Issue 49

Y. Saadallah et alii, Frattura ed Integrità Strutturale, 49 (2019) 666-675; DOI: 10.3221/IGF-ESIS.49.60 670 The results obtained are described by the strain-strain curves of Fig. 2. It clearly shows a time-dependent rheological behavior. The strain rate plays remarkably influence on the stress-strain relationship both in the viscoelastic domain and in the viscoplastic domain. In terms of quality, the shape of the curves is insensitive to the speed of strain. However, quantitatively, the difference between the curves as a function of the rate of strain is clearly distinguished. There is an increase in the resistance of the material with the increase in the rate of strain. I DENTIFICATION OF RHEOLOGICAL PARAMETERS Genetic algorithms t is generally accepted that genetic algorithms [11] are particularly suited to multidimensional global search problems where the search space potentially contains multiple local minima [14]. Unlike other research methods, genetic algorithms do not require a thorough knowledge of the search space, such as the limits of probable solutions or the derivatives of functions. They begin with a set of potential solutions chosen at random; and evolve by iteratively applying a set of stochastic operators, known as selection, crossover, and mutation. No gradient information is needed. Only the objective function and the constraints are necessary to determine the solution of the problem. Thus, they have the possibility of facing problems with a complicated objective function, where its derivative is difficult to obtain, or even non-existent. As a result, these techniques are well placed to be applied in the present work. Identification of parameters The identification of the three viscoelastic (E, K, ve  ) and four viscoplastic ( e  , H, n, vp  ) parameters is done by setting up respectively objective functions ve Q and vp Q minimizing the difference between the experimental measurements and the values of the model. So the optimization problems are formulated as follows:       2 1 , , , , , , , , N i i ve ve c ex ex c ve i Q E K E K              (8)       2 1 , , , , , , , , , , N i i vp e vp c ex ex c e vp i Q H n H n                (9) Where N is the number of measurement points ; i ex σ and i c σ respectively represent the experimental stress and simulated by the model. The genetic algorithm optimization technique was applied in the Matlab environment to determine the viscoelastic and viscoplastic parameters of the model. The elastic limit corresponds to the stress at which the material begins to have a permanent strain. For metals, this limit is practically determined at the stress at which a 0.2% strain is attained. Moreover, according to the references [8, 33], polymers have an elastic limit corresponding to a strain of 1%, where the stress-strain curve becomes clearly nonlinear. R ESULTS AND DISCUSSION he proposed viscoelastic-viscoplastic rheological model was applied to simulate the behavior of the polyamide 6 material. The following sections present the experimental and simulation results obtained from a tensile test at several strain rates. Identified parameters Tabs. 1 and 2 represent respectively the viscoelastic and viscoplastic identified parameters. It can be seen that the modulus E is constant and independent of the strain rate, whereas the viscoelastic parameters K and ve  depend considerably on it. It should be noted that with the increase of the strain-rate, the parameter K increases while the ve  parameter decrease. I T