Qianhua Kan

A truncated conical beam model for analysis of the vibration of rat whiskers

A truncated conical beam model is developed to study the vibration behaviour of a rat whisker. Translational and rotational springs are introduced to better represent the constraint conditions at the base of the whiskers in a living rat. Dimensional analysis shows that the natural frequency of a truncated conical beam with generic spring constraints at its ends is inversely proportional to the square root of the mass density. Under all the combinations of the classical free, pinned, sliding or fixed boundary conditions of a truncated conical beam, it is proved that the natural frequency can be expressed as f = α(rb/L(2))E/ρ and the frequency coefficient α only depends on the ratio of the radii at the two ends of the beam. The natural frequencies of a representative rat whisker are predicted for two typical situations: freely whisking in air and the tip touching an object. Our numerical results show that there exists a window where the natural frequencies of a rat whisker are very sensitive to the change of the rotational constraint at the base. This finding is also confirmed by the numerical results of 18 whiskers with their data available from literature. It can be concluded that the natural frequencies of a rat whisker can be adjusted within a wide range through manipulating the constraints of the follicle on the rat base by a behaving animal.

Uniaxial Time-Dependent Ratcheting of SS304 Stainless Steel at High Temperatures

The uniaxial time-dependent strain cyclic behaviors and ratcheting of SS304 stainless steel were studied at high temperatures (350 °C and 700 °C). The effects of straining and stressing rates, holding time at the peak and/or valley of each cycle in addition to ambient temperature on the cyclic softeninglhardening behavior and ratcheting of the material were discussed. It can be seen from experimental results that the material presents remarkable time dependence at 700 °C, and the ratcheting strain depends greatly on the stressing rate, holding time and ambient temperature, Some significant conclusions are obtained, which are useful to build a constitutive model describing the time-dependent cyclic deformation of the material.

Damage-based life prediction model for uniaxial low-cycle stress fatigue of super-elastic NiTi shape memory alloy microtubes

Based on the experimental observations for the uniaxial low-cycle stress fatigue failure of super-elastic NiTi shape memory alloy microtubes (Song et al 2015 Smart Mater. Struct. 24 075004) and a new definition of damage variable corresponding to the variation of accumulated dissipation energy, a phenomenological damage model is proposed to describe the damage evolution of the NiTi microtubes during cyclic loading. Then, with a failure criterion of Dc = 1, the fatigue lives of the NiTi microtubes are predicted by the damage-based model, the predicted lives are in good agreement with the experimental ones, and all of the points are located within an error band of 1.5 times.

Experimental observations on uniaxial whole-life transformation ratchetting and low-cycle stress fatigue of super-elastic NiTi shape memory alloy micro-tubes

In this work, the low-cycle fatigue failure of super-elastic NiTi shape memory alloy micro-tubes with a wall thickness of 150 μm is investigated by uniaxial stress-controlled cyclic tests at human body temperature 310 K. The effects of mean stress, peak stress, and stress amplitude on the uniaxial whole-life transformation ratchetting and fatigue failure of the NiTi alloy are observed. It is concluded that the fatigue life depends significantly on the stress levels, and the extent of martensite transformation and its reverse play an important role in determining the fatigue life. High peak stress or complete martensite transformation shortens the fatigue life.

An energy-based fatigue failure model for super-elastic NiTi alloys under pure mechanical cyclic loading

The fatigue failure of a super-elastic NiTi alloy was observed by uniaxial stress-controlled cyclic tests. During the cyclic loading a hysteresis loop with a varied but stabilized size after certain cycles was obtained, which is similar to plastic shakedown. The material exhibits unique brittle fracture with a large transformation strain. The fatigue life of the material greatly depends on the applied peak nominal stress, the nominal stress amplitude and the mean nominal stress. A relation between the dissipation energy at the stabilized stage of cyclic loading and the number of cycles at failure was derived from the experimental results. Based on the obtained experimental results, a uniaxial fatigue failure model based on the energy approach was proposed to predict the fatigue life. It was shown that the proposed model provides good predictions to the uniaxial fatigue lives of super-elastic NiTi alloys with different types of cyclic stressing.

