DETERMINATION OF THE CONSTITUTIVE AND FAILURE PARAMETERS OF PA12 BY A COMBINED STRATEGY OF INSTRUMENTED IMPACT TESTS AND GENETIC ALGORITHMS

FEDERICO RUEDA; CAMILA QUINTANA; PATRICIA FRONTINI

Congreso; SAM CONAMET 2022; 2022

Polymeric materials used as structural components have delivered significant benefits for both design andmanufacturing cost and speed. Among the engineering thermoplastics, polyamide (PA) is of particularinterest to the industrial sector. This is mainly due to its excellent mechanical properties, including hightensile strength, high flexibility, low creep and high impact strength. Polyamide is widely used formanufacturing load-bearing components, particularly by the automotive industry and for many other impactloading applications [1, 2]. When components are subjected to demanding in-service loading conditions—like those mentioned above, the characterization of the constitutive and failure behavior of the involvedmaterials is of paramount importance. The premise of material models application is to determine theoptimal model parameters of a material, i.e. those that best represent its actual behavior. Model robustnessis crucial in engineering problems to ensure a trustworthy and accurate calibration. This means that best thechoice would be a model capable to capture the material response under a given stress state, while ensuringrobustness and computational efficiency as much as possible. Along with the choice of material models, andintrinsically related to each other, are the definitions of the methodology and experimental program todetermine the model parameters. In this way, the inverse methods, among them the intelligent algorithms-based approaches, open the door to calibrate constitutive models with more complex and/or relevantexperimental tests. For such methods, there are two important aspects to highlight about the experiment orexperiments to be performed. On the one hand, the experimental data should offer enough information tocover the actual service conditions. On the other hand, the information should be available to be“extracted” during the optimization stage.Taking into account the above statements, this work presents an optimization strategy based on GA for thedetermination of constitutive and failure parameters of robust material models from a single instrumentedimpact test. The development of the scheme is presented for Polyamide PA12 given the technologicalimportance of this material. The isotropic elasto-plasticity [3] and ductile damage initiation criterion [4]were implemented to capture the constitutive and failure behaviors of the polyamide, addressing objectivelytheir feasibility for that purpose. Impact tests under a SENB configuration were carried out to obtain theexperimental data for the calibration of the material models. We showed that this specimen allows apractical way of capturing the stable and unstable transitions in PA failure mode just by varying the notchdepth. The NSGA II Genetic Algorithm, implemented in Python, was selected to find together with abaqusfinite element modeling (FEM) simulation software, the optimal PA parameters, which must satisfy bothstable and unstable impact curves.In order to identify the best strategy in obtaining failure and constitutive information from experiments, threeoptimization schemes were addressed to infer the eight parameters of the model: (i) optimization function( f1) computed with a single unstable experimental curve -SENB specimen with a 1.36 mm notch depth-; (ii)optimization function ( f2 ) computed with a single stable experimental curve -SENB specimen with a3.18mm notch depth- and (iii) optimization function computed with both stable and unstable curvessimultaneously ( f1+f2 multi-objective). The accuracy of each set of parameters, i.e. each of which obtainedby a different optimization strategy, was evaluated by applying it in predictive FEA simulations, not only toreproduce the dependence of SENB impact behavior on notch depth beyond optimized objective(s) but alsoto predict a completely different stress state: a dynamic tensile test. Figure 1 shows that using singleobjectives has not produced accurate predictions of the tensile test. The reason for this is evident from thefigure: each single-objective is over-fitting the parameters to its specific conditions. The f1 objective predictsan exceedingly brittle behavior, while the f2 objective predicts lower toughness and no hardening. In otherwords, they are increasing the fitting accuracy during calibration at the expense of the model’s capability togeneralize to other conditions. On the other hand, the parameters from the multi-objective optimizationdelivered a prediction that is in much better agreement with the experiment, meaning that they are better atextrapolating the material (and failure) response to different stress states. This result suggests an acceptablecompromise between accuracy and experimental cost and computational effort if the prediction task is toestimate the general aspects of the material response (such as stiffness, onset of plasticity, overall toughnessand initiation of failure) in an engineering application. However, a more thorough validation coveringadditional stress states (such as multiaxial compression or pure-shear) is recommended to further establishthis approach.