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, J_I,lim, and a crack growth parameter, m_s) 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 J_I,lim and m_s were obtained. The observed effect of the specimen size on the aforementioned fracture parameters is presented and discussed.     

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 measurement of the fracture resistance of polyacrylamide hydrogels by wire cutting tests

The applicability of wire cutting in determining the fracture resistance, G_c, of polyacrylamide (PAAm) hydrogels, with different polymer contents and mechanical stiffness, was investigated. The various gels were synthesized both in the form of cylindrical and bar-shaped samples. Following the experimental scheme proposed in literature for wire cutting, each hydrogel, in the form of cylindrical specimen, was subjected to wire cutting with wires of different diameters. For each hydrogel, G_c was also separately measured by more conventional fracture tests on notched specimens prepared from the bar-shaped samples.The results demonstrated that, although G_c of the PAAm hydrogels here examined could not be evaluated by the direct application of the simple scheme proposed in literature, wire cutting is a promising approach for the measurement of the fracture resistance of chemical gels with relatively high stiffness, also in consideration of its proven experimental simplicity.     

A probabilistic theory on the time to fracture of amorphous crosslinked polymers

The energy probability theory of fracture proposed by Valanis has been extended to apply to the global fracture of a large material region and has been generalized to take into account the probabilistic distribution among bonds of the free energy of the region. In contrast to the theory of fracture initiation of the first author, it is assumed, in the present paper, that global fracture is brought about by the fracture of a critical number N_cr of primary bonds. Whereas this condition alleviates some of the problems encountered in the application of the theory to fracture initiation and propagation—such as determination of the local energy field at the root of a developed crack—it introduces the difficulty that N_cr may, in general, depend on the geometry of the specimen and the directionality of the stress field, though it was found to be relatively insensitive to the rate of deformation, as corroborated in this paper. The theory is used in this work to predict the time of global fracture, under conditions of constant load, constant strain, and constant strain rate.     

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.     

Failure analysis of plain woven glass/epoxy laminates: Comparison of off-axis and biaxial tension loadings

An experimental study was focused on investigation of the failure properties of plain woven glass/epoxy composites under off-axis and biaxial tension loading conditions. Four fibre orientations (0°, 15°, 30° and 45° with respect to the load direction) were considered for off-axis tests and two biaxial load ratios for biaxial tests to study failure characteristics and mechanism. Four classical polynomial failure criteria - Tsai-Hill, Hoffman, Tsai-Wu and Yeh-Stratton - were analysed comparatively to predict off-axis and biaxial failure strength of the composites. For failure prediction of the plain woven composites under multiaxial tension loads, the Tsai-Wu criterion was modified by introducing an interaction coefficient F₁₂ obtained from 45° off-axis or biaxial tension tests and the Yeh-Stratton criterion was modified with the interaction coefficient B₁₂ = 0 or obtained from the biaxial tension test. The former criterion was found to have higher accuracy. Finally, according to macroscopic and microscopic studies, the failed specimens showed mostly distinct failure with a specific fracture orientation, mainly exhibiting fibre or fabric tensile fracture mode and a combination of matrix cracking and delamination, both in off-axis and cruciform samples.     

Essential work of fracture,crack tip opening displacement,and J-integral relationship for a ductile polymer film

A unique set of double-edge notched tension specimens of a Polyethylene Terephthalate Glycol-modified film was tested in mode I, plane stress. The load was registered on a universal testing machine. The displacements, ligament lengths, and video frames were recorded by a Digital Image Correlation system. With these registered data, the essential work of fracture, J-integral, and crack tip opening displacement (CTOD) fracture concepts have been applied. The onset of crack initiation was through a complete yielded ligament. The analysis showed that the intrinsic specific work of fracture, w_e, is the specific energy just up to crack initiation, which is an initiation value. w_e has both a coincident value and the same conceptual meaning as J_o, the J-integral at the onset of crack initiation. The relationship between J_o and CTOD is also determined. The influence on the notch quality when the specimens were sharpened by two different procedures, femtosecond laser ablation and razor blade sliding, was analysed in detail.     

The fracture testing of ductile polymer films: Effect of the specimen notching

The fracture of a ductile polymer film, a heterophase ethylene-propylene block copolymer, has been studied, combining a range of characterisation methods in an attempt to provide a better understanding of the intricate details that play an important role in the repeatability and reproducibility of the essential work of fracture test. The experimental factors that have a strong influence on the resulting parameters are clearly explained, with particular attention to the effect of the quality of the notches, the non-collinearity of the two edge notches in double edge notched tension specimens, and the lack of alignment of the specimen with the load axis once it is mounted on the load train. Furthermore, the influence of these experimental factors on the registered stress-displacement curves is also studied, and a criterion and the method for separating non-valid specimens are established.     

