Analysis of Metal Forming Processes;

Home , Forming processes

A 3-D DIE CONTACT ALGORITHM FOR FINITE ELEMENT ANALYSIS OF METAL FORMING PROCESSES;

A Thesis Presented to

The Faculty of the college of Engineering and Technology

Ohio University

In Partial Fulfillment

of the Requirements for the Degree

Master of Science

Lohitha £ewasurendraIf June, 1991 CONTENTS

CHAPTER 1 INTRODUcrION 1

1.1 General background 1

1.2 New developments 6

CHAPTER 2 FORMULAnON USED IN ALPID3D 8

2.1 Overview 8

2.2 Boundary conditions 11

CHAPTER 3 COMPLEX DIE SHAPES 13

3.1 Overview 13

3.1.1 Die Touching nodes 14

3.1.2 Free nodes 16

3.2 Contact algorithm 18

3.2.1 Die definition 18

3.2.2 Updating the die touching nodes and determination of

the die normal 21

3.2.2.1 Die patches 22

3.2.2.2 Edges 32

3.2.2.3 Vertices 34

3.2.3 Determination of the time step 38

3.2.4 Nodes separating from the die 42

3.3 Implementation 43

3.3.1 Node oscillation 43

3.3.2 Die patch arrangements 45 CHAPTER 4 SAMPLE APPLICATION OF 3-D DIE CONTACf

A.LGORITI-IM 47

4.1 Analytical modeling ofround-to-square extrusion through

a streamlined die 47

4.2 Physical modeling ofround-to-square extrusion 65

4.3 Analytical modeling of closed die forging of a hexagonal

bolt head 70

CHAPTER 5 PRE- AND POST-PROCESSING 90

5.1 Overview 90

5.2 Pre-processor 92

5.3 Post-processor 96

CHAPTER 6 CONCLUSIONS AND RECOMMENDAnONS 99

6.1 Conclusion 99

6.2 Future developments 102

APPENDIX A USER'S MANUAL ~ 104

A.I Overview 104

A.2 Master control data 105

A.3 Die Geometry data 108

A.4 Nodal point data 111

A.5 Element data 111

A.6 Boundary nodal point data 111 APPENDIX B USER'S MANUAL FOR PRE- AND

POST-PROCESSmG 112

B.I Pre-processing 112

B.2 Post-processing 114

REFERENCE 116 1

Chapter 1

INTRODuCTION

1. 1 General background

In a manufacturing process, a given part which is shapeless or of simple geometry is transformed into a useful part with a desired geometry, tolerance, strength, appearance etc.. Manufacturing processes can be divided into four basic categories[l].

(a) Primary shaping processes such as various casting processes, and powder

metal compacting processes,

(b) Metal forming processes,

(d) Joining processes.

Usually, a complete process of manufacturing of a finished part includes more than

one of the above processes. Among these manufacturing processes, metal forming plays a

very important role towards the quality, raw material utilization, metallurgical requirements,

cost, near net shape and structural properties of the finished part. Metal forming can be

further classified[ 1] as: 2

(a) Massive forming processes such as forging, rolling, drawing and extrusion

etc.

(b) Sheet metal forming processes such as bending and straight flanging,

surface contouring, linear contouring, deep recessing, and shallow

recessing.

The main difference in the massive forming processes compared to the sheet metal

forming processes is that the workpiece undergoes a considerable change in the cross

sectional area with the change in the geometry. In sheet metal forming processes, the

workpiece does not significantly change its cross section as the geometry changes.

Different methods are applied to analyze these two categories of metal forming processes

due to the different mechanics of deformation.

Until recently, metal forming was more an art than a science and it was mainly an

experience oriented technology. With very little analysis and trial and error based design of

the forming processes, forming industry can no longer compete in the today's very

competitive market with increasing material, energy, and labour costs and on the other

hand, analysis is vital for newly developed difficult-to-form materials which usually have

narrow processing windows. Thus, the design, analysis and optimization of the forming

processes is vital for the production of high quality defect free parts at low production

costs.

Recent developments in CAD/CAM systems and advanced numerical methods have

enhanced the computer aided design/optimization of the metal forming processes.

Computer simulations of metal forming processes enable the process design engineer to

, perform the die and preform alterations on the computer to obtain a better product while 3 optimizing the process avoiding costly and time consuming trial and error based experimentation. The results are high quality finished parts, reduced lead time, reduced manufacturing cost and moreover, a better understanding of the process.

The input parameters for the process analysis and design include;

(a) Workpiece geometry,

(b) Workpiece material property behavior,

(d) Frictional properties at tool/material interface,

(e) Temperature and thermal properties of the workpiece and the die,

(t) Process conditions such as load or deformation rates (die velocity), and

environment (temperature etc.),

(g) Equipment characteristics. 4

The results comprise of

(a) The energy requirement for the forming process

(b) The distribution of local process variables such as strain, strain rate, and

stress etc.

(d) Die filling

(e) Production rate and cost

(0 Final dimensions of the finished product.

Among many analysis methods, the Finite Element Method (FEM) has recently become very popular because of low hardware cost, accurate results and many more advantages over the other methods.

Under the current investigation, the FEM based metal forming simulation package

ALPID3D (Analysis of Large Plastic Incremental Deformation 3-D) which was originally developed at Battelle Columbus Laboratories under the US Air Force sponsorship was further enhanced by implementing a new 3-D die contact algorithm. A three dimensional extrusion process and a forging process were simulated using this modified program to test the new die contact algorithm. The program is based on the rigid-viscoplastic formulation 5 which is originally developed by Lee and KobayashijZ] and has been successfully applied to simulate many fanning processesfs-S].

Current version of ALPID3D was capable of simulating massive forming processes with linear die movements and predicting the following.

(a) Load-stroke relationship

(b) Material flow

and strain rate.

These data can be used to predict

(a) Whether or not the part can be fanned without internal and external defects

(b) The local distribution of material properties

A major drawback in the original version of ALPID3D was that it could use only simple shaped (flat) dies. Specific die numbers are used in the data file to represent corresponding dies. 6

1.2 New developments

Under the current investigation, a die contact algorithm was developed to handle dies of any shape and added to the ALPTD3D source code. Hence, the die contact boundary value problem was solved using the method of multi-point constraints in which the nodes which are in contact with the dies are applied with the die velocity in the normal direction to the die. More details of this procedure are given in later chapters.

The interface software called IRMALP was also developed to interface with

Intergraph Rand-Micas (IRM) thus developing an excellent pre- and post-processor for

ALPID3D. Details are given in chapter 5. The graphic oriented IRM pre-processor was used to prepare the ALPID3D input data file except the master control data card and die geometry data.

Similarly, IRMALP can be used to post process ALPID3D output results to obtain contours of stress, strain, strain rate, velocity and the deformed mesh geometry. The design file created by IRM can be used for color shading of contours, mirroring, rotating, hidden line removing, smooth shading and many more Intergraph graphic operations.

Simulation of round-to-square extrusion through a streamlined die and a closed die forging of a hexagonal bolt head were carried out to test the die contact algorithm.

Streamlined die design package STREAM, ALPID3D and IRM were integrated into a complete CAD system for analyzing of 3-D extrusion through stream-lined dies using a module called STALP which translates STREAM output MOVIE compatible die coordinate file into ALPID3D format containing die coordinates and die patch connectivities in the 7 proper order. Round-to-square extrusion was experimentally carried out to validate the results of the FEM model and found be in good agreement with experimental results.

Results show that the modified version of ALPID3D can be used for simulation of any massive forming process with complex shaped dies. 8 Chapter 2

FORMuLATION uSED IN ALPID3D

2. 1 Overview

ALPID3D is based on three-dimensional rigid-viscoplastic finite element formulation[2] which is an efficient and computationally economic method of analyzing material deformation. The material is assumed to follow rigid-viscoplastic material behavior where the flow stress depends on the strain-rate (£), the strain (£), and the temperature (T) and obey Huber-Mises yield criterion and its associated flow rules. The rigid-viscoplastic formulation and the necessary boundary condition for a material deformation process is summarized in this chapter.

(i) Equilibrium equations

(2.1)

where O'ij is the component of stress tensor, OVi is an arbitrary variation of velocity and "," denotes the partial differentiation.

