Multiscale modelling and simulation of micro machining of titanium

The microscale morphology of micro machined component surfaces is directly connected to the heterogeneous microstructure. The deformation depends on the crystal structure, in case of the considered cp-titanium, the hcp crystal structure. In a first approach the crystal plastic deformation is modeled with isotropic hardening. A visco-plastic evolution law accounts for the rate dependency. The concept of configurational forces is used with the framework of crystal plasticity to model the cutting process of cp-titanium. The setting is implemented into the finite element method. The examples show the effect of the material heterogeneity on the deforamtion behavior and on the related configurational forces. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Simulation of micro cutting considering crystal plastic deformations

The micro cutting process of microstructured material is simulated with consideration of the heterogeneities of the microstructure. In the case of cp-titanium with its hcp crystal structure the basal and prismatic slip systems are taken into account. The concept of crystal plasticity for large deformations is applied considering elastic anisotropy, self and latent hardening. The visco-plastic evolution law incorporates rate dependent material behavior. This setup is implemented within the finite element method. The effects of the microstructure are demonstrated by an illustrative example and a comparison to an isotropic von Mises elasto-plastic material. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Configurational Forces in Crystal Plasticity

The surface morphology of micro machined surfaces depends on the heterogeneous microstructure. A crystal plasticity model is used to describe the plastic deformation in cp-titanium with its hcp crystal structure. Therefore the basal and prismatic slip systems are taken into account. Furthermore, self and latent hardening are considered. The rate dependency is motivated by a visco plastic evolution law. The cutting process of cp-titanium is modeled within the concept of configurational forces for a standard dissipative media. This framework is implemented into the finite element method. An example illustrates the effects of the microstructure on plastic deformation and configurational forces. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Simulation of micro-cutting considering finite deformation crystal plasticity

Micro-machining processes on metalic microstructures are influenced by the crystal structure, i. e. the grain orientation. Furthermore, the chip formation underlies large deformations. To perform finite element simulations of micro-cutting processes, a large deformation material model is necessary in order to model the hyperelastic and finite plastic material behaviour. In the case of cp-titanium material with hcp-crystal structure the anisotropic behaviour must be considered by an appropriate set of slip planes and slip directions. In the present work the impact of the grain orientation on the plastic deformation is demonstrated by means of finite element simulations of a finite deformation single slip crystal plasticity model. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Particle Finite Element Simulations of Cutting Processes in Manufacturing

The cutting of metals is an important process in manufacturing and challenges established methods in the field of computational mechanics. The particle finite element method (PFEM) combines the benefits of particle based methods and the standard finite element method (FEM) to account for large deformations and separation of material. In cutting simulations the workpiece is realised as a set of particles, whose boundary is detected by the α-shape method. After the boundary detection, the particles are meshed with finite elements. Since metals show a plastic behavior under large deformations, a suitable material model needs to be considered. Numerical examples show the effect of the choice of the parameter α on the cutting force. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

An integrated approach to the one-dimensional cutting stock problem in coronary stent manufacturing

This paper presents a two-stage approach for pattern generation and cutting plan determination of the one-dimensional cutting stock problem. Calculation of the total number of patterns that will be cut and generation of the cutting patterns are performed in the first stage. On the other hand, the second stage determines the cutting plan. The proposed approach makes use of two separate integer linear programming models. One of these models is employed by the first stage to generate the cutting patterns through a heuristic procedure with the objective of minimizing trim loss. The cutting patterns obtained from Stage 1 are then fed into the second stage. In this stage, another integer linear programming model is solved to form a cutting plan. The objective of this model is to minimize a generalized total cost function consisting of material inputs, number of setups, labor hours and overdue time; subject to demand requirements, material availability, regular and overtime availability, and due date constraints. The study also demonstrates an implementation of the proposed approach in a coronary stent manufacturer. The case study focuses on the cutting phase of the manufacturing process followed by manual cleaning and quality control activities. The experiments show that the proposed approach is suitable to the conditions and requirements of the company.     

