• 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.

• Transactions of Materials Processing
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• v.31 no.2
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• pp.81-88
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• 2022

Numerical analysis and dynamic material properties are required to analyze the behavior of workpiece during an electrohydraulic forming (EHF) process. In this study, EHF experiments were conducted under three conditions (6, 7, 8 kV). Dynamic material properties of Al 5052-H34 were inversely estimated through an ANN (Artificial Neural Network) model constructed based on LS-Dyna analysis results. Parameters of Cowper-Symonds constitutive equation, C and p, were used to implement dynamic material properties. By comparing experimental results of three conditions with ANN model results, optimized parameters were obtained. To determine the reliability of the derived parameters, experimental results, LS-Dyna analysis results, and ANN results of three conditions were compared using MSE and SMAPE. Valid parameters were obtained because values of indicators were within confidence intervals.

• Journal of Ocean Engineering and Technology
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• v.25 no.3
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• pp.73-84
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• 2011

This is the fifth in a series of companion papers dealing with the dynamic hardening properties of various marine structural steels at intermediate strain rates. Five steps of strain rate levels (0.001, 1, 10, 100, 200/s) and three steps of temperature levels (LT ($-40^{\circ}C$), RT, and HT ($200^{\circ}C$)) were taken into account for the dynamic tensile tests of three types of marine structural steels: API 2W50 and Classifications EH36 and DH36. The total number of specimens was 180 pieces. It was seen that the effects of dynamic hardening became clearer at LT than at RT. Dynamic strain aging accompanying serrated flow stress curves was also observed from high temperature tests for all kinds of steels. The dynamic hardening factors (DHFs) at the two temperature levels of LT and RT were derived at the three plastic strain levels of 0.05, 0.10, 0.15 from dynamic tensile tests. Meanwhile, no DHFs were found for the high temperature tests because a slight negative strain rate dependency due to dynamic strain aging had occurred. A new formulation to determine material constant D in a Cowper-Symonds constitutive equation is provided as a function of the plastic strain rate, as well as the plastic strain level. The proposed formula is verified by comparing with test flow stress curves, not only at intermediate strain rate ranges but also at high strain rate ranges.

• 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.

• Journal of the Society of Naval Architects of Korea
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• v.33 no.3
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• pp.48-55
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• 1996

The aim of the present study is to investigate the scaling and dynamic erects on the plate cutting response. A series of cutting tests for unstiffened and longitudinally stiffened steel plate specimens in a quasi-static condition were carried out, varying the plate thickness. Based on the previous as well as the present test results, the scaling effect of Plate thickness on the cutting response is investigated. Dynamic erects are also clarified from the devious theoretical and experimental results. The Cowper-Symonds constitutive equation originally derived for mild steel is modified to consider the influence of strain-rate sensitivity on yield strength of high tensile steel.

• International Journal of Automotive Technology
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• v.8 no.2
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• pp.193-201
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• 2007

The present paper deals with the application of the explicit finite element code, PAM-CRASH, to simulate the crash behavior of steel thin-walled tubes with various cross-sections subjected to axial loading. An isotropic elastic, linear strain-hardening material model was used in the finite element analysis and the strain-rate sensitivity of mild steel was modeled by using the Cowper-Symonds constitutive equation with modified coefficients. The modified coefficients were applied in numerical collapse simulations of 11 types of thin-walled polygon tubes: 7 convex polygon tubes and 4 concave polygon tubes. The results show that the thin hexagonal tube and the thick octagonal tube showed relatively good performance within the convex polygon tubes. The crush strengths of the hexagonal and octagonal tubes increased by about 20% and 25% from the crush strength of the square tube, respectively. Among the concave tubes, the I-type tube showed the best performance. Its crush strength was about 50% higher than the crush strength of the square tube.

• Journal of Ocean Engineering and Technology
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• v.29 no.3
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• pp.241-248
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• 2015

A subsea pipeline for oil/gas transportation or gas injection is subjected to extreme variations in internal pressure and temperature, which can involve a strain rate effect on the pipeline material. This paper describes the flow stress characteristics of a pipeline material called API 5L X52N PSL2, using and experimental approach. High-speed tensile tests were carried out for two metal samples taken from the base and weld parts. The target temperature was 100℃, but two other temperature levels of –20℃and 0℃ were taken into account. Three strain rates were also considered for each temperature level: quasi static, 1/s, and 10/s. Flow stress data were proposed for each temperature level according to these strain rates. The dynamic hardening behaviors of the base and weld metals appeared to be nonlinear on the log-scale strain rate axis. A very high material constant value was required for the Cowper-Symonds constitutive equation to support the experimental results.