(ii) Strain rate - velocity relations

£1"JO = (v""IJ + v,J,10) / 2 (2.2)

where £ij is the component of strain rate tensor. 9

(iii) Constitutive equations (Levy-Mises flow rule)

cr.. = 2....iL Pil (2.3) IJ 3...!..~J E

where,

Effective stress o = '"(3/2) a/ij a/ij . Effective strain f, = ...; (3/2) tij tij

and cr 'ij = deviatoric stress tenser.

Force prescribed boundary SF

Velocity prescribed boundary S V

Figure 2.1 : Schematic representation of the continuum. 10

(iv) Boundary conditions

O"ij ni = Fi on SF where force is prescribed

Vi = Vi on S, where velocity is prescribed,

and n; is the unit normal to the surface.

By incorporating all these equations and using the divergence theorem, the final form of governing integral equation before discretization is obtained as;

(2.4)

Here K is a penalty constant which has to be very large in order to conserve volume of the workpiece. This non-linear equation is solved by using the modified Newton

Raphson method over the discretized continuum with the necessary boundary conditions.

More details can be found in references [6-7]. 11

2. 2 Boundary conditions

Essentially, in metal forming simulations, zero nodal forces are prescribed on the free boundary nodes which are not in contact with the dies. Complex boundary conditions exist at nodes which are in contact with the dies and special attention has to be given when applying these boundary conditions.

Boundary conditions on the die touching nodes can be divided into two categories:

(a) velocity boundary condition in the direction normal to the die surface and (b) force boundary condition in the direction tangential to the die surface in terms of frictional force.

Then the nodal force normal to the die and velocity tangential to the die will be the results.

Two types of frictions can be applied in ALPID3D; (a) shear friction, and (b) coulomb friction. The frictional stress caused by shear friction is a function of the yield stress of the material and the frictional stress by Coulomb friction is a function of nodal reaction normal to the die and both will be opposite to the direction of tangential velocity of the node with respect to the die. The friction factor or the friction coefficient used in these cases depends on the workpiece material, lubricant, and die surface condition and usually determined by experiment[8] such as ring test, extrusion forging test, etc. It can be noticed here that if usual expressions for friction are used, a discontinuity of the frictional stress occurs at the neutral point as frictional stress depends on the relative tangential velocity of the node. This is highly impossible and in ALPID3D, this has been resolved by adopting a velocity dependent modified expression for frictional stress proposed by Chen and

Kobayashi[2] as shown in figure 2.2. 12

mk r-----======----

Distance Modified Frictional Stress '"

-mk

Figure 2.2 : frictional stress (shear friction) around the neutral point

For shear friction, the frictional stress is expressed as

(2.5)

where

fs = frictional stress

Vr = relative velocity

A = a small constant of order 10-4

m = friction factor

k = material yield stress 13

Chapter 3

COMPLEx DIE SHAPES

3 .1 Overview

As mentioned earlier, the three dimensional FEM code ALPID3D was incomplete without the capability of handling three dimensional dies though it could handle three dimensional deformation, This was perfected by adding a new module to handle complex shaped die contact boundary condition.

In rigid-viscoplastic finite element formulation, two kinds of boundary conditions are applied as velocity and force prescribed boundary conditions. The boundary nodes are divided into three categories in order to implement these boundary conditions such as,

(a) Nodes touching the dies

(b) Nodes separating from the dies

process. 14

3.1.1 Die Touching nodes

As quoted in the previous chapter, essentially, the velocity boundary condition is applied on the die touching nodes in the normal direction to the die surface and the force boundary condition is applied in the tangential direction. More precisely, the normal component of the die velocity is prescribed on the nodes which are in contact with the dies. The frictional nodal forces in the tangential direction in fact depend on the sliding velocity (and nodal reaction too, in the case of coulomb friction) and hence the force

boundary condition adds another non-linear term to the problem which is already non- linear.

Updated node lies outside the die caviry

Die cavity

Updated node lies inside the die cavity

Figure 3.1 : Updated nodes may bepositioned inside or outside of the die cavity 15

According to the incremental solution approach implemented in ALPID3D, the finite element grid is updated with the calculated velocity field and the step size in the current step. In this process, as shown in figure 3.1, in the general case of warped die surfaces, node may temporarily move away (tangentially) from the die surface and the resulting nodal positions may lie inside or outside the die cavity. In the real situation, a

node which is in contact with a die has to remain on the die surface (it can slide along the

die surface) unless it separates from the die surface and move into the die cavity during the

deformation process. Therefore, prior to the determination of the next step solution, all the

touching nodes are forced back on to the die surface accordingly. This procedure is termed

as the Multi-point Constraints Method.

r S S r

Figure 3.2 : Local coordinate systems 16

In general, the die surface is inclined to global axes x, y, and z. Then, an additional relationship has to be used to define the zero relative velocity in the direction of die normal in terms of velocity components x, y, and z. This difficulty is overcome by using a local coordinate system (r.s.t) for each die touching node oriented in such a way that the t-axis is perpendicular to the die surface and the vectors such as velocities and nodal tractions are then mapped back and forth to the local coordinate system from the global coordinate system. Figure 3.2 shows local coordinate system for each sides of an octagonal prism.

3.1.2 Free nodes

The boundary nodes which may touch the dies during the deformation process fall into this category. If velocity boundary conditions are not applied, zero nodal forces are prescribed on these nodes. But these nodes have to bechecked in each time step to see whether they come into contact with the dies.

As shown in figure 3.3, if any free node penetrates the die during the step, the time step is truncated (~T1) so that it is just enough for the node to touch the die surface and the boundary condition codes of that node is modified to be a die touching node. The remainder (~T2) is used as an additional time step and the solution procedure is continued to complete the original time step (~T). If another node tends to penetrate, the time step is again reduced and the same procedure is applied. 17

Die cavity

figure 3.3 : Free node touching the die

3.1.3 Nodes releasing from the dies

The nodes which are already in contact with the dies may move away from

the dies during the forming process. Such nodes are identified and released from the dies

without forcing them to be on the die surface. These nodes then act as free boundary

nodes.

After the calculation of the velocity field and nodal forces, the forces at the

nodes which are in contact with the dies are checked prior to the updating of the workpiece

geometry. Iftensile nodal reactions which indicate the nodal movement away from the die

exist, the boundary condition codes of such nodes are modified to be free boundary nodes

and the velocity field is recalculated until no tensile nodal reactions exist at the nodes

touching the dies.

In the case of complex shaped dies, special care should be taken since the releasing

, nodes may touch another part of the die during the same time step. 18

3 . 2 Contact algorithm

As discussed in the earlier section, the main objective of the algorithm is to bring the nodes which are to be in contact with the dies to the die surface and to find the die normal vector at the node in the case of die touching node. In the case of free boundary nodes, the time taken to penetrate the die by each node and thereby the minimum time step for a free node to touch the die is to be found in order to decide the time step. The developed algorithm for this purpose consists of the following steps.

(a) Die definition

(b) Obtaining the new position of the nodes which are in contact with

the dies and the normal vector to the die surface at the node

3 . 2.1 Die definition

The die surfaces can be defined by using Bezier surfaces, B-surfaces,

Coons patches, Planer patches etc. Shiau and Kobayashi[9] defined the die surface using

Bezier surfaces for open die forging. The die surface is generated using the control points

which are adjusted interactively until the required die surface is obtained. In the general

case, when more complex die shapes are encountered, it is very difficult to define the die

surface using Bezier or B-surfaces in this manner. But, this algorithm can be modified to

r read the points on the die surface and then to find the control points correspondingly and 19 hence to define the die surface more accurately. A disadvantage of this method is that a set of non-linear equations has to be solved to find the projections of the die touching nodes and the consequent computational effort becomes more difficult when more control points are used to define the die surface.

(b) Rectangular

(a) Portion of a cone (c) Sphere

(d) Portion of a anulus (e) Torus

Figure 3.4 : Primitive shapes used to define the die[ 10] 20

Pillinger and Hartley[lO] used an integration ofprimitive shapes (as shown in figure 3.4) to define the die surface when handling the die contact problem. They used another layer ofimaginary boundary elements by extending the existing finite element mesh beyond the die surface for the modeling of the effect of lubricant or the friction. This is an attractive method if different friction factors are to be used at different regions on the die surface. A great deal of user effort is needed to integrate these primitive part to fonn very complex shaped dies such as 3-dimensional streamlined extrusion dies etc. and only 2 dimensional simulations were found in the literature which uses this contact algorithm.