On the experimental measurement of fracture toughness in SENT rubber specimens

This work provides a direct comparison of several experimental approaches used in the literature to measure fracture toughness of rubber of rubber using single edge notched in tension (SENT) specimens, with the final aim to provide guidelines for an optimal testing procedure. Digital image correlation measurements were used to get new insights into the fracture process. SENT is experimentally advantageous because of the simple preparation from laboratory plates and the small amount of material required. The most common experimental approaches to measure fracture toughness of rubber rely on the energy release rate, measured by the tearing energy or the J-integral parameters. This work points out the importance of experimental conditions and test procedures: long specimens and short notches are preferred, identification of fracture initiation from the front view is necessary, strain energy density should not be evaluated from un-notched specimens at the critical stretch level, rather alternative strategies are shown in this work.     

Interlaminar fracture toughness of unidirectional DCB specimens: A novel theoretical approach

A novel theoretical approach is presented to calculate the mode I interlaminar fracture toughness (G_Ic) of double cantilever beam (DCB) specimens with low ratio of initial crack length-to-thickness (a₀/2h). This method is based on a sixth-order beam theory, namely Reddy-Bickford beam (RB), on Winkler elastic foundation (WEF) to account for both transverse shear deformation of the beam and local effects at the delamination front (root rotation). RB with only two generalized displacements w and ?; and three boundary conditions at ends and loading points of a shear deformable beam gives more accurate results than the fourth-order Timoshenko beam theory. The accuracy of the proposed method in prediction of initiation G_Ic values is evaluated together with other available models considering the experimental fracture toughness for moderately thick unidirectional E-glass/epoxy DCB specimens with small initial delamination lengths.     

Finite element modelling of mode I delamination specimens by means of implicit and explicit solvers

The simulation of delamination using the Finite Element Method (FEM) is a useful tool to analyse fracture mechanics. In this paper, simulations are performed by means of two different fracture mechanics models: Two Step Extension (TSEM) and Cohesive Zone (CZM) methods, using implicit and explicit solvers, respectively.TSEM is an efficient method to determine the energy release rate components G_Ic, G_IIc and G_IIIc using the experimental critical load (P_c) as input, while CZM is the most widely used method to predict crack propagation (P_c) using the critical energy release rate as input.The two methods were compared in terms of convergence performance and accuracy to represent the material behaviour and in order to investigate their validity to predict mode I interlaminar fracture failure in unidirectional AS4/8552 carbon fibre composite laminates.The influence of increasing the loading speed and using mass scaling was studied in order to decrease computing time in CZ models.Finally, numerical simulations were compared with experimental results performed by means of Double Cantilever Beam specimens (DCB).Results showed a good agreement between both FEM models and experimental results.     

The influence of physical aging on the creep rupture behavior of polystyrene

The effects of postannealing aging time on the brittle fracture behavior of polystyrene were studied. A combination of mechanical properties, including creep and creep rupture under constant load and the behavior under constant extension rate deformation were examined for polystyrene samples of different prior aging times (from 1h to 2 months). The specimens and fracture surfaces were examined by optical microscopy and SEM to observe any change in the fracture behavior. It was found that longer aging times caused not only a change in the time-dependent modulus of the material but also a significant decrease in the creep rupture life and a decrease in strain to failure. It was found that the reasons for this are that although aging delays craze formation, craze breakdown and ultimate failure are accelerated by aging. The importance of these findings are discussed, particularly in relation to failure criteria involving the use of critical strains. © 1993 John Wiley & Sons, Inc.     

Application of second derivative spectrophotometry for the determination of uranium in yellow cake

A derivative spectrophotometric method has been developed for the determination of uranium at mg level in presence of iron in 1M HNO₃ medium. Its application was extended to the determination of uranium is magnesium diuranate (Yellow Cake), an input material to the Uranium Conversion Plant. The second derivative absorbance at 408.2 nm was used for its quantification since at this wavelength the absorbance due to iron is negligibly small and that due to uranium is significant. The uranium content was found to be directly porportional to the amplitude at 408.2 nm. It was demonstrated that the impurities present in yellow cake do not interfere. The method is simple, fast, needs no prior separation and enables direct measurement of yellow cake samples which is an important requirement from the point of view of nuclear materials accounting.     

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

The 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.     

Evaluation of hybrid laser-cut and cast miniature fracture specimens

This paper presents a new hybrid laser-cutting method for producing fracture test specimens from thermosetting materials. The hybrid approach combines casting of a sheet of material with subsequent laser-cutting of the test specimens. The new approach was compared to the traditional casting method using a fracture toughness test. For this study, a compact version of the tapered double cantilever beam (cTDCB) was used as a specimen geometry for both manufacturing methods. The cTDCB specimen is crack length independent, and crack length investigations were performed to ensure the crack length independence of the cTDCB specimens. The specimens that were made by the hybrid laser-cut method were found to be comparable to the specimens obtained by the traditional casting method. Moreover, the laser-cut method provides a fast and accurate method to make a significant number of samples in a reasonable time. These tests show that the hybrid laser-cut method could be a good alternative to the traditional casting method.     

