Modelling and testing of transformation-induced plasticity and stress-dependent phase transformations in steel via simple experiments

Stress-dependent phase transformations (SDPT) and transformation-induced plasticity (TRIP) of steel are some of the reasons for distortion of workpieces. Investigation and modelling of SDPT and TRIP in the framework of thermal treatment are very active fields of research. Because of the complexity of the material response of steel it is necessary to investigate model approaches for effects like TRIP or SDPT in an isolated manner in model situations. We present a strategy for investigation of TRIP and SDPT via evaluating the data obtained for steel probes in simple experiments like uniaxial tensile or torsion tests. The effects of TRIP and SDPT can partially be separated. Using the results obtained under constant temperature and loading we can test the material behaviour under time-dependent conditions. This information can be integrated in complex models on material behaviour in order to simulate the behaviour of work-pieces in real situations such as heat treatment example.     

An approach for modeling the active transformation of microstructure of two‐phase Alloys in FEM simulation of technological chains in superplastic forming (SPF)

Optimization and broadening of the technological regimes of superplastic forming require more accurate accounting of the transformation of microstructure during all stages of the forming process. On the one hand, it is very important to predict the resultant microstructure in different parts of the formed structure as it determines the operation properties, and on the other hand, active transformation of microstructure can lead to either hardening (grain coarsening) or softening (grain refinement) of the material. These changes in the mechanical behavior of a material can be quite significant and need to be taken into account in the FEM simulation of superplastic forming processes to achieve the required accuracy. One approach for modeling the microstructural transformation in an FEM simulation for a two‐phase alloy is proposed herein. Constitutive model with internal variables is described. The questions of validity of macroscopic and microscopic equations are discussed. The approach for taking into account the transformation of metallographic texture is proposed.     

Prediction of Distortion of Cylinders without Phase Transformations

The rule of Ameen whereby steel made cylinders with no phase transformations during quenching approach the spherical shape is contrary to the finding of Berger, who observes an elongation of thin and long work pieces. If the prediction of Ameen is correct, cylinders should decrease in length during heat treatment. This paper describes a first step of broader investigation of strain hardening and distortion of cylinders during gas quenching in a gas nozzle field. To make more general predictions about the distortion of cylinders which show no phase transformations during heat treatment, different dimensions of cylinders (lengths 50 mm, 100 mm and 200 mm, diameters 10 mm up to 100 mm) were investigated by means of numerical and experimental methods. The prediction of dimension and shape changes during gas quenching of steel cylinders has been performed by numerical simulation using the commercial Finite Element Program SYSWELD. The austenitic steel SAE30300 (German grade X8CrNiS18.9) was selected as investigated material; it shows no phase transformations during performed heating and cooling. The investigations show a good agreement between the kinematic strain hardening model and the experimental data, whereas the isotropic model is not in line with the experimental data. If the ratio of length and diameter is greater than 3, the relative changes in length displayed against the Biot number give uniform curves for all investigated geometries and heat transfer coefficients.     

Experimental study and modelling of the crystallization of a water droplet

Modelling the crystallisation of a water droplet into a cold humid airflow is the first step in modelling the behaviour of water droplets sprayed out of a snow gun. This modelling, which is based on an experimental study, deals with the behaviour of the droplet which is transformed successively from the supercooled liquid phase to the liquid–solid phase and then the solid phase. These three transformations are brought about by various exchanges: heat transfer with conduction and convection as well as mass transfer with evaporation and sublimation. The supercooling phenomenon is naturally observed during experiments and taken into account in the modelling.     

Characterisation of quasi‐stationary temperature fields in laser welding by infrared thermography

In this work, high‐speed thermography is shown to effectively capture quasi‐stationary temperature fields during the laser welding of steel plates. This capability is demonstrated for two cases, with one involving the addition of a ferritic‐bainitic filler wire, and the other involving the addition of a low‐transformation‐temperature (LTT) filler wire. The same welding parameters are used in each case, but the temperature fields differ, with the spacing between isotherms being greater in the case where the low‐transformation‐temperature filler material is added. This observation is consistent with the differences in the extent of the heat‐affected zone in each sample, and the shape of the weld pool ripples on the weld bead surfaces. The characterization of temperature fields in this way can greatly assist in the development of novel methods for reducing residual stresses, such as the application of low‐transformation‐temperature filler materials through partial‐metallurgical injection (PMI). This technique reduces or eliminates tensile residual stresses by controlling the temperature fields so that phase transformations take place at the optimum times, and success can only be guaranteed through precise knowledge of the temperature fields in the vicinity of the welding heat source in real time.     

