Craze development in poly(methyl methacrylate) during stable fatigue crack propagation

In order to obtain a more complete understanding of failure mechanisms in glassy polymers subjected to fatigue loading conditions, craze zone dimensions (i.e., length and thickness at the crack tip) were measured simultaneously with fatigue crack propagation data in poly(methyl methacrylate) (PMMA) by optical interferometry. Since the craze shape was observed to assume a wedge-shaped configuration similar to the one described by the Dugdale plastic strip model, crazing stresses were inferred on the basis of this model. When varying the stress ratio (R = minimum load/maximum load) of the applied cyclic load in the range from 0.1 to 0.7, it was found that both craze length and craze thickness are essentially independent of the R-ratio and can be correlated in terms of the maximum stress intensity factor only. On the other hand, significant variations in craze dimensions with test frequency occurred over the range from 0.1 to 250 Hz. The results are discussed in terms of the viscoelastic nature of the material and a competition between the effects of strain rate and hysteretic heating.     

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.     

Effects of residual stress and orientation on the fatigue of injection molded polysulfone

The tensile fatigue behavior of unnotched injection molded polysulfone specimens has been investigated. The effects of orientation and residual stress were studied by comparing asmolded specimens with annealed or annealed and quenched specimens with a known residual stress pattern. The treatments are shown to have differing effects at high stresses, where failure is by shear yielding and necking, and at intermediate stresses, where failure is by fatigue crack propagation. The geometries of fatigue cracks are described for each case. An attempt is made to separate the effects of crack and craze initiation from crack propagation, and cyclic loading from cumulative time under load.     

Craze initiation,crack growth,and lifetime trends in fatigue of poly(vinylchloride)

The fatigue behavior of pure poly (vinylchloride) (PVC) and a PVC pipe compound has been investigated. Unnotched S-N lifetime, fatigue-crack growth, and craze/crack-initiation data are presented. The data trends, coupled with direct-microscopic observation, suggest that the unnotched-specimen lifetime in fatigue is dominated by the craze/crack-initiation process. This differs from the observed consistency of crack propagation and specimen-lifetime trends in several other polymers, whose failure can be traced to the initiation and growth to instability of a single dominant craze/crack.     

Temperature dependence of craze shape and fracture in poly(methyl methacrylate)

The shape of the craze at the tip of a slowly moving crack has been determined by optical microscopy for poly(methyl methacrylate) over the range of temperatures ?30° to +45°C. In all cases the craze shape can be described by the Dugdale model for the plastic zone at a crack tip. It was of particular interest that the crack opening displacement was found to be constant over the whole temperature range. Fracture toughness values deduced from the craze shape were in good agreement with those obtained directly. Quantitative estimates of the craze stress were obtained and are discussed.     

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.     

模拟压力容器接管的新型十字试板的角裂纹疲劳扩展性能

用新型十字试板进行了双轴载荷下的角裂纹疲劳扩展性能的研究,以模拟压力容器接管处角裂纹的疲劳扩展行为。试板角裂纹尖端的应力强度因子采用三维边界元法计算,裂纹疲劳扩展的形貌变化采用降载勾线法记录。试验结果表明,裂纹疲劳扩展规律与双向载荷比及裂纹初始形状有关,裂纹沿长度方向的扩展速率可以用 Paris 公式表示,但在深度方向则不然。     

Craze shape and fracture in poly(methyl methacrylate)

The shape of the primary craze at the tip of a crack has been studied by optical microscopy for two grades of poly(methyl methacrylate). The craze shapes are compared with the predictions of the Dugdale model for the plastic zone at a crack tip, and used to obtain a quantitative estimate of the craze stress and the effective stress intensity factor. The values of the stress intensity factor are then compared with those obtained directly from fracture toughness measurements.     

