Rapid crack propagation and arrest in polymers

Published results on dynamic fracture toughness vs crack velocity relations of polyester resin (Homalite-100), epoxy resin Araldite-B, modified epoxy resins and polycarbonate are reviewed. Commonality between the seemingly diversified experimental results as well as the existences of minimum dynamic fracture toughness, K_Im, and crack arrest stress intensity factor, K_Ia, as inherent material properties are discussed.     

Strain rate dependence of failure processes in polycarbonate and nylon

A study has been made of two types of failure, namely, monotonic fractures using Charpy-type specimens and fatigue crack propagation using rectangular plates containing an initial central notch. The work was conducted on an amorphous polymer (polycarbonate) and a semicrystalline polymer (nylon N 6.6). Monotonic tests were performed in an Instron testing machine between 0.002 and 20 in./min, and in a Charpy testing machine between 2000 and 11800 in./min. The cyclic tests (under constant K conditions) were carried out at frequencies that ranged from 0.1 to 20 Hz. A model for the relationship between the cyclic rate of crack growth and appropriate LEFM parameters, previously described, has now been converted into cyclic strain energy transformations. In computing the strain energy, the value of the time-dependent modulus of the material was used; and under cyclic loading conditions the glassy (short time) value was employed. The authors have proposed that the modulus measurements obtained at very low temperatures, where the viscous response of the material is highly restricted, will approximate the glassy value, E_g, found by conducting relaxation measurement tests at different temperatures down to ?197°C. Within the range of tests conducted, the fracture toughness values of both PC and N 6.6 apparently decrease with increase in loading rate. Fatigue crack growth in both materials is influenced by loading frequency and cyclic waveform. These variations may be related to the magnitude of the viscous energy loss and hence to the available energy for crack extension per cycle.     

Application of instrumented impact test in polymer testing

Advanced methods of conducting and analyzing instrumented Charpy impact tests are described and used in measuring the initiation fracture toughness K_1c at a range of impact velocities and temperatures. Improvements developed in the impact testing of metals are discussed and applied in the toughness evaluation of polymers. In lower-speed impact tests where load–displacement records are nearly linear, the maximum recorded load may be used to evaluate K_1c by stress analysis K calibration formula. In high-speed impact tests, where the load trace is highly oscillatory, the fracture load to be used in the calculation must be derived indirectly. The indirect derivation of fracture load for this purpose from a “low blow” stiffness measurement and specimen deflection has been studied in detail, and the use of the periodic time of the “low blow” test has been found to offer a reliable method of calculating the system stiffness.     

Fracture toughness of glasses as measured by the SCF and SEPB methods

The fracture toughness, K_Ic, of six glasses was measured by the surface crack in flexure (SCF) and single-edged precracked beam (SEPB) methods. Results depended upon the loading rate as well as the test environment. Environmentally-assisted slow crack growth affects the results for tests done in air. Dry nitrogen testing is preferred. Crack healing may be a severe complicating factor with precracked flexure bar type specimens if the specimens are unloaded between the precracking and final fracture test. Success in K_Ic testing depends to a large degree on upon the ability to make good precracks.     

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.     

Effect of temperature on fracture toughness of PC/ABS based on J-integral and hysteresis energy methods

