Craze Tip Research Articles

On the interaction between a full craze and a near-by circular inclusion in glassy polymers

Abstract Crazing is the common reason in polymer composites to cause failure. So far research work on craze phenomenon has been done only in homogenous polymer materials. The first time in our current study, the stress analysis has been carried out on the interaction between a circular inclusion and a full craze in polymer composites. A craze can be treated as a crack with fibrils bridging the two crack surfaces. The forces applied by the bridging fibrils to the crack surfaces (pulling the two surfaces closer) depend on the crack opening displacement, while the crack opening displacement is directly related on the forces applied by the bridging fibrils. To solve this dilemma, an iterative procedure is created and introduced to solve the formulated singular integral equations. The influences of the inclusion's elastic properties on the craze thickness profile and the stress intensity factors are investigated in details. It is found that the case with a “stiffer” inclusion produces smaller craze thickness. Also, the craze thickness profile is strongly affected by the inclusion size and the craze-inclusion distance. The shielding effect of a stiffer inclusion on the craze is discussed by evaluating the stress intensity factors at both craze tips.

New criterion for craze initiation

Existing criteria for craze initiation are reviewed, and their limitations are discussed. The most obvious problem is that they are formulated simply in terms of principal stresses, making no provision for the known effects of small inclusions and surface imperfections. To solve this problem, a new criterion is proposed, which is based on linear elastic fracture mechanics. Craze initiation is treated as a frustrated fracture process rather than a yield mechanism. Calculations show that the strain energy release rate, G I(nasc), required to generate a typical 20 nm thick nascent craze, is less than 1 J m −2. This explains why flaws less than 1 μm in length are capable of nucleating crazes at stresses of 20–30 MPa. Subsequent craze propagation is dependent upon two flow rates, one relating to fibril drawing at the craze wall and the other to shear yielding at the craze tip. Under biaxial stress, the second principal stress σ 2 affects craze tip shear yielding but not fibril drawing. This model is used in conjunction with the von Mises yield criterion to derive a new expression for the crazing stress σ 1(craze), which provides a good fit to data on visible crazes obtained by Sternstein, Ongchin and Myers in biaxial tests on cast PMMA [Sternstein SS, Ongchin L, Silverman A. Appl Polym Symp 1968;7:175; Sternstein SS, Ongchin L. Polym Prepr Am Chem Soc Div Polym Chem 1969;10:1117; Sternstein SS, Myers FA. J Macromol Sci Phys 1973;B8:539].

The deformation mechanism of polyphenylquinoxaline films

The deformation mechanism of polyphenylquinoxaline (PPQ-E) film has been studied by theoretical prediction and microscopic observation. The entanglement density, estimated from the plateau modulus on the dynamic mechanical property curves, was used to predict the deformation mechanism of PPQ-E. Polarized light microscope (PLM) was used to observe the morphology of the PPQ-E film during tensile deformation. It is found that the deformation mechanism of PPQ-E is both crazing and shear yielding, which is in agreement with the prediction by entanglement density. The craze morphology of PPQ-E is mainly of fibril craze consisting of micro-fibrils and micro-voids as observed by transmission electron microscope (TEM). The interface between the bulk and craze is distinct. Multiple crazes, blunting of craze tips and homogeneous deformation zones have also been observed.

Micromechanical and thermodynamical aspects of environmental crazing

The present study aims 1) to investigate theoretically the relation between the craze microstructure and the basic materials parameters such as the yield stress and the surface energy and 2) to provide a detailed thermodynamic treatment of a single isolated craze in glassy polymer tested in an aggressive liquid environment. Based on the assumption that the craze tip is somewhat blunted by small scale yielding and on the Taylor meniscus instability as the mechanism responsible for the propagation of the leading edge of the craze, the detailed micromechanical analysis is used to provide estimates of the critical opening displacement of the craze for growth initiation, mean fibril spacing, mean fibril diameter and fibril volume fraction at the craze tip. The influence of aggressive liquid environments on the yield stress and the surface energy is discussed together with predicted changes in the craze microstructure. The thermodynamic analysis starts with the recognition that induced high negative pressures around the craze tip can increase the solubility of a liquid at this site by several orders of magnitude. As a consequence the local density of thermodynamic potential drops significantly. This unbalanced fall in thermodynamic potential provides an additional driving force for the craze advance. It is shown that a corresponding release of external load is required to preserve the overall balance of the specimen with craze.

