On the Hall–Petch relation between flow stress and grain size

2006 ◽  
Vol 97 (12) ◽  
pp. 1661-1666 ◽  
Author(s):  
W. Blum ◽  
Y. J. Li ◽  
J. Chen ◽  
X. H. Zeng ◽  
K. Lu
Keyword(s):  
Grain Size ◽  
Flow Stress ◽  
Petch Relation

Modeling of Size Effect on Tensile Flow Stress of Sheet Metal in Microforming

2008 ◽  
Vol 131 (1) ◽  
Author(s):  
Daw-Kwei Leu
Keyword(s):  
Grain Size ◽  
Flow Stress ◽  
Size Effect ◽  
Sheet Metal ◽  
Sheet Thickness ◽  
Hyperbolic Function ◽  
Zone Model ◽  
Petch Relation ◽  
Simple Tension ◽  
Dependent Factor

This investigation considers the size effect on the deformation behavior of simple tension in microforming and thus proposes a simple model of the tensile flow stress of sheet metal. Experimental results reveal that the measure of the flow stress can be represented as a hyperbolic function tanh(T/D), which is a function of T/D (sheet thickness/grain size). The predicted flow stress agrees very well with the published experiment. Notably, a specimen with smaller grains has lower normalized flow stress for a given T/D. Since the material properties of the macroscale specimen do not pertain to the microscale, a critical condition (T/D)c that distinguishes the macroscale from the microscale in the tensile flow stress is subsequently proposed, based on the “affected zone” model, the pile-up theory of dislocations, and the Hall–Petch relation. The distribution of the predicted (T/D)c is similar to the experimental finding that the (T/D)c decreases as the grain size increases. However, the orientation-dependent factor β is sensitive to (T/D)c. Hence, further study of the orientation-dependent factor β is necessary to obtain a more accurate (T/D)c and, thus, to evaluate and understand better the tensile flow stress of sheet metal in microforming.

Localized Plastic Flow Autowaves and the Hall-Petch Relation for Al

2013 ◽  
Vol 592-593 ◽  
pp. 271-274
Author(s):  
Lev B. Zuev ◽  
Natalya Zarikovskaya
Keyword(s):  
Plastic Deformation ◽  
Grain Size ◽  
Flow Stress ◽  
Plastic Flow ◽  
Flow Patterns ◽  
Localized Deformation ◽  
Polycrystalline Aluminum ◽  
Petch Relation ◽  
Grain Sizes ◽  
Localization Of Plastic Deformation

The localization of plastic deformation was examined for polycrystalline aluminum samples having grain sizes in the range from 8·10-3to 10 mm. It is found that the length of localized deformation autowaves is determined by the grain size of material. The localized plastic flow patterns emergent in the polycrystalline aluminum samples are found to be connected to the Hall-Petch relation. Two types of flow stress dependencies of grain size are distinguished.

The Combined Effect of Grain Size and Strain Rate on the Mechanical Behavior in Ultra-High Purity Aluminum

2011 ◽  
Vol 179-180 ◽  
pp. 662-667
Author(s):  
Yong Gang Wang ◽  
Chun Lei Wang ◽  
Hong Wei Liu
Keyword(s):  
Mechanical Properties ◽  
Grain Size ◽  
Flow Stress ◽  
Strain Rate ◽  
Pure Aluminum ◽  
Testing Machine ◽  
Tensile Tests ◽  
Hydraulic Testing ◽  
Petch Relation ◽  
Split Hopkinson

The effect of grain size on the mechanical properties in ultra-high pure aluminum had been investigated as a function of strain rate. Specimens with average grain diameter sizes of 243, 678 and 1070 m were compressed and elongated at quasi-static and high strain rates by a computer controlled servo-hydraulic testing machine and a Split Hopkinson Pressure (Tension) Bar (SHPB and SHTB). The mechanical properties were found to vary significantly with grain size, and strain rate. The relationship between flow stress and grain size can be expressed by a Hall - Petch relation with the different slope for both compressive tests and tensile tests. The influence of strain rate on the slope of the Hall - Petch relation is such that in compression, the slope does not change much, but in tension, there is an increase in the slope value. The strain hardening rate was seen to increase with increasing strain rate. The strain rate dependence of flow stress is obvious, and is seen to be more significant for the smallest grain size specimens. The 3D fractographs illustrated that the numbers of the dimples decrease with the increase of the grain size.

