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.     

Stepwise fatigue crack propagation in poly(vinyl chloride)

The kinetics and mechanism of fatigue crack growth in poly(vinyl chloride) (PVC) compounds of different molecular weight were studied. The fatigue crack propagation rate of all the PVC compounds followed the Paris law: da/dt = A_f ΔK. Fatigue crack propagation rate, as reflected by the pre‐factor A_f in the Paris law, was highly dependent on molecular weight of the resin, strain rate, and temperature. A stepwise mechanism of fatigue crack propagation was observed in all the PVC compounds. Steps were formed by discontinuous growth of the crack through a single craze in the shape of a narrow strip. Step length and lifetime were used to characterize fatigue crack propagation. J. Vinyl Addit. Technol. 10:5–10, 2004. © 2004 Society of Plastics Engineers.     

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.     

Shear and craze competition in subcritical fatigue crack growth: Fatigue lifetime inversions

In some ductile amorphous polymers, the fatigue lifetime behavior can exhibit two distinct crack propagation modes: a craze dominated sub-critical discontinuous crack growth mode, which leads to a low stress, short fatigue lifetime branch and a shear fracture mode, which produces a higher stress, long lifetime branch. When both branches coexist, the fatigue lifetimes at higher stress amplitudes are often longer than those at lower stress amplitudes! This unusual lifetime inversion has been explored for a polyestercarbonate at various temperatures, frequencies, degrees of physical aging, and fatigue overload histories.     

A stochastic approach for continuous and discontinuous crack growth in polycarbonate under cyclic loading

This article presents a stochastic approach to predict fatigue crack propagation (FCP) diagrams of continuous crack growth (CCG) and discontinuous crack growth (DCG) in polycarbonate (PC) under cyclic loading. First, it is assumed that the macroscopic fatigue crack propagates stochastically. The transition probability is then expressed in conjunction with the craze fibril breakdown model for CCG. Second, the stochastic process is applied to DCG assuming that DCG occurs because of an unstable crack growth in the craze zone. A fracture criterion using a stress intensity factor is introduced for the unstable crack growth. As a result, we obtain an FCP diagram where the rate in CCG is lower than that in DCG. The stress intensity factor range for the DCG–CCG transition can be theoretically determined. Finally, to verify the present approach, the experimental data of DCG and CCG of PC are fitted to the Paris equation. In addition, the relationship between the DCG band size and the number of cycles required for DCG is predicted in order to compare it with the experiment data. POLYM. ENG. SCI., 2013. © 2013 Society of Plastics Engineers     

The effects of frequency on fatigue threshold and crack propagation rate in modified and unmodified polyvinyl chloride

The cyclic fatigue crack behavior of polyvinyl chloride (PVC), with (PVC‐M) and without (PVC‐U) chlorinated polyethylene (CPE) impact modifier, was studied. The effect of impact modifier upon fatigue crack growth rate and threshold was evaluated at frequencies of 1, 7, and 20 Hz. It was shown that the addition of CPE lowered the threshold stress intensity factor amplitude for crack growth (ΔK_th) of PVC‐M compared to that of PVC‐U at lower frequencies, and that the effect became more pronounced at lower frequency. At lower stress intensity factor amplitudes (below ΔK = 1 MPa·m^1/2), there was a slight difference between the crack growth rates of U‐ and M‐PVC. The crack advance mechanism is investigated by microscopic observation of the crack tip process zone. Although the zone is relatively large in PVC‐M, associated with higher toughness, it did not improve the fatigue crack growth resistance significantly. Fracture surface observations reveal a higher density of fibrils on the fatigued surface of PVC‐M with the density, relative to that observed in PVC‐U, reducing with frequency. It is therefore hypothesized that accelerated fibril failure is a mechanism of fatigue. POLYM. ENG. SCI., 2009. © 2009 Society of Plastics Engineers     

Size and mechanical properties of craze zones at propagating crack tips in poly(methyl methacrylate) during fatigue loading

In specimens of high molecular weight poly(methyl methacrylate) the microregion at the crack tip has been investigated during fatigue crack propagation by applying the optical interference method in a specially constructed experimental set-up. Thus, in the frequency range of 0.4 to 50 Hz the size and contour of the craze zone were directly measured at upper and lower load of the cycles. In contrast to previous assumptions it is established that the maximum craze width at the crack tip and hence the maximum length of stretched fibrils increases strongly with crack propagation rate. The directly measured craze data and also the material parameters indirectly derived by the aid of the Dugdale model are related to those data which have been measured during continuous crack propagation under quasi-static tensile load. The spacings of the fatigue striations on the fracture surfaces are compared with the lengths of the craze zones.     

