Evaluation of impact fracture toughness of polymeric materials by means of the J‐integral approach

The most commonly accepted method of determining impact fracture toughness of polymeric materials that exhibit small scale yielding and negligible influence of dynamic effects is given by the ISO/DIS 17281 Standard, which states that for brittle behavior, basically a linear relationship exists between the fracture energy, U, and the energy calibration factor, ?. This relationship allows calculation of the critical strain energy release rate, G_IC from the slope of the U vs. BW? plot. This paper describes a simpler alternative methodology capable of evaluating impact fracture toughness using the J_c parameter. The J‐integral is evaluated at the instability load point, by calculating the fracture energy required to produce cleavage behavior of a pre‐cracked specimen. The methodology is limited to single edge notched three‐point‐bending specimens with a crack to depth ratio equal to 0.5. Tests were carried out on an instrumented falling weight impact testing machine on the following materials: PP (polypropylene), HDPE (high‐density polyethylene), MDPE (mid‐density polyethlene) and RT‐PMMA (rubber toughened polymethylmetacrylate). Results are in excellent agreement with the critical values determined by the ISO/DIS 17281 Standard.     

Effects of rubber content and temperature on dynamic fracture toughness of ABS materials

The effects of rubber content and temperature on dynamic fracture toughness of ABS materials have been investigated based on the J‐integral and crack opening displacement (COD, δ) concepts by an instrumented Charpy impact test. A multiple specimens R‐curve method and stop block technique are used. It is shown that the materials exhibit a different toughness behavior, depending on rubber content and temperature. The resistance against stable crack initiation (J_0.2 or δ_0.2) increases with increasing rubber content. However, J_0.2 first increased with increasing temperature until reaching the maximum value; after that, it decreases with further increasing the temperature. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 75: 1605–1614, 2000     

Glass fiber‐reinforced polyamide composites toughened with ABS and EPR‐g‐MA

A series of glass fiber‐reinforced rubber‐toughened nylon 6 composites was prepared. The mechanical properties and morphology of the composites toughened with ABS were investigated and compared with composites toughened with EPR‐g‐MA. A study of the mechanical properties showed that the balance of the impact strength and stiffness for both types of systems can be significantly improved by proper incorporation of glass fibers into toughened nylon 6. The differences between these two types of rubber‐toughened composites are significant at a high rubber content. However, the ductility of both composites toughened with rubber was significantly lower than that of blends without glass fiber. The relationships between rubber content, nylon 6 molecular weight, compatibilizer, processing, and mechanical properties are discussed. © 2001 John Wiley & Sons, Inc. J Appl Polym Sci 80: 484–497, 2001     

Effect of rubber particle size and rubber type on the mechanical properties of glass fiber reinforced, rubber-toughened nylon 6

The effects of rubber type and particle size on the mechanical properties of glass fiber reinforced blends of nylon 6 and EPR/EPR-gMA or SEBS/SEBS-g-MA were investigated; rubber particle size in the two systems could be controlled by varying the ratio of EPR to EPR-g-MA or SEBS to SEBS-g-MA. Unreinforced materials with the highest levels of toughness did not necessarily lead to the highest fracture energy when reinforced with 15 wt% glass fibers. Materials toughened with SEBS/SEBS-gMA, which are tougher in the absence of glass fibers had lower fracture energies when 15 wt% glass fibers are present. In general, smaller rubber particles led to higher fracture energies. Fracture analysis according to a modified essential work of fracture analysis reveals that SEBS/SEBS-g-MA have high values of the dissipative energy density, u_d, in the absence of glass fibers. When 15 wt% glass fibers are added, u_d is essentially zero for all the materials tested. The limiting specific fracture energy, u₀, on the other hand, was higher for both unreinforced and glass fiber reinforced EPR/EPR-g-MA toughened blends than for SEBS/SEBS-g-MA based materials. Transmission electron microscopy observations of fractured specimens indicate that glass fibers decrease the size of the damage zone of rubber toughened nylon 6. Shear yielding was seen in fractured specimens of reinforced nylon 6 blends containing either SEBS/SEBS-g-MA or EPR-g-MA, but the size of this shear yielded zone was larger for EPR/EPR-g-MA. In addition, EPR/EPR-g-MA based materials displayed craze-like deformations, while SEBS-g-MA materials did not exhibit this deformation process.     

