Finite element calculation and measurement of thermal stresses in quenched plates of high–strength 7075 aluminium alloy

Abstract

Thick parts of high–strength aluminium alloys usually undergo a drastic quench which gives rise to thermal stresses and may cause distortion of products. The control of complex phenomena involved during quenching is achieved by determining the temperature distribution, thermal strains, and residual stresses using the MARC finite element program. In this approach, the thermo mechanical problem is assumed to be uncoupled, i.e. the thermal and mechanical calculations are solved consecutively. First a non–linear heat transfer analysis is performed taking the temperature dependence of the thermophysical properties and transient conditions of convection at the surface of the plate into account. This is followed by a thermo–elastoplastic stress analysis using the predicted temperature distributions, assuming an isotropic behaviour of the material and taking the temperature dependence of its mechanical properties into account. The calculation of thermal stresses occurring during the cold and hot water quenching of a 70 mm thick plate of 7075 alloy using this method shows a good agreement between theoretical predictions and experimental values of residual stresses, as measured by the layer removal method.

MST/2     

Effects of transformation plasticity on welding residual-stress fields in thin-walled pipes and thin plates

Abstract

Stress accumulation during cooling after single–pass butt welding is numerically studied for a pipe and a plate made of a microalloyed fine–grain C–Mn steel. The finite–element method is applied. Transformation plasticity is modelled by use of low yield stress values in the weld metal and in the heat affected zone during the final phase transformation. It is found that the stress changes induced in the pipe during the final phase transformation will partly remain at room temperature because of the low circumferential restraint during the final cooling. In the plate, however, the residual–stress field is governed mainly by the strong stress increase occurring after the final phase transformation. Stress changes induced in the plate before that event are thus hardly noticeable in the residual field.

MST/25     

Coupling between stress,temperature, and metallic structures during processes involving phase transformations

Abstract

A study has been made of constitutive relations for a time–dependent inelastic material within the framework of continuum thermodynamics, and of the heat conduction equation and transformation kinetics for processes involving phase transformations. Calculations of the stress, temperature, and structures of a half–spaced body, heated and cooled from the surface have been made using the finite element method, and are presented as an illustrative example. The effects of coupling between stress, temperature, and metallic structures, and of time dependence on the constitutive model for melting during welding are evaluated.

MST/14     

Numerical calculations of residual–stress relaxation in quenched plates

Abstract

Methods of thermal stress relief such as stretching and compression are compared for different thermal and mechanical properties during quenching. The heat equation for a simple geometric model, such as an infinite plate, is solved with an experimental surface conductance and a step–by–step method of determining the temperature field in the thickness of the plate. This field is introduced as data for the uncoupled thermal elastic–plastic model for quenching. In the calculation of the plastic–strain path, the thermal and mechanical properties are considered as temperature dependent for a homogeneous and isotropic material. Good agreement is found between the calculated residual stresses and experimental values for an aluminium alloy and a stainless steel. The predicted residual–stress distributions and strain history are then used as data for the numerical simulation of stress–relief methods with an incremental integration of the Prandtl–Reuss equation. This analysis allows the observation of the effects of small variations in mechanical properties during quenching on the residual–stress field after mechanical stress relief and the theoretical comparison of different processes.

MST/6     

Prediction of residual stress distributions for single weld beads deposited on to SA508 steel including phase transformation effects

Abstract

The sensitivity of residual stress distributions in bainitic–martensitic steel welds to the transformation strains that arise when austenite decomposes on cooling has been assessed by examining the predictions of three models for a simple bead-on-plate configuration. These cover the following scenarios: case I, no phase transformations; case II, transformations with volume change effects only; case III, transformations with volume change effects and associated Greenwood–Johnson transformation plasticity. Austenite decomposition was predicted by implementing Kirkaldy's reaction rate equations as a subroutine in the finite element code Sysweld, eliminating the need for a continuous cooling transformation diagram. Predicted residual stresses were then compared and rationalised alongside measurements obtained by neutron diffraction and the contour method. It was found that serious errors in predicting the location and magnitude of the peak stresses occurred if transformations were not included, while cases II and III gave similar results generally in agreement with the stress maps. Indeed, the trends in the experimental results were intermediate between cases II and III. Differences between the models and the potential for further improvements are discussed.     

