Modelling metal punching using ductile failure criteria

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Universidade de Aveiro AGH

Ano 2014

Departamento de Engenharia Mecânica

Catarina de Lemos

Grilo Ferreira

Barbosa

MODELLING METAL PUNCHING USING

DUCTILE FAILURE CRITERIA

Dissertação apresentada à Universidade de Aveiro para cumprimento dos requisitos necessários à obtenção do grau de Mestre em Engenharia Mecânica, realizada sob a orientação científica do Doutor Pawel Packo, Professor Wojciech Lisowski do Departamento de Engenharia Mecânica da Universidade de AGH University of Science and Technology

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o júri

presidente Prof. Dr hab. inż. Wojciech Lisowski

professor associado da Faculdade de Engenharia Mecânica e Robótica da AGH University of Science and Technology, Krakow

Prof. Dr. Hab. Inz Janusz Szpytko

professor associado da Faculdade de Engenharia Mecânica e Robótica da AGH University of Science and Technology

Dr. Pawel Packo

professor associado da Faculdade de Engenharia Mecânica e Robótica da AGH University of Science and Technology

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First of all, I would like to thank my Master’s Thesis advisors Dr. Pawel Packo and Dr. Wojciech Lisowski for their support and guidance

I am especially grateful to my colleagues, and friends who turn the distance shorter

I would also like to thank Ricardo for all this time together, always believing me and being fond, supportive and helpful during this journey.

And, my family, for the support along these years. To my sister for everything.

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keywords Simulation. ABAQUS. Punching.

abstract During the process of mechanical conforming of metal sheet by punching process, several factors influence the accuracy and final geometry of the hole punched. The properties of material used and its behavior in the face of

imposed deformations, as well as process parameters influence the final result. High Strength Low Alloy steels (HSLA) are particularly suitable for structural parts that do not require severe forming, such as industrial shelving systems or furniture. Knowledge of mechanical punching operation is of utmost importance to planners of product, process and tooling, so you can get quality products at an acceptable level of waste. The numerical simulation can contribute

significantly to the prediction of behavior, still in the planning phase of the product. The goal of this paper is analyze the influence of gap between punch and die during punching. The metal plate material was used with a thickness of 8mm DIN EN 10268 H 360 LA with gaps between punch and die ranging from 2% to 10%. For this we developed a 2D axisymmetric model in

ABAQUS/Explicit software, Version 6.7 and the result were compared with literature data and practical experiment. Test showed that the gap of 2% showed the best result..

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palavras-chave Simulação, ABAQUS, Embutidura

resumo Durante o processo de conformação metálica por embutidura vários fatores influenciam na geometria final do puncionado. As propriedades do material usado e o seu comportamento perante conformações impostas, assim como característica do processo comprometem o resultado final. Aços HSLA são particularmente apropriado para componentes estruturais que não requerem conformação profunda, tal como os usados na industria de mobiliário metálico. Conhecimento em operações de embutidura mecânica é de maior importância para gestores de produto, processo e ferramentas, para obtenção de produtos de elevada qualidade e desperdício mínimo. A simulação numérica contribui significativamente para a previsão do comportamento ainda na fase de planeamento. O objetivo deste trabalho é analisar a influência da distância entre o punção e a matriz. Considerou-se uma variação entre 2 a 10% nesta análise. Para cumprir estes objetivos criou-se um modelo axissimetrico 2D no ABAQUS/Explicit Software versão 6.7 e o resultado foi comparado com dados bibliográficos e ensaios laboratoriais. Testes demonstraram que a distância entre o punção e a matriz de 2% proporciona o melhor resultado.

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List of Figures

FIGURE 1 INITIAL AND FINAL DIAMETER ... 11

FIGURE 2 PUNCHING PROCESS ... 16

FIGURE 3 GAP, PENETRATION AND FRACTURE ON PUNCHING SCHEME ... 17

FIGURE 4 PROPERTIES OF STAMPING EDGE (APUD MELLO,2001) ... 17

FIGURE 5 EFFECT OF INADEQUATE GAP (APUD MELLO,2001) ... 18

FIGURE 6 ELEMENTS TYPES COMMONLY USED TO STRESS ANALYSIS (ABAQUS V.6.7) ... 21

FIGURE 7 BRICK ELEMENTS, LINEAR AND QUADRATIC ... 21

FIGURE 8 ELEMMENTS WITH NODES REPRESENTED ... 22

FIGURE 9 CONTAC AND INTERACTION DISCRETIZATION ... 22

FIGURE 10 MESH REFINEMENT ... 24

FIGURE 11 STRESSES IN GIVEN COORDINATE SYSTEM AND MAX SHEAR STRESS SCHEME ... 27

FIGURE 12 MAX SHEAR STRESS HEXAGON ... 28

FIGURE 13 TRIAXIAL STATE OF STRESS ... 29

FIGURE 14 ELLIPSE MAX DISTORTION ENERGY THEORY ... 31

FIGURE 15 BODY DIMENSIONS-OF-EVIDENCE USED IN TEST ... 33

FIGURE 16 PUNCHING MODEL AXISYMMETRIC (MM) ... 34

FIGURE 17 PLATE MESH WITH 128 ELEMENTS (IN THICKNESS) ... 35

FIGURE 18 DIAGRAM STRAIN VS. DEFORMATION OF H360 LA ... 38

FIGURE 19 DIAGRAM TRUE STRAIN VS. TRUE STRESS OF STEEL H 360 LA ... 38

FIGURE 20 SIMULATION OF STEEL H 360 LA WITH 2% GAP BETWEEN PUNCH AND DIE ... 39

FIGURE 23 SIMULATION OF STEEL H 360 LA WITH 7.5% GAP BETWEEN PUNCH AND DIE ... 42

FIGURE 24 SIMULATION OF STEEL H 360 LA WITH 10% GAP BETWEEN DIE AND PUNCH ... 43

FIGURE 25 GRAPHIC STRENGTH VS. DISPLACEMENT USING 2% GAP BETWEEN PUNCH AND DIE ... 44

FIGURE 28 GRAPHIC STRENGTH VS. DISPLACEMENT USING 7,5% GAP BETWEEN PUNCH AND DIE ... 45

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Symbols List

Ao real area Ad deformed area A elongation E Young's modulus e plate thickness ε strain ε0 nominal strain

f gap both side of plate

F force

G elastic modulus

l deformed length

l0 initial length

n hardening coefficient

q Von Mises stress

K resistance factor

T triaxial stress factor

TS tensile strength

Ud distortion energy density

Uo Strain energy density

p hydrostatic pressure

σ real stress

σnom nominal stress

σy yield stress

σu tensile strength limit

σ1,σ2,σ3 stress in main axis

σmáx maximum principal stress

σmin minimum principal stress

σmed mean principal stress

σVQ equivalent stress of Von Mises

ζabsmáx maximum shear stress

YS Yield stress

PD plastic deformation

ω parameter of damage

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1

INTRODUCTION

The industries in the printing segment and mainly the automobile, have benefited greatly from the numerical simulation of the stamping process, as this has contributed to the quality and reliability of the calculated results and the exact description of the behavior of the conformation of the materials. As for examples, has the indication part regions which may suffer cracks, creasing, reduced thickness and elastic return during the printing process and also a decrease cycles in tool development, called try-out or even the elimination, in order to obtain quality products at lower costs and time.

