Fracture mechanics parameters for polystyrene under high speed impact

A series of commercial polystyrenes was tested using an instrumented impact tester to determine the fracture toughness K_c and critical strain energy release rate G_c. Over the range of M_w, 201,000 to 336,000, K_c increased from 1.38 MN/m^3/2 to 1.76 MN/m^3/2and G_c from 0.92 kJ/m² to 1.60 kJ/m². A linear correlation for K_c and G_c was seen with melt index, and an inverse relationship was obtained against molecular weight. Examination of the fracture surfaces revealed the presence of crack growth bands corresponding to the crack tip plastic zone size. It is suggested that these bands are the consequence of variations in crack growth along crazes that form in the crack tip stress field. As the crack propagates, the stress is relaxed locally, decreasing the growth rate allowing a new bundle of crazes to nucleate along which the crack advances. The spacing of these bands corresponds to the craze length formed in the plastic zone, and the band spacing increases with molecular weight.     

The effects of stress cracking on the fracture toughness of polycarbonate

The growth of crazes from a sharp crack in extruded polycarbonate sheets immersed in ethanol was measured. Below a critical level of the stress intensity factor craze growth was controlled by solvent diffusion through the end of the notch and fracture was prevented by craze arrest. Above a critical level, growth was controlled by either end diffusion or a combination of end diffusion and diffusion through the faces of the extruded sheet, and in both cases the final result was brittle fracture. The effects of annealing and quenching was studied at various sheet thicknesses. In thin specimens annealing and/or quenching had a significant effect on crack growth rate, which was predictable in terms of the state of stress. As the specimen thickness increased, causing a transition from plane stress to plane strain conditions, the previous thermal history had a diminishing effect on craze growth rate. The effects of thermal history and thickness on the fracture toughness of polycarbonate was also investigated. It was found that thickness was the more important variable and that at a ½ in. thickness the effects of thermal history were statistically insignificant. The effect of ethanol exposure on fracture toughness was studied. It was found that exposure to solvent initially caused an increase in k_IC with time to a maximum value, followed by a substantial decrease with time which eventually led to brittle fracture. This behavior was explained as a competition between plasticization of the crack tip and coalescence of crazes to form microcracks.     

Temperature/rate dependence of yield and fracture behaviour of phenolphthalein poly(ether ketone)

The rate/temperature dependence of yield stress, tensile modulus and crack opening displacement of phenolphthalein poly(ether ketone) (PEK-C) has been investigated. The rate/temperature dependence of crack opening displacement and the correlation established between stress intensity factor, K_IC, yield stress, and type of crack growth suggest that the extent of crack tip blunting largely governs the relative toughness of PEK-C and induces transitions in the types of crack growth observed. A quantitative expression is then presented which successfully describes the fracture toughness values over a wide range of temperatures and rates.     

Deformation and fracture behaviour of a rubber-toughened epoxy: 2. Failure criteria

In part 1 the microstructure and fracture characteristics of a rubber-modified epoxy, and for comparison that of the unmodified epoxy, were examined in detail. Based on this analysis a qualitative mechanism involving cavitation, shear yielding and plastic flow was proposed. As an extension of this work, the present paper considers the yield behaviour of the epoxy material and uses the data determined, together with the previously reported fracture results, to calculate values of the crack opening displacement. The rate/temperature dependence of the crack opening displacement and the correlations established between stress intensity factor, K_Ic, yield stress and type of crack growth suggest that the extent of crack tip blunting largely governs the relative toughness of the epoxy materials and induces transitions in the types of crack growth observed. A quantitative expression is then presented which successfully describes the fracture toughness values over a wide range of temperatures and rates. The two parameters in this expression are shown to be material constants and therefore provide a unique failure criterion. They can be viewed simply as curve-fitting parameters but they may also have some significance in terms of a critical stress that must act over a critical distance ahead of the crack tip to produce crack growth.     

Mechanical and Fracture Behaviour Evaluation of Commercial Acrylic Bone Cements

The deformation and fracture behaviour of some commercial acrylic bone cements have been investigated. Cements were characterized by gel permeation chromatography, dynamic mechanical analysis and scanning electron microscopy. The influence of liquid to powder ratio, curing temperature, strain rate and non-reacted monomer was analysed for one radiolucent cement. Results showed that the β transition activation process influences both deformation and fracture behaviour. Fracture surface stress whiteness revealed the presence of crazes as the main plastic deformation mechanism. Non-reacted monomer acted as a plasticizer leading to materials with lower yield strength, σ_y, that induces crack tip blunting and improves toughness. It appears that the presence of radiopacifier fillers also improves fracture toughness by promoting interactions between the crack and the second phase dispersion. © 1997 SCI.     