The most convenient method is to use planer patches using which any die shape can be approximately defined with less computational difficulties. Finer patches can be used for better approximation.

Figure 3.5 : A streamlined die and billet container defined by triangular patches 21

In the implemented scheme, planer triangular patches were used for die geometry definition. Figure 3.5 shows a streamlined extrusion die from circular to T section and billet container defined with triangular patches.

The triangular patch connectivities are defined anti-clockwise when viewed from the interior of the die. This helps determination of the direction of the normal vector pointing inwards the die surface.

3.2.2 Updating the die touching nodes and determination of the die normal

This task can be considered as the heart of the contact algorithm. According to the scheme used for applying the die contact boundary condition, the nodes which are in contact with the dies (may be now away from the die surfaces after updating the billet geometry with the velocity field of the previous time step) may be mapped on to a patch edge, not into a patch or on to a patch vertex, not on to an edge or into a patch. The approach is hence divided into three layers.

1. Triangular die patches

2. Patch edges

3. Patch vertices

The reason for this subdivision is explained in detail in later sections. 22

3.2.2.1 Die patches

The first step is to find the equations of the triangular patches which are used for the die geometry definition and the equation is taken in the form of

F = Cl x + C2 Y + C3 Z + C4 = 0 (3.1)

The coefficients of the equation (3.1) of the plane containing corresponding patch are found using the equation

X-X2 Y-Y2 Z-Z2 = 0 (3.2)

where (x 1,Yl), (x2,Y2), and (x3,Y3) are the coordinates of the three vertices of the triangular patch. By comparing equations (3.1) and (3.2), it can be found that

(3.3) 23

The normal vector to the plane can be expressed as

(JF · (JF · aF k n = -1 + -J + - (3.4) '- ax N ay N az '-

where F = 0 is the equation of the plane as in equation (3.1).

This can be further simplified by evaluating the partial derivatives of F of equation (3.1) as

(3.5)

and the direction cosines of the normal vector are

I = Cl -Vel + el + el

m= C2 (3.6) ,yet + C} + el

C3 n = ,yet + el + el 24

.--_ . . -'~ . " jII' ••••••..::,. " ,- . jII- ••••••... " . Die Stroke " . per step zO) ,jII ••••••• o = (Xo' Yo, JIIjII' ••••••• " O· C ~.: ~ A = (xl' Yl ' Z 1) ,,~ ....,II ~••."

B = (X2' Y2 ' Z2)

C = (X3' Y3' Z3)

D = (X4' Y4 ' Z4)

Figure 3.6 : Updating the nodes which are in contact with the die

Let us consider a case where a node (0 = [xo,Yo,zO]) is mapped on to the die in the direction normal to the die sutface and let the new position be D = [x4,Y4,z4] as shown in figure 3.6. Since the line OD is normal to the die patch ABC, the equation ofthe line OD can be written as

X- Xo Y- YO z - ZO -1- = ----m- = -n- (3.7) 25

The intersection point of this line and the plane containing the patch ABC can be found by resolving the equations (3.1) and (3.7). However, it should be noted that the equation (3.7) will be indeterminate if either I or m or n becomes zero. Slightly different approaches are applied in each of these cases.

Case (I) : n ~ 0

Rewriting the equations of the plane (Eqn. 3.1) and the normal to the plane through the point [xo,YO,zo] (Eqn. 3.7) :

Cj x + C2 Y + C3 z = - C4

x - zln= X() - lZO n (3.8)

Y- z mn= YO - m n ZO

The intersection point of aforementioned plane and the line

(D = [x4,Y4,z4]) is found by solving the set of equations (3.8) as;

CI [(YO - w- ZO) i - (X() - kZO) w-] - [~C4 - (Yo - w- ZO) C3] Y4 = (3.9) - Cl (1)n+ C2 (m) n + C3

- CdX() - It zo) - [C2 (YO - ~ zO) + C4] Z4 = - Cl (1) + C2 (m) + C3 n n 26

Case ell) : n = 0

For this case, the equations (3.1) and (3.7) can be written as;

Cl x + C2 Y = - C4 - C3 z

z = ZO (3.10)

The intersection point D = [x4,Y4,z4] is found as;

Z4=ZO

(3.11 )

l X4 = Y4 m + xQ - YO .Lm 27

Case (III) ; n = Q, m = Q

For this case, the intersection point D = [x4,Y4,z4] can be directly found from equations (3.1) and (3.7) as;

Y4 = Yo

Z4 = ZO (3.12)

X4 = (- C2Y4 - C3 z4 - C4)

A A=(X1,Y1,Zl) B = (X2, Y2' Z 2) C = (X 3, Y 3' Z 3) D = (X4, Y4 , Z 4)

Figure 3.7 : Node Mapping into the patch 28

The intersection point found in the above methods may not lie within the triangular patch. The next step is to check whether point D lies within the patch or not. As shown in figure 3.7, let us consider a triangular patch (ABC) and a point

(D) on the plane containing the patch and their projections on the x-y plane.

Since ABC and AIBICI are in anti-clockwise direction,

AIBID1, BIC1D1 and C1A1D1 will also be anti-clockwise (as shown in figure 3.7) if point

D1 lies within the projection of the patch. If point Dj lies outside, at least one of the above triangular connectivities will be in clockwise direction. The direction of the connectivities can be easily checked by evaluating following determinants ~ l' ~2 and ~3 and negative value indicates clockwise direction.

1 1 1

~1 = (3.13)

Yl Y2 Y4

1 1 1

~2 = (3.14)

Y2 Y3 Y4 29

1 1 1

~3 = X4 (3.15)

Y3 YI Y4

If the plane is perpendicular to the x-y plane, projection on the x-y plane becomes a line and projection on y-z plane is then considered to evaluate the determinants, If the plane is perpendicular to both x-y and y-z planes, projection on x-z plane is considered.

Figure 3.8 : The normal vector pointing outwards the die cavity 30

Similarly, all triangular patches are considered for each touching node in order to find the new position. When a touching node is considered, first the patches into which the node cannot be mapped are discarded. Since the node is mapped on to the closest patch, the distance (OD in figure 3.6 ) from the node to the patch is calculated and compared with that of each patch into which the node can be mapped.

The next task is to find the direction cosines of the die normal at the touching node. As given in equation (3.5) the direction cosines are C1, C2 and C3; the coefficients of the planer patch on which the node currently is. But this has to be oriented properly so that the die normal vector!! is pointing outwards the die cavity as shown in figure 3.8. In order to do this, the die patch connectivities are defined anti clockwise when viewed from the die cavity. The direction of the normal is determined by screening all the patches in the following manner.

First the orientation of triangular patches are checked to see whether they are perpendicular to x-y plane. If a patch is inclined to x-y plane, the projected area of the patch on x-y plane is calculated by

1 1 1

A = 1 (3.16) 2 YI Y2 Y3 31

The direction of the 1f component (along z axis) of the normal vector can be decided by the sign of area (A) calculated in the above expression. As shown in figure 3.8, positive area indicates the die cavity above the patch and hence negative k component of the normal vector and vise versa if the area is negative. Ifthe area calculated in the above expression is zero, the planer patch is perpendicular to the x-y plane and the projection on x-z plane is then considered to determine the direction of the normal vector. If the plane is perpendicular to both the planes x-y and x-z, the projection is y-z plane is considered.

In this manner, flags are set for k component of the normal vector if the planer patch is inclined to x-y plane, for i component if the patch is perpendicular to x-y plane and inclined to x-z plane, and for i component if the patch is perpendicular to the both x-y and x-z planes. Knowing the direction of one of the components (i, i, k) of normal vector, the calculated direction cosines, which may be opposite to the required direction, can beadjusted accordingly. 32

3.2.2.2 Edges

normal

Figure 3.9 : Node mapped onto an edge

In cenain cases, the node cannot be projected to any of the die patches in the perpendicular direction to the die and it may be positioned in the wedge created by projections of the adjacent patches as shown in figure 3.9. Then the closest point on the die may be on an edge. Node is mapped on to the edge in such cases. After screening all the patches to fmd the new position for the node, patches are again screened to find the nearest edge onto which the node can bemapped. 33

When projecting the node to the edge, a special technique was used in order to use same subroutines written for previous task; intersection of a plane and perpendicular line passing through the node 0 = [xO,YO,ZO] (in figure 3.6). Since the line OD is perpendicular to the line AB, a plane passing through nodal point 0 with normal direction AB is considered and the intersection of that plane and perpendicular line passing

through A or B is found as the required point D. The coefficients ofequation defining the

plane passing through 0 with normal AB are found to be

(3.17)

But there is no guarantee for the intersection point D to lie

within the line segment AB. The coordinates of point D are checked to see whether they

are in between points A and B and the particular edge is skipped in the process of screening

all the edges if the point D found to be outside AB.