Chemical toughening of epoxies. II. Mechanical,thermal, and microscopic studies of epoxies toughened with hydroxyl-terminated poly(butadiene-co-acrylonitrile)

Diglycidyl ether–bisphenol-A-based epoxies toughened with various levels (0–12%) of chemically reacted liquid rubber, hydroxyl-terminated poly(butadiene-co-acrylonitrile) (HTBN) were studied for some of the mechanical and thermal properties. Although the ultimate tensile strength showed a continuous decrease with increasing rubber content, the toughness as measured by the area under the stress-vs.-strain curve and flexural strength reach a maximum around an optimum rubber concentration of 3% before decreasing. Tensile modulus was found to increase for concentrations below 6%. The glass transition temperature T_g as measured by DTA showed no variation for the toughened formulations. The TGA showed no variations in the pattern of decomposition. The weight losses for the toughened epoxies at elevated temperatures compare well with that of the neat epoxy. Scanning electron microscopy revealed the presence of a dual phase morphology with the spherical rubber particles precipitating out in the cured resin with diameter varying between 0.33 and 6.3 μm. In contrast, a physically blended rubber–epoxy showed much less effect towards toughening with the precipitated rubber particles of much bigger diameter (0.6–21.3 μm).     

Effect of molecular weight between crosslinks on the fracture behavior of rubber‐toughened epoxy adhesives

The effect of molecular weight between crosslinks, M_c, on the fracture behavior of rubber‐toughened epoxy adhesives was investigated and compared with the behavior of the bulk resins. In the liquid rubber‐toughened bulk system, fracture energy increased with increasing M_c. However, in the liquid rubber‐toughened adhesive system, with increasing M_c, the locus of joint fracture had a transition from cohesive failure, break in the bond layer, to interfacial failure, rupture of the bond layer from the surface of the substrate. Specimens fractured by cohesive failure exhibited larger fracture energies than those by interfacial failure. The occurrence of transition from cohesive to interfacial failure seemed to be caused by the increase in the ductility of matrix, the mismatch of elastic constant, and the agglomeration of rubber particles at the metal/epoxy interface. When core‐shell rubber, which did not agglomerate at the interface, was used as a toughening agent, fracture energy increased with M_c. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 79: 38–48, 2001     

Comparison of the toughening effects of different elastomers on nylon 1010

The toughness of three different elastomer‐toughened nylon 1010 blends was investigated via standard notched Izod impact test and single edge notched three‐point bending test. The toughness of nylon 1010 blends varies much with different elastomer types and components. All three kinds of nylon/elastomer/maleated‐elastomer blends showed high impact strength (over 50 kJ m^?2) as long as at appropriate blending ratios. With increasing maleated elastomer content, brittle‐ductile transition was observed for all three kinds of elastomer‐toughened nylon 1010 blends. The number average dispersed particle size (d_n) of ethylene‐1‐octene copolymers or ethylene‐vinyl acetate copolymers toughened nylon 1010 blends significantly decreased from over 1 to 0.1 μm with increasing corresponding maleated elastomer content. Investigation on the fracture toughness showed the dissipative energy density gradually increased with decreasing d_n, while the limited specific fracture energy increased with increasing d_n when d_n was below 1 μm and then sharply decreased with further increasing d_n. The energy consumed in the outer plastic zone was the main part of the whole energy dissipated during the fracture process. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2011     

The fracture behavior of rubber-toughened,short-fiber composites of nylon 6,6

This study critiques the use of both rubber particles and short-glass fibers for the improvement of polymer fracture toughness (K_c). Although dry neat nylon is brittle with only a moderate K_c value (4.2 Mpa√m), additions of either second phase produce rising K_R-curves and associated high K_c values (8.1 Mpa√m for rubber-toughened nylon, and 10.0Mpa√m for 17 vol% Glass-fiber neat nylon). In the rubber -modified resin, the high K_c value is associated with extensive plastic blunting at the crack tip. In the fiber-reinforced neat resin, K_c is improved due to a combination of fiber-bridging and increased strength, the latter being associated with additional load carrying capacity of the fibers. When both rubber and fibers are added, however, no further increase in K_c is noted (K_c = 9.3 Mpa√m for 17 vol% glass-fiber rubber-modified nylon). The extent of ductile blunting in the rubber + fiber resin is not as great as in the rubber-only resin. Furthermore, the fracure strength of the rubber + fiber resin is not as high as the fiber-only resin. The net result is a balance of properties for the rubber-toughened composite.     