Analytical modeling of chatter stability using multi-dimensional approach

Machining is one of the most common manufacturing processes in industry due to its high flexibility and ability to produce parts which excellent quality. Chatter, a type of self excited vibrations arising in metal cutting operations, is a major limitation in machining resulting in poor quality and reduced productivity. Under certain conditions, the cutting process may become unstable yielding oscillations with high amplitudes and cutting forces. Stability analysis of the dynamic cutting process can be used to determine chatter-free machining conditions with high material removal rate. Usually, one dimensional models are used for stability analysis of machining. However, based on the geometry of the actual machining process, multi-directions would have to be used for accurate modeling of the process dynamics and the stability. In this presentation, multi directional models for turning and milling processes are presented. The effects of multi directional process mechanics on the stability are demonstrated by applications. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Cutting optimization of structural tubes to build agricultural light aircrafts

In this study we deal with the one-dimensional cutting of metallic structural tubes used in the manufacturing of agricultural light aircrafts. The problem is modeled by mixed integer linear formulations aiming to minimize material trim losses and considering the possibility of generating remainders (leftovers) with enough size to reuse. To validate the application of the models in practice, we carried out experiments with real data of order lists from Ipanema, an agricultural airplane produced by a Brazilian aeronautical company. The models were solved using a modeling language and an optimization software. The computational results show that the models are useful in supporting decisions in this cutting process.     

An Approach for Micromechanical Modelling of Damage Mechanisms

In the framework of numerical simulation of damaged materials, softening behaviour represents an important topic. Thereby, the decrease of stiffness is mainly caused by the evolution of microvoids. In contrast to the established phenomenological damage approaches, the explicit consideration of effects on the micro scale can lead to an improved approximation quality. In this work, we discuss an approach to describe microstructural evolution. Based on a two phase micro model representing the macroscopical material behaviour, the structural evolution on the micro scale will be modelled based on configurational forces. Besides some theoretical basics on configurational forces at two phase systems and the definition of suitable evolution laws, we present an application of this approach on void growth process in rubberlike material. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Application of the discrete element method to model cohesive materials

In this contribution we show how the discrete element method (DEM) can be applied to model cohesive materials which exhibit ductile behaviour by introducing connective elements that can bear a certain load. The modelled material is verified by simulating a orthogonal cutting process which is compared to experimental results. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Exploitation of Configurational Forces in Extended Nonlocal Continua with Microstructure

We investigate aspects of the application of configurational forces in extended nonlocal continua with microstructure. Focussing on multifield approaches to gradient–type inelastic solids, the coupled problem is governed by the macroscopic deformation field, while nonlocal inelastic effects on the microstructure are described by a family of order parameter fields. The dual macro– and micro–field equations are derived within an incremental variational framework. Using an incremental principle, due to the variation with respect to the material position, an additional balance in the material space appears with the dual macro–micro–balances in the physical space. In view of the numerical implementation of this coupled problem by a finite element method, the incremental variational framework is recast into a discrete format in terms of discrete macro– and micro–physical nodal forces and configurational nodal forces. Applying a staggered solution scheme, the configurational branch is used as a postprocessing procedure with all the ingredients known from the solution of the coupled macro–micro–problem. The procedure is implemented for a nonlocal, viscous damage model. The consequences with regard to the configurational nodal forces are assessed by means of a numerical example. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the role of energy in chip formation

The implicit code ABAQUS/Standard is used to simulate the formation of continuous and segmented chips. Using the described model, the idealized process of friction‐less machining of an elastic ideally‐plastic material is studied. It is shown that Merchant's classical shear angle relation does not hold, as chip formation does not minimize the energy as assumed by Merchant. The model is also used to study segmented chip formation using a realistic material law for the Titanium alloy Ti6Al4V at high cutting speeds.     

MPM simulations of high-speed machining of Ti6Al4V titanium alloy considering dynamic recrystallization phenomenon and thermal conductivity

Ti6Al4V titanium alloy is often used in the aircraft industry due to its good strength and toughness etc. However, it is very difficult to simulate high speed machining of titanium alloy using the finite element method (FEM). The reason is that the high speed, large deformation and high strain rate of metal material at high temperature etc. will lead to the element distortions and other numerical difficulties. In contrast with FEM, material point method (MPM) has the advantage of simulating extreme large deformation, fracture and impact problems. Therefore, it is specially suitable for dealing with high speed cutting process. In many existing researches about the high speed cutting process using Johnson−Cook constitutive model, the material dynamic recrystallization softening effect under high pressure and high temperature has not been considered. For this, three modified Johnson−Cook constitutive models for Ti6Al4V titanium alloy are adopted and the parameters for these models were obtained by the split Hopkinson pressure bar (SHPB) test considering the critical strain values, high-temperature range and dynamic recrystallization phenomenon. Furthermore, to ensure the numerical accuracy, the transient heat conduction algorithm is employed in MPM implementation. Finally, comparison and discussion are carried out between the experimental and the simulation data, which show that the high speed cutting process can be better simulated using the modified Johnson−Cook constitutive models.     

