Load Separation Criterion Research Articles

Quasistatic fracture analysis of multicomponent polypropylene blends containing brominated polystyrene

AbstractBrominated flame retardants can be added to many thermoplastics to meet flammability requirements for a range of applications, but can lead to undesirable brittleness. This reduction in toughness can be mitigated by encapsulating the rigid flame retardant with an elastomer. The present study explores the effectiveness of elastomer‐coated brominated polystyrene (BPS) in commercial polypropylene (PP) compositions for improved fracture resistance, where inorganic fillers such as antimony trioxide (ATO) and talc are usually included as synergists for flame‐retardancy. Quasi‐static fracture toughness was determined by J‐integral based on the load separation criterion and the crack growth resistance curve (J vs. Δa). It is found that well dispersed elastomer‐coated BPS can help disperse ATO and talc to exert enhanced toughening effect in PP. Possible fracture mechanisms behind these observed phenomena are discussed.

Determination of the Fracture Resistance of Ductile Polymers: The ESIS TC4 Recent Experience

Abstract Round-robin (RR) tests carried out under the direction of the Technical Committee 4, “Polymers, Polymer Composites and Adhesives,” of the European Structural Integrity Society (ESIS TC4) showed that the multispecimen methodology employed for the construction of the crack growth resistance curve (J vs crack extension, Δa) of polymers often does not provide reliable data because of the uncertainties associated with the measurement of Δa. With this in mind, the ESIS TC4 attention has been more recently focused on the analysis of a testing scheme based on the load separation criterion, which does not require the measurement of Δa. With the aim to employ this new approach into a standardized procedure, the degree of reproducibility of the results obtainable with the application of this testing scheme to ductile polymers has been assessed by means of multilaboratory RR testing exercises that started in 2011. An ESIS TC4 reference draft protocol was prepared and 10 laboratories participated in the RR activities. The present work describes the load separation criterion-based testing procedure recently examined by ESIS TC4 and gives a summary of the results obtained in the RR activities, which appear encouraging.

J-testing of polymers via the load separation criterion based ESIS TC4 procedure: Effect of the specimen size

The Technical Committee 4, “Polymers, Polymer Composites and Adhesives”, of the European Structural Integrity Society (ESIS TC4) developed a draft protocol based on the load separation criterion to determine two fracture parameters (an initiation parameter, JI,lim, and a crack growth parameter, ms) without the need to measure the crack growth (Δa). This is especially beneficial, since the measurement of Δa is prone to errors. The developed testing scheme displays promising results, as shown in a round-robin testing exercise. To further push this testing scheme, it is necessary to verify the specimen size scaling possibility. Hence, in this work, single edge notched in bending (SE(B)) specimens with different sizes, but geometrically similar, were manufactured. ESIS TC4 testing scheme was successfully applied to specimens with the different sizes, and data of JI,lim and ms were obtained. The observed effect of the specimen size on the aforementioned fracture parameters is presented and discussed.

Rubber Toughening of Polylactic Acid (PLA) with Poly(butylene adipate-co-terephthalate) (PBAT): Mechanical Properties, Fracture Mechanics and Analysis of Ductile-to-Brittle Behavior while Varying Temperature and Test Speed

The present work fits into the stream of study and analysis of biobased and/or biodegradable materials, considering the need to improve their properties from a technological point of view to allow their wider use in final products. In this paper a blend of an extrusion grade poly(lactic acid) (PLA) and a percentage of a particular type of high molecular weight poly(butylene adipate-co-terephathalate) (PBAT) was investigated. The blend was such that the PBAT resulted in a dispersed phase in the PLA matrix. Tensile properties, Charpy impact strength, energy absorbed by the sample during three-point bending tests, melt flow index, fracture behavior and morphology were determined to characterize PLA/PBAT blends with the aim of correlating the composition to processability and final properties. Furthermore, analytical models were applied to check if variations of the mechanical properties with an increase of the rubber content were in agreement with existing predictive theories. To evaluate the fracture behavior, starting from the Load Separation Criterion, “material key curves” of the materials, a support for a comparative study (macroscopic scale) of the plastic deformational mechanisms involved in the fracture process was achieved.The influence of the deformation rate and the temperature on the toughness of the PLA/PBAT was investigated. In particular, the ductile-to-brittle transition temperature, at a fixed test speed was estimated and a theoretical model, which is useful to predict the absorbed energy by varying the deformation rate, was proposed. This last model was validated by comparing the resulting analytical equation with the experimental data obtained through three-point bending and impact tests at different velocities.