Mechanical and thermal properties of novel rubber‐toughened epoxy blend prepared by in situ pre‐crosslinking

A novel method is used for preparing liquid rubber‐toughened epoxy blend, in which an initiator was added to the liquid rubber–epoxy mixture to initiate crosslinking reaction of liquid rubber, and then curing agent was added to form the thermoset. Two epoxy blends with carboxyl‐terminated butadiene‐acrylonitrile copolymers were prepared using traditional and novel methods respectively. Results indicated that the novel rubber‐toughened epoxy blend exhibited much better mechanical properties than its traditional counterpart. The morphologies of the blends were explored by transmission electron microscopy (TEM), it was revealed that the use of the novel method formed a local interpenetrating network structure in the blend, which substantially improved the interfacial adhesion. The impact fracture surfaces of the two blends were observed by scanning electron microscopy (SEM) to explore the toughening mechanism, it was found that crack pinning was the major toughening mechanism for the novel rubber‐toughened epoxy blend. Dynamic mechanical analysis (DMA) was applied to determine the T_g values of the blends, which were found to be close. © 2014 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2014 , 131, 41110.     

High-Speed fracture mechanics by photography of polypropylene copolymers

The use of photography applied to stroboscopy in analyzing the processes inherent to the starting and propagation of cracks in materials is a technique which has proved to be of great interest, especially since it enables one to check and “directly” study the evolution of such phenomena. Using fracture mechanics criteria this technique has been applied to the study of the impact behavior of some polypropylene copolymers at different rubber contents obtained either by blending or by synthesis. This technique makes it possible to determine numerous parameters of fracture mechanics, including C.O.D. (crack opening displacement), C.O.A. (crack opening angle), JIc, the plastic work parameter, determined from the resistance curve R, tearing modulus, and crack propagation velocity. Furthermore, under high strain rate conditions, the value taken on by the coefficient “λ” relating the J-integral to C.O.D. (1, 2) were checked for those materials using the equation J = λ. σy · C.O.D., Hayes and Turner (3) and Boyle (4). From analysis of the materials it was possible to note that the synergetic effect of the EP (ethylenepropylene) rubber increased, especially when present at percentages of more than 10 percent. Annealing the materials, on the other hand, produced an increase in fracture toughness for those products having a low rubber content; however it did not have any effect on those with an elevated rubber content (26 percent).     

The plane-strain essential work of fracture as a measure of the fracture toughness of ductile polymers

We have extended the essential work of fracture technique to allow for the determination of the plane-strain essential work of fracture. The new technique is to measure the specific work of fracture as a function of ligament length in deeply double edge notched samples. This type of data is then experimentally corrected to remove the plastic work of fracture and leave only the essential work of fracture as a function of ligament length. By extrapolating the essential work of fracture to zero-ligament length, we claim to be measuring the plane-strain essential work of fracture. This new technique was applied to two rubber toughened nylons and to a series of polyethylenes. The plane-strain essential work of fracture was found to be independent of thickness. Where comparison can be made to J-integral testing, the plane-strain essential work of fracture was similar to the critical J-integral, J_Ic.     

Impact thermoplastics: Combined role of rubbery phase volume and particle size on toughening efficiency

A relationship has been found for OSA (olefin-acrylonitrile-styrene) polymers between normalized Izod impact strength (ΔI/N) or yield stress (Δσy/N) with mean particle radius. These normalized functions (which analytically include radius and rubbery phase volume) are representative of the toughening effect of a single particle with respect to the styrene-acrylonitrile (SAN) rigid matrix. ΔI/N and Δσy/N increase exponentially as a function of the radius. This approach, for Izod, was also applied to HIPS and toughened nylon reported in the literature and similar results were obtained. In the case of nylon, however, the ΔI/N values are split in two different curves related to the tough-brittle transition described in that literature. Referring to OSA, three samples (with the largest radii more than 0.22 μm) fail in a brittle manner and do not fit the curve of ΔI/N: they fit, however, that of Δσy/N. Further work must be done in order to investigate a decisive role either of interfacial adhesion (eventual lack for these three materials) or of tough-brittle transition mentioned before for shear-yielding deforming materials. In fact, OSA has behavior intermediate between that of nylon and HIPS which deforms by crazing.     