The distances from the node to each edge are compared to

find a point on an edge closest to the node. If an edge is found to be closest to the node,

node will be moved to that edge on the die instead of a triangular patch. The direction

cosines of the normal vector to the die is then found by the normalized resultant of the

normal vectors of surrounding patches. 34

3.2.2.3 Vertices

As shown in figure 3.10 in 2-D representation, the closest point on the die to the node may be a vertex of a die patch so that the node cannot be projected to either a patch or an edge in perpendicular direction to the die. In that case the node is mapped on to the vertex which is closest to the nodal point.

After determining shortest distance from patches and edges,

all the vertices of the patches are scanned to determine the closest vertex to the node and the

distance. The direction cosines of the die normal is found by normalizing the resultant of

normal vectors of surrounding patches.

Nodal int Normal

\ I \ I \ I \ I \ I \ I \ I \ I \ I \ I \ I

Edges of the die patches

Figure 3.10 : Node mapped on to a patch vertex 35

Summarizing the approach, the closest point on the die is deterrnined by comparing

(a) Shortest distance to the patches along the normal vector of

each patch

(b) Shortest distance to the edges

The nodal coordinates are updated with the coordinates of the closest point which may be on a triangular patch or on a patch edge or on a patch vertex along with the appropriate directional cosines to adjust the local coordinate system of the particular node so that the t-axis is perpendicular to the die pointing inwards the die surface.

The complete procedure for updating the touching nodes and the determination of unit normal vector to the die surface at the nodes is summarized in the flow chart shown in figure 3.11. 36

START

Input the coordinates of the die nodes

Input the patch connectivities (Anti-clockwise when viewed from die interior)

Update the die position using the current stroke

Set Flags for each patch to indicate the die cavity side

Find equations of the planes containing each patch

Drop normals from the node to each plane containing relevent die patches and fmd the intersection points

Omit the patches into which the node cannot be mapped Nearest Patch Compare the distances and find the nearest patch and the normal vector

Adjust the direction of the normal vector so that it is pointing outward the die cavity using the flags which are already set 37

C?. :-:-: :> I Findtheequations of thedie patch edges I -:-:.: :::

/. .-:-:-: : -:-: Project thedie touching nodeontothelines containing the patch edges in thenormal direction .::: :-::-:::::-.::-: :::: -;' (?-:.:-:: :-:. .::--. ...••••••••••••••••••••••••••••••••••••••••••.••.•••l!' .: :-:-: '.:-' :: Omittheedges ontowhich thenodecannot be mapped .·..... 1 ;:: :.-::- :.: Nearest ..-. <::..:: .:., .... '-:: ::.:.: ::::'-::..:J.':'::::<:' .::-:-: :.::.:.... ,:...... :: :-: - .::» • -::: Edge Compare thedistances to thedie patche edges which are closerthan the nearest die patch and find the neraest edge if exists

-::-: : .:- I ... ::-: '-::::-.': -:.. .-.:: ::-:::. ::: .,-:,,::, '.:-::.:-:-:.: '.: '.: .': y :...... '-: Findthedie normal by adding the normals of the surrounding die patches and by normalizing theresultant

...... :-: .}<:> -; -::':':-:::'-'.:-: . .: .' ...... :

'.:- '.' , .. ':> ,:: -: ::: Find thenearest die node

:: . ::: ::<::;<1 -:-:: '.,< Nearest..... :: '-:.:: -::::: ::.:::::>:y ·:i:.:'· :.:.:.: ..... : .. Die nod~ Find thedie normal by adding thenormals of the surrounding die patches and by normalizing the resultant

': -::.

I Find the point on thedie which is nearest to thenodal point

Update thenodal coordinates and store the direction cosines of thedie normal

STOP

Figure 3.11: Node updating and time step determinarion scheme 38

3.2.3 Determination of time step

In ALPID3D, the time step is determined by the minimum of:

(a) User defined time step

(b) Time step to reach user described maximum strain

Out of these three factors, the time step for a free node to touch a die is directly related to the contact boundary condition and other two factors have no relation to the die contact problem.

As shown in figure 3.3, the time step (~T) has to be truncated (~T1) if the node penetrates the die during the current time step, so that it is just enough for a free boundary node to touch the die. Then the boundary condition of the particular free boundary node is updated to be a die touching node and the simulation is continued with the remainder of the truncated time step (L\T-~ T1) to complete the original time step ~T.

With the step solution of the velocity field, die penetration point for each free node is found by the intersection point of the die surface and the line passing through the node in the direction of nodal velocity with respect to the die. 39

The direction cosines ofthe relative velocity vector are found as

1 = (Vx - Vdie,x) VR

(3.18)

where relative velocity

The equation of the path of the nodal point can beexpressed as

(z - ZO) (y - Yo) = (3.19) m n

similar to the equation (3.5), where (xo, YO' zo) is the nodal point. A similar procedure as in the case of updating touching nodes described in section 3.2.1 is then followed to find the intersection of this line and the die surface. When the penetration point (intersection) is found, the time is calculated to penetrate the die as

~Tl = ..j(x4 - xg)2 + (Y4 - Yo)2 + (z4 - zri (3.20) VR

where (x4' Y4' z4) is the penetration point. 40

All the nodes are scanned in a similar fashion to determine the minimum time step for a free node to just touch the die. Nodes which are going away from the die are skipped in the scanning process. The direction of the nodal movement is checked by checking the sign of the scalar product of velocity vector and the vector CD which can be expressed as

where 1, m, and n are direction cosines of the velocity vector, 0 = (xO, Yo, ZO) is the nodal point and D = (x4' Y4,z4) is the die penetration point. Negative sign of the above quantity indicates the node movement away from the die. If this time step is less than the (a) time step prescribed by user and (b) time step to reach prescribed strain, current time step is truncated for the step solution.

The simulation is continued with the remainder as an additional time step and same procedure is carried out to check any other free boundary node touching the die.

For the computational efficiency, ifmore nodes touch the die within an interval of one tenth of original time step, these touching nodes are considered as a group and the boundary condition code are updated by (L\T / 10) in one stroke. The complete procedure for determination of the time step is summarized in the flow chart shown in figure 3.12. 41

Find the equations of the plenes containing the die patches

Proj ect the free boundary node to the planes along the velocity vector

Omit the patches into which the node cannot be mapped

Omit the patches from which the node moves away by checking the normal vector and the velocity vector

Compare the distance to the projected point and find the nearest patch through which the node tend to penetrate the die

Find the t 1me taken to penetrate the die

Figure 3.12 : Determination of the minimum time step for a free node to touch the die 42

3.2.4 Nodes separating from the die

As explained earlier, the boundary conditions of the nodes which are separating from the dies have to be altered if such nodes exist during the forming process.

Since the direction cosines of the die normal are known at this stage nothing has to be changed in the original ALPID3D source code for this task. 43

3. 3 Implementation

This section discusses special difficulties that arose in the implementation of the die contact algorithm and how they were overcome.

3.3.1 Node oscillation

Figure 3.13 : Nodes oscillating between two patches

As shown in figure 3.13, it was observed that some nodes tend to oscillate between two adjacent patches during the deformation process. Such nodes can separate from one patch and touch the other several or infinite number of times during a single time step leading to a wastage of CPU time or impossible simulation. Practically, this node is supposed to travel along the edge between two patches. Thus, special care was taken to 44 force such nodes on to the edge in order to overcome this problem in most of the cases where the node is symmetric to both the die patches (ie. equi-distant to both the patches) as shown in figure 3.14. The normalized resultant of the normal vectors of surrounding patches is taken as the die normal, This technique reduces oscillation of nodes which are supposed to travel along an edge between two die patches. But, in some cases where the node is not symmetrical (closer to one patch), such oscillations can occur and give minor difficulties. The only remedy to this difficulty is to use smaller time steps.

