Precrack hysteresis energy in determining polycarbonate ductile–brittle transition. IV. Effect of strain rate

Effect of deformation rate on the ductile–brittle transition behavior for polycarbonate (PC) with different molar mass, notch radius, and rubber content has been investigated. PC with higher molar mass, notch radius, or rubber-modification possesses a higher critical strain rate when the ductile–brittle transition occurs. Whether a notched specimen will fail in a ductile mode or a brittle mode is already decided before the onset of the crack initiation. If size of the precrack plastic zone exceeds a critical level prior to onset of crack initiation, the crack extension developed later will propagate within the plastic zone and result in a ductile mode fracture. The precrack elastic storage energy, the input energy subtracting the hysteresis energy, is the main driving force to strain the crack tip for crack initiation. The precrack hysteresis energy (directly related to the precrack plasticity) increases with the decrease of the applied strain rate. Therefore, the strain rate is also closely related to the size of the precrack plastic zone. If the strain rate is lower than the critical strain rate, the specimen is able to grow a precrack plastic zone exceeding the critical plastic zone and results in a ductile mode fracture. © 1997 John Wiley & Sons, Inc. J Appl Polym Sci 65: 655–665, 1997     

Precrack hysteresis energy of elastomer-modified polycarbonates in determining its ductile–brittle transition

For ductile fracture, the precrack plastic zone has to exceed a critical value, and precrack hysteresis energy has been employed to characterize the plastic zone. The presence of elastomer in polycarbonate is able to enhance precrack hysteresis and, therefore, toughens the polycarbonate matrix. Higher precrack hysteresis means that a greater fraction of the input energy converts into plasticity and leaves less storage energy available to strain the crack tip for crack Initiation. If the precrack plastic zone is above the critical value before onset of initiation, the crack growth developed thereafter will be effectively contained within the domain of the plastic zone and results in mass shear, yielding ductile fracture. In this paper, the elastomer toughening is classified as promotion of ductile failure through mass shear yielding and the localized energy dissipation processes. The localized energy dissipations are further divided into the activities occurring on and underneath the fracture surface. A different approach in interpreting the elastomer-toughening mechanism is discussed in detail. © 1993 John Wiley & Sons, Inc.     

Effect of polycarbonate molecular weight on precrack hysteresis energy in determining its ductile-brittle transition

The distinctive ductile-brittle transition behavior of pseudoductile polymeric materials such as polycarbonate (PC) has been discovered to be closely related to the precrack hysteresis loss energy. The higher molecular weight (MW) PC with higher ductility also results in higher precrack hysteresis energy and therefore greater precrack plastic volume under condition of constant loads. If the precrack plastic volume exceeds a critical value, crack initiation thereafter will propagate within the domain of the plastic zone and results in ductile fracture. The deformation displacement is closely related to the precrack plastic volume, and the critical displacement actually determines the critical plastic volume. The higher molecular weight polycarbonate with higher entanglement density is able to withstand earlier crack initiation more effectively. Toughening plastics, such as rubber modification, is simply the result of delaying or retarding the crack initiation and allows the precrack plastic zone to grow over its critical value. A model of crack criterion based on precrack plastic zone is proposed to interpret the ductile-brittle transition phenomenon.     

Mechanical fracture behavior of polyacetal and thermoplastic polyurethane elastomer toughened polyacetal

Polyacetal (POM) toughening with thermoplastic polyurethane (TPU) elastomer was investigated in terms of Theological, mechanical, and morphological properties. Polyacetal can be effectively toughened by the blending with TPU elastomer and the improvement on toughness is found most significant with TPU content from 20 to 30 percent. POM does fracture in ductile mode under extremely low deformation rate and the ductile-brittle transition rate is at 0.5 mm/min. The transition rate is increased with the increase of elastomer content. The precrack hysteresis energy is important in dictating the failure mode. The experimental results show the hysteresis energy (under constant load) increases with the increase of elastomer content and the decrease of deformation rate. Greater hysteresis energy results in larger precrack plastic zone size and thus tends to shift the fracture mode from brittle to ductile as the critical size of the plastic zone is reached. The adoption of the slow rate fracture method has the advantages of ranking toughness of very brittle polymeric materials vs. the conventional Izod or Charpy impact method by varying temperatures. FTIR shows significant interaction between POM and TPU which is probably responsible for the TPU elastomer being such an efficient toughening agent for POM. Delamination in the buffer zone between the plane-strain and the plane-stress is discovered and the possible mechanism is discussed.     

