Fracture strains in biaxially loaded 2024 aluminum tubes

2024 aluminum tubes, heat treated to a T6 and T8 temper, were proportionally loaded to failure with combinations of tension and internal pressure. We measured diffuse instability and fracture strains and compared these to the ductile fracture model of Ghosh (1976). Agreement was quite good. Fracture strains measured in axial tension and pure hoop tension were equivalent even though anisotropies were observed in the plastic deformation of the tubes.     

Development of a Vacuum Bagging Technique for Autoclave Curing of Filament Wound Thin-Walled Tubes

The investigation of techniques for the manufacture of hoop wound composite tubes for use as in-plane shear specimens was undertaken. The principle concerns were achieving a smooth surface finish, uniform wall thickness, acceptable laminate consolidation and minimal defects. Filament winding of Hercules AS4/3501-6 12K pre-preg tow was used to manufacture 19 hoop wound thin-walled tubes. Four main vacuum bagging techniques were evaluated. The most successful of these utilized a thin external mild steel sheet together with shrink tape prior to autoclave curing. Ultrasonic C-scan results indicated that the tubes were free of detectable voids and defects. Microscopic analysis showed excellent laminate consolidation and very good geometric tolerances (tube thickness, roundness, concentricity and straightness). Of particular note was the exceptional surface finish and thin axial seam for the final specimens. It was found during torsion testing of the tubes that a thin axial seam was associated with a higher ultimate shear strength. The vacuum bagging techniques are described and discussed in detail.     

Residual Stress Assessment in Thin Angle Ply Tubes

This preliminary study aims to investigate the residual stresses developed in hot cured thin-walled angle-ply filament wound tubes made of E-glass/epoxy, Kevlar/epoxy and carbon/epoxy materials. The residual stresses were estimated from change in geometry of these tubes when axially slitted at ambient temperature. Three basic deformation modes; namely opening up, closing-in and twisting, were observed and these depended on the winding angle, material and wall thickness. The residual stresses were also determined from hoop and axial strain gauges mounted on both the inner and outer surfaces at various locations around the tube. The stresses were compared with theoretical prediction based upon a linear thermo-elastic analysis. Both the predicted and measured values were found to increase with increasing hoop stiffness but there was a large discrepancy between the predicted and measured data, reaching a factor of 5 for the thinnest case. When compared with predicted failure stresses, the experimentally determined stresses were some 15% of the computed compressive strength.     

Size effect on deformation behavior and ductile fracture in microforming of pure copper sheets considering free surface roughening

In meso/micro-scaled plastic deformation, material deformation and ductile fracture are quite different from those in macro-scale. The roughness of the free surfaces of workpiece increases with deformation and the decrease of grain number in the sample thickness direction, leading to the nonuniformity of specimen thickness. The so-called size effect and free surface roughening may in turn affect the deformation behavior, ductility and fracture morphology of the samples. To explore the coupled effect of workpiece geometry and grain size on material flow behavior in meso/micro-scaled plastic deformation, uniaxial tensile test of pure copper sheets with different thicknesses and comparable microstructure was performed. The experimental results reveal that the material flow stress, fracture stress and strain, and the number of microvoids on fracture surface are getting smaller with the decreasing ratio of specimen thickness to grain size. In addition, the modified Swift’s equation and the corrected uniform strain are closer to the experimental ones considering the thickness nonuniform coefficient induced by the free surface roughening. Furthermore, the observation of fracture morphologies confirms that the local deformation caused by the free surface roughening leads to strain localization and a decreased fracture strain when there are only a few grains involved in plastic deformation.     

Denting and fracture of sheet steel by blunt and sharp obstacles in glancing collisions

The different types of denting, scoring and fracture that occur in “glancing collisions” between sheet steel and blunt or sharp obstacles, have been investigated. These collisions have a component of motion along the surface of the sheet or plating as well as perpendicular to it, and are to be distinguished from the usual sort of penetration/perforation problem. Crack initiation for blunt obstacles occurs by in-plane stretching and the biaxially dependent in-plane fracture strain pairs are well described by the fracture-forming limit diagram. Crack initiation for sharp obstacles is less easy to put in terms of critical strains, owing to the highly localised deformation regions. For both types of obstacle, crack propagation is modelled successfully using rigid-plastic fracture mechanics. Applications to ship grounding, motor vehicle crashworthiness, etc., are discussed.     

