Kwangsoo Ho

Optical Power Transfer of Grating - Assisted Directional Coupler with Three - Guiding Channels : TM modes Case

Newly developed modal transmission-line theory(MTLT) is used to analyze rigorously the optical power distribution in grating-assisted directional couplers(GADCs) with three guiding channels. By defining a novel coupling efficiency

A Phenomenological Constitutive Model for Pseudoelastic Shape Memory Alloy

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An Improved Constitutive Model of Shape Memory Alloy

amenable to the rigorous analytical solutions of modal transmission-line theory, we explicitly evaluate the power coupling and distribution of TM modes. The results reveal that the incident power is sensitively partitioned through three output channels in terms of such grating parameters as the grating period, the duty cycle, and the operating wavelength.

The Rate Dependent Deformation Behavior of AISI Type 304 Stainless Steel at Room Temperature

Abstract Shape memory alloys (SMAs) have the ability to recover their original shape upon thermo-mechanical loading even after large inelastic deformation. The unique feature is known as pseudoelasticity and shape memory effect caused by the crystalline structural transformation between two solid-state phases called austenite and martensite. To support the engineering application, a number of constitutive models, which can be formally classified into either micromechanics-based or phenomenological model, have been developed. Most of the constitutive models include a kinetic law governing the crystallographic transformation. The present work presents a one-dimensional, phenomenological constitutive model for SMAs in the context of the unified viscoplasticity theory. The proposed model does not incorporate the complex mechanisms of phase transformation. Instead, the effects induced by the transformation are depicted through the growth law for the back stress that is an internal state variable of the model.

A Constitutive Model for the Rate-dependent Deformation Behavior of a Solid Polymer

Abstract Shape memory alloys(SMAs) exhibit pseudoelastic behavior, characterized by the recovery of an original shape even after severe deformation, during loading and unloading within appropriate temperature regimes. The distinctive mechanical behavior is associated with stress-induced transformation of austenite to martensite during loading and reverse transformation to austenite upon unloading. To develop a material model for SMAs, it is imperative to consider the difference in moduli of active phases. For example, the Young’s modulus of the martensite is one-third to one half of that of the austenite. The model proposed herein is a modification of the one proposed recently by Ho[17]. The prediction of the behavior of SMAs during unloading before the onset of reverse transformation was improved by introducing a new internal state variable incorporating the variation of the elastic modulus. Key Words : Shape Memory Alloy, Pseudoelasticity, Constitutive Model, Elastic Modulus

On the Role of Kinematic Hardening Rules in Predicting Relaxation Behavior

Uniaxial displacement controlled tests were performed on annealed Type 304 stainless steel at room temperature. A servo-controlled testing machine and strain measurement on the gage length were employed to measure the response to a given input. The test results exhibit that the flow stress increases nonlinearly with the strain rate and the relaxed stress at the end of the relaxation periods depends strongly on the strain rate preceding the relaxation test. The rate-dependent inelastic deformation behavior is simulated using a new unified viscoplasticity model that has the rate-dependent format of nonlinear kinematic hardening rule, which plays a key role in modeling the rate dependence of relaxation behavior. The model does not employ yield or loading/unloading criteria and consists of a flow law and the evolution laws of two tensor and one scalar-valued state variables.

Viscoplastic Constitutive Equations for Ratchetting Behavior

Abstract Solid polymers exhibit rate-dependent deformation behavior such as nonlinear strain rate sensitivity and stress relaxation like metallic materials. Despite the different microstructures of polymeric and metallic materials, they have common properties with respect to inelastic deformation. Unlike most metallic materials, solid polymers and shape memory alloys (SMAs) exhibit highly nonlinear stress-strain behavior upon unloading. The present work employs the viscoplasticity theory [K. Ho, 2011, Trans. Mater. Process. 20, 350-356] developed for the pseudoelastic behavior of SMAs, which is based on unified state variable theory for the rate-dependent inelastic deformation behavior of typical metallic materials, to depict the curved unloading behavior of polyphenylene oxide (PPO). The constitutive equations are characterized by the evolution laws of two state variables that are related to the elastic modulus and the back stress. The simulation results are compared with the experimental data obtained by Krempl and Khan [2003, Int. J. Plasticity 19, 1069-1095].

A unified constitutive law for cyclic viscoplasticity

Numerous experimental investigations on metallic materials and solid polymers have shown that relaxation behavior is nonlinearly dependent on prior strain rate. The stress drops in a constant time interval nonlinearly increase with an increase of prior strain rate. And the relaxed stress associated with the fastest prior strain rate has the smallest stress magnitude at the end of relaxation periods. This paper deals with the performance of three classes of unified constitutive models in predicting the characteristic behaviors of relaxation. The three classes of models are categorized by a rate sensitivity of kinematic hardening rule. The first class uses rate-independent kinematic hardening rule that includes the competing effect of strain hardening and dynamic recovery. In the second class, a stress rate term is incorporated into the rate-independent kinematic hardening rule. The final one uses a rate-dependent format of kinematic hardening rule.

Effect of the rate dependence of nonlinear kinematic hardening rule on relaxation behavior

Inelastic deformation behavior of metals and alloys is considered rate dependent. Uniaxial ratcheting experiments performed by Ruggles and Krempl, and Hassan and Kyriakides exhibited that higher mean stress for a fixed stress amplitude resulted in higher ratchet strain within a rate independent framework and higher stress rate resulted in lower ratchet strain, respectively. These phenomena are qualitatively investigated by numerical experiments through unified viscoplasticity theory. The theory does not separate rate-independent plasticity and rate-dependent creep, and thus uses only one inelastic strain to describe inelastic deformation processes with the concept of the yield surface. The growth law for the kinematic stress, which is a tensor valued state variable of the constitutive equations, is modified to predict the linear evolution of long-term ratchet strain.