Multiscale modelling of stress and strain partitioning in high strength dual phase steels

Multiscale modelling of stress and strain partitioning in DP steel was carried out using both realistic microstructure-based RVE models as well as stochastic microstructures generated by Monte Carlo method. The stochastic microstructure models were shown to resemble that of realistic microstructures, enabling research on the specific aspects of the microstructure that could be difficult to control and study during experimental work. One such feature of the realistic microstructures studied in this work was the grain size and microstructure morphology. The microstructures were generated with varying average grain sizes while all other parameters, such as boundary conditions, material properties and volume fractions of martensite and ferrite were kept constant. It is found that the effect of grain size is much more pronounced during the initial localisation of the plastic deformation at and around the interface of the phases. In addition, the decrease in ductility and increase in strength of the DP steels are directly related to the refinement of grain sizes of each phase and the stress-strain partitioning in between them.

Numerical investigation on stable crack growth in plane stress

Large deformation finite element analysis has been carried out to investigate the stress-strain fields ahead of a growing crack for compact tension .a=W D 0:5/ and three-point bend .a=W D 0:1 and 0:5/ specimens under plane stress condition. The crack growth is controlled by the experimental J -integral resistance curves measured by Sun et al. The results indicate that the distributions of opening stress, equivalent stress and equivalent strain ahead of a growing crack are not sensitive to specimen geometry. For both stationary and growing cracks, similar distributions of opening stress and triaxiality can be found along the ligament. During stable crack growth, the crack-tip opening displacement (CTOD) resistance curve and the cohesive fracture energy in the fracture process zone are independent of specimen geometry and may be suitable criteria for characterizing stable crack growth in plane stress.

A strain-based failure criterion for pillar stability analysis

Strain-based failure criteria have several advantages over stress-based failure criteria: they can account for elastic and inelastic strains, they utilise direct, observables effects instead of inferred effects (strain gauges vs. stress estimates), and model complete stress-strain curves including pre-peak, non-linear elasticity and post-peak strain weakening. In this study, a strain-based failure criterion derived from thermodynamic first principles utilising the concepts of continuum damage mechanics is presented. Furthermore, implementation of this failure criterion into a finite-element simulation is demonstrated and applied to the stability of underground mining coal pillars. In numerical studies, pillar strength is usually expressed in terms of critical stresses or stress-based failure criteria where scaling with pillar width and height is common. Previous publications have employed the finite-element method for pillar stability analysis using stress-based failure criterion such as Mohr-Coulomb and Hoek-Brown or stress-based scalar damage models. A novel constitutive material model, which takes into consideration anisotropy as well as elastic strain and damage as state variables has been developed and is presented in this paper. The damage threshold and its evolution are strain-controlled, and coupling of the state variables is achieved through the damage-induced degradation of the elasticity tensor. This material model is implemented into the finite-element software ABAQUS and can be applied to 3D problems. Initial results show that this new material model is capable of describing the non-linear behaviour of geomaterials commonly observed before peak strength is reached as well as post-peak strain softening. Furthermore, it is demonstrated that the model can account for directional dependency of failure behaviour (i.e. anisotropy) and has the potential to be expanded to environmental controls like temperature or moisture.

Micromechanics Of Fatigue Crack-Growth At Low Stress Intensities In A High-Strength Steel

An attempt to systematically investigate the effects of microstructural parameters in influencing the resistance to fatigue crack growth (FCG) in the near-threshold region under three different temper levels has been made for a high strength low alloy steel to observe in general, widely different trends in the dependence of both the total threshold stress intensity range, DELTA-K(th) and the intrinsic or effective threshold stress intensity range, DELTA-K(eff-th) on the prior austenitic grain size (PAGS). While a low strain hardening microstructure obtained by tempering at high temperatures exhibited strong dependence of DELTA-K(th) on the PAGS by virtue of strong interactions of crack tip slip with the grain boundary, a high strength, high strain hardening microstructure as a result of tempering at low temperature exhibited a weak dependence. The lack of a systematic variation of the near-threshold parameters with respect to grain size in temper embrittled structures appears to be related to the wide variations in the amount of intergranular fracture near threshold. Crack closure, to some extent provides a basis on which the increases in DELTA-K(th) at larger grain sizes can be rationalised. This study, in addition, provides a wide perspective on the relative roles of slip behaviour embrittlement and environment that result in the different trends observed in the grain size dependence of near-threshold fatigue parameters, based on which the inconsistency in the results reported in the literature can be clearly understood. Assessment of fracture modes through extensive fractography revealed that prior austenitic grain boundaries are effective barriers to cyclic crack growth compared to martensitic packet boundaries, especially at low stress intensities. Fracture morphologies comprising of low energy flat transgranular fracture can occur close to threshold depending on the combinations of strain hardening behaviour, yield strength and embrittlement effects. A detailed consideration is given to the discussion of cyclic stress strain behaviour, embrittlement and environmental effects and the implications of these phenomena on the crack growth behaviour near threshold.