Plane of symmetry I Nodal point ~./

I ,-I\ , \ I\ I \ I \ I \ I \ I \ I \ I \

Figure 3.14 : Node likely to oscillate 45 normal vectors of surrounding patches is taken as the die normal. This technique reduces oscillation of nodes which are supposed to travel along an edge between two die patches.

3.3.2 Die patch arrangements

(a) Unsymmetric (b) symmetric

Figure 3.15 : Patch arrangement on a hemispherical punch

When a node comes into contact with a vertex of a die patch (die node), the normal is taken by adding the normal vectors of the surrounding die patches and normalizing the resultant. Figure 3.14 shows a hemispherical punch die defined by triangular die patches in different styles. According to the method implemented the die 46 shown in figure 3.15 (a) will have normals at the patch vertices inclined to one side because the surrounding patches are not symmetric about the patch vertex (die node). This type of a patch arrangement cannot be used if a quarter or half of the billet is used for the simulation since the die normal is not symmetric at the die nodes along the line of symmetry. The patch arrangement shown in figure 3.15 (b) is the best for the ALPID3D simulation. 47

Chapter 4

SAMPLE APPLICATION of 3e D DIE CONTAcT ALGORITHM

Two simulations were carried out to test the implemented die contact algorithm under the current investigation. A three dimensional extrusion process with a stream-lined die and a closed die forging of a hexagonal bolt head were simulated. A physical modeling was carried out to validate the results ofround-to-square extrusion simulation.

4 . 1 Analytical modeling of round-to-square extrusion through a stream lined die

Extrusion through a cubic stream-lined die having circular entry section and square exit section with an extrusion ratio of 3.21:1 was simulated. The stream-lined die design package STREAM[ 11] was used to generate the die surface and a translator called STALP developed under the current investigation was used to translate the MOVIE.BYU compatible STREAM output file or the APT file to generate the die patches with proper patch connectivities. The die land and the billet container were also added by STALP.

For the simulation of round-to-square extrusion process, the stream-lined die shown in figure 4.1 was generated using STREAM and then patch connectivities, die land and billet container were introduced using STALP as shown in figure 4.2. 48

Figure 4.1: Stream-lined die generated by STREAM

Figure 4.2: Stream-lined die, billet container, and die land with triangular patches

generated by STALP. 49

The pre-processor of IRM (Intergraph Randlvlicas) was used to generate the billet geometry with the finite element mesh with proper boundary condition and then IRM' output neutral file was translatedinto ALPID3D format by using the translator IRMALP. One quarter of the billet was usedfor the simulation as shown in figure 4.3. The mirrored complete billet is shown in figure 4.4.

Following process parameters were used in the simulation.

1. Die type: cubic streamlined 2. volume inside the die: 0.4981 in3

3. Extrusion ratio: 3.1214 : 1

4. Diameter of thecylindrical billet : 1 in. 5. Product dimensions : 0.5" x 0.5" square

6. Material : Lead 7. Ram speed: 0.25 in/sec 8. Process temperature : 250C (isothermal) 9. Friction type : sticking friction

10. Friction factor: 0.20

Simulation parameters.

1. Number of nodes in the billet: 436

2. Number of elements in the billet: 288 3. Number of nodes on the streamlined die : 512 4. Number of triangular patches on the die : 288

5. Number of time 4' 65 50

The deformed shapes of the quarter billet and the mirrored whole billet, contour plots of stress components, total effective strain, strain rate component, and velocity components are shown in figures 4.3 - 4.16. The load-stroke relationship for the extrusion process is shown in figure 4.17.

Figure 4.3: One-quarter of the initial billet geometry used for the simulation 51

model. Figure 4.4: Complete initial billet obtained by mirroring the one-quarter 52

-~-

Figure 4.5: Deformed billet at a stroke of 0.625" (one quarter model) 53

Figure 4.6: Deformed billet at a stroke of 0.625" (whole billet) 54

Gc::::r 2.524E-82 F c::::r 8.009E .. 90 Ec::::r -2.524E-82 oc::::r -5.04~-82 C r=:t -7.573E-82 Bc::::r -1."18E-8l A r=:t -1.262E-81 LC1..LS1.VELX

Figure 4.7: Contours ofvelocity in x-direction at a stroke of0.625" 55

G~ 7.324E-Bl F ~ S.5Q2E-81 E ~ 5.B~q£-81 oc::::r 5.121£-81 C c::::r ~.3~-tl1 Bc::::r 3.662E-91 A c::::r 2.93eE-B 1 LC1.l.S1. YELl

Figure 4.8: Contours of velocity in z-direction at a stroke of 0.625" 56

F e::::t S.22SE-81 E c::=::r 6.85eE -e1 Dc::=::r 5.48eE-Bl C c::::r ~.118E-el B c::::r 2.748E-el A e::::t 1.37SE· e1 LC1-LS1IEFF_RATE

Figure 4.9: Contours of effective strain rate at a stroke of 0.625" 57

Fc::J. q. ~eE -01 Ec::::t B.80eE·Bl oe::::t 8.4~-01 Cc::::t 4.~eE-01 Be::::t 3.208E -01 Ac::J. 1. 601:- ~1 LCl-lSl:TOT_STRAIN

Figure 4.10: Distribution of total strain at a stroke of 0.625" 58

Figure 4.11: Deformed billet at a stroke of 0.875" (one quarter model) 59

Figure 4.12: Deformed billet at a stroke of 0.875" (whole billet) 60

G c::=:::J- 0. tIlfJE ~ ee F c::=:::J- -2.433E-82 E c::=:::J- -4 •866E .. 82 o c::::J- -7•2

Figure 4.13: Contours of velocity in x-direction at a stroke of 0.875" 61

Gc:::} 7.1~-Bl F c::::r S.398E-01 E c:::} 5.SS7E-01 o c:::} ~.q76E-01 C c:::} ~.266E-01 Bc:::} 3.554E-01 Ac:::} 2.843£-01 LC1..LS1:VELZ

Figure 4.14: Contours of velocity in z-direction at a stroke of 0.875" 62

F c::::r 7. 365E-01 E c:J- S.l38E-fJl Dc:J- 4.~10E-~1 Ce::::t 3.S83E-01 B c::::r 2. 455E-01 A c:J- 1.228E-al LC1_LS1:EFF_RATE

Figure 4.15: Contours of total effective strain-rate at a stroke of 0.875" 63

F r=:::J- 1.20BE toB0 E c::::r Q.QQ7E-81 Dr=:::J- 7.~E-Bl Cc::::r 5.qqaE-81 Bc::::r 3.999E-Bl ~ c::::r 1.~qE-~1 LC1JLS1:TOT_STRAIN

Figure 4.16: Distribution of total strain at a stroke of 0.875" 64

0.8 -r------.

0.6

~ en c.

~ '""'" 0.4 "C II' 0 -J 0.2

0.0 .....---.....--.-.....- ...... - ...... ---.-.....- ...... -...-~ 0.0 0.2 0.4 0.6 0.8 1.0

stroke 1(1ncn)

Figure 4.17: Load-Stroke curve for round-to-square extrusion 65

4. 2 Physical modeling of round-to-square extrusion

The newly developed 3-D die contact algorithm was experimentally validated through physical modeling of round-to-square extrusion. Cylindrical split billets were precisely machined out of commercially pure lead to the required dimensions. A streamlined die with a circular entry section of 1" diameter and a square exit section of 0.5" x 0.5" with a die length of 1" (shvvn in figure 4.18) manufactured using CAD/CAM tools[12] was used in the experiment, A similar grid pattern as in the FEM modeling was drawn on the interface as shown in figure 4.19. Grease was applied on the split surface in order prevent cold welding of the two split halves. Grease was also applied as the lubricant. Billet was taken out of the die after extrusion and the deformed grid patterns on the split section at different ram strokes were compared with the analytical results. The steady-state extrusion load was also measured. Figures 4.20 and 4.21 show the comparison of grid deformation obtained in physical and analytical modeling of the extrusion process. Figure 4.22 shows a comparison extrusion load obtained by both analytical andexperimental models.