Fracture toughness of polymers in the ductile‐to‐brittle transition region: Statistical approach and lower bound determination

A method available in literature was adapted and proposed for treating scatter and nonlinearity effects in fracture toughness of polymers in the ductile‐to‐brittle transition regime. The materials used were polypropylene homopolymer (PPH) and a polypropylene‐elastomeric polyolefin blend (PPH/POes 20 wt %), at room temperature and at 20‐mm/min test rate. Under such conditions, the fracture toughness presents a large scatter and a mean value can not be used as a design parameter because it leads to toughness overestimation. Then, there is a need to find a threshold of toughness, as a safe characteristic value for design. The toughness was evaluated by using the J‐integral approach. Large sets of specimens, 53 samples per each material, were tested with the purpose to reveal a reliable tendency in fracture behavior. As the toughness was considered nonuniform throughout the material, a weakest link model was assumed, and then results were analyzed statistically by means of a three‐parameter Weibull model (3P‐W). The PPH responded well to this 3P‐W model, whereas some deviations from the original model were observed in the PPH/POes blend. However, lower‐bound toughness values could be determined for both materials by censoring nonvalid data (Δa > 0.1b₀). From an engineering point of view, the results are very encouraging, since this methodology allows to obtain a threshold of fracture toughness from a given population, that is suitable to characterize the material fracture toughness at a given temperature and strain rate. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 3674–3684, 2005     

Elastic–inelastic behavior of PET and nylon 66 monofilaments under lateral compression

Results of experiments on short lengths of nylon 66 and PET monofilament specimens, subjected to lateral compressive force between two parallel platens, are described. In the experimental procedure the change in the compressed diameter and the area of contact were determined as a function of the applied force. From these data elastic moduli in lateral compression were estimated. The load–deformation behavior beyond the elastic range exhibited a yield-like phenomenon. SEM examination of the deformed specimen suggest the possible modes of deformation in the post-yield behavior. It is inferred that the yield occurs due to concentration of deformation along the maximum shear planes. The deformed specimens also show specific forms of fracture initiation and growth.     

Fracture behaviour of β‐polypropylene as a function of processing conditions

The commercial grade of isotactic polypropylene (iPP) homopolymer (Mosten 58.412) was doped with different amount of β‐nucleant (NJ Star NU‐100). The fracture behavior of the β‐iPP was examined on injection‐ and compression moulded specimens under dynamic load. The fracture toughness K_Id and J_Id, respectively, were used to describe the fracture behavior. The influence of processing conditions (the mould temperature and injection velocity) and the distance from the gate were also taken into the consideration. Structural changes during processing were characterized by DSC analysis. It was found that: (i) the amount of 0.03% of β‐nucleant gives the highest toughness (ii) the toughness of the β‐iPP depends on the distance from the moulding gate and on the processing conditions (iii) the degree of crystallinity correlates with the fracture parameters.     

Durability study of flexible bonded joints: The effect of sustained loads in mode I fracture tests

Adhesives in bonded structures are exposed both to external loads and environmental conditions; durability studies are currently needed to assess their service lifetime. Conditioning strategies differ in considering external load conditions (such as stressed or not stressed) for the durability analysis of double cantilever beam (DCB) bonded joints. Different test procedures such as ASTM D3762 (wedge testing) or ISO-25217 (DCB testing) exist to characterise the evolution of the fracture strength and toughness found in bonded joints. These methods depend on crack-length measurements, however, and achieving an accurate visual determination may be difficult due to the large fracture process zones (FPZs) that develop in the adhesive layer, especially in flexible or degraded bonded joints. To compensate, crack-length-independent data-reduction methods such as the compliance-based beam method (CBBM) or the J-integral method can be used, but experimental research is lacking on the suitability of these methods in ageing tests. A lack of consensus also exists in testing methodologies to evaluate the durability of bonded joints, especially when examining flexible bonded joints. The present work evaluates the influence of damage on fracture toughness within flexible bonded joints exposed to service conditions. Wedge tests and DCB tests are conducted using DCB specimens bonded with a flexible structural adhesive, proving that the degradation of flexible bonded joints exposed to environmental conditions is significantly accelerated when external loads act on them. The findings show that crack length estimation is affected due to environmental effects and thus, that crack-length-dependent test methods are not applicable in ageing tests.     

The effects of annealing on fatigue crack propagation in polyethylene

Fatigue crack propagation tests on annealed and quenched medium-density polyethylene showed the annealed specimens to have much lower resistance to crack initiation and subsequent propagation. Although the same fracture mechanism, in which the brittle crack gradually becomes more ductile, prevailed in both cases, the voided and fibrillated crack tip root craze in the annealed material was much weaker that the nonfibrillated quenched root craze. Microstructural analyses indicate that the annealed material had separate crystallite populations, whereas the quenched material had a more homogeneous morphology. The highest melting fraction of the annealed material was composed of lamellae that were about 270 Å thick, and the quenched lamellae were estimated to be 160 Å thick. The reduced fatigue crack propagation resistance of the annealed material was suggested to be a result of a lower concentration of tie molecules and its reduced damping capability, compared to the quenched material. © 1995 John Wiley & Sons, Inc.