Internal friction behaviour of Ni–Mn–Ga

The internal friction (IF) behaviour of shape memory alloys (SMA) is characterised by an IF peak and a minimum of the elastic modulus during the martensitic transformation (MT), and a higher IF value in the martensitic state than in parent phase. The IF peak is considered to be built of three contributions, the most important of them being the so-called “transient” one, existing only at non-zero temperature rate. On the other hand, the ferromagnetic Ni–Mn–Ga system alloys undergoes a MT from the L2₁ ordered parent phase to martensite, the characteristics of the transformation depending largely on the e/a ratio of the alloys. Indeed, a variety of transformation sequences, including intermediate phases between parent and martensite and intermartensitic transformations, have been observed for a wide set of studied alloys. Furthermore, the IF and modulus behaviour during cooling and heating these alloys show specific characteristics, such as modulus anomalies, strong temperature dependence of the elastic modulus, temperature dependent internal friction in martensite, and, as a general trend, a low transient contribution to the IF. In the present work, the IF and modulus behaviour of several Ni–Mn–Ga alloys will be reviewed and compared to that observed for “classical” systems like Cu- or NiTi-based shape memory alloys.     

Minimizing Stress and Distortion for Shafts and Discs by Controlled Quenching in a Field of Nozzles

A coupled gas‐dynamical and thermo‐mechanical model for simulation of the gas flow, gas and specimen temperature, phase, stress, strain, and displacement transient‐fields during quenching of cutting discs and shafts of steel is introduced. The material properties (e. g. density, conductivity, heat capacity, hardness) are obtained by homogenization procedures. The material behaviour is described as an extension of the classical J₂‐plasticity theory with the extension of temperature and phase fraction dependent yield criteria. The coupling effects such as dissipation, phase transformation enthalpy, and transformation induced plasticity (TRIP) are considered. Simulations were carried out for cutting discs of knives, and for shafts made of steel SAE 52100 with varying diameter. For the validation of the simulations, these work pieces were heated in a roller hearth kiln up to 850 °C, and than quenched in a field of nozzles in which the heat transfer coefficient was known and could be locally adjusted by the volume flow of each nozzle. The phase fractions, surface hardness, distortion, and residual stresses were measured. The simulated and measured results fit quite well. According to optimization‐simulations the shafts were quenched with a certain heat transfer coefficient distribution. The bigger diameter parts of the shaft were more intensively quenched by an increased gas flow so that the hardness profiles were equalized and the residual stresses at the edges were significantly reduced.     

Validation of a novel algorithm for the adaptive calculation of transient stratified flow of gas,oil and water in pipelines

In this paper, a mathematical model for three‐phase flow in pipelines is developed and a novel algorithm for solving the resulting system of partial differential equations is presented. The numerical solution is based on an adaptive mesh refinement technique. Significant gains in the numerical performance have been achieved by using this technique combined with high‐resolution schemes like FCT. This approach is highly beneficial in terms of speed while preserving accuracy. An explicit adaptive numerical solver adaptive conservation law solver (ACLS) has been developed in fortran90 using object‐oriented methods, which give a modular and flexible code. Some numerical tests are performed to show the good behaviour of this solver and to compare the numerical results against the experimental data. Copyright © 2001 John Wiley & Sons, Ltd.     

Adaptive generation of hexahedral element meshes for finite element analysis of metal plastic forming process

A method for the adaptive generation of hexahedral element mesh based on the geometric features of solid model is proposed. The first step is to construct the refinement information fields of source points and the corresponding ones of elements according to the surface curvature of the analyzed solid model. A thickness refinement criterion is then used to construct the thickness-based refinement information field of elements from digital topology. The second step is to generate a core mesh through removing all the undesired elements using even and odd parity rules. Then the core mesh is magnified in an inside–out manner method through a surface node projection process using the closest position approach. Finally, in order to match the mesh to the characteristic boundary of the solid model, a threading method is proposed and applied. The present method was applied in the mesh construction of different engineering problems. The resulting meshes are well-shaped and capture all the geometric features of the original solid models.     