Effect of strain rate on the high-temperature low-cycle fatigue properties of a nimonic PE-16 superalloy

Strain-rate effects on the low-cycle fatigue (LCF) behavior of a NIMONIC PE-16 superalloy have been evaluated in the temperature range of 523 to 923 K. Total-strain-controlled fatigue tests were per-formed at a strain amplitude of +/-0.6 pct on samples possessing two different prior microstructures: microstructure A, in the solution-annealed condition (free of gamma' and carbides); and microstructure B, in a double-aged condition with gamma' of 18-nm diameter and M23C6 carbides. The cyclic stress response behavior of the alloy was found to depend on the prior microstructure, testing temperature, and strain rate. A softening regime was found to be associated with shearing of ordered gamma' that were either formed during testing or present in the prior microstructure. Various manifestations of dynamic strain aging (DSA) included negative strain rate-stress response, serrations on the stress-strain hysteresis loops, and increased work-hardening rate. The calculated activation energy matched well with that for self-diffusion of Al and Ti in the matrix. Fatigue life increased with an increase in strain rate from 3 x 10(-5) to 3 x 10(-3) s-1, but decreased with further increases in strain rate. At 723 and 823 K and low strain rates, DSA influenced the deformation and fracture behavior of the alloy. Dynamic strain aging increased the strain localization in planar slip bands, and impingement of these bands caused internal grain-boundary cracks and reduced fatigue life. However, at 923 K and low strain rates, fatigue crack initiation and propagation were accelerated by high-temperature oxidation, and the reduced fatigue life was attributed to oxidation-fatigue interaction. Fatigue life was maximum at the intermediate strain rates, where strain localization was lower. Strain localization as a function of strain rate and temperature was quantified by optical and scanning electron microscopy and correlated with fatigue life.

Comparative study on flexural response of full and partial depth fiber-reinforced high-strength concrete

This study presents the results of an experimental and analytical comparison of the flexural behavior of a high-strength concrete specimen (no conventional reinforcement) with an average plain concrete cube strength of nearly 65 MPa and containing trough shape steel fibers. Trough shape steel fibers with a volume fraction ranging from 0 to 1.5% and having a constant aspect ratio of 80 have been used in this study. Increased toughness and a more ductile stress-strain response were observed with an increase in fiber content, when the fibers were distributed over the full/partial depth of the beam cross section. Based on the tests, a robust analytical procedure has been proposed to establish the required partial depth to contain fiber-reinforced concrete (FRC) so as to obtain the flexural capacity of a member with FRC over the full depth. It is expected that this procedure will help designers in properly estimating the required partial depth of fibers in composite sections for specific structural applications. Empirical and mechanistic relations have also been proposed in this study to establish the load-deflection behavior of high-strength FRC.

Tension-compression asymmetry in an extruded Mg alloy AM30: temperature and strain rate effects

The effect of strain rate, (epsilon) over dot, and temperature, T, on the tension-compression asymmetry (TCA) in a dilute and wrought Mg alloy, AM30, over a temperature range that covers both twin accommodated deformation (below 250 degrees C in compression) as well as dislocation-mediated plasticity (above 250 degrees C) has been investigated. For this purpose, uniaxial tension and compression tests were conducted at T ranging from 25 to 400 degrees C with (epsilon) over dot varying between 10(-2) and 10 s(-1). In most of the cases, the stress-strain responses in tension and compression are distinctly different; with compression responses `concaving upward,' due to {10 (1) over bar2} tensile twinning at lower plastic strains followed by slip and strain hardening at higher levels of deformation, for T below 250 degrees C. This results in significant levels of TCA at T < 250 degrees C, reducing substantially at high temperatures. At T=150 and 250 degrees C, high (epsilon) over dot leads to high TCA, in particular at T=250 degrees C and (epsilon) over dot=10 s(-1), suggesting that twin-mediated plastic deformation takes precedence at high rates of loading even at sufficiently high T. TCA becomes negligible at T=350 degrees C; however at T=400 degrees C, as (epsilon) over dot increases TCA gets higher. Microscopy of the deformed samples, carried out by using electron back-scattered diffraction (EBSD), suggests that at T > 250 degrees C dynamic recrystallization begins between accompanied by reduction in the twinned fraction that contributes to the decrease of the TCA.

Effect of temperature and strain rate on the deformation behavior and microstructure of a homogenized AZ31 magnesium alloy

The plastic deformation behavior and dynamic recrystallization (DRX) in homogenized AZ31 Mg alloy was investigated in uniaxial compression in the temperature range between 150 and 400 degrees C with strain rates ranging from 10(-3) to 10(2) s(-1). Twinning was found to contribute significantly during the early stages of deformation. The onset of twinning was examined in detail by recourse to the examination of the appearance of first local maxima before peak strain in the stress-strain responses and the second derivative of stress with strain. High strain hardening rate was observed immediately after the onset of twinning and was found to increase with the Zener-Hollomon parameter. DRX was observed at temperatures above 250 degrees C whereas deformation at lower temperatures (< 250 degrees C) leads to extensive twinning at all the strain rates. At intermediate temperatures of 250-300 degrees C, plastic strains tend to localize near grain/twin boundaries, confining DRX only to these regions. Increase in the temperature promotes non-basal slip, which, in turn, leads to uniform deformation; DRX too becomes uniform. Deformation behavior in three different regimes of temperature is discussed. The dependence of critical stress for the onset of DRX and peak flow stress on temperature and strain rate are also described. (C) 2013 Elsevier B.V. All rights reserved.

