A Theory of Autofrettage for Open-Ended, Polar Orthotropic Cylinders

Autofrettage is a widely used process to enhance the fatigue life of holes. In the theoretical investigation presented in this article, a semi-analytic solution is derived for a polar, orthotropic, open-ended cylinder subjected to internal pressure, followed by unloading. Numerical techniques are only necessary to solve a linear differential equation and evaluate ordinary integrals. The generalized Hooke’s law connects the elastic portion of strain and stress. The flow theory of plasticity is employed. Plastic yielding is controlled by the Tsai–Hill yield criterion and its associated flow rule. It is shown that using the strain rate compatibility equation facilitates the solution. The general solution takes into account that elastic and plastic properties can be anisotropic. An illustrative example demonstrates the effect of plastic anisotropy on the distribution of stresses and strains, including residual stresses and strain, for elastically isotropic materials.

Numerical Evaluation of Plastic Buckling of Short Cylinders Under Combined Loading

The so-called “plastic buckling paradox” originates from the fact that the Prandtl–Reuss’ flow theory of plasticity overestimates the plastic buckling load of plates and shells, whereas Hencky’s deformation theory of plasticity provides results that are more accurate. However, it has been shown that this problem can be overcome by introducing certain initial imperfection in accurate finite element (FE) simulations based on the flow theory of plasticity. 1 – 4 The present study goes deeper into the problem and reveals that in the case of short cylinders under combined loading, which have long been the object of extensive research in the elastic range, 5 a different modeling of the material behavior can also trigger a mode jumping from the initial imperfection, which may even reverse the reported predictions by the flow and deformation theories of plasticity. This fact must be taken in maximum consideration when performing nonlinear FE analyses for estimating the plastic buckling of thin and moderately thin short cylindrical shells.

Aluminium plates with pre-formed slits subjected to blast loading

The dynamic response of thin, perforated aluminium plates subjected to blast loading was studied both experimentally and numerically. Two different blast intensities were used and the plates were pre-cut with four horizontal and vertical slits prior to testing. The applied AA6016-T4 plates had an exposed area of 0.3 m x 0.3 m and a thickness of 1.5 mm. Special focus was placed on the dynamic response and failure characteristics of the plates. Uniaxial tensile tests were conducted in three different directions to determine the material behaviour and material parameters were found by inverse modelling using the optimization tool LSOPT. Finally, numerical simulations were performed in the finite element code Abaqus/Explicit where the plates were uniformly loaded with time-dependent pressure histories from similar tests on massive plates. The material behaviour was assumed to follow the J2 flow theory of plasticity and an uncoupled damage model was used in combination with element erosion to predict material failure. The numerical results were in good agreement with the experimental observations and predicted both the dynamic response and the complete tearing of the centre part of the plates.

An Analytical Insight into the Buckling Paradox for Circular Cylindrical Shells under Axial and Lateral Loading

A large number of authors in the past have concluded that the flow theory of plasticity tends to overestimate significantly the buckling load for many problems of plates and shells in the plastic range, while the deformation theory generally provides much more accurate predictions and is consequently used in practical applications. Following previous numerical studies by the same authors focused on axially compressed cylinders, the present work presents an analytical investigation which comprises the broader and different case of nonproportional loading. The analytical results are discussed and compared with experimental and numerical findings and the reason for the apparent discrepancy on the basis of the so-called “buckling paradox” appears once again to lay in the overconstrained kinematics on the basis of the analytical and numerical approaches present in the literature.

Efficient pseudo-inverse approach for damage prediction in cold forging process simulation

This article presents an efficient pseudo-inverse approach for the damage prediction in cold forging process simulation. Pseudo-inverse approach combines the advantages of the fast inverse approach and accurate incremental approaches. Some intermediate configurations are created geometrically and corrected mechanically to well describe the deformation path. The formulation of an axi-symmetrical element based on pseudo-inverse approach is presented. A strain-based damage model is introduced in the flow theory of plasticity. A direct scalar integration algorithm of plasticity-damage is developed, leading to a fast and robust algorithm for large strain increments. The cold forging processes of two axi-symmetrical parts are simulated to validate pseudo-inverse approach by the incremental approach ABAQUS/Explicit. Pseudo-inverse approach gives very good results, but uses much less CPU time.

Novel Plasticity Integration Algorithm in Improved Inverse Analysis Method and its Verification in Clover-Shaped Cup Drawing

An improved inverse analysis method is developed based on the final workpiece in Euler coordinate system. The drawbeads and the radius of the die introduce a complex bending-unbending loading history as the material passes through these regions. Unlike the widespread inverse analysis using deformation theory of plasticity, in order to consider loading history, the improved inverse analysis method uses the constitutive equation based on flow theory of plasticity. In order to avoid numerous iterations to ensure the numerical stability in Newton-Raphson scheme to obtain plastic multiplier , a novel plastic integration algorithm is proposed to consider bending–unbending effects. A clover-shaped cup drawing example is numerically simulated with the inverse analysis method based on deformation theory of plasticity and the improved one based on flow theory of plasticity. These simulated results are compared with those of the incremental forward finite element solver LS-DYNA simultaneously. The comparisons of blank configurations and the effective strain distribution show that the proposed plasticity integration algorithm is effective and reliable.

Effect of Local Imperfections on the Collapse of Tubes Under Bending and Internal Pressure

Previous work by the authors investigated the inelastic response and stability of pipes bent in the presence of internal pressure [1,2]. It was shown that internal pressure tends to stabilize the pipe by reducing initial geometric imperfections and reducing the induced ovalization. Consequently pressurized pipe can sustain significantly higher bending strains before collapse than pipe bent in the absence of pressure. Pipelines have girth welds and other local imperfections such as dents. The present phase of this work uses experiment and analysis to investigate the effect of local dents on the collapse capacity of pressurized pipes under pure bending. A series of experiments was conducted on stainless steel 321 seamless tubes with diameters of 1.5 inches and D/t of 52. Small imperfections in the form of transverse dents were introduced to the specimens using a custom technique that limits the axial and circumferential spans of the dents. The dented tubes were loaded by pure bending at a fixed internal pressure (approximately one half the yield pressure) to collapse. Tubes with dent depths ranging from very small to about 1.7 times the pipe wall thickness were tested. It was found that such local imperfections tend to reduce the bending strain capacity of the pipe quite significantly. Smaller depth dents tend to cause relatively larger reduction in the bending strain at collapse whereas at larger depths the bending strain at collapse tends to level off. The inelastic response and the eventual localized collapse are being simulated using FE models. The material is represented as an anisotropic elastic-plastic solid using the flow theory of plasticity. The modeling includes simulation of the denting process followed by pressurization and bending. It will be shown that all aspects of the observed behavior including the sensitivity of collapse strain to the local imperfection are reproduced well by the models.