Dynamic buckling of thin thermoviscoplastic cylindrical shell under radial impulsive loading

The dynamic plastic buckling of a homogeneous and isotropic thin thermoviscoplastic cylindrical shell loaded radially is studied analytically by analyzing the stability of its stressed/deformed configuration under superimposed infinitesimal perturbations. The wave number of the perturbation that maximizes its initial growth rate is assumed to determine the buckling mode. Cubic algebraic equations are obtained for both the maximum initial growth rate of perturbation and the corresponding wave number. The buckled shape of a cylindrical shell is found to match well with that observed experimentally. The sensitivity of the buckled shape to the impact velocity, the hardening modulus, and the material viscosity has been delineated. For axially restrained shells, it is found that for materials exhibiting strain rate hardening only the maximum initial growth rate of the perturbation and the corresponding wave number vary as and , respectively. For axially unrestrained cylindrical shells made of strain hardening only materials, the maximum initial growth rate of a perturbation and the corresponding wave number vary as and , respectively. Here is the mean value of the generalized stress, ρ the mass density, β the material viscosity, h the shell thickness, and R the mean radius of the shell.     

Secant stiffnesses for ultimate analysis of strain hardening indeterminate RC structures

This paper presents the iterative use of secant distributions in stiffness analysis to determine ultimate load factors for statically indeterminate concrete structures which strain harden at critical sections. The computational procedure is novel in that it directly seeks the failure state without considering pre-ultimate behaviour, and also in that it permits clear insight into the important effect of the distribution on moments at failure. The procedure iterates until the output moments–in addition to satisfying capacity–give an distribution which returns those very moments on input to the stiffness analysis with the same loads. A flowchart for iterating to these conditions is given, with illustrative examples. Then, removal of higher-order terms from nonlinear distributions is shown algebraically and by stiffness analysis to compromise neither predictive accuracy nor analysis speed in specific cases. Further algebraic analysis of an encastered span with two section stiffnesses shows that, for elastic (e.g. over-reinforced) failure, a unique coincidence exists between the moment diagram and the distribution when turning values of moment occur for any given ratio of the two section stiffnesses. It is concluded that distributions are key to assessing failure states of RC structures.     

High-cycle fatigue behavior of riveted connections for railway metal bridges

The evaluation of existing structures, in particular bridges, is becoming increasingly important. In particular for railway bridges, service loads and stress cycles accumulated under traffic loads, and the consequent ageing of existing structures, lead to the need for an assessment of their remaining fatigue life, in order to decide on retrofit or structure replacement. In this context, a 12.4 m span railway bridge near Sacile, Italy, with a common structural scheme for railway bridges, about ninety years old, was taken out of service, transported to a structural laboratory and subjected to both material characterization, monotonic and high-cycle fatigue shear tests. Materials exhibited a yield strength and a tensile strength of about 322 and 421 MPa, respectively, and the hot-spot critical details resulted in the riveted connections of the shear diaphragms that carried the rails. Other material properties that affected the fatigue endurance in a favorable way, and are not taken explicitly into account in structural Codes, were determined. As a result, the equating of riveted shear splices with splices jointed with non-preloaded bolts has been shown, and Eurocode 3-1-9 [EN 1993-1-9. Eurocode 3: Design of steel structures — part 1-9: Fatigue, Brussels: CEN; 2005] design rules have resulted on the safe side, even though no specific category of riveted details has been found to be available.     

Fracture morphology and viscous transport

The morphology of a fracture in a granite block is sampled using a high resolution profiler providing a 3999×4000 pixel image of the roughness. We checked that a self-affine model is an accurate geometrical model of the fracture morphology on the basis of a spectral analysis. We also estimated the topothesy of the experimental surface to be and the roughness exponent to be ζ≈0.78. A finite difference scheme of the Stokes equation with a lubrication approximation was used to model the viscous flow through a fracture aperture defined as the gap between the experimental fracture surface and a flat plane. We finally compare our numerical results to experimental measurements of the flux through the fracture of a glycerol/water mixture (to be at sufficiently low Reynolds number where Stokes equations holds) changing the average aperture of the fracture. The comparison is successful despite a limited resolution of the experimental measurements. Interestingly we show that only long wavelengths of the fracture morphology control the fracture hydraulic conductivity.     