Figure 4.18: Streamlined die[12] and the ram used in the experiment 66

(a) Experimental (b) Analytical

Figure 4.19: Initial grid in the billet 67

~1 !lIfJ [\\ ~ /1 I \\\\ L/ I I )\\\ f J l \

(a) Experimental (b) Analytical

Figure 4.20: Comparison of Grid distortion patterns at a stroke of 0.555" in Analytical

and Physical modeling of round-to-square extrusion 68

(a) Experimental (b) Analytical

Figure 4.21: Comparison of Grid distortion patterns at a stroke of 0.6875" in Analytical and Physical modeling of round-to-square extrusion 69

Analytical Experimental

o.....-...... ~...... ---....--...... ---.....---...... ---.------. 0.0 0.2 0.4 0.6 0.8

Stroke/inch

Figure4.22: Comparison of extrusion loads obtained by both analytical and

physical models 70

4 . 3 Analytical modeling of closed die forging of a hexagonal bolt head

Single stage closed die forging of a hexagonal bolt head was simulated with a cylindrical initial billet. The dies used in the simulation are shown in figure 4.23. Due to symmetry, one quarter of the billet was used. Figures 4.24 and 4.25 show one quarter model and the complete configuration of the starting billet. Following process parameters were used in the simulation.

Die velocity: 1.173 in/sec

Billet dimensions: 1" dia x 2.98" height

Billet material: Al 1100

Process temperature: 250 C isothermal

Friction factor: 0.1 (constant shear friction)

Product dimensions: 1.732" face-to-face hexagonal x 0.75 height

Following simulation parameters were used.

Total number of elements in the billet: 246

Total number of nodes in the billet: 396

Total number of elements in the top die: 19

Total number of nodes in the top die: 30

Total number of elements in the bottom die: 109

Total number of nodes in the bottom die: 180

Number of time steps: 54 71

Deformed billet, contour plots of velocity components, effective strain, and total strain at different reductions obtained from the finite element model are shown in figures

4.26 - 4.40. The predicted load-stroke curve is shown in figure 4.41.

Figure 4.23: Dies used in bolt forging simulation 72

Figure 4.24: One-quarter model of the initial billet 73

Figure 4.25: Complete initial billet obtained by mirroring the one-quarter model 74

Figure 4.26: Deformed billet at 40.6% height reduction (one-quarter model) 75

Figure 4.27: Deformed billet at 40.6% height reduction 76

Gc::::J 4.6I6E -81 F c::::J 3.83tI-81 Ec::::J 3.871E-81 oc::::J 2.3I3E-m cc::r l.m-m Bc::::J 7.677£-82 Ac::::J S.NeE+m LCll.Sl·VEU

Figure 4.28: Contours of x-velocity component at 40.6% height reduction 77

Fc::::r -2.472E-01 D Ec::::r -4.944E-01 oc::::r -7.~16E-el E Cc::::r -9.887E-01 Bc::::r -1. 2~E +0~ Ac::J- ·1. 4S3E ·ee LCLl.Sl :VELZ

Figure 4.29: Contours of z-velocity component at 40.6% height reduction 78

FD- l.fHtl Ec::J- l.fM+~ Dc::J- 1. all +~ Cc::J- Q.822E-Jl Bc::J- 6. 815E-81 Ac::J- J.~-81 LCIJLSl:EFF-RATE

Figure 4.30: Contours of effective strain-rate at 40.6% height reduction 79

6 c::::r 9. 397E-81 Fe::::t B.985E-81 Ee::::t 6.712E-0] oe::::t 5. 378E-Bl Cc::::r 4.827E-0J Bc::::r 2.S85E-81 Ac::::r 1.342E-al LCIJLSl.TOT_STRA1N

Figure 4.31: Distribution of total strain at 40.6% height reduction 80

Figure 4.32: Deformed billet at 52.25% height reduction (one-quarter model) 81

Figure 4.33: Deformed billet at 52.25% height reduction 82

Gc=J- G.5S7E-el \ F c::::r 5.472E-el Ec::::r 4.376E-Sl oc::::r 3.283E-81 B Cc::::r 2.189E-et B c:::=r 1.tmE-el A c:::=r fJ.008E t 00 LCl-LSl. VELX

Figure 4.34: Contours of x-velocity components at 52.25% height reduction 83

Figure 4.35: Contours of z-velocity components at 52.25% height reduction 84

oc:::r 2.784Etfl F c:::J. 2.38GE •m E c:::J. 1. ~.~ o c:::J. 1.5qIE·ee C c:::J. 1.1qj£•{I3 B c:::J. 7.~-Bl A c:::::r 3.

Figure 4.36: Contours of effective strain-rate at 52.25% height reduction 85

6 c:::::J- 1.487E t fJ8 F c:::::J- 1.296E·Be E c:::::J- 1.005Etee De::::t 8.S38E-Bl Ce::::t G.828E-Bl Be::::t ~.81qf-81 A e::::t 2.aeqf-81 LCI-LSl:TOT_STRAIN

Figure 4.37: Distribution of total strain at 52.25% height reduction 86

Figure 4.38: Deformed billet at 58% height reduction (one-quarter model) 87

Figure 4.39: Deformed billet at 58% height reduction 88

Gc::::} 1.721E·0~ F c::::} 1.476E+0~ Ee::::t 1.230E+e~ oc::::} q.837E-01 C c::::} 7.378E-01 Be::::t 4.918E-~1 A c::::} 2.45qE-01 LC1_LS1:TOT_STRAIN A

Figure 4.40: Distribution of total strain at 58% height reduction 89

100 -r------.

""'""tI) Q. 60 ~ ......

"'0 as 40 0 ..J

0-+------...... -----..-----.------1 o 2

Stroke 1(lnch)

Figure 4.41: Predicted load-stroke curve for bolt head forging 90

Chapter 5

PRE· AND POST-PROCESSING

5.1 Overview

Pre-processor ALPID-3D Post-processor (pATRAN) (MOYIE.BYU)

Simulation control

DataExtractor

Figure 5.1 : Architecture of the ALPID3D system 91

As shown in figure 5.1, ALPID3D system consists of

(a) FEM code ALPID3D

(b) Pre-processing unit (PATRAN and translator)

There are several commercial graphic CAD/CAM packages to pre and post process finite element data such as Patran, Supertab, ANVIL-4000, Unigraphics and etc. The original ALPID3D system uses PATRAN through a translator called PATAL3.

The pre-processing unit which prepares the ALPID3D input data file cannot be used because of the unavailability of the PATRAN interface module. The post-processing unit does not have any graphic support and can only extract data from the output binary files.

The usage of remaining "handicapped" ALPID3D system hence becomes very tedious and almost impossible. A complete pre-processing unit and a post-processing unit for

ALPID3D were developed by using the Intergraph elastic stress analyzing package

Intergraph Rand-Micas (IRM). ALPID3D was interfaced with the pre- and post-processing units of IRM through a translator called IRMALP which was developed under the current research. 92

5.2 Pre-processor

HEADING I MASTER CONlROL DATA 1 PARAMETERS 2. DIES I --.« .'.:.:-:.«<-:-:.»:-:---: ' , .. DIE(jE()1y1EJ'l{rI>~'f~< •....•..• .. •••• T.DlEl'f(J)I:lJ\fC()(jRD~ATJ3§> newly 2.])!E.PA.TCIICONNEC'TIVITIES added I

NODAL POINT DATA 1 COORDINATES 2. VELOCITIES 3 BOUNDARY CONDmONS I ELEMENT DATA 1 CONNECI1YITY 2. MATERIAL PROPERTY 3 STRAIN I

BOUNDARY NODAL POINT DATA 1 LOCAL COORDINATE SYSTEMS 2. PRESCRIBED FORCE

Figure 5.2 : ALPID3D input data file structure 93

ALPID3D requires the input data shown in figure 5.2 in fixed format. The pre processing procedure basically consists ofrunning IRM to generate the finite element mesh in the billet geometry with the appropriate boundary conditions and running the translator

IRMALP to translate the IRM neutral file into ALPID3D format. The pre-processor of

IRM is very user friendly and very efficient and a little knowledge about Intergraph drafting

software IGDS or MEDS in sufficient for the usage.

User can select any material property in IRM and it will not be included in the

ALPID3D data file and the default material AL 1100 will be used instead. Data file has to

be edited if this material needs to be changed. However, since material property behavior

is hardcoded in ALPID3D source code as a separate module, material property subroutines

(HARD) will have to be edited in order to include a new material in addition to the currently

available materials in the source code. The finite element mesh is generated in the usual

manner with 8-noded solid elements. As usual, the nodes and elements can be deleted,

copied, moved, and many more operations can be done very effectively.