Stress analysis around a three-dimensional craze in glassy polymers

Stress analysis around a three-dimensional craze and a three-dimensional craze containing a penny-shaped crack has been made. The craze is treated as a transversely isotropic, oblate spheroid embedded in an isotropic glassy polymer. The craze is assumed to consist of primary fibrils and cross-tie fibrils, such that a penny-shaped crack may form at the central regime of the craze. The craze surface stress, the stress field near the craze tip outside the craze region, and the stress intensity factor in the crack tip are determined by using Eshelby's equivalent inclusion method. Numerical values of the fracture toughness and the stress needed to sever a craze fibril at the crack tip are calculated and the results appear to be in good agreement with the data given in the literature.     

Stress and displacement fields at the tip of a craze containing a crack

Plane elasticity theory is utilized to obtain expressions for the stress and displacement fields at the tip of a craze containing a crack. The craze is modeled as a very thin elliptical inclusion with different elastic properties from hat of the surrounding bulk polymer. Problem is solved by superimposing the solution of a crack problem onto the solution for a uniformly loaded homogeneous craze. Invoking stress free boundary conditions on the crack surface provides a singular integral equation of Hilbert type with a unique solution. Contour lines of constant hydrostatic stress and constant maximum shear stress around the craze tip are shown graphically. These two stress combinations have played prominent roles in a number of proposed craze growth criteria. Results show that even for relatively long cracks within the craze, very little stress enhancement at the craze tip occurs. Only as the crack tip approaches the craze tip does the enhancement become significant, tending to drive the craze region ahead of the crack.     

Time-dependent craze zone growth at a crack tip in polymer solids

By considering the polymer bulk as a linear viscoelastic body and the craze zone at crack tip as a nonlinear damage zone, the control equation for craze zone growth has been derived. It is shown that for a time-independent craze-zone stress, the craze zone would grow only if the crack-tip stress intensity factor is changed. If the crack-tip stress intensity factor remains constant during loading, the growth rate of the craze zone length will be interrelated to the crack-tip stress, the craze zone length and the rate of change of the craze-zone stress. If both the craze-zone stress and the crack-tip stress intensity factor are time-independent, the craze zone length will be constant during the crack growth, which is the case of self-similar crack growth. Moreover, a new stress distribution model in craze zone is presented based on the constructed damage evolution law, and the lengthening and thickening of the craze zone at the crack tip are also formulated. The numerical calculations from the proposed model agree well with the published experimental data.     

Stress analysis of crazes at moving crack tips

Summary The finite element method is applied to contours of craze zones in front of moving crack tips in polymethylmethacrylate (PMMA), measured by interferometry, in order to compute the stress distribution. In contrast to the constant stress assumed in the Dugdale model, a stress distribution is found with a maximum at the crack tip then a sharp decrease and a more gradual decline over the larger part of the craze length. Computed stresses as well as the Dugdale stress increase with increasing crack speed and, hence, decreasing loading time. Generally the results obtained are in good agreement with those already found for growing crazes at stationary crack tips.     

Fatigue-resistant nylon alloys

Crystalline nylon 66 was modified by blending with both an amorphous nylon and a rubbermodified amorphous nylon. The ternary blends exhibit a 50–100-fold decrease in fatigue crack propagation rates, even at rubber concentrations of only 1 or 2%. These same blends do not necessarily exhibit improved impact strength and the examination of a variety of alloys and blends demonstrates that fatigue and impact fracture mechanisms are distinctly different. The fracture surface morphologies indicate that the basic fatigue fracture mechanism of craze coalescence for nylon 66 is not changed by alloying. However, the presence of the rubbery phase leads to cavitation and ductile drawing that retard the craze breakdown and coalescence processes without evidence of crack tip blunting. Surprisingly, the addition of rubber-modified nylon 66 to a nylon 66 matrix does not impart as great an improvement in fatigue resistance as does the miscible amorphous nylon. Also, alloys having improved impact strength are observed to exhibit inferior fatigue resistance. These results demonstrate that the excellent fatigue resistance of crystalline polymers can be improved even further by judicious selection of alloying ingredients optimized specifically for fatigue fracture. © 1994 John Wiley & Sons, Inc.     

