Simulation of failure under cyclic plastic loading by damage models

The purpose of this work is to simulate the evolution of ductile damage and failure involved by plastic strain reversals using damage models based on either continuum damage mechanics (CDM) or porosity evolution. A low alloy steel for pressure vessels (20MnMoNi55) was chosen as reference material. The work includes both experimental and simulation phases. The experimental campaign involves different kinds of specimens and testing conditions. First, monotonic tensile tests have been performed in order to evaluate tensile and ductile damage behaviour. Then, the cyclic yielding behaviour has been characterized performing cyclic plasticity tests on cylindrical bars. Finally, cyclic loading tests in the plastic regime have been made on different round notched bars (RNBs) to study the evolution of plastic deformation and damage under multiaxial stress conditions. The predictions of the different models were compared in terms of both, the specimens macroscopic response and local damage. Special emphasis was laid on predictions of the number of cycles prior to final failure and the crack initiation loci.     

Moment-curvature relations for a pseudoelastic beam

Pseudoelastic bodies have very simple stress-strain diagrams for uniaxial tensile and compressive loading. In particular, yield and recovery occur at fixed stresses. And yet, the moment-curvature diagrams for bending and unbending of a beam are fairly complex, because the stress and strain fields are non-uniform. The paper shows stress profiles within the beam for pure bending and arrives at explicit equations for loading and unloading curves.     

Application of a discrete polycrystal model to the analysis of cyclic straining in copper

A discrete polycrystal model, designed to simulate a metal aggregate macro-element, is applied to the study of cyclic straining in copper. The numerical method of solution (an adaptation of the “finite element method”) incorporates a convergent discrete Green's function within the constrained minimum principle which governs the (crystallographic) plastic shear increments at each load step. Isothermal elastic moduli of copper crystals and Taylor's hardening rule with constant hardening modulus are used in the calculations. Numerical results are obtained for macroscopic elastic properties, cyclic stress-strain curves (which indicate the contribution of aggregate heterogeneity to macroscopic hardening), macroscopic plastic work, and residual (latent) strain energy through four loading cycles between fixed macrostrain limits. Other estimates for elastic properties also are included, and all results are compared, both qualitatively and quantitatively, with published experiments. The predictions of the model are in general satisfactory.     

Evaluation of cyclic plasticity models in ratcheting simulation of straight pipes under cyclic bending and steady internal pressure

This paper evaluates seven cyclic plasticity models for structural ratcheting response simulations. The models evaluated are bilinear (Prager), multilinear (Besseling), Chaboche, Ohno–Wang, Abdel Karim–Ohno, modified Chaboche (Bari and Hassan) and modified Ohno–Wang (Chen and Jiao). The first three models are already available in the ANSYS finite element package, whereas the last four were implemented into ANSYS for this study. Experimental responses of straight steel pipes under cyclic bending with symmetric end rotation history and steady internal pressure were recorded for the model evaluation study. It is demonstrated that when the model parameters are determined from the material response data, none of the models evaluated perform satisfactorily in simulating the straight pipe diameter change and circumferential strain ratcheting responses. A detailed parameter sensitivity study with the modified Chaboche model was conducted to identify the parameters that influence the ratcheting simulations and to determine the ranges of the parameter values over which a genetic algorithm can search for refinement of these values. The refined parameter values improved the simulations of straight pipe ratcheting responses, but the simulations still are not acceptable. Further, improvement in cyclic plasticity modeling and incorporation of structural features, like residual stresses and anisotropy of materials in the analysis will be essential for advancement of low-cycle fatigue response simulations of structures.     

