THE INTERNATIONAL ASSOCIATION FOR THE ENGINEERING MODELLING, ANALYSIS AND SIMULATION COMMUNITY

Technology GuideMaterial Characterisation

for Metal Forming Simulation

Material Characterisation for Metal Forming Simulation

Material Characterisation for Metal Forming SimulationThis guidance has been developed to guide analysts on the factors to be considered whencharacterising metals for a range of common manufacturing process simulations.

Metal forming simulations are increasingly adopted by manufacturers to improve the quality andperformance of products and processes while shortening development cycles so that theseproducts can be brought to market earlier [1]. An important consideration is the way themanufacturing process is modelled which depends, in turn, on the quality of the input data usedfor the model. The main input data that is used to define a metal forming process model are:

• A description of the way the material deforms and its failure (the material model).

• The geometry of the component to be manufactured.

• The boundary conditions of the model.

• The number of elements used to describe the geometry of the tooling andworkpiece and the time-step used to describe the number of calculations that willhave to be carried out to carry out the simulation.

Material models are one of the most difficult inputs to define because they rely on data obtainedthrough physical tests. For example, the Young’s modulus and yield strength are obtained byconducting a tensile test.

This publication describes the material characterisation required for stamping, machining,casting and forging simulations. The following sections will contain the aim of the simulations,the appropriate material models and the type of input data required by the models. For example:

• Stamping simulation primarily requires anisotropic material data for cold stamping.

• Machining simulation requires strain rate and temperature dependent data forplastic deformation.

• Casting simulation requires heat transfer, solidification and fluid flow data.

• Forging simulation requires strain rate data for cold forging and temperaturedependent properties for hot forging.

The Fidelity of a Simulation ModelThe detail incorporated in a material model and the context of use will affect the fidelity of thesimulation model. As a development programme proceeds, knowledge about the process aswell as knowledge about its material and tooling increases. This improved knowledge may beused to refine the models, thus increasing their fidelity.

Low fidelity models are used to reveal the ball-park performance of the process as well as itssensitivity to variations to process boundary conditions and material properties. This type ofsimulation is carried out early in a development programme and is used to estimate‘deformation modes’ in the process and its financial feasibility. Medium fidelity simulationscontain more precisely defined material models to obtain more accurate results of the processperformance. These models are used to improve the process performance and the predictionscan be used as the basis for tooling geometries. High fidelity models may incorporateinformation on the variations to boundary conditions and material parameters in order topredict a ‘process window’. Higher fidelity models may also be used as a ‘digital twin’ of theactual manufacturing process.

Analysts should ensure that the quality and reliability of material data used to feed a simulationimproves as the process design progresses. General datasheet values may be inappropriate touse in high fidelity modelling, while it is unnecessary to have detailed characterisation data forlow fidelity modelling.

Materials Characterisation for Stamping SimulationStamping simulation aims to predict the level of strain, thinning (compared to a forming limitcurve), wrinkling and springback behaviour of a sheet component. Sheet metal is generallyanisotropic (i.e. its material properties vary with respect to the rolling direction) and cold formingoccurs at room temperature at quasi-static strain rates. Deformation is therefore modelled withyield models and flow curves, failure is described with forming limit curves and springbackbehaviour by the elastic modulus.

The yielding of sheet materials is defined with anisotropic yield models [2] and these fall in thequadratic and non-quadratic families. It is generally regarded that while the quadratic modelsrequire fewer parameters to define, they are less accurate, particularly with lightweight materialssuch as aluminium.

Model Type sy0 sy45 sy90 syb r0 r45 r90 rb

von Mises quadratic x

Hill ‘48 quadratic x x x x

Barlat ‘89 Non-quad x x x x x x

Barlat 2000 Non-quad x x x x x x x x

Table 1: Parameters required for a selection of yield models.

Examples of common models are provided in Table1 where sy0, sy45, sy90 are yield stresses in the0°, 45° and 90° to the grain direction. r0, r45, r90 are anisotropic parameters in the 0°, 45° and90° to the grain direction and syb, rb and biaxial yield stress and anisotropic parameterrespectively.

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Material Characterisation for Metal Forming Simulation

Yield stresses, anisotropic parameters and work-hardening indices (n-values) are measured bycarrying out standard sheet tensile tests (eg. ISO 6892-1:2009 [3]). To obtain yield andanisotropic parameters in different directions, the sample is cut at different angles to the grainin the as received sheet. The derivation of yield stresses is described in ISO 6892-1:2009. Thederivation of the anisotropic r-values is described in ISO 10113:2006 [4] while the n-values aredescribed in ISO 10275:2007 [5]. When required, the biaxial yield and anisotropic parameters(syb and rb) are determined using a bulge test and are measured using the procedure recentlystandardised in ISO 16808:2014 [6].