How to adaptively resolve evolutionary singularities in differential equations with symmetry

Many time-dependent partial differential equations have solutions which evolve to have features with small length scales. Examples are blow-up singularities and interfaces. To compute such features accurately it is essential to use some form of adaptive method which resolves fine length and time scales without being prohibitively expensive to implement. In this paper we will describe an r-adaptive method (based on moving mesh partial differential equations) which moves mesh points into regions where the solution is developing singular behaviour. The method exploits natural symmetries which are often present in partial differential equations describing physical phenomena. These symmetries give an insight into the scalings (of solution, space and time) associated with a developing singularity, and guide the adaptive procedure. In this paper the theory behind these methods will be developed and then applied to a number of physical problems which have (blow-up type) singularities linked to symmetries of the underlying PDEs. The paper is meant to be a practical guide towards solving such problems adaptively and contains an example of a Matlab code for resolving the singular behaviour of the semi-linear heat equation.     

Metallurgical influence on distortion of the case‐hardening steel 20MnCr5

In literature, only few works are published that make statements on influences between material properties and distortion. There are some investigations on the influence of carbides and their distribution in the structure. Other authors report on a distinct influence of the texture on distortion. However, the operational sequences during solidification as well as the following deforming processes affect the homogeneity of the chemical composition. Local fluctuations of the chemical composition lead to locally different phase transformations. As a result there will be differences in the structure and therefore inhomogeneous distortion. The hardenability could be suitable as an integrating parameter to describe the effect of the alloying elements as well as their homogeneity in distribution in the structure on distortion. Additionally, the preheating treatment of the material as well as the carburizing process can influence the size alteration and the deformation. Therefore, in this work steel of the quality 20MnCr5 with different hardenability grades were varied concerning their preheating treatment conditions. Three conditions were adjusted: annealing to a specific structure, pre‐aging and the condition after cooling from the hot rolling heat. The extend of distortion was evaluated by measurements on a coordinate measuring apparatus before and after hardening.     

Grundlagen,Herstellung und Anwendungsaspekte des Supersolidus Flüssigphasensinterns von hochlegierten Werkzeugstählen und Metallmatrix‐Verbundwerkstoffen

Principles, manufacturing and application aspects of super solidus liquid phase sintering of high‐alloyed tool steels and metal matrix composites Iron‐based metal matrix composites (MMC) are applied for abrasive wear resistant applications. A common production route uses hot isostatic pressing (HIP) of metal and carbide powders, a comparatively cost intensive process. Using high‐alloyed tool steels as matrix materials it is possible to obtain dense materials by liquid phase sintering with an internally formed liquid phase. This contribution describes the basic principles of densification of the matrix materials taking thermodynamic calculations into consideration. It points out a production route for processing particulate reinforced, high wear resistant composite materials by sintering. Beside the sintering behaviour concepts for heat treatment as well as the abrasive wear resistance are discussed.     

Three‐dimensional grayscale‐free topology optimization using a level‐set based r‐refinement method

In this paper, we propose a three‐dimensional (3D) grayscale‐free topology optimization method using a conforming mesh to the structural boundary, which is represented by the level‐set method. The conforming mesh is generated in an r‐refinement manner; that is, it is generated by moving the nodes of the Eulerian mesh that maintains the level‐set function. Although the r‐refinement approach for the conforming mesh generation has many benefits from an implementation aspect, it has been considered as a difficult task to stably generate 3D conforming meshes in the r‐refinement manner. To resolve this task, we propose a new level‐set based r‐refinement method. Its main novelty is a procedure for minimizing the number of the collapsed elements whose nodes are moved to the structural boundary in the conforming mesh; in addition, we propose a new procedure for improving the quality of the conforming mesh, which is inspired by Laplacian smoothing. Because of these novelties, the proposed r‐refinement method can generate 3D conforming meshes at a satisfactory level, and 3D grayscale‐free topology optimization is realized. The usefulness of the proposed 3D grayscale‐free topology optimization method is confirmed through several numerical examples. Copyright © 2017 John Wiley & Sons, Ltd.     

