M. L. Williams

Reaction‐Rate Model for Fracture in Polymeric Fibers

Electron paramagnetic resonance (EPR) techniques were used to determine the number of free radicals produced during deformation leading to fracture of nylon 6 fibers. A reaction‐rate molecular model is proposed to explain some of the deformation and bond‐rupture behavior leading to fracture. High‐strength polymer fibers are assumed to consist of a sandwich structure of crystalline‐block and amorphous‐flaw regions along the fiber axis. In the flaw regions, tie chains connecting the crystalline blocks are assumed to have a statistical distribution in length. These chains are, therefore, subjected to different stresses. The length distribution was determined by EPR. The probability of bond rupture was assumed to be controlled by reaction‐rate theory with a stress‐aided activation energy and behavior of various loadings determined by numerical techniques. The model is successfully correlated with experimental stress, strain, and bond‐rupture results for creep, constant‐rate‐of‐loading, and cyclic‐stress tests.

The Effects of Plasticity in Adhesive Fracture

Abstract From the viewpoint of continuum mechanics, and particularly the energy concept of fracture, adhesive and cohesive failures are similar. The essential difference involves the interpretation of the energy required to create new (adhesive or cohesive) surface area. This fracture mechanics approach has in the past been applied to a number of different elastic problems. In this investigation an elastic-perfectly plastic analysis for adhesive failure of a beam is presented. This analysis accounts for the energy dissipated during plastic bending. Experimental results with 6061-T6 alumimum are presented as evidence of the validity of the approach.

The Relation of Continuum Mechanics to Adhesive Fracture

Abstract From the standpoint of continuum mechanics, there is an essential similarity between cohesive and adhesive failure. Continuum mechanics can, therefore, be used to analyze adhesive fracture including certain cases of interfacial debonding, by applying an extension of the Griffith energy balance concept. Present researches permit a consideration of the influence of material behavior such as viscoelasticity and geometric parameters such as interlayer bond thickness. These advances and quantitative predictions of failure are reviewed with special reference to the characteristic adhesive fracture energy, new or applicable test methods, and its connection with the association between macro- and micro-constitution of the media. Various testing methods for determination of the adhesive fracture energy are discussed. A pressurized bubble or blister at the interface is shown to have certain advantages. Experimental results from various materials using this test will be presented as confirmation of the model.

The influence of loading direction upon the character of adhesive debonding

Abstract Adhesive fracture surfaces have a topology that is affected by the type or mode of applied loading that induced the separation. In fracture mechanics these modes are commonly designated as I, II, and III, identified primarily with normal separation, sliding shear, and rotational shear, respectively. When the energy per unit area required to create new fracture surface, e α (ergs/cm 2 ) is measured, it is common practice to associate this area with the projected fracture area on the fracture plane irrespective of the actual surface topography. Hence the ratio of actual to projected fracture area introduces a perhaps artificial variation into the deduced value of fracture energy, which otherwise might turn out to be more of a universal (time-temperature dependent) quantity, independent of mode of loading. The paper describes the qualitative SEM fractrographic analysis conducted for adhesive debonds between polyurethane and polymethylmethacrylate. This analysis tends to explain part of the apparent differences in e α when deduced from different loading modes, and hence should put us closer to relating the continuum mechanic deductions for e α to more fundamental parameters of the molecular systems.

A reaction rate model for deformation and fracture in polymeric fibers

SummaryA model to describe bond rupture and fracture in polymeric fibers is described. An experimentally determined distribution in stresses is incorporated with absolute reaction rate theory in the model to predict bond rupture. Model predictions are compared with experimentally determined fracture and free radical concentrations for various loadings. The experimental parameters in the model are discussed and their “best fit” values given. In general, these values are found to compare quite satisfactorily with accepted values from theory or other tests in the literature.

Cohesive-Adhesive Fracture in a Pressurized Double Blister

Abstract If two infinite sheets of different elastic properties are bonded together by an adhesive material of even different elastic properties except for an unbonded strip of width 2a into which pressure is introduced, adhesive fracture can occur by unbonding between the adhesive and either of the two sheets, of cohesive fracture can arise from an unstable flaw within the adhesive. This paper describes an approximate analysis through which the critical applied pressure and preferred locus of fracture initiation can be estimated as a function of the geometrical and mechanical properties of the three layers involved.

