Failure of spheroplastics under axial tension and hydrostatic compression

The problem of determination of the external pressure and axial tensile force, which fail spheroplastics — a structurally inhomogeneous material consisting of hollow glass microspheres of different diameters, the latter being distributed in a random manner in a continuous epoxy matrix — is examined.Translated from Problemy Prochnosti, No. 9, pp. 59–61, September, 1990.     

Discrete element modelling of unidirectional fibre-reinforced polymers under transverse tension

The mechanical behaviour of unidirectional fibre-reinforced polymer composites subjected to transverse tension was studied using a two dimensional discrete element method. The Representative Volume Element (RVE) of the composite was idealised as a polymer matrix reinforced with randomly distributed parallel fibres. The matrix and fibres were constructed using disc particles bonded together using parallel bonds, while the fibre/matrix interfaces were represented by a displacement-softening model. The prevailing damage mechanisms observed from the model were interfacial debonding and matrix plastic deformation. Numerical simulations have shown that the magnitude of stress is significantly higher at the interfaces, especially in the areas with high fibre densities. Interface fracture energy, stiffness and strength all played important roles in the overall mechanical performance of the composite. It was also observed that tension cracks normally began with interfacial debonding. The merge of the interfacial and matrix micro-cracks resulted in the final catastrophic fracture.     

Failure behaviour of particulate-reinforced aluminium alloy composites under uniaxial tension

Tensile tests were carried out at room temperature on 6061-aluminium alloy reinforced with SiC and Al₂O₃ particulates. Although a significant increase in strength could be achieved by introducing ceramic reinforcements into the aluminium alloy matrix, it is associated with a substantial decrease in fracture strain. In order to understand the reason for the inferior ductility of such composites, analytical solutions were obtained using a simple composite model. SEM studies were carried out on the side surfaces of the fractured specimens to verify the proposed failure behaviour. Failure modes observed to operate in such composites under uniaxial tension are described.     

Stability of void growth in an incompressible solid under uniaxial tension and shear

Stability of a growing single prolate spheroidal cavity in linear elastic incompressible solid is considered. It is shown from the classical theory of elasticity that a single void becomes unstable in pure shear loading. Considering finite incremental deformation of the matrix in the presence of a void, it is proved that a prolate spheroidal cavity can become unstable under the application of an uniaxial initial tensile stress. The applied tensile stress produces only a pure torque on the void for such unstable (internal shear buckling) mode of deformation. For an incompressible solid, the condition of instability in shear loading depends entirely on the shape of the spheroid (i.e. the ratio of major axis to minor axis). On the contrary, in uniaxial tension, there exists a single shear property of the material which decides the instability for a given void size. Plane strain longitudinal (and radial growths of the void are also studied considering finite simple shear and finite pure shear deformations. These theoretical analyses are in excellent agreement with the experimental observations of other people.     

Failure of pultruded GRP single-bolt tension joints under hot–wet conditions

An experimental study of the effects of hot–wet conditions on the load carrying capacity of pultruded GRP (glass reinforced plastic) single-bolt tension joints has been carried out. The bolted joints were failed in tension after being immersed in water at three temperatures for two periods of time. Two joint geometries, defined in terms of end distance and width to bolt diameter, were tested with the pultrusion and tension axes coincident. The reductions in the load capacities of the joints due to the hot–wet conditions were quantified and shown to be very large. For example, it was found that more than 60% of the load carrying capacity of a single-bolt tension joint was lost after being immersed in water for 6.5 weeks at 60 °C. This temperature is lower than the manufacturer’s recommended maximum service temperature for this type of pultruded GRP material.     

Hydrostatic extrusion of solid polymers

Hydrostatic extrusion of a high density polyethylene rod was carried out. Both the process of plastic deformation during hydrostatic extrusion and the changes of properties of the polyethylene with extrusion were studied. Particular attention was paid to the process of molecular orientation and the destruction of the original lamellae. To obtain a better understanding of the deformation process, the lateral dimension of crystallite and the long period were obtained from the X-ray diffraction data. Furthermore, the influence of extrusion conditions on the structure and properties of the extrudate were investigated. The Vickers hardness number and thermal shrinkage of the extrudates were affected considerably by the extrusion conditions, i.e. extrusion temperature and extrusion ratio. In order to determine the relationship between the properties and extrusion conditions, it is necessary to consider not only the molecular orientation but also the crystallinity, fibrosity and the fine-structure of the extrudates.     