The process of numerical simulation seeking the model of plastic behavior of metals and their interaction with the tool during punching shear. Therefore, knowledge of the behavior of material has fundamental importance during the stamping process on an industrial scale, the deformations do not exceed a safe percentage, and thus ensure the final part quality. It is also possible to identify thru simulation software the addition of draw-bead, changing radius, the change in pressure gland-plate, changes in lubrication, etc. (HONGZHI and ZHONGOI, 2000).

In cutting tools of stampings parts, there is certain gap between punches and dies. This gap is necessary to prevent the parts leave with burrs, to increase tool life and reduce cutting force (Fang et al, 2002; HAMBLI, 2002; HILDITCH and HODGSON, 2005).

Depending on the type of material and thickness of the part to be stamped, this gap may vary greatly (FAURA et al, 1998 and Schaeffer, 1999). The larger the gap, the greater the possibility of the rupture occurs (overflow) at the end of the material cut (Schaeffer, 1999).

According to the literature, the over outflow effect worsens with increasing hardness of the work material and especially with increasing plate thickness. When this occurs, the diameter of the hole in the cut end is different (larger) from diameter at the start of cutting, as shown in Figure 1. Therefore, when there is a piece of thick plate, and is needed a nominal dimension along the entire hole (e.g., hole for fixing of a guide pin) workpiece must be machined, using mandrel or drills, as holes obtained by punching have taper and lower quality.

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11 FIGURE 1 INITIAL AND FINAL DIAMETER

The objective of this work is therefore to study, via numerical simulation, the influence of gap between punch and die for punching thick plate operations. The software used is ABAQUS / Explicit, Version 6.7, and the gap of the tooling shall be between 2% to 10%. Furthermore, in this paper, be sought to achieve a number of specific objectives, which are:

- Development of a numerical model for simulating punching operations. - Conducting tensile test on the material of the metal plate, to compile their

mechanical properties.

- Use of techniques for characterization of early failure for ductile material. - Validation of numerical simulation (ABAQUS software) based on the

experimental results and the results obtained with gaps in the literature. To meet the objectives, this paper presents a methodology of experimental type based on modeling in software and data analysis quantitatively. The inductive method, observation and logic of scientific research are used. As for structure, this work has been divided into five chapters, as follows:

We present the problems, motivations, purpose, method and overall structure of the work in the first chapter, introduction. In the second chapter, the theoretical background is performed, a literature review of the process of punching (definition, tools and equipment, gap between punch and die, process) and numerical simulation (definition, finite element method, characterization of elements according to ABAQUS / Explicit, triangular, tetrahedral and prism elements, contact surfaces, establishing contact, elements mesh and plasticity). At the end of this chapter, theories of failures in ductile material are presented. In chapter three, referring to the experimental procedure, is described the method to obtaining the mechanical properties of the material and construction of a mathematical model used in the punching simulation. Detailed experimental procedure and techniques of analysis used in research and are identified variables and levels of the experiment, materials, equipment and procedures. Results exposure in chapter four, the influence of the tested parameters is discussed, confirming the necessity of choosing the correct gap in the die as well as on its geometry. In

Initial diameter

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12 this chapter the further discussions and findings of the research are also presented. The fifth chapter presents conclusions about the work.

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THEORETICAL

2.1 Concepts of numerical simulation

The dictionaries define simulation as follows: "representation of the operation of a system or process for the operation of other (simulation of an industrial process computer), analysis of a problem is not always subject to direct experimentation, the use of a device simulation. Simulator: "which simulates; specifically a tool that enables the operator to reproduce or represent, under test conditions, a phenomenon, just as in their actual performance.”

To understand better what simulation is needed to know the definitions of systems and models. A system is a set of distinct elements, which play each other an interaction or interdependence. By nature, these systems are limited, i.e. they must be defined limits or boundaries. Therefore, systems can be defined in other systems, and so forth. A model according HILLIER and LIEBERMANN (1988) is a representation of a real system, in which only those relevant for a particular analysis aspects of this system are considered. To HILLIER and LIEBERMANN (1988), the simulation is nothing more or less, that the technique of sampling experiments on a model system. Experiments are done in the model, rather than the actual system itself, because it is more convenient and less expensive.

According to CHASE AND AQUILANO (1989), these settings are somehow incomplete. Perhaps the best way to define and understand simulation considering it in two parts. First, there must be a model of what one wants to be simulated. There are several classifications of models, but the most common types are: physical (e.g., airplane model), schematics (electrical circuit diagrams) and symbolic (computer program or mathematical model that represents a bank teller or a machine).

In computer simulation, this is particularly interested in the symbolic model, which is used to represent a real system on a computer. The main point we have to consider here is that a model is created to represent something. (AHZI et al, 2008).

The second part to be considered is the model moves over time. Simulation brings "life" to the model. Simulation is a series of actions the model reactions with the environment. According to AL-MOMANI et al (2008), the prediction of the behavior of the arrays through numerical simulation is an important design tool, because it allows the reduction of the required number of practice tests before completion and delivery to the customer. The simulation also enables the prediction of the critical zones of deformation of parts, allowing changes to be made at headquarters or in the product, still in the design phase. Furthermore, experimental or analytical solutions that can easily describe all possible paths strain for this type of operation are virtually impossible.

2.2 Punching

The punching is a process of cutting by shearing machine, using a tool called punch. The pressure applied by the cutting tool on the surface to be cut causes punching. When this

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14 pressure causes a strain higher than the permissible shear stress of the material cut, the separation occurs.

In this regard, MARCOS (1975) states that the process of cutting sheet is typically a mechanical operation, whereby it is possible to achieve designs of predetermined profile, separating them from the rest of the material using a special tools.

According to HILDITCH and HODGSON (2005), cutting a metal plate is an integral part of the stamping process by shear, so it is important to maintain the quality factor of the final piece.

According POLACK (1974), the only type of cutting in stamping operations is the one which occurs simultaneously across the cut line by means of a punch. It is usually taken as synonymous concepts cutting and punching, even this is not a particular case of cutting.

The shear cutting process is a separation process, which is usually treated together with the printing processes, because is very common with these. Cutting is effected by two sharp edges that are facing each other with a gap between them (Schaeffer, 1999).

As VAZ and BRESSAN (2002), the cut consists of a metal forming operation characterized by the complete separation of the material.

MARCONDES et al (2008), express that the punching generates a series of products applicable in various areas of the industry, particularly in the automotive area, citing as examples the door locks, gears of the gearbox and the reclining seat adjusters. It is noted, however, that for implementing the puncturing process, basic tools are required as punches and dies.

In recent years, HATANAKA et al (2003a and / or 2003b) which highlight the numerical simulations cutting metal plates have been made based on the finite element method, in order to reduce time and cost of production process. As confirmation of the results of finite element simulations, we seek to analyze the influence of the gap between punch and die, the propagation of rupture with the penetration of the punch and the shape of the cut end. Experimental results show good agreement with the results obtained by finite element simulation.

