from 13% for samples parallel to the rolling direction (RD) to 20% for those perpendicular to the RD. A measurable nonlinear strain recovery was also observed on unloading that is orientation dependent. The level of springback is characterised as the sum of elastic recovery and the contributions from both the degradation in Young's modulus and anelastic strain recovery. It is shown that the Chord modulus can estimate springback with a reasonable accuracy taking into consideration the elastic strain recovery, degradation in Young's modulus and anelastic strain recovery.

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Section: Introductionmentioning

confidence: 93%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Characterisation and modelling of in-plane springback in a commercially pure titanium (CP-Ti)

Khayatzadeh

Thomas

Millet³

et al. 2018

J Mater Sci

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A Mechanical Model of Cellular Solids for Energy Absorption

Avalle

Belingardi

2018

Adv Eng Mater

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Cellular materials, also known as foams, have a variety of applications in the field of packaging, and shock mitigation in the case of crash of vehicles, due to their ability to protect goods by absorbing energy in the case of impact while reducing the transmitted loads. To properly design energy absorption devices and systems such as bumpers, road barriers, helmets, sole paddings, packages, etc. it is necessary to use precisely predictive models of cellular materials, in order to select the most suitable foam for the considered application. The model must describe the stress-strain behavior, at least uniaxial compression, but also sometimes the tension and multiaxial loading, then energy absorption characteristics is evaluated. Moreover, it must take into account affecting factors like the strain-rate. Secondarily, modeling the influence of the density heavily helps designer in selecting the best solution in terms of minimum weight per given energy to dissipate. In previous works, the authors present more than one model able to describe the quasistatic stress-strain behavior of several cellular materials. The current paper presents a very general model able to describe, with properly identified parameters, the mechanical characteristics of a much larger variety of cellular materials including metal foams, foam mechanical properties (like, e.g., the dependence on density), and takes into account the influence of strain-rate. Among the considered materials are the Foaminal 1 aluminum foam and the APM 1 hybrid foam. The model is fitted to experimental tests with parameters identified based on past experimental data from the authors themselves. Tests include quasi-static, dynamic, and impact tests at different loading speed and impact energy. It is shown that the proposed model is fundamentally suitable for most materials, virtually any foamed material, and it is an outstandingly useful tool for designers in the mentioned areas.

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Work Hardening Response of Transformation‐Induced Plasticity and Dual‐Phase Steels to Prestrain

2013

steel research int.

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Standard uniaxial tension and repetitive uniaxial tension at different prestrain levels have been conducted for cold-rolled TRIP780 and DP590 steels. Scan electron microscope (SEM) was performed to observe the microstructures response to prestrain. The instantaneous work hardening rate and transient hardening behavior changing with the prestrain in repetitive tension were discussed in detail. The elastic modulus degradation with prestrain was also identified for the two steels. Results indicated that TRIP780 and DP590 had different work hardening responses to prestrain although they both have preferable work hardenability. When prestrain was small, DP steel had higher work hardening rate than TRIP steel had. While when the prestrain was larger than 2.5%, TRIP780 displayed higher work hardening rate than DP590 did. After each unloading in repetitive tension, the work hardening rate of TRIP780 and DP590 steels fell off and then tended to come back to the original level. The drop of work hardening rate decreased with the prestrain only for TRIP780. It was discerned that the max elastic modulus degradation could reach 18 and 10% for TRIP780 and DP590 steels, respectively.

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Complex unloading behavior: Nature of the deformation and its consistent constitutive representation

Cited by 194 publications

References 53 publications

Characterisation and modelling of in-plane springback in a commercially pure titanium (CP-Ti)

Characterisation and modelling of in-plane springback in a commercially pure titanium (CP-Ti)

A Mechanical Model of Cellular Solids for Energy Absorption

Work Hardening Response of Transformation‐Induced Plasticity and Dual‐Phase Steels to Prestrain

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