The critical fracture toughness J_1c of the polycarbonate (PC)/acrylonitrile–butadiene–sty-rene (ABS) blend at different temperatures was obtained from ASTM E813-81, E813–87, and the recently developed hysteresis energy methods, respectively. The J_1c value increases with increase of the test temperature ranging from −60 to 70°C. the hysteresis energy method and the ASTM E813–81 method result in comparable J_1c values, while the ASTM E813–87 results in about 80–110% higher values. the critical initiation displacements determined from the plots of hysteresis energy and the true crack growth length vs. crosshead displacement are very close. This indicates that the critical initiation displacement determined by the hysteresis method is indeed the displacement at the onset of true crack initiation and the corresponding J_1c represents a physical event of crack initiation. The fracture toughness, K_1c value, based on linear elastic fracture mechanics (LEFM), was determined by using K_Q analysis (ASTM E399–78), and the obtained K_Q value decreases with the increase of the test temperature. The K_Q value is not the real LEFM K_1c value because the criterion of P_max/P_Q < 1.1 has not been satisfied. However, the corresponding J_Q obtained from the K_Q analysis is comparable to the J_1c obtained from the E813–81 method at lower temperature (−45 or −60°C), an indication of LEFM behavior at lower temperature. The various schemes and size criterion based on LEFM and the J-method are explored for the validity of J_1c and K_1c values. © 1996 John Wiley & Sons, Inc.     

Instrumented charpy impact test of epoxy resin filled with irregular-shaped silica particles

The effect of particle size on the impact properties of an epoxy resin has been studied. This resin was filled with irregular-shaped silica particles prepared by crushing fused natural raw quartz. These particles were sorted into six groups of different mean sizes ranging from 2 to 47 μm. The impact properties were measured by an instrumented Charpy type impact tested, which can record a load-displacement curve during impact fracture. The impact absorbed energy (U) was measured using specimens having a U-shaped blunt notch, and the impact fracture toughness (K_CI) was measured using specimens having a sharp crack introduced by a fresh razor blade. As the particle size decreased. U increased and K_CI decreased. The fractured surfaces and crack tip regions were observed using a scanning electron microscope to clarify the above phenomena.     

Fracture toughness of injection molded glass fiber reinforced polypropylene

The fracture behavior of polypropylene reinforced with 30% by weight of short glass fibers was studied using single and double feed plaque moldings. Plaques were injection molded using several gate types and gate positions. Fracture toughness K_c, was calculated at different positions in the plaque moldings using single edge notched tension specimens. Fracture toughness was assessed in the directions parallel and perpendicular to the mold fill direction through measurements of the load to produce complete fracture. Results indicated that the value of fracture toughness is affected by the type of gate as well by size of gate. Position of the specimen also affected fracture toughness. Generally, specimens taken from positions near cavity walls gave higher toughness values than those taken from the center of the moldings. Furthermore, fracture toughness in the transverse direction was consistently higher than in the melt flow direction. Finally, in the case o double feed moldings, a much higher fracture toughness was obtained when the initial crack was perpendicular to the weld line than when it was placed inside the weld line.     

Fracture behavior of oriented poly(ether-ether-ketone) (PEEK)

Poly(ether-ether-ketone) (PEEK) is a newly developed engineering thermoplastic with potentially vast application in advanced composites due to its exceptional performance. It is thus desired to understand the relationship between physical processing, microstructure and fracture in this semicrystalline polymer. Both oriented and unoriented PEEK were mechanically characterized using static test of three-point bend specimens. The molecular chain orientation was imposed using a rolltrusion technique. The effects of thickness, strain rate, Initial crack length ratio, and orientation on fracture toughness (K_c) are investigated. The crystallinity is also examined by density measurement. The degree of orientation is determined qualitatively by wide-angle X-ray scattering diffraction patterns and quantitatively by further measurement using an image analysis system. Fractographic analysis, using scanning electron microscopy, provides precise information about the mode of fracture, Results indicate that both the modulus and the fracture toughness are remarkedly increased in the direction of drawing (T-type) as opposed to the transverse direction (L-type).     

Impact fracture toughness tests on polymers

A series of impact tests are described in which the plane strain fracture toughness, K_c1, of five different polymers is measured using a three point bend specimen at striker speeds up to 5m/s. At low speeds K_c1 is determined using the maximum load and a static analysis, but at speeds greater than 1 m/s the dynamic effects render the load signal unusable. For the higher speeds the fracture is timed using contact and crack propagation gages and the analysis is performed using the striker displacement at fracture. A dynamic analysis is used to convert this measurement to the true specimen displacement and K_c1 is determined from this. The apparent downward trends in the K_c1 results obtained, especially at speeds above 3m/s, are discussed.     

