• Transactions of the Korean Society of Mechanical Engineers A
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• v.31 no.2 s.257
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• pp.182-189
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• 2007

This paper is concerned with the empirical flow stress constitutive equation of steel sheets for an auto-body with the variation of temperature and strain rate. In order to represent the strain rate and temperature dependent behavior of the flow stress at the intermediate strain rates accurately, an empirical hardening equation is suggested by modifying the well-known Khan-Huang-Liang model. The temperature and strain rate dependent sensitivity of the flow stress at the intermediate strain rate is considered in the hardening equation by coupling the strain, the strain rate and the temperature. The hardening equation suggested gives good correlation with experimental results at various intermediate strain rates and temperatures. In order to verify the effectiveness and accuracy of the suggested model quantitatively, the standard deviation of the fitted result from the experimental one is compared with those of the other two well-known empirical constitutive models such as the Johnson-Cook and the Khan-Huang-Liang models. The comparison demonstrates that the suggested model gives relatively well description of experimental results at various strain rates and temperatures.

• Magazine of the Korean Society of Agricultural Engineers
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• v.30 no.3
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• pp.38-50
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• 1988

carried out to present a rheology model which is able to treat time-dependent properties of clay. The results were summarized as follow ; 1. The slope (a(e1)) of deviator stress in strain rate test was independent on axial strain, and pore water pressure was decreased with increment of strain rate. 2. The pore water pressure in a stress relaxation condition was not changed when the strain rate before stress relaxation was 0.05%/min., but it was increased with increment of time when the strain rate before stress relaxation was 0.2%/min 3. The greater the stress condition (q/qmax) and the strain rate before creep test became, the greater the increment rate of axial strain in creep test became. 4. SEKIGUCHI's constitutive equation was slightly overpredicted while empirical equation proposed in the study was well coincided with measured values. 5. The constitutive equation induced by a strain function could be dealed with a behavior of the pore water pressure increased with increment of elapsed time after primary consolidation.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.27 no.7
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• pp.1152-1158
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• 2003

The mechanical behavior of a commercially pure titanium (CP-Ti) is investigated at high temperature Split Hopkinson Pressure Bar (SHPB) compression test with high strain-rate. Tests are performed over a temperature range from room temperature to 1000$^{\circ}C$ with interval of 200$^{\circ}C$ and a strain-rate range of 1900 ∼ 2000/sec. The true flow stress-true strain relations depending on temperature are achieved in these tests. For construction of constitutive equation from the true flow stress-true strain relation, parameters for the Johnson-Cook constitutive equation is determined. And the modified Johnson-Cook equation is used for investigation of behavior of flow stress in vicinity of recrystalization temperature. The Modified Johnson-Cook constitutive equation is more suitable in expressing the dynamic behavior of a CP-Ti at high temperature, i.e. about recrystalization temperature.

• Structural Engineering and Mechanics
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• v.20 no.5
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• pp.495-504
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• 2005

This article explores a constitutive equation that is able to correlate stress, strain and strain rate. In order to show the advantages of the constitutive equation here proposed and how its material parameters are obtained, data extracted from the literature, for materials as different as polymers and metallic alloys, are used. Finite element simulation of the impact behaviour of a beam is presented to highlight the care one needs to exercise when using the more traditional Cowper-Symonds equation. The present constitutive equation has shown to be accurate for a wide range of strains, stresses and strain rates.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1995.10a
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• pp.724-727
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• 1995

Dynamic deformation behavior under the high strain rate loading condition obtained with the aid of Split Hopkinson Pressure Bar(SHPB) technique is simulated by DYNA2D (an hydrodynamic code). A constitutive equation such as Johnson-Cook model is used by adjusting various parameters to fit experimentally determined dynamic stress-strain relationship.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1994.04a
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• pp.181-188
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• 1994