Fracture and impact properties of polycarbonates and MBS elastomer-modified polycarbonates

Mechanical properties of polycarbonates (PCs) and elastomer-modified polycarbonates with various molecular weights (MW) are investigated. Higher MW PCs show slightly lower density, yield stress, and modulus. The ductile–brittle transition temperature (DBTT) of the notched impact strength decreases with the increase of PC MW and with the increase of elastomer content. The elastomer-modified PC has higher impact strength than does the unmodified counterpart if the failure is in the brittle mode, but has lower impact strength if the failure is in the ductile mode. The critical strain energy release rate (G_c) measured at ?30°C decreases with the decrease of PC MW. The extrapolated zero fracture energy was found at M_n = 6800 or MFR = 135. The G_c of the elastomer-modified PC (MFR = 15, 5% elastomer) is about twice that of thee unmodified one. The presence of elastomer in the PC matrix promotes the plane–strain localized shear yielding to greater extents and thus increases the impact strength and G_c in a typically brittle fracture. Two separate modes, localized and mass shear yielding, work simultaneously in the elastomer-toughening mechanism. The plane–strain localized shear yielding dominates the toughening mechanism at lower temperatures and brittle failure, while the plane–stress mass shear yielding dominates at higher temperatures and ductile failure. For the elastomer-modified PC (10% elastomer), the estimated extension ratio of the yielding zone of the fractured surface is 2 for the ductile failure and 5 for the brittle crack. A criterion for shifting from brittle to ductile failure based on precrack critical plastic-zone volume is proposed.     

Fracture behavior of polypropylene/ ethylene- diene-terpolymer blends : Effect of temperatures,notch radius and rubber content

The mechanical fracture and ductile-brittle transition (DBT) behavior, hysteresis phenomenon and the plastic zone size of polypropylene (PP) / ethylene-propylene-diene terpolymer (PP/EPDM) blends were investigated by varying EPDM content and notch radius under different temperatures. An increase in test temperature or rubber content in the PP/EPDM blend results in lower yield stress and Young's modulus. The ductile-brittle transition temperature (DBTT) of the notched impact strength decreases with the increase of the EPDM content. However, the DBTT is fairly independent of the notch radius. SEM morphologies of the fracture surfaces indicate that two separate modes, localized and mass shear yielding, work simultaneously in these blends. The plane-strain localized shear yielding dominates the brittle failure at lower temperatures, whereas the plane stress mass shear yielding dominates the ductile fracture at higher temperatures. The presence of EPDM rubber decreases the yield stress of the PP/EPDM blend due to the overlapping stress fields of adjacent particles, resulting in higher hysteresis energy. The relationships among the test temperature, hysteresis loss energy and the size of plastic zone are discussed in detail.     

Co-existence of ductile,semi-ductile,and brittle fractures of polycarbonate

The ductile–brittle transition behavior of polycarbonate and methylmethacrylate–butadiene–styrene (MBS) elastomer modified polycarbonate has been investigated in terms of notch radius and temperature. At?40°C and 21-mil notch radius, polycarbonate fractures in three possible modes, ductile (25%), semi-ductile (50%), and brittle (25%). This semiductile mode fracture has never been reported previously with brittle characterization, but to a greater extent in localized shear yielding on the fracture surface and intermediate toughness. A two-dimensional fracture mode diagram in terms of temperature and notch radius has been constructed to interpret the observed phenomena. This diagram can also predict the existence of other conditions under which the triplet fracture modes may also occur. Another unstable zone has also been identified where the fracture occurs in either ductile mode or brittle mode over a broad temperature range, instead of the narrow temperature range typically observed for polycarbonate. A model based on the excessive precrack strain just below yielding due to the greater notch radius is proposed to explain such observed semi-ductile mode fracture.     

A fatigue crack initiation map for polycarbonate

The mechanisms of fatigue crack initiation for various stress levels and thicknesses have been determined for single-edge notched specimens of polycarbonate and used to assemble a map. Three basic fatigue crack initiation mechanisms were identified and named as cooperative ductile (the damage zone formed ahead of crack consisting of yielded material), solo-crack brittle (very little damage zone development), and cooperative brittle (identified as a cloud of microcracks or crazes that developed at the notch tip). With a given applied stress and within the same failure mechanism, the values of the number of cycles to crack initiation decrease with increase in thickness. The transition from cooperative ductile to solo-crack brittle initiation mechanisms is sudden with increasing thickness. Transition from cooperative ductile to cooperative brittle with decreasing stress was less well defined. Regions where combinations of mechanisms were observed are also identified in the map. © 1993 John Wiley & Sons, Inc.     