Multiple crazing at crack tips in PVC under plane strain conditions

The nature of the yield zone at the crack tip of poly(vinyl chloride) (PVC) pipe materials has been investigated. Microscopy studies employing a plasma etching technique reveal the presence of multiple crazes ahead of the crack tip in the interior of specimens of pure PVC, CaCO₃ filled PVC, and PVC pipe compound. The craze zone and the fracture toughness of blade-notched specimens are compared with those of fatigue pre-cracked specimens. Both types of specimens have similar fracture toughness values and form multiple crazes upon loading, suggesting that multiple crazing Is an intrinsic property of the material. The kinetics of craze initiation and the development of the multiple craze zones have also been explored.     

Temperature and loading rate effects in the mode II interlaminar fracture behavior of carbon fiber reinforced PEEK

The combined effect of varying loading rate and test temperature on the mode II interlaminar fracture properties of AS4/carbon fiber reinforced PEEK has been investigated. End notch flexure tests have shown that this thermoplastic‐based composite system offers a very high value of interlaminar fracture toughness at room temperature. Increasing the test temperature leads to a reduction in the mode II interlaminar fracture toughness of the composite, with the value at 150°C being approximately one half of the room temperature value. In contrast, increasing the crosshead displacement rate has been shown to increase the value of G_IIc by up to 25%. A more detailed understanding of the effect of varying temperature and loading rate on the failure mechanisms occurring at the crack tip of these interlaminar fracture specimens has been achieved using the double end notch flexure (DENF) geometry. Here, extensive plastic flow within the crack tip region was observed in all specimens. It is believed that the rate sensitivity of G_IIc reflects the rate‐dependent characteristics of the thermoplastic resin.     

Plane strain fracture toughness testing of high density polyethylene

The concepts of linear elastic fracture mechanics (LEFM) are applied to three grades of high density polyethylene in an attempt to determine their fracture behavior in terms of a linear elastic fracture toughness, K_c. The effect of specimen size (thickness and width), crack length and the mode of loading on K_c has been investigated in order to determine the plane strain fracture toughness, K_Ic, of these materials. The effect of temperature (between +23 and ?180°C) on their fracture behavior has also been investigated and compared in terms of their plane strain fracture toughness values.     

Fatigue fracture behaviour of PEEK: 2. Effects of thickness and temperature

Experimental results on the effects of specimen thickness and environmental temperatures on fatigue fracture behaviour of poly(ether ether ketone) (PEEK) are reported. Low cycle fatigue experiments are conducted on injection moulded single-edge notched specimens of 1.57, 2.70 and 5.42 mm in thickness at ambient temperatures, and on specimens 2.70 mm thick at environmental temperatures of 39, 50, 63, 75 and 100°C. In all the thickness experiments and in the experiments with temperatures of 39 and 50°C, the crack tip profile is initially round. At long crack lengths the crack tip profile changes to a triangular shape. When the test temperature is 63, 75 and 100°C, the crack tip remains round throughout the fracture process. The crack tip angle is primarily dependent upon the test temperature. Examinations of the fracture surfaces and transverse sections indicate that in the thickest specimen, relatively rough fracture surfaces are observed and a few discontinuities (crazes or cracks) underneath the main crack path. Thus, crack propagates in a ‘brittle’ manner. In all other experiments both ‘brittle’ and ‘ductile’ modes of fracture are observed. The point of transition from ‘brittle’ to ‘ductile’ fracture is dependent upon the specimen thickness and test temperature. Fatigue striations are seen throughout the fracture surfaces. Correlation of the striations and the number of cycles indicates a one-cycle crack growth mode. Hysteretic losses during fatigue crack growth are negligible until a few cycles prior to unstable fracture. Crack opening displacements are independent of the specimen thickness and increase with rise in temperature. When crack growth rates are correlated with the elastic energy release rate, they are independent of specimen thickness and increase with increase in temperature.     

Effects of processing conditions and aging on the fracture toughness of rigid PVC pipe materials

Results for given for the fracture toughness of rigid polyvinylchloride (PVC) pipe materials over a range of test temperatures as a function of extrusion temperature. The fracture toughness is shown to be reduced as the extrusion temperature is reduced below standard conditions. The transition temperature for valid fracture toughness tests is increased by reducing the extrusion temperature. The results of a fractographic analysis are also presented, including quantitative data for the extent of drawn, fibrillated material at the crack tip. Although annealing above T_g reduces the fracture toughness relative to as-received pipes, no significant effect of controlled physical aging could be identified.     