Determination of J-R curves by load separation criterion in highly ductile TP-based composites under high temperature conditions

This work was aimed at determining the J-integral in 5-harness satin weave carbon fabrics reinforced PolyPhenylene Sulphide (PPS) structures at 120°C>Tg (glass transition temperature). The use of the linear elastic fracture mechanics (LEFM) framework to investigate the fracture behavior is not relevant in C/PPS laminates whose angle-ply stacking sequence is characterized by a highly ductile behavior. Thus the corresponding strain energy release rate (denoted J) in angle-ply laminates can be evaluated by means of the J-integral to account for the elastic-plastic fracture mechanics (EPFM). To this aim, a particular attention was paid to determine ηel- and ηpl-factors which are key points in the evaluation of J. ηel is classically evaluated using the compliance method, whereas, ηpl is determined by means of the load separation method applied to both elastic and total displacements. The comparison between initial crack length calculated using plastic and total displacement allows us to conclude that ηpl-factor based on total displacement leads to more accurate results. Using the Sij parameter, it is therefore possible to estimate transverse crack growths for different initial notch lengths. The predicted crack growth is in a good agreement with the experimental evolution obtained using Digital Image Correlation (DIC). Finally, the present work provides the J-R curves of highly ductile composite systems for different initial crack length over width ratios (a/w).

Application of the load separation criterion in J-testing of ductile polymers: A round-robin testing exercise

Round robin tests carried out under the direction of the Technical Committee 4 of the European Structural Integrity Society (ESIS TC4) have shown that, for determining the fracture resistance of ductile polymers at low loading rates, the multi-specimen methodology based on the construction of the material crack growth resistance curve often does not provide reliable data due to the uncertainties associated with the measurement of crack advancement (Δa). With the aim of strengthening this multi-specimen methodology, the ESIS TC4 attention has been recently focused on the analysis of a testing scheme based on the load separation criterion, which does not require the measurement of Δa.The present work gives the results of a multi-laboratory round-robin testing exercise carried out by ESIS TC4 in order to assess the degree of reproducibility of the fracture parameters obtainable with the application of this load separation criterion based testing scheme. Encouraging results have been obtained.

On the determination of the point of fracture initiation by the load separation criterion in J-testing of ductile polymers

The application of an experimental approach based on the load separation criterion for the determination of the point of fracture initiation in a fracture test on a ductile polymer was critically examined. To this aim, the fracture process outlined by the application of this method was related to that described by the visual analysis of the fracture surfaces obtained in fracture tests on nominally identical specimens, in which different levels of crack extension were produced. The material examined was an acrylonitrile-butadiene-styrene (ABS) resin, and the fracture tests were performed at low loading rate on single-edge notched in bending specimens.The results demonstrated that this load separation criterion based methodology is a promising approach for the determination of the point of fracture initiation, and for material fracture resistance, JIc, evaluation. The method also has experimental simplicity and a high degree of repeatability.

On the applicability of the load separation criterion in determining the fracture resistance (J Ic) of ductile polymers at low and high loading rates

In this work, the applicability of a procedure based on the load separation criterion in determining the fracture resistance (JIc) of a rubber modified polyamide 66 (PA66) was analyzed and discussed. In particular, the effects of the testing conditions, with particular reference to geometry and loading rate, on the applicability of the method were investigated. The tests were performed both at low (from 0.5 to 50 mm/min) and moderately high (0.6 m/s) loading rates, on single edge notched in bending specimens with different initial crack length to width ratios (a0/W), which ranged between 0.3 and 0.7. Among the various findings it is worthwhile to point out that this analysis revealed that the plastic displacement at the end of the blunting process (at fracture initiation) resulted geometry independent. A clear dependence of such a parameter on the loading rate was observed. Further, it was shown that load separation is maintained beyond the blunting phase, as observed in the experiments carried out at low rate.

