On the application of Normalization method to infer J-R curves of semicrystalline ductile polymers,

FASCE, LAURA; RUEDA, FEDERICO; FRONTINI, PATRICIA

Congreso; SAM/CONAMET; 2011

The determination of a polymer resistance curve, J–R, is generally performed through the so-called Multiple-specimen technique [1,2]. In this procedure, several identical specimens are loaded to obtain different amounts of crack growth, thus involving a large number of tests and large quantity of test material. It is also hard to apply in situations such as under high-loading rate conditions, elevated temperatures and/or aggressive environments where it is difficult to stop the test to measure crack extension. Consequently, alternative single specimen techniques like the Normalization method appear attractive. They are based on the validity of Load Separation principle, which assumes that the load can be represented as a multiplication of two separate functions: a crack geometry function and a material deformation function. Normalization method utilizes the Material Key Curve, calibrated using one individual normalized load-displacement record, to infer the instantaneous crack length [2]. In this work, the Load Separation Principle and the deformation function were expressed in terms of total displacement without distinguishing between elastic and plastic displacement components. Hence, calculations were made using the J- Integral formula based on total energy. In contrast to ASTM method [3], this leads to a non-iterative procedure for crack extension estimation. The performance of proposed method was evaluated and compared with the standard Multiple-specimen technique for three semicrystalline ductile polymers. Several features of the approach like suitability of functional forms, influence of blunting assumption and method limitations were analyzed. The polymers assayed were ultrahigh molecular weight polyethylene (UHMWPE), rubber- modified nylon (RT-Nylon) and propylene copolymer (PPc). Proportional sharp and blunt single edge notched specimens were used in the fracture experiments. Mechanical characterization was carried out using an Instron 4467 testing machine at room temperature. Due to their inherent ductility, dry RT-Nylon, PPc and UHMWPE were respectively bended at a crosshead speed of 2, 5 and 50mm/min. In order to generate suitable load-displacement records for the application of Normalization method sharp specimens were bended up to a certain displacement level allowing the crack to grow to a length of about 10% of the initial remaining ligament. After unloading the actual initial and final crack lengths, a0 and af, were physically determined. The measured force and displacement data were transformed into normalized force PNi and normalized displacement vi, using the blunting crack length (J=k σyΔab) and the measured final crack length. All useful data were fitted to the Four Parameter Analytical Function and the J–R curve was constructed. were used to verify Load Separation principle validity. Blunt notched specimens were loaded up to sufficiently large displacement levels or up to the instability point in which the assumption of stationary behavior was violated. Additionally, a set of 10 to 15 identical sharp notched specimens were loaded up to different displacement levels allowing the crack to reach different crack growth lengths to construct benchmark Multiple-specimen J-R curves. Load line displacement records of blunt notched specimens differing in their initial crack length were used to evaluate the separation parameter, Sij. Load Separation Principle assumption was verified and the η factor was practically equal to 2 for the three studied polymers, as expected. Multi-specimen J-R curves exhibited the typical scatter. JIQ data did not meet plane strain requirements; hence the developed J-R curves may be not strictly geometry independent. Fracture experiments on UHMWPE reconfirm that a value of k equal to 4 should be used in the Blunting line equation [4] while for PPc and RT-Nylon, theoretical blunting line (k=2) seem to describe pretty well the blunting behavior. PPc shows an “almost flat” J-R curve instead of the typical rising resistance curve. The reproducibility of the J-R curves obtained by the Normalization method was verified by fitting two separate specimens having essentially different crack extensions. Reliable J-R curves were obtained with the Normalization procedure for all of the materials studied but for PPc. For the latter, different experiments led to different J-R curves. A flat J-R curve could not be predicted using the Normalization methodology. The reason of the failure may be simply the definition of the Material Key curve. As it relates univocally load, displacement and crack length, in a flat R curve a low degree of correlation between J values and crack growth actually exists. To evaluate the suitability of Material deformation function, additional R-curves were developed using the power law function. According to metals experience and the present results it appears that the Four Parameter Analytical Function can accurately capture the behavior of most of ductile materials and seems to be more versatile than power law and LMN functions for polymers [5]. Regarding the influence of the adopted k value in the Normalization method prediction capability, we found that its influence is practically negligible, allowing the use of the theoretical value of 2 for predictive proposes. In addition, J-R curves were developed following the standard iterative procedure using the Four parameter analytical function based on plastic displacement as the Key Curve. J-R curves practically superimposed the ones developed using the Four Parameter Analytical function based on total displacement without the need of iteration. The results demonstrate the ease and the accurate of the Normalization method based on total displacement for raising J–R curve determination of ductile semicrystalline polymers.