The effect of moisture and loading rate on the interfacial fracture properties of sandwich structures

The skin‐core interfacial fracture properties of a number of dry and moistureconditioned sandwich structures have been investigated over a range of crosshead displacement rate using the three point bend sandwich (TPBS) structure. It has been shown that the interfacial fracture toughness, G_c, of a crosslinked PVC system decreases rapidly with loading rate, whereas the toughness of a linear PVC remains roughly constant. In contrast, the interfacial fracture toughness of the balsa core material increased steadily with increasing crosshead displacement rate, an effect that was attributed to the rate dependent properties of the glass fibers in the wake of the primary crack. Prolonged seawater exposure in an aluminum honeycomb structure was found to attack the bond between the epoxy matrix and the aluminum core, facilitating crack advance along the skin‐core interface. Finally, it is concluded that great care should be exercised before selecting sandwich structures for hostile marine environments.     

The effect of temperature and loading rate on the mode II interlaminar fracture properties of a carbon fiber reinforced phenolic

The combined effect of varying loading rate and test temperature on the mode II Interlaminar fracture properties of a carbon fiber reinforced phenolic resin has been investigated. End notch flexure tests at room temperature have shown that this composite offers a relatively modest value of G_IIc^NL at non‐linearity and that its interlaminar fracture toughness decreases with increasing loading rate. As the test temperature is increased, the quasistatic value of G_IIc^NL increases steadily and the reduction in G_IIc^NL with loading rate becomes less dramatic. At temperatures approaching the glass transition temperature of the phenolic matrix, the interlaminar fracture toughness of the composite begins to increase sharply with crosshead displacement rate. A more detailed understanding of the effect of varying the test conditions on the failure mechanisms occurring at the crack tip of these interlaminar fracture specimens has been achieved using the double end notch flexure (DENF) geometry.     

Crack initiation in PVC for subsequent linear elastic fracture mechanics analysis

Reproducible starter-cracks for subsequent linear elastic fracture mechanics analysis have been grown in PVC by fatigue cycling at 80 Hz. The crack growth rate has been related to the fracture surface markings and to the opening mode stress intensity factor (K_I) of the fatigue cycle. Termination of the fatigue crack growth when crack growth rate is constant ensures a smooth mirror fracture surface and a sharp crack tip.     

Polymer fatigue fracture diagrams: BPA polycarbonate

A fatigue fracture diagram for BPA polycarbonate has been created from fatigue lifetime data obtained from knit line notched samples. This fatigue fracture diagram maps out stress-temperature zones where fatigue fracture is dominated by crack growth through leading crazes and zones where fatigue fracture occurs through shear fracture at 45 degrees to the load direction. Both craze and shear planes coexist in the fatigue crack tip plastic zone, and both compete to determine the ultimate crack growth behavior. The shear planes preferentially develop (and fracture) at higher temperatures and stresses, but this fracture process is quite slow. Consequently, an inversion in the fatigue lifetime curve is observed, with longer lifetimes at higher stresses. This inversion is easily understood as a transition between a craze branch and a shear branch on the fatigue lifetime plot. When the fatigue lifetime curve is plotted for data at different temperatures, with the stresses normalized to the yield stress at the respective test temperatures, the craze branch data from different temperatures overlap. This overlap can be explained by the N = 2 power law dependence of crack growth in the discontinuous crack growth regime.     

Temperature and rate dependent fracture in glass-filled polystyrene

The rate and temperature dependent fracture behavior of glass-filled polystyrene has been investigated over the crack speed range of 10¹³ to 1 mm/sec and in the temperature range 283 to 396°K for three environmental conditions: (i) air; (ii) water; and (iii) hot water exposure at 363°K and subsequent drying. Relationships between fracture toughness (K_c), crack speed and temperature have been obtained experimentally and analysed according to the concepts of fracture mechanics and reaction rate theories. Crack propagation in air is shown to be controlled by a β-relaxation process associated with crazing. Activation energies of 200 ～ 210 kj/mole in air and 80 ～ 120 kj/mole in water are reported. At a given temperature and crack speed, the glass-filled polystyrene is shown to display smaller crack propagation resistances in a water environment when compared with the air results. Specimens subjected to hot water exposure and then tested after drying also possess less cracking resistance. This toughness degradation phenomenon is a result of the damaging effects of the water which penetrates into the glass-filled composite.     