High-rate J-testing of toughened polyamide 6/6: Applicability of the load separation criterion and the normalization method

This paper examines the applicability of the load separation criterion and the normalization method in determining J R curve of a toughened polyamide 6/6 at high loading rates (1 m/s). The analysis of procedure problems associated to this high experimental rate is performed. The results obtained using the normalization method are then compared with those measured via multi-specimen testing procedures proposed by ESIS (Technical Committee 4). The results show that, unlike low loading rate tests, the presence of the oscillations in the load vs displacement traces, due to the inertial effects produced during the impact, complicate considerably the elaboration of the data, with particular reference to the identification of the separable blunting region. The comparison of J Ic values obtained according to the different procedures examined indicates that the values of J Ic = J 0.2 (taken at 0.2 mm crack growth) are in good agreement, whereas consistent differences among the values of J Ic = J-blunting (taken at the blunting line) are observed.

J-R curve determination of magnesium hydroxide filled polypropylene using the normalization method

The normalization method is applied to different magnesium hydroxide filled polypropylenes. As the load separation principle is the basis of the method, its validity is checked using the load separation criterion developed by Sharobeam and Landes. Load separability is checked for all the materials when the condition of stationary crack length is fulfilled. During the determination of the deformation function using the normalization method, the large decrease of the load value of highly filled materials make it impossible to describe the load normalization variation with plastic displacement by a power law equation. Nevertheless, for the lower-filled materials, i.e. up to 40 wt% with copolymer PP and 20 wt% with homopolymer PP, the J-R curve can be determined and high concordance is found with the J-R curve obtained by multiple specimen method. The applicability of the normalization method is discussed in terms of the geometry of the plastic deformation zone. It is found that the materials that are not suitable for normalization method application are characterized by a very small plastic zone, due to the restriction of plastic flow caused by mineral filler.

Load separation principle in determination of J‐R curve for ductile polymers: Suitability of different material deformation functions used in the normalization method

AbstractThe load separation principle states that the load, P, can be represented as the multiplication of two independent functions: A crack geometry function, G(a), and a material deformation function, H(v). The principle constitutes the theoretical basis for the single‐specimen J‐integral experiment and the incremental calculation of J‐integral crack growth resistance (J‐R) curves. The normalization method is a new method, which assumes load separation and uses characteristic deformation properties of materials to relate load, displacement and crack length in a functional form. From the deformation material function or “material key curve”, J‐R curve can be developed from a single precracking experiment. This investigation deals with the applicability of the load separation criterion to evaluation of ductile fracture mechanics parameters in rubber‐modified polystyrene, polypropylene, rubber‐modified PMMA, ABS resin and high‐density polyethylene in the bending configuration. Different mathematical relationships for the deformation function (power law function, LMN function and combined power law straight line relationship) have been proposed and compared. The resulting J‐R curves are in good agreement with those obtained by the traditional multiple‐specimen technique. The results presented here imply that the use of a single load‐displacement method for evaluation of J‐integrals for ductile polymers is possible and hence also the normalization method can be used for evaluation of J‐R curves from a single‐test record.

On the applicability of the load separation criterion to acrylonitrile/butadiene/styrene terpolymer resins

