An implicit consistent algorithm for the integration of thermoviscoplastic constitutive equations in adiabatic conditions and finite deformations

Zaera, R.; Fernández-Sáez, J.

doi:10.1016/j.ijsolstr.2005.03.070

Cited by 62 publications

(44 citation statements)

References 25 publications

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“…The consistency algorithm has also been validated for the Taylor test by comparing the numerical results obtained with ABAQUS (commercial version) and ABAQUS coupled with this algorithm (VUMAT) for a Johnson Cook hardening equation. The results yield a good agreement [39].…”

Section: Specimen Geometries and Simulation Modelsupporting

confidence: 52%

“…During the numerical simulations the constitutive relation has been coupled with an original thermoviscoplastic algorithm allowing to calculate the equivalent quantities. The details are reported in [39,40]. To demonstrate the efficiency of our thermoviscoplastic approach, the stress strain curves obtained through numerical simulation of tensile tests at two different strain rates were compared to that given by Eqs.…”

Section: Specimen Geometries and Simulation Modelmentioning

confidence: 99%

“…Having demonstrated the efficiency of the constitutive relation and consistent algorithm [39,40] a FE analysis of the dynamic tension test is reported next to complete some previous FE simulations such as dynamic ring expansion [41], crash-box test, Taylor test [39] and shear test [2].…”

Section: Specimen Geometries and Simulation Modelmentioning

confidence: 99%

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Analysis of inertia and scale effects on dynamic neck formation during tension of sheet steel

et al. 2005

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It is well known that a specimen for impact testing must be optimized in terms of its dimensions. The main reason is to reduce strain gradients due to the effects of elastic plastic wave propagation. On the other hand, when a split Hopkinson bar in tension is applied, the net displacement of the specimen ends is very limited, usually from 2.0 to 3.0 mm. Thus, to reach a maximum strain of 0.5 the specimen length must be reduced in dimensions from 4.0 to 6.0 mm. Consequently, small diameters or lateral dimensions and lengths must be applied to assure one dimensional deformation. Such small lengths substantially perturb the determination of real material behavior. So the main motivation of this study was to perform a systematic analysis, numerical and analytical, to find differences in the behavior of short and long specimens loaded in impact tension. The finite element code ABAQUS/Explicit has been used to simulate several spec imen lengths from 10 to 40 mm submitted to impact velocities ranging from 10 to 100 m/s.Keywords: Constitutive relation; Dynamic tension; Normalization; Plastic instability; Numerical simulations Thermoviscoplastic modelingTo study the dynamic processes of plastic deformation in sheet metals, a well defined constitutive relation has earlier been proposed. Several processes of fast deformation have been previously studied by applying that relation: perforation [1], double shear by direct impact [2], the Taylor test and fast tension test [3]. With the constitutive relation, Eq. (1), the effect of temperature and strain rate on the flow stress can be studied and analyzed. It is clear that the adiabatic increase of temperature has a substantial effect on the flow stress and it induces a decrease in the ultimate tensile stress. In order to describe precisely the behavior of materials at high strain rates and temperatures, the equivalent stress r needs to be taken as the sum of two components r l and r * which are, respectively, the internal and the effective stress. The first component is directly related to the strain hardening of the material and the second defines the contribution due to the thermal activation (a combination of temperature and strain rate). The constitutive relation can be written in terms of equivalent scalar quantities:where e p is the equivalent plastic strain, T is the absolute temperature, E 0 is the YoungÕs modulus at T 0 K and E(T) is the evolution of the modulus as a function of temperature. Eq. (1) is based to some extent on physical considerations [2]. The explicit expressions for both stress components are given below:where Bð _ e p ; T Þ and nð _ e p ; T Þ are the modulus of plasticity and the strain hardening exponent, respectively. These quantities, defined by Eqs. (3) and (5), respectively, take into account the experimental observations that the strain hardening itself depends on temperature and strain rate.

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Section: Specimen Geometries and Simulation Modelsupporting

confidence: 52%

Section: Specimen Geometries and Simulation Modelmentioning

confidence: 99%

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Analysis of inertia and scale effects on dynamic neck formation during tension of sheet steel

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“…The RK constitutive relation has been implemented into the code using the implicit consistent algorithm proposed by Zaera and Ferná ndez Sá ez [46].…”

Section: Finite Element Simulation Of the Impact Process In Order To mentioning

confidence: 99%

Temperature measurements on ES steel sheets subjected to perforation by hemispherical projectiles

Rodríguez-Martínez

Rusinek

Chévrier

et al. 2010

International Journal of Impact Engineering

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a b s t r a c tIn this paper is reported a study on the behaviour of ES mild steel sheets subjected to perforation by hemispherical projectiles. Experiments have been conducted using a pneumatic cannon within the range of impact velocities 5m=s V 0 60m=s. The experimental setup allowed evaluating initial velocity, failure mode and post mortem deflection of the plates. The tests have been recorded using high speed infrared camera. It made possible to obtain temperature contours of the specimen during impact. Thus, special attention is focussed on the thermal softening of the material which is responsible for instabilities and failure. Assuming adiabatic conditions of deformation, the increase of temperature may be related to the plastic deformation. The critical strain leading to target failure is evaluated coupling temperature measurements with numerical simulations and with analytical predictions obtained by means of the Rusinek Klepaczko constitutive relation [Rusinek, A., Klepaczko, J.R. Shear testing of sheet steel at wide range of strain rates and a constitutive relation with strain rate and temperature dependence of the flow stress. Int J Plasticity. 2001; 17, 87 115]. It has been estimated that the process of localization of plastic deformation which leads to target failure involves local values close to 3 p f z1 for the boundary value problem approached. Subsequently, this failure strain level has been applied to simulate the perforation process and the numerical results obtained show satisfactory agreement with the experiments in terms of ballistic limit, temperature increase and failure mode of the target.

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“…Numerical investigations in thermoviscoplasticity are frequently related to overstress models [18,19]. Recently, Zaera and Fernán-dez-Sáez [20] have extended the consistency model to analyse the thermoviscoplastic behaviour of metals. They have proposed a fully implicit scheme which is easily implemented and inherits the robustness and stability of return mapping algorithms.…”

Section: Introductionmentioning

confidence: 99%

Consistent integration of the constitutive equations of Gurson materials under adiabatic conditions

Vadillo

Zaera

Fernández-Sáez

2008

Computer Methods in Applied Mechanics and Engineering

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In this paper, a consistent integration procedure for the thermoviscoplastic version of the complete Gurson model is proposed. With adiabatic conditions considered and with the use of the backward Euler integration scheme, a numerical algorithm implicit in all vari ables as well as the corresponding algorithmic operator have been developed. The proposed algorithm was implemented in a finite ele ment code and its performance is demonstrated with the numerical simulation of different examples.

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An implicit consistent algorithm for the integration of thermoviscoplastic constitutive equations in adiabatic conditions and finite deformations

Cited by 62 publications

References 25 publications

Analysis of inertia and scale effects on dynamic neck formation during tension of sheet steel

Analysis of inertia and scale effects on dynamic neck formation during tension of sheet steel

Temperature measurements on ES steel sheets subjected to perforation by hemispherical projectiles

Consistent integration of the constitutive equations of Gurson materials under adiabatic conditions

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