TY - GEN
T1 - Size Effect on the Statistical Distribution of Stress and Strain in Microforming
AU - Feng, Z. Y.
AU - Li, H.
AU - Zhang, D.
AU - Fu, M. W.
N1 - Publisher Copyright:
© 2024, The Author(s), under exclusive license to Springer Nature Switzerland AG.
PY - 2023/8/29
Y1 - 2023/8/29
N2 - The frequency distribution of local stress or strain across the micromechanical field in plastic deformation tends to universally follow a normal or lognormal distribution, regardless of the variety of microstructural inhomogeneity. However, it has not been reported how size effect (SE) influences the grain-scale statistical distribution of stress and strain in microforming, and thus an in-depth investigation is further needed. Taking the polycrystalline Cu sheets with thickness t = 0.1–1.5 mm and t/d = 1–29 as the case materials, this study implements the full-field CPFE simulation incorporated with a size-dependent dislocation-based constitutive model and statistical analyses to explore the influence of SE on the frequency distribution of grain-scale stress and strain in micro-scaled plastic deformation. With increasing t/d, the stress frequency consistently follows a normal distribution. In contrast, the frequency distributions of strain and dislocation density undergo a transformation from a lognormal distribution to an approximately normal distribution. The results indicate that the distribution law of stress is dominantly influenced by the dislocation density, while that of strain is determined by a multiplicative process of slip activities. The established knowledge will help to elucidate the nature of the distribution law of stress or strain, and to seek for effective approaches to alleviate the scatter and uncertainty of deformed part geometry during a microforming process.
AB - The frequency distribution of local stress or strain across the micromechanical field in plastic deformation tends to universally follow a normal or lognormal distribution, regardless of the variety of microstructural inhomogeneity. However, it has not been reported how size effect (SE) influences the grain-scale statistical distribution of stress and strain in microforming, and thus an in-depth investigation is further needed. Taking the polycrystalline Cu sheets with thickness t = 0.1–1.5 mm and t/d = 1–29 as the case materials, this study implements the full-field CPFE simulation incorporated with a size-dependent dislocation-based constitutive model and statistical analyses to explore the influence of SE on the frequency distribution of grain-scale stress and strain in micro-scaled plastic deformation. With increasing t/d, the stress frequency consistently follows a normal distribution. In contrast, the frequency distributions of strain and dislocation density undergo a transformation from a lognormal distribution to an approximately normal distribution. The results indicate that the distribution law of stress is dominantly influenced by the dislocation density, while that of strain is determined by a multiplicative process of slip activities. The established knowledge will help to elucidate the nature of the distribution law of stress or strain, and to seek for effective approaches to alleviate the scatter and uncertainty of deformed part geometry during a microforming process.
KW - Crystal plasticity
KW - Microforming
KW - Size effect
KW - Statistical distribution
KW - Stress/strain frequency
UR - http://www.scopus.com/inward/record.url?scp=85174844079&partnerID=8YFLogxK
U2 - 10.1007/978-3-031-41341-4_42
DO - 10.1007/978-3-031-41341-4_42
M3 - Conference article published in proceeding or book
AN - SCOPUS:85174844079
SN - 9783031413407
T3 - Lecture Notes in Mechanical Engineering
SP - 413
EP - 421
BT - Proceedings of the 14th International Conference on the Technology of Plasticity - Current Trends in the Technology of Plasticity - ICTP 2023 - Volume 3
A2 - Mocellin, Katia
A2 - Bouchard, Pierre-Olivier
A2 - Bigot, Régis
A2 - Balan, Tudor
PB - Springer Science and Business Media Deutschland GmbH
T2 - 14th International Conference on Technology of Plasticity, ICTP 2023
Y2 - 24 September 2023 through 29 September 2023
ER -