Failure mechanisms in polyolefines: The role of crazing, shear yielding and the entanglement network

Macroscopic deformation and failure modes of polyolefines are reviewed in terms of deformation and failure models based on the craze initiation and propagation model of Kramer-Berger and the craze-crack transition model of Kramer-Brown. Although these models were formulated for amorphous polymers they are also valid for semi-crystalline polymers. The important role of the underlying molecular entanglement network in this approach is reflected by the strain hardening behaviour which is shown to be a robust measure for predicting slow crack growth performance. The polymer network response explains the experimentally observed presence of two Brittle-Ductile transitions, one at low temperature or high strain rates, linked with chain scission which dominates crazing, the other at elevated temperatures or low strain rates which involves disentanglement crazing. The relation between these two Brittle-Ductile transitions and the major transition temperatures for molecular mobility such as the glass transition and the crystal α relaxation temperature are discussed. Valid strategies for increasing the crack propagation resistance in polyolefines are reviewed. Finally an outlook for further research to complement the present knowledge base is formulated.     

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.     

Role of surface chain mobility in crazing

Thin film experiments have shown that glassy thermoplastics exhibit enhanced molecular mobility across a 10 nm surface layer. This study examines its relevance to crazing. Surface mobility produces a steep yield stress gradient, which constrains the growth of plastic zones from surface flaws. During tensile tests, stresses in these zones increase until the bulk specimen either yields or fractures. Polycarbonate can sustain rising local stresses and strains without damage because its chains have relatively small cross-sectional areas, but high stresses in polystyrene produce chain scission, accelerated relaxation and cohesive failure. The partially degraded plastic zone breaks down to form craze fibrils, an internal necking process that is repeated during craze propagation and fibril drawing. In combination with the linear elastic fracture mechanics model for craze initiation, constraints on yielding around symmetrical surface flaws account for the strong dependence of critical tensile crazing stress σ_1cz on the second principal stress σ_2cz in biaxial tests.     

Crazing in polypropylene

The subject of crazing in crystalline polymers is reviewed and specific consideration given to crazing in polypropylene (PP). Tensile tests conducted over a wide spectrum of temperatures and strain rates indicate that, for a given test temperature, there exists a critical strain rate above which crazing is the dominant deformation mode of PP. Similarly, for a given strain rate, there exists a critical temperature which demarcates crazing from shear yielding as the characteristic process of deformation. High deformation rates and low temperatures favor crazing, while low rates and high temperatures favor shear yielding. Crazes in crystalline PP were found to be morphologically similar to those in glassy polymers: high reflectivity, large area-to-thickness ratio, and planarity. They have a higher tendency to bifurcate than those in glassy polymers. Two types of craze fibrils could be identified: those parallel to σ₁₁, and the randomly oriented interconnecting fibrils. It is demonstrated that microtome-trimming at low temperature followed by suitable chemical treatment is an effective technique of sample preparation for SEM examination of craze morphology in crystalline polymers. Further evidence has been provided that crazes in spherulitic polymers do not in general follow an interspherulitie path, but propagate through spherulites. The length of a craze in PP is not restricted to one spherulite diameter, nor does it grow radially.     

Measurement of the residual mechanical properties of crazed polycarbonate. I: Qualitative analysis

A new technique to quantify the bulk craze density of transparent plates was used to characterize the craze growth behavior of polycarbonate at various stress levels. The craze growth rates were found to exponentially increase with an increase in stress, obeying the Eyring equation for thermally activated processes in the presence of an applied stress. The residual mechanical properties of crazed polycarbonate were then correlated to the crazing stress, relative craze density and strain rate. The results show that increasing the bulk craze density does not affect the yield stress but decreases both the failure stress and ductility of polycarbonate. Also, a crazing stress of 40 MPa was found to cause a much larger degree of degradation of failure properties than a crazing stress of 45 MPa. Correlating the crazing stress to the craze microstructure revealed that fewer, larger crazes form at the lower crazing stress. Therefore, flaw size has a greater effect on the failure properties of polycarbonate than flaw quantity.     