Model for cooling and phase transformation behaviour of transformation induced plasticity steel on runout table in hot strip mill

Abstract

A mathematical model has been developed considering non-symmetric cooling in the thickness direction of strip on a runout table (ROT). In order to solve a one-dimensional transient heat transfer equation including the heat evolved from phase transformation, a finite element method was applied, coupled with thermodynamic and kinetic analyses. The heat capacities of each phase and heat evolution owing to phase transformation were obtained from thermodynamic analysis of the Fe–C–Mn–Si system using Thermo-Calc. The phase transformation kinetics of a transformation induced plasticity (TRIP) steel were derived by using continuous cooling experiments and thermodynamic analysis. Heat transfer coefficients of strips on the ROT were, by applying an inverse method, determined from actual mill data under various cooling conditions. Using the developed model, temperature–time variations of plain carbon and TRIP steels on the ROT were calculated. The calculated results were in good agreement with the actual mill data. In addition, quantitative phase evolution during cooling could also be predicted by the model. From this analysis, the optimum cooling pattern on a ROT for the production of TRIP steel could be determined.     

Physical significance and reliability of Larson–Miller and Manson–Haferd parameters

Abstract

Both the Larson–Miller and the Manson–Haferd parameters are used to extrapolate rupture data from high temperature creep. The first of these is in agreement with the theoretical equation for low temperature deformation only, and cannot describe the high temperature properties accurately. The second parameter has no physical basis. Starting from data taken from a theoretical stress–rupture time diagram, both extrapolation methods are tested. At the lower stresses the Larson–Miller method considerably overestimates the resistance of the material to rupture. Despite the lack of physical significance, the Manson–Haferd parameter coincidentally describes to some extent the complex deformation patterns due to the different deformation mechanisms, and is more reliable for high temperature predictions.

MST/1882     

Anisotropic phase transformation strain in forged D2 tool steel

Abstract

Heat treatment of forged D2 tool steel produces anisotropic dimensional change. It has been observed that tools have a larger dimensional change along the forging direction than perpendicular to it. This paper investigates anisotropic dimensional change by means of dilatometry. The results show that anisotropic phase transformation strain is produced in forged D2 steel during heat treatment. The anisotropic transformation strain is the main reason for anisotropic distortion in heat treatment of forged D2 steel. Anisotropic transformation strain produced during martensite transformation increases with higher austenitising temperature and is little influenced by cooling rate. A suggested mechanism is that transformation induced plasticity is produced under the internal stresses caused by the anisotropic microstructure (carbide bands) in the steel.     

Simulation of temperature field,flow field and solidification structure for Ag–28Cu–2Ge–0.4Co alloy

ABSTRACT

The temperature field, flow field and solidification structure of Ag–28Cu–2Ge–0.4Co alloy during solidification under water cooling, air cooling and slow cooling conditions were investigated, respectively. The results indicate that the temperature distribution is the most uniform and the solid–liquid phase region is the widest under slow cooling condition. The temperature gradient at the solidification front is the largest under water cooling condition. The solidification rate increases with the distance away from the sidewall under three cooling conditions. Under water-cooled conditions, the liquid flow at the front of the liquidus is much smaller than that in the other two conditions. The ratio of equiaxed crystals and columnar crystals in the solidified structure is different under different cooling conditions.     

A study of the heat parameters during bidirectional solidification

The temperature field and heat parameters are important in controlling metal liquid crystallinity in unidirectional and bidirectional solidification. The temperature field can be divided into three cases: a liquid temperature field; solid temperature field; and a temperature field on the solid-liquid (S–L) interface. Heat parameters can be divided into two cases: technical heat parameters; and solidification heat parameters. The temperature field on the S–L interface and solidification heat parameters are the most important for the structures and properties of materials. The temperature field on the S–L interface is determined by the alloy system, and solidification heat parameters are related to the temperature ield of the environment and technical heat parameters. The temperature ield on the S–L interface is closely related to the solidiication heat parameters.

A theoretical model describing precisely the temperature field on the S–L interface during bidirectional solidification was proposed. A series of heat parameters, including temperature gradients G, solidification rate R, cooling velocity V and characteristic temperature T_c have been derived from this model. A superalloy has been chosen as the experimental object in order to verify the theoretical model. The theoretical calculations are found to be in agreement with the experimental results.     