Crack propagation in biaxially oriented polypropylene at low temperature

The crack growth behavior of polypropylene biaxially oriented by cross-rolling was studied at low temperature. Single edge notch testing produced a stable tearing type of crack growth in both 50% and 80% biaxially oriented polypropylene at ?40°C, in contrast to the brittle fracture of unoriented polypropylene. The crack growth in the two oriented materials began slowly and accelerated to a constant rate that was higher in the 80% oriented material than in the 50% oriented material. The main difference between the crack growth behavior of the two was the longer period of initial slow growth in the case of 80% orientation. This period of slow growth corresponded to crack growth through the notch tip damage zone. Residual strength diagrams were used to present the crack growth data obtained when the stress state was intermediate between plane stress and plane strain. Fractography revealed large differences among the fracture surfaces of the three materials with the unoriented polypropylene showing a grainy appearance from the brittle fracture. The two oriented materials showed considerable ductility. The 50% oriented material showed many voids in the fracture surface, indicating that voiding during the fracture process contributed significantly to the toughness improvement. The 80% oriented polypropylene showed delamination crazing on the fracture surface with layered material and fibrils bridging the crazes.     

Temperature dependence of craze shape and fracture in polycarbonate

The shape of the craze at the tip of a loaded crack has been determined by optical microscopy for polycarbonate. The effect of temperature was examined, and measurements were made on samples of different molecular weight. In all cases the craze shape can be described to a good approximation by the Dugdale model for the plastic zone at a crack tip. The crack opening displacement depended on sample molecular weight, but was independent of temperature. Fracture toughness values deduced from the craze shape were in good agreement with plane strain fracture toughness obtained from direct cleavage fracture measurements, on the assumption that failure occurs by combined plane strain and plane stress fracture modes.     

Mechanisms of fatigue damage and fracture in semi-crystalline polymers

Fatigue crack profiles and fracture surfaces of poly(vinylidene fluoride) (PVDF), nylon-6,6 (N66), and poly(acetal) (PA) were studied to ascertain the mechanisms of cyclic damage and fatigue crack propagation in semicrystalline polymers. Crack tip damage is believed to begin as small trans-spherulitic and inter-spherulitic tensile crazes. However, compressive yielding within the reverse plastic zone at the crack tip crushes and elongates the spherulites in the direction of crack growth. Consequently, the microstructure of the polymer in advance of the crack front is different from the original morphology of the spherulitic bulk material as evidenced by the resulting fracture surface appearance. When the test temperature is below the glass transition temperature, however, plastic deformation is limited, and fatigue fracture occurs before significant disruption of the spherulitic structure. In this case, the fracture surface morphology reflects the original microstructure of the bulk polymer.     

Designing against fracture in brittle plastics

The fracture toughness of a variety of sharply notched tension, bending and rotating disc specimens of PMMA is examined using linear fracture mechanics. It is observed that rapid fracture with a brittle glassy appearance usually follows a period of slow crack growth, denoted by fan shaped markings of local ductility, though still brittle overall. In this near brittle regime the fracture toughness is sensitive to strain rate so that high values of effective surface energy are easily induced by rapid testing or notch bluntness. At impact rates the toughness increases again. For design purposes, in the absence of environmental effects, the onset of slow cracking and rapid (glassy) fracture, can be associated with fracture toughness K_1c of about 800 Ibf/in^3/2 (90 kg/cm^3/2) and 1600 Ibf/in^3/2 (180 kg/cm^3/2) respectively. Detailed studies have not been made on other materials but a guide to the levels of notch toughness and notch brittle temperatures are given for several plastics.     

Influence of thickness and processing history on fatigue fracture of nylon 66. Part II: Crack tip morphology

Fatigue crack propagation rates in injection molded nylon 66 were previously shown to be strongly affected by prior processing history. To provide a physical basis for the observed acceleration in crack growth rates, microtomed sections were cut through the tips of stable fatigue cracks and examined by optical microscopy. A reduction in spherulite size occurs with reprocessing along with an accompanying decrease in the amount of deformation at the crack tip. For the initially processed nylon 66 this deformation consists of a vast array of independently initiated craze-like zones. Patchy type regions observed on the fatigue fracture surface are similar in size to the initially formed crazed zones. Crack advance occurs by the breakdown and coalescence of the crazed regions via matrix shearing. The extensive damage zone is believed to result in a reduction in stress intensity at the crack tip thereby reducing the crack propagation rates. For the reprocessed nylon 66, one observes fewer crazes and a sharper fatigue crack tip with a consequent acceleration in crack propagation rates and a smoother fracture surface.