Crazing within glassy occlusions in rubber particles of toughened glassy polymers: a micromechanical investigation

The possibility that crazing initiates within glassy occlusions in rubber particles of toughened glassy polymers has been explored theoretically. A micromechanical analysis of the stress distribution and of some craze initiation factors has been performed using an elementary, single particle model. The results show that this possibility falls within theoretical predictions, if dilation is assumed to be the dominant factor in craze initiation criteria.     

Craze fibril formation and breakdown

As crazes grow in areal extent they also increase in width. The areal growth involves craze tip advance which has been shown to occur by the Taylor meniscus instability. Craze widening, at least for air crazes, occurs by drawing more fibrillar material from the craze-bulk polymer interfaces at essentially constant extension ratio. Simple arguments will be given to predict the scale of the fibrillation in terms of the stress S at the craze tip and interfaces and an effective polymer surface energy (Γ) where: which assumes that all entangled chain crossing the surface are broken [γ represents the van-der-Waals (intermolecular) surface energy, d is the entanglement mesh size, v_E is the entanglement density, and U_b is the energy required to break a single backbone bond]. These arguments also give the rate of fibrillation as a function of S, a nominal plastic resistance σ_y and Γ and can explain the fact that the stress for crazing increases relative to that for shear deformation as the entanglement density of the polymer is increased. The geometrically necessary entanglement loss (either by scission as assumed above or by disentanglement- at temperatures just below T_g) that accompanies fibril formation has important consequences for fibril stability. The probability p that a given entangled chain is lost can be computed from simple geometrical considerations knowing the fibril diameter D, its extension ratio λ and the mesh size d; p increases rapidly as Dλ^½ becomes comparable to or less than d. These concepts can be tested in blends of high molecular weight polymer with chains of the same polymer that are too short to entangle.     

Study on viscosity of polymer melt flowing through microchannels considering the wall‐slip effect

For polymers with long, complicated, branched chains, it is difficult to measure the real shear viscosity and slip velocity, using the capillary rheometer based on the adsorption–desorption mechanism. In this study, a double‐barrel capillary rheometer was used to investigate the viscosities of four polymers including polypropylene, high‐density polyethylene, polystyrene, and polymethylmethacrylate in a microchannel. A general model of polymer viscosity based on the entanglement–disentanglement was presented. The proposed model is important in understanding the mechanism of wall slip. This general model can be transferred to the other different models when changing the parameters. Actually, the entanglement–disentanglement model can also be transformed to the adsorption–desorption model. Using the model, it was found that the viscosities of polystyrene and polymethylmethacrylate were reduced with decreasing die diameter, and the slip velocities were increased with the increase of shear stress which agrees well with polymer microrheology based on the microscale effect. For polymers with long, complicated, branched chains, the proposed model improves the accuracy of the calculated viscosity and gains the real slip velocity when polymer melt flows through a microchannel. POLYM. ENG. SCI., 2012. © 2012 Society of Plastics Engineers     

The stress and displacement fields at the tip of crazes in glassy polymers

This analysis models a craze region in glassy polymers as an elastic transversely isotropic homogeneous inclusion of thin elliptical shape with different elastic properties from the bulk polymer. The plane elasticity problem for an applied uniform stress field is solved and the results dimensionalized with respect to the craze tip radius. Stress and strain enhancements of several times far field values are found to occur at the craze tip and are independent of craze tip radius. These results are consistent with experimentally observed characteristics of craze growth and should be important in assessing the relative merits of different criteria that have been proposed for craze growth in glassy polymers.     