Nonlinear process machine interaction in tool grinding

The manufacturing of high performance cutting tools, like drills and chamfers, is done by a deep grinding process. This tool grinding process shows nonlinear relations between predefined process parameters, as cutting depth, feed speed and cutting speed, and the process characteristics, as process forces, surface properties and stability. Within an interdisciplinary research project a process model is built up to represent the process machine interaction and to predict process forces, deformation of the workpiece and geometry errors caused by this deformation. In this paper, the process model and the coupling of the included submodules will be described. The focus is thereby on the explanation of the contact module and the implementation in the dynamical model. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the macroscopic material behaviour of textile reinforced concrete undertensile loading

This paper concerns with the development of the macroscopic material behaviour of textile reinforced concrete (TRC) using an analytical approach. Therefore the heterogeneous structure of TRC is modelled on the mesoscopic level. The overall material behaviour on the macroscopic level is obtained by means of the homogenisation technique. The analytical approach is based on the micro mechanical solution for a single inclusion according to Eshelby . In extension of this solution for multidirectional reinforced concrete an effective field approximation is used. This approach considers the interactions between the different orientated rovings and the micro cracks in an average sense. For the mechanical modelling of the bond behaviour between roving and matrix after initiating of the macro cracking a slip based bond model with a multiple linear shear stress-slip relation is used. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modeling multistage cutting stock problems

In multistage cutting stock problems (CSP) the cutting process is distributed over several successive stages. Every stage except the last one produces intermediate products. The list of intermediate products may be given or arbitrary. The goal is to minimize the total amount of material taken out of stock to cut finished products sufficient to meet customer demands. If the intermediate sizes are given, the column generation technique can be applied to multistage cutting problems. If the intermediate sizes are not given then another dimension is added to the problem complexity. We propose a special procedure for this case that dynamically generates both rows (intermediate sizes) and columns (patterns). We refer to this method as row-and-column generation. The method uses an auxiliary problem embedded into the frame of the revised simplex algorithm. It is a non-linear knapsack problem that can be solved efficiently. In contrast to the column generation method the developed technique cannot guarantee the optimal solution. However, the results of computational experiments are very promising and prove that the method is a valuable addition to the set of tools for modeling and solving multistage CSPs.     

Deep Drawing Simulations Based on Microstructural Data

For the optimization of process chains in sheet metal forming it is required to accurately describe each partial process of the chain, e.g. rolling, press hardening and deep drawing. The prediction of the thickness distribution and the residual stresses in the blank has to be of high reliability, since the subsequent behavior of the semi-finished product in the following subprocesses strongly depends on the process history. Therefore, high-quality simulations have to be carried out which incorporate real microstructural data [1,2,3]. In this contribution, the ferritic steel DC04 is analyzed. A finite strain crystal plasticity model is used, for the application of which micro pillar compression tests were carried out experimentally and numerically to identify the material parameters of DC04. For the validation of the model, a two-dimensional EBSD data set has been discretized by finite elements and subjected to homogeneous displacement boundary conditions describing a large strain uniaxial tensile test. The results have been compared to experimental measurements of the specimen after the tensile test. Furthermore, a deep drawing process is simulated, which is based on a two-scale Taylor-type model at the integration points of the finite elements. At each integration point, the initial texture data given by the aforementioned EBSD measurements is assigned to the model. By applying this method, we predict the earing profiles of differently textured sheet metals. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

New model and heuristic solution approach for one-dimensional cutting stock problem with usable leftovers

In the one-dimensional cutting stock problem with usable leftovers (1DCSPUL), items of the current order are cut from stock bars to minimize material cost. Here, stock bars include both standard ones bought commercially and old leftovers generated in processing previous orders, and cutting patterns often include new leftovers that are usable in processing subsequent orders. Leftovers of the same length are considered to be of the same type. The number of types of leftovers should be limited to simplify the cutting process and reduce the storage area. This paper presents an integer programming model for the 1DCSPUL with limited leftover types and describes a heuristic algorithm based on a column-generation procedure to solve it. Computational results show that the proposed approach is more effective than several published algorithms in reducing trim loss, especially when the number of types of leftovers is limited.     

Thermal Residual Stresses and Triaxiality Measures

High performance ceramics have found their way into many highly challenging engineering tasks. For example silicon nitride is one of the best choices, if a material for demanding applications like metal forming and cutting is required. Due to the brittle nature of these hard and strong materials it is useful to know about thermal residual stresses, which can arise during the sintering process. In order to gain insight into the material behaviour, a single grain inclusion is exposed to thermal loads. Due to thermal mismatch, it undergoes a residual stress and strain field. The geometry of the model and the material data are motivated by the properties of silicon nitride. The stress fields are analyzed by three different measures for stress triaxiality. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)