Three-dimensional interaction of crazes and micro-shearbands in PC-SAN microlayer composites

The three-dimensional interaction of crazes and micro-shearbands in co-extruded microlayer sheets with 49 alternating layers of polycarbonate (PC) and styrene-acrylonitrile copolymer (SAN) was investigated as a function of the relative layer thickness. The deformation processes were observed when microspecimens were deformed under an optical microscope. Deformed specimens were sectioned and examined further in the transmission electron microscope. Two types of craze were observed in the SAN layers: surface crazes initiated at a strain of about 1.8% and gradually lengthened to a maximum of 70 μm when they were arrested by micro-shearbands at 4.2% strain, while tunnel crazes appeared above 4.2% strain and rapidly grew through the entire SAN layer. Surface crazes did not prevent yielding and stable neck propagation, while tunnel crazes were responsible for fracture prior to neck formation. The density of surface crazes relative to tunnel crazes increased as the PC-SAN ratio increased or as the strain rate decreased. The surface crazes stimulated micro-shearbanding in both PC and SAN layers. After micro-shearbands initiated in the PC layers where the craze impinged on the PC-SAN interface, they propagated rapidly along the edges of the craze. As they overtook the craze tip, the micro-shearbands penetrated through the PC-SAN interface and continued around the craze tip to entirely engulf the craze. This terminated craze growth, and further strain in the SAN layer was accommodated by shear deformation.

The craze‐tip deformation zone in PC/SAN microlayer composites

AbstractCrazing in styrene‐acrylonitrile copolymer (SAN) layers of polycarbonate (PC)/SAN microlayer composites and the deformation zone that formed in the PC layer in response to the stress concentration created at the PC/SAN interface by the craze tip were examined by optical and scanning electron microscopy. A 49‐layer composite with relatively thick layers, on the size scale of tens of microns, was chosen in order to confine interactions to the region of a single PC/SAN interface. The SAN craze density, which increased with applied stress, was shown to fit the Weibull distribution function. The distance between crazes was described by a correlation length, and the distribution of correlation lengths indicated that crazing occurred randomly in the SAN layers. In the PC layer, the crazetip deformation zone consisted of a colinear plastic zone together with a pair of microshearbands that grew away from the craze tip at an angle of about 45°. Assuming a blunted craze tip, the plastic zone was analyzed using the slip‐line field theory. The dependence of the micro‐shearband length on remote stress was similar to that predicted by both the BCS and Vitek models. © 1994 John Wiley & Sons, Inc.

Mechanisms of interactive crazing in PC/SAN microlayer composites

AbstractMechanisms are proposed for the two types of interactive crazing that have been observed in PC/SAN microlayer composites when the PC layer thickness is on the micron‐size scale. It is demonstrated that when the PC layer is thin enough the deformation zone that forms at a craze tip can interact with the next‐neighboring SAN layer. By measuring the dimensions of the craze tip in scanning electron micrographs, it was found that the craze‐tip opening does not depend on the SAN layer thickness, i.e., the length of the SAN craze. Consequently, the size and shape of the resulting plastic zone in the PC layer are also independent of layer thickness. The zone that forms in the PC layer consists of a colinear plastic zone together with a pair of micro‐shearbands that grow at an angle of about 45°. When the PC layer is less than 6 μm, the elastic stress concentration from the colinear plastic zone increases the probability of crazing in the neighboring SAN layer with the formation of craze doublets that consist of two aligned crazes in neighboring SAN layers. By taking into consideration the Weibull distribution of crazing, a craze doublet fraction comparable to the 30% observed experimentally was predicted with a stress intensification factor in the range of 1.03–1.05. When the PC layer thickness is less than 1.3 μm, the length of the colinear plastic zone is comparable to the PC layer thickness. Formation of a craze at the point of impingement of the plastic zone on the neighboring SAN layer leads to craze arrays with many aligned crazes in neighboring SAN layers. At higher strains, the micro‐shearbands grow through the PC layers and extend into several adjacent SAN and PC layers. This produces a change in deformation mechanism in the SAN layers at the yield instability, from craze opening to shear yielding. © 1994 John Wiley & Sons, Inc.