Hydrostatic extrusion of solid polymers

The hydrostatic extrusion of high density polyethylene rod was studied over a wide range of temperatures. The extrudates had smooth surfaces. Those with high extrusion ratios possessed unusual properties being highly transparent and fibrous. The molecular orientation and structural changes due to the hydrostatic extrusion were investigated using wide- and small-angle X-ray diffraction techniques and birefringence. The partial transformation from the orthorhombic to the monoclinic structure occurred in the extrudate obtained at low temperatures (especially at room temperatures). The small-angle X-ray scattering pattern of extrudate for low extrusion ratio showed a diagram with six intensity maxima. On the other hand, for the high extrusion ratio, a diagram with two meridional intensity maxima elongated perpendicular to meridian was observed. At the extrusion ratio R _E?6, the chain axes of polyethylene became aligned to the extrusion direction. Small-angle X-ray scattering patterns showed that the new fibre structure began to appear at an extrusion ratio as low as R′_E=3.0. The structure of the extrudate at a high extrusion ratio was accounted for by the highly-oriented fibre structure consisting of stacks of folded chain crystallites and the interfibrillar amorphous chain bundles.     

Failure behavior of E-glass fiber- and fabric-reinforced IPC composites under tension and compression loading

This paper analyzes the failure behavior of E-glass reinforced inorganic phosphate cement composites in tension and compression. The first part of the study experimentally evaluates the behavior of different composite systems resulting from three different manufacturing processes (hand lay-up, pultrusion and pultrusion/compression). Tensile and compression tests are performed on fiber orientations ranging from 0° to 90°, and the mechanical tests are analyzed in terms of failure strength and failure modes. The prediction of failure strength is approached using mechanical models found in the literature. The comparison of experimental and modeling results is unsatisfactory, confirming the necessity of establishing adapted fracture criteria. The second part of this paper concerns the establishment of a failure envelope based on the Tsai–Wu and Mohr–Coulomb criteria. The anisotropic nature of the composite is accounted for by the Tsai–Wu criterion, while the Mohr–Coulomb criterion allows for the modeling of the mineral matrix’s brittle behavior. The maximum stress criterion is also compared to the obtained envelope curves.     

Failure in laminates in tension under increasing stress,constant stress,and cyclic stress

Both monotonic and cyclic tension experiments have been carried out to fracture on transparent laminates made from flat ribbon glass and polyethylene sheets by heat bonding in a vacuum. The distribution of the measured tensile fracture stresses in monotonic loading correlates very well with the distribution of fracture stresses calculated from the measured distribution of element fracture stresses and the yield strength in shear of the polyethylene, according to a detailed statistical theory worked out earlier by Scop and Argon. Although the expected mode of fatigue damage by propagation of delamination cracks emanating from isolated stable fractures in reinforcing elements was observed, actual fatigue failure was a result of a more rapid mechanism of continued fracturing in reinforcing elements by a humidity-induced time-integrated static fatigue process. While laminates subjected to static stresses of the same magnitude as those in the dynamic experiments failed by the development of an identical form of damage during the same length of time under stress in laboratory air, other laminates tested in the same manner in dry air had 5 to 10 fold increased lives. In addition re-testing of individual elements of delaminated composites showed that elements can often be damaged during lamination, which must be taken into account in any quantitative study.     

The stress intensity factor for a flat elliptical crack in an elastic solid under uniform tension

Making use of simple results concerning 2-dimensional Fourier transforms an expression is derived for the stress-intensity factor at the rim of a flat elliptical crack in an infinite elastic solid under uniform tension.     

