Virtual Rolling Technique from AMAG
How to use modelling as a method for faster product development
Mathematical modelling and computational analyses allow to deepen the understanding of manufacturing processes, to ensure high quality of AMAG`s products and to reduce experimental efforts for the improvement of product properties and production processes. In order to predict the evolution of flat rolled aluminium product properties and their interdependence with process parameters, virtual representations of the entire process route including process models of hot rolling, coiling, and cold rolling operations are highly beneficial.
AMAG`s modelling strategy is based on complex numerical three-dimensional models for hot rolling of aluminium alloys that were established in the past (see AluReport 03/2019). They include elastic deformations of the work rolls and their thermal crowns, backup rolls, and stand deformations. In addition to roll separating forces, temperature, and microstructure evolution, these models provide reliable predictions of the strip profile and edge deformation. Due to the high level of detail, the computational costs of such models are immense, which makes them impractical for advanced numerical studies or multi-pass simulations in an industrial environment. Extending these models to include successive cold rolling passes increases the computational complexity even more. Therefore, a reduced thermo-mechanical cold rolling model using the commercial finite element code LS-DYNA to predict roll separating forces, temperatures, and microstructure evolution is established.This newly at AMAG developed cold rolling model, like the hot rolling model, consists exclusively of a series of three-dimensional volume elements in the width direction. The imposed boundary conditions limit the degrees of freedom of the nodes to translations only in length and thickness direction. Movements in width direction are suppressed, leading to plane strain conditions of the elements.
Setup of the Model
The basic setup and boundary conditions are shown in Figure 1. Both work rolls are modelled, and the symmetry is deliberately not used, since rolling conditions may occur where the strip centre in thickness direction is not horizontally aligned with the roll gap pass line. The backward strip tension S0 and forward strip tension S1 are modelled by applying forces corresponding to the respective strip tension stresses at the nodes of each strip end. The purpose of the strip tension is to reduce the roll separating forces, especially during cold rolling, and to stabilise the strip tracking.Furthermore, it is imperative to consider the thermal effects that arise during the process of cold rolling. The deformation in the roll gap that occurs during the cold rolling process introduces heat into the strip. This heat is transferred to the work rolls within the roll gap and subsequently released into the environment (hstrip) outsides the roll gap. The cooling of the work rolls is achieved through the spray application of rolling oil or emulsion. This necessitates the consideration of a heat transfer coefficient (hroll), in the analysis.
The strip is accelerated in rolling direction to a defined velocity vstrip, which enables the contact between work rolls and strip (roll bite). An angular velocity ωroll is applied to the rigid work rolls, which corresponds to the rolling velocity of the rolling at the work roll circumference. The material behaviour of the aluminium strip during cold rolling is considered by means of a user-defined material model according to a modified dislocation density-based flow stress model of Kocks-Mecking type. Consequently, tensile tests were conducted at conventional cold rolling temperatures up to 150 °C and various strain rates. These tests were employed to calibrate the material model. Measured temperature dependencies of material properties such as Young's modulus, specific heat capacity and thermal conductivity are implemented, since considerable temperature rises may occur during the deformation process. The thermal expansion of the strip is also taken into account
To avoid front and tail end effects of the strip and to reach a steady state within a short period of computational time, a minimum virtual strip length was determined iteratively. As shown in Figure 2, only twelve elements are used in thickness direction to obtain approximately accurate simulation results. Furthermore, a fixed element aspect ratio of 0.5 in length direction must be employed, in order to avoid large element distortions during the cold rolling process. The total number of elements and corresponding computational time therefore depends on the actual strip thickness and increases with thinner strips. The work roll elements are wider than the strip elements. This helps to avoid line-on-line contact, which may cause numerical problems.
Validation of the model
To validate the developed model, an industrial pass schedule for a 6xxx aluminium alloy is used. A process route of hot and cold rolling is considered, where a cast slab with an initial thickness of 600 mm is reduced to a 1 mm thin strip. The hot rolling process consists of 21 passes and the cold rolling process of three passes. Strip tensions are applied during the last two passes during hot rolling in which the material is coiled and all cold rolling passes.
For the cold rolling passes, the actual initial strip temperatures for each pass vary due to different downtimes between successive passes and are implemented based on measurements. Between the first and second cold rolling pass the coiled strip is annealed to reduce the work hardening and to increase formability. As the heat treatment is not modelled, the material history is not transferred between these passes. Instead, a new mesh with initial material model variables for cold rolling is used as a simplification. The calculated microstructural and deformation history of the hot rolled strip is considered as input for the developed cold rolling model allowing for seamless prediction of product properties.
Figure 3 depicts the roll separating forces along the entire process route, normalised by the measured value of the first hot rolled pass.Thus, the information about the development of the roll separating force along the pass schedule is given. With an average error below 5 % in predicting the roll separating forces, the model agrees astonishingly well with measured data from the rolling mills. The greatest deviation in prediction of the roll separating force occur at the 20th pass.
At the 20th pass, the roll separating force is underestimated by about 12 %. By evaluating the strip exit temperature in Figure 4, this can be correlated with an overestimation of the material temperature. As the yield stress decreases at higher temperatures, this results in lower roll separating forces. Inaccurate variables in the thermal contact definitions due to increased coolant supply may be responsible for the increased temperature deviations during both hot rolling coil passes.Nevertheless, the predicted exit temperatures of the strip after leaving the roll gap as shown in Figure 4 agree well with the measurements. The entry temperature of the first pass is used to normalise the temperature values in Figure 4. The temperature measurements should be taken with caution as different measurement methods are used for the plate and coil passes and experience has shown that measurement errors may occur.
The results confirm that the developed modelling strategy is suitable for predicting width-independent variables like specific roll separating forces, temperatures, and the microstructural behaviour of the strip with good accuracy.Using the established model to simulate an entire process route of hot and cold rolling operations shows excellent agreement with measured roll separating forces.Figure 5 shows the transient temperature, strain and dislocation density at the surface position, at the quarter thickness position and at the strip centre in strip thickness direction for an exemplary cold rolling pass. The temperature curves have been normalised to the strip entry temperature at the strip centre thickness position.
The objective of using these virtual methods is to facilitate the estimation of the behaviour of the aluminium alloy under specific process conditions, and to predict the properties of the final end product.
Benefits for customer
The utilisation of virtual methodologies, particularly the employment of finite element method (FEM) simulations in conjunction with physically based material models, provides AMAG`s customers with a number of benefits that have a direct impact on the quality and reliability of the products supplied: The virtual representation of the rolling process allows complex physical relationships such as stress, strain and temperature distributions to be captured and analysed in a realistic manner, enabling in-depth process improvement already at the development stage - long before physical testing is required. Combined with physically based material property modelling, specific strengthening mechanisms and texture developments can be taken into account for individual aluminium alloys and help to customize the product to the customers need.
Finally, it should be noted that these virtual methods also contribute to more efficient use of resources in production, as the number of failed trials, material and energy consumption and as well as material trials are reduced in general. This, in turn, leads to a more sustainable production strategy, an aspect of increasing importance to a considerable number of AMAG's customers. The developed rolling model by AMAG allows the entire rolling process chain to be mapped much faster and at a much lower computational effort than traditional models which allows for quicker virtual process development, allowing the simulation to be a viable tool for product development.