Stress analysis around a three‐dimensional craze in glassy polymers

AbstractStress 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.

Analysis of the internal crazes in notched SAN

AbstractCrazing in styrene–acrylonitrile copolymer (SAN) under a triaxial stress state was examined. The damage zone that formed ahead of a semicircular notch under slow tensile loading consisted of two kinds of crazes: internal notch crazes that grew out from the notch root and discontinuous surface crazes. Examination of the damage zone in the optical and scanning electron microscopes revealed that the internal notch crazes sometimes extended through most of the thickness but never penetrated the free surfaces, whereas the surface crazes penetrated about 10–50 μm inward from the surface. Initially, the internal craze tips defined a crescent‐shaped zone. The plane strain elastic stress distribution at the zone boundary satisfied a constant mean stress condition, and the critical mean stress for craze tip growth was determined to be about 35 MPa. This value varied slightly for different resins but was independent of thickness. Propagation of the internal notch crazes occurred in a straight line parallel to the minor principal stress vector at the point of origin on the notch surface, whereas the surface crazes followed the minor principal stress trajectories. The presence of the internal notch crazes resulted in significant stress redistribution, the stress redistribution was described quantitatively using both the deviation of the craze trajectory from the minor principal stress trajectory, and the deviation of the zone shape from the critical elastic mean stress condition.

Environmental stress cracking of PVC: Effects of natural gas with different amounts of benzene

Craze initiation, craze growth and ultimate fracture were studied in PVC (Polyvinylchloride) and PVC-CPE (PVC blend with 10% chlorinated polyethylene) under a constant load in air and in natural gas enriched with benzene. The craze initiation results are similar for PVC and PVC-CPE. The craze initiation stress is decreased dramatically at high benzene concentrations (≥ 25000 p.p.m.). Preferential and enhanced sorption of benzene molecules near surface inhomogeneities, the craze initiators, are held responsible for this phenomenon. Initial crazegrowth rates in natural gas enriched with benzene increase compared to those in air. However, in all the environments studied, a limited logarithmic craze growth is observed, and growth seems limited to this constant logarithmic interval. The logarithmic craze growth and the termination of craze growth are attributed to a reduction of the stress at the craze tip. The failure mode of PVC and PVC-CPE in air and in gas with 5000-6000 p.p.m. benzene is yielding. A brittle branch appears in the failure curve (failure stress against loading time) in the more concentrated benzene vapours. This branch is attributed to a reduction in the stability of the crazes. © 1991 Chapman & Hall.

A model of fibril deformation in crazes

AbstractA theoretical model is proposed to describe quantitatively the steady‐state deformations of fibrils in crazes. In the model, the total force is represented as the sum of high elastic, plastic (actually, nonlinear viscous), and surface tension forces; the first two being modeled by using elongational rheology and the third represented in exact form. The model description is reduced to a boundary value problem for a second‐order ordinary differential equation describing the profile of fibrils. This problem results in an energy balance which, in turn, leads readily to a thermodynamic description of the equilibrium conditions for the deformations of homogeneous fibrils far from the interface (z → ∞). Two possible regimes of fibril deformation were found, depending on the periodicity of the fibrils in the craze. The first is Paredes and Fischer's regime of static deformations of fibrils under action of elastic forces and surface tension where the periodicity is determined by the condition for the static regime to exist. The second is Kramer's drawing regime where the fibril periodicity is found from the Fields and Achby maximization of craze tip advance speed. The choice between these two regimes is made to minimize the complete Gibbs' free energy including surface tension for the equilibrium state of fibrils at z → ∞. The model predicts that the static regime usually appears under moderate stresses and changes for the drawing regime when stresses increase. Hence, this model solves the contradictions between the static and drawing approaches proposed in literature. Examples of both the static and drawing regimes of fibril deformations are demonstrated and some comparisons with data are represented.

