A Universal Reduced Rupture Creep Approach for Prediction of Long Term Failure Behavior of Aged Glass Polymers from the Short Term Test of Rupture Creep Compliance by the Unified Master Curved Extrapolation

The prediction of long term failure behaviors and lifetime of aged glass polymers from the short term tests of reduced rupture creep compliance (or strain) is one of difficult problems in polymer science and engineering. A new “universal reduced rupture creep approach” with exact theoretical analysis and computations is proposed in this work. Failure by creep for polymeric material is an important problem to be addressed in the engineering. A universal equation on reduced extensional failure creep compliance for PMMA has been derived. It is successful in relating the reduced extensional failure creep compliance with aging time, temperature, levels of stress, the average growth dimensional number and the parameter in K-W-W function. Based on the universal equation, a method for the prediction of failure behavior, failure strain criterion, failure time of PMMA has been developed which is named as a universal “reduced rupture creep approach”. The results show that the predicted failure strain and failure time of PMMA at di?erent aging times for different levels of stress are all in agreement with those obtained directly from experiments, and the proposed method is reliable and practical. The dependences of reduced extensional failure creep compliance on the conditions of aging time, failure creep stress, the structure of fluidized-domain constituent chains are discussed. The shifting factor, exponent for time-stress superposition at differentlevels of stress and the shifting factor, exponent for time-time aging superposition at different aging time are theoretically defined respectively.     

Molecular conformation and craze fracture

A craze may fracture either by the breaking of covalent bonds or by a process of “viscous rupture” involving the movement of bulk material in the craze. In the latter case it is necessary that the majority of the chain ends of the polymer molecules passing through the craze-matrix interface terminate within the craze. We have therefore calculated the probability of a polystrene macromolecule spanning a thin craze and shown that for viscous rupture a craze in a normal commercial polystyrene must be something more than 40 nm thick. As the measured craze thicknesses have generally exceeded 100 nm, a viscous fracture process is clearly possible, though, of course, chain rupture is not excluded by the argument. More difficulties arise when fracture occurs within a specified region of the craze and the possibility of a bond fracture under these circumstances is briefly discussed.     

Relating creep and creep rupture in PMMA using a reduced variable approach

Creep and creep rupture of PMMA at high stresses have been characterized and found to be relatable by use of reduced variables. It is shown that when the creep compliances can be correlated by a superposition principle for which the vertical shift is the ratio of the applied stress to a reference stress and when strain at failure is a constant, a commonly used failure criterion (that the product of the strain rate at failure and the time to failure is constant) becomes valid. The reduced variables approach is found to apply to two greatly different thermal histories. Consistent with the concept of physical aging, the response of a quenched sample is simply shifted along the log time axis to shorter times relative to the response of the aged sample.     

Craze growth and healing in polystyrene

The kinetics of craze growth and craze healing were studied by dark-field optical microscopy in monodisperse molecular weight polystyrene (PS) that varied in molecular weight from 88,000 to 1,334,000. The following observations were made. (1) G₁ the virgin growth rate, decreased rapidly with increasing molecular weight until M_n ～ 200,000 and then remained constant. (2) G₁ decreased with increasing craze density. (3) The growth rates of approaching craze tips decreased when the craze tips overlapped, and the effect was less for crazes whose parallel growth paths were greater than 40 μm apart. (4) Complete craze healing was observed by comparison of the nucleation times, τ₂, and growth rates, G₂, of healed individual crazes with the craze kinetics of the virgin sample. (5) The extent of healing was characterized using four cases in which τ and G were measured as a function of healing time, temperature, constant stress, and molecular weight. (6) Craze healing times were found to increase with molecular weight and were analyzed in terms of the modified molecular weight of the craze zone. (7) Significant bond rupture was determined to occur during crazing by comparison of healing times with stress relaxation and diffusion data. (8) Craze healing studies provide insight into both crack healing and fracture of glassy polymers.     

Energy absorption in polymer crazing

The total energy absorbed by a craze during its development in creep is analyzed and calculated on the basis of a time-dependent theory of crazing. Experimental measurements of the craze length have been utilized in the energy calculations. For polystyrene the initial energy absorption in the craze region is found to be several hundred times that in the uncrazed medium. This ratio decreases sharply in a short period of time to about 50 to 1 and less and remains low afterward. For polycarbonate, somewhat similar behavior has been found. The initial strain energy absorption by crazing is about 200 times that in the uncrazed region. The energy ratio reduces rapidly to about 55 to 1 and tends to level off thereafter. However, in general, the amount of strain energy absorbed does increase as a function of time, as it should.     