GOIJAERTS et al (2000), report that the cutting process is not fully understood due to situations that continuously change the resistance of the material; the process is too complex for analytical model. Therefore, the finite element method has been used to simulate the cutting process successfully. Accordingly, the correlation of the numerical simulation is well consistent with the experimental investigation of the cutting process. The numerical model predicts the surface strain of the force field and the resistance properly.

2.2.1 Tools and Equipment Punching

There are three different types of cutting tools, as the number of parts produced and the required accuracy. The simplest type consists of punch, die and extractor. In this tool, the punch is guided only by the guide of the press; this way is not possible to work with very small gaps, thus impairing the accuracy of the parts and introducing a high wear on the tools. These tools are cheaper, but the adjustment and swap is very difficult and time consuming. Currently, only apply to the production of parts in small batches.

The second type is guided punching tool. This guide is made by the plaque that function also as puller. This tool is used for more accurate parts and to manufacture small quantities. The advantages of the tools with guided punching is a combination of low cost and good handling at the time of the swap and the preparation of the press.

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15 The most advanced type is the tool with guide pins and bushings. Is usually built leveraging a base of stamping with guide pins. This tool allows to work with minimum gaps for standards mass production of high precision parts (SCHAEFFER, 1999).

2.3 Punch

It is understood by punch a tool that transmits compressive forces and generates shear stresses on the workpiece to be cut. Important parameters to produce a punch are: relation between the hardness of punch and material to be punched, the punch length and geometry (Schaeffer, 1999).

2.4 Die

As BRITO (1981), the punches and dies are the most important parts of stamping. The die, which is the inverse of the punch brings the cut profile of the product to be produced and is one of the stamping elements that suffers more shear stress to the cut part. In the preparation of the die, there is need to consider the angle of escape, the thickness, the profile to be cut and the gap between punch and die (BRITO, 1981). In this sense, PROVENZA (1976) considers that the main features of the cutting dies are the exit angle (which facilitates the exit of material cut) and the gap between the punch and the die (which is responsible for the perfect cut of the desired part).

As the punch, the die will also be built with special steels. These steels requires the greatest care and attention, both from the point of view of manufacturing as its application, i.e., as to its casting, heat treatment and even assembly (BRITO, 1981). According PROVENZA (1976), the die should be made with great quality materials (high hardness and high wear resistance) and fine finish (rectified). The following are some of the fundamental characteristics of steels used for punch and die:

- high hardness at room temperature (essentially depends on carbon content); - high wear resistance (favoring maximum durability of the stamping);

- satisfactory hardenability (ensure uniformity in heat treatment); - appreciable toughness (ability to absorb energy before breaking);

- High mechanical strength (optimal values for the elastic limits and yield). The five above requirements are very important, and there are other factors that also affect, for example, the chemical composition of the steel, the type of operation, heat generated during operation and even quality and the types of lubricants used.

The die must be locked onto the lower base with screws or other means, in such a way creates a very stable set. The cutting face of a die, however simple it may be, should be free of burrs or rough edges, in order to make better use of their work.

The cutting force which must overcome the resistance of the material plays its effects on cutting edges, which wear after having produced a large amount of parts. Marks often appear on the face of the array, from burrs, small patches or foreign bodies.

On the need for economy, reconditions the die, rectifying enough, leaving it in good condition. This reconditioning should be studied in the act of designing, predicting an increase in thickness over the die (Brito, 1981).

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2.5 Punching Process

Figure 2 illustrates a punching process. Represents the position of the punch, the punch-plate and die. In these longitudinal section, we can observe that the die is wider at the bottom than at the top.

According Society of Manufacturing Engineers (1990), in stamping process, the metal being punctured is subject to tensile and compressive stresses. As Figure 2, compression in the upper fibers of the plate and occurs traction on the lower fibers. This fact is due to the effects of bending, acting on the punched metal. It is observed that the part being compressed has a reduced section, while being pulled has expanded its section. The punch continues its action and the material in the plastic state, expands into the die. When the force exerted by the punch to match the resistance of the materials tested, the separation of the cut piece from the rest of the material will occur.

FIGURE 2 PUNCHING PROCESS

During punching process, due to the elasticity of the material and the effort that is being undertaken, deformations occur in the fibers of the metal plate around the cut area. Such deformation causes friction on the die walls, so punch expulsion and extraction from the hole made on plate, is very difficult. In order to avoid this fact, it is considered a gap between punch and the die (CHAMBERT et al, 2005).

2.6 Gap between punch and die

Gap is the measure of space between punch and di. For proper cutting surface finish, it is necessary that the gap is thoughtful (typically 2 to 15% of plate thickness to be punctured). Insufficient gap cause the mismatch of cracks, already excessive gap cause intense plastic deformation. In this second case, led to appearance of burrs and sharp protrusions at the upper edge (Schaeffer, 1999).

According MEROZ and CUENDET (1980), the diametrical gap between punch and die can be set to 7% of the thickness for hard metals (steel), 6% for semi-hard steels and 4 to 5% for soft metal.

For ALTAN (1998), the optimal cut off is from 2 to 10% of the thickness of the metal sheet, and the lower value applies to thinner sheets or more ductile metal.

punch traction Metal plate die die compression Moving direction of punch

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17 SCHAEFFER (1999), gap recommended for shearing off thin sheets of low-carbon is 3 to 5% of the thickness plate.

Figure 3 shows schematically gap, penetration and fracture in a punching process.

FIGURE 3 GAP, PENETRATION AND FRACTURE ON PUNCHING SCHEME

In an ideal cutting operation, the punch penetrates into the material to a depth equal to about 1/3 the thickness before the fracture occurs, forcing an equal portion of material at the die opening (SCHAEFFER, 1999). The proportion of material which penetrates die has highly polished appearance, presenting around outline cut a brilliant band, surrounding adjacent corners, indicated buy B and B1 in Figure 4.

FIGURE 4 PROPERTIES OF STAMPING EDGE (APUD MELLO,2001)

In this context, it is noted that when the gap is not sufficient, additional metal bands should be cut before a complete separation, as shown in Figure 5.

Gap Metal plate punch penetration Fracture punch materia l die e flap

Rounded area: A , A-1 Cutting bandwidth: B , B-1 Fracture: C , C-1

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18 FIGURE 5 EFFECT OF INADEQUATE GAP (APUD MELLO,2001)

Finally, with the correct gap, the material beneath cut gets wrinkles in both sides of the flap. Fracture angle allows a clean separation below the bandwidth cut, because superior and inferior fractures will expand in both directions. Excessive gap will result in a surface with strips, wherein the material from de opposite side of punch will, after cut, have the same measure of die.

Then are shown relations between gap and thickness of the plate. - F=e/20 mild steel

- F=e/16 steel - F=e/14 hard steel

Where e is plate thickness, measured in millimeters, and F is the gap in both sides. Gap between punch and die is crucial to reduce shear force, enhance durability and produce pieces with known tolerances. Note that gaps bad programmed are responsible for rupture of die, as well as decrease of finishing quality.

BRITO (1981) affirms that precision of finished piece obtained by cutting in simple stamping depends on punch and die construction precision. When the gap is insufficient, superior cutting power is required, there is formation of burrs and increased tool wear. On the other hand, if the gap is excessive, will happen deformation and the product edge will be tapered.