Mechanical properties of the rubber-toughened polymer blends of polycarbonate (PC) and poly(ethylene terephthalate) (PET)

The intrinsically impact-brittle PC/PET blends can be effectively toughened, in terms of lower ductile brittle transition temperature (DBTT) and reduced notch sensitivity, by incorporating butylacrylate core-shell rubber. The rubber particles are distributed exclusively in the PC phase. Varying the PC melt flow rate (MFR) is more important than varying the PET I.V. to vary the low temperature toughness of the blends. PC with MFR = 3 is essential to produce the toughest PC/PET/rubber blend. The presence of rubber slightly relieves the strain rate sensitivity on yield stress increase. Lower MFR PC in the blend results in smaller activation volume and, therefore, higher strain rate sensitivity, because a greater number of chain segments are involved in the cooperative movement during yielding. Two separate modes, localized and mass shear yielding, work simultaneously in the rubber toughening mechanism. The plane-strain localized shear yielding dominates the toughening mechanism at lower temperatures and brittle failure, while the plane-stress mass shear yielding dominates at higher temperatures and ductile failure. The critical precrack plastic zone volume has been used to interpret the observed phenomenon. © 1994 John Wiley & Sons, Inc.     

Toughening behavior of elastomer-modified polycarbonates based on the j-integral

The J-integral method to determine the fracture toughness of tough and ductile polymeric materials previously developed has been applied to the elastomer-modified polycarbonates. This investigation compares three different methods to obtain Jc: the conventional crack growth length, the stress whitening zone, and the newly developed hysteresis method. Jc values obtained from these three comparative methods are fairly close. The hysteresis method has the advantage over the other two methods of obtaining Jc without requiring the measurement of the crack growth length or the stress whitening zone, therefore avoiding the controversy in defining crack blunting. Results also indicate that the effect of elastomer quantity in polycarbonate on Jc is insignificant as long as the crack is in a stable condition. Higher elastomer contents in polycarbonate result in higher dJ/dΔa, dJ/dΔl, and tearing modulus (Tm). This indicates that the elastomer toughening mechanism is due to the increase of the energy required for crack growth extension. The hysteresis loss energy is directly related to the size of the crack tip plastic zone, and the presence of more elastomer indeed increases the crack tip plastic zone, thus making the polycarbonate tougher. Besides, the presence of elastomer tends to increase the crack initiation displacement and shift the failure modes from an unstable fracture. Jc and the criterion for crack initiation based on rate change of hysteresis energy are discussed in detail.     

Fracture behavior of poly(vinyl chloride)/methyl methacrylate/butadiene/styrene polymer blends

The fracture mode of poly(vinyl chloride)/methyl methacrylate/butadiene/styrene (PVC/MBS) polymer blends can change from ductile to brittle in accordance with the changes in shape of the test specimen or test conditions. Therefore, the mechanisms of impact energy absorption and the main cause of stress whitening are complicated. The following results on PVC/MBS blends were obtained by carrying out fracture experiments at different test speeds and temperatures:

• (1) The ductile/brittle fracture mode of the PVC and PVC/MBS blends can be explained by σ (the craze initiation stress)/σ_y (the shear yield initiation stress), which depends on the strain rates and temperature.
• (2) The fracture behavior of the PVC/MBS blends can be classified into the following types from the standpoints of fracture mode and whitening degree: Fracture I: ductile fracture without whitening; Fracture II: ductile fracture with whitening; and Fracture III: brittle fracture without whitening.
• (3) The following concepts can be estimated from the measurements of yield stress, specific gravity and SEM, TEM and visual observations. In Fracture I, shear yield occurs mainly. In Fracture II, both shear yield and crazing occur. In Fracture III, deformation of the rubber and local crazing occur.
• (4) The main cause of stress whitening in PVC/MBS blends is light scattering by cavities in the rubber particles.
• (5) In Fracture II, at first, crazes with cavities in the rubber particles occur. Then, shear yield occurs. Finally, crazes are healed by the heat, and only the cavities in the rubber remain.

