Micro-asperity Contact Area considering Strain Hardening for Metallic Materials

A novel micro-asperity contact area model, which considers influences of strain hardening, is proposed to describe contact area between a deformable sphere and a rigid flat for metallic materials. Firstly a generalized formula considering work-hardening behaviors (Pilling-up or Sinking-in) between contact area and interference is proposed for fully plastic regime based on the definition of plastic contact area index. Then a relationship to calculate the critical interference at the inception of fully plastic deformation is derived. In order to incorporate the transition from elastic regime to fully plastic regime, a quadratic rational form formula is proposed based volume conservation model for mixed elastoplastic regime. Therewith a modification is conducted to ensure continuity of contact area model at critical interference for fully plastic regime. Ultimately several representative models and experiment results are exhibited to analyze the availability of present model. It is noted considering work-hardening fully plastic contact area index is not a constant value of 2 for any metallic materials, which is a function of strain hardening exponent. Demonstration testifies that smoothness constraint is not necessary at the critical interferences. The prediction data of present model is consistent with experiment results contrasting that of other models. Current generalized contact area model considering influence of work-hardening results in a better understanding of the contact area between a deformable sphere and a rigid flat and indicates a probability to analyze contact characteristics of two mating rough surfaces accurately.

Influence of Different Strain Hardening Models on the Behavior of Materials in the Elastic–Plastic Regime under Cyclic Loading

In exact analyses of bodies in the elastic–plastic regime, the behavior of the material above critical stress values plays a key role. In addition, under cyclic stress, important phenomena to be taken into account are the various types of hardening and the design of the material or structure. In this process, it is important to define several groups of characteristics. These include, for instance, the initial area of plasticity or load which defines the interface between elastic and plastic deformation area. The characteristics also include the relevant law of plastic deformation which specifies the velocity direction of plastic deformation during plastic deformation. In the hardening condition, it is also important to determine the position, size and shape of the subsequent loading area. The elasto-plastic theory was used for the analysis of special compliant mechanisms that are applied for positioning of extremely precise members of the Compact Linear Collider (CLIC), e.g., cryomagnets, laser equipment, etc. Different types of deformation hardening were used to simulate the behavior of particular structural elements in the elastic–plastic regime. Obtained values of stresses and deformations may be used in further practical applications or as default values in other strain hardening model simulations.

Fine-tuning of stress-induced martensite in TRIP/TWIP Ti alloys

Fine-tuning of stress-induced martensitic (SIM) transformation was studied in Ti-Mo based β metastable alloys, showing combined Transformation Induced Plasticity (TRIP) and Twinning Induced Plasticity effects (TWIP) effects. The work aimed to clarify the transition and interaction between the two deformation mechanisms and their influences on the mechanical properties of Ti-Mo based alloys. Electron parameter design methods (Bo-Md and e/a ratio) were cross-used to increase the β phase stability from near-TRIP to near-TWIP by adding third alloying elements. SIM α″ transformation and mechanical twinning were traced by in-situ EBSD (Electron backscatter diffraction) mapping under cyclic tension. The deformation modes of β phase exhibited significant changes when shifting its metastability via chemical composition modifications. In near-TRIP conditions (dominated by the growth of SIM α″ in plastic regime), SIM α″ transformation and internal twinning of martensite were the main mechanisms to accommodate the local stress-strain conditions. In near-TWIP ones (dominated by the growth of {332}<113>β twinning in plastic regime), SIM α″ was observed only at twinning interface during strain process and disappeared after stress release.

Elastic–Plastic Response of Clamped Square Plates Subjected to Repeated Quasi-Static Uniform Pressure

In this paper, an elastic–plastic analytical method is proposed to predict the cyclic deformation of the fully clamped square plates made of elastic–perfectly plastic material under repeated quasi-static uniform pressure. The whole process can be divided into the loading and unloading phases. The loading phase is formulated as three separate regimes: the elastic regime, the mixed elastic–plastic regime and the fully plastic regime. Unloading from a status in each phase is modeled as an elastic process. The total and elastic strain energies are characterized by the loading and unloading paths together with the displacement profiles, respectively. It is theoretically revealed that the elastic strain energy and the structural stiffness of the plate increase with the increasing transverse deflection. In addition, the effect of material elasticity is highlighted in the scenario of repeated loadings. The theoretical results are validated against the numerical simulations conducted by the commercial software ABAQUS. It is shown that the proposed elastic–plastic theoretical model has reasonable accuracy and can be employed to predict pressure–deflection relationship for this class of problems.

Contact Law and Coefficient of Restitution in Elastoplastic Spheres

A complete contact cycle of an elastoplastic sphere consists of loading and unloading phases. The loading phase may fall into three sequential regimes: elastic, mixed elastic–plastic, and fully plastic. In this paper, we distinguish the transition points among the three regimes via the material hardness and a dimensionless geometric parameter corresponding to the onset of the fully plastic regime. Based on Johnson’s simplified spherical expansion model, together with the well-supported force–indentation relationships in the elastic and fully plastic regimes, we build an analytical approximation for the mixed elastic–plastic regime by enforcing the C1 continuity of a loading force–indentation curve. Unloading responses of the elastoplastic sphere are characterized by an elastic force–indentation relation, which has a Hertzian-type form but takes into account the effects of the strain hardening that occurs in the mixed elastic–plastic regime. We validate the model by comparing with existing quasi-static and impact experiments and show that the model can precisely capture the force–indentation responses. Further validation is performed by employing the proposed compliance model to investigate the coefficient of restitution (COR). We achieve agreement between our numerical results and the experimental data reported in other studies. Particularly, we find that the COR is inversely proportional to the impacting velocity with an exponent equal to 1/6, instead of 1/4 reported by many other models.

Analytical Study of an Isotropic Viscoplastic Sea Ice Model in Idealized Configurations

Analytic solutions of a mechanical sea ice model are computed in idealized configurations. They are then used to study the properties of this model. It classically assumes that the ice behaves at large scale as an isotropic viscoplastic medium. The plastic regime is characterized by a Mohr–Coulomb yield curve. The flow rule corresponds to the one used in granular mediums and depends on a parameter δ that characterizes the expansion properties of the medium. Using simple model configurations, this study first shows that a sliding of the ice along the coast must be permitted; otherwise, the model generally has no solution when the plastic regime is active. This study then shows that the viscous regime is reached only if the stress remains nearly uniform over a large area. For a stress having no particular properties, the plastic regime acts everywhere. In this case, the compressive stress may reach the maximum value allowed by the model close to the coastline. The extension of the domain where the compressive stress is at its maximum depends on δ and the direction of the forcing field. Over this domain, the ice behaves as a fluid material with a small negative viscosity. Last, the authors found that neither the existence of the solution nor its unicity are guaranteed in this stationary model. This result does not imply that the unicity is lost in the transient problem; it suggests that the evolution of sea ice depends not only on the forcing, but also on the initial conditions or history of the system.