The ideal measurement gap depends on the thickness of the metal plate, shear strength, type of cut, as well as the surface quality of the final product.

FAURA et al (1998) proposes a method to obtain a better gap between punch and die to a specific material and thickness to be cute, using finite element method through ANSYS software.

HAMBLI e GUERIN (2003) have developed a method to obtain the optimum gap by cutting simulation process using a combination of finite element and neural network model. The comparative study shows good agreement between the numerical results and experimental.

HILDITCH and HODGSON (2005) reported that the experimental results obtained, show that the heights of the burrs and cutting height of the beginning of the rounding radius increases with increasing cutting off.

The finite element model was also used by HILDITCH e HODGSON (2005) to analyze too fife span, ideal gap and prognosis fracture profile in cut.

(B) Excessive gap

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2.7 ABAQUS

Abaqus is a software suite for finite element analysis and computer-aided

engineering. Consists of five core software products:

- Abaqus/CAE or "Complete Abaqus Environment". It is a software application used for both the modeling and analysis of mechanical components and assemblies (pre-processing) and visualizing the finite element analysis result.

- Abaqus/Standard, a general-purpose Finite-Element analyzer that employs implicit integration scheme.

- Abaqus/Explicit, a special-purpose Finite-Element analyzer that employs explicit integration scheme to solve highly nonlinear systems with many complex contacts under transient loads.

- Abaqus/CFD, a Computational Fluid Dynamics software application which provides advanced computational fluid dynamics capabilities with

extensive support for preprocessing and post processing provided in

Abaqus/CAE.

- Abaqus/Electromagnetic, a Computational electromagnetics software application which solves advanced computational electromagnetic problems.

This software is a graphical interface that allows the user a quick and efficient definition of the geometry of the problem, allocation of material properties, loads and applying the boundary conditions of the problem, selection of the number of steps required in the analysis, and finally generates the finite element mesh corresponding to the analyzed body.

The consistency and adequacy of the model can be followed along the various steps. Therefore the model can be followed by special tools ABAQUS / CAE, of monitoring various aspects of the partitions defined for the model geometry (PART module), mechanical properties of the materials involved (PROPERTY module), grouping these partitions (module ASSEMBLY) and the imposition of sequence analysis steps (STEP module) and their nature - linear or nonlinear, definition of boundary conditions and loading (LOAD module), generation of finite element mesh (MESH module) and finally obtain the input file (JOB module) (ABAQUS v.6.7).

After generating the pre-processor, the file containing the problem of data entry, which can in turn be further manipulated by the user to situations not adequately addressed by the ABAQUS / CAE, can then be executed by the computer simulation finite element method, using the modules ABAQUS / STANDARD and ABAQUS / Explicit (in the case of metal punching). The software also has the ABAQUS / Viewer post-processor, operating on the output files, allows to interpret the numerical results, graphical visualization procedures and animation.

The various capabilities of ABAQUS allow complex engineering problems involving complicated geometries, nonlinear constitutive relations, occurrence of large deformations, transient loads and interactions between materials, can be modeled numerically. It should be noted, however, that the process of building a suitable model is not simple to user novice task, precisely because they involve a very large number of parameters and options, stemming

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20 from the high range of possible problems that can be modeled with the software (ABAQUS

v.6.7).

2.7.1 Data input

The data input file to run the finite element program ABAQUS / STANDARD (or ABAQUS

/ Explicit) is generated by the preprocessor ABAQUS / CAE and later modified or completely

created by the user using a text editor.

It is also observed that input file can be subdivided into two large groups of information:

- Data model geometry, with a description of the nodes, element types and their connectivity, material properties, the boundary conditions and the type of analysis (static or dynamic);

- Loading history data, information about the sequence of events or imposed loads, which can be characterized as specific forces, surface, body, generated by variations in temperature, pressure and other fluid. The ABAQUS program offers a wide variety of finite element characterized by different numbers and types of degrees of freedom and selected by the user depending on the nature of application. It also presents several significant relationships to simulate the mechanical behavior of materials such as linear elastic model, elasto-plastic model associated with the Mohr-Coulomb criterion, Drucker-Prager, the viscoelastic and other models (ABAQUS v.6.7).

2.8 Symmetry types

An important aspect of system behavior is the consideration of symmetry. When applied, this procedure helps reduce the problem size, making it easier to model and analyze, by spending less time in general (ABAQUS v.6.7).

Symmetry types are:

- Axisymmetric: when its geometry, loading, bonding conditions are all symmetrical about a particular axis of the structure.

- Mirror symmetry: when the geometry, loading and support conditions of the model are symmetrical about one or more axes.

- Cyclic symmetry: when there are a finite number of sectors with the same behavior conditions, around an axis of rotation.

- Repetitive symmetry: The template can be designed with only one sector of which is repeated in behavior, geometry and loading.

2.9 Characterization of the Elements according to the ABAQUS

For many applications, formulations or problems, the finite element method uses various types of elements, each with its approaches and features functions that enable an appropriate solution for each situation being studied or simulated (MARYA et al, 2005).

A formulation element refers to the mathematical theory used to define the element's behavior. All ABAQUS elements, which are strain/displacement type, are based on the description of Lagrangian or Eulerian behavior. In Eulerian alternative, or spatial, the

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21 description of the elements is fixed in space, with the material flowing through it. The Euler method is commonly used in fluid mechanics simulations (MARYA et al, 2005).

In order to accommodate different types of behavior, some types of elements include a number of different formulations. For example, the shell elements have three classes: a satisfactory shell tests for general purpose, another for thin shells and yet another for thick shells. In Figure 6, you can see some of the most commonly used elements for stress analysis. Some element types have a standard formulation, as well as some alternative formulations, such as, for example, the hybrid formulation used to handle incompressible and inextensible behavior.

FIGURE 6 ELEMENTS TYPES COMMONLY USED TO STRESS ANALYSIS (ABAQUS V.6.7)

Displacements or other freedom degrees are calculated on an element node. At any other point in the element, the displacement is obtained by interpolation of the nodal displacements. Generally, the order of interpolation is determined by the number of nodes used in the element. The elements that we have only their vertices as the 8-node brick shown in Figure 7, employ linear interpolation in each direction.

FIGURE 7 BRICK ELEMENTS, LINEAR AND QUADRATIC

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22 These elements are used in cases where the type of test stress / displacement, where complex geometry is involved, allowing the mesh to which it is as close as possible to the actual geometry (BARISIC et al, 2008). In Figure 7 you can see these elements with the numbering convention we used in ABAQUS.

FIGURE 8 ELEMMENTS WITH NODES REPRESENTED

2.11 Contact between Surfaces

There are some special formulations for finite elements that allow, in an analysis, to be considered the possibility of contact between surfaces. This implies a definition of the contact surfaces, a slave and a master, that during the simulation, interact with each other creating new boundary conditions for the analysis. During an analysis involving contact, ABAQUS tries, for each node of the slave surface, find the point closest to the surface of the master contact pair where the normal to the surface passes through the master node to the slave surface, as represented on Figure 9.