     

Effect of temperature on the compressive stress-strain properties of polystyrene

The compressive stress-strain behavior of a commercial polystyrene has been studied and the effect of deformation temperature on modulus, yield stress, percent yield strain and yield energy was determined. Yield energy is the only one of these parameters that is linear with temperature in the ductile region. A change in the mode of failure from ductile to brittle occurs between 5–30°C at a strain rate of O.1/in./in./min. At all temperatures studied, the yield or fracture stress varied linearly with the rate of deformation for strain rates ranging from 0.1 to 1.0 in./in./min. The yield data as a function of temperature were analyzed via a rate expression modified to incorporate the Coulomb-Navier yield criterion, Activation energy was found to be a function of deformation temperature with a change in slope occurring near the β transition. Activation volume increased linearly with deformation temperature, for the range studied. Agreement of dynamic mechanical and yield activation energies imply that the type of motion and the height of the energy barrier are similar for both. However, an increase in activation volume for stressed vs unstressed conditions suggests that a greater number of chain segments move as a result of stress biasing. Also the increase of both activation volume and activation energy with temperature implies that the correlated length of chain movement increases as temperature is increased. Similar to activation energy, yield stress exhibits a change in temperature dependence near the β transition. Data on other glassy polymers suggest that the highest temperature sub-T_g, transition is related to the change in the temperature dependence of yield stress.     

Rubber-Toughened polymer blends of polycarbonate (PC) and poly (ethylene terephthalate (PET)

The intrinsically impact brittle nature of the PC/PET blends can be effectively toughened by incorporating butylacrylate core-shell rubber. The rubber-modified PC/PET blend possess both excellent low temperature impact properties and reduced notch sensitivity. The ductile-brittle transition temperature of the blend decreases with the increase of rubber content. The presence of rubber in the PC/PET blend does not relieve the strain rate induced yield stress increase. Two separate modes, localized shear yielding and mass hear yielding, work simultaneously in the rubber toughening mechanism. The plane-strain localized shear yielding dominates the toughening mechanism at lower temperature and results in brittle failure. At higher temperature, the planestress mass shear yielding dominates the toughening mechanism and results in ductile failure. The critical plastic zone volume can be used to interpret the observed phenomenon.     

Plastic zone in front of mode I crack in phenolphthalein polyether ketone

The plastic zone size and crack opening displacement of phenolphthalein polyether ketone (PEK-C) at various conditions were investigated. Both of them increase with increasing temperature (decreasing strain rate), i.e. yield stress steadily falls. Thus, the mechanism increasing the yield stress leads to increased constraint in the crack tip and a corresponding reduction in the crack opening displacement and the plastic deformation zone. The effect of the plastic deformation on the fracture toughness is also discussed.     

Correlation between nodular morphology and fracture properties of cured epoxy resins

Various bulk epoxy resin formulations, based on diglycidyl ether of bisphenol A (DGEBA) and cured with diethylene triamine (DETA) were studied. Methods of linear elastic fracture mechanics were employed and all systems were characterized by the corresponding values of the critical strain energy release rate for crack initiation and crack arrest. Fracture morphology was studied by scanning electron microscopy and transmission electron microscopy of carbon—platinum surface replicas. An apparent correlation between morphology and ultimate mechanical properties has been found. All fracture surfaces are shown to be characterized by distinct nodular morphology. Nodules, ranging in size from 15–45 nm, represent the sites of higher crosslink density in an inhomogeneous network structure. Fracture surfaces were further characterized by three crack propagation zones. A smooth, brittle fracture zone was preceded and followed by crack initiation and crack arrest zones, respectively. An apparent plastic flow was confined to the initiation and arrest regions. No crazing phenomenon was seen in the initiation zone; instead a step-like fracture was observed, typified by the ‘flow’ of internodular matrix during step formation. Local plastic deformation in the initiation zone and the corresponding value of critical strain energy release rate, G_Ic, were correlated with the nodular morphology. The size of nodules was found to vary with the curing agent concentration, thus allowing us to establish a fundamental correlation between the nodular morphology and the ultimate mechanical properties of epoxy resins.     

The mechanical performance of cross-plied composites

The mechanical performance of fiber glass epoxy, cross-plied laminates having either ductile or brittle matrices, was evaluated in tension. The laminates with ductile matrices have higher initial strength, slower crack propagation in the transverse layers and higher ultimate stress and strain. In both the ductile and brittle systems, the laminae have higher strength, stiffness and toughness than equivalent unidirectional composites. This improved performance results from the interaction between the perpendicular layers which gives them additional stiffness due to shear and transverse coupling effects and also increases the resistance of each individual layer to crack propagation and plastic flow.     