Application of low Ms temperature consumable to dissimilar welded joint

Abstract

The welding of dissimilar joints is very common in systems used in oil exploration and production in deep sea waters. Commonly involves welding of low carbon steel pipes with low alloy steel forgings both with inner Inconel clad. The forged steel part undergoes a process of buttering with Inconel or carbon steel electrode before the weld of the joint. The buttering process is followed by a process of residual stresses relief. The conventional way of reducing the level of residual stresses in welded joints is to apply post welding heat treatments. Depending on the size and complexity of the parts to be joined, this can become a serious problem. An alternative technique for reducing residual stresses is to use an electrode that during the cooling process undergoes a displacive transformation at a relatively low temperature so that the deformation resulting from the transformation compensates the contraction during the cooling process, and, although many papers have been published in this direction using Fe–Cr–Ni alloys, most of them report a loss of toughness in the weld metal. Maraging steel is a family of materials with M_s temperature below 200°C and even without the final heat treatment of aging has superior mechanical properties to low alloy steels used in forgings. In this work, forged piece of AISI 4130 was buttered with Maraging 350 weld consumable and subsequently welded to ASTM A36 steel using Inconel 625 filler metal. In addition, the dissimilar base metal plates were welded together using Maraging 350 steel weld consumable. The levels of residual stress, and the toughness and microstructures of heat affected zone and weld metal were investigated.     

Modelling thermal and microstructural evolution on runout table of hot strip mill

Abstract

A mathematical model has been developed to predict the thermal and phase transformation response of a 0·34 and a 0·05 wt-%C steel during cooling on the runout table of a hot strip mill. The model incorporates the cooling characteristics of laminar water bar sprays, the austenite–ferrite plus pearlite phase transformation kinetics as a function of the austenite grain size, and the heat of transformation. Overall heat transfer coefficients for the laminar water banks were determined from data obtained from in-plant trials carried out at the Stelco Lake Erie Works (LEW) hot strip mill. Isothermal and continuous cooling diametral dilatometer tests were performed on a Gleeble 1500 thermomechanical simulator at temperatures and cooling rates that simulate LEW hot strip mill conditions. The isothermal data were used to establish the phase transformation kinetics as afunction of austenite grain size and temperature. The continuous cooling results were used to obtain the relationship between cooling rate, transformation start temperature, and fraction of ferrite formed. The model was tested and validated by simulating the LEW cooling conditions while monitoring the phase transformation behaviour and by comparison of predicted and measured microstructural detail.

MST/1331     

Stress–phase-transformation interactions – basic principles,modelling, and calculation of internal stresses

Abstract

The two main effects of stress on phase transformation, kinetics modification and transformation plasticity, are reviewed for both diffusional and non-diffusional transformations. Results for these interactions during the pearlitic and martensitic transformation of steels under uniaxial tensile stress are analysed from a metallurgical point of view. These results are used to produce a model for a triaxial stress state, and in a finite element program for calculating internal stresses during quenching. Transformation plasticity is introduced in the calculation of internal stresses as an additional strain related to the stress state and to the progress of transformation, and the kinetics of martensitic transformation are also related to the stress state. The calculated results show that these phenomena have important consequences on the stress and plastic strain histories during quenching.

MST/9     

Residual stresses in two laser surface melted stainless steels

Abstract

Residual stresses were studied in two laser surface melted stainless steels: one martensitic, Fe–12Cr–0·2C, and the other austenitic, Fe–17Cr–11Ni–2·5Mo (compositions in wt-%). Stresses were measured by X-ray diffractometry over a range of depths, processing conditions, and stress relieving heat treatments. The volume increase associated with the martensitic transformation develops compressive stresses in single tracks of the martensitic steel and modifies the subsurface stresses of the laser surface melted steel. However, interactions between tracks offset the compressive surface stresses at all but the slightest overlaps. Residual stresses in the martensitic steel are minimized by increasing the advance between tracks and are reduced to a lesser extent by increasing the beam diameter and decreasing the traverse velocity. The austenitic steel, undergoing no solid state phase transformation on cooling, develops tensile residual stresses of the order of the yield stress for all the processing conditions evaluated. Suitable stress relieving heat treatments were identified for each steel.