Super-elastic constitutive model considering plasticity and its finite element implementation

Based on the experimental results of super-elastic NiTi alloy, a three-dimensional super-elastic constitutive model including both of stress-induced martensite transformation and plasticity is constructed in a framework of general inelasticity. In the proposed model, transformation hardening, reverse transformation of stress-induced martensite, elastic mismatch between the austenite and martensite phases, and temperature-dependence of transformation stress and elastic modulus of each phase are considered. The plastic yielding of martensite occurred under high stress is addressed by a bilinear isotropic hardening rule. Drucker-Prager-typed transformation surfaces are employed to describe the asymmetric behavior of NiTi alloy in tension and compression. The prediction capability of the proposed model is verified by comparing the simulated results with the correspondent experimental ones. Based on backward Euler’s integration, a new expression of consistent tangent modulus is derived. The proposed model is then implemented into a finite element package ABAQUS by user-subroutine UMAT. Finally, the validity of such implementation was verified by some numerical samples.

Observation on the transformation domains of super-elastic NiTi shape memory alloy and their evolutions during cyclic loading

The strain field of a super-elastic NiTi shape memory alloy (SMA) and its variation during uniaxial cyclic tension-unloading were observed by a non-contact digital image correlation method, and then the transformation domains and their evolutions were indirectly investigated and discussed. It is seen that the super-elastic NiTi (SMA) exhibits a remarkable localized deformation and the transformation domains evolve periodically with the repeated cyclic tension-unloading within the first several cycles. However, the evolutions of transformation domains at the stage of stable cyclic transformation depend on applied peak stress: when the peak stress is low, no obvious transformation band is observed and the strain field is nearly uniform; when the peak stress is large enough, obvious transformation bands occur due to the residual martensite caused by the prevention of enriched dislocations to the reverse transformation from induced martensite to austenite. Temperature variations measured by an infrared thermal imaging method further verifies the formation and evolution of transformation domains.

A finite viscoelastic–plastic model for describing the uniaxial ratchetting of soft biological tissues

In this paper, a phenomenological constitutive model is constructed to describe the uniaxial ratchetting (i.e., the cyclic accumulation of inelastic deformation) of soft biological tissues in the framework of finite viscoelastic-plasticity. The model is derived from a polyconvex elastic free energy function and addresses the anisotropy of cyclic deformation of the tissues by means of structural tensors. Ratchetting is considered by the evolution of internal variables, and its time-dependence is described by introducing a pseudo-potential function. Accordingly, all the evolution equations are formulated from the dissipation inequality. In numerical examples, the uniaxial monotonic stress-strain responses and ratchetting of some soft biological tissues, such as porcine skin, coronary artery layers and human knee ligaments and tendons, are predicted by the proposed model in the range of finite deformation. It is seen that the predicted monotonic stress-strain responses and uniaxial ratchetting obtained at various loading rates and in various loading directions are in good agreement with the corresponding experimental results.

FINITE ELEMENT IMPLEMENTATION OF A SUPER-ELASTIC CONSTITUTIVE MODEL FOR TRANSFORMATION RATCHETTING OF NiTi ALLOY

In the previous work, a new constitutive model describing the transformation ratchetting of super-elastic NiTi alloy was proposed. The finite element implementation of the proposed model is discussed in this work, because such implementation is necessary to launch a numerical analysis for the cyclic stress–strain responses of NiTi alloy devices including the transformation ratchetting. During the implementation, a new stress integration algorithm is adopted, and a new expression of the consistent tangent modulus is derived for the forward transformation and the reverse transformation. The finite element implementation is elaborated by the user subroutine of UMAT in ABAQUS based on backward Euler method. The accumulated error during cyclic transformation is controlled by a robust convergence criterion. Finally, the validity of such implementation is verified by several numerical examples.

A New Kinematic Hardening Rule Describing Different Plastic Moduli in Monotonic and Cyclic Deformations

To describe the different plastic moduli of the metal materials presented in the monotonic and cyclic deformations, a new nonlinear kinematic hardening rule is proposed by modifying the Chaboche’s one (Chaboche 1989). In the proposed rule, the back stress is assumed to be decomposed into three components as done by Chaboche (1989), but the linear hardening and dynamic recovery terms of each back stress component are further divided into two parts, respectively, and a part in each of them is only activated when the reverse loading occurs so that the cyclic stress-strain hysteresis loops can be predicted more accurately; moreover, a rachetting coefficient is introduced into one part of dynamic recovery term to describe the ratchetting. The proposed rule can be reduced to the Chaboche’s one under the monotonic loading conditions, or by setting some material parameters as zero. Finally, the proposed model is verified by comparing the predicted results with corresponding experimental ones. It is seen that the predicted results are in good agreement with the corresponding experimental ones.