The nodes and elements are then re-sequenced to get an optimized bandwidth which

leads to a better performance of ALPID3D. The velocity and die contact boundary

conditions are represented by applying translational and rotational constraints which are

accordingly converted to velocity and traction (die contact) boundary conditions. Shown

below is the list of constraints with corresponding situations required by ALPID3D.

Tl- Velocity specified nodes in X-direction.

T2- Velocity specified nodes in Y-direction.

TI- Velocity specified nodes in Z-direction.

Rl- Nodes in contact with die number 1. 94

R2- Nodes in contact with die number 2.

R3- Boundary nodes which may come into contact with the dies during

the deformationprocess.

As noted above, the number of dies which can be represented in these boundary condition is limited to two and this is sufficient in most of the metal forming simulations.

The design file is then closed and IRM translator is activated in the IRM main menu. Neutral file can be obtained by choosing proper menu selection. This file is then sent through IRM-ALPID3D translator called IRMALP which was developed under this project. The output gives the following information in the required format:

(a) Master control data (incomplete)

-Number of nodes, elements and boundary nodes

(b) Nodal point data

- nodal coordinate

- velocities (zero, modify ifnon-zero values are used)

- Boundary condition codes

- connectivity

- Material property

- Strain (zero, modify if non-zero values are used) 95

As indicated above, the ALPID3D input data file has to be edited to complete master control data, die geometry data. In certain cases, the velocity boundary condition will be modified if non-zero values are used. Although this could be overcome by providing these data interactively, it is left to the user to edit the data file which is more convenient. But, in most of the cases data file can be fed to the ALPID3D system without modification except the master control data and the die geometry data.

A complete user's manual for pre-processing using IRM is given in APPENDIX B. 96

5.3 Post processor

i'--..... ALPID-3D

Figure 5.3 : File arrangement in ALPID3D

As shown in figure 5.3, ALPID3D results are stored in sequential binary files for post processing and in the ASCII file. Data can be extracted from the binary files corresponding to each step. Currently there is no graphics supported post-processor for

ALPID3D. Interface software were developed under this project to load ALPID3D output into IRM data base. Separate IRM data bases are created for separate step solutions of

ALPID3D. 97

The post processing involves the following steps. (Complete procedure is given

Appendix B under post processing users manual)

1. Extract the following data from the binary file relevant to the required step

solution.

(a) X,Y,Z coordinates

(b) Elementconnectivities

(d) Elemental stress components

(e) Elemental strain-rate components

(t) Elemental total effective strain

2. Execute the interface software IRMALP and select the post processing

option. This will prepare a data file with specific IRM commands to

handle ALPID3D data such as solid 8-noded elements and materials tables

etc.

3. Invoke IRM and change element check limits in Active Parameters if much

distorted elements exist in the deformed billet.

4. Invoke Loaders in IRM and feed the data file created by interface software

to IRM. This will load all the post processing data to the IRM database.

5. Invoke Graphics Interface and obtain stress, strain, velocity contours using

PDM operations. 98

Here the interface program converts elemental stress, strain and strain rate data supplied by ALPID3D into nodal data by using a simple averaging technique.

Various contour plots can be stored in different levels and many Intergraph and

IRM features can be used such as hidden line removal, color shading, smooth shading, positioning, mirroring the deformed billets, sectioning etc. 99 Chapter 6

CONcLuSIONS AND REcoMMENDATIONS

6.1 Conclusion

Under the current investigation, two metal forming simulations involving 3 dimensional dies were carried out to test the die contact algorithm which was newly added to the ALPID3D simulation system. Round-to-square extrusion through a streamlined die and a closed die forging of a hexagonal bolt head were successfully simulated without any difficulty pertaining to the die contact boundary condition. The extrusion was experimentally carried out to validate the analytical results. The grid deformation and the steady state extrusion load were found to be in good agreement with the experimental results. However, the new version of ALPID3D has to be further tested through a thorough parametric study emphasizing the die shapes.

According to the method used in handling the die contact problem, unstable nodes may exist in the finite element grid as shown in figure 6.1. These nodes may slide down to a side introducing non-symmetry to symmetric problems. But, in most symmetric cases, this can be overcome by using simulation strategies. As an example figure 6.2 shows two different configuration for the simulation ofan extrusion process through a streamlined die.

If the configuration shown in figure 6.2 (a) is used, the nodes along the sharp edge may slide down to a side thereby losing the symmetry of the billet geometry. This can be overcome by using the configuration shown in figure 6.2 (b) for this particular problem. 100

According to the implemented die contact algorithm, the die normal is not continuous across die patch edges. Consequently, if a node is positioned just inside a patch (almost on the edge), an unbalanced forces may act on the particular node resulting oscillation about the patch edge as shown in figure 6.3. This is a direct result of the discretization of the contoured die surface into planer triangular patches. One method to smoothen the undesirable sharp comers produced by discretization is to introduce patch edge curvature to blend the adjacent die patches. This will certainly produce computational difficulties in this three dimensional application. Another method which is simpler compared to the above mentioned method is to calculate the normals at each vertex by averaging the normals of the surrounding patches and then applying a suitable interpolation function to describe the die normal over each triangular patch as shown in figure 6.4 (b).

Currently, to overcome the undesirable nodal oscillations, a smaller margin along the patch

edge is given the same normal as the edge which is the average of the normals of adjacent

patches as shown in figure 6.4 (a).

Figure 6.1: An unstable node 101

(a) Unfavorable (b) favorable

Figure 6.2: Avoiding unstable nodes.

Nodal oscillation

Figure 6.3: Nodal oscillation due to unbalanced force 102

(a) Current algorithm (b) Another possible algorithm

Figure 6.3: Distribution of die normal vector

6 . 2 Future developments

A major drawback of most of the metal forming simulation packages is that, only a uniform friction condition can be used on the entire die surface. The die definition used in the die contact algorithm has the potential to introduce varying friction conditions on the die surface by providing different friction coefficients or friction factors on each triangular patch used to define the die. It also has capability of applying constant shear friction and coulomb friction in different regions on the die surface.

It was' noticed that the solution convergence usually occurs after about ten iterations. The adaptive adjustment of the deceleration coefficient of the modified Newton

Raphson iteration scheme was found to be inefficient. The implemented method uses the velocity error norms and the force error norms in previous steps and it sometimes over estimates the declaration coefficient resulting in oscillation of the solution thus delaying the

convergence. 103

In the current version of ALPID3D, the material behavior is hard-coded in a separate module of the source code in the form ofequations. But, the property behavior of most modern engineering alloys cannot be expressed in the equation form and the

ALPID3D program needs to be modified to read material property data bases which contain experimental data. For this purpose, interpolation schemes have to introduced in a similar manner to the ALPID2D modification by Murali[ 13] which interpolates flow stress based on strain, strain rate, and temperatureat integration points in each element

In 3-dimensional metal forming simulation with complex die shapes, the finite element grid can be quickly distorted leading to frequent remeshing of the billet thereby resulting tedious extra work. The ALPID3D program can be further developed to accommodate an automatic adaptive remeshing scheme as proposed by Zienkiewizf l-l] for

2-dimensional case which not only reduces simulation time but also gives accurate results. 104

APPENDIX A

uSER'S MANuAL (to be annexed to the ALPID3D user's manual)

A.I Overview

As shown in figure 5.2, ALPID3D input data file for an initial run basically consists of:

1. Master control data

2. Die geometry data

3. Nodal point data

4. Element data

5 . Boundary nodal point data

Out of these modules, Master control data and Die geometry data preparation are discussed in this section. User must refer the ALPID3D user's manual for the preparation

of the rest of the input data file. 105

A. 2 Master control data

1. Heading

Refer ALPID3D user's manual

2. Master control data : parameters

Refer ALPID3D user's manual

3. Master control data: Die

Each line defines one die. Enter as many lines as the number of dies defined by NUMDIE in master control data (parameters).

Notes Columns Variables Entry

(a) 1 - 5 NDIEN(N) Die number

(b) 6 - 10 NFTP(N) Number for friction type

1 = constant shear friction

2 = coulomb friction

ifNFfP = 1, provide m factor

ifNFfP = 2, provide Jl factor

(d) 21 - 30 VDIE(I,N) x - velocity 106

(d) 31 - 40 VDIE(2,N) Y- velocity

Cd) 41- 50 VDIE(3,N) z - velocity

(e) 51- 60 POSIT(1,N) Die position in x - direction

(e) 61- 70 POSIT(2,N) Die position in y - direction

(e) 71 - 80 POSIT(3,N) Die position in z - direction

NOTES /

(a) This Entry defines the Die subroutine by its number where the

corresponding die described. In the original version of ALPID3D,

different dies of simple shape (flat) were defined in different

subroutines.

