Role Of Strain Rate Sensitivity Research Articles

Role of strain rate sensitivity of extrafibrillar matrix on fracture in mineralized collagen fibril arrays

Bone is a biological composite possessing complex hierarchical structure, which endows it with extraordinary damage tolerance. Despite the progress on the relationship between fracture behavior and the hierarchical structure of bone, contributions of the submicroscale constituents to fracture resistance of bone remain elusive. In this study, the calculations are carried out for fracture in staggered mineralized collagen fibril (MCF) arrays using the cohesive zone framework. The strain rate hardening of extrafibrillar matrix (EFM), post-yield strain hardening of the EFM, plastic deformation of the MCF caused by mineral/collagen sliding, and debonding of the interface between MCF and EFM are accounted for in the analyses; the individual and combined effects of strain rate sensitivity of the EFM and fracture properties of the EFM-MCF interface are revealed. It is found that for the strong EFM-MCF interface, high degree of strain rate sensitivity of EFM gives rise to low toughness of MCF arrays. Compared with plastic deformations in MCFs and EFM, interfacial debonding provides smaller contribution to toughness of MCF arrays, and plastic dissipation of MCFs is the major source of toughening. For the tough EFM-MCF interface, the toughness of MCF arrays increases with increasing degree of strain rate sensitivity of EFM, and the EFM with high degree of strain rate sensitivity promotes spreading of plastic deformation, leading to amplified damage energy dissipation in interfaces. We have further identified that strain rate sensitivity of the EFM has negligible influence on toughness of MCF arrays in the case of weak EFM-MCF interface, where interfacial debonding serves as the major toughening mechanism. However, the strain rate sensitive EFM can still activate the mechanism of spreading plastic deformation in this case, giving rise to the increase in relative contribution of plastic dissipation in MCFs with increasing strain rate sensitivity of the EFM.

Plastic Instabilities in Spherical Vessels for Static and Dynamic Loading

Significant changes were made in design limits for pressurized vessels in the 2007 version of the ASME code (Sec. VIII, Div. 3) and 2008 and 2009 Addenda, and these are now a part of the 2010 code. There is now a local damage-mechanics based strain-exhaustion limit, including the well-known global plastic collapse limit. Moreover, Code Case 2564 (Sec. VIII, Div. 3) has recently been approved to address impulsively loaded vessels. It is the purpose of this paper to investigate the plastic collapse limit as it applies to dynamically loaded spherical vessels. Plastic instabilities that could potentially develop in spherical shells under symmetric loading conditions are examined for a variety of plastic constitutive relations. First, literature survey of both static and dynamic instabilities associated with spherical shells is presented. Then, a general plastic instability condition for spherical shells subjected to displacement-controlled and short-duration dynamic pressure loading is given. This instability condition is evaluated for six plastic and viscoplastic constitutive relations. The role of strain rate sensitivity on the instability point is investigated. Conclusions of this work are that there are two fundamental types of instabilities associated with failure of spherical shells. In the case of impulsively loaded vessels, where the pulse duration is short compared with the fundamental period of the structure, one instability type is found not to occur in the absence of static internal pressure. Moreover, it is found that the specific role of strain rate sensitivity on the instability strain depends on the form of the constitutive relation assumed.

Computational evaluation of strain-rate-dependent deformation behavior of rubber and carbon-black-filled rubber under monotonic and cyclic straining

The molecular chain network model for elastic deformation behavior and the reptation theory for viscoelastic deformation behavior are used to derive a constitutive equation for rubber. The new eight-chain-like model contains eight standard models consisting of Langevin springs and dashpot to account for the interaction of chains with their surroundings. Monotonic and cyclic deformation behavior of rubber with relaxation under different strain rates have been examined. The results reveal the roles of the individual springs and dashpot, and the strain rate dependence of materials in the monotonic and cyclic deformation behaviors, particularly softening and hysteresis loss, that is, the Mullins effect, occurring in stress–stretch curves under cyclic deformation processes. The validity of the results is checked through comparison with experimental results. The deformation behaviors of a plane strain rubber unit cell containing carbon-black (CB) under monotonic and cyclic straining are investigated by computational simulation using the proposed constitutive equation and homogenization method. The results reveal the substantial enhancement of the resistance of CB-filled rubber to macroscopic deformation, which is caused by the marked orientation hardening due to the highly localized deformation of rubber. The role of strain rate sensitivity on such characteristic deformation behaviors as increases in the resistance to deformation, hysteresis loss, and the effects of the distribution morphology and the volume fraction of CB on the deformation behavior is clarified. The increases in the volume fraction and in the aggregation of the distribution of CB substantially raise the resistance to deformation and hysteresis loss.

Role of strain-rate sensitivity in the crystal plasticity of hexagonal structures

In the first part of this paper the stress and strain-rate response of hexagonal crystal structures are examined when slip is viscoplastic according to a power law. The stress and strain-rate equi-potential surfaces are constructed and discussed as a function of the strain-rate sensitivity index m. The second part of this paper deals with the case of linear viscous slip; i.e., for the case when m is equal to one. A simple analytic solution is presented to obtain the deviatoric stress state for a given strain-rate. It is shown that the plastic spin is not zero for m = 1 in hexagonal crystal structures, contrary to the cubic case where the plastic spin vanishes. In addition, the rate of texture evolution in simple shear of a magnesium polycrystal is examined as a function of m.

A Classification of flow-Stress Anomalies, and the Specific Role of Strain Rate Sensitivity

We propose a classification of stress anomaly mechanisms based on two limiting cases, according whether the macroscopic behaviour directly reflects the individual dislocation properties, or involves the whole dislocation population. We show that, in the second case, some typical anomalies can be defined according to the relative efficiencies of mechanisms responsible for an increase or a decrease of the mobile dislocation density, and are associated with specific strain rate sensitivities. The way in which such an analysis can help in deciding which models are most relevant is discussed.