INVESTIGADORES
RUEDA federico
congresos y reuniones científicas
Título:
On the application of Normalization method to infer J-R curves of semicrystalline ductile polymers,
Autor/es:
FASCE, LAURA; RUEDA, FEDERICO; FRONTINI, PATRICIA
Reunión:
Congreso; SAM/CONAMET; 2011
Resumen:
The determination of a polymer resistance curve, JR, 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 JR 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 JR curve determination of ductile semicrystalline polymers.