Fracture toughness and crack instability in tough polymers under plane strain conditions

The plane strain fracture toughness and fracture mechanisms of several tough engineering plastics have been studied and compared with poly(methyl methacrylate) (PMMA), a relatively brittle polymer. The tough polymers all are observed to form a multiple craze zone at the crack tip, which is shown to be the primary source of plane strain fracture toughness in these materials. The multiple craze zone is retained during slow crack growth but is metastable, and at a critical stress intensity and associated crack velocity, the system passes through a transition to a greatly accelerated single craze mode of unstable propagation.     

Fracture toughness of polymers in shear mode

This paper presents a new test method that measures fracture toughness of polymeric materials when subjected to in-plane shear loading (mode II), and compares the toughness with that in tension mode (mode I). The new test method uses an Iosipescu device to apply the shear load, and determines the toughness based on the concept of essential work of fracture (EWF). Three physical-based criteria were used to verify the occurrence of mode II fracture. The new test method was then used to evaluate toughness of poly(acrylonitrile–butadiene–styrene) (ABS). The results suggest that for the ABS, the ratio of toughness in mode II to mode I is about 2.5 which leads to the dominance of mode I fracture in most loading conditions. The results also showed that for ABS in mode I fracture, the specific work of fracture (defined as the absorbed energy for fracture divided by the cross sectional area of the ligament between the notch tips) depends on ligament length; while in mode II fracture, it depends on ligament thickness. The study concludes that the new test method has a good potential for evaluation of mode II fracture toughness of polymers, though further study using polymers of different characteristics will be needed to confirm universality of the test method in the measurement of mode II fracture toughness.     

Fracture toughness of impact-modified polymers based on the J-integral

The fracture toughness characterization of four impact-modified polymers based on the J-integral concept was studied. We have discovered that the use of the “crack blunting line” concept needs revision. Direct measurements of the crack growth can be made (as opposed to indirect readings from the fracture surface) that test the applicability of the crack blunting concept. Our results indicate that for rubber-toughened polymers the use of the blunting line fails to specify properly the critical J-integral value for crack initiation.     

Fracture toughness of interfaces between glassy polymers in a trilayer geometry

We studied the fracture behavior of trilayer A/B/A assemblies based on polystyrene (PS) and poly(methylmethacrylate) (PMMA) where the central layer of the A polymer was confined (0.5–200 μm) between two thick plates of the B polymer (1– 3 mm). Diblock and random P(S-MMA) copolymers were used to provide a good stress transfer across the interfaces. Fracture experiments were performed with the double-cantilever beam method and the fracture mechanisms were observed by optical microscopy on microtomed slices of the damaged zone. The measured _c of the A/B interface fractured during the test was dependent on the molecular structure at the interface (random copolymer, diblock copolymer or no copolymer), on the crazing stress of the bulk materials and on the interfacial shear stresses. When the phase angle of the loading was even slightly positive, oblique crazes were observed in the PS increasing greatly _c. If PS was the central layer, this resulted in a very marked dependence of _c on the thickness of the central layer for a thickness range 10–200 μm which was not observed when the PMMA was the central layer. Thermal treatments modifying the interfacial shear stresses were also found to have a very strong effect on _c.     

Toughened multiphase thermosetting polymers

In recent years a new generation of advanced structural adhesives has become available. They are typically based upon epoxy resins modified by the presence of a second phase of dispersed rubbery particles. This multiphase microstructure results in the material possessing a considerably higher toughness or crack resistance, compared to the unmodified, single-phase resin, but with only a minimal reduction in other important properties such as modulus and high-temperature and creep resistance. Even more recently, polyimide adhesives have also been toughened employing this principle. The present paper considers the following aspects:

• 1 The chemistry of rubbery-toughened thermosetting polymers developed for adhesive applications.
• 2 Structure-property relationships of multiphase adhesives which incorporate a dispersed rubbery phase or rigid particulate fillers. The mechanisms of toughening are discussed and related to the microstructure. The effects of volume fraction, particle size and particle size distribution on the polymer's fracture energy are also described
• 3 The particular problems encountered when using such toughened multiphase adhesives in structural joints are reviewed, including aspects of joint design and environmental effects.

     

Oxidation effects on toughness and slow crack growth in polycrystalline graphites

The fracture toughness (K_Ic) and slow crack growth behavior of four fine-grained polycrystalline graphites, oxidized to 5, 10 and 20% weight losses, were measured in air at room temperature. Exponential decreases in the elastic moduli as well as decreases in the fracture surface energy contributed to lowering K_Ic. Oxidation generally shifted the stress intensity-crack velocity (K_I-V_I) diagram to lower stress intensity values, and decreased the slope, or N-value. Scanning electron microscope fractography revealed that a combination of filler particle and binder phase degradation with increasing oxidation was responsible for the decreased toughness and changes in the (K_I-V_I) characteristics. Oxidation conditions were shown to significantly affect the magnitude of decreases in the physical, elastic and mechanical properties of these graphites.     