Flow curves are obtained by fitting post-yield tensile test data. Commonly used fitting equationsare the Swift equation for steels and the Voce equation for aluminiums and some grades of highstrength steels [2]. In both equations, the n-value is required to completely define them. Flowcurves are usually treated as isotropic and therefore the n-value measured in the grain directionis used to represent the flow behaviour of a material in all directions.

Forming limits are regarded as anisotropic and standardised tests are carried out according toISO 12004 2:2008 [7]. Samples of varying sizes are bulged using a dome shaped punch.Extensive lubrication is applied between the sample and the punch to minimise friction.Significant post processing is required to obtain forming limits and the procedure is described inthe standard [7]. It can take 5 days to machine, test and post-process the data to obtain theforming limits for a single alloy and thickness (Figure 1). Typically, forming limits increases withincreasing thickness [2], so tests have to be repeated for each available thickness of the alloy.

Figure 1: Example of a forming limit curve for an aluminium alloy. The testused was the Nakazima test and the slight bending strain in the test shifts

the plane strain position in the positive direction

Material Characterisation in MachiningThe main aims of machining simulation is to predict tool forces, tool wear and effectiveness ofthe metal removal. Machining typically takes place under strains of 100–700%, strain-rates upto 106 s-1, temperatures between 500 and 1400 °C, high heating rates close to 106 °Cs-1, andhigh pressures near 2–3 GPa [8]. The Johnson and Cook (JC) model [9] is well accepted as themost common material model for machining as it has a relatively small number of parametersand gives adequate predictions for a range of metals. The model describes flow stress as aproduct of strain, strain rate and temperature.

The material parameters for the JC models are measured with the Split-Hopkinson Pressure Bar(SHPB) equipment or by conducting machining experiments as proposed by Ozel and Zeren [11].The SHPB test is the more common test, but the test setup is better suited to compressive ratherthan tensile loads and the test equipment is not widely available. Ozel and Zeren’s [11] methoddetermines material flow stress by performing orthogonal machining experiments underdifferent conditions and measuring machining forces, chip thickness and tool-chip contactlength. The data is used with the von Mises criterion and Oxley model to determine equivalentstress, strain rate and temperature in the primary deformation zone around the cutting edge.Finally, the JC model can be used to characterise the work flow stress in the primary deformationzone. This methodology can be applied to Inconel and titanium alloys to solve the JC parametersthat are used for finite element simulation in metal cutting. Other approaches that useorthogonal machining experiments have also been proposed e.g. M. Daoud et al. [12].

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Figure 2: Turning simulation performed to predict chip morphology andcutting forces. Image courtesy of Scientific Forming Technologies Corp.

Material Characterisation for Metal Forming Simulation

Figure 3: Validation of a prediction of temperature profile (right) with a measurementof the temperature profile of the casting of a V6 engine block (left).

Materials Characterisation for Casting SimulationCasting simulation aims to analyse material flow during die/mould filling, the temperaturechange during casting solidification and the resulting structure of the component. It requiresfluid dynamics, thermodynamics and thermo-mechanical dynamics modelling. All materialproperties that affect these physics phenomena are critical for casting simulation, especially thetemperature dependent material characteristics because the casting process is mainly a heattransfer manufacturing process. The key material characteristics of a casting alloy are: chemicalcomposition, liquidus temperature, solidus temperature, enthalpy, latent heat, specific heat,fraction solid curve, density, surface tension, thermal expansion coefficient, viscosity, heatconductivity, mechanical properties and yield hardening. In addition, mechanical properties suchas Young’s modulus and yield stress are strongly affected by the cooling rate during castingsolidification (Figure 3). The key material characteristics of the die/mould are: chemicalcomposition, heat conductivity, specific heat, thermal expansion coefficient, mechanicalproperties such as constitutive stress-strain curve, hardness, tensile strength, elongation andtoughness.

There are several ways to obtain these material properties. Firstly, software vendors usuallyprovide database of common materials. Secondly, simulation practitioners collect data fromresearch reports and literature. Thirdly, simulation practitioners measure certain critical materialcharacteristics with experimental investigations, especially for newly developed casting alloys.However, experimental investigation is very expensive, especially for these temperaturedependent properties. An alternative is to carry out a material thermodynamics analysis with adedicated commercial software package. Whatever the methodology used to obtain thematerial properties, simulation practitioners should always validate the simulation results withreal casting foundry data and modify the estimated material characteristic parametersaccordingly.

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Materials Characterisation for Forging SimulationForging can be carried out on heated (hot or warm forging) and non-heated (cold forging)material. The aim of forging simulations is to predict final component shape (Figure 4), formingloads, the strain and temperature evolution, tooling stresses/wear and the occurrence of defectssuch as die under-fill and cracks in the component. The workpiece is typically deformed between10-2s-1 to 102s-1 and even cold forging processes will experience temperatures between 30% and50% of the material melting temperature.