Biaxial yielding behaviour of highly oriented polypropylene tube

Polypropylene tubes with highly oriented molecular structures induced by die-drawing have been tested at various axial/hoop stress ratios to study the first quadrant (tensile-tensile) failure surface with particular regard to the effect of draw ratio. The experimental tests have been conducted on a flexible test rig designed for testing flat sheet and tube under different loading conditions whilst controlling the applied strain rate to within 120–200 s^–1. A microcomputer-based system has been developed to control the test and automatically log the data. The experimental results are compared with the predictions of the available anisotropic failure theories. The first-quadrant failure surfaces obtained indicate that the yield behaviour of polypropylene in both isotropic and anisotropic states is hydrostatic-pressure dependent with the degree of pressure dependency increasing with draw ratio. The anisotropic tubes are very weak in the hoop direction compared to the axial direction even when biaxially drawn, and yield by rapid circumferential expansion except when the applied axial stress is very much greater than the hoop stress.     

Biaxial cyclic deformation of an epoxy resin: Experiments and constitutive modeling

Biaxial (proportional and non-proportional) cyclic tests were conducted on thin-walled tubular specimens to investigate deformation behavior of an epoxy resin, Epon 826/Epi-Cure Curing Agent 9551. The focus was placed on the biaxial stress-strain response and their dependency on the load control mode, stress or strain range and loading path. Experimental results indicated that under strain-controlled equi-biaxial (proportional) cyclic loading, mean stress relaxation occurred in both axial and hoop directions, whereas under stress-controlled equi-biaxial cyclic loading, ratcheting strains accumulated in both principal directions. Under strain- or stress-controlled non-proportional cyclic loading, anisotropy in stress-strain responses was induced in both axial and hoop directions, and the axial and hoop hysteresis loops rotated in opposite directions. This was particularly evident at high stress or strain levels. The experimental results were further used to evaluate the predictive capabilities of a nonlinear viscoelastic constitutive model. Qualitative and quantitative comparison with the test data indicated a good agreement in predicting the complex stress-strain response under biaxial cyclic loading with various loading paths, applied stress or strain ranges and loading control modes.     

Analysis of the fatigue failure of a mountain bike front shock

We present an analysis of a mountain bike front shock failure. The failure of the 1-year-old shock occurred catastrophically as the bike was ridden off of a 1-m drop. The failure was the result of fast fracture through both shock tubes at the location where the tubes were press fit into the shock upper crown. Examination of the fracture surfaces of the tubes revealed regions of fatigue crack growth that nearly penetrated the entire thickness of both tubes. An estimate of the forces during use, coupled with stress analysis, revealed three stresses near the fracture site—axial compression, bending, and hoop stresses. During operation, the axial compressive stress is negligible while the hoop and bending stresses are significant. Based on fracture mechanics, and an estimate of the bending stress from a 1-m drop, it is confirmed that the fatigue cracks present on the fracture surface were large enough to induce fast fracture. Prior to the existence of the fatigue cracks, the stresses were magnified locally near the fracture site by a significant stress concentration caused by the sharp transition from the shock tube to the crown. The fatigue cracks initiated at a circumferential location in the tube commensurate with high tensile bending stress and the stiffest region of the crown (highest stress concentration). Based on the evidence, the most probable cause of the bike shock fatigue failure was the shock design, which facilitated high local stresses during use.     

Tensile Response of Hoop Reinforced Multiaxially Braided Thin Wall Composite Tubes

This paper presents the tensile response of thin-walled composite tubes with multi-axial fibre architecture. A hybrid braid-wound layup has the potential to optimise the composite tube properties, however, stacking sequence plays a role in the failure mechanism. A braid-winding method has been used to produce stacked overwound braid layup [(±45°/0°)₅/90°₄]_T. Influence of stacking sequence on premature failure of hoop layers has been reported. Under tensile loading, a cross-ply composite tube with the alternate stacking of hoop and axial fibre show hoop plies splitting similar to the overwound braided composite tube. However, splitting has been restricted by the surrounding axial plies and contained between the adjacent axial fibre tows. This observation suggests hoop layers sandwiched between braid layers will improve structural integrity. A near net shape architecture with three fibre orientation in a triaxial braid will provide additional support to prevent extensive damage for plies loaded in off-axis. Several notable observations for relatively open braid structures such as tow scissoring, high Poisson’s ratio and influence of axial tow crimp on the strain to failure have been reported. Digital Image Correlation (DIC) in conjunction with surface strain gauging has been employed to capture the strain pattern.     

Biaxial Loading of Continuously Graded Thermoviscoplastic Materials

In this paper we study the problem of biaxial loading of a sheet made of a continuously graded thermoviscoplastic material. The material phases are supposed to exhibit thermal softening, strain-rate sensitivity and strain hardening, continuously varying along all directions. First we formulate the plane stress problem of a non-homogeneous material and study the behavior of temperature, strain and strain-rate related to inhomogeneities of thermomechanical parameters and geometrical defects. Next we present the “effective” instability analysis of Dudzinski and Molinari (Int J Solids Struc 1991), adapted to the non-homogeneous case, to define the critical conditions and select the localization modes by studying the overall strains for which a certain level of instability growth is developed. Finally, we present the numerical simulation of the fully non-linear dynamical problem. Several aspects of the deformation process and the related role of non-homogeneities are analyzed onset of strain and temperature localization, ductility, contours of temperature increase as detectors of instability, interplay with initial defects, multiple necking, decrease of thinning-rate, variation of the multiple necking due to boundary conditions.     