Modeling of Piezocomposites using Variational Asymptotic Method

This work presents the development of piezocomposites made up of Macro Fiber Composites (MFCs) for aerospace applications and specifically involves, their computational analysis, material characterization and certain parametric studies. MFC was developed by NASA Langley Research Center in 1996 and currently is being distributed by Smart Material Co. 1] worldwide and finds applications both as an actuator as well as for sensor in various engineering applications. In this work, MFC is being modeled as an actuator and a theoretical formulation based on Variational Asymptotic Method (VAM) 2] is presented to analyse the laminates made up of MFCs. VAM minimizes the total electro-mechanical energy for the MFC laminate and approaches the exact solution asymptotically by making use of certain small parameters inherent to the problem through dimensional reduction. VAM provides closed form solutions for 1D constitutive law, recovery relations of warpings, 3D stress/strain fields and displacements and hence an ideal tool for carrying out parametric and design studies in such applications. VAM is geometrically exact and offers rigorous material characterization through cross-sectional analysis and dimensional reduction.

Large strain field near a crack tip in a rubber sheet

The distribution of stress-strain near a crack tip in a rubber sheet is investigated by employing the constitutive relation given by Gao (1997). It is shown that the crack tip field is composed of two shrinking sectors and one expanding sector. The stress state near the crack tip is in uniaxial tension. The analytical solutions are obtained for both expanding and shrinking sectors.

Plane strain asymptotic fields for cracks terminating at the interface between elastic and pressure-sensitive dilatant materials

The plane strain asymptotic fields for cracks terminating at the interface between elastic and pressure-sensitive dilatant material are investigated in this paper. Applying the stress-strain relation for the pressure-sensitive dilatant material, we have obtained an exact asymptotic solution for the plane strain tip fields for two types of cracks, one of which lies in the pressure-sensitive dilatant material and the other in the elastic material and their tips touch both the bimaterial interface. In cases, numerical results show that the singularity and the angular variations of the fields obtained depend on the material hardening exponent n, the pressure sensitivity parameter mu and geometrical parameter lambda.

Deflections and curvatures of a film-substrate structure with the presence of gradient stress in MEMS applications

The close form solutions of deflections and curvatures for a film-substrate composite structure with the presence of gradient stress are derived. With the definition of more precise kinematic assumption, the effect of axial loading due to residual gradient stress is incorporated in the governing equation. The curvature of film-substrate with the presence of gradient stress is shown to be nonuniform when the axial loading is nonzero. When the axial loading is zero, the curvature expressions of some structures derived in this paper recover the previous ones which assume the uniform curvature. Because residual gradient stress results in both moment and axial loading inside the film-substrate composite structure, measuring both the deflection and curvature is proposed as a safe way to uniquely determine the residual stress state inside a film-substrate composite structure with the presence of gradient stress.

Determination of plastic properties by instrumented spherical indentation: Expanding cavity model and similarity solution approach

The present paper aims to develop a robust spherical indentation-based method to extract material plastic properties. For this purpose, a new consideration of-piling-up effect is incorporated into the expanding cavity model; an extensive numerical study on the similarity Solution has also been performed. As a consequence, two semi-theoretical relations between the indentation response and material plastic properties are derived, with which plastic properties of materials can be identified from a single instrumented spherical indentation curve, the advantage being that this approach no longer needs estimations of contact radius with given elastic modulus. Moreover, the inconvenience in using multiple indenters with different tip angles can be avoided. Comprehensive sensitivity analyses show that the present algorithm is reliable. Also, by experimental verification performed oil three typical materials, good agreement of the material properties between those obtained from the reverse algorithm and experimental data is obtained.

Determination Of Plastic Properties By Instrumented Spherical Indentation: Expanding Cavity Model And Similarity Solution Approach

The present paper aims to develop a robust spherical indentation-based method to extract material plastic properties. For this purpose, a new consideration of-piling-up effect is incorporated into the expanding cavity model; an extensive numerical study on the similarity Solution has also been performed. As a consequence, two semi-theoretical relations between the indentation response and material plastic properties are derived, with which plastic properties of materials can be identified from a single instrumented spherical indentation curve, the advantage being that this approach no longer needs estimations of contact radius with given elastic modulus. Moreover, the inconvenience in using multiple indenters with different tip angles can be avoided. Comprehensive sensitivity analyses show that the present algorithm is reliable. Also, by experimental verification performed oil three typical materials, good agreement of the material properties between those obtained from the reverse algorithm and experimental data is obtained.