Yielding is typically described by the von Mises model while subsequent hardening andsoftening is described by flow stress curves. For hot forging, the most common material modelis the Hansel Spittel law [13], which models temperature, strain and strain dependency of thematerial. In cold forging, failure can be described with the Cockcroft-Latham model [14]. Hotand warm forging applications require detailed models of the thermal history of the workpieceand tooling during the manufacturing process. In particular, heat transfer, heat generation and

Figure 4: Prediction of the evolution of the shape of an automotivesuspension component through a forging process. Image courtesy ofScientific Forming Technologies Corporation and LC Manufacturing.

Material Characterisation for Metal Forming Simulation

their effect on the material properties need to be accounted for within the model. Sources ofheat generation arise from deformation and friction. Conduction heat transfer takes placebetween the workpiece and tooling and convective and radiation heat transfer takes placebetween the workpiece and the surrounding environment. Temperature dependent materialproperties include Young’s modulus, Poisson’s ratio, flow stress, heat capacity, coefficient ofthermal expansion and emissivity. Simulations to predict phase composition, such as themartensitic transformation during quenching of steels, should include data for thetransformation kinetics (such as Continuous Cooling Transformation curves) as well as latentheat, volume change and transformation plasticity of each phase of the material. In general,each phase of material will have its own thermal and mechanical properties.

Material data can determined from physical tests and/or physics-based software codes. Twotypical physical tests are the compression and double cone test [15]. Compression tests can beused to characterise flow stresses at various temperatures and strain rates, peak strain torecrystallization and recovery. Double cone tests can be used to determine recrystallizationkinetics, phase volume fractions and grain size evolution.

The data used to define these models should reflect the range of strain rates and temperaturesthat can be expected during the whole process. If the real process ranges extend beyond thesimulation data set available then care should be taken to understand how the simulation codeextrapolates the material data.

How to Obtain Data to Characterise MaterialsTwo aspects are required to characterise a constitutive material: a model that describes an aspectof behaviour and the actual data for the model’s parameters. For example, yielding can bedescribed with the von Mises equation, but the size of the yield ellipse can only be fully definedby measuring the uniaxial yield stress of the material. Multiple models are usually used todescribe the various elements of material deformation during a process. As a minimum, mostmanufacturing processes require models to describe elasticity, yielding, hardening and failure.More complex models may be used to describe deformation at different and/or elevatedtemperatures, variable strain rates or additional models may be used for specific behaviours suchas solidification (casting). The choice of model will depend on the fidelity of the simulationmodel and the effort required to measure the data for the model parameters. Thus, the tests tobe carried out will depend on the choice of model.

Test data can be acquired from several sources including open repositories, material suppliersand commissioning tests. Open repositories range from uncontrolled online databases to datapublished in literature and peer-reviewed journals. Material suppliers usually supply basicmaterial property data that can be used for the ‘standard’ material models e.g., von Mises foryielding. In some instances, if the analyst intends to use an advanced model or to validatepredictions, they may have to commission bespoke tests. It is preferable that when available,these tests are carried out in accordance with published standards. However, the analyst has theimportant responsibility to carry out due diligence on the data that is used for their model andto ensure that the data is applicable to the conditions of the simulation model. Figure 5 showsa validation carried out during a benchmark study of a formed component.

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If a bespoke test is required, this can be commissioned at test houses or universities withappropriate equipment. Because of the potential complexity of bespoke tests, the analyst shouldwork as closely as possible with the test house to design the test. Even published standard testmethods can contain options that need to be specified. Factors that the analyst should bear inmind include the requirements of the material model, the capability of available test machines,the test method used, measurement techniques and the required data post-processing.Particular care should be taken to factor in the effort required to convert the format of the testdata to the format required for the simulation model. Frequently, the formats will be differentand significant effort may be required to translate the data into a solver-readable format.

Figure 5: Dimensional deviation between a simulation prediction and scanned componentfrom a sheet metal forming process [16]

Material Characterisation for Metal Forming Simulation

The NAFEMS Manufacturing Process Simulation Working GroupThis pamphlet is published by the Metals Focus Group which is part of the NAFEMSManufacturing Process Simulation Working Group [17] to guide analysts on the factors to beconsidered when characterising metals for a range of common manufacturing processsimulations. For more information or to get involved visit nafe.ms/manwg.

References[1] T. Dutton, Why do Manufacturing Simulation. NAFEMS, 2017.

[2] W. F. Hosford and R. M. Caddell, Metal Forming: Mechanics and Metallurgy, 4th editio. CambridgeUniversity Press, 2011.