Strength failure and crack coalescence behavior of brittle sandstone samples containing a single fissure under uniaxial compression

Uniaxial compression experiments were performed for brittle sandstone samples containing a single fissure by a rock mechanics servo-controlled testing system. Based on the experimental results of axial stress-axial strain curves, the influence of single fissure geometry on the strength and deformation behavior of sandstone samples is analyzed in detail. Compared with the intact sandstone sample, the sandstone samples containing a single fissure show the localization deformation failure. The uniaxial compressive strength, Young’s modulus and peak axial strain of sandstone samples with pre-existing single fissure are all lower than that of intact sandstone sample, which is closely related to the fissure length and fissure angle. The crack coalescence was observed and characterized from tips of pre-existing single fissure in brittle sandstone sample. Nine different crack types are identified based on their geometry and crack propagation mechanism (tensile, shear, lateral crack, far-field crack and surface spalling) for single fissure, which can be used to analyze the failure mode and cracking process of sandstone sample containing a single fissure under uniaxial compression. To confirm the subsequence of crack coalescence in sandstone sample, the photographic monitoring and acoustic emission (AE) technique were adopted for uniaxial compression test. The real-time crack coalescence process of sandstone containing a single fissure was recorded during the whole loading. In the end, the influence of the crack coalescence on the strength and deformation failure behavior of brittle sandstone sample containing a single fissure is analyzed under uniaxial compression. The present research is helpful to understand the failure behavior and fracture mechanism of engineering rock mass (such as slope instability and underground rock burst).     

An iterative procedure for determining effective stress–strain curves of sheet metals

An iterative correction procedure using 3D finite element analysis (FEA) was carried out to determine more accurately the effective true stress–true strain curves of aluminum, copper, steel, and titanium sheet metals with various gage section geometries up to very large strains just prior to the final tearing fracture. Based on the local surface strain mapping measurements within the diffuse and localized necking region of a rectangular cross-section tension coupon in uniaxial tension using digital image correlation (DIC), both average axial true strain and the average axial stress without correction of the triaxiality of the stress state within the neck have been obtained experimentally. The measured stress–strain curve was then used as an initial guess of the effective true stress–strain curve in the finite element analysis. The input effective true stress–strain curve was corrected iteratively after each analysis session until the difference between the experimentally measured and FE-computed average axial true stress–true strain curves inside a neck becomes acceptably small. As each test coupon was analyzed by a full-scale finite element model and no specific analytical model of strain-hardening was assumed, the method used in this study is shown to be rather general and can be applied to sheet metals with various strain hardening behaviors and tension coupon geometries.     

Spatio-temporal characteristics of plastic instability in AA5182-O during biaxial deformation

Spatio-temporal characteristics of plastic instability denoted by locally extreme values in strain rate contours computed with digital image correlation are investigated in biaxial deformation of AA5182-O sheet. Temporal characteristics are similar to those of Portevin–Le Châtelier (PLC) bands in uniaxial tension. Spatial characteristics, however, dramatically differ from PLC band morphologies in uniaxial tension. Initiation occurs in a localized deformation ring (LDR) that does not include the pole, followed by a rapid transition to a circular region that includes pole, i.e. a localized deformation circle (LDC). A critical strain is required to trigger serrated flow at the pole, and a negative strain rate sensitivity of the flow stress at the pole suggests that the underlying microstructural mechanism is dynamic strain aging. Plastic instability hops between the LDR and the LDC until a critical strain is reached at which it appears in a localized deformation band, with no circular symmetry, that hops around the pole. Future model development will require modifications to existing theoretical frameworks to account for the unique spatial characteristics of plastic instability during biaxial deformation of AA5XXX alloys.     

Ductile fracture in sheets under transverse strain gradients

The fully plastic fracture of a metal sheet subjected to a small transverse gradient of tensile strain near a reinforcement is modeled as mode I fracture under transverse plane strain (TPS). Necking and fracture were analyzed by assuming that they were set by prior uniform strains and then necking displacements. Equations for the spreading of TPS necking and fracture were thus derived for a sheet with strain gradient. Experiments on tapered specimens confirmed the expected fracture displacements within 12 percent, but Moiré studies suggest the agreement may be fortuitous. In any event, in-plane transverse displacements and normal strains in the crack growth direction, as well as shear strains, were negligible. This should simplify any future numerical analysis.     