FIGURE 9 CONTACT AND INTERACTION DISCRETIZATION

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23 ABAQUS defines the contact conditions between two bodies using an algorithm, master-slave drive. In mechanical problems, we have that:

- each condition of potential contact is defined in terms of the slave node and a master surface;

- slave nodes are constrained not to penetrate the master surface; however, the nodes of the master surface can, in principle, penetrate the slave surface; - contact direction is always normal to the master surface.

2.13 Mesh Elements

Mesh, as it is known, is the set of elements and nodes used in the discretization of a geometric model for the calculation with the finite element method (Soderberg, 2006).

The process of mesh generation in a model is something of fundamental importance to define the level of accuracy of the results to be obtained. The greater the number of elements and nodes, the greater the accuracy of the result. The mesh should be adjusted optimally to the geometric shape of the part model studied. However, its density may vary locally, depending on the need geometric. This means that, in regions with very small details, a higher density of mesh to best represent is required.

When it comes to rupture, the most likely region to suffer it should have a good mesh refinement, because the accuracy of the stresses obtained in the region must be the best possible. At the same time, these regions usually have complex geometries, which reinforces the need to have a refined mesh in this region.

According MARCONDES et al (2007), the mesh density substantially affects the results of deformation. In this study due to the high gradient plastic deformation of the cutting area, a sufficiently dense mesh should be applied in this area.

SODERBERG (2006) examined the influence of mesh density on cutting geometry and rupture "stroke" in a simulation of punching forces. He conducted a study with different mesh refinements. Figure 9 illustrates the knitwear used by SODERBERG (2006). In their work it was concluded that 64-128 elements in thickness are sufficient to assess the influence of parameters on the breaking strength.

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24 FIGURE 10 MESH REFINEMENT

2.14 Explicit Method

According LAI et al (2007), the explicit method advances to the solution of the finite element method without requiring a rigid matrix, simplifying the process. For a given size of 'time-step', the explicit formulation usually requires fewer and less complicated computations for 'time-step'. Complicated boundary conditions or other forms of nonlinearity are easily treated, it is approached after step has been processed.

The explicit method is unstable and can rapidly diverge from the correct solution unless you use small and short 'time-step'. The critical value calculated maximum is characterized by a large number and relatively small 'time-steps' being suitable for highly dynamic applications short.

2.15 Plasticity

ABAQUS offers several constitutive models that consider elastic and inelastic responses, and the inelastic response modeled by the theory of plasticity. For metals, the most widely used model is the plasticity model with isotropic hardening and surface runoff Von Mises.

When we consider that the structure will suffer finite strains, the curve stress vs deformation does not adequately represent their behavior. So should be regarded stresses and deformations calculated based on the actual geometry of the deformed structure. Deformation can be calculated by equation 1.

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25 EQUATION 1

Where:

l deformed length

lo original length

ε "true strain" or logarithmic strain

The stress corresponding to the true strain is called "real stress" is defined as next equation.

σ = F A

Where F is the force in the material and A is the instantaneous area. The ratio of the true strain (ε) and the nominal (εnom) can be determined by considering that the nominal

strain is given by

EQUATION 2

Where rearranging the terms, and taking the natural logarithm of both sides of the equation, there is the true strain given by

EQUATION 3

The relation between the nominal strain (σnom = F / Ao) and the real (σ = F /

Ad) is determined by considering the deformed area is related to the original area by Ad = At

(lo / l) and noting that (l / lt) = (1 + εnom), therefore,

EQUATION 4

ABAQUS considers plastic material behavior defined by these measures with the true stress-related portion of the plastic true strain.

2.16 Concepts about Failure Criteria

The first task is to analyze is the behavior of proposed projects, subject to specified loads. For simple structural elements, we can use the basic equations to calculate stress and strain. For more complex structural elements, it is customary to use the finite element method to obtain the distribution of stresses and strains. In some particular cases, the solutions can be obtained by the theory of elasticity or the theory of plates and shells.

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26 The second task is to determine what strain and/or deformation will lead to failure of the object designed (LAI et al, 2007).

According KLINGENBERG and SINGH (2006), a tensile test is performed on a specimen of a ductile material, for purposes of the design object, the specimen fails when the axial strain reaches the yields stress σy, the failure criterion is outflow. If the specimen is made

of a brittle material, the common failure criterion is the brittle fracture in tensile strength limit, σu.

But a structural element is invariably subjected to a multiaxial stress state, for which it is harder to predict what amount of strain causes the failure (LAI et al, 2007).

A tensile test is done using the procedures described in the standards of materials testing and results are available for various materials. However, to apply the results of a tensile test (or a compression test) to an element that is subjected to multi-axial loading, it is necessary to consider the actual failure mechanism. I.e., the failure was caused by the maximum normal stress reached a critical value or the maximum shear stress reached a critical value or the strain energy or some other variable reached its critical value (HAMBLI, 2002).

According to the ASM HANDBOOK (1993a to 1993b), on tensile test, the criterion for failure can be easily stated in terms of strain Main σ1, but for multiaxial strain must consider the real cause of the failure and say that combinations stress will cause failure of the element under study.

Thus, two theories of failure will be considered, applying materials that behave in a ductile mode, i.e., the material reaching the outflow before fracturing. For flat strain, the failure theories are expressed in terms of the main, σ1 and σ2 strains. For the triaxial state of strain, σ1, σ2 and σ3 are used.

2.17 Maximum Shear Stress Theory - Theory of Tresca

According to ASM HANDBOOK (1993a to 1993b) when a ductile material plate, such as carbon steel, is tensile tested, it is observed the mechanism that is actually responsible for the disposal is the sliding. That is, shear along planes of maximum shear stress at 45 ° to the axis of the element. The initial flow is associated with the appearance of the first line of the specimen slide surface and, as the deformation increases, more slip lines appear,

until the entire specimen has dissipated. If this slip is considered the real failure mechanism,

then the strain that best characterizes this failure is the shear stress on the slip planes. Figure 10 shows the Mohr circle for state of uniaxial strain, indicating that shear stress in the slip planes has a value of σy / 2. Thus, it is postulated that in a ductile material, in any state of

strain (uniaxial, biaxial or triaxial), when the failure occurs in any plane shear stress reaches the value of σy / 2, then the failure criterion for theory of maximum shear stress can be stated

as:

EQUATION 5

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27 FIGURE 11 STRESSES IN GIVEN COORDINATE SYSTEM AND MAX SHEAR STRESS SCHEME

Knowing, that the equation of the shear stress is given by equation 6, we obtain the equation 7 of the yield strength, i.e.

EQUATION 6

EQUATION 7

Wherein:

σmáx maximum principal stress

σmín minimum principal stress

For plane stress, the failure criterion of maximum shear stress can be stated in terms of the principal stresses acting on the plane, σ1 and σ2, as follows. When the mains strain and the

mains strains 1 2 have the same sign, we have,

EQUATION 8

When the principal stress 1 and the principal stress 2 have opposite signs we have:

EQUATION 9

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28 FIGURE 12 MAX SHEAR STRESS HEXAGON

For an element under plane stress, the stress state at all points of the body can be represented by a point of strain (σ1, σ2) in plan σ1-σ2, as indicated in the previous

figure. If the state of strain for any point on the body corresponds to a strain point which is situated outside the hexagon, or its border, it is said that the failure has occurred, according to the theory of maximum shear stress (ASM HANDBOOK 1993a to 1993b).

