Kinking and compressive failure in uniaxially aligned carbon fibre composite tested under superposed hydrostatic pressure

Initiation and propagation of failure in uniaxially aligned 60% volume-fraction Type III carbon fibre-epoxide compressive specimens, strained parallel to the fibre axis, was studied at atmospheric and superposed hydrostatic pressures, H, extending to 300 MN m^–2. The atmospheric axial compressive strength was approximately 1.5 GN m^–2 and equal to the tensile strength, but mechanisms involving shear-operated failure of the fibres must be discounted since the failure process was very pressure sensitive above H 150 MN m^–2. The results also could not be satisfactorily interpreted by theories involving micro-buckling of individual fibres or laminae when the matrix shear modulus controls the compressive strength. For atmospheric tests and for H<150 MN m^–2 the initiation of failure was associated with transverse cracking (longitudinal splitting) which was followed by kinking. Ahead of the propagating kink band, groups of fractured fibres were observed, which is consistent with failure of these groups by buckling; this process causes composite catastrophic failure. At higher pressures splitting was suppressed, as was interlaminar cracking in doubly-notched (in-plane shear) specimens, but kinking, which became increasingly more difficult to initiate, was the precursor of the failure process. An attempt was made to analyse failure using the fracture mechanics model of Chaplin with some success for the notched specimens.     

Fracture of a plasticized epoxide under superposed hydrostatic pressure

The deformation and fracture behaviour of rubber-coated and uncoated epoxy specimens has been studied under superposed hydrostatic pressures extending to 300 MN m^–2. Maximum shear stress at yield for this epoxy were about 25 MN m^–2 at atmospheric pressure and rose to about 48 MN m^–2 at 300 MN m^–2 superposed pressure. Yielding and failure of all specimens tested beyond pressures of 75 MN m^–2 took place when all the (macroscopic) principal stresses, though unequal, were compressive. Fractographic examination revealed three distinct zones of the failure surfaces at atmospheric pressure. The behaviour of all uncoated specimens and those coated and tested below 100 MN m^–2 was similar. A fracture-mechanics interpretation of failure could be applied to these tests assuming the deformation-produced first zone was the fracture initiating site. Coated samples tested beyond 100 MN m^–2 superposed pressure failed with no evidence of Zones II or III of failure; Zone I appeared to spread over the entire failure surface. An interpretation involving fluid penetration of Zone I failure nuclei, along the lines suggested by Duckett, can account for the failure stresses of the uncoated specimens but is not tenable for the coated samples. It appears that crack nucleation and (slow) growth, as opposed, perhaps, to (catastrophic) crack propagation, can take place in this polymer when all the principal stresses are compressive.     

The tensile properties of pultruded GRP tested under superposed hydrostatic pressure

The failure mechanisms in waisted tensile specimens of pultruded 60% volume fraction glass fibre-epoxide were investigated at atmospheric and superposed hydrostatic pressures extending to 350 MN m^–2. The maximum principal stress at fracture decreased from 1.7 GN m^–2 at atmospheric pressure to 1.3 GN m^–2 at 250 MN m^–2 superposed pressure and remained approximately constant at higher pressures, as had been observed with carbon fibre reinforced plastic (CFRP) and a nickel-matrix carbon fibre composite. In the high-pressure region the failure surfaces were fairly flat, consistent with the fracture process being solely controlled by fibre strength. Pre-failure damage, in particular debonding, was initiated at 0.95 GN m^–2 at atmospheric pressure and this stress rose to 1.2 GN m^–2 at 300 MN m^–2 superposed pressure, i.e. by about 9% per 100 MN m^–2. Unlike the pressure dependence in CFRP, this contrasts with the pressure dependence of the resin tensile strength, about 25% per 100 MN m^–2, but can be associated with that of the fibre bundle/resin debonding stress, about 12% per 100 MN m^–2 superposed pressure. Consistent with this interpretation, glass fibres of the failure surfaces were resin-free, again in contrast to CFRP.     

Deformation of a carbon-epoxy composite under hydrostatic pressure

This paper describes the behaviour of a carbon-fibre reinforced epoxy composite when deformed in compression under high hydrostatic confining pressures. The composite consisted of 36% by volume of continuous fibres of Modmur Type II embedded in Epikote 828 epoxy resin. When deformed under pressures of less than 100 MPa the composite failed by longitudinal splitting, but splitting was suppressed at higher pressures (up to 500 MPa) and failure was by kinking. The failure strength of the composite increased rapidly with increasing confining pressure, though the elastic modulus remained constant. This suggests that the pressure effects were introduced by fracture processes. Microscopical examination of the kinked structures showed that the carbon fibres in the kink bands were broken into many fairly uniform short lengths. A model for kinking in the composite is suggested which involves the buckling and fracture of the carbon fibres.List of symbols d diameter of fibre - E _f elastic modulus of fibre - E _m elastic modulus of epoxy - G _m shear modulus of epoxy - k radius of gyration of fibre section - l length of buckle in fibre - P confining pressure (= ₂ = ₃) - R radius of bent fibre - V _f volume fraction of fibres in composite - _t, _c bending strains in fibres - angle between the plane of fracture and ₁ - ₁ principal stress - ₃ confining pressure - _c strength of composite - _f strength of fibre in buckling mode - _n normal stress on a fracture plane - _m strength of epoxy matrix - shear stress - tangent slope of Mohr envelope - slope of pressure versus strength curves in Figs. 3 and 4.     