Measurements of the craze-bulk interfacial active zone

The width of the active zone, a region of strain softened material at the craze-bulk interface, was measured as a function of temperature in polystyrene (PS) using a gold decoration technique. Thin trilayer films of PS (total thickness 0.6 μm) with a central layer of buried gold “islands” were made. The films were strained at a controlled rate and various temperatures. When the films crazed, the gold particles act as markers which reveal the deformation of the PS. The strain in the PS could be seen in transmission electron microscopy (TEM) as a change in areal density of the gold particles. The width of the active zone was determined by measuring the distance between the edge of the change in areal density of the gold particles and the craze-bulk interface. It was found that the width of the active zone was a function of the distance behind the craze tip at room temperature. The width of the active zone was ∼10 nm at the craze tip and increased linearly to a value of ∼25 nm at a distance 250 to 300 μm from the craze tip. The active zone width was independent of the distance from the craze tip for distances greater than 300 μm. The active zone width at the craze tip is in good agreement with previously reported results. The higher strain rates at the craze tip are believed to be responsible for the change in the width of the active zone as a function of distance behind the craze tip. The active zone width increased linearly with increasing temperature from 25 nm at room temperature to 60 nm at 93 °C. The increase in the active zone width can be accounted for by the decrease in strain softening of PS at higher temperatures.

Correlation between craze formation and mechanical behaviour of amorphous polymers

The formation, growth and fracture of crazes have been studied for several amorphous polymers (PS, PMMA, SAN, NEC, PC). From bulk polymeric materials 0.5 to 5μm thick sections were prepared and investigated after uniaxial deformation or duringin situ deformation in a 1000 kV high voltage electron microscope (HVEM). The use of the HVEM also allows one to study irradiation-sensitive polymers (PMMA and PC). The size of crazes (length and thickness), the shape (opening angle at the craze tip, craze thickness profile), the thickness of a pre-craze zone, the structure of the material inside the craze (fibrillar or more homogeneous), and the degree of deformation were measured. Correlations have been found between the type and the size of crazes and their mechanical properties, particularly fracture toughness and elongation at break. There are notable differences between unannealed and annealed samples (SAN and PC) as well as in the craze formation and in the fracture toughness.

Thickness effects in microlayer composites of polycarbonate and poly(styrene-acrylonitrile)

Coextruded microlayer sheet consisting of alternating layers of polycarbonate (PC) and styrene-acrylonitrile copolymer (SAN) exhibits improved properties such as toughness and ductility as the number of layers is increased. In this study, the composition was kept essentially constant, as was the sheet thickness at 1.2 mm, and the layer thickness was changed by varying the total number of layers from 49 to 776. All the compositions exhibited macroscopic yielding in uniaxial tension but the fracture strain, which represents neck propagation, increased with the number of layers. The increased ductility was attributed to a transition in the microdeformation behaviour observed when microspecimens were stretched in the optical microscope. When the layers were thicker, individual layers exhibited behaviour characteristic of the bulk, that is SAN crazed or cracked while shear bands initiated in PC from the craze tips. As the layer thickness decreased, crazing or cracking of the SAN was suppressed and shear bands that extended through several layers produced shear yielding of both PC and SAN. Calculations showed that when the layer thickness is sufficiently small, impingement of a PC shear band on the interface creates a local shear stress concentration. As a result the shear band continues to grow through the SAN layer and subsequently, at the point of instability, shear yielding can occur in both PC and SAN layers.

ＰＭＭＡ中を高速進展するき裂先端付近の開口変位測定

Pulsed holographic microscopy was applied to take an instantaneous microscopic photograph of a rapidly propagating crack in PMMA. The crack was in the opening mode and its speed was at several hundred m/s. The crack and craze opening displacement, which are both called COD, were measured as a function of distance r from the craze tip within the region of r up to 8mm. The crack opening displacement was nearly proportional to √r, while the craze opening displacement deviated from the curve of √r. The crack tip opening displacement (CTOD) was determined from the measured COD data, and the dynamic stress intensity factor KI(v) was also obtained. Furthermore, the value of J-integral was calculated by assuming small scale yielding. It happens that cracks which have the same KI(v) value and crack speed show different COD profile in the craze layer.