[3] “ISO 6892-1:2009: Metallic materials -- Tensile testing -- Part 1: Method of test at roomtemperature.” International Organization of Standardization, 2016.

[4] “ISO 10113:2006: Metallic materials - Sheet and strip - Determination of plastic strain ration.”2006.

[5] “ISO 10275:2007: Metallic materials - Sheet and strip - Determination of tensile strain hardeningexponent.” International Organization for Standardization, 2007.

[6] “ISO 16808:2014: Metallic materials - Sheet and strip - Determination of biaxial stress-strain curveby means of bulge test with optical measurement systems.” .

[7] "ISO 12004-2:2008: Metallic materials: Part 2: Determination of forming limit curves in thelaboratory,” 2008.

[8] P. Arrazola, T. Ozel, D. Umbrello, M. Davies, and I. Jawahir, “Recent advances in modelling of metalmachining processes,” CIRP Ann. - Manuf. Technol., vol. 62, pp. 695–718, 2013.

[9] G. Johnson and W. Cook, “A constitutive Model and Data for Metals subjected to Large Strains,High Strain Rates and High Temperature,” in Proceeding of the 7th Int. Symposium on Ballistic,1983, pp. 541–547.

[10] M. Calamaz, D. Coupard, and F. Girot, “A New Material Model for 2D Numerical Simulation ofSerrated Chip Formation When Machining Titanium Alloy Ti–6Al–4V,” Int. J. Mach. Tools Manuf.,vol. 48, pp. 275–288, 2008.

[11] T. Ozel and E. Zeren, “Determination of work material flow stress and friction for FEA of machiningusing orthogonal cutting tests,” J. Mater. Process. Technol., vol. 153–154, pp. 1019–1025, 2004.

[12] M. Daoud, W. Jomaa, F. Chatelain, and A. Bouzid, “A machining-based methodology to identifymaterial constitutive law for finite element simulation,” Int. J. Adv. Manuf. Technol. Manuf Technol,vol. 77, no. 2019–2033, 2015.

[13] A. Hansel and T. Spittel, Kraft- und Arbeitsbedarf Bildsamer Formgebungsverfahren. Leipzig,Germany: Deutscher Verlag für Grundstoffindustrie, 1978.

[14] M. Cockroft and D. Latham, “Ductility and workability of metals,” J. Inst. Met., vol. 96, pp. 33–39,1968.

[15] F. Warchomicka, C. Poletti, M. Stockinger, and T. Henke, “Microstructure evolution during hotdeformation of Ti-6Al-4V double cone specimens,” Int. J. Mater. Form., vol. 3, no. Suppl 1, pp.215–218, 2010.

[16] Allen M, Olivera M, Hazra S, Adetoro O, Das A, Cardoso R, Benchmark 2 – Springback of a JaguarLand Rover Aluminium Panel, J of Physics: Conference series, Vol 734, no. 022002, 2016

[17] "Manufacturing Process Simulation Working Group" nafems.org. nafe.ms/manwg (accessed 21Jan, 2020).

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Further Reading

“Why do Manufacturing Simulation”is a NAFEMS publication that demonstrates why it isbeneficial to carry out computer based simulation of themanufacturing process that transforms raw materialinto a formed product as part of the development cycle.The book is aimed at engineering and managers whomay be unfamiliar with the scope of manufacturingsimulation methods but wish to understand thebenefits that utilising these techniques can bring.

More information including details on how to purchase the publication can be found at nafe.ms/why-do-man-sim

When the NAFEMS Manufacturing ProcessSimulation Working Group was formedone of its first activities was to takeownership for an issue of our quarterlymagazine “benchmark”. TheManufacturing Process SimulationWorking Group curated and reviewed thetechnical articles that featuring in thisissue and it provides an excellentintroduction and overview to the issuesinvolved in simulating the manufacturingprocess.

The magazine is available for free to allNAFEMS members and can be purchasedby non-members at nafe.ms/man-sim-mag

THE INTERNATIONAL ASSOCIATION FOR THE ENGINEERING MODELLING, ANALYSIS & SIMULATION COMMUNITY

Why Do ManufacturingSimulations?

BENCHMARKTHE INTERNATIONAL MAGAZINE FOR ENGINEERING DESIGNERS & ANALYSTS FROM NAFEMS

October 2016 issue . . .

• How to Systematically Reap The Business Benefits

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• Austenitic Steel Plate Groove Weld Simulation

Benchmark

• Delivering Metal Forming Properties with Multi-

Scale Modelling

• Stress-free Simulation: The Art of Accurate

Polymer Modelling

• Novel Simulations for Predicting Fibre Path Defect

Formation in Composites Manufacturing

• Simulation of Additive Manufacturing

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