Finite elastic straining

Summary Finite elastic straining is analysed with all quantities referred consistently to the deformed body taken as the function domain. The straining-displacement of a typical point is relative to a set of axes imbedded in the body at one arbitrary point and rotating in fixed space with that neighborhood if necessary in a particular problem. The resulting |plane stress' equations have precisely the same form as in the classical theory but relate to |true' quantities in the deformed body.The solution of a circular hole in a deformed sheet under simple tension is given and checks closely with experiment on rubber. Cauchy strains of order 65% and local rotation of order 30° are found to occur at the hole boundary.The solution of a deformed quadrantal cantilever is given. Cauchy strains of several hundred percent and local rotation of order 90° occur.Any boundary value problem already solved for the classical infinitesimal strains theory can be applied directly as a finite strains solution for the deformed body.Notation x, y, z, r, , z Cartesian and polar co-ordinates respectively - , Normal and shear true stresses respectively - , Normal and shear true strains respectively - r Position vector - Airy stress function - S Simple tensile stress applied to sheet - a Radius of circular hole in deformed sheet - a, b Inner and outer radii of quadrantal cantilever - u Straining-displacement vector - u, v Straining-displacement scalar components - E, True Young's modulus and Poisson's ratio respectively - c ₁, c ₂ Local unit vectors in principal normal strains directions - i, j Cartesian axes constant unit vectors - Stress dyadic or tensor - First stress invariant - I Idemfactor or spherical tensor - P Shear load per unit thickness applied to quadrantal cantilever - A, B, D, N, H, K, L Arbitrary constants of integration     

On strain and straining

Communicated by K. R. Rajagopal For Máirín and Siobhán     

Mechanical requirements and structures of cyclic plasticity models

The condition of continuity in the large and in the small and Masing effect as the mechanical requirements for cyclic plasticity are first formulated. The basic characteristics of several well-known and frequently used cyclic plasticity models are examined with respect to fulfillment of these requirements, and their inevitable defects are indicated. It is concluded that among these models only the extended subloading surface model fulfills these requirements and is applicable to the prediction of elastoplastic deformation for cyclic loading, although unfortunately the other models, especially the multi, the two, and the initial subloading surface models, have been frequently adopted for metals, geomaterials, concretes, and so forth.     

Investigation of high elastoplastic straining of shells of revolution under complex tensile and torque loading

A method of the numerical solution of nonlinear unsteady problems of axisymmetric elastoplastic straining of shells of revolution with allowance for torque loading at high strains is proposed. The method is based on the geometrically nonlinear theory of the Timoshenko shells and the plasticity theory with due allowance for combined isotropic and kinematic hardening. The problem is solved with the use of the variational difference method. Results of numerical and experimental investigations of elastoplastic straining of cylindrical shells under proportional and sequential kinematic tensile and torque loading are reported.     

Plastic flow under multiaxial cyclic loading

An experimental study of the inelastic behavior of annealed aluminum alloy 6061-T6 tubular specimens subjected to combined axial and torsional stress cycles is presented. Particular attention is paid to the question of how plastic strain is developed and how the yield surface moves along the 90-deg out-of-phase stress cycle. Experimental results agree qualitatively with the predictions of the two-surface plasticity theory. Paper was presented at the 1985 SEM Spring Conference on Experimental Mechanics held in Las Vegas, NV on June 9–14, 1985.     

Mechanical model of round window membrane under reverse excitation

According to the vibration characteristics of the round window, a mechanical model of a round window membrane is established. The Euler equation of the round window and the complementary boundary conditions are derived by the variational principle. Combined with the Bessel function, an analytical solution of the round window displacement is obtained by MATHEMATICA. Combined with clinical characteristics of round window membrane lesion, the effect of sound transmission due to thickening of the round window membrane caused by the otitis media, shrinkage of the round window membrane area caused by otosclerosis, and hardening of the round window membrane itself is analyzed. The results show that with thickening of the round window membrane, the displacement of the round window membrane is decreased. In the meantime, with hardening of the round window membrane and shrinkage of the membrane area, the maximum displacement of the round window membrane is gradually reduced, leading to a decrease in sound transmission. Thus, the analytical analysis can avoid interference of environment and the technical level of personnel, and it can evaluate transmission performance of the round window membrane efficiently, providing a theoretical basis for the reverse excitation of artificial prosthesis.     

