Analysis of thermomechanical behaviour in billet castingwith differentmould corner radii

Two decades of operating experience have shown that reducing the corner radius from 12–16 mm to 3 or 4 mm A finite element thermal stress model to compute is beneficial in reducing longitudinal corner cracking.4 In the thermomechanical state of the solidifying shell addition to lessening crack frequency, decreasing the corner during continuous casting of steel in a square billet radius also tends to move the crack location from the casting mould has been applied to investigate corner itself to the off corner region. Unfortunately, billets longitudinal cracks. A two-dimensional with sharp edges tend to ‘fold over’ during the rolling process.5 thermoelastoviscoplastic analysis was carried out Therefore, mould designers struggle to satisfy these two conwithin a horizontal slice of the solidifying strand flicting requirements. A better way to solve the longitudinal which moves vertically within and just below the corner crack problems is desirable. An important step towards mould. The model calculates the temperature this end is the achievement of an accurate, quantitative distributions, the stresses, the strains in the understanding of the crack formation mechanism(s). This solidifying shell, and the intermittent air gap understanding would aid mould design optimisation, especially between the casting mould and the solidifying for high speed casting. strand. Model predictions were verified with both Over the years, many mathematical models have been an analytical solution and a plant trial. The model was then applied to study the effect of mould developed to help to understand the origin of defects in corner radius on longitudinal crack formation for complex processes such as continuous casting.6–11 Howcasting in a typical 0·75%/m tapered mould with ever, quantitative understanding of the re-entrant corner both oil and mould powder lubrication. With this phenomenon of the solidifying shell in the billet mould has inadequate linear taper, a gap forms between the received relatively little attention. Furthermore, the effect shell and the mould in the corner region. As the of the billet mould corner radius on the temperature, corner corner radius of the billet increases from 4 to 15 mm, gap, and stress development has not been studied. this gap spreads further around the corner towards In the present work, a thermal–elastic–plastic–creep finite the centre of the strand and becomes larger. This element model has been developed to study the thermal– leads to more temperature non-uniformity around mechanical behaviour of the solidifying shell in and just the billet perimeter as solidification proceeds. below a billet mould. The model was validated with plant Longitudinal corner surface cracks are predicted to measurements including solid shell thickness and mould form only in the large corner radius billet, owing thermocouple temperatures. The model was then applied to tension in the hotter and thinner shell along the to the re-entrant corner phenomenon to investigate the corner during solidification in the mould. Off corner influence of corner radius on longitudinal crack formation. internal cracks form more readily in the small corner radius billet. They are caused by bulging below the mould, which bends the thin, weak shell PREVIOUSWORK around the corner, creating tensile strain on the solidification front where these longitudinal cracks Longitudinal cracks are ultimately observed. I&S/1675 Longitudinal cracks are one of the most common mould related quality problems encountered in billet casting. They Dr Park is at the University of British Columbia, 141–2355 East Mall, are associated with hot tearing close to the solidification Vancouver, BC, Canada, Professor Thomas ([email protected]) front,2 and are manifested in at least two different forms: is in the Department of Mechanical and Industrial Engineering, ‘longitudinal corner cracks’ and ‘off corner internal cracks’. University of Illinois at Urbana–Champaign (UIUC), 1206 W Green Street, Urbana, IL, 61801, USA, and Professor Samarasekera is in Longitudinal corner cracks run along the surface near the Department of Metals and Metallurgical Engineering, University the exact corner of the billet and are usually 1–2 mm of British Columbia, 111–2355 East Mall, Vancouver, BC, Canada. in depth,12 as shown in Fig. 1a. Although several studies Manuscript received 27 February 2002; accepted 16 July 2002. suggest that longitudinal corner cracks are related to the © 2002 IoM Communications Ltd. Published by Maney for the rhomboid condition of the billet,12,14–17 these cracks also Institute of Materials, Minerals and Mining occur in the absence of rhomboidity, as a result of improper corner radius 12,18 or mould distortion and wear.14,15 Aketa and Ushijima18 observed that with a large corner radius, the longitudinal corner cracks appear along the corner, INTRODUCTION while with smaller radii, these surface cracks form more During the continuous casting of steel billets, the corner frequently at the off corner region. They suggested that regions of the cast section often experience local thinning. the optimal corner radius to minimise longitudinal crack This phenomenon, sometimes referred to as ‘re-entrant formation should be one-tenth of the section size.2However, corners’, results from the complex behaviour of the air gap, Samarasekera and Brimacombe12 believed that the modern which forms between the mould and the solidifying shell in trend of smaller corner radii such as 3 or 4 mm may solve the corner region. This common occurrence can lead to the longitudinal corner cracking problem, but at the expense problems such as longitudinal cracks near the billet corner, of creating more off corner cracks. Mori15 observed that especially at high casting speed.1–3 In extreme cases, the the incidence of longitudinal corner cracks increases with corners may be so thin that a breakout occurs, even though the time that a mould is in service during a campaign. He the average shell thickness is easily large enough to withstand the ferrostatic pressure at the mould exit. suggested that overall reverse of taper may be an important