• Computers and Concrete
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• v.26 no.3
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• pp.227-237
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• 2020

Strain rate investigations are needed to calibrate strain-rate-dependent material models and numerical codes. An appropriate material model, which considers the rate effects, need to be used for proper numerical modeling. The plastic concrete cut-off wall is a special underground structure that acts as a barrier to stop or reduce the groundwater flow. These structures might be subjected to different dynamic loads, especially earthquake. Deformability of a structure subjected to dynamic loads is a principal issue which need to be undertaken during the design phase of these structures. The characterization of plastic concrete behavior under different strain rates is essential for proper designing of cut-off walls subjected to dynamic loads. The Cowper-Symonds model, as one of the most commonly applied material models, complies well with the behavior of a plastic concretes in low to moderate strain rates and will be useful in explicit dynamics simulations. This paper aims to present the results of an experimental study on mechanical responses of one of the most useful types of plastic concrete and Cowper-Symonds constant determination procedures in a wide range of strain rate from 0.0005 to 107 (1/s). For this purpose, SHPB, uniaxial, and triaxial compression tests were done on plastic concrete samples. Based on the results of quasi-static and dynamic tests, the dynamic increase factors (DIF) of this material in different strain rates and stress state conditions were determined for calibration of the Cowper - Symonds material models.

• 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.

• 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.

• International Journal of Naval Architecture and Ocean Engineering
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• v.10 no.1
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• pp.103-118
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• 2018

When collision accident between ships or between ship and offshore platform occurs, a common phenomenon that occurs in structures is the plastic deformation accompanied by a large strain such as fracture. In this study, for the rational design against accidental limit state, the plastic material constants of steel plate which is heated by line heating and steel plate formed by cold bending procedure have been defined through the numerical simulation for the high speed tension test. The usefulness of the material constants included in Cowper-Symonds model and Johnson-Cook model and the assumption that strain rate can be neglected when strain rate is less than the intermediate speed are verified through free drop test as well as comparing with numerical results in several references. This paper ends with describing the future study.

• Journal of Aerospace System Engineering
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• v.17 no.5
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• pp.19-27
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• 2023

In this study, we used finite element analysis to conduct a containment capability evaluation of a turbine case. When analyzing the impact behavior of structures subjected to impact loads, it is important to consider the strain rate, as it affects the increase in flow stress. Therefore, we applied three material models (Cowper-Symonds, Johnson-Cook, and Modified Johnson-Cook) for the impact analysis. To validate these material models, we performed an impact test on an aluminum 6061 plate. By comparing and analyzing the experimental and analytical results, we determined that the Modified Johnson-Cook material model exhibited the least error. As a result, we applied this material model to evaluate the containment capability of the turbine case. This evaluation involved determining the occurrence of penetration, as well as the stress and strain induced at the collision area due to the initial velocity of the blade.

• 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.

• Transactions of Materials Processing
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• v.33 no.2
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• pp.87-95
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• 2024

The current study aims to prove that high-speed forming has better formability than conventional low-speed forming. Experimentally, the quasi-static forming limit diagram was obtained by Nakajima test, and the dynamic forming limit diagram was measured by electrohydraulic forming. For the experiments, the LS-DYNA was used to create the optimal specimen for electrohydraulic forming. The strain measurement was performed using the ARGUS, and comparison of the forming limit diagrams confirmed that EHF showed better formability than quasi-static forming. Theoretically, the Marciniak-Kuczynski model was used to calculate the theoretical forming limit. Swift hardening function and Cowper Symonds model were applied to predict the forming limits in quasi-static and dynamic status numerically.

• 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.