Influence of overlap configuration on compressive behavior of CFRP-confined normal- and high-strength concrete

This paper presents the findings of an experimental investigation on the effect of overlap configuration on carbon fiber-reinforced polymer (CFRP)-confined normal- and high-strength concrete. A total of 33 specimens were prepared and tested under monotonic axial compression. All specimens were cylinders with 152 mm diameter and 305 mm height and confined by CFRP tubes. Two different concrete mixes were examined, with average compressive strengths of 52.0 and 84.7 MPa. The effect of overlap configuration was examined by manufacturing the specimens with different properties at the overlap region including overlap length, continuity and distribution. Axial and lateral behavior was recorded to observe the axial stress–strain relationship and hoop strain behavior for concentric compression. Ultimate axial and lateral conditions are tabulated and stress–strain curves have been provided. Detailed plots of hoop strain development and lateral confinement pressure at ultimate are presented. The results indicate that FRP overlap length has no significant influence on strain enhancement ratio (ε_cu/ε_co), but an increase in overlap length leads to a slight increase in strength enhancement ratio (f′_cc/f′_co), with these observations equally applicable to both continuously and discontinuously wrapped specimens. The results also indicate that continuity of the FRP sheet in the overlap region has some influence on the effectiveness of FRP confinement. Furthermore, it was observed that the distribution of FRP overlap regions for discontinuously wrapped specimens can influence the axial compressive behavior of these specimens in certain overlap configurations. Finally, it is found that the distribution of lateral confining pressure around specimen perimeter becomes less uniform for specimens with higher concrete strengths and those manufactured with overlap regions that are not evenly distributed.     

THE USE OF KINEMATIC HARDENING MODELS IN MULTI-AXIAL CYCLIC PLASTICITY

Abstract— The use of kinematic hardening models are examined for tubes subjected to (a) cyclic plastic torsion with a sustained axial stress and (b) cyclic plastic tension-compression with a sustained hoop stress. It is shown that the kinematic model predicts a limit to the plastic strain accumulation resulting from the sustained loads. Experimental results show that the strain accumulation is not limited and that the mode of deformation within a cycle of plastic strain cannot be predicted using a kinematic hardening model. The development of the yield surface under cyclic loading is examined. The results indicate that contraction and expansion of the yield surface along the stress axes can occur and it is shown that the direction of the sustained stresses, relative to the direction of the cyclic stresses is an important factor in the development of any cumulative plastic strains.     

Deformation of single-walled carbon nanotubes under large axial strains

The deformations of single-walled carbon nanotubes (SWCNTs) under large axial strains are investigated. The Tersoff-Brenner potential is adopted to describe the interactions between carbon atoms. Results show that the changes of strain energies are dependent on chirality but independent of the tubes' radii. Under large axial tension, abrupt changes of the configurations of SWCNTs may occur when the strains exceed 0.382 for armchair patterns and 0.43 for zigzag patterns. The reason is that the changes of bond lengths and angles lead to corresponding changes of many-body coupling interactions between atoms. Then the tubes reach new equilibrium states. Such abrupt changes of configurations must trigger fracture of CNTs in a dynamic deformation.     

Fracture initiation at a sphrerical inclusion in a matrix plastically deformed by shear

The critical strain for fracture initiation of a metallic material with a spherical inclusion has been analysed using EaheIby,s inclusion method forthree types of fracture initiation models including the recovery effect by diffusion of atoms. When the elastic constant of inclusion approaches that of the matrix, the critical strain for fracture initiation becomes large in the case of uniform shear deformation of the matrix. It was found that the critical strain becomes large due to the diffusion of atoms, especially for inclusions of small size and a large elastic constant. The model in which the inclusion is cracked by the localized shear deformation can explain the observed inclusion size dependence of the strain for fracture initiation. The inclusion size dependence of the critical strain for fracture initiation by uniform shear deformation of the matrix is different from that by localized shear deformation. Therefore, it is important to know which mechanism governs the fracture.     

Bifurcation and post-bifurcation phenomena of elastic-plastic circular tubes subjected to uniform shrinkage under plane strain condition

Bifurcation and post-bifurcation behaviors of thick-walled elastic-plastic circular tubes subjected to uniform shrinking are analyzed numerically under plane strain condition. Bifurcation analysis to determine the condition for onset of bifurcation away from the axisymmetric deformation is carried out within the framework for such analyses, due to Hill. The influence of the material properties and the dimensions of the tubes, upon the bifurcation behavior is clarified. In order to simulate the post-bifurcation behaviors of the tubes after the onset of surface type bifurcation, a finite element analysis of uniform compression of a block is performed under the plane strain condition. The localization of deformation into a narrow band induced by the nonlinear growth of surface undulation is clarified.