The stress and strain fields in the neighbourhood of a notch in polyethylene

The stress and strain fields were determined in the neighbourhood of a sharp notch in a single edge-notched tensile specimen. The effects of notch opening, distance from the notch and unloading the specimen and the difference between plane stress and plane strain were investigated. From the measurements of the strain field, the stress was inferred directly from the stress-strain curve of the material. In general, the stress field is fairly uniform between the notch and the craze tip, in good conformity with the assumption of the Dugdale theory. Complexities in the strain field arise from the stress concentration at the corners of the bottom of the notch and from the characteristics of the craze.

Solvent‐induced embrittlement in a crystallizable polyarylate

AbstractThe effects of solvent‐induced crystallization on the micromechanical properties of thin films of polyarylate (PAr) were studied. Under uniaxial extension amorphous polyarylate was observed to deform exclusively by shear deformation with no evidence of crazing. Upon exposure to methylethyl ketone, vapor, or liquid, PAr crystallizes and is subsequently embrittled. Our transmission electron microscopy results clearly show that this embrittlement results from a transition in plastic deformation mechanism from shear yielding to crazing. A detailed examination of the samples revealed that the crazes formed preferentially within the noncrystalline regions and that the craze tips followed a complex trajectory around the crystallites. In some cases the craze tip advance deviated by as much as ±30 from a direction normal to the tensile axis. Because crazes are inherently more susceptible to forming cracks than shear deformation zones, crystallization reduces the fracture toughness of the polymer. This type of embrittlement, via a transition in plastic deformation mechanism, is believed to be a general behavior for solvent‐crystallizable thermoplastics.

Craze yielding and fracture mechanism in PE/PS/PE laminated films

Mechanical behaviour of laminated films of PS and PE, especially the altered mechanical properties of PS in the laminated state, were studied as functions of PE volume fraction. It was observed that crazing in PS can be modified by laminating layers of PE to both sides. Elongation at break and hence fracture energy increased conspicuously when PE volume fraction increased. Craze yielding stress in PS layers also increased with increasing PE volume fraction because craze formations in PS layers were suppressed by the reduction of tensile stress concentration effect at craze tips. Craze initiations were always found at the free side edges of the laminated films, which can be correlated with the transverse interlaminar shear stress concentrations existing at the edges of the laminated films caused by the difference in Poisson's ratios between PS and PE.

A Nonlinear Analysis of an Equilibrium Craze: Part I—Problem Formulation and Solution

This study investigates the effect of nonlinear cohesive forces on crack growth with the special problem of craze mechanics in mind. The work is presented in two parts. In the first and present one, we develop a numerical method for determining the equilibrium shape of a craze in an infinite elastic plane whose fibrils exhibit very general nonlinear force-displacement (P-V) behavior, including strain softening characteristics. The second part of this study deals with the numerical simulation of craze and crack growth (Ungsuwarungsri and Knauss, 1986).1 The problem formulation is based on the superposition of the relevant elasticity Green’s function and the solution for the resulting nonlinear problem is effected by using Picard’s successive approximation scheme. Both field equilibrium and the Barenblatt condition for vanishing stress and strain singularities are satisfied simultaneously, rendering the craze tip profile cusp-like. The formulation allows the stress distribution profile and the corresponding P-V relation to be computed from experimentally measured craze/crack displacement contours; it also allows the computation of the craze or crack/craze profile if the P-V relation, far-field load, and craze or crack size are specified. Numerical investigations indicate that only certain classes of the fibril P-V relations are consistent with measured craze profiles. In addition, it is found that for a given P-V relation, nontrivial solutions exist only for certain ranges of craze lengths.

Craze growth and healing in polystyrene

AbstractThe 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 Mn ∼ 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.