Graphene/nanorubber reinforced electrically conductive epoxy composites with enhanced toughness

Graphene platelets (electrically conductive 2D filler) and rubber nanoparticles (0D soft filler) can work together to develop electrically conductive and toughened epoxy composite adhesives. In this study, complementing effect between graphene platelets (GnPs) and rubber nanoparticles (RnPs) within an epoxy matrix is reported. In the 3-phase composite adhesive, the 2D graphene platelets form global conductive network and rubber nanoparticles provide a viscoelastic phase inside the epoxy, both complementing each other to develop electrically conductive and toughened epoxy composite adhesives. Fracture toughness (K_1c) and critical strain energy release rate (G_1c) of the epoxy were augmented by 422% and 872%, respectively by adding 1 wt% RnPs and it recorded electrical percolation threshold at 0.78 vol% GnP. Also, the Young's modulus and strength of epoxy/1 wt% RnP composite were promoted from 1.57 to 2.32 GPa when 1 wt% GnP is added. Scanning electron microscopy analysis was conducted to investigate the toughening mechanism of epoxy/RnP/GnP and epoxy/GnP composites. Lap shear strength tests on epoxy composite adhesives confirm the reinforcement effect of GnPs and toughness effect of RnPs.     

Comparison of fracture behavior of nylon 6 versus an amorphous polyamide toughened with maleated poly(ethylene-1-octene) elastomers

The fracture behavior of an amorphous polyamide (Zytel 330 from DuPont), a-PA, and nylon 6 toughened by maleated poly(ethylene-1-octene) elastomers are reported. The deformation mechanisms during fracture were verified by examining an arrested crack tip and the surrounding regions using transmission electron microscopy analysis. a-PA blends show higher levels of impact strength and lower ductile-brittle transition temperatures than nylon 6 blends. Fracture toughness, characterized by both linear elastic fracture mechanics techniques in terms of the critical strain energy release rate, G_IC, and the essential work of fracture methodology, i.e. the limiting specific fracture energy, u_o, and the dissipative energy density, u_d, using thick (6.35 mm) samples with sharp notches, depends on ligament length, rubber content, rubber particle size and test temperature. In general, a-PA blends show larger values of u_d than do nylon 6 blends while the opposite is seen for u_o. The amorphous polyamide shows a similar critical upper limit on rubber particle size, or interparticle distance, for toughening as the semi-crystalline nylon 6; thus, it is clear that the crystal morphology around the rubber particles must not be the dominant cause of this critical size scale. The deformation mechanisms involved include cavitation of rubber particles followed by some crazing and then massive shear yielding of the matrix.     

Fracture properties of nanoclay‐filled polypropylene

Maleic anhydride‐modified polypropylene was compounded with commercially available surface‐modified montmorillonite in a twin‐screw extruder. Recompounding ensured the removal of visible tactoids from the extrudate but TEM and XRD techniques showed nonuniform dispersion of clay platelets. In this study, we investigated the mechanical and fracture properties of nanoclay‐filled polypropylene. Emphasis was placed on the fracture characterization of the clay‐filled polypropylene. Tensile strength and stiffness increased steadily with an increase in the clay loading. The toughness of compounded materials was characterized using rigorous fracture mechanics. J‐integral fracture resistance decreased with an increase in the clay content. The resistance against stable crack growth was compared using the slopes derived from the J–R curve and the tearing modulus concept. A significant amount of crack growth resistance was evident in the nanoclay‐filled polypropylene as opposed to other brittle nanocomposites such as the nylon–clay systems. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 88: 3298–3305, 2003     

The essential fracture work concept for toughness measurement of ductile polymers

The essential work of fracture method is explored. The method was used to determine the fracture toughness of a series of toughened polymer blends and the crack resistance of a thin ductile polymer film, which could not be tested using the J-integral method. A comparison between J-integral and the specific essential work of fracture was carried out to test the equivalence of the two methods. The effects of geometry on the essential work of fracture and the plane-stress/plane-strain transition were studied. It has been shown that the specific essential work of fracture is a material constant, independent of sample geometry, and equivalent to the critical J-integral. The plane-stress/plane-strain transition is found to depend on the nature of the material tested. The sample thickness requirement for valid plane-strain specific essential work of fracture is discussed, and it is proposed that the size requirement for the plane-strain specific essential work of fracture may be less rigorous than that for plane-strain J_IC measurement.     