2.18 Theory of Maximum Distortion Energy - Theory of Von Mises

ASM HANDBOOK (1993a to 1993b) states that, although the theory of maximum shear stress provides a reasonable outflow in ductile materials, the theory of maximum distortion energy hypothesis correlates better with the experimental data and is usually preferred. In this theory, it is considered that yielding occurs when the distortion energy per unit volume of a body under multiaxial load is equal to or smaller than the distortion energy per unit volume in a tensile specimen when subjected to outflow occurs in uniaxial Yield stress σy, in a simple tensile test. Consider the strain energy stored in a volume

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29 FIGURE 13 TRIAXIAL STATE OF STRESS

The energy density of multi-axial deformation due to the load is given by equation 10 which can be written using the three principal axes, as:

EQUATION 10

Combining this equation with Hooke's Law, we obtain

EQUATION 11

The first portion of this deformation energy is related to volume change of element while the second is associated with the variation, that is, the distortion. The volume change is produced by the average stress.

EQUATION 12

The resulting stress produce distortion without change in volume. Tests show that materials are not flowing when subjected to hydrostatic pressure (equal stress in all directions - a state of hydrostatic stress) to extremely high values. Thus, it was postulated that stress that actually cause runoff are the strains that produce distortion. This hypothesis is the yield criterion (failure) of the maximum distortion energy, which states:

"The outflow of a ductile material occurs when the distortion energy per unit volume equals or exceeds the distortion energy per unit volume when the same material flows in a simple traction test." (ASM HANDBOOK 1993a to 1993b).

When the stresses causing distortion, are substituted in equation 11, we obtain the following expression for the energy density of distortion:

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30 EQUATION 13

In the above expression, we also used the relationship:

EQUATION 14

The energy density of distortion in a tensile specimen in the strain yield strength, σy, is given by equation 15, thus σ1=σ2=σ3 and σy = 0

EQUATION 15

Outflow occurs when the distortion energy for a general load, given by equation 14 equals or exceeds the value (UD)/y in equation 15. Therefore, the failure criterion

of maximum energy of distortion can be stated in terms of the three principal stresses as shown on equation 16.

In terms of normal stresses and shear stresses in arbitrary three mutually orthogonal planes, one can show that the failure criterion of maximum distortion energy has the following form (ASM HANDBOOK, 1993a to 1993b),

EQUATION 17

In the case of plane stress, the corresponding expression for the failure criterion of maximum power distortion can be easily obtained from equation 16, using σ3 = 0.

EQUATION 18

Equation 18 it is an ellipse formula in the plane σ1 - σ2, as shown in Figure 13. For the purpose of comparison, the hexagon theory fails to outflow the maximum shear stress is also shown in dashed lines. The six vertices of the hexagon, the two failure theories are coincident, namely, both theories predict that the outflow state occurs if the strain state (plane) at a point corresponding to any of the six states of strain. On the other hand, the

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31 theory of maximum shear stress gives a more conservative (i.e., a smaller value) to the drain strain required to produce estimate for the hexagon is located on or within the ellipse (ASM HANDBOOK 1993a to 1993b).

FIGURE 14 ELLIPSE MAX DISTORTION ENERGY THEORY

According ASM HANDBOOK (1993a to 1993b) a convenient way to apply the theory of maximum distortion power mode is to take the square root of the terms on the left side of the equation 16 or 2:191.18 for an equivalent amount of strain, which is called the equivalent stress Von Mises. Any one of the following two equations can be used to calculate the equivalent Von Mises stress, σVM:

EQUATION 19

Or

EQUATION 20

In case of flat strain, the corresponding expressions for the equivalent Von Mises stress can be easily obtained from the equations 1.19 and 1.20 using σ3=0 or σy=ζzz=

ζyz=0.

Comparing the value of von Mises stress, at any point, with the value of yield stress in strain, σy, it is possible to determine whether the slip occurs according to the theory of maximum power failure distortion. Therefore, the equivalent Von Mises stress is largely used when the calculated stresses are presented in tables or as strain color graphics.

According Wu (2008), at any time of strain vector analysis of the material is given by a scalar equation, which assumes that the equivalent plastic strain at the beginning of damage is a function of the relationship between the hydrostatic pressure p, and Von Mises stress q, which is the ductile failure criterion used in ABAQUS. Represented on equation 20.

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32 EQUATION 21

Where:

T triaxial strain factor p hydrostatic pressure q Von Mises stress

If T assumes a positive value mean we are in a compression case, if T value is negative it is a triaxle traction case.

This model is based on the value of the equivalent plastic strain at the point of integration of the element and failure is indicated when the damage parameter ω exceeds the value of one. The parameter ω is defined as showed

EQUATION 22

Where:

Initial deflection at the beginning of the fault Increment of plastic deformation

Final deformation

The hydrostatic stress p and equivalent strain q, in terms of its main components are formulated by:

EQUATION 23

And

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33

3

METHODOLOGIES AND WORK PLAN

3.1 Planning the Work

A series of experiments was carried out by ETO (2005), with purpose of improving the precision stamped holes, by using a combined punching and broaching tool. In this study was used a gap in die of 7,5%.

Aiming to evaluate the ability of ABAQUS program to reproduce the gap used in the experiment discussed in ETO (2005) and data reported in the literature, we proposed a method divided in following steps:

3.1.1 Survey of Experimental Data

Was considered in this work, a steel plate H 360 LA with 8 mm thick, as in ETO (2005).

Knowing the mechanical properties of the material it is important to correctly characterize the simulation application. The mechanical properties of steel H 360 LA were found by a tensile test. Body dimensions of the specimen are shown in Figure 15. The tensile test was carried out with the specimen, provided information on the material's mechanical properties, such as tensile strength (TS), yield stress (YS) and elongation (A). These properties characterize the material as to its limits in terms of strength, i.e., the maximum strain reached throughout the (TS) test, the maximum strain reached at the end of the elastic deformation and consequent initiation of plastic deformation (PD) and finally, the ultimate elongation (A) of the material until the time of fracture. Other data calculated at the end of the tensile tests were the resistance factor ("K"), which quantifies the level of strength that the material can withstand, and the work hardening coefficient (exponent "n") of the material, which is the ability distribute the material to deformation. These two parameters characterize the material in the plastic region.

FIGURE 15 BODY DIMENSIONS-OF-EVIDENCE USED IN TEST

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34 An explicit model, which uses a layout point of direct integration of structural dynamic equations, which is more suited to this case. This approach is suitable for highly dynamic problems with non-linear behavior, which is the case for metal fracture simulation.

There are usually four bodies involved in sheet metal forming problems: punch, die, plate and gland plates. In Figure 16 can be seen the elements modeled in ABAQUS program, the 2D axisymmetric shape. They are punch, die and press plates, considered as solid/rigid structural elements.

This kind of definition allows all node freedom degrees to be connected to their gravity center, so that it becomes independent of nodes number. Were used to plate axisymmetric structural elements composed of quadrilaterals, with four nodes and reduced integration (CAX4R), triangular with three nodes (CAX3), and matrices, with gaps of 2% (d1=10,32), 3% (d2=10,48), 5% (d3=10,80), 7,5% (d4=11,20) and 10% (d5=11,60) of metal sheet thickness .