Fracture toughness evaluation of polytetrafluoroethylene

The objective of this preliminary work was to explore the fracture resistance of polytetrafluoroethylene (PTFE) (DuPont tradename Teflon) as part of materials characterization work related to the development of “reactive” material projectiles. Little mechanical property data is available on this material since it is commonly used only as a coating material with the dominant properties being its low friction coefficient and high application temperature. Additional end products of the “7C” derivative, however, includes sheet, gaskets, bearing pads, piston rings, and diaphragms. In this work, standard ASTM E1820 fracture toughness specimens were machined from a 14‐mm‐thick sheet of this material obtained from NSWC Dahlgren Laboratory. These specimens were tested at three test temperatures and four test rates to determine if fracture would occur in this material, and if so, how the fracture toughness depends on the test temperature and specimen loading rate. Standard axial tensile specimens were also tested at quasi‐static and elevated loading rates at temperatures from ambient to ?73°C. The major results are that while crack extension is difficult at ambient (20°C) temperature, for temperatures slightly below ambient, a rapid degradation of fracture resistance occurs. This reduction in fracture resistance is enhanced by rapid loading, and the material loses approximately 75% of its toughness (fracture energy absorption ability) at ?18°C if the crack opening loading rate of the C(T) specimen approaches 0.25 m/s. Further reductions in temperature or increases in the loading rate appear to result in a reduced rate of degradation of fracture toughness.     

二维随机裂纹的断裂分析

将随机有限元方法引入断裂分析中 ,考虑到裂纹尺寸的随机性 ,进行了J积分的随机分析。首先基于Tay lor级数展开的随机有限元方法 ,讨论了位移和应力的数字特征表示方法 ,指出位移和应力的偏导数计算是随机有限元的关键 ,并推导了位移和应力的偏导数计算公式以及刚度矩阵的偏导数和Jacob矩阵的偏导数的计算公式。然后推导了二维弹性J积分的随机有限元列式 ,编制了随机有限元程序。最后对程序进行了精度考核 ,与Monte carlo方法相比 ,误差为 0 3 5 %。     

Fracture toughness of cement paste and mortars

The effective fracture toughness of a range of cement pastes and mortars have been measured using both a notched beam and a doublt cantilever beam method. The influence of size and quality of aggregate on the effective toughness has been studied as the cracks advance. The observed values of fracture toughness are dependent on crack velocity.     

Fracture and toughness of crystalline polymer solids

The development of plastic deformation and crazing in the neighborhood of a notch has been studied in connection with nonlinear fracture processes of crystalline ductile polymers, polyethylene, polypropylene, and propylene-ethylene block copolymers. After revealing the morphology of plastic deformation around the notch and studying the effects of crystalline structure on ductile fracture processes, the J-energy analysis was applied to give a criterion for crack initiation in the fracture of these elastic-plastic materials. The material resistance to stable and unstable cracking was characterized using the curves of J against crack extension Δα.     

Molecular weight dependence of the fracture toughness of glassy polymers arising from crack propagation through a craze

We investigate criteria for craze failure at a crack tip and the dependence of craze failure on the molecular weight of the polymer. Our micromechanics model is based on the presence of cross-tie fibrils in the craze microstructure. These cross-tie fibrils give the craze some small lateral load bearing capacity so that they can transfer stress between the main fibrils. This load transfer mechanism allows the normal stress on the fibrils directly ahead of the crack tip in the center of the craze to reach the breaking stress of the polymer chains. We solve for stress field near the crack trip and use it to relate craze failure to the external loading and microstructural quantities such as the craze widening (drawing) stress, the fibril spacing, the molecular weight, and the force to break a single polymer chain. The relationship between energy flow to the crack tip due to external loading and the work of local fracture by fibril breakdown is also obtained. Our analysis shows that the normal stress acting on the fibrils at the crack tip increases linearly as the square root of the craze thickness, assuming that the normal stress distribution is uniform and is equal to the drawing stress acting on the craze-bulk interface. The critical crack opening displacement, and hence the fracture toghness is shown to be proportional to [1–(M_e/qM_n)]², where M_e is the entanglement molecular weight, M_n is the number average molecular weight of polymer before crazing, and q is the fraction of entangled strands that do not undergo chain scission in forming the craze.     

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.     

An investigation on craze growth at a crack tip in polymers

A craze zone model with damage at the crack tip in polymers under creep is presented. By taking into account a power law material, time‐dependence of both craze advance and thickening at the tips of a center crack is investigated. Numerical results show that both length and thickness of the craze zone increase with time while the mean stress decreases. It is also shown that the calculated craze zone profile is coincident with previous experiments, and the size of the craze zone with a damage model is larger than that without considering damage at crack tip zone.     