Physical and chemical aging in PMMA and their effects on creep and creep rupture behavior

Samples of PMMA were aged at 80°C for between 1 h and 254 days and tested in creep in uniaxial extension at large stresses and at room temperature. Both chemical and physical aging effects were found to be important in determining the failure behavior of the samples. This behavior was found to be describable within the context of a commonly used failure criterion that the time to failure multiplied by the strain rate at failure is constant. The creep behavior was found to follow classical time–aging time and time–stress correspondence principles.     

Fracture behavior of PBX simulation subject to combined thermal and mechanical loads

The fracture behavior and mechanical properties of a Polymer Bonded Explosives (PBX) simulation material were studied using the Digital Image Correlation (DIC) method. The fracture mechanism was analyzed as the material was subjected to combined thermal and mechanical loads. The macroscopic fracture mode changed from mainly shear action to a combination of extension and shear action, whereas the microscopic fracture changed from cleavage fracture and transcrystalline rupture to interfacial debonding, breaking of filler particles and a combination of transcrystalline and intercrystalline rupture. Micro-analysis of the creep properties showed the random nature of initial damage and the interaction between creep, damage and nearby damage, were the main reasons for the local creep strain repetition increase. During the process of high temperature creep, extensive cracks are first formed followed by the initiation and extension of shear cracks, eventually joining and causing a macroscopic fracture within the material. The main microscopic fracture mode has been found to be intercrystalline cracking and binder tearing failure.     

Cyclic stress–strain behavior of the dry polycarbonate craze

Equipment and methods have been developed which allow photomicrographic determination of the stress–strain properties of the individual craze. Serial cyclic tensile tests on polycarbonate crazes are described. Under stress the typical dry polycarbonate craze thickens solely by straining; no adjacent polymer of normal density is converted to craze material. The craze exhibits a yield stress followed by a recoverable flow to roughly 40–50% strain at 6000–8000 psi. On return to zero stress the craze exhibits creep recovery at a decelerating rate. The yield stress and loss factor of each cycle decrease with increasing initial strain and cycles initiating at 50% strain or more show completely Hookean behavior. Creep recovery results in recovery of yield stress and loss factor also. Craze tensile behavior is suggested to be essentially an extension of the craze formation process. Decrease in elastic modulus and yield stress with increasing strain are rationalized in terms of strain-produced decrease in density and resultant increase in stress concentration factor on the microscopic polymer elements of the craze. Polymer surface tension and the large internal specific surface area of the craze are suggested to be important factors in the large creep recovery rates of the craze.     

Mechanisms of fracture in an oriented polystyrene

Fracture surfaces of an oriented polystyrene (by stretching 150% at 280°F) show many of the same features observed in the fracture of ordinary polystyrene: craze formation followed by quasi-viscous separation of the craze layer or by quasi-brittle fracture along the craze boundary. In cleavage fracture along the direction of orientation, advance fractures are initiated in flat areas covered, if at all, by an extremely thin layer of craze: the initiation of the “crazeles” fractures appears to arise from the orientation of the molecules rather than the presence of impurity particles.     

Physical aging of a polyetherimide: Creep and DSC measurements

Creep and differential scanning calorimetry (DSC) measurements have been used to study the physical aging behavior of a polyetherimide. Isothermal aging temperatures ranged from 160°C to T_g with aging times ranging from 10 min to 8 days. The only measurable effect of physical aging on the short-time creep curves is a shift of the creep compliance to longer times. Andrade plots of the compliance versus the cube root of time are linear at short times with the slope β decreasing with increasing aging time to a constant value once equilibrium is reached. Log β³ is related directly to the degree to which the creep curves shift to longer times with physical aging, and is used in this work as a measure of physical aging. A reduced curve of log β³ versus log aging time is obtained for the aging temperatures investigated by appropriate vertical and horizontal shifts. The enthalpy change during aging increases linearly with the logarithm of the aging time, t_a, leveling off at equilibrium at values which increase with decreasing aging temperature. Hence, both nonequilibrium and equilibrium temperature shift factors can be calculated from the DSC data. Good agreement is observed between the equilibrium temperature shift factors obtained from the creep and DSC data. The temperature dependence of the nonequilibrium temperature shift factors is found to be an order of magnitude smaller than that of the equilibrium shift factors. The time scales to reach equilibrium for enthalpy and for mechanical measurements are found to be the same within experimental error. © 1995 John Wiley & Sons, Inc.     