Influence of crack speed on fracture energy in amorphous and rubber toughened amorphous polymers

Abstract

To study the influence of the crack speed at initiation on measurements of the toughness of amorphous polymers such as polycarbonate (PC) and rubber toughened poly(methyl methacrylate) (RTPMMA), ‘compact tension’ specimens were tested at a medium loading rate (0·6 m s^-1 ). The specimens were equipped to allow location of the position of the crack tip and to trigger a photograph on passage of the crack. The experimental procedure was validated using PC for which the crack speed was found to change suddenly over very short distances, owing to stick–slip propagation. Conversely, fracture tests on RTPMMA showed that the acceleration of the crack tip, due to the decrease in fracture energy with crack speed, is controlled by a process zone, the size of which did not allow the systematic use of linear elastic fracture mechanics. The rapid crack propagation regime in RTPMMA corresponds to a propagation stabilised at the macroscopic crack branching velocity. This constant crack speed corresponds to frustrated microbranching and leads to non-unique values of the fracture energy at the macroscopic branching velocity.     

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.     

Fracture toughness of a short-fiber reinforced thermoplastic

Thin plates of carbon short-fiber reinforcement polycarbonate were injection molded. The mold was designed to produce a uniform melt flow across the cavity and an extended knock-out pin was incorporated to form a circular hole at the center of the molded plate. The elastic constants of the plaques were determined using sections cut from the plate at different angles to the direction of flow. Analysis of the data showed that the plates could be treated macroscopically as being orthotropic. Microscopic observations revealed that the fiber orientation was primarily in the flow direction and was tangential in the vicinity surrounding the hole. The fracture toughness, as measured by the stress intensity (K), was determined using the compliance method. Experimental calibration curves were constructed at 0° and 90° to the axis of flow by loading specimens containing saw cuts of varying length. The resultant curves were non-dimensionalized by incorporation of the elastic moduli, thickness, and width. The fracture toughness values were determined using a razor notch as a starter crack. The crack growth during testing was found to be stable, which could allow several determinations to be made on each plate. The effects of crack length, flow in the cavity, and fiber orientation around the hole were investigated. The fracture toughness was found to decrease with increasing crack length, but was not found to reach a limiting value within the practical range of testing. The effect of flow was also found to be significant. Specimens oriented 90° to the axis of flow showed higher toughness values. This was attributed to the fibers being oriented perpendicular to the axis of the crack. The samples tested with razor notches cut at the edge of the molded holes had still higher apparent toughness values. Similarly, this effect was explained by the higher fiber orientation shown with photomicrographs of specimens cut near the edge of the hole.     

Temperature effect on impact fracture toughness and fracture mechanism of phenolphthalein poly(ether ketone)

Phenolphthalein poly(ether ketone) (PEK-C) was tested using an instrumented impact tester to determine the temperature effect on the fracture toughness K_c and critical strain energy release rate G_c. Two different mechanisms, namely the relaxation processes and thermal blunting of the crack tip were used to explain the temperature effect on the fracture toughness. Examination of the fracture surfaces revealed the presence of crack growth bands. It is suggested that these bands are the consequence of variations in crack growth along crazes that are formed 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.     

Fracture toughness of PC/PBT blend based on J-integral methods

The fracture toughness of a polycarbonate/poly(butylene terephthalate) (PC/PBT) blend was determined using three different J-integral methods, ASTM E813-81, E813-87, and hysteresis energy. The critical J values (J_1c) obtained are largely independent of the cross-head speed (range from 0.5 to 50 mm/min). ASTM E813-81 and hysteresis energy methods result in comparable J_1c values, while the E813-87 method estimates J_1c to be 60–80% higher. The critical displacement determined from the plots of hysteresis (energy and ratio) and the true crack growth length vs. displacement is very close. This indicates that the critical displacement determined by the hysteresis energy method is indeed the displacement at the onset of crack initiation and the corresponding J_1c represents a physical event of crack initiation. © 1995 John Wiley & Sons, Inc.     