Fracture toughness testing of dental biomaterials

The adaptation of a cylindrical geometry fracture toughness test specimen to testing of polymeric dental biomaterials is demonstrated. The specimen configuration facilitates the fabrication of small specimens and simplifies the experimental study of environmental effects on properties of dental biomaterials. The test method is used to measure critical stress intensity factor, K_IC for poly (methyl methacrylate) (PMMA), particulate composite restorative materials, and dental polymers. Values obtained are in agreement with data reported for other specimen configurations.     

Fracture toughness of inorganic-organic hybrid coatings

The concepts of fracture toughness and the energy release rate at fracture for thin polymeric films are introduced. Fracture toughness and energy release rate data for ceramer films based on a linseed oil alkyd, a sunflower oil alkyd, and a commercial alkyd with titanium diisopropoxide bis(acetylacetonate), titanium(IV) isopropoxide, and zirconium(IV) propoxide are presented and compared to previously reported tensile data. Differences between the fracture data and the tensile data demonstrate the usefulness of fracture toughness testing. The energy release rate at fracture may be the one property to maximize in order to optimize all of the other coating properties. It may therefore be a great aid in the optimization of coating formulations. Data from dynamic mechanical thermal analysis indicate that there may be a correlation between fracture properties and secondary relaxation processes in the films. Department of Polymers & Coatings, Fargo, ND 58105.     

Fracture toughness of autoclaved aerated concrete

So far, few experiments to determine fracture toughness of autoclaved aerated concrete have been reported in the literature. Tests on three different types of autoclaved aerated concrete using six different specimen geometries have been carried out. Four of the six specimen geometries chosen lead to nearly identical results for K_IC. The two other types of specimen were used to determine fracture energy G_f. K_IC increases with compressive strength of the material. Fracture energy is about one tenth of the corresponding value of normal concrete. The influence of rate of loading on K_IC can be expressed by means of a power law. These results suggest that linear elastic fracture mechanics is a suitable approximation for the calculation of crack propagation in autoclaved aerated concrete.     

Fracture toughness of an epoxy system

The fracture toughness of epoxy used in the bulk and adhesive form was measured by a previously developed technique. The uniform double cantilever-beam specimen, which was described earlier, was modified to a tapered beam, which simplified the experimental procedure and calculations for obtaining toughness measurements. by varying the ratio of hardener to resin and post-cure temperature on a single epoxy system (DER 332-TEPA), it was found that the toughness of the epoxy used in either bulk or bond form varied by a factor of approximately five. A particular combination of composition and post-curing temperature generally yielded higher toughness in the bulk than in the bond form. This was not always the case, however. At high post-cure temperatures, where the bonds were very tough, their toughness exceeded that of the bulk material. Hence, it does not appear possible to predict joint toughness from bulk toughness measurements. The toughness of joints was found to be a single-valued function of tensile modulus. For the bulk material, on the other hand, the toughness obtained on the epoxy having a specific modulus depended on the combination of composition and post-cure temperature. Joint toughness for any combination of composition and post-cure temperature depended only on the cracking rate. If the epoxy was the type that caused cracks to jump rapidly, the epoxy was tough and vice versa. For a particular epoxy system, toughness was increased by driving the crack at an increasing rate.     

Fracture toughness of phenolphthalein polyether ketone

The static and impact fracture toughness of phenolphthalein polyether ketone (PEK-C) were studied at different temperatures. The static fracture toughness of PEK-C was evaluated via the linear elastic fracture mechanics (LEFM) and the J-integral analysis. Impact fracture toughness was also analyzed using the LEFM approach. Temperature and strain rate effects on the fracture toughness were also studied. The enhancement in static fracture toughness at 70°C was thought to be caused by plastic crack tip blunting. The increase in impact fracture toughness with temperature was attributed two different mechanisms, namely, the relaxation process in a relatively low temperature and thermal blunting of the crack tip at higher temperature. The temperature-dependent fracture toughness data obtained in static tests could be horizontally shifted to match roughly the data for impact tests, indicating the existence of a time–temperature equivalence relationship. © 1995 John Wiley & Sons, Inc.     

Fracture toughness of urethane-modified methacrylate resins

This paper reports the synthesis of a series of urethanetoughened methacrylate resins and evaluation of the fracture toughness (K_IC) of these materials. The incorporation of high-molecular-weight polyfunctional urethanes produced resins with the best mechanical properties, important to applications as dental biomaterials.     

Fatigue crack growth in polymers. I. Effect of frequency and temperature

The effects of frequency, from 0.1–100 Hz, and temperature, ?60°C to +21°C, on fatigue crack propagation in poly (methyl methacrylate) and polycarbonate were investigated. A cyclic crack propagation law proposed by Arad-Radon-Culver, namely where λ is (K_max²-K_min²) and K_max and K_min are the respective values of maximum and minimum stress intensity factor, was applied to describe a relationship between crack growth and cyclic life. Cyclic tests performed in tension between zero load and K_max showed a linear relationship between the crack lengths and the number of cycles for all temperatures and frequencies tested. It was found that, in general, the cyclic crack growth decreased with decreasing temperature and increasing frequency. However, important exceptions to this rule have been noted.