Chain scission in polystyrene by impact fracture

The number of chain scissions n_s per unit fracture area by impact in high-molecular weight polystyrene is determined to be approximately 3.3 × 10¹⁴/cm² at room temperature. This is almost 20 times larger than would be expected if chain scissions took place only at, or very close to, fracture surfaces. This result was obtained by measuring the molecular weight decrease and the total fracture area of the impact fragments by using size exclusion chromatography and statistical particle size measurements, respectively. The large n_s strongly indicates that significant chain breakage occurs during crazing before the propagation of cracks. An average craze thickness before breakdown under impact is estimated from n_s to be around 2 μm. In a diluted polymer, n_s is found to be significantly lower than the extrapolated value, assuming a linear dilution of entangled chain crossings at the fracture surface. This low chain scission density, however, can be explained by taking into account the reduction of craze breakdown strain in the diluted polymers. Finally, the broken chain ends of polystyrene appear to be stable under ambient conditions. © 1992 John Wiley & Sons, Inc.     

微量稀土对奥氏体耐热钢高温力学性能的影响

研究了微量稀土对Cr21Ni11N奥氏体耐热不锈钢高温热塑性及高温持久性能的影响.结果表明:在750～1250℃范围内,稀土显著提高耐热钢的热塑性,消除800℃的塑性低凹区,扩宽安全热加工温度范围近75℃.稀土显著延长耐热钢的高温持久寿命约3～5倍,并提高持久断裂塑性.钢中添加稀土后,其蠕变断裂机制由楔形裂纹为主的机制逐渐转变为空洞裂纹为主的机制,高温持久断口附近的楔形裂纹明显减少,且断口呈典型的韧窝状塑性断口特征.     

The effect of preliminary orientation of polymers via tensile drawing at elevated temperature on solvent crazing

We studied how the preliminary orientation of an amorphous glassy PET via its uniaxial tensile drawing above the glass transition temperature affects the deformation behavior during subsequent tensile drawing in the presence of adsorptionally active environments. The tensile drawing of the preoriented PET samples with a low degree of preliminary orientation (below 100%) in the presence of liquid environments proceeds via the mechanism of solvent crazing; however, when a certain critical tensile strain is achieved (150% for PET), the ability of oriented samples to experience crazing appears to be totally suppressed. When the tensile drawing of preoriented samples is performed at a constant strain rate, the craze density in the sample increases with increasing degree of preliminary orientation; however when the test samples are stretched under creep conditions, the craze density markedly decreases. This behavior can be explained by a partial healing and smoothening of surface defects during preliminary orientation and by the effect of entanglement network. The preliminary orientation of polymers provides an efficient means for control over the craze density and the volume fraction of fibrillar polymer material in crazes.     

Dependence on strain rate of the nucleation of cracks in polystyrene at 293°K

The processes associated with the deformation and fracture of polystyrene tested in uniaxial tension have been studied over a range of strain rates from 1.4 × 10^?2 to 4.3 × 10^?7 sec^?1 and at constant stresses between 4.1 and 2.9 kg/mm². The effect of strain rate on the surface craze distribution prior to fracture, the fracture stress, the mechanism of nucleation of cracks, and the nature of fracture surfaces associated with slow and fast crack propagation have been determined. The changes in fracture surface appearance have been studied using optical and stereoscan microscopy. The observations are consistent with the model presented in a previous paper. Fracture is preceded by craze formation, cavitation in the craze, coalescence of cavities to form large planar cavities which propagate slowly until a critical stage is reached at which fast crack propagation occurs. The effect of changes of strain rate and material variables on these processes is discussed.     

Effect of ionic additives on deformation behavior of bisphenol a polycarbonate

The deformation behavior of bisphenol A polycarbonate containing only a small amount of oligoionomeric additives in the range of a few parts per hundred parts of resin was examined. The impact strength of polycarbonate markedly decreased as the content of additive increased, and brittle fracture of polycarbonate was observed in tensile tests when the concentration of additive was above 2.5 phr. The ductile‐to‐brittle transition that was determined using a comparison of the critical shear yield stress and the critical craze stress appeared to exist in the range of 2.5–3.5 phr of additive. The measured entanglement density was also found to decrease significantly with the addition of a few parts per hundred parts of resin of additives, and the change of the dominant deformation mechanism from ductile to brittle failure was recognized as a result of the change of the entanglement density of polycarbonate. Therefore, it was concluded that the presence of a small amount of ionomeric additives caused the loss of entanglement density that induced transition of the deformation mechanism of polycarbonate from ductile to brittle failure and led to the corresponding deterioration of impact strength. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2635–2643, 2001     