Due to the high gradient of plastic deformation in the cutting region, a sufficiently dense mesh should be applied in this area. In this paper, 128 elements were applied in thickness only in the region where shear deformations are concentrated. In other regions, a less refined mesh was applied, to decrease the computational time. The exposed previously is shown in Figure 17.

FIGURE 16 PUNCHING MODEL AXISYMMETRIC (MM)

punch

plate

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35 FIGURE 17 PLATE MESH WITH 128 ELEMENTS (IN THICKNESS)

The characteristic of the material used in ABAQUS was isotropic hardening Von Mises. It is assumed that material has similar properties in all directions. The characterization of the behavior of the material in ABAQUS can be divided into six stages. They are:

- report the material density: 7,8E-9 g/mm3_{for steel H 360 LA;}

- inform the elastic properties of the material: the elastic properties are defined as Young's modulus (E = 210 000 MPa), Poisson's ratio (v = 0,3) and the properties obtained in tensile test

- characterize the properties of the plastic region, points b and c, and the criterion for the onset of material failure

- inform of friction coefficient: a coefficient of 0,1 was used in all simulations, this validated coefficient (SODERBERG, 2006);

- to establish contacts and steps;

- Determining the punching speed: the ABAQUS, 250 cm/s; in dynamic explicit analysis, it is possible to use higher than the actual speed (KLINGENBERG, 2006).

In ABAQUS there are two criteria to characterize the material of shear failure and the failure of ductile failure. The criterion used was the ductile failure, which is described by the rate of degradation of stiffness of the element. In ABAQUS/Explicit is assumed that the degradation in the rigidity is associated with each mechanism, which can be modeled using a variable scalar damage. The characterization of the onset criterion of failure of the material was obtained as follows:

I. For uniaxial strain has σ2 ≠ 0, σ1 = σ3 = 0

The value of the triaxle strain factor can be obtained by substituting the values of σ2 ≠ 0 and σ1 = σ3 = 0 in equations 21, 23 and 24 resulting T = 0.272

II. For biaxial strain has σ1 = σ2 and σ3 = 0 obtaining T = 0.667 III. For shear has σ1=-σ2 and σ3 = 0 resulting T=0

Deformations (ε) were obtained experimentally by tensile test.

Contacts were established between the surfaces of rigid bodies and the surfaces of the plate through penalty contact method option, using the definition of contact surfaces,

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36 slave and one master. These surfaces, during simulation, interact with each other, creating new boundary conditions for the analysis, with the punch, the blank holder and matrix surface, masters and plate, slave.

The simulation of the punching was divided into two steps. At first, a boundary condition was applied to restricted rotation and displacement of all rigid bodies through option displacement / rotation. In side coincident with the axis of symmetry of the plate, a so-called constraint (symmetry/anti-symmetry/embedding) was applied. The second step, the plunger displacement has changed to 9 mm in the vertical direction, causing the plunger to exceed the sheet thickness. The load applied by the press-plate on the plate was 10000N, ensuring that it is kept immobile.

3.1.3 Simulation Model

For simulations of punching was used for computer modeling of the problem, the finite element program ABAQUS (v. 6.7). This software, in a very general character and has great versatility for applications in many areas of engineering, consists of several modules, among which the graphics modules CAE (preprocessor), Viewer (post-processor) and the main modules STANDARD and EXPLICIT, employees this dissertation and addressed in Chapter 2.

The simulation modeling obeyed the following:

I. Pre-processing: in this phase, the input data were analyzed in the pre-processing phase, such as geometry data, material and loading experimentally available, simplifying assumptions and the delineation of the problem;

II. Problem processing defined in the pre-processing stage;

III. Post-processing: In this stage, the data have been analyzed and compared with experimental data. The best combination of simulation parameters were chosen at this stage.

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37

4

RESULTS AND DISCUSSION

4.1 Tensile test

You can check the results on the mechanical properties of the material obtained in the tensile test, compared to the values determined by the technical standard steel H 360 LA in Table 1.

Traction tests TS (MPa) 587

YS (MPa) 521 E (%) 29 H 360 LA TS (MPa) 460 - 600 YS (MPa) 380 – 530 E (%) Min. 23 TABLE 1

The results in Table 1 show that both the values of the tensile strength (TS) and the Yield stress (YS) and elongation (A) obtained by the Traction tests, are consistent within the values pre-set by the standard without exceeding the specified limits. This ensures that, in terms of mechanical properties, the steel sample to be used is perfectly released, without any restriction that may influence the results of the simulations.

Plasticity parameters, indicated by the resistance coefficient (K) and work hardening coefficient (n) of the plate obtained by the tensile test are shown in Table 2.

Material: H 360 LA

parameters values

K 1010 MPa

N 0,2

TABLE 2

The diagram strain vs. deformation of steel H 360 LA, obtained in the tensile test, is shown in Figure 18.

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38 FIGURE 18 DIAGRAM STRAIN VS. DEFORMATION OF H360 LA

Curve of strain vs. deformation in Figure 18 can be seen that it is a ductile material due to the outflow region defined and large plastic deformation, and supports the choice of ductile failure criterion used for the simulations.

Already the diagram strain vs. true deformation of steel H 360 LA appears in Figure 19 the curve was constructed by Hollomon equation σ = Kε n_{, from the parameters in Table 2.}

For the construction of this curve was used in the procedure adopted (ASM HANDBOOK, 1993a to 1993b).

FIGURE 19 DIAGRAM TRUE STRAIN VS. TRUE STRESS OF STEEL H 360 LA

The points b and c of Figure 19 allow to be defined stresses vs true strain, to plastic characterization of this region correctly in ABAQUS software the c point indicates the start point of failure and the bard points start and end of the tensile test.

Str ai n (MPa ) Deformation (mm/mm) tru e stres s (MP a) True strain (mm/mm)

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39 The results of the tensile test conducted allow confirmation of characteristics of plasticity and mechanical strength, according to expected.

4.2 Numerical Simulations with Different gaps in Die

The following topics describe the results of numerical simulations for gaps from 2% to 10%.

After analyzing the simulations, some common features among them were verified. These common characteristics are: strains are concentrated in the yellow regions of the mesh, indicating that was correct to apply more elements in thickness in this region.

The start failure criterion reaches 1, fracture occurs. The crack found in punching is of ductile material characteristic, since deforms material before break. The punch penetrates the plate about a third of its thickness before the fracture occurs endorsing the criteria used.

4.2.1 Simulation with clearance of 2%

Figure 20 shows the result of numerical simulation of punching with a gap of 2% (d = 10,32mm) in the array.

FIGURE 20 SIMULATION OF STEEL H 360 LA WITH 2% GAP BETWEEN PUNCH AND DIE

Figure 20 gives a clear picture that punctured plate, with a gap of 2% in the die does not show the mismatch of the cracks between the beginning and the end of the process. There occurrence of burst effect, because the profile section features a smooth surface (region A) and the other with roughness (region B) that taper in the latter, provoked by stripping the material.

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40

4.2.2 Simulation with Gap of 3%

Figure 21 shows the result of punching numerical simulation with a gap of 3% (d= 10,48mm) in the array.

