Uniaxial tension tests were conducted on thin commercially pure titanium sheets subjected to electrically-assisted deformation using a new experimental setup to decouple thermal-mechanical and possible electroplastic behavior. The observed absence of stress reductions for specimens air-cooled to near room temperature motivated the need to reevaluate the role of temperature on modeling the plastic behavior of metals subjected to electrically-assisted deformation, an item that is often overlooked when invoking electroplasticity theory. As a result, two empirical constitutive models, a modified-Hollomon and the Johnson-Cook models of plastic flow stress, were used to predict the magnitude of stress reductions caused by the application of constant DC current and the associated Joule heating temperature increase during electrically-assisted tension experiments. Results show that the thermal-mechanical coupled models can effectively predict the mechanical behavior of commercially pure titanium in electrically-assisted tension and compression experiments.Copyright © 2013 by ASME

Characterization of flow stress for commercially pure titanium subjected to electrically assisted deformation

Adiabatic heating at a dislocation pile-up avalanche

Constitutive equations are often used to describe the stress–strain behaviour of metallic materials. This allows the execution of parametric studies for various purposes. Despite the large number of developed stress–strain equations, all frequently applied ones fail to accurately describe a strain hardening behaviour in two distinct stages, which many metallic materials tend to show. For this purpose, the authors developed a new stress–strain model, based on the well-known Ramberg–Osgood equation, which focuses on this two-stage strain hardening behaviour. This article describes the model and its analytical background, along with a graphical method to derive suited model parameters. To validate the proposed methodology, it is applied on stress–strain curves of two high-strength steels, an aluminium alloy and a duplex stainless-steel alloy. Whereas a good correspondence for the stainless-steel alloy is confined to limited plastic strains, excellent agreements are observed for the steels and the aluminium alloy. Following the proposed method, it was possible to obtain model parameter values that give a good correspondence within a detectable strain range.

A generic stress–strain model for metallic materials with two-stage strain hardening behaviour

The regime of sheet metal deformation extends from pure shear, 1= - 2, through plane strain, 2=0, to balanced biaxial tension, under which 1=2. During deformation a material passes into different states, termed (1) uniform straining, (2) diffuse straining, and (3) localized straining, respectively. Depending on the strain ratio, (1) alone, (1) & (2) & (3), (1) & (3) or (1) & (2) can be experienced by a sheet between zero strain and fracture. In this work the deformation behaviour, in tensile and hydraulic bulge testing, of steel, aluminium and 70-30 brass has been studied. The onset of state (3) has been correlated with strain measurements, taken from a cine film of the deformation, indicated by a grid electrochemically marked on the sheet surface. Various theories predict the major and minor strains at the initiation of these states, and the theoretical and experimental results are compared for the various materials; also the implications with respect to forming-limit diagrams are discussed.

https://iopscience.iop.org/article/10.1088/0022-3727/7/7/307/pdf

Instability and fracture in sheet metal

Tensile behavior of functionally graded steels produced by electroslag refining has been studied. Functionally graded steels containing layers of ferrite, austenite, bainite, and martensite may be fabricatedvia diffusion of alloying elements during electroslag remelting. Tensile strength of the composites depends on the composition and number of layers and those have been modeled based on the tensile behavior of individual phases. The yield stress of each element in the composites is related to the microhardness value of that element. Considering the Holloman relation for the true stress-strain behavior of each element, the tensile strength of an individual element is also related to the microhardness value of that element. By applying the rule of mixtures, the tensile strengths of the composites were determinedvia the numerical method. The obtained results are in good agreement with the experimental results.

Tensile behavior of functionally graded steels produced by electroslag remelting

Conventional strength and strain-hardening parameters have been derived for idealized true-stress/true-strain curves obeying the Hollomon equation σ=Kpn, where K and n have values typical of real metals. All stress parameters are proportional to the constant K. The true tensile strength is almost independent of n, but the stress at 0·2% plastic strain is strongly dependent on n. The strain-hardening rate dσ/dp is significantly affected by n only when p 0·2. The strain-hardening rate is not easily related to the parameters nσmax, nK or the 0·2% proof-stress/true-tensile-strength ratio. The magnitude of the strain hardening, given by Δσ = (σ2 - σ1), also has a maximum between n=0·1 and 0·3. With these results, assumptions and conclusions in the published literature are discussed and some are shown to be incorrect. It is concluded that for maximum strength and strain hardening in materials obeying the Hollomon equation, large values of K and n values between 0·1 and 0·3 are required.

http://iopscience.iop.org/article/10.1088/0022-3727/7/7/305/pdf

A W Bowen

Papers

Limitations of the Hollomon strain-hardening equation