梯形交变加载作用下聚碳酸酯的应变与寿命

对聚碳酸酯在交变 持久载荷复合作用下应变与寿命研究表明 ,其疲劳 蠕变曲线与纯蠕变曲线十分相似 .加载时间周期越短和交变载荷变化越频繁 ,普弹应变阶段的斜率和应变越小 ,进入延迟弹性变形的平台应变阶段越早 .随每一次循环中的最大载荷加载保持时间延长 ,聚碳酸酯断裂寿命减小 .以最大载荷为恒载荷一直加载的纯蠕变曲线 ,平台最高 ,断裂时间最早 .而最大载荷加载作用时间为 0的纯疲劳曲线 ,平台最低 ,断裂时间最迟 .在交变 持久载荷复合作用下聚碳酸酯存在疲劳和蠕变的交互损伤 ,其断裂寿命N Nf 和 ∑t tr比纯疲劳或纯蠕变的断裂寿命低 ;断裂寿命减小 .并且 ,疲劳 蠕变的交互损伤程度与温度密切相关 .聚碳酸酯在较低温度的疲劳 蠕变交互损伤作用大于较高温度的交互损伤作用 .随温度升高 ,疲劳 蠕变断裂寿命下降是疲劳和蠕变各自的单独损伤增加所致     

The optical interference pattern in a polystyrene craze layer

In the interference pattern seen in monochromatic light reflected from a craze layer in polystyrene, the bright fringes are of alternating intensity. The phenomenon is explained in terms of a four-beam interference. Apart from the two reflections from the outer surfaces of the craze layer others arise from a thin layer of approximately constant thickness within the craze layer at its median plane. The phenomenon provides independent evidence to support the electron microscopic observations of the microstructure of crazes in polystyrene.     

Effect of temperature on the rupture behavior of highly stretchable acrylic elastomer

Dielectric elastomer has been recently explored extensively to make diverse soft actuators and energy harvesting devices. The lack of study on the rupture behavior under the influence of temperature hinders further applications where heat generation and accumulation are unavoidable. In this paper, an experimental study has been carried out to investigate the effect of temperature on the rupture behavior of acrylic dielectric elastomer. By using VHB 4910 films with and without an initial crack, the fracture energy at different temperature and stretch rate is measured by pure shear test. The storage modulus and phase angle have been investigated by dynamic mechanical analysis (DMA). The images of defects and rupture surface are provided by scanning electron microscope (SEM). It is found that the stretch at rupture is insensitive to the temperature for both pristine and precut samples. In addition, the maximum nominal stress and fracture energy linearly decrease with environmental temperature, especially at high stretch rate. Furthermore, we measure the stretch at rupture for rectangular strips with a single edge-notch under uniaxial tension and compare them with the theoretical prediction using nonlinear fracture mechanics based on the measured fracture energy. The results obtained in this paper will give a reference to the engineering design and applications of dielectric elastomer, especially for those working at different temperatures.     

Properties of fracture surfaces of glassy polymers: Chain scission versus chain pullout

Fresh fracture surfaces formed by tensile failure of craze in molded polystyrene (PS) bars have been compared with the molded surfaces of the same bars, using an atomic force microscope with a thermal probe and operated in local thermal analysis. The results indicate that molecular weight is much higher in the interior of the sample than at the surface. No evidence was found for degradation of the PS chains via chain scission during crazing. Alternative explanations for the low‐molecular weights at the molded surface are discussed. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2010     

Crazing in two polystyrene/polybutadiene block copolymers

Crazing was investigated in two commercial polystyrene/polybutadiene block copolymers made by the Phillips Petroleum Co. and marketed under the trade names of KRO-1 and KRO-3 resins. The two block copolymers each with 23% polybutadiene (PB), have radically different microstructure and radically different crazing behavior, leading to strains to fracture of 0.1 and 1.0, respectively. Of these, the KRO-1 Resin has a phase microstructure that consists of randomly wavy and often interconnected rods of PB of 20 nm diameter surrounded by polystyrene (PS). The microstructure of KRO-3 Resin consists of lamellae of PB with 20 nm thickness and large aspect ratio which range in packing from regular aligned lamellar domains with randomly varying misorientation in the annealed material, to randomly corrugated and wavy sheets in the as-received material. Crazes in KRO-1 Resin have well delineated planar shapes with a conventional, tufty craze matter structure which suggests growth by the now well-established meniscus instability mechanism proposed by one of us. In KRO-3 Resin, on the other hand, crazing involves profuse cavitation if the PB lamellae, giving rise to less well delineated zones of cavitational growth dispersed over the volume and suggests a mechanism of craze growth by stable, interfacial cavitational degradation in a process zone ahead of the craze tip. The measured stress and temperature dependences of craze velocities in these two polymers is in partial support of the suggested mechanisms which are also developed in outline.