The detergent stress-cracking of polythene

Whenever the fracture of a polymer is preceded by crazing or other types of cavity formation, energy must be supplied both for local yielding and for the generation of a new surface. However previous calculations for rigid glassy polymers have shown that the surface energy contribution required for the formation of a craze, compared with that associated with plastic and elastic strains is small. In order to study this problem further, we have now made a finite element analysis of the cavitation of an elastic-plastic solid introducing a surface energy term. This shows that the ratio of the plastic energy requirement to surface energy depends, not unexpectedly, on (I) the ratio of yield stress/ surface tension and (II) cavity size. Thus for polymers with a low yield stress such as polythene, the surface tension becomes significant if the hole diameter is below 100 nm. In these circumstances crazing and cracking is predictably accelerated by dilute aqueous detergents which do not need to penetrate the polymer, provided of course that the detergent has access to the cavities. Hole growth also depends on the extent of orientation hardening during plastic strain and this contributes to the greater stress crack resistance of high molecular weight polythene. The occurrence of a larger amount of plastic deformation on the fracture surfaces of high molecular weight polymer has been demonstrated by Harman for high density polythene and is confirmed here in scanning electron micrographs of low density material. Other electron micrographs show that very small cacities are indeed formed when high density polythene is broken in the coventional detergent stress cracking test, thus accounting for the accelerating effect of the detergent.     

Craze initiation in glassy polymers - Revisited

In spite of the continued interest in the yield, flow and fracture behavior of glassy homopolymers and the important role that crazing plays in their ultimate mechanical response, the basic understanding of the molecular level processes that govern craze initiation still remains murky. Here we revisit some early experiments of Argon and Hannoosh of the 1970s on craze initiation in homo polystyrene under combinations of both deviatoric shear stress and mean normal stress and also take note of more recent computer simulations of ultimate plastic flow and cavitation response of model glassy polymers. We then formulate a new craze initiation model and compare its predictions with the earlier experiments to find much better agreement over a wider range of applicability that sheds new light on this hitherto inadequately understood phenomenon.     

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.     

An investigation of brittle failure in ductile,notch-sensitive thermoplastics

Brittle failure, a significant design issue for plastic components subject to impact loads, is especially catastrophic when the material is normally ductile. Such behavior is not adequately understood relative to the micromechanisms, controlling parameters, and design consequences in plastics. Previous work has identified the process of crazing as being relevant to these failures in thermoplastics. The relationship between crazes generated through mechanical loading and subsequent brittle failure of amorphous thermoplastics is discussed and the hypothesis that the craze event is a necessary but insufficient condition for brittle failure is employed. Emphasis is focused upon the engineering prediction of craze formation and its use as a conservative brittle failure criteria for defining geometric details to prevent brittle failure. First, a series of experiments using one geometry is applied to study the concept of crazing as a precursor to brittle fracture in the two amorphous polymers polycarbonate and polyetherimide. Second, three-dimensional finite element analyses are used to assess the effects of changes in geometric detail upon the continuum stress state and eventual failure of the specimen for these two materials.     

Schädigungskriterien glasiger polymer im hinblick auf deren schlagzähmodifizierung

In rubber-modified, stiff and brittle polymers an applied stress generates multiaxial stress concentrations in the matrix material at the rubber interface and initiates a large number of limited regions of plastic deformation. In order to understand this toughening mechanism, one needs a certain knowledge of the kind of plastic flow which is initiated within a glassy polymer according to the type and amount of stress, the so-called failure criteria. Unlike criteria which apply to the onset of shear flow, craze criteria are still contro-versially discussed in the literature. Argon has suggested a theoretical criterion of bulk crazing. Sternstein et al. have studied experimentally the surface crazing of PMMA. Based on experimental results of Rehage and Goldbach and ourselves, calculations have given the following results: The Sternstein criterion, measured and formulated for surface crazing under the condition of plain stress has till now been incorrectly transformed for use in principal stress space. Correctly transformed, it deviates strongly from Argon's criterion in the range of states of stress with large portions of hydrostatic tension. The Sternstein criterion obviously lends itself to describing multiaxial corrosion. For rubber-modified systems, however, one needs bulk craze criteria, for which no experimental results exist. Preliminary results show that these can more easily be estimated for PS than for PMMA. These two polymers therefore show markedly different shapes of the failure surfaces.     

Stress-strain behavior of the craze

The constitution and properties of crazes in glassy polymers and their relation to crack propagation are reviewed. New evidence is discussed which shows the craze to be much softer than the parent polymer but capable of sustaining large stresses and strains up to the point of failure. Craze failure is much more dependent on polymer molecular weight than is craze formation, and this difference is reflected in changes in both fracture surface morphology and crack toughness with molecular weight. Finally craze mechanical properties are thought to be integrally related to the mechanical behavior of high impact plastics.     