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.     

Strain-induced crystallization around a crack tip in natural rubber under dynamic load

The local degree of crystallinity around a crack tip in natural rubber under dynamic load was measured by time-resolved scanning wide-angle X-ray diffraction (WAXD). Using a high-flux synchrotron microbeam, WAXD patterns with less than 20 ms exposure time were acquired while the notched rubber sample was subjected to cyclic dynamic stretching at a frequency of 1 Hz, similar to the loading conditions in tear fatigue experiments. By scanning the continuously cycling sample, a complete crystallinity map at any given strain phase angle was obtained. The crystallinity at the crack tip is considerably reduced compared to static crack tip scans. Further investigations revealed the underlying structural reasons for the well-known relation between R-ratio and crack growth resistance. By performing static crack tip scans on increasingly stretched rubber samples, the mechanisms behind crack deflection and branching were studied.     

Relaxation of stresses in crazes at crack tips and rate of craze extension

The Barenblatt theory of cohesive stresses at crack tips is used to investigate the effect of the relaxation of craze stresses at crack tips on the rate of craze extension. The craze stresses are equated to the cohesive stresses of the Barenblatt theory. The cancellation by the cohesive/craze stress of the singularity that would exist at the crack tip in their absence is assumed to hold for an extending craze. With this assumption, relaxation of the craze stresses produces craze extension, an effect which has been called ‘relaxation controlled growth’ by Williams and Marshall. A general equation relating the rate of change of craze length to the rate of change of stress intensity factor (K₁) and the rate of change of the craze stress is derived. It is argued from this equation that uniform crack growth with a constant craze length can occur only at constant K₁. Using plausibility arguments for the behaviour of the craze stress with time and position in the craze, and assuming a generalized Dugdale model, differential equations for the rate of craze extension with no crack growth are derived for the constant load and constant K₁ cases. These equations relate the rate of change of craze length to the craze stress at the tip of the crack. Assuming a specific form for the time dependence of this stress, the equation for the constant K₁ case is solved to yield an expression for the craze length as a function of time.     

Static fatigue and compressive stress generation in an aged crack

In classic experiments by Michalske and others, it was found that cracks aged statically below the fatigue limit acquired a temporary strength increase compared to the non‐aged crack. In our previous publication we observed that cracks growing near the fatigue limit exhibited a time dependent slowing down of crack growth. Both of these phenomena are related to a toughening of the crack tip that we attribute to a water‐assisted surface stress relaxation mechanism. To test this hypothesis, the K‐v crack growth curves have been measured using the double cantilever beam (DCB) experimental technique for two commercial glasses, a sodium aluminosilicate, and a potassium aluminosilicate, both of which exhibit clear fatigue limits in air. Using polarimetry, it is shown that the stress state near an unloaded but previously aged crack tip is opposite in sign to the stress state near the tip of a crack held in Mode I loading. These results clearly indicate that a stress relaxation mechanism is occurring at the crack tip.     

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.     

Failure analysis of carbon black filled styrene butadiene rubber under fatigue loading conditions

Abstract

The present paper deals with the fatigue crack growth in a carbon black-filled styrene butadiene rubber (CB-SBR) under fully relaxing loading conditions. More precisely, it is devoted to the determination of the scenario of crack growth. For that purpose, an original ‘microcutting’ technique, previously applied by the authors on natural rubber (NR), is used to observe microscopic phenomena involved in fatigue crack growth thanks to scanning electron microscopy (SEM). Results show that the crack tip grows following a tearing line by generating ligaments; it explains the differences between fatigue responses of crystallisable and non-crystallisable rubbers during crack propagation. So, contrary to crystallisable elastomers such as NR, the microstructure of SBR is similar at crack tip and in the bulk material, and the crack tip does not resist crack propagation. Moreover, the morphology of fracture surfaces only depends on particles encountered by the fatigue crack during its propagation.