The Charpy impact fracture behaviour in ABS materials

The effects of rubber content and temperature on impact fracture behaviour of ABS materials with rubber particle diameter of 110 nm were studied by means of an instrumented Charpy impact tester which can record a load-deflection curve at impact fracture. From the load-deflection curves, some important parameters, such as the maximum impact load, the maximum deflection, the J-integral corresponding to the total impact absorbed energy, dynamic yield stress and Young's modulus etc. were obtained and their rubber content and temperature dependencies were investigated. Stable crack extension and plastic zone size are studied as a function of rubber content and temperature by the use of optical microscope. The fractured surfaces were observed using a scanning electron microscope to clarify the fracture mechanism under impact condition.     

The freezing-in of non-equilibrium values of the limiting compliances as a mechanism of physical ageing

The theory of a new method for measuring the temperature dependence of the limiting compliances, J_R and J_U, is described. The method is based on the observation of secondary creep; this is a small effect generated in a stressed specimen by a T-jump. In the experiment, the specimen is maintained isothermally under a constant stress until the primary creep rate is negligible. A T-jump of several degrees, positive or negative, is then imposed and this generates the secondary creep. If J_R and J_U are independent of temperature there is no secondary creep. The secondary creep has the same time dependence as primary creep. A comparison of the magnitudes of secondary and primary creep — at equivalent reduced times — leads by means of the theory of thermoviscoelasticity to the determination of α and β, the temperature coefficients of (J_R-J_U) and J_U. For isotactic polypropylene in the α-region at 40°C both coefficients are positive: α = 0.7 × 10^?2 and β = 0.1 × 10^?2°C^?1. It is clear from the positive sign for the coefficient of (J_R-J_U) that the α-relaxation is of the type in which stress increases the entropy. The magnitudes of the coefficients support the conclusion that the use of un-normalized time-temperature superposition to determine activation energy in polypropylene will be highly erroneous. The magnitude of the coefficient of (J_R-J_U) is sufficiently large to account partially for physical ageing in crystalline polymers. Quenching from T down to T₀ will freeze in a non-equilibrium value of (J_R-J_U), considerably in excess of the equilibrium value at T₀. Storage at T₀ permits the equilibrium value to be slowly attained, so that with increasing ageing time the polymer becomes stiffer and exhibits lower creep rates.     

New evidence derived from the discrimination of Henry and Langmuir modes parameters in glassy polymeric film revealed by the Freeze‐Purged‐Desorption method

The Freeze‐Purged‐Desorption (FPD) method was developed for the experimental measurement of gas permeability coefficients as a new technique using a desorption curve of gas immobilized in polymeric films. The FPD method was effectively used to evaluate four gas permeation parameters (C_D, C_H, D_D, and D_H) of glassy polymeric films (polycarbonate and polystyrene) by using CO_2. The modes of the CO₂ gas desorption response curve (D‐curve) obtained were sensitively characterized by the proportion of sorption in the Henry and Langmuir modes in the polymeric films accompanied by their own gas diffusivity. A graphical analysis of the D‐curve of CO₂ reasonably proposed a linear relation between the desorption rate and the sorption amount of CO_2, which was strongly influenced by the kind of sorption gas, film, temperature, and other factors. The desorption rate of sorbed CO₂ gas for the PC and PS films gave a characteristic straight line with an inflection point indicating a shift in the gas‐diffusion mechanism from the complex type of the Henry and the Langmuir modes to the Langmuir mode. The characteristic D‐curves obtained were graphically analyzed, and they clearly discriminated the Henry mode part and the Langmuir mode part. This discrimination process quantitatively and individually evaluated C_D, C_H, D_D, and D_H. By using the four parameters evaluated, a mathematical model to describe the D‐curve was proposed, and it consistently explained the experimental D‐curves. © 2004 Wiley Periodicals, Inc. J Appl Polym Sci 93: 934–941, 2004     

SEC–viscometer detector systems. I. Calibration and determination of mark–houwink constants

Five different types of calibration curve currently used in size exclusion chromatography-differential viscometer (SEC–DV) systems were identified and their use summarized. A simple method of deriving weighting factors for fitting local intrinsic viscosity calibration curves was shown to greatly improve the precision of calculated molecular weight distributions. The problem of reliably extrapolating the fitted curves to allow for differences in sensitivity among detectors has yet to be examined. With regard to Mark—Houwink constants, a method of fitting data from the SEC–DV system to obtain more statistically sound values was derived. For the data used here, the new method involves fitting a plot of logarithm of the local intrinsic viscosity of the sample vs. logarithm of the universal calibration curve parameter, J_i. Results for the data obtained appeared only slightly more precise than those for the traditional method. However, the new method promises improved reliability. © 1993 John Wiley & Sons, Inc.