Effect of grain size on flow stress of textured Zn alloy

Metal Science ◽  
1983 ◽  
Vol 17 (7) ◽  
pp. 317-324 ◽  
Author(s):  
N. R. Ecob ◽  
B. Ralph
Keyword(s):  
Grain Size ◽  
Flow Stress ◽  
Zn Alloy

Model of Microstructure Development in Hot Deformed Magnesium Alloy AZ31 Type

2013 ◽  
Vol 197 ◽  
pp. 232-237 ◽  
Author(s):  
Dariusz Kuc ◽  
Eugeniusz Hadasik
Keyword(s):  
Grain Size ◽  
Flow Stress ◽  
Magnesium Alloy ◽  
Rolling Process ◽  
Microstructure Development ◽  
Compression Tests ◽  
Magnesium Alloy Az31 ◽  
Hot Rolling Process ◽  
Alloy Type ◽  
Relaxation Curves

The paper presents a model of microstructure changes elaborated for magnesium alloy type AZ31. In previous papers, the function of flow stress was defined on the basis of uniaxial hot compression tests. On the basis of marked relaxation curves and quantitative tests of structure the softening indicators were defined together with elaboration of equations which describe the changes in the grain size. Marked coefficients of equations were introduced in the code of simulation program. Calculations were conducted for given temperature values from 450 ÷ 250°C and strain rate from 0.01 to 10 s-1, which correspond with rolling temperature range of this alloy. Prepared model will allow the proper choice of parameters in hot rolling process of this alloy to achieve the assumed microstructure.

The grain size dependence of flow stress in a Cu–26Ni–17Zn alloy

2000 ◽  
Vol 48 (8) ◽  
pp. 1807-1813 ◽  
Author(s):  
S. Nagarjuna ◽  
M. Srinivas ◽  
K.K. Sharma
Keyword(s):  
Grain Size ◽  
Flow Stress ◽  
Size Dependence

Modeling of Size Effects on the Flow Stress of Type 304 Stainless Steel and Application in Coining Process

2007 ◽  
Author(s):  
Gap-Yong Kim ◽  
Muammer Koc ◽  
Jun Ni
Keyword(s):  
Grain Size ◽  
Stainless Steel ◽  
Flow Stress ◽  
Size Effect ◽  
Size Effects ◽  
Specimen Size ◽  
304 Stainless Steel ◽  
Length Scales ◽  
Type 304 ◽  
Type 304 Stainless Steel

Application of microforming in various research areas has received much attention due to the increased demand for miniature metallic parts that require mass production. For the accurate analysis and design of microforming process, proper modeling of material behavior at the micro/meso-scale is necessary by considering the size effects. Two size effects are known to exist in metallic materials. One is the “grain size” effect, and the other is the “feature/specimen size” effect. This study investigated the “feature/specimen size” effect and introduced a scaling model which combined both feature/specimen and grain size effects. Predicted size effects were compared with experiments obtained from previous research and showed a very good agreement. The model was also applied to forming of micro-features by coining. A flow stress model for Type 304 stainless steel taking into consideration the effect of the grain and feature size was developed and implemented into a finite element simulation tool for an accurate numerical analysis. The scaling model offered a simple way to model the size effect down to length scales of a couple of grains and extended the use of continuum plasticity theories to micro/meso-length scales.

Turning Force Prediction of AISI 4130 Considering Dynamic Recrystallization

2017 ◽  
Author(s):  
Zhipeng Pan ◽  
Yixuan Feng ◽  
Xia Ji ◽  
Steven Y. Liang
Keyword(s):  
Grain Size ◽  
Flow Stress ◽  
Dynamic Recrystallization ◽  
Analytical Model ◽  
Cutting Forces ◽  
Material Flow ◽  
Explicit Calculation ◽  
Material Microstructure ◽  
Machining Forces ◽  
Aisi 4130

Thermal mechanical loadings in machining process would promote material microstructure changes. The material microstructure evolution, such as grain size evolution and phase transformation could significantly influence the material flow stress behavior, which will directly affect the machining forces. An analytical model is proposed to predict cutting forces during the turning of AISI 4130 steel. The material dynamic recrystallization is considered through Johnson-Mehl-Avrami-Kolmogorov (JMAK) model. The explicit calculation of average grain size is provided in an analytical model. The grain size effect on the material flow stress is considered by introducing the Hall-Petch relation into a modified Johnson-Cook model. The cutting forces prediction are based on Oxley’s contact mechanics with consideration of mechanical and thermal loads. The model is validated by comparing the predicted machining forces with experimental measurements.

Effect of relative grain size on the flow stress of polycrystalline FCC sheets

2012 ◽  
Vol 27 (3) ◽  
pp. 477-483
Author(s):  
Mei Yang ◽  
Jitao Du ◽  
Houjia Li ◽  
Xiaoyan Zhang
Keyword(s):  
Grain Size ◽  
Flow Stress
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