A possible mechanism for cross-tie fibril generation in crazing of amorphous polymers

A possible mechanism for cross-tie fibril generation in crazes of amorphous polymers is proposed. Detailed finite element calculations are performed on an axisymmetric model of a single fibril inside the craze. These calculations suggest that the hydrostatic stress inside the fibril is large enough to cause cavitation and subsequent growth of initial imperfections inside the fibril. The calculations demonstrate that these cavities will then grow by local plastic flow around them, leading to a continuous network of main fibrils interconnected by cross-tie fibrils.     

Chain structure,phase morphology,and toughness relationships in polymers and blends

We present chain structure, phase morphology, and toughness relationships in thermoplastic polymers and polymer/rubber blends. In neat polymers, molecular aspects of craze/yield behavior are controlled by two chain parameters: entanglement density ν_e and characteristic ratio C_∞. The crazing stress is proportional to ν, and the yield stress is proportional to C_∞. The dispersed rubber toughens a polymer/rubber blend mainly by promoting energy dissipation of the matrix. The toughening efficiency correlates with the rubber phase morphology and the chain structure of the matrix.     

A criterion for craze formation

A general criterion for craze formation is presented. Crazes are deformation zones that are common to both glassy and semicrystalline polymers. Crazes are composed primarily of fibrils. This paper attempts to describe the process that transforms unoriented glassy and semicrystalline polymeric solids into a fibrous state. The criterion for crazing discussed is a local phase transition. The transition occurs at the draw temperature. Unoriented solid-phase macromolecules, at local high-stress regions, undergo a transition to the elastomeric phase. Rapid extension and accompanying resolidification produce the fibrous morphology of craze fibrils. Cavitation of the deforming rubber phase ocurs because the local length increase is riot compensated for by an overall area decrease. Craze formation in glassy polymers has long been suspected to involve a local solid-to-rubber phase change. To relate crazes in glassy and semicrystalline polymers, one can assume that a solid-to-rubber phase change is required to produce craze fibrils in semicrystalline polymers. The transient melt phase would undergo rapid elongation, causing the formation of extended chain crystallites. These subsequently nucleate the remaining melt, which then crystallizes epitaxially as lamellae. Crystallization during flow would, therefore, be the mechanism of fiber formation.     

Deformation and entanglement in semicrystalline polymers

Transmission electron microscopy and optical studies of thin films of isotactic polystyrene (iPS) and polyoxymethylene (POM) provide evidence for a distinction between crazing mechanisms in semicrystalline polymers above and below T_g. In the latter temperature regime, deformation in iPS and POM crystallized at high supercooling has been discussed in terms of existing models for crazing in amorphous glassy polymers, based on entanglement ideas. Above T_g, where the difference in mechanical behavior of the amorphous and crystalline regions becomes marked, the fibrillar nature of local deformation appears to be a consequence of the inhomogeneity of the undeformed polymer.     

Micro-drawing of glassy polybenzoxazole rigid rods and the molecular interactions with carbon nanotubes

The high-temperature (T_g > 650°) wholly aromatic polybenzoxazoles (PBO) polymer chains in thin films underwent elastic energy release via local deformation of crazing when stretched beyond a critical strain around 0.5%. The strain localization in the ultra-rigid polymer was quickly superseded by craze fibril breakdown, triggering catastrophic fracture at low extensions below ～3%. Although the drawing stress of craze fibrillation, determined to be ～3 GPa, was insufficient to separate chains in PBO crystallites, it forced the chains in the amorphous regions to flow into large molecular deformations (～300% strain) at room temperature. The poor craze fibril stability of the rigid-rod chains was enhanced dramatically when surface-functionalized single-walled carbon nanotubes (SWCNTs) were dispersed into the polymer. No toughening effects were observed, however, for multi-walled carbon nanotubes (MWCNTs) although the elastic enhancement leading to increase of strain delocalization was still operative. The toughening selectivity was attributed to the PBO/CNT load transfer coupling during nanoplastic flows in which only the CNTs of compatible bending moments permitting fibril drawing were allowed to participate.