Reliability-based load and resistance factor design of composite pressure vessel under external hydrostatic pressure

A reliability-based load and resistance factor design procedure for subsea composite pressure vessel subjected to external hydrostatic pressure is presented. The failure criterion for defining the performance function is considered as buckling. A sensitivity analysis is conducted to research influences of statistical characteristics of variables on the partial safety factors and the thickness of pressure vessel. The results shows the longitudinal modulus, inside radius of composite layers, unsupported length and external pressure significantly affect the design results, whereas transversal modulus, Poisson’s ratio, shear modulus and winding angle have little effects. In order to validate the design results, a filament-wound composite pressure vessel is manufactured, and the buckling test is performed. It is observed that when the applied external hydrostatic pressure is a little more than the designed critical buckling pressure, the buckling and subsequent burst behaviours occur, which shows a good agreement between the experimental and analytical results.     

On instability failure of corroded rings under external hydrostatic pressure

Analytical formulations were derived for bifurcation pressure and non-linear static analysis of a corroded ring under external pressure. The mid-surface inextensional condition was included in the derivation which resulted in much improved accuracy in the prediction of bifurcation pressure. Afterwards, an analytical method was presented to solve the non-linear deformation problem of a corroded ring with initial ovality included under external pressure. A finite element analysis was carried out to verify the accuracy of the developed model. By setting the initial yielding as the failure criterion, a parametric study was carried out to study the effect of corrosion depth and corrosion angular extent. Moreover, the interaction effect of two circumferential corroded regions on the critical pressure was studied. Finally, some comments on the analytical methods were given to consider the case of continuously varying thickness and an alternative perturbative method was proposed. This research is intended to enhance the understanding of instability and failure for a corroded tube under external pressure mainly applicable to offshore industry.     

Tensile failure of pultruded glass-polyester composites under superimposed hydrostatic pressure

The tensile properties of five types of pultruded 0·52 V_f glass-fibre-polyester rods were investigated by extending waisted round specimens at atmospheric and superimposed hydrostatic pressures, −H, to 300 MPa. The maximum principal stress at fracture, −700 MPa, decreased, with the superimposition of −H, approximately by its magnitude. As −H increased the failure surfaces became flatter, the amount of fibre pull-out decreased and transverse cracks became shorter or were eliminated. Glass fibres in the failure surfaces were resin free, and failure of the glass fibre bundles appeared to control the fracture process in the entire pressure range for all materials. The decrease in maximum principal tensile stress with increasing −H indicates that the glass fibre failure process is not controlled by a critical tensile stress. Failure criteria are discussed, and in the tension-compression-compression octant of stress space the relevant criteria appear to be strain energy and deviatoric tensile stress, strain and strain energy for these GRPs and glass itself.     

On the buckling and collapse of moderately thick composite cylinders under hydrostatic pressure

This paper presents a summary of the work carried out at Washington University in recent years on the buckling and associated non-linear response and collapse of moderately thick composite cylindrical shells. Ring elements in conjunction with a three-dimensional elasticity formulation are employed in the analysis. The buckling and postbuckling imperfection sensitivity in individual modes is studied first. The problem of interaction between local and overall instabilities is then investigated in detail. Imperfection sensitivity of typical ring-stiffened shells is established by using a simple and effective approach that combines the asymptotic procedure and the amplitude modulation technique. The influence of dynamic application of the hydrostatic pressure is investigated with the simplified model. The results obtained are compared with those produced by a two-dimensional program package which includes full-fledged non-linear analysis with ring elements, and commercial programs wherever possible. The study has thrown light on several issues regarding the modeling and behavioral aspects of thick composite shells which are summarized at the conclusion of the paper.     

Crack kinking under high pressure in an elastic-plastic material

Directional crack growth criteria in compressed elastic–plastic materials are considered. The conditions at the crack tip are evaluated for a straight stationary crack. Remote load is a combined hydrostatic stress and pure shear, applied via a boundary layer assuming small scale yielding. Strains and deformations are assumed to be small. Different candidates for crack path criteria are examined. Maximum non-negative hoop stress to judge the risk of mode I and maximum shear stress for mode II extension of the crack are examined in some detail. Crack surfaces in contact are assumed to develop Coulumb friction from the very beginning. Hence, a condition of slip occurs throughout the crack faces. The plane in which the crack extends is calculated using a finite element method. Slip-line solutions are derived for comparison with the numerically computed asymptotic field. An excellent agreement between numerical and analytical solutions is found. The agreement is good in the region from the crack tip to around halfway to the elastic–plastic boundary. The relation between friction stress and yield stress is varied. The crack is found to extend in a direction straight ahead in shear mode for sufficiently high compressive pressure. At a limit pressure a kink is formed at a finite angle to the crack plane. For lower pressures the crack extends via a kink forming an angle to the parent crack plane that increases with decreasing pressure.     