Failure of brittle polymers by slow crack growth

The variation of crack velocity (V) with stress intensity factor (K _I) at the tip of a crack has been measured for an epoxy resin containing 42% by volume of irregularly-shaped silica particles. It has been found that at crack velocities above 10^–5 m sec^–1 the crack propagates primarily through the silica particles, whereas at velocities below this value, failure occurs primarily by particle pull-out. This variation in fracture mode is accompanied by a corresponding change in slope of the V(K) curve. Using data obtained from creep rupture experiments and the derived V(K) relationship, it has been possible to estimate the size of the inherent flaw in the composite. This was found to be approximately twice the average particle diameter which is also equal to the size of the largest particles (140 m). Fracture of the unfilled epoxy resin and the effect of environment upon slow crack growth in the composite have also been investigated.     

Singular stresses in an infinite solid with a flat annular crack around a spherical cavity under tension

The problem of singular stresses in an infinite elastic solid containing a spherical cavity and a flat annular crack subjected to axial tension is considered. By application of an integral transform method and the theory of triple integral equations the problem is reduced to that of solving a singular integral equation of the first kind. The singular integral equation is solved numerically, and the influence of the spherical cavity upon the stress intensity factor and the influence of the annular crack upon the maximum stress at the surface of the spherical cavity are shown graphically in detail.     

The interaction between a penny-shaped crack and a spherical inhomogeneity in an infinite solid under uniaxial tension

Summary This paper presents an approximate three-dimensional analytical solution to the elastic stress field of a penny-shaped crack and a spherical inhomogeneity embedded in an infinite and isotropic matrix. The body is subjected to an uniaxial tension applied at infinity. The inhomogeneity is also isotropic but has different elastic moduli from the matrix. The interaction between the crack and the inhomogeneity is treated by the superposition principle of elasticity theory and Eshelby's equivalent inclusion method. The stress intensity factor at the boundary of the penny-shaped crack and the stress field inside the inhomogeneity are evaluated in the form of a series which involves the ratio of the radii of the spherical inhomogeneity and the crack to the distance between the centers of inhomogeneity and crack. Numerical calculations are carried out and show the variation of the stress intensity factor with the configuration and the elastic properties of the matrix and the inhomogeneity.     

Creep rupture under tri-axial tension

The design of a three-axis specimen is described which can be used to subject moderately large volumes of material to relatively homogeneous tri-axial tension stresses. Constitutive equations developed for uni- and bi-axial stress states to describe high-temperature creep deformation and rupture are used to predict lifetimes and the deformation of copper and of aluminium alloy specimens. The theoretical predictions are shown to compare favourably with experimental results, so vindicating the use of bi-axial constitutive equations for more complex tri-axial stress states. Metallographic studies show that grain boundary cavitation occurred, without preferred orientation, in the centre of the test cubes in both materials.     

Failure of brittle polymers by slow crack growth

The mechanical properties of a silica particle-filled epoxy resin composite system have been investigated in air as a function of volume fraction of particles for volume fractions ranging from 0 to 0.52. The Young's modulus and the compressive yield stress both increase as the volume fraction of silica particles is increased and various models of particle strengthening have been used to explain this behaviour. Slow crack growth in the various particulate composites has been studied using a fracture mechanics approach. The variation of crack velocity (V) with stress intensity factor (K _I) has been measured for each of the compositions investigated. In each case, a unique relationship between V and K _I has been found with K _I increasing with volume fraction of particles at a given value of V. The failure mechanisms and the variation of other fracture mechanics parameters, for example, crack opening displacement and plastic zone size with increasing particle volume fraction have been discussed.     

Micromechanics of fracture of solid polymers in dynamic loading

The results of investigation of the influence of temperature on the micromechanics of fracture ofpofymethyl methacrylate and epoxy materials in dynamic loading are presented, A method was developed for determination of the value characterizing the formation and development of microcracks in front of the front of the main crack. Anomalous temperature relationships of crack length and the density of microfractures in polymethyl methacrylate were established. The influence of the processes of stress concentration, local inelastic deformation, and thermofluctuation rupture of polymer chains on the micromechanics of fracture of polymers is considered. It is shown that a change in temperature may lead to a qualitative change in the processes of microfractures. The formation of microcracks in front of the front of a propagating crack may transform into outstripping of it by the leading microcracks and the reverse. It is established that a thermofluctuation character is characteristic of fracture of polymers in intense short-term loading.Translated from Problemy Prochnosti, No. 2, pp. 80–85, February, 1990.