Fatigue‐Fracture Growth in Linearly Viscoelastic Material

Based upon the thermodynamic formulation for linearly viscoelastic fracture developed earlier, an extension has been made to fatigue fracture resulting from repeated (oscillatory) load applications. The theoretical analysis of internal spherical‐flaw growth, due to a uniformly distributed radial oscillatory input of displacement, predicts a growth‐rest cycle whose characteristics depend upon the mechanical properties of the medium. The results for this idealized problem are compared to experimental data for crack growth in a precracked sheet specimen subjected to oscillatory displacement input, and a qualitative similarity is observed. It is therefore believed that the analytical model is representative, and its study can reveal the main features of macroscopic flaw growth.

An experimental investigation of some models of polymer fracture

It has recently been shown that the techniques of EPR spectroscopy can be used to monitor atomic bond rupture during fracture of polymeric materials and thus provide important new insights of the molecular mechanisms of fracture in these materials. In particular, this method can be used as a fundamental check of the several atomistically-derived theories of polymer fracture. In this paper such a check is made of two representative such theories, those of S. N. Zhurkov and W. G. Knauss. It is shown that these theories do not provide physically realistic models of the fracture mechanisms in oriented polymeric fibers and it is suggested that their lack of relevance is due to the unique morphological structure of highly oriented polymers.RésuméOn a montré récemment que les techniques de spectroscopie électronique a résonnance paramagnétique peuvent être utilisées avec succès pour la detection des ruptures des liaisons atomiques au cours de la rupture des matériaux polymeres; ces techniques ont permis de jeter de nouvelles lumières sur les mécanismes moléculaires qui interviennent au cours de la rupture de ces matériaux.En particulier, la méthode permet de procéder a un controle, sur une base fondamentale, de quelques théories atomiques de la rupture des polymères.Dans le présent mémoire, on procède à un tel controle de deux théeories des plus typiques, celles de Zhurkov et de Knauss.On démontre que ces theories ne conduisent pas à des modèles physiquement représentatif du mécanisme de rupture des polymères à fibres orientées. On suggère que cette inadaptation résulte de la structure morphologique particulière des polymères à orientation marquée.ZusammenfassungNeuerdings wurde gezeigt, daß die Verfahren der elektronischen Spektroskopie erfolgreich für den Nachweis von Zerstörungen in den atomaren Bindungen während des Zerreissens von Polymeren herangezogen werden können. Sie führen somit zu wichtigen neuen Erkenntnissen über die molekularen Mechanismen der Zerstörung dieser Werkstoffe.Im besonderen kann dieses Verfahren für eine grundlegende Kontrolle verschiedener atomistisch abgeleiter Theorien über den Bruch von Polymeren herangezogen werden. Im vorliegenden Bericht werden zwei dieser Theorien, nämlich diejenigen von S. N. Zhurkov and W. G. Krauss, überprüft.Es wird gezeigt, daß these Theorien kein physikalisch realistisches Modell des Bruchmechanismus von Polymerfasern geben, and es wird vorgeschlagen diesen Mangel an Zutrefflichkeit durch die spezielle morphologische Struktur der streng gerichteten Fasern zu erklären.Major portions of this work were supported by the National Science Foundation and the National Aeonautics and Space Administration.

Electron paramagnetic resonance investigation of molecular bond rupture due to ozone in deformed rubber

Abstract Electron paramagnetic resonance (EPR) provides a sensitive tool by which microscopic bond rupture can be monitored simultaneously with observations of macroscopic deformation and failure. Past techniques for studying fracture in semicrystalline polymers have been extended to investigate degradation of unfilled ruber in the presence of ozone. It was found that the rate of free radical production was linearly proportional to stretch ratio and ozone concentration and that stress relaxation and creep were not directly proportional to this production rate. The latter behavior was attributed to the particular dependence of crack density and growth on stress. It was concluded that at low strains, comparatively few surface cracks form; however, at higher strains, many more crack centers become active. Although many more surface cracks are present, they do not progress into the material as rapidly. Therefore, although more bonds were broken at higher strains and stresses, the stress relaxation rate and cr...

Electron Paramagnetic Resonance Measurements of Strain Induced Ozone Cracking in Rubber

An electron paramagnetic resonance (EPR) method for monitoring the rate of atomic bond rupture in rubber subjected to uniaxial tensile strain in an ozone environment is described. The free radicals so formed are found to be quite stable and present in large, easily detectable concentrations. The initial rate of bond rupture was found to be approximately proportional to ozone concentration at fixed strain. Below a prestrain of three percent, no effect of the ozone environment was detected; above this threshold, the rate of rupture increases with strain up to strains of approximately 20 percent. It appears that this EPR technique is very sensitive and can yield information not readily obtainable by more conventional techniques.