Effect of plastic deformation and boundary conditions combined with elastic wave propagation on the collapse site of a crash box

Several papers have been published recently on the crashworthiness studies. The main task was to predict the energy absorption W_p and average collapse force in time of sheet steel structures. The main objective of this contribution is to design a component that allows absorbing and dissipating a high energy W_p allowing improvements of the survivability of passengers in vehicles. However, the range of applications is larger since it includes all civil and military applications related to safety of components, or more generally of construction elements being loaded by impacts or explosions. In the present 3D case, the aim of this numerical study on dynamic loading in adiabatic conditions of deformation is to analyze the effect of elastic wave propagation combined with plastic behavior on the collapse site of a rectangular tubular structure made of steel sheet. To demonstrate the strong coupling between the effects of strain-rate sensitivity, accounted for in the constitutive relation that is used in numerical simulations, with the process of elastic wave reflection on the boundary conditions, a series of numerical simulation was performed. It is shown in this numerical study that the strain-rate sensitivity influences the position of the first collapse site. Moreover, the first collapse initiation of a structure defines the level of power absorption. Since the process of folding may be combined with bending of the structure (in particular when a local buckling appears close to the opposite side of impact), in this non-axial case the energy absorption W_p decreases and the effectiveness of the structure to the energy absorption is insufficient.     

Transverse drilling-induced tensile fractures in the West Tuna area, Gippsland Basin, Australia: implications for the in situ stress regime

Drilling-induced tensile fractures (DITFs) have been interpreted on image logs from vertical wells in the Gippsland Basin, offshore southeastern Australia. Interpreted axial (vertical) DITFs have previously been well described worldwide. We also interpret transverse (horizontal) DITFs, which are horizontal fractures that are electrically conductive, non-planar, bimodal and constrained to the tensile region of the wellbore.Elasticity theory predicts formation of both transverse and axial drilling-induced tensile fractures (DITFs) in vertical wells depending on the magnitude of the principal in situ stresses, pore-pressure and mudweight. Drilling-induced tensile fractures initiate in very specific stress environments. Axial DITFs can closely constrain a lower bound to the maximum horizontal stress (S_H max) magnitude where the minimum horizontal (S_h min) stress is known. If transverse DITFs are observed, they can constrain a lower bound to maximum and minimum horizontal stress magnitudes. The observation of transverse DITFs on image logs can constrain the stress field to one on the border of strike-slip and reverse faulting () without requiring knowledge of the S_h min or S_H max magnitude. The observation of transverse DITFs in the West Tuna area combined with wireline log data, leak-off tests and pore pressure data are used to constrain the in situ stress tensor. The interpreted in situ stress tensor lies on the border of a strike-slip and reverse faulting regime (S_H max40.5 MPa/km>S_h min≈S_v21 MPa/km). Interpreted data from leak-off tests in the West Tuna area confirm that S_h minS_v.     

Deviation of hydraulic fractures through poroelastic stress changes induced by fluid injection and pumping

This paper presents an analysis of the deviation of hydraulic fractures associated with the poroelastic change of the in situ stress field caused by fluid injection and pumping in the reservoir. This mechanism is studied within the confines of a simple model involving one injection and one pumping well, and a hydraulic fracture propagating along the path initially equidistant from the two wells. Analysis of the fracture deviation from its straight-ahead path and determination of the conditions leading to attraction of the fracture by the injection well are both based on a theoretical study of the stress trajectories. Comparison of the analytical prediction of the fracture path with the computed path using a numerical technique shows excellent agreement between the two methods, provided that a certain dimensionless toughness is small.The principal results of this study can be summarized as follows. First, a fracture propagating along a path, initially midway between an injection and a pumping well, will always be deviated by the injection well due to the shear stress induced by fluid injection and pumping along the initial path.Second, the injection well acts as an attractor of hydraulic fractures propagating within its “attraction basin”. Then, the fracture will propagate toward the injection well rather than simply be deviated by it. One of the features of this attraction basin is the existence of a “fracture barrier” characterized by a 90° rotation of the principal stress directions, with respect to far-field principal directions.Third, fracture deviation and attraction towards the injection well appears to be primarily controlled by only two dimensionless quantities: ., the ratio of the stress deviator at infinity over the characteristic stress σ∗ associated with injection and pumping of fluid, and π = 4ct/L², a dimensionless time (where c is the diffusivity and L is the half-distance between the two wells). The number of significant parameters is thus remarkably less than expected from a dimensional consideration. Only in the region close to the injection well is there an influence of an additional number , the ratio of the difference between the mean pressure at infinity and initial pore pressure to the characteristic stress σ∗.     

Concise formula for the critical buckling stresses of an elastic plate under biaxial compression and shear

This study aims to develop a concise formula for the critical buckling stresses of a simply supported plate under biaxial compression and shear. The critical stresses are obtained for different aspect ratios using classical plate theory and the Ritz method. The four-dimensional critical stress formula, which is expressed in terms of the three in-plane stresses and the aspect ratio, is developed empirically according to the two-dimensional relationships between the in-plane stresses. The findings that are of interest are: (1) the critical stress relationship is linear for the aspect ratios within the range 1 to and nonlinear for the aspect ratios within the range to 5; and (2) as shear stress approaches its critical value, the critical stress relationship becomes increasingly linear and less dependent on aspect ratio.