Die No. Description

1 Horizontal top die

2 Horizontal bottom die

3 Spherical die of 2 inch. diameter. 107

4 Vertical die

5 Vertical die x = y

10 or greater Any shaped die defined by triangular patches. This

option is newly added with the modification done

under this project. Different three dimensional dies

should be assigned different numbers equal or

greater than 10.

(b) This entry defines the type offriction at the die/workpiece interface.

ALPID3D allows different friction types with different dies.

NFTP = 1 for constant shear friction

NFTP = 2 for coulomb friction

friction and the friction coefficient in the case of coulomb friction.

(d) Die velocity components in terms of global coordinate system

(inch/sec in British unit system). Material property behavior defined

in the HARD routines should also be in the same unit system.

(e) This entry defines the die position. In case of three dimensional

complex shaped dies which are defined by triangular patches, this

entry defines the current position of die node number one. This 108

enables the user to shift the die in x, y, and z directions simply by

defining the new position of the die node number one for this entry.

The die coordinates defined in the next section need not to have the

same coordinates for die node number one. Refer note for die

coordinates for more details.

A.3 Die Geometry data

Each data packet defines a 3-D die. Define as many packets as the number of dies of which die identification number (NDIEN(N)) is greater or equal to 10.

1. Number of die nodes and patches.

Notes Columns Variables Entry

(a) 1-5 NDPNT Total number ofdie nodes.

(a) 5-10 NDELT Total number ofdie patches.

NOTES/

(a) 3-dimensional dies have to be defined using triangular patches. 109

2. Coordinates ofDie nodes

Each line defines one nodal point. Enter as many lines as the number of nodal points defined by NDPNT.

Notes Columns Variables Entry

(a) 1-5 N Node number

(b) 6-15 DXYZ(l,ID) x-coordinate ofdie node N

(b) 16-25 DXYZ(l,ID) y-coordinate ofdie node N

(b) 26-35 DXYZ(l,ID) z-coordinate of die node N

NOTES/

(a) The nodal coordinates should be placed in order of the node

number. If two node numbers are not consecutive, intermediate

nodes will be evenly distributed between the two nodes.

(b) The nodal coordinates should be given in terms of global coordinate

system. 110

3 . Die patch connectivities

Each line defines one die patch. Enter as many lines as the total number of die patches defined by NDELT.

Notes Columns Variables Entry

(a) 1-5 N Die patch number

(b) 6-10 IDCON(1,N) 1st node of the die patch N

(b) 11-15 IDCON(2,N) 2nd node of the die patch N

(b) 16-20 IDCON(3,N) 3rd node of the die patch N

NOTES/

(a) The patch connectivities should be placed in order of the patch

number

(b) The patch connectivities should be defined in the anti-clockwise

direction when viewed from the die cavity. This convention is used

to determine the die cavity side. 111

A.4 Nodal point data

Refer ALPID3D user's manual

A.5 Element data

Refer ALPID3D user's manual

A.6 Boundary nodal point data

Refer ALPID3D user's manual 112

APPENDIX B

uSER'S MANuAL FoR PRE- AND PoST-PRoCESSING

A.I Pre-processing

The pre-processing procedure basically includes running IRM with conditions required by ALPID and running the interface software to translate IRM neutral file into

ALPID format. The complete procedure is given below in steps.

1. Invoke IRM

2. Select mechanical design graphic interface.

3. Defme material properties (arbitrary)

4. Define element properties

- solid 3D element

5. Draw the billet geometry and generate the mesh with solid 8-noded

hexahedral elements. 113

6. Define the constraints

Tl - for velocity in X-direction

T2 - for velocity in Y-direction

T3 - for velocity in Z-direction

Rl - for nodes in contact with die No.1

R2 - for nodes in contact with die No.2

R3 - free boundary nodes

7. Close the design file

8. Invoke the translator

9. Obtain a Generic Neutral file

10. QuitlRM

11. Execute the interface software IRMALP. This will create an ALPID3D

compatible data file without the master control data card. 114

B.2 Post-processing

Post-processing basically includes extracting data from ALPID3D binary file in which the results are stored and arranging then in IRM format. The complete steps are given below.

1. Extract ALPID3D results from corresponding binary files by running

DATEXT which is the data extractor of ALPID

- nodal coordinates

- element connectivities

- nodal velocity components

- elemental stress components

- elemental strain rate components

- total effective strains

2. Store results in different files

3. Run interface software IRMALP and obtain an IRM compatible neutral file

4. Invoke IRM

5 . Select Mechanical design

Input the case name

Select the model size (this will decide the size of the DGN file)

Select 3-D solid element (space truss) 115

6. Open Graphic interlace

Invoke active parameters and change element check limits to get the

maximum flexibility. (Maximum warping factor - 3.1).

Reduce the node size and tolerance.

7 . Close the Graphics Interface and Select Alphanumeric Interface

8. Select Analysis option

9. Type "LOGR fn.ft" (- file created by translator IRMALP). This will load

all the variables extracted from ALPID3D output binary file.

10. Open the PDM tutorial in page 3 of IRM screen menu and note the DIN for

each variable.

11. Obtain contours with shapes for color fill for each desired variable and store

them in different levels.

12. Obtain the outside faces of the deformed billet from the facing option in

page 2 of the screen menu.

13. Close IRM and use the DGN file to do hidden line removal, color filling of

contours, smooth shading of the deformed billet etc. 116

REFERENcE:

1. Altan, T., Oh, S.I., snd Gegel, H.L., "Metal Forming: Fundamentals and

Applications", American Society for Metals, 1983.

2. Lee, C.H., and Kobayashi, S., "New solutions to rigid plastic deformation plastic

problems using a matrix method", Trans, ASME, J. Engr for Industry, 95, p 865

(1973).

3. Park, J.J., and Kobayashi, S., "Three-dimenstional finite element analysis of block

forging", IntI. J. of Mech. Sci., vol. 26, p 165-176, 1984.

4. Chen, C.C., and Kobayashi, S., "Rigid-plastic finite element analysis of ring

compression", ASME publication, AMD, vol. 28, p 163-174, 1978.

5. Kiridena, V.S., "A 3-D search and inpolate alggorithm", Masters Thesis, Ohio

University, 1989.

6. Processing Science Research to develop scientific methods for controling metal

flow, microstructure, and properties in 3-dimensional metal forming processes.

AFW AL Final report for the period Aug 1978 - Oct 1986, Battele Columbus

division. 117

7. "Processing Science Research to Develop Fundamental Analytical, Physical and Material modeling techniques for Difficult-to-process materials", AFWAL Interim Report for period 1 Jan. 1988 - 31 Dec. 1988, Universal Energy Systems, Inc.

8. Goetz, R.L., Jain, V.K., Morgan, J.T., Wierschke , M.W., "effects of Material and Processing conditions upon Ring-Calibration curves", IEXTRU '89, Ohio University, p 27-67., 1989.

9. Shiau, Y.C., and Kobayashi, S., "Three-Dimensional Finite Element Analysis of Open-Die Forging", Intl. J. for Numerical Methods in Engineering, Vol. 25, p 67

85, 1988.

10. Pillinger, I., Hartley, P., and Sturgess, C.E.N., "Modeling of Frictional Tool Surfaces in Finite-Element Metalforming Analyses", Modelling of Metal Forming Processes, Proc. of the Euromech 233 Colloquium, Sophia Antipolis, France, p 85-92, 1988.

11. Gunasekera, J.S., "Computer-Aided Modeling and Design of Shaped Extrusion Dies", ASME, International Computer Technology Conference, San Francisco, p

452-459, 1980.

12. Patel, H., "Computer Aided Manufacturing of a Stream-lined Extrusion Die", Master's Thesis, Ohio University, 1990.

13. Gudawali, M., "Modeling of Ring Joining Processes", Master's Thesis, Ohio

University, 1990. 118

14. Zienkiewicz, D.C., Huang, G.C., and Liu, Y.C., "Error control, Mesh updating

schemes and Automatic Adaptive remeshing for Finite Element Analysis of

Unsteady Extrusion processes", NUMIFORM, 1990