Generally, the structural material shows rate dependent behaviors, which require to constitute different strain-stress relations according to strain rates. Conventional rate- independent constitutive equations used in general purpose finite analysis programs are inadequate for dynamic finite strain problems. In this paper, a rate dependent constitutive equation for elastic-plastic material was developed. The plastic stretch rate was modeled based on slip model with dislocation velocity and density so that there is no yielding condition, and no loading conditions. Non-linear hardening rule was also introduced for finite strain. Material constants of present constitutive equation were determined by experimental data of mild steel. The constitutive equation was applied to uniaxile tension. It was appeared that the present constitutive equation well simulates rate dependent behaviors of mild steel.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 2004.08a
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• pp.145-152
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• 2004

The flow stress value was calculated by comparing predicted and measured roll force. Using basic on-line roll force model and logged mill data the flow stress equation of high strength steel for automobile was derived. The flow stress equation consists of the flow stress equation of carbon steel and flow stress factor calculated by neural network with input parameters not only carbon contents, strip temperature, strain, and strain rate, but also compositions such as Mn, p, Ti, Nb, and Mo. Using the flow stress equation and basic roll force model, precision roll force model of high strength steel for automobile was derived. Using test set of logged mill data the flow stress equation was verified.

• International Journal of Railway
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• v.3 no.4
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• pp.117-122
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• 2010

In transportation geotechnical engineering, stress-strain behavior of earth structures has been analyzed by numerical simulations with the implemented plasticity constitutive model. It is a fact that many advanced plasticity constitutive models on predicting the mechanical behavior of soils have been developed as well as experimental research works for geotechnical applications in the past decades. In this study, recently developed, a unified constitutive model for both clay and sand, which is referred to as CASM (clay and sand model), was compared with a classical constitutive model, Cam-Clay model. Moreover, integration methods of stress-strain rate equations using CASM were presented for simulation of undrained and drained triaxial compression tests. As a conclusion, it was observed that semi-implicit integration method has more improved accuracy of capturing strain rate response to applied stress than explicit integration by the multiple correction and iteration.

• Proceedings of the KSME Conference
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• 2004.11a
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• pp.377-382
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• 2004

The dynamic material characteristics on some mild steel sheets were observed. The dynamic tests were conducted on the ESH servo-hydraulic test machine. It was observed that the mechanical properties of mild steel are highly sensitive to the value of strain rate. The well known Cowper-Symonds constitutive equation was used to generalize the strain rate sensitivity effect. Modified constitutive equations were suggested to couple the strain hardening to the strain rate sensitivity. The dynamic stress-strain relationships for the mild steel sheets used in the present study were reasonably predicted using these modified constitutive equations.

• Magazine of the Korean Society of Agricultural Engineers
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• v.30 no.4
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• pp.134-153
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• 1988

This paper was carried out to investigate the existence of a unique stress- strain behavior by obtaining some factors influencing the time dependent stress- strain behavior of clay. The results obtained from this study were summarized as follows ; 1. The relationship between stress ratro and strain in normally consolidated clay was in- dependent on pre-shear consolidation pressure. Therefore, shear strain could be expressed as a function with stress ratio. 2. The constitutive equation of shear strain on Modified Carn Clay Model coincided better with the observed value than Cam Clay Model. 3. The relationships between deviator stress and shear strain, between pore water pressure and shear strain were unified by the mean equivalent pressure. 4. The shear strain contour in norrnally consolidated clay was increased linearly through origin, but that in overconsolidated clay was not in accordance with the result of the former. 5. Because the effective stress path of normally consolidated clay was unified by the mean equivalent pressure, state boundary surface in (e,p,q) space was transformed into two dimensional surface. But it was considered to be suitable that the unified stress- strain in overconsolidated clay be expressed by a function with overconsolidation ratio. 6. The deviator for constant strain was increased linearly with increment of strain rate ($\varepsilon$) on semi-log scale, but pore water pressure was decreased. 7. The behavior of stress relaxation was transformed from linear to curvilinear with inc - rement of strain rate before stress relaxation test, and pore water pressure was increased in total range. 8. The strain of creep was increased linearly with increment of time on semi-log scale. The greater the strain rate before creep test became, the greater the increment of strain of creep became. And the pore water pressure during creep test was increased generally with increment of time on semi-log scale.