Extraction of Equivalent Uniaxial Plastic and Viscoplastic Behavior from Bending Using a Mechanistic Approach

Abstract

The present work is aimed at the extraction of material’s yield and creep parameters using cantilevers by conducting constant deflection rate and constant load tests respectively. Under the assumption of Euler-Bernoulli’s beam theory, stress and strain components are considered along beam length only. A stress and strain gradient throughout the cantilever makes bending rich in information as stress-strain rate-strain at every location of the beam corresponds to a single uniaxial test. By extracting these stress-strain rate strain information from multiple locations of the cantilever throughout deformation, high throughput feature of bending is utilized by extracting all the material yield and creep parameters from a single cantilever. The position dependent strain is measured using digital image correlation (DIC) in this work. The estimation of stress in a cantilever during non-linear deformation (i.e., non-linear dependence of stress on strain and/or strain rate), however, needs numerical methods which solve for stress distribution throughout the cantilever using equilibrium equations based on material’s constitutive behavior, beam geometry, loading and boundary conditions. Such numerical methods are developed to gain understanding of the stress redistribution which is found to be transient in nature and finally saturates when permanent (plastic or creep) strain are large (∼3-4%) such that elastic strain are negligible. The influence of material’s yield and creep parameters on stress redistribution profile and associated timelines is studied and limitations of the existing analytical expressions for saturated stress profile are discussed. The numerical method is also utilized to estimate the effect of limitations on strain accuracy measured by DIC on the extracted parameters. Therefore, the present work aims at developing cantilever bending combined with DIC for strain measurement as an alternative testing technique to extract material’s yield and creep parameters from a single cantilever.

The procedure for extraction of yield parameters like yield strength and strain hardening exponent is established for a beam of tension-compression symmetric, strain rateinsensitive material using the concept of the ‘invariant point’. These points are identified using numerical methods as the unique locations at every cross-section of the cantilever, one each in tensile and compressive regions, where stress remains almost unchanged during stress redistribution. The hardening exponent and yield strength are measured from a single cantilever with better statistics and thereby improved reliability using strain measured at the invariant points in tensile and compressive regions within an accuracy of 99.5% and 90% respectively for pure copper and aluminium alloys. The procedures for measuring strain rate sensitivity for a tension-compression symmetric, strain-rate sensitive material and yield parameters for a tension-compression asymmetric, strain-rate insensitive material are also proposed and the challenges are highlighted with the understanding that bending has the potential to measure yield parameters for these latter systems as well in future. The timelines associated with stress saturation under creep deformation have been quantified using numerical methods in terms of a parameter stress saturation time (SST). Based on the recommendations obtained from SST, loading profile for T22 boiler steel is redesigned in the form of small loading steps due to which stress gets sufficient time to relax during loading itself and does not exceed yield strength during redistribution. Thus, creep parameters can be extracted at loads as high as yield strength, which is not possible otherwise. This makes testing faster and thereby efficient because creep rates are higher at high load and steady state is achieved faster. In contrast, a high SST at low loads has been identified to explain the misinterpretation of experimental data in terms of mechanism shift at low loads for P91 steel. The numerical method is further developed to include primary creep response at loads above yield which holds relevance to room-temperature creep response of an hcp system, i.e., titanium alloy Ti-6Al. In case of Ti-6Al, it is found from uniaxial creep tests conducted above yield that prior plastic deformation does not affect creep behaviour which implies that plasticity affects only the initial stress distribution. The invariant points which remain invariant to stress redistribution even under the combined effect of creep and plastic deformation are identified based on the numerical methods. The strain at these locations in tension as well as in compression, measured using DIC, are utilized to extract equivalent primary creep response for Ti-6Al using a single cantilever. Therefore, the present work aims at establishing bending as the testing technique to measure yield and creep parameters for a range of materials (FCC, BCC, HCP) and testing conditions (RT-600oC) utilizing minimum sample volume with reduced testing and better statistics.