MST/422     

Computer predictions of progressive induction hardening of cylindrical components

Abstract

In this paper progressive induction hardening is treated mainly on a theoretical basis. In contrast to stationary induction hardening, the progressive treatment makes it necessary to include a heat flow in the axial direction of the work piece; a single coil also leads to a magnetic field which changes in the axial direction. A model for heat generation (caused by the magnetic field) is derived based on the magnetic vector potential. The heat conduction equation, in two dimensions, is solved assuming steady–state conditions. The coordinate system is transformed to take the movement of the workpiece into consideration. After adopting steady–state conditions there will be no explicit time dependency in the heat conduction equation. Phase transformations are therefore calculated by following a node when it travels under the inductor and quenching ring. The actual speed gives temperature as a function of time. Stresses are evaluated in a similar way; it is assumed that a state of generalized plane strain exists, a one–dimensional model can then be used and a strip travelling under the inductor and quenching ring is studied. Some. theoretical results and comparisons with measurements are presented.

MST/20     

Particle break-up during heat treatment of 3000 series aluminium alloys

Abstract

In wrought aluminium alloys, the fragmentation of coarse, iron bearing intermetallic particles by hot rolling is an important development in industrial processing. Here a model 3000 series alloy is used to show that fragmentation can occur prior to hot rolling, during the homogenisation heat treatment. Some fragmented particles display a curved morphology of break-up that results from matrix wetting of two phase (or 'duplex') interfaces in Al₆(Fe,Mn) particles partially transformed to an α-Al–(Fe,Mn)–Si phase. In contrast, samples rapidly heated to temperature in a fluidised bath show an angular break-up indicative of tensile stresses induced by thermal expansion mismatch between the intermetallic particles and aluminium matrix. Although this break-up should not be industrially significant, the transformation induced break-up by wetting may be. More generally, internal boundaries resulting from the transformation to α-Al–(Fe,Mn)–Si phase may be mechanically weak fracture initiation points during hot rolling.     

Quantifying the metallurgical response of a nuclear steel to welding thermal cycles

Solid-state phase transformations can drastically influence the evolution of stress in welds due to the strains associated with the transformations and related changes in mechanical properties. As such, finite-element predictions of welding residual stresses need reliable materials data including, where applicable, information on phase transformation kinetics and phase- and temperature-dependent material properties. Owing to a scarcity of such data, many authors have used uncalibrated empirical modelling approaches for the prediction of welding residual stresses. This paper addresses this critical shortage for an important nuclear pressure vessel (SA508) steel. Austenite formation, grain growth and decomposition data are presented and subsequently used to calibrate transformation models. These models are shown to accurately predict microstructure and residual stresses for experimental test cases.

This paper is part of a Themed Issue on Measurement, modelling and mitigation of residual stress.     

Structural control of Fe-based alloys through diffusional solid/solid phase transformations in a high magnetic field

Abstract

A magnetic field has a remarkable influence on solid/solid phase transformations and it can be used to control the structure and function of materials during phase transformations. The effects of magnetic fields on diffusional solid/solid phase transformations, mainly from austenite to ferrite, in Fe-based alloys are reviewed. The effects of magnetic fields on the transformation temperature and phase diagram are explained thermodynamically, and the transformation behavior and transformed structures in magnetic fields are discussed.     

A study of the heat parameters during bidirectional solidification

The temperature field and heat parameters are important in controlling metal liquid crystallinity in unidirectional and bidirectional solidification. The temperature field can be divided into three cases: a liquid temperature field; solid temperature field; and a temperature field on the solid–liquid (S–L) interface. Heat parameters can be divided into two cases: technical heat parameters; and solidification heat parameters. The temperature field on the S–L interface and solidification heat parameters are the most important for the structures and properties of materials. The temperature field on the S–L interface is determined by the alloy system, and solidification heat parameters are related to the temperature field of the environment and technical heat parameters. The temperature field on the S–L interface is closely related to the solidification heat parameters.A theoretical model describing precisely the temperature field on the S–L interface during bidirectional solidification was proposed. A series of heat parameters, including temperature gradients G, solidification rate R, cooling velocity V and characteristic temperature T_c have been derived from this model. A superalloy has been chosen as the experimental object in order to verify the theoretical model. The theoretical calculations are found to be in agreement with the experimental results.