The effect of straining mode on void growth

Large strain finite element method is employed to investigate the effect of straining mode on void growth. Axisymmetric cell model embedded with spherical void is controlled by constant triaxiality loading, while plane-stress model containing a circular void is loaded by constant ratio of straining. Elastic-plastic material is used for the matrix in both cases. It is concluded that, besides the known effect of triaxiality, the straining mode which intensifies the plastic concentration around the void is also a void growth stimulator. Experimental results are cited to justify the computation results. This paper is jointly supported by the National Natural Science Foundation of China (19872064), the Chinese Academy of Sciences (KJ951-1-201) and the Laboratory for Nonlinear mechanics of Continuous Media of the Institute of Mechanics     

Mechanical annealing under low-amplitude cyclic loading in micropillars

Mechanical annealing has been demonstrated to be an effective method for decreasing the overall dislocation density in submicron single crystal. However, simultaneously significant shape change always unexpectedly happens under extremely high monotonic loading to drive the pre-existing dislocations out of the free surfaces. In the present work, through in situ TEM experiments it is found that cyclic loading with low stress amplitude can drive most dislocations out of the submicron sample with virtually little change of the shape. The underlying dislocation mechanism is revealed by carrying out discrete dislocation dynamic (DDD) simulations. The simulation results indicate that the dislocation density decreases within cycles, while the accumulated plastic strain is small. By comparing the evolution of dislocation junction under monotonic, cyclic and relaxation deformation, the cumulative irreversible slip is found to be the key factor of promoting junction destruction and dislocation annihilation at free surface under low-amplitude cyclic loading condition. By introducing this mechanics into dislocation density evolution equations, the critical conditions for mechanical annealing under cyclic and monotonic loadings are discussed. Low-amplitude cyclic loading which strengthens the single crystal without seriously disturbing the structure has the potential applications in the manufacture of defect-free nano-devices.     

Modelling of crack growth under cyclic contact loading

The paper describes a general computational model for modelling of subsurface fatigue crack growth under cyclic contact loading of mechanical elements. The model assumes that the initial fatigue crack develops along the slip line in a single crystal grain at the point of the maximum equivalent stress. The position and magnitude of the maximum equivalent stress are determined with the Finite Element Analysis of the equivalent contact model, which is based on the Hertzian contact conditions with the addition of frictional forces. The Virtual Crack Extension method is then used for simulation of the fatigue crack propagation from the initial to the critical crack length, when the surface material layer breaks away and a pit appears on the surface. The pit shapes and relationships between the stress intensity factor and the crack length are determined for various combinations of contacting surface curvatures and contact loadings. The computational results show that the model reliably simulates the subsurface fatigue crack growth under contact loading and can be used for computational predictions of surface pitting for various contacting mechanical elements.     

Plasticity model for metals under cyclic large-strain loading

This paper deals with mathematical modeling of one of the effective technologies of plastic metal forming — multistep cold metal forging. Experimental results are given on the plastic behavior of metals under cyclic loading at large strains accumulated for one cycle. Based on the experimental data obtained, a plasticity model is developed and shown to be effective in testing and improving the technology of forging a nut blank by using a computer-aided engineering analysis system.     

Transverse isotropic poroelastic osteon model under cyclic loading

The poroelastic problem associated with a hollow cylinder under cyclic loading is solved. This cylinder models an osteon, basic unit of cortical bone. Both fluid and solid phases are supposed compressible. Solid matrix is modeled as an elastic transverse isotropic material. An explicit close-form solution for the steady state is obtained. Fluid flow distribution as a function of poroelastic properties and cyclic loading is discussed as it could influence bone remodeling. Strain rate of loading is shown to play a significant role in mass flux in the porous material.