Voxel‐based meshing and unit‐cell analysis of textile composites

Unit‐cell homogenization techniques are frequently used together with the finite element method to compute effective mechanical properties for a wide range of different composites and heterogeneous materials systems. For systems with very complicated material arrangements, mesh generation can be a considerable obstacle to usage of these techniques. In this work, pixel‐based (2D) and voxel‐based (3D) meshing concepts borrowed from image processing are thus developed and employed to construct the finite element models used in computing the micro‐scale stress and strain fields in the composite. The potential advantage of these techniques is that generation of unit‐cell models can be automated, thus requiring far less human time than traditional finite element models. Essential ideas and algorithms for implementation of proposed techniques are presented. In addition, a new error estimator based on sensitivity of virtual strain energy to mesh refinement is presented and applied. The computational costs and rate of convergence for the proposed methods are presented for three different mesh‐refinement algorithms: uniform refinement; selective refinement based on material boundary resolution; and adaptive refinement based on error estimation. Copyright © 2003 John Wiley & Sons, Ltd.     

Locally Refined T‐splines

We extend Locally Refined (LR) B‐splines to LR T‐splines within the Bézier extraction framework. This discretization technique combines the advantages of T‐splines to model the geometry of engineering objects exactly with the ability to flexibly carry out local mesh refinement. In contrast to LR B‐splines, LR T‐splines take a T‐mesh as input instead of a tensor‐product mesh. The LR T‐mesh is defined, and examples are given how to construct it from an initial T‐mesh by repeated meshline insertions. The properties of LR T‐splines are investigated by exploiting the Bézier extraction operator, including the nested nature, linear independence, and the partition of unity property. A technique is presented to remove possible linear dependencies between LR T‐splines. Like for other spline technologies, the Bézier extraction framework enables to fully use existing finite element data structures.     

A new automatic adaptive 3D solid mesh generation scheme for thin‐walled structures

A new algorithm to generate three‐dimensional (3D) mesh for thin‐walled structures is proposed. In the proposed algorithm, the mesh generation procedure is divided into two distinct phases. In the first phase, a surface mesh generator is employed to generate a surface mesh for the mid‐surface of the thin‐walled structure. The surface mesh generator used will control the element size properties of the final mesh along the surface direction. In the second phase, specially designed algorithms are used to convert the surface mesh to a 3D solid mesh by extrusion in the surface normal direction of the surface. The extrusion procedure will control the refinement levels of the final mesh along the surface normal direction. If the input surface mesh is a pure quadrilateral mesh and refinement level in the surface normal direction is uniform along the whole surface, all hex‐meshes will be produced. Otherwise, the final 3D meshes generated will eventually consist of four types of solid elements, namely, tetrahedron, prism, pyramid and hexahedron. The presented algorithm is highly flexible in the sense that, in the first phase, any existing surface mesh generator can be employed while in the second phase, the extrusion procedure can accept either a triangular or a quadrilateral or even a mixed mesh as input and there is virtually no constraint on the grading of the input mesh. In addition, the extrusion procedure development is able to handle structural joints formed by the intersections of different surfaces. Numerical experiments indicate that the present algorithm is applicable to most practical situations and well‐shaped elements are generated. Copyright © 2004 John Wiley & Sons, Ltd.     

Effect of pro-eutectoid ferrite on subsequent bainite transformation kinetics simulation

The kinetics of multiphase transformation is more complicated than single phase transformation due to the effects of prior phase transformation on the subsequent transformations. The authors have previously proposed a new method to estimate the parameters related to the isothermal kinetics of single phase transformation. This current paper investigates the application of the authors’ method to the bainite transformation process of multiphase steel G18CrMo2-6. The mathematical relationship between Pro-eutectoid ferrite (Pro-EF) fractions and the kinetics related parameters of the subsequent bainite transformation during heat treatment processes in the G18CrMo2-6 multiphase steel has been investigated. The results show the significant effect of Pro-EF fractions on the start and finish temperatures and the isothermal phase transformation parameters ‘b’ of subsequent bainite transformation.     

An approach to refining three-dimensional tetrahedral meshes based on Delaunay transformations

A technique for refining three-dimensional tetrahedral meshes is proposed in this paper. The proposed technique is capable of treating arbitrary unstructured tetrahedral meshes, convex or non-convex with multiple regions resulting in high quality constrained Delaunay triangulations. The tetrahedra generated are of high quality (nearly equilateral). Sliver tetrahedra, which present a real problem to many algorithms are not produced with the new method. The key to the generation of high quality tetrahedra is the iterative application of a set of topological transformations based on the Voronoi–Delaunay theory and a reposition of nodes technique. The computational requirements of the proposed technique are in linear relationship with the number of nodes and tetrahedra, making it ideal for direct employment in a fully automatic finite element analysis system for 3-D adaptive mesh refinement. Application to some test problems is presented to show the effectiveness and applicability of the new method.