The effects of water and frequency on fatigue crack growth rate in modified and unmodified polyvinyl chloride

A study of the influence of water environments on the cyclic fatigue crack behavior of polyvinyl chloride (PVC), with (PVC‐M) and without (PVC‐U) chlorinated polyethylene (CPE) impact modifier was undertaken and compared with corresponding results in air. Two frequencies of 1 and 7 Hz were applied to assess the influence of frequency on the fatigue behavior; a higher fatigue resistance and threshold were obtained with increasing frequency. This trend is more significant in water. However, in this environment, the fatigue resistance deteriorated under conditions of higher stress intensity factor amplitude (ΔK) and frequency. The fatigue properties of PVC‐U are the most affected by the presence of water, particularly at low frequency and higher ΔK. Examination of the fracture surface showed the interaction of water molecules and the PVC matrix with the formation of (1) a nodular structure, close to the fatigue threshold and (2) plasticized structures at high ΔK, which are associated with a greater threshold value and fatigue resistance. The absorption of the water retarded the fibrillation of craze and caused crack blunting effects. Water functions as a plasticizer, particularly at high ΔK, through the formation of the plasticized structures. Results are compared with those observed from an in‐service failure. POLYM. ENG. SCI., 2009. © 2009 Society of Plastics Engineers     

Diffraction studies of craze structure

Recent work using small angle scattering techniques to study craze structure is reviewed. Three different radiations, electrons, X-rays, and neutrons were used to study four problems in the area. These were (1) the structure of crazes in thin films, (2) the structure of a single craze/crack in a bulk material, (3) the effect of organic environments, and (4), the effect of mechanical fatigue on craze structures. It is shown that the high intensity of a synchrotron source permits the examination of the process of growth and breakdown of a single craze in polystyrene and also the study in real time of the short- and long-term changes during fatigue of crazes. The H/D neutron contrast effects for neutrons were used to study environmental crazes with the environment still present.     

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.     

氧化锆增韧陶瓷的室温动态疲劳

用动态疲劳试验法研究了３Ｙ－ＴＺＰ和３Ｙ－ＴＺＰ／Ａｌ_２Ｏ_３（２０ｗｔ％）陶瓷在空气中的室温动态疲劳，并讨论了疲劳慢裂纹扩展特性。另外利用动态疲劳数据对两种陶瓷的平均寿命进行了预测。两种陶瓷材料在室温下均存在着慢裂纹扩展，主要是由空气中水蒸汽的应力腐蚀所造成的，且裂纹是沿晶界玻璃相扩展的。相变诱发的表面压应力和裂纹尖端的正应变可提高疲劳抗力。在８００ＭＰａ应力作用下，３Ｙ－ＴＺＰ和３Ｙ－ＴＺＰ／Ａｌ_２Ｏ_３（２０ｗｔ％）的平均寿命分别为２４ｍｉｎ和７２ｈ，平均寿命随应力的增大而缩短．     

Stress cracking of rigid polyvinyl chloride by plasticizer migration

Environmental stress cracking (ESC) (failure caused by crack and craze formation at a stress less than the yield stress) reduces the service life of many plastic products. This paper is concerned with ESC of rigid PVC products which are in contact with a plasticized PVC material. The ESC affect (as measured by elongation to break) is reduced at faster strain rates and by higher plasticizer viscosity, which suggests a mechanism requiring flow of plasticizer into a growing craze. Well fused (gelled) PVC made at a higher melt temperature slowed but did not eliminate environmental stress cracking. Rubber impact modifier added to the rigid PVC had no effect on ESC. Environmental stress cracking can be avoided by using flexible PVC that has a non-migrating plasticizer or by designing the product so that rigid PVC is not stressed while in contact with plasticized PVC.     