Crack bifurcation under hydrostatic pressure

Glass tubes were fractured by internal pressure under atmospheric or superimposed hydrostatic pressure. It is found that the crack length at bifurcation is significantly increased by superimposed hydrostatic pressures. The dynamic energy release rate for a crack propagating with superimposed hydrostatic pressure is calculated. It is shown that the pressure effect on crack length at bifurcation may be explained by combining the energy balance condition and the Yoffe's concept for crack bifurcation.     

Compressive failure of fibre-reinforced composites: buckling,kinking, and the role of the interphase

Recent experimental studies of compressive failure in fibre-reinforced polymeric composites have been analysed. It is shown that the parametric basis for most compressive strength models, i.e. pure plastic buckling controlled by matrix shear strength and initial fibre misorientation, is probably incomplete. It is argued that, instead, failure is triggered by the initiation of an unstable kink band prior to buckling instability, and that additional parameters (interfacial shear stress/strain; fibre strength) are responsible for this transition in mechanisms.     

Compressive failure of composite plates during one-sided heating

Intermediate-scale, one-sided heating tests were performed on compressively loaded E-glass vinyl ester composite laminates. The tests were designed to investigate the effect of varying the applied stress, applied heat flux, and laminate dimensions on structural response. Three failure modes were observed in testing: large-scale buckling, localized kinking, and forced-response deflection. The failure modes were dependent on applied stress and independent of applied heating. The times-to-failure of the laminates exhibited an inverse relationship with the applied stress and heating levels. The use of a single temperature was incapable of quantifying laminate failure due to variations in temperature at failure for a given stress level. A dimensionless relationship was developed as a function of temperature for the applied stress and slenderness ratio. This relationship compares the applied stress, slenderness ratio, and laminate temperature at failure and may be used in design of composite laminate structures to determine failure.     

Fracture of notched polycarbonate under hydrostatic pressure

The brittle fracture behaviour and plastic deformation of round-notched polycarbonate bars subjected to three-point bending under hydrostatic pressure have been studied. Below a certain critical pressure, the brittle fracture initiated from an internal craze nucleated at the tip of the local plastic zone ahead of the notch rooT. The position of the nucleation of the craze receded from the tip of the notch with increasing applied pressure. When the pressure was increased over a critical value, general yielding occurred by passage of the plastic zone across the notched cross-section, that is, the brittle to ductile transition took place. A qualitative analysis of the stress distribution within the plastic zone explains that the brittle to ductile transition under hydrostatic pressure occurs when the general yield takes place before a critical stress for brittle crack propagation is reached.     

Crystallization of glassforming melts under hydrostatic pressure and shear stress: Part I Crystallization catalysis under hydrostatic pressure: possibilities and limitations

This is the first part of a thorough study of the kinetics of melt crystallization under applied static pressure, P, and under shear stress. The thermodynamic and kinetic consequences of increased external pressure on nucleation rate, non-steady-state time lag, rate of crystal growth and overall crystallization kinetics in undercooled melts are analysed. Two types of undercooled liquids (with either positive or negative volume dilatation upon crystallization) are considered. Particular attention is given to the effect of pressure on the specific interface energy, σ, at the crystal/melt phase boundary. Using an appropriate thermodynamic model it is shown that for one-component systems, (∂σ/∂p)<0 is to be expected as a rule. Thus an additional decrease of the thermodynamic barrier of nucleation in pressurized melts is to be expected. However, it is also shown that the increase of melt viscosity with pressure in most cases reduces the effect of this decrease. Thus increased pressure has a limited effect as a nucleation catalyst. The possibilities in this respect are analysed and conditions under which static pressure may lead to enhanced crystallization are outlined. This revised version was published online in November 2006 with corrections to the Cover Date.     

Birefringence measurement under hydrostatic pressure in twistedhighly birefringent fibers

A new method of birefringence measurement in highly birefringent fibers influenced by hydrostatic pressure conditions up to 100 MPa is presented. The birefringence measurement method is based on twist-induced effects and has never been applied before in a high-pressure environment. The experiments were conducted using a specially designed pressure facility, which made it possible to simultaneously generate several mechanical perturbations, including twist and hydrostatic stress, and to investigate their effects on mode transmission in optical fibers. The results indicate that in the case of HB single-mode bow-tie fibers, hydrostatic pressure up to 100 MPa increased birefringence with a mean coefficient of (1/ΔB₀ )(Δβ)/dp=0.2%/MPa which is in very close agreement with our previous measurement based on Rayleigh scattering     

Structural transformations of carbon nanotubes under hydrostatic pressure

We used simulations with a classical force field to study the transformation under hydrostatic pressure of isolated single-walled nanotubes (SWNT) from a circular to a collapsed cross section. Small-diameter SWNTs deform continuously under pressure, whereas larger-diameter SWNTs display hysteresis and undergo a first-order-like transformation. The different behavior is due to the changing proportions in the total energy of the wall-curvature energy and the van der Waals attraction between opposite walls of the tube.