PA6/CaCO3复合材料的单边缺口拉伸断裂研究

研究了尼龙6(PA6)/CaCO3复合材料的单边缺口拉伸断裂。结果表明,PA6/CaCO3复合材料在拉伸速率为0.1～300 mm/min的缺口拉伸实验中,裂纹扩展均为脆性断裂。断口主要分为塑性屈服变形区和弹性变形区两部分。塑性屈服变形区形貌是以缺口根部为底边的圆弧型,弹性变形区将塑性屈服变形区包围在里面。塑性屈服变形区面积到达临界尺寸后,材料瞬间断裂。断裂后观察到的塑性屈服变形区面积即为在该实验条件下的裂纹源面积。随着拉伸速率增加,其裂纹源面积减小,而弹性变形区域增加,弹性储存能的储存速度增加,在其裂纹源面积较小的情况下即可发生瞬间脆断。     

Internal fracture of notched epoxy resins

The brittle fracture of round-notched epoxy resin bars subjected to plane strain bending has been studied at varying strain rates. Observations of fracture processes and surface morphologies revealed that the internal crack was nucleated at the plastic-elastic boundary when the plastic deformation zone at the notch root reached a certain size. A slip-line field theory allows calculation of the stress components at the plastic-elastic boundary from a knowledge of the location of the internal crack. An analysis of the data concluded that the triaxial stress level ahead of the plastic zone was raised by plastic constraints to an ideal fracture stress which is considerably larger than that of glassy thermoplastics.     

Mechanical evaluation of propylene polymers under static and dynamic loading conditions

The present investigation is concerned with the evaluation of the impact toughness of commercial‐grade Propylene polymers. Conventional impact static stress–strain and static fracture experiments were carried out. Static stress–strain experiments revealed different pattern behaviors among the materials that were reflected in the fracture behavior. Under static conditions, all materials exhibited ductile behavior and crack grew under J‐controlled conditions displaying stress whitening through the whole fracture surface with the sole exception of the homopolymer, which displayed a ductile instability after some stable crack growth. Under dynamic conditions the homopolymer exhibited brittle behavior, the block copolymer exhibited some plastic deformation at the crack tip, and the random copolymer samples exhibited a whitening effect due to voiding and craze formation through the whole fracture surface, indicating that stable crack propagation was occurring. Fracture mechanics tests were analyzed by following different methods, depending on the mode of fracture presented by the polymer. The Normalization J‐method was used under static conditions. The elastic method, the corrected elastic method, and the essential work of fracture methodology were used to characterize brittle, semibrittle, and ductile behavior, respectively. Fracture mechanics parameters arisen from both static and dynamic conditions are compared. © 1999 John Wiley & Sons, Inc. J Appl Polym Sci 74: 2681–2693, 1999     

Dynamical Flow Properties of Single Crystals of Sapphire, I

The tensile deformation of sapphire was studied as a function of the temperature and of the strain rate. The ranges of the two variables were approximately 1200° to 1700°C and 10⁻³ to 10⁻¹in. per in. per minute. The work showed the existence of a relatively sharp temperature transition between completely brittle fracture and massive plastic flow, the specific transition temperature being sensitively related to the strain rate. For the limits of the rate range used, the transition temperature increased from approximately 1270° to 1520°c. In going through a range of only a few degrees of temperature near the transition, it was possible to obtain either no plastic flow on the low-temperature side or a relatively large amount of the order of a 100% extension on the high-temperature side. The stress-strain relation for plastic flow was found to be characterized by a pronounced yield-point drop; i.e., the stress required to initiate macroscopic flow was approximately double that required for subsequent flow. The magnitudes of both the upper and lower yield stresses were temperature sensitive and both decreased approximately exponentially with increasing temperature for a given strain rate. An inverse dependency of a similar kind was found for the effect of strain rate under conditions of isothermal testing. On the other hand, the fracture stress before yielding was found to be essentially independent of both temperature and strain rate, lying in a scatter band of approximately 16,000 to 20,000 psi. As the testing temperature at a given strain rate was lowered, the plastic yield stress therefore rose sharply. The transition temperature between ductile and brittle behavior was interpreted to correspond to the temperature at which the upper yield stress equaled the fracture stress. Since the lower yield stress was only half the upper yield stress, extensive flow then became possible whenever the transition temperature for yielding was exceeded.