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.     

塑料管道失效分析及寿命预测的研究进展

综述了慢速裂纹增长（SCG）和快速裂纹增长（RCP） 2种常见的塑料管道失效模式,详细阐述了塑料管道的失效机理及寿命预测方法,线弹性断裂力学、标准外推法、弹塑性断裂力学、银纹机理等,并分析了各方法的局限,指出了塑料管道寿命预测理论还不成熟,方法还不完善,有待进一步研究。     

Statistical Analysis of the Fatigue Life Distribution of Monolithic Silicon Nitride

Cyclic fatigue testing of silicon nitride ceramics was performed at a frequency of f = 150 Hz and a stress ratio of R = 0.1 using a piezoelectric bimorph fatigue device. Based on the method proposed by Fett and Munz, a fatigue crack growth diagram ( K ₁– V diagram) was estimated from fatigue lifetime distribution data. A change in the slope of the K _I– V diagram was observed. A statistical analysis for predicting the lifetime of ceramics exhibiting a transition in a K _I– V diagram was devised on the basis of this observation. Analytical results obtained with this method showed good agreement with experimental data.     

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.     

ABS/GF疲劳裂纹扩展的研究

通过对(丙烯腈/丁二烯/苯乙烯)共聚物(ABS)/玻璃纤维(GF)复合材料疲劳裂纹扩展速度研究,得到ABS/GF复合材料在不同应力和振动频率下疲劳性能随GF填充量变化的趋势.结果表明,高频(0.85 Hz)低应力(0.8 kN)条件下,GF对裂纹的扩展具有阻滞作用,其中GF质量分数为20%时ABS/GF复合材料疲劳性能最好;低频(0.25 Hz)高应力(1.6 kN)条件下,试样疲劳性能最差,疲劳周次均在2000次以下,加入GF有利于裂纹的扩展.     

Fatigue behavior of medium-density polyethylene pipes

A round bar specimen and a square bar specimen cut out from medium-density polyethylene pipes with a notch were made and a fatigue test was conducted to cause a brittle fracture. The initiation and growth of a craze and crack at the tip of a notch was observed. In the range where loading cycles are few and displacement of the specimen does not increase, the craze prior to crack initiation occurs. Also, the effect of frequency was investigated. The pure creep failure and the fatigue failure at low frequency were compared. The lower the frequency, the smaller the reciprocal of the actual loading time T_f becomes. It is also found that this tensile fatigue test is a useful test method to assure the quality of pipes.     

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.     

Effect of residual stresses on fatigue crack growth behavior of aluminum substrate repaired with a bonded composite patch

Composite patches bonded to cracked metallic aircraft structures have been shown to be a highly cost-effective method for extending the service life of the structures. The fatigue crack growth behavior of pre-cracked 7075-T6 aluminum substrate with the 12.7-mm V-notch crack repaired with boron/epoxy composite patches was investigated. 1-ply, 2-ply, 3-ply and 4-ply composite patches were studied. The residual stresses due to mismatch of the coefficients of thermal expansion between the aluminum plate and boron/epoxy composite patch were calculated based on the classical equation. The effects of the residual stresses and patch layers on fatigue lifetime, fatigue crack growth rate, and fatigue failure mode of the repaired plates were examined experimentally. A modified analytical model, based on Rose's analytical solution and Paris power law, was developed for this research. This model considered the residual stress effect and successfully predicted the fatigue lifetime of the patched plates. Results showed that the composite patch had two competing impacts on the structure. The composite patch could cause residual tensile stress in the aluminum substrate, which could consequently increase the crack growth rate. Moreover, reinforcement with the composite patch could also retard the crack propagation in the aluminum plate. If a 4-ply composite patch was used, it resulted in high residual stresses and effectively would not extend the fatigue lifetime of cracked aluminum plates.