Slow crack propagation in a heavily-filled particle reinforced epoxide resin

The fracture properties of two proprietary composite dental restorative materials and a model composite system were studied to determine the effects of filler concentration, exposure to water, and particle/polymer adhesion on subcritical crack propagation. Particle content ranged from 36 to 60 volume percent. The double torsion (DT) test was used to measure relationships between the stress intensity factor (K₁) and the speed of decelerating cracks or the rate of loading in dry and wet materials in air at laboratory conditions. Materials with weak particle/polymer interfaces fractured by continuous crack growth in both dry and wet conditions. In dry and wet materials with strong interfaces, continuous cracking also occurred at the low end of the range of speeds observed (10⁻⁷ to 10⁻³ m/s), but under test conditions of high crack speeds unstable (stick-slip) crack propagation was found in dry specimens and in wet model composites with 41 percent vol, filler. Water had a corrosive effect lowering K_1c for continuous crack propagation. The exponential dependence of K_1c on crack velocity, representing the viscoelastic response of the materials, was positively correlated to the filler concentration and the plasticizing effect of water. Observations on fracture surfaces indicate that low velocity cracks (<10⁻⁵ m/s) propagate through regions of high stress concentrations (interfaces, corners, pores) while at higher crack velocities failure occurs by a combination of interparticle and transparticle fracture.     

Fracture toughness of autoclaved portland cement/silica mixtures

Fracture toughness measurements made at 11% RH on autoclaved cement/silica mixtures having a wide range of silica contents and porosities yielded a series of curves for K_c versus porosity and K_c versus silica content. Those for preparations having low porosity and silica content were unique. Apparently αC₂S-hydrate, unreacted silica and pores having specific size distribution can act as crack arrestors. K_c versus hardness curves were similar to those for K_c versus porosity. Simple microhardness tests may be useful in predicting fracture toughness of autoclaved cementitious systems.     

Time and temperature effects on the fracture toughness of rigid poly(vinylchloride) pipe materials

The fracture toughness of rigid poly(vinylchloride) pipe materials has been investigated over a range of temperatures and rates. Conditions are described for valid fracture toughness (K_IC) tests and notch insensitive (ductile) behavior; time-temperature effects on transitions in K_IC are defined. The modes of crack extension are characterized over a range of temperatures, and the mechanisms of crack resistance are discussed, including some quantitative data for the yielded zone at the crack tip.     

Anisotropy of Mechanical Properties of Zirconia-Based Ceramics Tested for Bending

The effect of bending stress s of different magnitudes and signs on the fracture toughness K _1c of polycrystalline specimens of partially stabilized zirconia (PSZ) is considered. A method for testing pre-stressed PSZ specimens by Vickers indentation using a four-point bending scheme is proposed. The dimensions of the impression from a diamond pyramid and the length of the radial cracks generated thereby are determined. An anisotropy of strength properties is revealed in the specimens tested, which is explained by the involvement of two mechanisms: forcing action of an external stress on the crack opening and activation of the tetragonal- monoclinic phase transition in the tensile stress field.     

Effect of the low-temperature relaxation on toughness of cured epoxy resins

The relation between the magnitude of low-temperature relaxation and toughness was investigated for epoxy resins cured with some position isomers of naphthalenediols. A well-defined relaxation was observed near room temperature for a system cured with 2,6-dihydroxynaphthalene. The relaxation was denoted here as the β′-relaxation. The values of the stress intensity factor, K_c, in this system was considerably higher than those of the other cured systems in the temperature region over the β′-relaxation temperature. This is explained by the increase in the plastic deformation region at the crack front with an increase in the temperature near the crack tip caused by the presence of the β′-relaxation. © 1994 John Wiley & Sons, Inc.