Load separation constitutes the basis for the experimental evaluation of the J-integral by using the single-specimen technique. The objective of this present paper is to investigate the applicability of the load separation criterion for evaluating the ductile fracture mechanics parameters of acrylonitrile/butadiene/styrene (ABS) terpolymers. This criterion allows the load to be represented as the product of two separate functions, namely a material deformation function and a crack geometry function. Load separation implies a method for J-integral evaluation by using only a single load—displacement measurement. The original method for evaluating J used an energy-rate interpretation, which required several load-displacement measurements to be made for identical specimens with varying crack lengths. J methodology based on load separation introduces new parameters, i.e. η, η e1 and η p1, which greatly simplify the calculation of J and constitute the basis for the J−R multiple specimen technique. Recently, a method for both the experimental determination of the η-factors and the verification of load separation, which is based on separation constants, has been proposed for the testing of steel. This method allows the calibration of the η-factors in new test specimen geometries. This present paper attempts to evaluate experimentally whether the principle of load separation is valid when testing ABS polymers in a bending configuration in order to obtain a valid single J-testing method, and to calculate the η plastic factor experimentally by using this new simple method based on the load separation criterion in non-growing-crack measurements. In addition, a new approach based on the load separation principle which allows not only the calculation of J from a single specimen, but also the calculation of J–R curves from one test measurement has recently appeared. This approach is called the ‘normalization method’ and has already been applied to the J-testing of two rubber-toughened nylons and one ABS polymer. However, load separation has only demonstrated for different specimen geometries in steels. In addition, the load separation in ABS terpolymers has been verified in this present paper for growing cracks, by using an experimental procedure available in the literature.

The use of load separation criterion and normalization method in ductile fracture characterization of thermoplastic polymers

Load separation is the theoretical basis for the single-specimen J-integral experiment and the incremental calculation of J-integral crack growth resistance (J-R) curves. This criterion has been experimentally studied in nongrowing crack records in several materials, and more recently a new method to extend the applicability to growing crack experiments has been proposed in testing steel. This article examines the applicability of the load separation criterion for evaluating ductile fracture mechanics parameters in rubber-modified polystyrenes and thermally treated polypropylene in the bending configuration. This criterion allows the load to be represented as the multiplication of two independent functions: a material deformation function and a crack geometry function. Its validity is evaluated with both stationary and growing crack experiments. η-factor calculation for smooth and side-grooved specimens was also tried using the simple method of Sharobeam and Landes, in order to identify material dependency. This article also investigates the applicability of the normalization method, based on the load separation criterion for evaluating J-R curves on PP and PS. A simple approach which combines a blunt notched and a precracked specimen experiment is proposed to determine the J-R curve of the materials studied. The resulting J-R curves are compared with multiple specimen results available in the literature for these materials. A good agreement between the J-R curves obtained from this simple method and from the multiple specimen technique was found. © 1996 John Wiley & Sons, Inc.

A simple method for J-R curve determination in ABS polymers

The objective of this paper is to investigate the applicability of a very simple new method, based on load separation criterion, developed for evaluating J-R curves in steels, when applied to ABS polymers. This technique proposes the testing of a single precracked specimen and a single blunt notched specimen. The latter provides a method to detect the plastic displacement range during crack tip blunting in which the assumption of load separation criterion in the precracked specimen is valid, and also allows determination of J IC independently of J-R curve determination. The deformation material function is assumed to be a Ramberg-Osgood type law deformation function which leads to a very easy procedure to determine J-R curves. The J-R curve resulting from this new method is compared with one resulting from a traditional multiple specimen J-R curve determination method. Both results are in good agreement.

The load separation criterion and methodology in ductile fracture mechanics

The objective of this paper is to investigate the implications of the load separation criterion for evaluating ductile fracture mechanics parameters. This criterion allows the load to be represented as the multiplication of two separate functions; a material deformation function and a crack geometry function. Load separation implies a method for J-integral evaluating using only a single load-displacement record. The original method for evaluating J, proposed by Begley and Landes, used the energy rate interpretation of Rice which requires several load-displacement records for identical specimens with varying crack lengths. A method based on load separation introduced a new parameter η, ηel and ηpl which greatly simplified J calculation. This parameter which can be a function of geometrical factors is generally evaluated experimentally using the energy rate interpretation of J. In this paper the load separation criterion is used to imply a simple method for evaluating η experimentally. Using blunt notched specimen load versus load point displacement results from the literature, four different configurations with a wide range of stationary crack lengths are evaluated. Also included are several different materials varying from low work hardening to high work hardening. The data include thin and thick sections so that both plane stress and plane strain conditions are evaluated. A new method for η-estimation derived from the implication of the load separation is proposed. This method avoids most of the errors that accumulate in the classical methods of estimation. Both the separation method and the energy rate method are evaluated by comparing the techniques and the results. The results show some new trends in ηpl results for the different configurations evaluated in this paper.