Comparing the simulation of 2% to 3%, there was a small increase in the taper region A of Figure 21, caused by the collapse effect and the occurrence of mismatch not of cracks.

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41

4.2.3 Simulation with Gap of 5%

Figure 22 shows the result of punching numerical simulation with a gap of 5% (d = 10,80mm) in the array.

Comparing the simulations of 2% and 3% to 5% simulation, there is an increase in the taper region A of Figure 22.

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42

4.2.4 Simulation with Gap of 7.5%

Figure 23 shows the result of punching numerical simulation with a gap of 7.5% (p = 11,20mm) in the array.

FIGURE 23 SIMULATION OF STEEL H 360 LA WITH 7.5% GAP BETWEEN PUNCH AND DIE

Comparing this simulation with others, it turns out that there was no clash of cracks, only larger taper between the diameters, region A of Figure 23.

Comparing with the results obtained with ETO (2005), verifies the occurrence of the same conicity.

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43

4.2.5 Simulation Clearance 10%

Figure 24 shows the result of punching numerical simulation with a gap of 10% (p = 11,60mm) in the array.

FIGURE 24 SIMULATION OF STEEL H 360 LA WITH 10% GAP BETWEEN DIE AND PUNCH

Simulation with a margin of 10%, compared with the others, showed a large taper diameters between region A in Figure 24.

Analyzing Figures 20 to 23, it turns out that the best gap for this plate thickness is from 2,3% and 5%, as showed slight taper.

It turns in all simulations the taper effect, namely the initial diameter is greater than the final diameter. According MELLO and MARCONDES (2006) this is due to the increased thickness of the plate.

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44

4.2.6 Graphics vs. Force displacement

In the graphs of Figures 24 to 28, are revealed stages of the punching process. During the beginning of the process, the plate is pushed into die and the material is deformed elastically first. The plastic deformation results in a rounding of the edge of the plate. During this phase, ductile fracture occurs after shearing of the material.

FIGURE 25 GRAPHIC STRENGTH VS. DISPLACEMENT USING 2% GAP BETWEEN PUNCH AND DIE

Analyzing the graph of Figure 25, it appears that the region of slip is between 140000N and 157502 N, with maximum cutting force of 157502N (Point A in Figure 25), followed by the plastic region. The ductile fracture occurs between 40000N and 20000N (point B), then the shear material. The burst effect occurs between 2 and 4mm.

S tr en g th ( N ) displacement (mm) Simulation 2% displacement (mm) Simulation 3% S tr en g th ( N )

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45 Comparing the graphs of Figures 25 and 26, there are similar characteristics in the outflow region, plastic deformation of the ductile fracture initiation and shearing effect and overflow region. However, there is an increase in the cutting force to 158823N.

Analyzing graph from Figure 27 and comparing the graphs of Figures 25 and 26, there is an increase in the outflow region to 162084N, with an increase of plastic deformation. The cutting force suffers a slight increase to 162084N.

FIGURE 28 GRAPHIC STRENGTH VS. DISPLACEMENT USING 7,5% GAP BETWEEN PUNCH AND DIE

Already on the graph of Figure 28, the flow region is included under the range 120000N 164326N. There has a maximum cutting force 164326N, then the plastic region. The ductile fracture occurs between 40000N 20000N to, then the shear. It is observed further plastic deformation compared to other simulated gaps. The overflow effect occurs between 3 and 4mm. displacement (mm) Simulation 5% S tr en g th ( N ) displacement (mm) Simulation 7.5% S tr en g th ( N )

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46 FIGURE 29 GRAPHIC STRENGTH VS. DISPLACEMENT USING 10% GAP BETWEEN PUNCH AND DIE

Comparing Figure 29 graph with the graph in Figure 28, there is a great expansion of the plastic region (region A of Figure 2), indicating that there were greater deformation before rupture.

In graphics of Figures 25 to 28 can be observed that the punch has penetrated the plate between 2 and 3 mm before the occurrence of the overflow material. Already in the graphs of Figures 28 and 29, there is an intense plastic deformation SCHAEFFER (1999) reported that excessive gaps cause severe plastic deformation.

displacement (mm) Simulation 10% S tr en g th ( N )

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47

5

CONCLUSION

Based on the results and previously held discussions, the following conclusions can be presented.

The dimension of hole diameter at the end of the cut is greater than the dimension of the diameter at the beginning of cutting, which requires adjusting the hole size by a subsequent machining operation or laser cutting.

As the gap increases, a rupture of the material tends to occur later in the cut. It is found that the profile of the cutting region has two distinct regions, namely one third of the material exhibits visually smooth surface without roughness; and the remaining features roughness, characterizing the effect of rupture of the punched plate.

2%, 3% and 5% gaps have better characteristics conicity, plasticity and shear strength than those made with gaps of 7.5% and 10%.

The 2% gap proved to be the most suitable for the thickness of molded plate because it has less conicity, shear strength and plastic deformation.

The start of damage criterion is reached before occurs to breakage. The punch penetrates plate 2 to 3 mm, or roughly one-third prior to occur to rupture.

The gap of 7.5% and simulated in this study present in the matrix used ETO (2005) showed greater plastic deformation of the punched plate, larger hole conicity and required higher shearing strength as compared with the gaps of 2%, 3% and 5%.

Based on the experimental results and literature, reported in the chapter of results and discussions, it was concluded that the modeling carried out by numerical simulation using the ABAQUS / Explicit software v 6.7 was validated.

5.1 Suggestions for Future Work

Considering the importance and relevance of this work and its rationale and results, it is suggested the following points for further work:

- Study the springback that occurs after the hole is punctured;

Modelling metal punching using ductile failure criteria

Catarina de Lemos

Grilo Ferreira

Barbosa

MODELLING METAL PUNCHING USING

DUCTILE FAILURE CRITERIA

Contents

List of Figures

Symbols List

1

INTRODUCTION

2

THEORETICAL

2.1 Concepts of numerical simulation

2.2 Punching

2.2.1 Tools and Equipment Punching

2.3 Punch

2.4 Die

2.5 Punching Process

2.6 Gap between punch and die

2.7 ABAQUS

2.7.1 Data input

2.8 Symmetry types

2.9 Characterization of the Elements according to the ABAQUS

2.11 Contact between Surfaces

2.13 Mesh Elements

2.14 Explicit Method

2.15 Plasticity

2.16 Concepts about Failure Criteria

2.17 Maximum Shear Stress Theory - Theory of Tresca

2.18 Theory of Maximum Distortion Energy - Theory of Von Mises

3

METHODOLOGIES AND WORK PLAN

3.1 Planning the Work

3.1.1 Survey of Experimental Data

3.1.3 Simulation Model

4

RESULTS AND DISCUSSION

4.1 Tensile test

4.2 Numerical Simulations with Different gaps in Die

4.2.1 Simulation with clearance of 2%

4.2.2 Simulation with Gap of 3%

4.2.3 Simulation with Gap of 5%

4.2.4 Simulation with Gap of 7.5%

4.2.5 Simulation Clearance 10%

4.2.6 Graphics vs. Force displacement

5

CONCLUSION

5.1 Suggestions for Future Work