Reza Adibi-Asl

Special Section on Ratcheting

The design methods for pressure vessels and piping are based on the avoidance of potential modes of failure, such as collapse, excessive deformation, and cracking. Collapse and excessive deformation from a single load application are addressed by methods such as buckling analysis, primary stress analysis, and plastic limit analysis. For instance, limit load design underlies the evaluation methods for design conditions in most existing pressure vessel design codes. When significant cyclic loading is applied, the evaluation of fatigue and ratcheting effects becomes necessary. Fatigue analysis is concerned with avoiding the initiation and propagation of cracks that could eventually cause a sudden fracture. Ratcheting is a failure mode typically associated with components that are subjected to pressure loading and simultaneously large cyclic thermal stresses. It is characterized by deformations or plastic strains that accumulate with increasing load cycles. Continued deformation can eventually render the component unserviceable and strain accumulation can accelerate fatigue cracking, which is not accounted for in the fatigue analysis. Ratcheting can occur in metals, but also in nonmetallic materials. In order to avoid ratcheting, the cyclic loads must be kept within a specific limit that depends on the level of simultaneously applied mechanical loading (shakedown limit). By maintaining the stresses below the shakedown limit, some incremental plastic deformation may occur during the initial loading cycles, but the deformation in the subsequent cycles will be stable cycling, either in the elastic range (elastic shakedown) or involving alternating plasticity (plastic shakedown). Typical simplified evaluation methods in the design codes are based on perfect (nonhardening) plasticity. Such methods and their extensions, such as direct methods of shakedown analysis, promise simple and efficient solutions and are still being developed. Due to the numerical methods that are now available, a full cyclic plastic simulation that could include work hardening is also becoming feasible. There are, however, some knowledge gaps in the application of hardening plasticity models to shakedown or ratchet analysis. For example, apparently equivalent descriptions of a plastic stress–strain curve by different plasticity models which give comparable results for static loading and even for steady cyclic response can have widely different ratcheting behavior. Depending on the plasticity model, the response may vary from guaranteed shakedown independent of loading to unexpected ratcheting under some stress states. Therefore, there is active research involving experimental studies of ratcheting and development of plasticity models to better describe the material response to various loading combinations. Simultaneously, efforts are underway to identify simple existing plasticity models that include hardening and are suitable for an engineering analysis of shakedown or ratcheting. This special section on ratcheting has a total of 12 papers which represent a good mixture of theoretical, numerical, and experimental research in this area.

Lower Bound Limit Loads Using the Reference Two-Bar Structure: An Improved Estimate Beyond Mura’s Lower Bound

Mura’s lower bound limit load multiplier (m′) has been obtained on the basis of a variational formulation (Mura et al., 1965). However, m′ is equal to or less than the classical lower bound multiplier (mL). In this paper, a relationship between the m′ multiplier and the reference two-bar multiplier (Seshadri, R., and Adibi-Asl, R., 2007) is obtained. The nature of the bounds is examined in the context of several pressure components.Copyright

Application of the Non-Cyclic Method of Shakedown Analysis to Problems With Cyclically Moving Thermal Stress

The non-cyclic method of shakedown analysis allows the entire ratchet boundary to be determined for a given set of monotonic and cyclic loads on a component. The method is based on an extension of the lower bound shakedown theorem. Typically, the loading of interest to shakedown consists of cyclic thermal loading acting in conjunction with cyclic and monotonic (mean) primary loads, such as pressure.To date, a certain class of spatially moving cyclic thermal loads could not be analyzed with numerical implementations of the non-cyclic method. In these cases, the mean thermal load cannot be balanced by a self-equilibrating stress state, and the component can ratchet under a purely thermal load. This paper examines why the restriction on the non-cyclic method and similar other approaches to shakedown analysis exists, and proposes an extension with the help of which an analysis of this class of problems becomes feasible. The method is demonstrated on a number of simple examples.Copyright

Plastic Response Estimation in Repeated Elastic Analyses for Strain Hardening Material Model

Simplified limit analysis techniques have already been employed for limit load estimation on the basis of linear elastic finite element analysis (FEA) assuming elastic-perfectly-plastic material model. Due to strain hardening, a component or a structure can store supplementary strain energy and hence carries additional load. In this paper, an iterative elastic modulus adjustment scheme is developed in context of strain hardening material model utilizing the “strain energy density” theory. The proposed algorithm is then programmed into repeated elastic FEA and results from the numerical examples are compared with inelastic FEA results.

Estimating Lower Bound Limit Loads: No Iterations/Modulus Adjustment

We use the extended variational form of Mura and co-workers to estimate the lower bound limit loads for structures acted upon by a single load. Our scheme requires one elastic stress field either from a conventional finite element computation or analytical solution. No iterative stress field adjustments are required. We also adapt the scheme for structures with flaws by advancing a criterion that may be used to select sub-volumes of the structure that do not participate in the collapse. For structures with flaws, no ad hoc elastic modulus reduction at the stress concentration is required. Application of the proposed method is illustrated for some typical flawed and flaw-free structures and it is shown that the obtained multipliers are not overly conservative.Copyright

Reference Volume Consideration in the mα-Tangent Method Based Linear Elastic Analysis

Limit loads for pressure components are determined on the basis of a single linear elastic finite element analysis by invoking the concept of kinematically active (reference) volume in the context of the “mα -tangent” method. The resulting technique enables rapid determination of lower bound limit load for pressure components by eliminating the kinematically inactive volume. This method is applied to a number of practical components with different percentages of inactive volume. The results are compared with the corresponding inelastic finite element results, or available analytical solutions.Copyright